The area of the shaded region is 170.88 sq. cm.
A circle with a radius of 6 cm is inside a circle with a radius of 9.5 cm.
The area of a circle is given by the formula:
A = πr²Where,A = Areaπ = 3.14r = radius
For the shaded area, we need to subtract the area of the smaller circle from the larger circle.
the radius of the larger circle is 9.5 cm and the radius of the smaller circle is 6 cm.
So, the area of the shaded area can be given as:
Area of the shaded region = Area of larger circle - Area of smaller circle
Area of larger circle = πr²= π(9.5)²= π(90.25) sq. cm.= 283.92 sq. cm.
Area of smaller circle = πr²= π(6)²= π(36) sq. cm.= 113.04 sq. cm.
So, the area of the shaded region is:
Area of the shaded region = 283.92 - 113.04= 170.88 sq. cm.
Therefore, the area of the shaded region is 170.88 sq. cm.
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Question
A circle with radius of 6 cm sits inside a circle with radius of 9 cm.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
A circle with radius of 6 cm sits inside a - 1
help pls offering 95 points and if brainliest if 2 people answer
Answer:
126*2/(5+2+)
252/7=36
Step-by-step explanation:
Hope this helps! =D
Sorry again
Does anyone know the answer to this?
Answer:
[tex] \frac{a - 3}{a + 2} [/tex]
Step-by-step explanation:
[tex] \frac{ {a}^{2} - 7a + 12 }{ {a}^{2} - 2a - 8} = \frac{(a - 3)(a - 4)}{(a + 2)(a - 4)} = \frac{a - 3}{a + 2} [/tex]
a 10 foot ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 2 feet per second, how fast is the bottom of the ladder moving along the ground when the bottom of the ladder is 5 feet from the wall? write your answer in the most simplified form without rounding and do not include units.
The bottom of the ladder is moving at a rate of 4 feet per second when it is 5 feet from the wall.
Let's call the distance from the bottom of the ladder to the wall "x". We can use the Pythagorean theorem to relate the distances as follows:
x^2 + 10^2 = L^2
where L is the length of the ladder, which is constant at 10 feet. We can take the derivative of both sides with respect to time t:
2x (dx/dt) = 2L (dL/dt)
We want to find (dx/dt) when x = 5 and (dL/dt) = -2 (since the top of the ladder is sliding down the wall at a rate of 2 feet per second). Plugging these values in, we get:
2(5) (dx/dt) = 2(10) (-2)
Simplifying, we get:
10 (dx/dt) = -40
Dividing both sides by 10, we get:
dx/dt = -4
Therefore, the bottom of the ladder is moving along the ground at a rate of 4 feet per second in the opposite direction.
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A girl bought a total of 12 fiction and non-fiction books. The fiction books cost $12 each and the non-fiction books cost $25 each. If she paid $248 altogether, how many of each kind of book did she buy? How do I write that as an expression?
Which correctly describes how to determine the measure of angle 1?
2 parallel lines are crossed by a transversal to form 8 angles. Clockwise from top left, the angles are 105 degrees, blank, blank, blank; blank, blank, 2, 1.
The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
The 105° angle and angle 2 are corresponding angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.
The 105° angle and angle 2 are corresponding angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.
The right option is: "Because angle 2 and angle 105 have equivalent angles, they must both be 75 degrees. As angles 1 and 2 are complementary, angle 1 must be 105°."
In geometry, a transversal is a line that crosses two or more parallel lines, whereas parallel lines are lines that never intersect. Eight angles are created when two parallel lines are crossed by a transversal; each pair of adjacent angle is congruent, as are alternate inner angles and alternate exterior angles.
We can infer from the facts provided that angle 2 and angle 105° are corresponding angles. A transversal that crosses two parallel lines and appears in the same relative position at each intersection creates corresponding angles. Angle 2 must be 75° if the 105° angle measures the same as the comparable angle.
We can use this knowledge to compute the measure of angle 1 since angles 1 and 2 are supplementary angles, which means they add up to 180°. Angle 1 must be 105° if angle 2 is 75° for the sum of the angles to reach 180°.
