Determine if true or false for ALL questions below

Answer:

She has 8 quarters and 3 dimes.

Step-by-step explanation:

8 times .25 is equal to 2. If you add .1 times 3 to this sum you get $2.30.

The question that best describes the equation of a / 4 = 20 is D. What number, when divided by four, is equal to negative twenty?

The best question for the given equation is the question shown in option D. This is because we have a mystery number that we shall call, a. We then have to divide this number by 4 which would mean we then have the formula :

= a / 4

Then, when this number is divided by 4, it would give - 20 so we then have the full relationship of:
a / 4 = - 20

This number can be solved to be - 80.

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The full question is:

Which of the following questions describes the equation a/4 = -20?

What number, when multiplied by four, is equal to negative twenty?

What number, when divided by negative four, is equal to twenty?

What number, when multiplied by negative twenty, is equal to four?

What number, when divided by four, is equal to negative twenty?

The value of the expression is 243

Index forms are simply described as mathematical forms that are used or the representation of numbers that are too large or in small sizes in more convenient forms.

These index forms are also termed;

Examples of index forms are;

a³, b², c²

From the information given, we have that;

3¹. 3⁴

Now, since they are of the same bases, add their exponent values

3⁵

Find the values, we get;

243

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The best measure of variability for the data, and its value is: D. The range is the best measure of variability, and it equals 9.

In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

From the data set, we have:

10, 1, 1, 4, 4, 2, 2, 2, 5, 5, 5, 3, 3, 3, 3

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 5 - 2

IQR = 3

For the range, we have;

Range = maximum - minimum

Range = 10 - 1

Range = 9.

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Answer:

Step-by-step explanation:

To calculate the expected payoff, we need to multiply the amount won by the probability of winning, and then add up all the results.

There are 10 odd numbers and 10 even numbers in the deck, so the probability of drawing an odd number is 10/20 = 1/2, and the probability of drawing an even number is also 1/2.

If we draw an odd number, we win $13, and if we draw an even number, we win $0. Therefore, the expected payoff is:

(1/2) × $13 + (1/2) × $0 = $6.50

So on average, we can expect to win $6.50 per game if we play this game many times.

To solve this problem, we the new length of the step should be 20 inches. the new length of the step should be 20 inches.  

What is volume?

Volume of cement = length × width × height

where the volume of cement is 4,500 cubic inches and the height can be assumed to be 1 inch (since we are dealing with a step

can use the formula:

Volume of cement = length × width × height

where the volume of cement is 4,500 cubic inches and the height can be assumed to be 1 inch (since we are dealing with a step).

So we have:

4,500 = length × width × 1

Simplifying this equation, we get:

4,500 = length × width

Now, since we want to use all the cement, we can assume that the volume remains the same, i.e., 4,500 cubic inches. But we need to find a new length that will give us this volume.

Let's say the new length is L inches. Then we can write:

4,500 = L × width

To solve for L, we need to know the value of width. Unfortunately, we don't have that information. However, we do know that a step is typically wider than it is long. So we can assume that the width is greater than the length, i.e.,

width > L

Under this assumption, we can say that the maximum value of L occurs when width is minimized. In other words, we want to find the smallest possible value of width that will still give us a volume of 4,500 cubic inches.

To do this, we can factor 4,500 and look for pairs of factors that differ by the least amount. We get:

4,500 = 2 × 2 × 3 × 3 × 5 × 5 × 2

The pairs of factors that differ by the least amount are 2 and 225, since they differ by only 223. So we can take width to be 225 inches and L to be:

L = 4,500 / 225 = 20 inches

Therefore, the new length of the step should be 20 inches.

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A)

There is a significant difference between the two recipes.

B)

We would expect approximately 30% of people to prefer recipe A over recipe B.

We have,

A.

To determine which recipe the baking company should add to its product line, we can perform a hypothesis test.

The null hypothesis would be that there is no difference between the two recipes (i.e., the proportion of people who prefer recipe A is the same as the proportion who prefer recipe B), and the alternative hypothesis would be that there is a difference between the two recipes.

