The two numbers that fit the description are 27 and 99.
There are two numbers that fit this description. To find them, we can solve the equation:
Difference = Number - Number’s Reverse
Difference = 72
Number - Reverse = 72
Let’s call the two-digit number “x” and its reverse “y”. So, we can rewrite the equation as:
x - y = 72
Now, we can solve the equation using algebraic methods. First, add “y” to both sides of the equation:
x - y + y = 72 + y
x = 72 + y
Next, let’s solve for “y” by subtracting “72” from both sides of the equation:
x - 72 = 72 + y - 72
x - 72 = y
Therefore, we can rewrite the equation as:
x - 72 = y
Now, we can solve for “x” and “y” by plugging in possible values for “x” and “y” and seeing which ones work. Since we’re dealing with two-digit numbers, let’s start with numbers between 10 and 99.
First, let’s try x = 10 and y = 82.
10 - 82 = -72
This doesn’t work, since the difference cannot be negative.
Next, let’s try x = 15 and y = 87.
15 - 87 = -72
Again, this doesn’t work.
Finally, let’s try x = 27 and y = 99.
27 - 99 = -72
This works! So, the two numbers that fit the description are 27 and 99.
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subtract 13 5/8 - 3 2/3
Answer:
9 23/24
Step-by-step explanation:
Change both mixed fractions to improper fractions
13 5/8=109/8
3 2/3=8
Now substract: 109/8 - 8/3= 10 23/24.
Hope this helps!!
On the graph below, quadrilateral ABCD has been dilated, with the center of dilation the origin, then translated down six units, to create quadrilateral A'B'C'D'
a. What is the scale factor of the dilation?
b. What is the ratio of the length of AB to the length of A'B'
c. How are the measures of angle A and angleA' related?
a. The scale factor of the dilation is 2, since the length of each side of the dilated quadrilateral is twice the length of the original quadrilateral.
What is quadrilateral?A quadrilateral is a polygon with four sides and four angles. It is a two-dimensional shape with an equal number of sides and angles, as well as four vertices and four interior angles. The most common examples of quadrilaterals include rectangles, squares, parallelograms, trapezoids, and rhombuses. All quadrilaterals have two pairs of parallel sides, and all four sides must be connected. Quadrilaterals can be classified based on their side lengths and the size of their angles.
b. The ratio of the length of AB to the length of A'B' is 2:1, since the length of AB is twice the length of A'B'.
c. The measures of angle A and angle A' are equal, since the dilation is centered on the origin and therefore the angles of the dilated quadrilateral are the same as the angles of the original quadrilateral.
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Solve the system of equations.
12x - 2y = 20
16x + 2y = 29
As a result, the following is the system of equations' solution as 12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.
what is equation ?A mathematical assertion proving the equality of two expressions is known as an equation. It has two sides—a left side and a right side—that are divided by the equal symbol (=). Variables, constants, and mathematical processes may be used in the expressions on either side of the equal sign. For instance, the expression 2x + 3 on the left is equivalent to the expression 7 on the right, as shown by the equation 2x + 3 = 7.
given
We can use the technique of elimination to solve this system of equations by adding or removing one of the variables from the equations. In this instance, by combining the two equations, we can remove y:
12x - 2y = 20
16x + 2y = 29
28x = 49
We can now find the value of x by multiplying both parts by 28:
28x/28 = 49/28
x = 7/4
We can solve for y by substituting this value of x into either of the initial equations. Let's employ the initial equation:
12x - 2y = 20
12(7/4) - 2y = 20
21 - 2y = 20
-2y = -1
y = 1/2
As a result, the following is the system of equations' solution as 12x - 2y = 20 in the calculation, x = 7/4 and y = 1/2.
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What two numbers can multiply to -18 and add to 3
Priya has a recipe for banana bread. She uses 7 1/2 cups of flour to make 3 loaves of banana bread. Andre will follow the same recipe. He will make b loaves of banana bread using f cups of flour. Which of these equations represents the relationship between b and f?
Answer:
Step-by-step explanation:
asdf
(x - 3)(x + 4) What is the horizontal distance between the two x-intercepts?