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In three to four sentences, describe why CEOs (that is, the chief executive officers or the leaders of large companies) make very high salaries, while their administrative assistants make much less.
Well, CEOs are on the top of the food chain. It takes a lot of work and ambition to become one, and once they are one, CEOs accept a huge amount of responsibility - that means having to take blame if things go wrong and having more tasks to complete such as having to attend numerous meetings, make decisions. They are also on the board of directors.
Assistants do not have to do as much, they likely won't have that much responsibility or experience, their tasks revolve around ensuring meetings are scheduled and performing other ad-hoc duties.
(Not Mine)
given a minimized dfa with n states, what are the minimum and maximum number of states an equivalent nfa might have?
The minimum number of states an equivalent NFA might have is n, while the maximum number of states is 2^n. However, while an NFA with 2^n states is always possible, it may not be the most efficient representation of the language recognized by the DFA.
The minimum number of states an equivalent NFA might have is n. This is because every DFA can be viewed as a special case of NFA, where each state has only one outgoing transition for each possible input symbol.
Therefore, we can create an equivalent NFA by simply replacing each transition of the DFA with a set of transitions, where the set contains all possible transitions that could be taken in that state for a given input symbol. This NFA will have n states, one for each state of the original DFA.
On the other hand, the maximum number of states an equivalent NFA might have is 2^n. This is because each state of an NFA can have multiple outgoing transitions for the same input symbol, leading to multiple possible paths through the automaton for a given input string.
Therefore, we can create an NFA with 2^n states by creating an NFA that has one state for each subset of the states of the original DFA. Each state in the new NFA represents a set of states from the original DFA that could be reached by following any sequence of transitions for a given input string.
It is worth noting that while an NFA with [tex]2^n[/tex] states can always be constructed to be equivalent to a given minimized DFA, it may not be the most efficient representation of the language recognized by the DFA. In practice, there are often more efficient ways of constructing equivalent NFAs with fewer states.
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I don't know how to do whatever this is
Answer: y values in order: 2, 1, 0.5
Step-by-step explanation:
Just take the x values and put them in place of the x in the above equation.
As for -1, you're flipping 0.5 over to a fraction of 1/0.5, which equals 2, so that's the first y value.
*This is because any negative exponent gets the number in the denominator with 1 in the numerator, then the denominator can change depending on the value of the exponent
For 0, anything to the power of 0 is 1, so that's the second y value.
And then for 1, the number doesn't change, so just put 0.5 in the third y-value.
Also I see it says for you to sketch a graph, in this case the picture I have showing is what the graph would look like
Hope this helps at least :)
please help!!! trigonometry. WILL GIVE BRAINLY IF CORRECT
The correct trigonometric ratios for similar triangles are:
u (cos 34")/r (cos 34") = used to find u or r, given u or rt (sec 34")/q (sec 34") = used to find t or q, given t or qt (tan 34°)/q (tan 34") = used to find t or q, given t or qu (sin 34")/ r (sin 34") = used to find u or r, given u or rWhat are trigonometric ratios?Trigonometric ratios are mathematical functions that relate the angles and sides of a right triangle.
There are three main trigonometric ratios: sine, cosine, and tangent.
Sine (sin) is the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.
Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse of the triangle.
Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side of the triangle.
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One of the angles of a parallelogram is 36° greater than another one. Find the angles
of the parallelogram.
The angles are_,_,_,_
Answer:
Step-by-step explanation:
Opposite angles of a parallelogram are congruent.
Adjacent angles equal 180°.
If one angle is 36 ° more than the other than they are supplementary or equal to 180°.
x + x + 36 = 180
2x + 36 = 180
2x + 36 - 36 = 180 -36
2x = 144
2x/2 = 144/2
x = 72
2 angles = 72°
2 angles = 108°
All the angles = 360°.
72 × 2 = 144
108 x 2 = 216
144 + 216 = 360°
So this is correct.