We can use a two-sample proportion test to test the hypothesis.

Using the given data, the proportion of people who preferred recipe A in sample 1 is 0.29, in sample 2 is 0.38, and in sample 3 is 0.24.

The overall proportion of people who preferred recipe A is the average of these proportions, which is (0.29 + 0.38 + 0.24)/3 = 0.30.

Similarly, the overall proportion of people who preferred recipe B is 1 - 0.30 = 0.70.

To perform the hypothesis test, we calculate the test statistic z as:

[tex](P_1 - P_2)/\sqrt{\hat{P}(1/n_1 + 1/n_2)[/tex]

where p1 and p2 are the proportions of people who preferred recipe A in the two groups being compared, n1 and n2 are the sample sizes, and [tex]\hat{P}[/tex] is the overall proportion of people who preferred recipe A.

The calculated z-value is -4.07, which corresponds to a p-value of less than 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the two recipes.

Based on the results of the hypothesis test, the baking company should add recipe B to their product line, as it was preferred by a higher proportion of people overall.

However, the company should be somewhat cautious in its decision, as there is a small chance (less than 0.05) that the difference in preference between the two recipes could have occurred by chance alone.

B.

The mean of the data for recipe A is the average proportion of people who preferred recipe A across the three samples, which we calculated to be 0.30.

This means that we would expect approximately 30% of people to prefer recipe A over recipe B.

Thus,

There is a significant difference between the two recipes.

We would expect approximately 30% of people to prefer recipe A over recipe B.

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The solution is : 200  people were in the sample.

We have,

given data:

In a sample 76 people or 38% voted  the mayor to be prosecuted.

solution:

how many people were in that sample

if 38% = 76 people

therefore;

let

p = total number of people

76/p = 38/100

cross multiply both sides

38p = 7600

divide both sides by 38

38p /38 = 7600 /38

p = 200

the number of people in the sample original was 200.

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complete question:

In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample

The ratio of the perimeters is 4/3.

If two quadrilaterals are similar, then their corresponding sides are proportional, meaning that there is a constant ratio between the lengths of corresponding sides. The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Let's call the scale factor between the two similar quadrilaterals "k". Then, we can write:

k^2 = 64 m^2 / 36 m^2

Simplifying the right side of the equation, we get:

k^2 = (8/6)^2

k^2 = (4/3)^2

Taking the square root of both sides, we get:

k = 4/3

Therefore, the scale factor between the two similar quadrilaterals is 4/3.

To find the ratio of their perimeters, we can use the same scale factor. Since the sides of the two quadrilaterals are proportional, we can multiply each side of the smaller quadrilateral by the scale factor to get the corresponding side of the larger quadrilateral.

Let's call the perimeter of the smaller quadrilateral "P1" and the perimeter of the larger quadrilateral "P2". Then, we can write:

P2 = k * P1

Substituting the scale factor k = 4/3, we get:

P2 = (4/3) * P1

Therefore, the ratio of the perimeters is:

P2/P1 = (4/3) * P1 / P1

P2/P1 = 4/3

So, the ratio of the perimeters is 4/3.

The scale factor is approximately 1.333. Since the quadrilaterals are similar, their perimeters are proportional to their corresponding sides. Therefore, the perimeter ratio is the same as the scale factor, which is approximately 1.333.

To find the scale factor, we need to take the square root of the ratio of the areas:

sqrt(64/36) = 4/3

So the scale factor is 4/3. This means that corresponding sides of the two quadrilaterals are in a ratio of 4:3.

To find the perimeter ratio, we can use the same ratio:

Perimeter of larger quadrilateral: 4x + 4y

Perimeter of smaller quadrilateral: 3x + 3y

We know that the areas are in a ratio of 64/36 = 4/3, so we can set up the following equation:

3x * 4y = 4x * 3y

Simplifying this gives:

12xy = 12xy

So the perimeters are equal! This means that the perimeter ratio is 1:1.
The areas of the two similar quadrilaterals are 36 m^2 and 64 m^2. To find the scale factor, you need to take the square root of the ratio of the areas:

Scale factor = √(Area2 / Area1) = √(64 m^2 / 36 m^2) = √(1.7777) ≈ 1.333

The scale factor is approximately 1.333. Since the quadrilaterals are similar, their perimeters are proportional to their corresponding sides. Therefore, the perimeter ratio is the same as the scale factor, which is approximately 1.333.

