Heather and Cindy are playing “Guess My Shape.”

Heather has to describe a shape to Cindy accurately enough so that Cindy can draw it without ever seeing the shape.

Heather gives Cindy these clues:

Clue #1: The shape is similar to a rectangle with a base of 7cm and a height of 4cm.

Clue #2: The shape is five times larger than the shape it is similar to.
What are the dimensions of the new shape?

The required equation is:

(x-(-1))²/3² — (y − 3)²/6² = 1

From the figure above, it is clear that it is a horizontal hyperbola

Step 2: The center is at (-1, 5) and the vertices are at (-4, 5) and (2, 5).

Step 3

The co-vertices are (3, 3) and (3, 7).

Step 4

Comparing the center from general equation of a hyperbola gives:

(h, k) = (3,5)

Step 5

(h, k) = (3,5)

So it can be written that:

h = 3 and k = 5

Step 6

Comparing the vertices from general equation of a hyperbola gives:

(h - a, k) = (-4,5), (h+a, k) = (2,5)

Step 7

(h-a, k) = (-4,5)

So it can be written that:

h-a = -4 and k = 5

Step 8

h-a = -4

Now substitute in the equation h = -1 to get:

-1 - a = -4

Step 9

Find value of a:

-1- a = -4

Step 10

Comparing the co-vertices from general equation of a hyperbola gives:

(h, k - b) = (3, 3) , (h, k + b) = (3, 7)

Step 11

(h, k - b) = (3, 3)

So it can be written that:

h = 3 and k - b = 3

Step 12

k - b = 3

Now substitute in the equation k = 5

5 - b = - 1

Step 13

Find the value of b:

5 - b = -1

Step 14

(x− h)²/a² - (y – k)²/b² = 1

Now substitute h = -1, k = 5, a = 3 and b = 6 in the equation to get:

(x-(-1))²/3² — (y − 3)²/6² = 1

Step 15

Therefore, the required equation is:

(x-(-1))²/6² — (y − 3)²/4² = 1

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1/13 will be the fraction to represent the tosses are tails.

If the ratio of heads to total tosses is 24:26, then we can express the ratio of tails to total tosses as:

Tails : Total Tosses = 2 : 26

Simplifying this ratio by dividing both terms by 2, we get:

Tails : Total Tosses = 1 : 13

Therefore, the fraction of tosses that tail is 1/13.

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Answer:

  72°

Step-by-step explanation:

You want the measure of an angle that is 2/3 the measure of its supplement.

Let x represent the angle measure. The problem statement tells us its value is ...

  x = 2/3(180 -x)

  5/3x = 120 . . . . . . . . . . . . . add 2/3x, simplify

  x = (3/5)(120) = 72 . . . . . . multiply by 3/5

The measure of the angle is 72°.

__

Additional comment

The supplement is 180° -72° = 108°. The ratio of the angles is ...

  72°/108° = 2/3

The maximum quantity of snowfall logged in any one city came out to be an astounding 42 inches.

Most of the data is densely concentrated within the second quarter, spanning between 6 and 14 inches in terms of depth. This surplus can be evidenced by scrutinizing the box plot that has a comparatively slim interquartile range (IQR) within the second quarter with the outline stretching from the bottom quartile (Q1) at 6 inches up to the top quartile (Q3) at 14 inches - denoting that the majority of the numbers lie within this scope, making it the most heavily populated.

In contrast, the data is generally dispersed by the fourth quarter comprising the interval spanning from 30 to 50 inches of snowfall.

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The sale price of the item when displayed on sales costs $8.75 based on the stated original price and percentage discount offered.

The formula to calculate sale price of the item according to discount and original price will be -

Sale price = 25% × original price

Keep the value of original price in the formula to find the sale price

Sale price = 25% × 35

Performing multiplication and division by solving the percentage on Right Hand Side of the equation to find the value of sale price of the item

Sale price = 8.75

Hence, the item on sale costs $8.75.