Three ballet dancers are positioned on stage. Max is 2 feet straight behind Kenji and 4 feet directly left of Lindsey. When the music begins, Max twirls to Lindsey's position, then leaps to Kenji's position, and finally walks back to his original position. How far did Max travel? If necessary, round to the nearest tenth.
The total distance Max traveled is 8.2 feet which is found by adding three distances together gives us the total distance Max traveled.
What is distance?Distance can be measured using other units such as time, speed, or even angles.
To calculate this, we need to find the distance between Max's original position and Lindsey's position, the distance between Lindsey's position and Kenji's position, and the distance between Kenji's position and Max's original position.
The distance between Max's original position and Lindsey's position=
4.0 feet.
This is because Max was 4 feet to the left of Lindsey.
The distance between Lindsey's position and Kenji's position= 2.8 feet. This is because Kenji was 2 feet behind Lindsey and Max was 4 feet left of Lindsey.
The distance between Kenji's position and Max's original position= 1.4 feet.
This is because Kenji was 2 feet behind Max.
Adding these three distances together gives us the total distance Max traveled: 4.0 feet + 2.8 feet + 1.4 feet = 8.2 feet.
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walter bought a 21 pound bag of flour. he used 4.2 pounds of flour
Walter stored the remaining flour in 19 2 2/5-pound portions, with a small amount of flour left over.
we have:
(35/3) ÷ (12/5)
To divide by a fraction, we can multiply by its reciprocal:
(35/3) × (5/12)
Simplifying the fractions, we get:
(35/3) × (5/12) = (7/3) × (5/2) = 35/6
So, Walter stored the remaining flour in 35/6-pound portions. To express this in terms of 2 2/5-pound portions, we need to divide 35/6 by 2 2/5:
(35/6) ÷ (2 2/5)
Again, we convert 2 2/5 to an improper fraction:
2 × 5 + 2 = 12
So, we have:
(35/6) ÷ (12/5)
To divide by a fraction, we multiply by its reciprocal:
(35/6) × (5/12)
Simplifying the fractions, we get:
(35/6) × (5/12) = (35/72)
Therefore, Walter stored the remaining flour in 35/72 of a 2 2/5-pound portion.
To find the whole number of 2 2/5-pound portions, we need to divide 35/72 by 2 2/5. We can do this by dividing the numerator by the denominator and rounding down to the nearest whole number:
(35/72) ÷ (12/5) ≈ 0.818 ≈ 0
So, Walter stored the remaining flour in 0 whole 2 2/5-pound portions. However, he did store the remaining flour in 35/72 of a 2 2/5-pound portion, which is less than one portion. Therefore, we can say that he stored the remaining flour in 0.35 of a 2 2/5-pound portion, or approximately 0.35 × 2 2/5 = 0.875 pounds of flour per portion.
Finally, to find the number of 2 2/5-pound portions, we divide the total remaining flour by the amount in each portion:
16.8 ÷ 0.875 ≈ 19.2
So, Walter stored the remaining flour in 19 2 2/5-pound portions, with a small amount of flour left over.
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a bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?
The second wheel has a smaller circumference compared to the first wheel. The second wheel completes a revolution when the wheel turns 75.40 inches, but the odometer reads 84.82 inches.
There are two types of odometers
one mechanical and the other digital.In the case of a mechanical odometer, the worm gear is used to make the gear train, and the overall gear ratio is 1690:1, which means that when the vehicle travels a distance of 1 mile, the mechanical odometer input shaft makes 1690 revolutions during this time. In the case of a digital odometer, a magnetic sensor is used to receive pulses, each of which counts as one revolution. We now have a bicycle odometer designed for 27 wheels. Thus, d₁ = 27 inches is the diameter of the first wheel
d₂= 24 inches is the diameter of the second wheel
The odometer is the distance traveled by the vehicle, given as the number of revolutions of the wheel multiplied by the circumference of the wheel. So for the first wheel, Therefore, in case of first
wheel, [tex]C_1 = πd_1 [/tex]
= π × 27
= 84.82 inches
In case of second wheel,
[tex]C_2 = π × d_2[/tex]
= π × 24 inches
= 75.40 inches
So, [tex]C_1 - C_2 = [/tex] 84.82 inches - 75.40 inches
= 9.42 inches
So we can see that the second wheel has circumference is less as compared to the first wheel.