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The probability of these three events occurring together is 14.7%.

The compound events involved in selecting 2 girls and 1 boy are:

Choosing a girl on the first draw, with a chance of 24/38 (due to the fact that, after one student has been chosen and replaced, there are 24 girls and 38 total passengers on the bus).

The likelihood of choosing a different girl on the second draw is 24/38 (because there are still 24 girls and 38 overall students on the bus after two pupils have been chosen and replaced).

Choosing a boy on the third draw, with a chance of 14/38 (due to the fact that there are now 14 boys and 38 total students on the bus after three kids were chosen and replaced).

To find the probability of these three events occurring together (i.e., selecting 2 girls and 1 boy), we multiply their probabilities:

P(2 girls and 1 boy) = (24/38) * (24/38) * (14/38)

= 0.14696019828, or approximately 14.7%.

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The LCM of m and n is equal to 1215500 and the HCF of 5m and 3n is derived to be 2, using prime factorisation.

The H.C.F. or H.C.M defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.

Using prime factorisation:

LCM of m and n is derived as follows;

m = 2 × 5³ × 17

n = 2² × 11 × 13

LCM = 2² × 5³ × 11 × 13 × 17

LCM = 1215500

HCM of 5m and 3n is derived as follows;

5m = 2 × 5⁴ × 17

3n = 2² × 3 × 11 × 13

HCF = 2

Therefore, the LCM of m and n is equal to 1215500 and the HCF of 5m and 3n is derived to be 2, using prime factorisation.

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Answer: The percentage is a 2/4

Step-by-step explanation:

Answer:

  50%

Step-by-step explanation:

You want to know the probability of drawing a divisor of 24 from the set of cards with numbers {4, 5, 6, 7}.

The divisors of 24 in this set are 4 and 6, which comprise half the cards. As a percentage, this is ...

  1/2 × 100% = 50%

The probability of picking a divisor of 24 is 50%.

The function value of f(-1) from f(x) = 6x^2 - 4 is 2

From the question, we have the following parameters that can be used in our computation:

f(x) = 6x^2 - 4

In f(-1), we have

x = -1

Substitute the known values in the above equation, so, we have the following representation

f(-1) = 6(-1)^2 - 4

Evaluate

f(-1) = 2

Hence, the solution is \f(-1) = 2

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A graph that correctly displays the data include the following: C. a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44.

In Mathematics and Geometry, a histogram can be defined as a type of chart that is used to graphically represent a group of data points (statistical information) into user-specified ranges through the use of rectangles or rectangular bars.

Based on the information provided about the random sample of 100 customers at a local ice cream shop that were asked what their favorite topping, we can reasonably infer and logically deduce that a graph that correctly displays the data is a histogram.

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Answer : So the value of x is 5

Step-by-step explanation:

As we know it is a right angled triangle which means that the angle from the origin(0,0) is 90 degree, so the angle right to it has a value of 37 degree and the angle above it has a value of 53 degree, and the value of sin37 degree is 3/5, So by applying Pythagoras theorem we get to know that the value of sin is actually Perpendicular by Hypotenuse, so we get to know that the value of x is actually 5 derived from it.

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The translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).

A mathematical vector called a translation vector expresses how far one point or object is moved away from another in a specific direction. To put it another way, it is a vector that shows how far and in which direction an item or point is moved from one position to another.

Subtract the corresponding vertices of the two quadrilaterals to determine the vector that converts Quadrilateral ABCD to Quadrilateral A'B'C'D'.

Let's consider vertex A:

Translation vector = A' - A

= (-6, 6) - (-2, 1)

= (-6+2, 6-1)

= (-4, 5)

Therefore, the translation vector that translates Quadrilateral ABCD to Quadrilateral A'B'C'D' is (-4, 5).