Answer:
The horizontal distance between the two x-intercepts is 7 units.
Step-by-step explanation:
What are the x-intercepts?The x-intercepts are the points at which the graph of a function or equation crosses the x-axis. At these points, the value of y is zero.
Therefore, to find the x-intercepts of the given expression, set the expression equal to zero and solve for x:
(x - 3)(x + 4) = 0
This equation is true if and only if either x - 3 = 0 or x + 4 = 0, which means the x-intercepts are at x = 3 and x = -4.
The horizontal distance between these two points is the absolute value of the difference between the x-coordinates of the x-intercepts:
|3 - (-4)| = |3 + 4| = 7
Therefore, the horizontal distance between the two x-intercepts is 7 units.
suppose 60% of american adults believe martha stewart is guilty of obstruction of justice and fraud related to insider trading. we will take a random sample of 20 american adults and ask them the question. then the sampling distribution of the sample proportion of people who answer yes to the question is: group of answer choices
Suppose 60% of American adults believe Martha Stewart is guilty of obstruction of justice and fraud related to insider trading.
We will take a random sample of 20 American adults and ask them the question. Then the sampling distribution of the sample proportion of people who answer yes to the question is a binomial distribution.
What is a binomial distribution?A binomial distribution is a statistical distribution that represents the likelihood of one of two outcomes in a sequence of independent trials. Binomial distributions can be used to model a variety of phenomena, including flipping coins, rolling dice, and performing multiple independent experiments.
The probability of getting k successes in n trials in a binomial distribution with probability of success p and probability of failure q is given by the following formula:P (k) = nCk * p^k * q^(n-k)Where nCk is the binomial coefficient, which represents the number of ways to select k items from a set of n items without regard to order.
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The temperature in a town is 36.6°F during the day and -18.6°F at night. Find the difference in the temperatures.
Answer:
Step-by-step explanation:
To find the difference between the temperatures, we need to subtract the night temperature from the day temperature.
Difference = Day temperature - Night temperature
Difference = 36.6°F - (-18.6°F) (Note: Subtracting a negative number is the same as adding the positive number)
Difference = 36.6°F + 18.6°F
Difference = 55.2°F
Therefore, the difference in temperature between day and night in the town is 55.2°F.
brenna is buying 15 tomato plants for her garden. she uses a lot of cherry tomatoes when she cooks, but she wants a variety of tomato plants. brenna plans to buy fewer than 7 cherry tomato plants. let c represent the number of cherry tomato plants brenna might buy. which inequality models the story?
Brenna is buying 15 tomato plants for her garden, because she uses a lot of cherry tomatoes when she cooks. The inequality models the this story is equals to c< 7. So, correct option is option (b). The graph for inequlity to model the story is present in above figure.
Inequality refers a relationship between two values that are not equal, i.e., a<b. We have, brenna bought 15 tomato plants for her garden. At a time of cooking , she used a lot of cherry tomatoes. So, she wants a variety of tomato plants. She has decided to buy fewer than 7 cherry tomato plants for garden. Let c be the number of cherry tomato plants bought by brenna. Now, as we know cherry tomato plants come into the tomato plants, so c< 15 . Also, she plans to buy cherry plants less than 7, so c < 7. That is we have to choices for inequlity, c < 15 or c< 7. But we know if a number is less than 7 then trivially, it is less than 15 ( 7< 15), so we use the c< 7, Inequality to model the story. The graph of this inequlity that models the story is present above in figure. Hence, required inequalty is c< 7.
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Complete question:
Brenna is buying 15 tomato plants for her garden. she uses a lot of cherry tomatoes when she cooks, but she wants a variety of tomato plants. brenna plans to buy fewer than 7 cherry tomato plants. let c represent the number of cherry tomato plants brenna might buy. which inequality models the story?
a) c> 7
b) c< 7
c) c>15
d) c<15
See the above Graph and find out the inequality that models the story. To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Should christians have supported the counterculture of the 1960’s? Arex there areas today in which Christians must not conform to the dominant culture? Give a specific example
We must prioritize biblical teachings and values over the cultural trends of the day. We should be salt and light to the world and live our lives in a way that honours God.