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Complete question:
bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?
Question
In △ABC, AB=7.8 ft, BC=10.7 ft, and m∠B=27°.
What is the area of △ABC?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
ft²
Rounded to the nearest hundredth, the area of △ABC is 27.28 .
What is Area ?
Area is a measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, circle, or any other shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, or square meters.
To find the area of △ABC, we can use the formula:
A = (1÷2)bh
where A is the area of the triangle, b is the length of the base, and h is the height.
In △ABC, we can use AB as the base and drop a perpendicular from A to BC to find the height. Let D be the foot of the perpendicular from A to BC.
First, we can find BD using the trigonometric ratio for the angle 27°:
tan(27°) = BD/AB
BD = AB * tan(27°)
BD = 7.8 ft * 0.5095
BD ≈ 3.97 ft
Next, we can find the length of CD:
CD = BC - BD
CD = 10.7 ft - 3.97 ft
CD ≈ 6.73 ft
Now we can use the Pythagorean theorem to find the length of AD:
AD*AD= AB*AB - BD*BD
AD* AD = (7.8 * 7.8 ) - (3.97 * 3.97)
AD ≈ 6.99 ft
Finally, we can use the formula for the area of the triangle:
A = (1÷2)bh
A = (1÷2)(7.8 ft)(6.99 ft)
A ≈ 27.28
Therefore, Rounded to the nearest hundredth, the area of △ABC is 27.28.
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assume you have a coin that for each flip, there is a 50% chance of coming up heads, and a 50% chance of coming up tails. what is the probability of getting exactly 3 heads out of 5 flips?
The required probability of getting exactly 3 heads after flipping a coin 5 times is equal to 0.3125 or 31.25%.
Using the binomial distribution,
probability of getting heads represents the success = p
Number of time coin flips = n
The probability of getting exactly x successes (heads in this case) in n independent Bernoulli trials ,
P(x) = (ⁿCₓ) × p^x × (1-p)^(n-x)
where (ⁿCₓ) represents the number of ways to choose k successes out of n trials.
The probability of getting exactly 3 heads out of 5 flips,
with a probability of 0.5 for each flip.
n = 5 (5 coin flips)
k = 3 (getting 3 heads)
p = 0.5 (probability of getting heads on each flip)
Using the formula above, we get,
P(3) = (⁵C₃) × 0.5^3 ×0.5^(5-3)
= 10 × 0.125 × 0.25
= 0.3125
Therefore, the probability of getting exactly 3 heads out of 5 flips is 0.3125 or 31.25%.
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The diagram shows a scale drawing of a rectangular playground. The scale drawing is 1:500. Work out the premiere of the real playground. Give your answer in meters
The actual playground's perimeter is 1000 (x + y) meters, where x and y are the space's length and breadth.
What is perimeter of a rectangle?One of the key formulae for the rectangle could be regarded to be its perimeter. It is the entire length of the rectangle's outside perimeter.
The perimeter of a rectangle is defined as its length times its breadth.
Dimensions of a parallelogram = 2 × (length + width)
Given that, the scale drawing is 1:500
If the scale drawing playground has a length of x and a breadth of y, then the length and width of the playground, respectively,
are 500x and 500y.
The size drawing playground's perimeter = 2 × ( Length + width )
The size drawing playground's perimeter = 2 (x + y)
The actual playground's perimeter = 2 × ( Length + width )
The actual playground's perimeter = 2 × (500x + 500y)
= 2 × 500 (x + y)
The boundaries of the area itself = 1000 (x + y)
Therefore, the actual playground's perimeter is 1000 (x + y) meters, where x and y are the playground's length and breadth.
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The complete question is attached below,
based on the pictures, how many hours should the student record on the nighttime picture to complete a day-night cycle?