Similarly, we can find the translation vectors for vertices B, C, and D:

For vertex B: Translation vector = B' - B = (-3, 7) - (-2, 5) = (-1, 2)

For vertex C: Translation vector = C' - C = (-4, 4) - (-3, 2) = (-1, 2)

For vertex D: Translation vector = D' - D = (-7, 3) - (-6, 1) = (-1, 2)

All the translation vectors have the same value (-1, 2), which means that the two quadrilaterals are translated by the same amount in the x and y directions.

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For a garden composite bin is cylindrical shape with height 40 inch and diameter 18 inch, the maximum recommended amount of composite added to bin is 6786 in³. So, option(d) is right one.

We have a garden compost bin on store. The shape of bin is cylindrical with the

Height of cylinder = 40 inch

diameter of cylinder = 18 inch

radius of cylinder= d/2 = 9 inch

We have to determine the maximum amount of compost added to bin. Manufacturer recommends that it not be filled more than 2/3. That is Volume of composit < 2/3 of volume of bin --(1)

As we know, Volume of cylinder is written as V = πr² h

where, h--> height of cylinder

r--> radius of cylinder

here, h = 40 inch, r = 9 inch

So, volume V = π× 9² × 40 in³= 10173.6 in³.

Now, from equation (1), the maximum amount of compost that can be added to the bin = [tex]10,173.6× \frac{2}{3}[/tex]

= 6785.50~ 6786 in³

Hence, required value is 6786 in³.

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Complete question:

A garden compost bin on sale at the hardware store is shaped like a cylinder with a 40 inch height and 18 inch diameter. To allow the compost to be mixed, the manufacturer recommends that it not be filled more than 2/3 full. What is the maximum recommended amount of compost that can be added to the bin, to the nearest ? Use for and round to the nearest

a) 2771 in³

b) 2374 in3

c) 10719 in³

d) 6786 in³

Check the picture below.

Answer:

C, (x-4)(x+5)

Step-by-step explanation:

when u simplify the equetion (x-4)(x+5)

we get x2 + z +20

Answer:

[tex](x-4)(x+5)=x^2+x-20[/tex]

Step-by-step explanation:

[tex](x*x)+(x*5)+(-4*x)+(-4*5)=x^2+5x+-4x+-20[/tex]

[tex]x^2+5x+-4x+-20=x^2+(5-4)x-20[/tex]

[tex]x^2+(5-4)x-20=x^2+x-20[/tex]

If earth travels 6.7 x 10(power of 4) mph in one orbit, the  Earth will travel 8.04 x 10^6 miles in 5 days.

We can begin by converting 5 days to hours since we were given the speed in miles per hour:

1 day = 24 hours

Therefore, 5 days = 5 x 24 = 120 hours

Now we can use the formula:

distance = speed x time

distance = (6.7 x 10^4) x (120)

distance = 8.04 x 10^6 miles

Therefore, Earth will travel 8.04 x 10^6 miles in 5 days.

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The comparison operation (the "<" and ">") is performed last in both expressions.


In the first expression, the order of operations (also known as PEMDAS or BEDMAS) dictates that we first evaluate the exponent, then the multiplication, and finally the comparison. So, we have:
3 * 2^2 = 3 * 4 = 12
12 < 16 is true, so the entire expression evaluates to "true".
In the second expression, the order of operations dictates that we first evaluate the division and multiplication (from left to right), then the subtraction, and finally the comparison. So, we have:
100 / 10 = 10
10 * 2 = 20
15 - 3 = 12
20 > 12 is true, so the entire expression evaluates to "true".
In both cases, the comparison operation is performed last.

Hence,  The comparison operation ("<" and ">") is performed last in both expressions, after all the other operations have been evaluated according to the order of operations.

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The ladder must be 21.26 feet long.

We can use trigonometry to solve this problem. Let's call the length of the ladder "L". We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse, to find the length of the ladder:

sin(70°) = opposite / hypotenuse

sin(70°) = 20 / L

To solve for L, we can rearrange the equation:

L = 20 / sin(70°)

Using a calculator, we can find that sin(70°) is approximately 0.9397. Plugging this value into the equation, we get:

L = 20 / 0.9397

L = 21.26 feet (rounded to two decimal places)

Therefore, the ladder must be about 21.26 feet long to reach the second story window that is 20 feet above the ground at a 70° angle.