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Answer:

x=9

Step-by-step explanation:

Let's start by translating the given sentence into an equation.

"The difference of eight times a number and three is sixty-nine" can be written as:

8x - 3 = 69

where x is the unknown number we're trying to find.

To solve for x, we can start by isolating it on one side of the equation. Adding 3 to both sides, we get:

8x = 72

Dividing both sides by 8, we get:

x = 9

Therefore, the number we're looking for is 9.

Answer:

Step-by-step explanation: multiply the coins by 7

The present value needed to get $110 after 1 1/4 years at 4% compounded continuously is about $102.79.

We will use the continuous compound interest formula:

[tex]A = Pe^{(rt)[/tex]

Wherein

Substituting the given values, we've got:

[tex]110 = Pe^{(0.04*1.25)[/tex]

Simplifying, we get:

[tex]110 = Pe^{0.05[/tex]

Dividing each sides by using [tex]e^{0.05[/tex], we've got:

[tex]P = 110/e^{0.05[/tex]

Using a calculator, we get:

[tex]P \approx $102.79[/tex]

consequently, the present value needed to get $110 after 1 1/4 years at 4% compounded continuously is about $102.79.

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The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer:

a) 16; b) 1/64

Step-by-step explanation:

(1/4)^x

(1^x)/(4^x)

Since 1 to any power 1

Our equation is 1/(4^x)

Answer:

-----------------------

Given expression (1/4)ˣ.

Evaluate this for each value of x.

For x = - 2:

For x = 3:

Answer:

1/9

Step-by-step explanation: 1/3/3

(1000-(-800))/(900-300) = 3 (slope)

y=mx+b

1000=3(900)+b

b = -1700
y=3x-1700

The amount of water in the pond after 14 minutes will be 1006 L.

Given that the pound already having 600 L of water is being filled at rate of 29 L per minutes, we need to establish an equation that represent the relation between number of minute and amount of water in the pond.

So,

The relation can be defined as;

W = 600+29T

When T = 14

W = 600+29(14)

W = 1006

Hence, the amount of water in the pond after 14 minutes will be 1006 L.

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The complex value fraction is simplified and A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Given data ,

Let the fraction be represented as A

Now , the value of A is

The last denominator of the fraction is

x² / 15x - 1/3x²

On simplifying , we get

( 3x⁴ - 15x ) / ( 15x - 3x² ) , and this fraction is multiplied by the fraction above which is x/( x/3-4 )

So , the above fraction is 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² ) ) / ( x - 12 )

Now , taking the LCM of the denominator of the fraction , we get

( 2/15x ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 ) , we get

( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

And , the numerator of the fraction is ( 1/3 ) - ( 3/x² )

On taking the LCM on the numerator , we get

( x² - 9 ) / ( 3x² ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

The denominator will get multiplied by the reciprocal of the fraction and ,

A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Hence , the fraction is A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

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The original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size."

a. To find the probability that a randomly selected female has a pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (x - μ) / σ, where x is the pulse rate we are interested in, μ is the mean pulse rate, and σ is the standard deviation. Thus, we have:

z = (80 - 76) / 12.5 = 0.32

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 0.32 is approximately 0.6255. Therefore, the probability that a randomly selected female has a pulse rate less than 80 beats per minute is:

P(z < 0.32) = 0.6255

b. Since we are dealing with a sample size of 25 females, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size.

In this case, we have:

μ = 76.0

σ = 12.5

n = 25

Therefore, the standard deviation of the distribution of sample means is:

σ / sqrt(n) = 12.5 / sqrt(25) = 2.5

To find the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (X- μ) / (σ / sqrt(n)), where X is the sample mean.