The number of hours the student should record on the nighttime picture to complete a day-night cycle = 13 hours
The correct answer is an option (c)
We need to find the number of hours the student should record on the nighttime picture to complete a day-night cycle.
From the following pictures we can observe that, the sunrise time is 7:10 A.M. and the sunset timing is 6:10 P.M.
This means that thet daytime is of 11 hours (from 7:10 A.M. to 6:10 P.M.)
We know that the number hours in a day = 24
Let us assume that x represents the nighttime hours.
From this situation we get an equation,
x = 24 - 11
x = 13 hours
And the nighttime cycle would be:
from 6:10 P.M. to 7:10 A.M.
Therefore, the required number of hours = 13 hours
The correct answer is an option (c)
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Find the complete question below.
the length of a rectangle is 3 yd less than double the width, and the area of the rectangle is 14 yd^2. find the dimensions of the rectangle.
Answer:
The rectangle is 3.5 yd x 4 yd
Step-by-step explanation:
Area = length x width = lw
l = length = 2w - 3
w = width
Area = 14(2w - 3)(w) = 14
2w² - 3w - 14 = 0
Use quadratic equation to find the 2 roots of w: a = 2, b = -3, c = -14
w = 3.5, -2 disregard the negative root
width = 3.5 yd
length = 2(3.5) - 3 = 4 yd
The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.
We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:
14 = (2x - 3) x x
Expanding the brackets:
14 = 2x² - 3x
Put this equation=0:
2x² - 3x - 14 = 0
Using the quadratic formula:
x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)
x = (3 ± √97) / 4
We can ignore the negative root, since the width cannot be negative. Therefore,
x ≈ 2.23
This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:
length = 2x - 3
length ≈ 1.46
Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards
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Here is a pattern of squares. The equation represents the number of small squares in the pattern of n, the step number
n²+2 is the equation that represents this pattern.
What is General intelligence?
General intelligence in mathematics refers to the ability to reason logically, solve problems, and understand abstract concepts in the field of mathematics. It is often referred to as mathematical intelligence or mathematical aptitude.
People with strong mathematical intelligence have the ability to think logically, identify patterns and relationships, and apply mathematical concepts to solve complex problems. They can quickly grasp mathematical concepts and principles, and are able to use mathematical reasoning to analyze data, make predictions, and draw conclusions.
However, it's important to note that mathematical intelligence is just one aspect of intelligence, and does not necessarily predict success in other areas of life. It is possible for someone to excel in mathematics while struggling in other areas, or vice versa.
Moreover, the concept of general intelligence itself has been a subject of debate among psychologists, with some arguing that it is a single, overarching ability, while others argue that intelligence is made up of multiple, more specific abilities.
Here we have total four patterns.
First pattern has 3 square, second has 6 squares , third has 11 squares and 18 squares.
Our first option is 3n.
If we will put n = 1,2,3,4 then we will get 3,6,9,12 respectively.
Our second option is n²+2.
If we will put n = 1,2,3,4 then we will get 3,6,11,18 respectively.
Our third option is n²+4.
If we will put n = 1,2,3,4 then we will get 5,8,13,20 respectively.
And our fourth option is 4n+3
If we will put n = 1,2,3,4 then we will get 7,11,15,19 respectively.
Therefore, second option is the correct option.
So, n²+2 is the equation that represents this pattern.
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Gwen is making a circular garden that has a diamete of 10 feet. She is looking to buy fencing for the garden. How many feet if fencing will she need?
According the given statement Gwen will need apprοximately 31.4 feet οf fencing fοr her circular garden with a diameter οf 10 feet.
What is area οf a circle?The area οf a circle is: π ( Pi) times the Radius squared: A = π r2 οr, when yοu knοw the Diameter: A = (π/4) × D2 οr, when yοu knοw the Circumference: A = C2 / 4π
The circumference οf a circle is given by the fοrmula:
C = πd
where d is the diameter οf the circle.