As Christians, it is our responsibility to be salt and light to the world. The dominant culture may be a reflection of the majority of the population's thoughts, but it may not necessarily align with the Bible's teachings. We should not be swayed by the current trends and instead prioritize God's standards.
The counterculture of the 1960s, according to some, promoted ideas that are contrary to Christian teachings. Many people who were part of this movement advocated for sexual freedom, drug use, and rebellion against authority. Christians should not have supported these behaviours or beliefs since they are inconsistent with biblical principles.
Likewise, in today's world, there are areas in which Christians must not conform to the dominant culture. One of the primary areas where Christians may be tempted to conform is in terms of sexual morality. Many people believe that premarital sex and homosexuality are acceptable practices, but these beliefs are not supported by the Bible.
As a result, Christians should not follow these cultural trends, but rather stick to biblical teachings and live their lives according to God's standards.Another example is in regards to materialism. The desire to accumulate wealth and material possessions is prevalent in modern culture.
Still, Christians must resist the temptation to make money and possessions their god, as this is against the Bible's teachings. Instead, we should focus on using our resources to glorify God and help others.In conclusion, Christians must be cautious about conforming to the dominant culture.
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Arianna is playing a board game. The probability that Arianna will lose a turn on her next turn is 0. Which word or phrase describes the probability that Arianna will lose a turn?
The probability that Arianna will lose a turn is impossible.
In probability, impossible events have a probability of 0. This means that there is no chance that the event will occur. In this case, the probability that Arianna will lose a turn on her next turn is 0, which means that it is impossible for her to lose a turn.
In probability theory, the term "probability" refers to the likelihood of an event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
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find two divergent series summation from n equals 1 to infinity of the quantity a sub n and summation from n equals 1 to infinity of the quantity b sub n such that summation from n equals 1 to infinity of the quantity a sub n times b sub n end quantity converges.
To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:
1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n
Solution:
1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.
2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.
Now, we need to verify that the product of these series converges:
3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)
4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.
5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.
In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and
summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.
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according to the scree plot, if we want to preserve 80% of the variance, what would be the smallest projection dimension d?
According to the scree plot, if we want to preserve 80% of the variance, the smallest projection dimension d would be 5.
The scree plot is a diagnostic tool in factor analysis that aids in determining the number of significant factors to retain. It plots eigenvalues against factor number, with the first factor representing the highest variance in the data set.
The scree plot represents the eigenvalues of the factors. The total variance in the original dataset can be expressed as the sum of the eigenvalues of the factors. If we choose to retain fewer factors, the overall variance preserved will be less, resulting in less precise results.
If we want to keep the most variance possible while maintaining a reasonable level of abstraction, we can look at the scree plot's “elbow.” This represents a point on the scree plot where the eigenvalues decrease dramatically.
Therefore, We should retain all of the factors to the left of the elbow, as they represent the most significant eigenvalues that account for the most variance in the data. If we want to preserve 80% of the variance, the smallest projection dimension d would be 5.
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Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if
The distance from each landing point to the boat pulled ashore at point C is given by:-d = sqrt(25^2 (y^2/x^2 + 1))
WHAT IS TRIGONOMETRY ?
Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving distances, heights, angles, and other geometric measurements. Trigonometric functions such as sine, cosine, and tangent are used to relate the angles of a triangle to its sides. Trigonometry has many practical applications in fields such as engineering, physics, and architecture, and is essential for understanding and solving problems involving waves, oscillations, and periodic phenomena. It is also used in navigation, surveying, and astronomy, among other areas.
To solve this problem, we need to use the concept of right triangle trigonometry.
Let's assume that point C is directly opposite the midpoint of AB, and that the distance from point C to the midpoint of AB is x. Then we can draw a right triangle with legs of length x and 25 (half of 50) and a hypotenuse of length d (the distance from point C to each landing point).
Using the Pythagorean theorem, we can write:
d^2 = x^2 + 25^2
We also know that the angles opposite the legs of the right triangle are complementary, so we can use the tangent function to write:
tan(theta) = x/25
where theta is the angle between the hypotenuse and the side of length 25.