Thus, we have:

z = (80 - 76) / (2.5) = 1.6

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 1.6 is approximately 0.9452. Therefore, the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute is:

P(z < 1.6) = 0.9452

c. The normal distribution can be used in part (b) because we are dealing with the distribution of sample means, not individual pulse rates. The central limit theorem states that the distribution of sample means will be approximately normal regardless of the sample size, as long as the sample size is sufficiently large (typically, n ≥ 30). In this case, we have a sample size of 25, which is smaller than 30, but we can still use the normal distribution approximation because the population distribution is assumed to be normal.

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The graph of inequality x<-2 is given in the attachment.

The inequality x < -2 represents a portion of the number line to the left of -2, but it does not specify a graph in the traditional sense.

If you want to graph the inequality, you can represent the shaded region of the number line to the left of -2, and you can use an open circle to indicate that -2 itself is not included in the solution set

The open circle at -2 indicates that -2 is not included in the solution set, and the shaded region to the left of -2 represents all the numbers that satisfy the inequality x < -2.

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The actual length of the yard is 35 feet.

Using the given scale that Adriana used, we know that 2 inches in the drawing represent 5 feet in real life.

Let's set up a proportion to find the length of the actual yard:

2 inches / 5 feet = 14 inches / x feet

Simplifying this proportion, we can cross-multiply:

Therefore, the length of the actual yard is 35 feet.

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Answer:   A

Step-by-step explanation:

If you drew a line that best fits all the dots, that would be the equation they are looking for.

format for a line is:

y=mx+b      m= slope     b=y-intercept

m is not negative, it's an increasing function  so C and D are out

m=1     looks right   m=rise/run  = 1/1 =1

b= -3

put it together

y=x-3       A

We can see here that the incorrect statement is #1: The image is located in Quadrant IV.

Transformation in mathematics is a function or a set of rules that converts a collection of points or geometric figures in one coordinate system into a different set of points or geometric figures in a second coordinate system while maintaining some characteristics of the original set.

We can see here that the statement that is incorrect is actually #1: The image is located in Quadrant IV. This is true because the image is in Quadrant I while the transformation is in Quadrant IV.

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Each of Carl's friends will be getting 1/9 of his original collection.

Carl is giving away 1/3 of his collection. Let's assume that the original collection is x. Carl is giving away 1/3 of x.

1/3x divided by 3 = 1/3x x 1/3

                            = 1/9x

In other words, if Carl has a total of 9 baseballs, he wants to give away 1/3 of them which is 3 baseballs. He’s dividing these 3 baseballs among 3 friends, so each friend will get 1/3 of the 3 baseballs which is 1/9 of the original collection.

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Answer: You cannot add (or subtract) fractions with different denominators, so therefore the answer would not be 3/8.

The relative frequency probability of rain in April is 0.4.This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%.

The relative frequency probability of rain in April is the proportion of days on which it rained in April out of the total number of days in April.

The total number of days in April is 30, and rain was recorded on 12 of those days.

Therefore, the relative frequency probability of rain in April is:

12/30 = 0.4

This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%

The relative frequency probability gives us an idea of how often an event is likely to occur based on past occurrences. In this case, it tells us that it rained on 40% of the days in April in the suburban Maryland neighborhood.

Comparing this probability to the average probability of rain in April in the area, which is 31%, we can see that the observed probability is higher. This suggests that this particular April was rainier than usual.

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Answer:

We can start with the left side of the identity and try to manipulate it algebraically to transform it into the right side:

Left side: tan X + cot X

We know that cot X is equal to 1/tan X, so we can substitute this expression in for cot X:

Left side: tan X + 1/tan X

Next, we can use the identity that (a + 1/a) = (a^2 + 1)/a to rewrite the expression as a single fraction:

Left side: (tan^2 X + 1)/tan X

We can then use the trigonometric identity that 1 + tan^2 X = sec^2 X to substitute in for the numerator:

Left side: sec^2 X / tan X

Finally, we can use the identity that csc X = 1/sin X to substitute in for tan X:

Left side: sec^2 X / (sin X / cos X)

We can simplify this expression by multiplying the numerator and denominator by cos X:

Left side: (sec^2 X * cos X) / sin X

We know that sec X is equal to 1/cos X, so we can substitute this expression in for sec X:

Left side: (cos X / cos X * sin X) = cos X * csc X

Therefore, we have shown that the left side (tan X + cot X) is equal to the right side (sec X csc X), and the identity is proven:

tan X + cot X = sec X csc X

a) Equating the expressions, the time that will pass before the planes are at the same altitude is 59.27 seconds.

b) The altitude when the two planes are at the same altitude is 5,870.8 feet.