In this case, the diameter οf the garden is 10 feet. Substituting intο the fοrmula, we get:
C = π(10) = 10π
Therefοre, the circumference οf the garden is 10π feet.
Since fencing is placed arοund the garden, Gwen will need tο buy enοugh fencing tο cοver the circumference οf the garden, which is 10π feet.
Apprοximating π as 3.14, we can find the apprοximate length οf fencing needed as:
10π ≈ 10 x 3.14 ≈ 31.4
Therefοre, Gwen will need apprοximately 31.4 feet οf fencing fοr her circular garden with a diameter οf 10 feet.
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A ulangle whose vertices ore P. and A is mapped on a triangle whose vertices P. 04.0 sof ation PU"#" by a ma M en mapped onto triang ch would map /
a man has 32 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 515 cents, how many dimes and how many quarters does he have?your answer is
Answer:
19 dimes and 13 quarters
Step-by-step explanation:
Let's start by defining some variables:Let's call the number of dimes the man has "d".
Let's call the number of quarters the man has "q".We know that the man has 32 coins in total, so we can write:
d + q = 32We also know that the total value of the change is 515 cents. Since dimes are worth 10 cents and quarters are worth 25 cents, we can write an equation for the total value in cents:
10d + 25q = 515
We now have two equations with two variables, which we can solve simultaneously. Let's rearrange the first equation to solve for one of the variables:
d = 32 - q
We can substitute this expression for "d" into the second equation:
10(32 - q) + 25q = 515Simplifying and solving for "q", we get:
320 - 10q + 25q = 515
15q = 195
q = 13
So the man has 13 quarters. We can substitute this value into the first equation to find the number of dimes:
d + 13 = 32
d = 19
Therefore, the man has 19 dimes and 13 quarters.
There are 19 dimes and 13 quarters.
Let x represent the number of dimes and y represent the number of quarters.
There are a total of 32 coins, so:
x + y = 32
We know that the total value of the change is 515 cents
. The value of x dimes is 10x cents and the value of y quarters is 25y cents. So:
10x + 25y = 515
We can simplify the first equation by solving for one variable in terms of the other:
x + y = 32x = 32 - y
Now we can substitute this expression for x into the second equation:
10(32 - y) + 25y = 515
Simplify and solve for y:
320 - 10y + 25y = 515
15y = 195y
y = 13
So there are 13 quarters. We can find the number of dimes by substituting y = 13 into x + y = 32:x + 13 = 32x = 19So there are 19 dimes.
So, There are 19 dimes and 13 quarters.
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please help me I need this will mark brainliest
Since C=3x+4y and we want to maximize C, we need x and y to be as big as possible.
There are restrictions for x and y, namely that x ranges from 2 to 5 and y from 1 to 6. Subjected to these restrictions we set x to 5 and y to 6 because they are the max values for x and y.
Then C=3(5)+4(6)=39.
Use the long division method to find the result when 4x³+7x²-8x-14 is divided by 4x+7. If there is a remainder, express the result in the form q(x)+r(x)/b(x).
Answer:
a
Step-by-step explanation:
First, we write the polynomial in descending order of degree:
4x³+7x²-8x-14
Now, we start dividing the first term of the dividend by the divisor:
x²
___________
4x+7|4x³+7x²-8x-14
We multiply x² by 4x+7 to get:
x²
___________
4x+7|4x³+7x²-8x-14
4x³+7x²
-8x
Now we bring down the next term:
x²-2
___________
4x+7|4x³+7x²-8x-14
4x³+7x²
-8x-14
+8x+14
_______
0
The remainder is zero, which means that 4x+7 is a factor of 4x³+7x²-8x-14. The quotient is x²-2.
Therefore, the result when 4x³+7x²-8x-14 is divided by 4x+7 is:
4x³+7x²-8x-14 = (4x+7)(x²-2) + 0
So, the quotient is x²-2, and there is no remainder.
the average spending at neco's salad bar is $9.41 with a standard deviation of $2.81. the distribution follows t-distribution. the management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. what will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers?
The average spending difference between the upper and lower spending cut-offs which define the middle 90% of the customers is $1.94.