We can rearrange this equation to solve for x:
x = 25 tan(theta)
Now we can substitute this expression for x into the equation for d^2:
d^2 = (25 tan(theta))^2 + 25^2
Simplifying this equation, we get:
d^2 = 25^2 (tan^2(theta) + 1)
Finally, we can use the fact that tan(theta) is equal to the height of the opposite bank divided by the distance from point C to the midpoint of AB. Let's call this distance y. Then we have:
tan(theta) = y/x
Substituting this expression for tan(theta) into the equation for d^2, we get:
d^2 = 25^2 (y^2/x^2 + 1)
So the distance from each landing point to the boat pulled ashore at point C is given by:
d = sqrt(25^2 (y^2/x^2 + 1))
where x and y are the distances from point C to the midpoint of AB and the opposite bank, respectively.
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Let sin(60)=√3/2 Enter the angle measure (0), in degrees, for cos(0)= √3/2
There is no angle (0) in degrees that answers the preceding equation since cos(0) = 3/2 is illogical.
what is trigonometric ratios ?To determine the angles of a right triangle, trigonometric ratios are ratios of the side lengths of the triangle. Sine (sin), cosine (cos), and tangent (tan) are the three fundamental trigonometric ratios, and their definitions are as follows:
Sine: The length of the angle's opposite side divided by the length of the hypotenuse is known as the sine of the angle.
Cosine: The length of the neighbouring side divided by the length of the hypotenuse is the angle's cosine value.
Angle's tangent is determined by dividing the length of the adjacent side by the length of the opposite side.
These ratios can be used to discover missing side lengths in right triangles and other situations with right triangles.
given
The number one is the value of cos(0).
There is no angle (0) in degrees that answers the preceding equation since cos(0) = 3/2 is illogical.
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if the area of a circle is less than $60\pi$ square inches, what is the greatest possible integer value in inches of the radius of the circle?
The greatest possible integer value of the radius of the circle is 7 inches.
The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.
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a random sample of 150 teachers in an inner-city school district found that 72% of them had volunteered time to a local charitable cause within the past 12 months. what is the standard error of the sample proportion?
The standard error for the sample proportion of 150 teachers in an inner-city school district is found to be 0.037.
The formula for the calculation of the standard error of a sample proportion is below,
SE = √((p × (1 - p)) / n)
Here,
SE is the standard error of the sample proportion
p is the sample proportion (in decimal form)
n is the sample size
In the mentioned case, the sample proportion is 0.72 (since 72% of 150 is 108), and the sample size is 150. Substituting these values into the formula, we will be getting,
SE = √((0.72 × (1 - 0.72)) / 150)
SE = √((0.2052) / 150)
SE = √(0.001367)
SE = 0.037
Therefore, the standard error of the sample proportion is 0.037.
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Vincent bought a lot with an area of 105. 7 square meters at 12,500. 00 pesos per square meter. He paid -0. 45 of the amount in cash and the rest 24 equal monthly installments. How many much is his monthly installment?
The amount to be paid as monthly installment for 24 equal monthly installments is given by 30,278.65 pesos.
Area bought by Vincent = 105. 7 square meters
Cost per square meters = 12,500. 00 pesos per square meter.
The total cost of the lot is the product of the area and the price per square meter,
Cost
= 105.7 sq m ×12,500.00 pesos/sq m
= 1,321,250.00 pesos
Amount paid by Vincent in cash is equals to
= 0.45 × 1,321,250.00 pesos
= 594,562.50 pesos
The remaining balance to be paid in installments is equals to,
= 1,321,250.00 pesos - 594,562.50 pesos
= 726,687.50 pesos
This balance will be paid in 24 equal monthly installments, so the monthly installment amount is equals to,
= 726,687.50 pesos / 24 months
= 30,278.65 pesos per month (rounded to the nearest cent)
Therefore, amount paid by Vincent as monthly installment is equal to 30,278.65 pesos.