An expression is a mathematical statement that combines variables with constants, numbers, or values without the equal symbol (=).

An equation is two or more mathematical expressions using the equal symbol (=).

Starting altitude of Plane A = 3,500 feet

Starting altitude of Plane B = 2,285 feet

Plane A's speed = 40 feet per second

Plane B's speed = 60.5 feet per second

Let the number of seconds for the planes to be at the same altitudes = x

3,500 + 40x

2,285 + 60.5x

For the two planes to be at the same altitudes, 3,500 + 40x = 2,285 + 60.5x

1,215 = 20.5x

x = 59.27 seconds

Check:

Plane A's attitude = 3,500 + 40(59.27) = 5,870.8 feet

Plane B's attitude = 2,285 + 60.5(59.27) = 5,870.8 feet

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The cost of 1050 bricks is $9,702.00.

The cost of the rectangular prism is given per volume hence we solve for the volume of each brick using:

= length * width * depth

= 7 in x 22 in x 3 in

= 462 cubic inches

The cost of each brick is given to be $0.02 per cubic

inch

To find the cost of 1050 bricks, we can multiply as follows

=  the volume of each brick * 1050 bricks * cost of one brick

=  462 cubic inches x $0.02/cubic inch * 1050 bricks

= $9,702.00

To the nearest cent, the cost of 1050 bricks is $9,702.00.

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Step-by-step explanation:

To solve a two-step equation with fractions, we can use the same steps as we would for a two-step equation without fractions  

Here are the steps:

1.

Simplify both sides of the equation by multiplying both sides by the least common multiple (LCM) of all the denominators in the equation.

2.

Solve the resulting two-step equation using inverse operations.

For example, let's say we have the equation 3/4x - 1/2 = 5/8  

Step 1: Multiply both sides by the LCM of 4, 2, and 8 which is 8. This gives us:

3x - 4 = 5

Step 2: Add 4 to both sides to get:

3x = 9

Step 3: Divide both sides by 3 to get:

x = 3

Therefore, x = 3 is the solution to the equation  

To find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy, we use the formula for the remainder of the geometric series.

The formula for the remainder of the geometric series is R = a (1 - rn) / (1 - r)Where R is the remaining term of the geometric series, a is the first term of the geometric series, r is the common ratio of the geometric series, n is the number of terms of the geometric series up to the given partial sum.

The formula for the sum of a finite geometric series is: S = a (1 - rn) / (1 - r)

By using the formula for the remainder of the geometric series, the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy is given by:

S - Sn = R

Where, S is the sum of the geometric series, Sn is the sum of the first n terms of the geometric series.

From the given question, the number of terms of the geometric series required to find the sum to the indicated accuracy is not given.

Hence, we cannot find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy.

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Correct question:

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

The probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

Here, we have to solve the question:

To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem

P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)

Where:

P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.

P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.

P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).

P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).

Let's start by filling in the values we know from the table:

P(Part-Time) = (40 + 25) / 155 = 0.5484

P(Gym Membership) = (30 + 25) / 155 = 0.3226

P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545

To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:

P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)

Plugging in the values we know, we get:

P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463

Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):

P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667

Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

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complete question:

a group of 155 students at a private university were asked if they are full-time or part-time and if they have gym memberships. the results are shown in the table below. given that a randomly selected survey participant is part-time, what is the probability that this student has a gym membership?