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The zeroes of function [tex]g(x) = x^2 + 8x + 16[/tex]  or  [tex]g(x) = (x+4)^2[/tex] is at x = -4.

We need to solve for x when g(x) equals zero in order to find the zeros of the function [tex]g(x) = x^2 + 8x + 16[/tex]. In simple words, we have to find the value of x that make the equation [tex]x^2 + 8x + 16 = 0[/tex] true.

By using the identity, [tex]a^{2} + 2ab + b^{2}= (a+b)^{2}[/tex]

[tex]x^2 + 8x + 16 = 0[/tex] can be easily factored as:

[tex](x + 4)^2[/tex] [tex]=0[/tex]

Using the zero-product property, each factor is equal to zero: x + 4 = 0. Solving for x, we get x = -4.

Therefore, there is only one zero of the function [tex]g(x) = x^2 + 8x + 16[/tex] is x = -4. This indicates that the function's parabola intersects the x-axis at x = -4.

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The Answer should be x=4

False. The peak of a normal distribution curve is determined by its mean, not its standard deviation.

The standard deviation measures the spread or variability of the distribution, with larger values indicating a wider distribution. However, the peak of the curve remains the same as long as the mean remains constant.

Therefore, when comparing normal distribution curves, the one with the highest mean will have the highest peak, regardless of the standard deviation. Additionally, it's important to remember that in a normal distribution, the peak occurs at the mean value and the curve is symmetric.

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The value of VX is determined as 2.02 units.

Trigonometry ratios are mathematical relationships between the angles and sides of a right triangle.

The short form of trig ratio is SOH CAH TOA;

SOH = opposite/hypotenuse

CAH = adjacent/hypotenuse

TOA = opposite/adjacent

The value of VX is calculated by applying trig ratio of TOA, opposite side and adjacent side.

tan 22 = VX/5

VX = 5 x tan (22)

VX = 2.02 units

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The numbers are written in increasing order as below

1. -5, -4, +1, +2, +3

2. -9, -6, -2, +5, +7

3. -8, -5, -3, +3, +4

4. -6, +2, +5, +7, +8

5. -7, -6, -4, +4, +6

6. -9, -6, +5, +8, +9

7. -7, -5, -2, -1, +4

8. -5, +2, +3, +5, +6

9. -8, -6, -2, +4, +7

10. -7, -4, -3, +1, +8

The numbers are arranged using the concept of effect of negative sign to the value of a number.

When a large number is being attached with a negative sign the number becomes smaller. For instance 7 is larger than 3 but -7 is smaller than -3.

The numbers can be arranged by comparing with the order below

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

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The number of guests that can sit in each arrangement, given the diagram would be:

To find the number of guests that are able to sit in each arrangement, you can look at the number of dots around each table arrangement on the diagram.

What we see is that for 1 table, six guests are able to sit around the table. When there are 2 tables, around 10 guests can sit around the table. This number increases by 4 to fourteen when there are 3 tables put together as shown in the diagram.

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The percentage of offspring that have sickle cell anemia as shown by the pedigree chart is B. 25 %

A pedigree chart employs completely shaded symbols to indicate individuals with a specific disease or condition, while half-shaded symbols represent carriers and unshaded symbols denote individuals without it.

Sickel cell anemia is represented by entirely shaded squares in this chart, thus there is one such square (#4) among the four offspring present.

The percentage is:

= (1 affected offspring / 4 total offspring) x 100

= 25%

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The image after the reflection over the line y = 4 is (4, 9)

We want to find the image of the point (4, -1) after the reflection over the line y = 4

Remember that for a general point (x, y), the reflection over the line y = a gives:

(x, a + |y - a|)

Then we will get:

(4, 4 + |4 - (-1))

(4, 4 + 5)

(4, 9)

That is the image after the reflection over the line y = 5.

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