Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
How many small cubes, with a side length of 1/4 cm , will fill the larger rectangular prism below?
Answer:The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.
Step-by-step explanation:
Another way to figure this is to compute the prism volume in the given dimensions (cm³) and the cube volume in the same dimensions, then find the number of cube volumes in the prism volume.
After t years, 20 grams of cesium-137 decays to a mass y (in grams) given by
t/30
20(1) 430
"
y = 20
t≥ 0.
How much of the initial mass remains after 110 years? (Round your answer to three decimal places.)
g
Therefore , the solution of the given problem of equation comes out to be rounded to three decimal places, is 17.483 grams.
What is equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Think about the information that y + 7 provides. When accompanied by generate y + 7, increasing results in b + 7 in this case rather than another method that could split 12 into two separate components.
Here,
We must enter t = 110 into the equation for y and solve for y in order to determine how much of the original mass is still present after 110 years:
=> y = 20(1 - 2^(-t/30))
=> y = 20(1 - 2^(-110/30))
=> y ≈ 2.517
As a result, there are roughly 2.517 grams of cesium-137 left after 110 years. We can deduct this amount from the original mass of 20 grams to determine how much of the initial mass is still present:
=> 20 - 2.517 ≈ 17.483
Thus, roughly 17.483 grams of the original 20 grams of cesium-137 are still present after 110 years.
The number, rounded to three decimal places, is 17.483 grams.
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The seats available to a baseball game come in four types: bleacher, box, club, and grandstand. There are 12,600 box seats and 5,400 club seats available. According to the graph, what is the total number of seats available?
Answer: 45,000
Step-by-step explanation:
Let x be the total number of seats available. According to the problem, 18% of the seats are bleachers, and 42% of the seats are grandstands. That means the remaining 40% of the seats are box and club seats combined since 100% - 18% - 42% = 40%.
The problem states that there are 12,600 box seats and 5,400 club seats available, which makes a total of 12,600 + 5,400 = 18,000 box and club seats.
Now, we can set up an equation to find the total number of seats:
0.40x = 18,000
To solve for x, divide both sides of the equation by 0.40:
x = 18,000 ÷ 0.40
x = 45,000
There are a total of 45,000 seats available at the baseball game.
HELP! MY ASSIGNMENT IS DUE TOMORROW. REWARD 15 PTS!
Rewrite each equation without absolute value symbols for the given values of x. y=|2x+5|-|2x-5|
if x<-2.5
if x>2.5
if -2.5<=x<=2.5
Answer: For x < -2.5:
y = |2x + 5| - |2x - 5|
y = -(2x + 5) - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 < 0 for x < -2.5)
y = -2x - 5 + 2x - 5
y = -10
For x > 2.5:
y = |2x + 5| - |2x - 5|
y = 2x + 5 - (2x - 5) (since 2x - 5 < 0 and 2x + 5 > 0 for x > 2.5)
y = 10
For -2.5 ≤ x ≤ 2.5:
y = |2x + 5| - |2x - 5|
y = 2x + 5 - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 > 0 for -2.5 ≤ x ≤ 2.5)
y = 4x
Step-by-step explanation:
What can be concluded about the line represented in the table? Select 3 options.
X
-6
2
8
The slope is 2.
The slope is 2.
y
-7
-3
0
The y-intercept is -4.
The y-intercept is 8.
The points (-2,-5) and (8, 0) are also on the line.
Mark this and return
O
Save and Exit
Next
Submit
The value of the y -intercept is -4 and the slope of the equation is 1/2.
What is slope of the equation?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The slope of the line is given by the formula:
m = y2 - y1 / x2 - x1
From the table the coordinates are: (-6, -7) and (2, -3).
m = -3 + 7 / 2 + 6
m = 4 / 8
m = 1/2
Now, using the slope intercept form we have:
y - y1 = m(x - x1)
y + 7 = 1/2 (x + 6)
2 (y + 7) = x + 6
2y + 14 = x + 6
2y = x - 8
The y- intercept is found when x = 0
Thus, 2y = -8
y = -4
Hence, the value of the y -intercept is -4 and the slope of the equation is 1/2.
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Pearl's Plumbing initially estimated the cost to fix Terrell's sink at $450. Fortunately for
Terrell, the prediction was 12.5% more than the actual cost. What was the actual cost of the
repair?
According to the given data the actual cost of the repair was $393.75.
What is meant by estimated cost?Estimated cost refers to the approximate amount of money that is expected to be spent on a particular project, task, or item. It is a prediction of the expected cost based on the available information and assumptions about the project or item being estimated. Estimated costs can be based on various factors such as labor, materials, equipment, overhead, and other expenses.
According to the given information:If the estimated cost was 12.5% more than the actual cost, then the actual cost was 100% - 12.5% = 87.5% of the estimated cost.