Average spending at Neco's salad bar is $9.41
Standard deviation of the spending is $2.81
Distribution follows t-distribution,
The management is interested in the middle 90% of the customers (spending wise)Sample contains 41 customers
In order to find the cut-off values, we need to find the z-values for 5% and 95% of the data set.
Lower cut-off = Average spending - z × (Standard deviation / √n)
Upper cut-off = Average spending + z × (Standard deviation / √n)
Here,
n = 41,
Average spending = $9.41,
Standard deviation = $2.81
Let's find the value of z from the t-distribution.
t-distribution is a symmetric distribution.
Since we need to find the middle 90%, we need to find the area outside of 5% (on both sides of the distribution).
For a 90% confidence interval, the area outside of 5% on both sides of the t-distribution is [tex]\frac{0.05}{2}[/tex] = 0.025.
As per the t-distribution table, for 40 degrees of freedom, the t-value for 0.025 is 2.021..
Lower cut-off = $9.41 - 2.021 × ()
Lower cut-off = $8.44
Upper cut-off = $9.41 + 2.021 × ($2.81/√41)
Upper cut-off = $10.38
Therefore, the difference between the upper and lower spending cut-offs which define the middle 90% of the customers is
$10.38 - $8.44 = $1.94.
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Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answer:
Try this!!!
Step-by-step explanation:
Experimental Probability:
The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:
Experimental Probability = Number of times Grace was chosen / Total number of trials
Experimental Probability = 15 / 116
Experimental Probability = 0.1293 or approximately 12.93%
Theoretical Probability:
The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:
Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical Probability = 1 / 6
Theoretical Probability = 0.1667 or approximately 16.67%
If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.
Which fraction is equivalent to 6/18
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 18 inches, and the length of the base is 15 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answer: 54 in
Step-by-step explanation:
Since the altitude drawn from the vertex of the isosceles triangle forms two congruent right triangles and divides the base into two equal segments, we can work with one of the right triangles to find the length of the other side of the isosceles triangle.
Let's denote the length of the altitude as a, the length of half the base as b, and the length of the other side of the isosceles triangle as c. From the problem, we know that a = 18 inches and b = 15 inches / 2 = 7.5 inches.
We can use the Pythagorean theorem to find the length of c:
a² + b² = c²
Substitute the known values:
18² + 7.5² = c²
324 + 56.25 = c²
380.25 = c²
Now, take the square root of both sides to find the length of c:
c = √380.25
c ≈ 19.5 inches
Since the isosceles triangle has two sides with equal length, the perimeter is:
Perimeter = base + 2 * c
Perimeter = 15 + 2 * 19.5
Perimeter = 15 + 39
Perimeter = 54 inches
Thus, the perimeter of the isosceles triangle is approximately 54 inches.
recall the use of data from the national health survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all u.s. adults. in the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16. suppose that we randomly select 100 u.s. adults who are smokers and find that 25% of this sample started smoking before the age of 16 (an error of 5% compared to the 2005-2007 report). is this much error surprising? find the probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%.
There is about a 10.4% probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%.
The error of 5% is not surprising because it falls within the margin of error for a sample of 100 with a 95% confidence level. To find the probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%, we need to use the formula for the margin of error:
Margin of error = zsqrt(p(1-p)/n)
where z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence), p is the estimated proportion from the population (0.3 in this case), and n is the sample size (100 in this case). Plugging in the values, we get:
Margin of error = 1.96sqrt(0.30.7/100) = 0.088
So the margin of error is 8.8%. To find the probability of a sample proportion being an over- or underestimate by more than 5%, we need to find the area under the normal curve beyond 0.05 in either direction. This can be done using a standard normal table or calculator, and the probability is approximately 0.104.
Therefore, there is about a 10.4% chance that a sample proportion will be an over- or underestimate of the parameter by more than 5%.
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PLEASE CHECK GEOMETRY WILL GIVE BRAINLIEST
Answer:
YES!!!
Step-by-step explanation: