#8
the results of a survey that asked 120 eighth graders if they prefer math or social studies are shown in the frequency table.

Mrs Sheperd was going  7.5 miles per hour

Let us assume that d represents the distance covered by Mrs Shepard, 't' represents the time required and 's' represents the speed of her bike.

Here, d = 5.25 miles

t = 0.7 hours

We know that the formula of speed is speed = distance/time

Using this formula we calculate the speed (s) of Mrs Shepard's bike.

speed = distance/time

⇒ s = d/t

⇒ s = 5.25/0.7

⇒s = 7.5 miles per hour

This means that the speed (s) of Mrs Shepard's bike was 7.5 miles per hour

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Mr. Cortez is comparing the cost to join two different gyms. Gym A charges a $55 registration fee plus $24 per month. Gym B does not charge a registration fee but charges $35 per month. The cost will be the same for both gyms on the 5 months.

What is gym?

A gymnasium or gym is a place where people can exercise indoors. The word is a translation of "gymnasium," which is Greek. They are typically seen in athletic and fitness facilities, in addition to acting as activity and learning spaces in educational institutions. Gym is slang for "fitness centre," which is often a location for indoor entertainment.

Given,

Gym A charges a $55 registration fee and $24 per month

Total charges after 5 months with registration fee= (24*5+55)= $175

Gym B charges $35 per month

Total charges after 5 months= 35*5= $175

Hence the correct answer is the cost will be the same for both gyms on the 5 months.

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Answer:

Step-by-step explanation:

1

Answer:

Step-by-step explanation:

it's -4.89279003

Answer:

0.38

Step-by-step explanation:

The answer to 13)/(15)-:(7)/(10)  in simplest form is (26)/(21).

To divide the fractions (13)/(15) and (7)/(10), we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of (7)/(10) is (10)/(7).

Now, we can multiply the two fractions as follows:
(13)/(15) * (10)/(7) = (13*10)/(15*7) = (130)/(105)

Next, we need to simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.The GCF of 130 and 105 is 5. So, we can divide both the numerator and denominator by 5 to get the simplest form of the fraction:
(130)/(105) = (130/5)/(105/5) = (26)/(21)

Therefore, the answer in simplest form is (26)/(21).

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The equation y^(2)-x+10=0 has no symmetry.

Symmetry is when one part of an equation is the mirror image of another part. In this case, there is no symmetry because the equation cannot be mirrored on any axis.

To check for symmetry with respect to the y-axis, we can replace x with -x and see if the equation is still true. In this case, y^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the y-axis.

Similarly, to check for symmetry with respect to the x-axis, we can replace y with -y and see if the equation is still true. In this case, (-y)^(2)-x+10=0 is not the same as the original equation, so there is no symmetry with respect to the x-axis.

Finally, to check for symmetry with respect to the origin, we can replace x with -x and y with -y and see if the equation is still true. In this case, (-y)^(2)-(-x)+10=0 is not the same as the original equation, so there is no symmetry with respect to the origin.

Therefore, the equation y^(2)-x+10=0 has no symmetry.

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The equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

equation of a line using point-slope form is-

y - y1 = m(x - x1)

Points: (17,-12) and  slope -3.

Put the values:

y - (-12) = -3(x - 17)

y + 12 = -3x + 51

y = -3x + 51 - 12

y = -3x + 39

Thus, the equation of a line that passes through the point (17,-12) with slope -3 is found as: y = -3x + 39.

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The value of x is if the 8th term of the expansion of given equation is equal to 25952256 = 2. The correct answer is option a.

In order to find the value of x, we first need to find the 8th term of the expansion of [tex](x^3 + 1)^12.[/tex] Using the binomial theorem, the general term in the expansion is given by: [tex]T(k) = C(n, k-1) * (x^3)^(n-k+1) * 1^(k-1).[/tex]where T(k) is the kth term, n is the power (in this case, 12), C(n, k-1) represents the binomial coefficient [tex](n! / [(k-1)! * (n-k+1)!]),[/tex] and x^3 is the term in the expansion.

Now, we plug in the values to find the 8th term: [tex]T(8) = C(12, 7) * (x^3)^(12-7+1) * 1^7, T(8) = 792 * (x^3)^6.[/tex] We are given that the 8th term of the expansion is equal to 25952256. So, 25952256 = 792 * (x^3)^6

Now, we need to solve for [tex]x: (25952256 / 792) = (x^3)^6, 32768 = (x^3)^6[/tex]
Taking the 6th root of both sides, we get:
[tex]x^3 = 2[/tex]
Now, taking the cube root of both sides, we find the value of x:
x = 2 (option a). The correct answer is option a.

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The length of the diagonal of this square is 11 and option 4 is the correct answer.

A diagonal line is a line segment that joins two of a shape's vertices when there isn't already an edge between them. It doesn't go directly above, below, or across. The diagonals are always in the form of a straight line. In other terms, a diagonal is a line that passes through the vertex of a polygon or polyhedron and links its opposing corners.

Given that, x is the length of the diagonal of the square.

Also, x² = 132

The value of x is:

x = √132

x = 11.48

Hence, the length of the diagonal of this square is 11 and option 4 is the correct answer.

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In order to outline the yard and the garden allotment with bricks and Using Pythagorean theorem, Mariah will need to buy about 69.4  yards³ of brick.

what is pythagoras theorem ?

According to the Pythagorean Theorem, the square of the length of the hypotenuse in a right triangle equals the total of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. In mathematics, it can be expressed as:

c² = a² + b²

where the lengths of the other two sides (the legs) of the right - angled triangle are a and b, and c is the length of the hypotenuse. Pythagoras, an ancient Greek mathematician, is attributed with discovering and proving this theorem, so it bears his name. Geometry, algebra, and other fields of mathematics and science all make extensive use of the Pythagorean Theorem.

given

The Pythagorean formula can be used to determine side C.

C² = A² + B²

C²= 30² + 50²

C² = 900 + 2500

C² = 3400

C ≈ 58.3

As a result, the triangle-shaped yard's circumference is:

30 + 50 + 58.3 ≈ 138.3 feet

We require information regarding the measurements of the rectangular garden plot. Let's assume it is 20 feet long and 15 feet wide.

Thus, the vegetable plot's perimeter is as follows:

2(20 + 15) = 70 feet

The perimeters must now be converted from feet to yards (since we are calculating square yards).

circumference of a triangular yard: 46.1 yards x 138.3 feet

Garden plot boundaries measured as 70 feet by 23.3 yards.

In order to calculate the overall number of bricks required, we add the two perimeters:

46.1 plus 23.3 equals 69.4 square yards.

In order to outline the yard and the garden allotment with bricks, Mariah will need to buy about 69.4  yards³ of brick.

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Answer:

   ∠e = 32°

   ∠d = 69°

   ∠f = 79°

Step-by-step explanation:

       Angle e and 32° are vertical angles, so this means that ∠e = 32° because vertical angles are congruent.

       Next, a straight line is equal to 180°, and angle e is equal to 32°, so we can write the following equation to solve for angle f:

69° + e + f = 180° ➜ 69° + 32° + f = 180° ➜ 101° + f = 180° ➜ f = 79°

       Lastly, angle d and 69° are also vertical angles, so this means that ∠d = 69° because vertical angles are congruent.

The given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

The given permutations can be expressed as products of cyclic permutations as follows:

S10 = ([1,2,3,4,5,6,7,8,9,10],[4,6,9,5,10,2,8,3,7,1])

= (1 4 5 10)(2 6)(3 9 7 8)(7 8 3 9)

= (1 4)(4 5)(5 10)(2 6)(3 9)(9 7)(7 8)(8 3)

= (1 4 5 10)(2 6)(3 9 7 8)

Therefore, the given permutations can be expressed as the product of the following cyclic permutations: (1 4 5 10)(2 6)(3 9 7 8).

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Answer:

962.084375 meters² or 306.25π

Step-by-step explanation:

A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.

The formula for the area of a circle is pi • r²

Since we know the radius (17.5), we can solve this expression:

pi • 17.5²

pi • 306.25

If we use 3.1415 for pi, we get962.084375 meters²

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The pool is 0.5 centimeters long in the drawing.

The ratio of 1 centimeter to 4 meters means that for every 4 meters in real life, Alice drew 1 centimeter in her drawing.

To find out how long the pool is in the drawing, we need to divide the actual length of the pool by the scale factor.

The scale factor is 4 meters : 1 centimeter, which is the same as 1 meter : 0.25 centimeters.

So to find the length of the pool in the drawing, we need to divide the actual length of the pool by 4 to get the length in meters, and then multiply by 0.25 to convert to centimeters:

Length in drawing = (32 meters / 4) x 0.25 = 2 x 0.25 = 0.5 centimeters

Therefore, the pool is 0.5 centimeters long in the drawing.

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The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.

We have, 120 rupees and 5 paise and we will express as rupees using decimals.

We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1

=> 1 paisa = Rs. 1/100

so, here conversation factor is = 1/100

The required value is obtained by multiplying the observed values by conversion factor. Therefore,

5 paise = Rs. (5×1/100)

= 5/100

= Rs. 0.05

Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05

Hence, required value is Rs. 120.05.

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Express in form of rupees

120 rupees 5 paise = — rupees.

The expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

What is the logarithms?

Logarithms are mathematical functions that help to simplify the representation of very large or very small numbers. They are the inverse functions of exponential functions.

Using the properties of logarithms, we can expand the expression as follows:

[tex]log4(xy^5 Z^4) = log4(x) + log4(y^5) + log4(Z^4)[/tex]

Now, we can simplify each logarithm using the property that log[tex](a^b[/tex]) = b log(a):

[tex]log4(x) + log4(y^5) + log4(Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

Hence, the expression can be expanded as a sum of three logarithms:

[tex]log4(xy^5 Z^4) = log4(x) + 5 log4(y) + 4 log4(Z)[/tex]

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Answer:

Step-by-step explanation:

Since tangent is negative and is equal to the ratio of opposite over adjacent, we can assume that the angle theta lies in either the third or the fourth quadrant, where the x and y coordinates have opposite signs.

In the third quadrant, sine is positive and cosine is negative. Therefore, we have:

tangent theta = opposite/adjacent = -1

sine theta = opposite/hypotenuse > 0

cosine theta = adjacent/hypotenuse < 0

Using the Pythagorean identity, we have:

sin² theta + cos² theta = 1

=> opposite²/hypotenuse² + adjacent²/hypotenuse² = 1

=> opposite² + adjacent² = hypotenuse²

Since we are given that 3π/2 < theta < 2π, we can place the triangle in the third quadrant with a reference angle of π/2. This means that the opposite side is equal to the absolute value of the adjacent side. Let's assume that the hypotenuse is equal to 1, then we have:

opposite/adjacent = -1

=> opposite = -adjacent

opposite² + adjacent² = hypotenuse²

=> adjacent² + (-adjacent)² = 1

=> 2adjacent² = 1

=> adjacent = ±1/√2

Since cosine is negative in the third quadrant, we have:

cosine theta = adjacent/hypotenuse = -1/√2

Finally, we can use the reciprocal identity to find secant:

secant theta = 1/cosine theta = -√2

Therefore, the answer is A. Negative StartRoot 2 EndRoot.

The value of tangent theta is equal to the negative 1. At this value the value of secant theta is [tex]\sqrt{2}[/tex].

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]

Given information-

The value of tangent theta is equal to the negative 1.

[tex]tan\theta=-1[/tex]

The tangent theta in a triangle is the ratio of sine theta and cos theta. It can be written as,

[tex]tan\theta=\dfrac{sin\theta}{cos\theta}[/tex]

The value of tangent theta is equal to the negative 1. Thus put the value in above expression as,

[tex]-1=\dfrac{sin\theta}{cos\theta}[/tex]

Simplify it further as,

[tex]-cos\theta=sin\theta[/tex]

When the value of cosine and sine theta is equal, then the angle exist in

4th quadrant with the value of [tex]\dfrac{7\pi }{4}[/tex]. Which extent to the [tex]\sqrt{2}/2[/tex] for the cosine function.

In the trigonometry cosine theta is the reciprocal of the secant theta. Thus,

[tex]\dfrac{1}{sec\theta} =\dfrac{\sqrt{2} }{}[/tex]

[tex]sec\theta=\sqrt{}\dfrac{2}{2}[/tex]

Thus the value of secant theta is [tex]\sqrt{2}[/tex]

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Option D is correct, the total purchase price is $111.65.

percentage, a relative value indicating hundredth parts of any quantity.

Lets find the price of each item

Inflatable shark: $12.99

8 gallons of chlorine at $1.99 each: 8 x $1.99 = $15.92

2 gallons of algaecide at $7.99 each: 2 x $7.99 = $15.98

1 thermometer for $12.99: $12.99

2 sets of fins at $22.99 each: 2 x $22.99 = $45.98

Now add the costs of all the items:

$12.99 + $15.92 + $15.98 + $12.99 + $45.98 = $103.86

we multiply the total cost by the tax rate to find the sales tax.

$103.86 x 0.075 = $7.79

Finally, we add the sales tax to the total cost to get the final purchase price:

$103.86 + $7.79 = $111.65

Therefore, the total purchase price is $111.65.Option D is correct.

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Adam should purchase the long-range weather forecast for $1. By doing so, he will have the best chance of minimizing his total expected cost for the summer.

The expected value of the sample information (EVSI) is the expected cost if Adam does not purchase the forecast and goes with the meteorological records, which is $16.6 ($15 for the season pass plus an average of $1.6 per rainy day).

The expected value of perfect information (EVPI) is the expected cost if Adam purchases the forecast and uses it to make the decision, which is $15.6 ($15 for the season pass plus an average of $0.6 per rainy day).

Thus, purchasing the long-range weather forecast is the best decision for Adam, as it will save him $1 in expected costs and allow him to minimize his total expected cost for the summer.

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Therefore, approximately 408 packages of paper can be put on the shelf.

Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units such as square meters, square inches, or square feet. The area of a shape can be found by multiplying the length of the shape by its width. The concept of area is used in many areas of mathematics and in a wide range of real-world applications, including architecture, engineering, physics, and geography. The ability to calculate the area of a shape is an important skill in many fields and is a fundamental concept in geometry.

Here,

To solve this problem, we need to find the number of packages of paper that can fit on the warehouse shelf by dividing the total shelf area by the area of each package.

First, we need to convert the height of the shelf from feet and inches to inches:

1 foot = 12 inches

1' 5" = 1 * 12 + 5 = 17 inches

Next, we need to convert the length of the shelf from yards to inches:

1 yard = 36 inches

2 yards = 2 * 36 = 72 inches

Now we can find the area of the warehouse shelf:

Area = length * height

Area = 72 inches * 17 inches

Area = 1224 square inches

The area of each package of paper is:

Area = height * width

Area = 2 inches * 1.5 inches

Area = 3 square inches

Now we can find the number of packages of paper that can fit on the warehouse shelf:

Number of packages = Shelf area / Package area

Number of packages = 1224 square inches / 3 square inches

Number of packages ≈ 408

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Answer:

please your question is incomplete

Step-by-step explanation:

if....... of a number

Answer:

y - 7 =  3/5 (x - 1)

Answer:

a = 13.3

Step-by-step explanation:

Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

c^2 = a^2 + b^2

15^2 = a^2 + b^2

a^2 = 15^2 - 7^2 = 225 - 49 = 176

a = √176 = 13.26 = 13.3

The function in standard form of f(x)=-4 x³-10 x¹²+13 is f(x)=-10 x¹²-4 x³+13 x. The function in standard form of  f(x)=8 x²¹-5 x²+13 x )  is f(x)=8 x²¹-5 x²+13 x. The function in standard form of  ( f(x)=x^³²-10 x¹⁴ is f(x)=8 x²¹-5 x²+13 x

7.  To determine the end behavior, we look at the highest degree term, which is -10 x^{12}. As x approaches positive infinity, -10 x^{12} will approach negative infinity. As x approaches negative infinity, -10 x^{12} will approach positive infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = -∞
lim_{x→-∞} f(x) = ∞

8. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is 8 x^{21}. As x approaches positive infinity, 8 x^{21} will approach positive infinity. As x approaches negative infinity, 8 x^{21} will approach negative infinity. Therefore, the end behavior is:
lim_{x→∞} f(x) = ∞
lim_{x→-∞} f(x) = -∞

9. The function in standard form is f(x)=8 x^{21}-5 x^{2}+13 x. To determine the end behavior, we look at the highest degree term, which is x^{32}. As x approaches positive infinity, x^{32} will approach positive infinity. As x approaches negative infinity, x^{32} will approach positive infinity. Therefore, the end behavior is:
limx→∞ f(x) = ∞
limx→∞f(x) = +∞

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The graph and the table show the high temperatures in a city over a 10-day period. here are the right answer:

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

The following group is shows a the high temperatures in a city for 10 -days. Where height temperature is on day 9, lowest temparature in day 7. Here the high temperature is a function of the day.            

Here we have

The graph and the table show the high temperatures in a city for 10-days    

From the table,

The high temperature on Day 7 = 60      

The high temperature 61 degrees on 2, 4, and 6 days

Since the graph shows the change in temperature as well as the change in the number of days the high temperature is a function of the day  

Therefore,

The answer are

a. 60, b. 2, 4, and 6 days

c. Yes, the high temperature is a function of the day.

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The standard form for the circle x² - 10x + y² + 14y - 7 = 0 is (x - 5)² + (y + 7)² = 81. The correct answer is D.

To find the standard form of the given circle, we must complete the square by rearranging the equation and adding constants to both sides of the equation to create perfect squares. Here are the steps:

1. Rearrange the equation so that the x and y terms are together:
x² - 10x + y² + 14y = 7

2. Complete the square for the x terms by adding (10/2)² = 25 to both sides of the equation:
x² - 10x + 25 + y² + 14y = 7 + 25

3. Complete the square for the y terms by adding (14/2)² = 49 to both sides of the equation:
x² - 10x + 25 + y² + 14y + 49 = 7 + 25 + 49

4. Simplify the equation by factoring the perfect squares:
(x² - 10x + 25) + (y² + 14y + 49) = 7 + 25 + 49

(x - 5)² + (y + 7)² = 81

So, the standard form for this circle is (x - 5)² + (y + 7)² = 81, which is option D.

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The range οf P-values wοuld be 0.01 < P-value < 0.02

In statistics, a test statistic is a numerical value that is calculated frοm a sample οf data and is used tο determine whether οr nοt tο reject a null hypοthesis in a hypοthesis test.

The chοice οf test statistic depends οn the specific hypοthesis test being perfοrmed and the nature οf the data being analyzed. Fοr example, in a t-test fοr the mean οf a nοrmally distributed pοpulatiοn, the test statistic is the t-value, which is calculated as the difference between the sample mean and the hypοthesized pοpulatiοn mean divided by the standard errοr οf the mean.

Using Table A-3 with n = 38 and a left-tailed test statistic t = 2.714, we find the cοrrespοnding P-value tο be between 0.01 and 0.02. Therefοre, the range οf values fοr the P-value is:

0.01 < P-value < 0.02

Sο the cοrrect respοnse is:

0.01 < P-value < 0.02

Hence, the range οf P-values wοuld be 0.01 < P-value < 0.02

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