Let x be the actual cost of the repair. Then, we can set up the following equation:
87.5% of estimated cost = actual cost
0.875 * 450 = x
Solving for x, we get:
x = $393.75
Therefore, the actual cost of the repair was $393.75.
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Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 4, -12, 36, ... Write your answer using decimals and integers. 30-1
Answer:
Step-by-step explanation:
The sequence starts with 4 and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the equation to describe the sequence is:
aₙ = 4(-3)^(n-1)
where aₙ represents the nth term in the sequence.
Using this equation, we can find the values of the first few terms in the sequence as follows:
a₁ = 4(-3)^(1-1) = 4(1) = 4
a₂ = 4(-3)^(2-1) = 4(-3) = -12
a₃ = 4(-3)^(3-1) = 4(9) = 36
and so on.
Note that the index n starts at 1, but in some contexts it may start at 0, in which case we would need to adjust the exponent accordingly.
25 points
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals.
To construct the parallelogram ABCD, follow these steps:
Draw a line segment AB of length 5 cm.From point A, draw a perpendicular line segment AD of length 5 cm.Draw a ray from point A, making an angle of 120 degrees with AB. Label the intersection of this ray and AD as point S.Draw a line through point S parallel to AB, and label the intersection with the extension of AD as point C.Draw a line through point B parallel to AD, and label the intersection with the extension of AB as point D.The parallelogram ABCD is formed by connecting points A, B, C, and D.The diagram of the parallelogram ABCD is shown below:
D - - - - -C
/ |
/ |
A - - - - - - - B
Note that AB is parallel to CD and AD is parallel to BC, and opposite sides of the parallelogram are congruent.
Geometry!
Use the figure below to solve for x
The diagram shows the sequence of three rigid transformations used to map TriangleABC onto TriangleA"B"C". What is the sequence of the transformations?
rotation, then reflection, then translation
rotation, then translation, then reflection
translation, then reflection, then rotation
translation, then rotation, then reflection
The sequence of the transformation are - translation, then rotation, then reflection
What in mathematics is a congruence?Congruent refers to having the same size and shape. Congruent hence involves comparing two numbers, and equivalent denotes the equality of two expressions. Hence, to state two line segments are congruent implies that the two lines have equal measurements.
Congruent implies a similar angle, right?Angle measure is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees. The angles of a regular polygon will always be congruent, regardless of its size or scale.
here, from given figure we have triangle ABC ,where
ABC is translation,
A'B'C' is rotation of triangle ABC
A''B''C'' is reflection ,
so,
the sequence of the transformations of triangle ABC is translation, then rotation, then reflection.
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Answer:
D
Step-by-step explanation:
Edge
what is pemdas and how is it used in math
PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations.
PEMDAS rule states that the order of operation starts with the parentheses first or the calculation, which is enclosed in brackets. Then, the operation is performed on exponents(degree or square roots), and later, we do operations on multiplication & division and at last addition and subtraction.
PEMDAS is the order that you solve a problem.
PEMDAS stands for:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.
In the equation
2 + 3 * 5,
first you would do 3 * 5 because multiplication is before addition.
2 + 15
Then you would do the addition to get the answer:
17.
Please give brainliest
workout 1/3 divided by 7/6 plus 1/5
Answer: To simplify the expression, we need to follow the order of operations, which is to perform the division first, then addition.
1/3 ÷ 7/6 + 1/5
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:
1/3 ÷ 7/6 = 1/3 × 6/7 = 2/7
Now we can substitute this value back into the original expression:
2/7 + 1/5
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 35:
2/7 × 5/5 = 10/35
1/5 × 7/7 = 7/35
Now we can add the two fractions:
10/35 + 7/35 = 17/35
Therefore, the simplified expression is 17/35.
Step-by-step explanation:
Write the equation for a parabola with a focus at (-4,3) and a directrix at y=5.
y=(blank)
The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex]
what is parabola ?A hyperbolic is a U-shaped symmetry curve that is created when a plane and a cone collide. The parabola has the characteristic that the distance between any point on the curve and a fixed point (referred to as the focus) is identical to the distance between that point and a telephone service (called the directrix). Equation y = ax2 + bx + c, at which a, b, and c are constants, gives the conventional form of a parabola. The parabola opens either upwards or downwards depending on the sign of coefficient a. The arc opens upwards if an is positive and downwards if an is negative.
given
A parabola with a vertex at (h, k) and a vertical axis of symmetry has the following standard form equation:
[tex](x - h)^2 = 4p(y - k) (y - k)[/tex]
where p is the separation between the vertex and the directrix or focus.
In this instance, the vertex's coordinates are (h, k) = since it is located halfway between the focus and directrix (-4, 4). As the directrix is a horizontal line with the coordinates y = 5, the separation between it and the vertex is p = 1.
When we enter these values into the equation in standard form, we obtain:
[tex](x + 4)^2 = 4(1)(y - 4) (y - 4)[/tex]
If we simplify, we get:
[tex](x + 4)^2 = 4y - 16[/tex]
The parabola's equation is as follows, with the directrix at y = 5 and the focus at (-4, 3). [tex](x + 4)^2 = 4y - 16[/tex] .
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Using sine tule find Obtuse angle B
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(B)}{7}=\cfrac{\sin(30^o)}{6}\implies \sin(B)=\cfrac{7\sin(30^o)}{6} \\\\\\ B=\sin^{-1}\left[ \cfrac{7\sin(30^o)}{6} \right]\implies B\approx 35.69^o[/tex]
Make sure your calculator is in Degree mode.
Question 7
Find the volume. Round to two decimal places if necessary. If your answer is correct you will see an image appear on your screen.
The formula for finding the volume of a cone is [tex]\pi[/tex][tex]r^{2}[/tex] [tex]\frac{h}{3}[/tex]
Please note the following:
Radius: 5 in
Height: 13 in
(1): Substitute the radius and height into the equation.
[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex]
(2): Using a calculator, solve the equation.
[tex]\pi[/tex][tex](5^{2})[/tex][tex](\frac{13}{3} )[/tex] = 340.33
(3): Round
If you were to round 340.33 to the next two decimal places, you'd get 340 as your final answer.
With that being said, the answer to your question is 340 in.
On the following checking account record, enter the figures and add or subtract them to keep the running total correct.
Balance Forward
Check
No.
Date
3427 2/14
3428 2/15
2/17
3429 2/22
3430 2/22
Checks Issued To
or Description of Deposit
Alfred's Market
Sunnyside Cafe
Deposit (paycheck)
City Water and Power
Amount of Check Amount of Deposit
$90.48
$65.00
$54.47
$375.99
$381.33
$299.88
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance
Check
or Dep.
The balances and the running total, given the checking account record is :
2 / 14 - $ 209. 402 / 15 - $ 144. 402 / 17 - $ 525.73 2 / 22 - $ 471.26 2 / 22 - $ 95.27How to find the balances ?The balance on the 14 th of February would be:
= Balance forward - Amount of check
= 299. 88 - 90. 48
= $ 209. 40
The balance on 2 / 15 :
= 209. 40 - 65
= $ 144. 40
The balance on 2 / 17 :
= 144. 40 + 381.33 which is a deposit
= $ 525.73
The balance and running total on 2 / 22 :
= 525. 73 - 54.47
= $ 471.26
The balance on 2 / 22 after the National Mortgage deduction is:
= 471. 26 - 375.99
= $ 95.27
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Please help with this equation I’ll give brainliest
Answer: it must be EXPONENTIAL as values are increasing exponentially
Step-by-step explanation:
Parents wish to have $130,000 available for a child's education. If the child is now 10years old, how much money must be set aside at 3% compounded semiannually to meet their financial goal when the child is 18?
To reach their financial objective of having $130,000 accessible for their child's schooling when the youngster turns 18, the parents must set aside roughly $97,209.87 at 3% compound semiannually.
To determine how much money needs to be set aside to meet the financial goal of $130,000 for the child's education, we can use the compound interest formula:
[tex]A = P(1 + r/n)^(nt)[/tex]
where A represents the future value, P represents the principal (or initial investment), r represents the annual interest rate, n is the frequency with which interest is compounded annually, and t represents the passage of time in years.
To solve for the principal, P, in this situation, we must first identify the principal, P.
[tex]P = A / (1 + r/n)^(nt)[/tex]
Given that the child is currently 10 years old and will need the money in 8 years (at age 18), we have t = 8. The interest rate is 3%, which we need to express as a decimal (r = 0.03), and the interest is compounded semiannually, so n = 2.
Using these values and the desired future value of $130,000, we can calculate the required principal:
P = [tex]130000 / (1 + 0.03/2)^(2*8)[/tex] = $97,209.87
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Margo borrows $700, agreeing to pay it back with 3% annual interest after 17 months. How much interest will she pay?
Margo will pay an interest of $29.75 on her loan.
Using an 8 sector spinner, let E be the event of getting an even. What is the probability of getting a perfect square given you got an even, i.e. P(S/E)? Are the two events independent or dependent?
Two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.
Describe Probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. For example, the probability of rolling a 6 on a fair dice is 1/6, or approximately 0.167.
In probability theory, events are often expressed as sets of possible outcomes, and probabilities are calculated based on the number of outcomes in the event relative to the total number of possible outcomes. For example, the probability of rolling an even number on a fair dice is 3/6, or 0.5, because there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
Since the event E is the event of getting an even number, the possible outcomes are 2, 4, 6, or 8.
Out of these, only 4 is a perfect square. Therefore, P(S/E) = 1/4.
These two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.
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You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years?
Answer:
$67,000 after 15 years.
Step-by-step explanation:
You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years? account will have $67,000 in it after 15 years
solve for a.
please answer i will rank what ever you want. thank you.
After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.
What is law of cosines?The law of cosines is a trigonometrical rule that links the lengths of a triangle's sides to the cosines of one of its angles, whether the triangle is spherical or flat. When two sides and the angle between them are known, it can be used to determine the length of a side or the angle of a triangular. There are two versions of the law of cosines: one for spherical triangles and one for planar triangles.
We can use the Law of Cosines to solve for the length of BC (denoted by a) in triangle ABC, since we know two sides and the included angle.
[tex]\rm a=\sqrt{c^{2}+b^{2}-2 c b \cdot \cos A}[/tex]
[tex]\rm a=\sqrt{4^{2}+3^{2}-2(4)(3) \cdot \cos(32^{\circ})}[/tex]
[tex]\rm a=\sqrt{16+9-24\cdot \cos(32^{\circ})}[/tex]
[tex]\rm a=\sqrt{1 \cdot \cos(32^{\circ})}[/tex]
a = 2.155654
a ≈ 2.2
Thus, After solving for side a, we have come to know that a = 2.2. Thus, option A is correct.
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Use a sum or difference identity to find the exact value. sin 10° cos 50° + cos 10° sin 50°
Answer:
√3/2
Step-by-step explanation:
sin(10°) • cos(50°) + cos(10°) • sin(50°)
= sin(10 + 50)
sin(60°) = √3/2
Help me find x using Pythagorean theorem
Using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
So, the Pythagorean formula is as follows:
c = √a² + b²
Now, insert values as follows:
c = √a² + b²
c = √12² + 9²
c = √144 + 81
c = √225
c = 15 units
Therefore, using the Pythagorean theorem we know that the value of x in the given situation is 15 units respectively.
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Rosa and Clarice have left over bread (not including the end pieces), so they decided to make sandwiches for the librarian, office staff, and custodian. How many sandwiches will they be able to make?
The number of sandwiches Rosa and Clarice can make depends on the amount of leftover bread they have.
To determine the number of sandwiches that Rosa and Clarice can make, we need to know how much bread they have.
Let's assume that they have 10 slices of bread left over. To make a sandwich, you typically use two slices of bread, so we can make 5 sandwiches with 10 slices of bread.
However, if they have more or less bread, the number of sandwiches they can make will change accordingly.
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A skydiver falls 4,800 feet in 4 seconds. Which graph has a slope that best represents this rate? ILL GIVE 1O POINTS
Answer:
The slope of a line represents the rate of change, which in this case is the rate at which the skydiver is falling. The rate of falling is 4,800 feet in 4 seconds, which simplifies to 1,200 feet per second, therefore, the graph that has a slope of 1,200 best represents this rate.
the length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of 0.7 minutes. what is the probability that a conversation lasts longer than 6 minutes?
The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:
z = (6 - 5) / 0.7 = 1.43
Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.
Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
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The table shows the number of video games sold worldwide for the five highest-selling video games in 2010. Assuming this trend continues and that the total sales of all other video games is negligible, if a person chooses to purchase one of these video games, determine the empirical probability that the person will purchase game 2,5 and 1.
Game 1: 18,200,00
Game 2: 17,360,000
Game 3: 11,410,000
Game 4: 11,160,000
Game 5: 8,450,000
total: 66,580,000
The empirical probability of an event is the ratio of the number of times the event occurred to the total number of observations.
So, for each game, the empirical probability of purchasing that game is given by:
Game 1: 18,200,000/66,580,000 = 0.273 or 27.3%Game 2: 17,360,000/66,580,000 = 0.261 or 26.1%Game 3: 11,410,000/66,580,000 = 0.171 or 17.1%Game 4: 11,160,000/66,580,000 = 0.168 or 16.8%Game 5: 8,450,000/66,580,000 = 0.127 or 12.7%So the empirical probability of purchasing game 1 is 27.3%, game 2 is 26.1%, and game 5 is 12.7%.
A runner sprinted 103.76 yd to finish a race.
Use the table of facts to find the distance she sprinted in feet.
Round your answer to the nearest tenth.
Answer:
311.3 feet
Step-by-step explanation:
1 yard = 3 feet
Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)
Rounding to the nearest tenth gives us 311.3 feet.
Which of the following is equivalent to 6³•
65
O 6^8
O 36^15
O 6^15
O 36^8
PLSS help.