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a centrifuge in a medical laboratory rotates at an angular speed of 3450 rev/min in the positive direction. when switched off, it rotates through 45.8 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge.
The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.
To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:
ω² = ω₀² + 2αθ
Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).
First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.
Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min
Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad
Now, substitute the values into the kinematic equation:
[tex]0 = (6900π)² + 2α(91.6π)[/tex]
[tex]α = - (6900π)² / (2 × 91.6π)[/tex]
[tex]α ≈ -331283 rad/min²[/tex]
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the mean cost of 4 computer keyboards is $12 each. if the cost of a fifth computer keyboard is $16, what is the mean cost for all 5 computer keyboards?
The mean cost for all 5 computer keyboards is $12.80.
The mean cost, also known as the average cost, is a measure of central tendency that represents the typical or average cost of a set of values
To find the mean cost of all 5 computer keyboards, we need to calculate the total cost of all 5 keyboards and then divide by the total number of keyboards.
The total cost of the first 4 keyboards is
= 4 keyboards x $12 each
Multiply the numbers
= $48
The total cost of all 5 keyboards is
= $48 + $16
Add the numbers
= $64
The mean cost of all 5 keyboards is
= $64 / 5 keyboards
Divide the numbers
= $12.80
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Alyssa was comparing the price of chicken thighs at two stores. At SuperGrocery B, 3 pounds of chicken thighs costs $34.80. The table below represents the total cost, in dollars and cents,
�
y, that it costs for
�
x pounds of chicken thighs at SuperGrocery A.
SuperGrocery A
Pounds (
�
)
Pounds (x)
Total Cost (
�
)
Total Cost (y)
1.5
1.5
$
13.52
$13.52
3
3
$
27.03
$27.03
3.5
3.5
$
31.54
$31.54
4.5
4.5
$
40.55
$40.55
How much more expensive is it, per pound, to buy chicken thighs at Store B than at Store A?
Answer:
To find out how much more expensive it is, per pound, to buy chicken thighs at Store B than at Store A, we need to compare the cost per pound at each store.
At SuperGrocery B, we know that 3 pounds of chicken thighs cost $34.80, so the cost per pound is:
$34.80 / 3 pounds = $11.60 per pound
At SuperGrocery A, we can use the information in the table to find the cost per pound for each amount of chicken thighs:
For 1.5 pounds of chicken thighs:
$13.52 / 1.5 pounds = $9.01 per pound
For 3 pounds of chicken thighs:
$27.03 / 3 pounds = $9.01 per pound
For 3.5 pounds of chicken thighs:
$31.54 / 3.5 pounds = $9.01 per pound
For 4.5 pounds of chicken thighs:
$40.55 / 4.5 pounds = $9.01 per pound
So the cost per pound of chicken thighs at SuperGrocery A is $9.01 per pound, which is less expensive than the cost per pound at SuperGrocery B, which is $11.60 per pound.
To find the difference between the two prices, we can subtract the cost per pound at SuperGrocery A from the cost per pound at SuperGrocery B:
$11.60 per pound - $9.01 per pound = $2.59 per pound
Therefore, it is $2.59 more expensive, per pound, to buy chicken thighs at SuperGrocery B than at SuperGrocery A.
please help me solve this i’ll mark brainliest
Answer:
m<CDB = m<GDE
Step-by-step explanation:
The assessed value of the Weber family’s house is $186,000. The annual property tax is 2. 15% of assessed value. What is the property tax on the Webers home?
the property tax on the Weber family's home is $3,999. To find the property tax on the Weber family's home, we can use the formula:
Property tax = assessed value x tax rate
First, we need to convert the tax rate from a percentage to a decimal. We can do this by dividing the tax rate by 100:
2.15% ÷ 100 = 0.0215
Now we can plug in the values we know into the formula:
Property tax = $186,000 x 0.0215
Property tax = $3,999
So the property tax on the Weber family's home is $3,999.
Property taxes are a common way for local governments to generate revenue to fund public services like schools, roads, and emergency services. The tax rate is usually based on the assessed value of the property, which is determined by a local assessor's office. It's important for homeowners to be aware of the property tax rates in their area so they can budget for this expense. Some homeowners may be eligible for property tax exemptions or reductions, so it's also worth checking with the local assessor's office to see if there are any options available.
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In the diagram, m∠1=45° and m∠3=57.5°.
What is m∠4?
Enter your answer as a decimal in the box.
m∠4 =
°
Triangle with horizontal base. Interior angles labeled from left clockwise 1, 2, 3. Left side of the triangle is extended at angle 2 to create the exterior angle labeled 4.
M∠4 is therefore equivalent to 102.5 degrees as Angles 1 and 3 are the opposing interior angles .
what is angles ?Angles are geometric shapes created by two rays that have a similar terminus, or vertex. Often, the rays are depicted as straight lines with arrows pointing in the appropriate directions. Angles are expressed in degrees, with 360 degrees being a full circle. Angles that are less than 90 degrees are referred to as acute angles, those that are precisely 90 degrees are referred to as right angles, those that are between 90 and 180 degrees are referred to as obtuse angles, and those that are exactly 180 degrees are referred to as straight angles.
given
Angles 1 and 3 are the opposing interior angles in this case, and the exterior angle 4 of a triangle is equal to the total of these angles. We thus have:
m∠4 = m∠1 + m∠3\sm∠4 = 45° + 57.5°
m∠4 = 102.5°
M∠4 is therefore equivalent to 102.5 degrees as Angles 1 and 3 are the opposing interior angles .
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in how many ways can you choose a committee of size 10 with at least 2 men if there are 30 women in the club and 20 men in the club lsing set difference?
Therefore, the number of ways to choose a committee of size 10 with at least 2 men is: 961379655
We are to find the number of ways to choose a committee of size 10 with at least 2 men if there are 30 women in the club and 20 men in the club using set difference. We can use the following formulas: (1) A set difference B = {elements of A that are not in B} (2) The number of ways to choose k elements from n elements is represented by nCk.
(3) The complement of an event E is the set of all outcomes in the sample space that are not included in the outcome of E.(4) If E is an event, then P(E) represents the probability of E happening.(5) P(E') + P(E) = 1 (where E' is the complement of E).
To choose a committee of size 10 with at least 2 men, we can first find the total number of committees possible (which includes committees with 0, 1 or 2 men) and then subtract the committees that do not have at least 2 men. So, the total number of ways to choose a committee of size 10 is 50C10. Using the formula nCk = n!/k!(n-k)!, we can write it as follows: 50C10 = 50! / 10!40! = 10272278170.
The number of ways to choose a committee of size 10 with no men is 30C10.Using the formula nCk = n!/k!(n-k)!, we can write it as follows:30C10 = 30! / 10!20! = 30045015. The number of ways to choose a committee of size 10 with exactly 1 man is (20C1) * (30C9).Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C1) * (30C9) = 20! / 1!19! * 30! / 9!21! = 47152200.
The number of ways to choose a committee of size 10 with exactly 2 men is (20C2) * (30C8). Using the formula nCk = n!/k!(n-k)!, we can write it as follows:(20C2) * (30C8) = 20! / 2!18! * 30! / 8!22! = 47502000. Therefore, the number of ways to choose a committee of size 10 with at least 2 men is:50C10 - 30C10 - (20C1) * (30C9) - (20C2) * (30C8)10272278170 - 30045015 - 47152200 - 47502000 = 961379655 Ways.
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Find the amount accumulated after investing a principal P for t years at an interest rate compounded k times per year.
P = $3,350 r = 6.2% t = 8 k = 365
Hint: A = P(1 + £)kt
A = $[?]
Round your answer to the nearest cent (hundredth).
The amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.
What is an amount?
Using the formula A = [tex]P(1 + r/k)^{kt}[/tex], where A is the amount accumulated, P is the principal, r is the annual interest rate, t is the number of years, and k is the number of times the interest is compounded per year, we can calculate the amount accumulated as follows:
P = $3,350 (given)
r = 6.2% = 0.062 (convert to decimal)
t = 8 (given)
k = 365 (given)
A = [tex]P(1 + r/k)^{kt}[/tex]
A = [tex]$3,350(1 + 0.062/365)^{365*8}[/tex]
A = [tex]$3,350(1.000170685)^{2920}[/tex]
A = $5,781.84
Therefore, the amount accumulated after 8 years is $5,781.84. Rounded to the nearest cent, this is $5,781.84.
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$800 deposit for 24 months earned $200 in interest
Answer:
The rate of interest applied for compound interest is 24.5 %
The rate of interest applied to simple interest is 37.5 %
Step-by-step explanation:
Given as :
The Principal amount that is deposited = $ 800
The Time period = 24 months = 2 years
The Interest earn = $ 200
Let the rate of interest = R %
So, The Amount = Principal deposited - interest earn
Or, A = $ 800 - $ 200
∴ Amount = $ 600
From compounded method
Amount = Principal ×
Or, $ 600 = $ 200 ×
Or, =
Or, 3 =
Or, = (1 +)
Or, 1.245 = (1 +)
or, 1.245 - 1 =
or, 0.245 × 100 = R
So, the rate is = 24.5 %
Hence The rate of interest applied fro compound interest is 24.5 % Answer
From Simple Interest method
Simple Interest =
Or, $ 600 =
Or, $ 600 × 100 = $ 800 × R × 2
Or, R =
∴ R = 37.5 %
So, The rate is 37.5 %
Hence The rate of interest applied to simple interest is 37.5 % Answer
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one business has a large amount of debt on which it pays an annual yield of 8%. a competitor has no debt, and any excess money goes into the bank and earns a yield of 2.3%. each of these businesses bids on a contract which pays $ 40,000 in one year and nine months. indicate which company gives this contract a higher present value, and calculate the difference between these present values, rounding to the nearest dollar. [hint: for both businesses the yield is treated as positive.]
This gives us a present value for the company with debt of $35,564 and a present value for the competitor without debt of $36,944. The difference in present values is $1,380, rounded to the nearest dollar. Therefore, the company with debt gives the contract a higher present value of $1,380.
The company with debt will have the higher present value for this contract. This is because, despite having a higher yield, the competitor without debt is only earning 2.3% on their excess money, while the company with debt is earning 8%.
To calculate the difference in present values, we need to first calculate the present value of each company's contract. To do this, we will use the present value formula, which is:
[tex]PV = C / (1 + r)n[/tex]
Where C is the contract amount, r is the rate of return, and n is the number of years. For the company with debt, we can substitute $40,000 for C, 8% for r, and 1.75 for n. For the competitor without debt, we can substitute $40,000 for C, 2.3% for r, and 1.75 for n.
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What is the remainder when the two-digit, positive integer x is divided by 3?
(1) The sum of the digits of x is 5
(2) The remainder when x is divided by 9 is 5
Answer:
22Step-by-step explanation:
You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.
(1) Digit sum is 5The sum of digits of a 2-digit number will be 5 if that number is one of ...
{14, 23, 32, 41, 50}
In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.
(2) Mod 9 value is 5In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:
{59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9
The remainders when divided by 3 are all 2 for these numbers as well.
__
Additional comment
The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.
Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.
one of four different prizes was randomly put into each box of a cereal. if a family decided to buy this cereal until it obtained at least one of each of the four different prizes, what is the expected number of boxes of cereal that must be purchased?
The expected number of boxes of cereal that must be purchased to obtain at least one of each of the four different prizes is 1.
Let X be the number of boxes of cereal that need to be purchased to obtain at least one of each of the four different prizes. We want to find E(X), the expected value of X.
To do this, we can use the concept of the geometric distribution. The probability of obtaining a new prize in a box of cereal is given by:
p = 4/4 = 1 (since there are four different prizes)
The probability of not obtaining a new prize in a box of cereal is
q = 1 - p = 0
Therefore, X follows a geometric distribution with parameter p = 1. The expected value of a geometric distribution with parameter p is
E(X) = 1/p
So in this case, we have
E(X) = 1/1 = 1
This means that on average, the family will need to purchase one box of cereal to obtain at least one of each of the four different prizes.
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