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Write a division problem such that the quotient is the same as 3/7 divided by 5/14


.

The statement does not make sense because the table showing z-scores and percentiles displays the percentage of data items between a given value of z and its opposite, -z. The correct answer is D.

The z-score table shows the percentage of data items between the mean and a certain number of standard deviations above or below the mean, which can be calculated using z-scores.

It provides information about the percentage of data items between a certain value of z and its opposite (-z) as well as the percentage of data items below and above a certain value of z. Therefore, the statement does not make sense because the z-score table does display the percentage of data items greater than a given value of z. The correct answer is D.

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Answer:

95 degrees

Step-by-step explanation:

in a triangle angles add up to 180 degrees.

a + b + c = 180

30 + 45 + c = 180

85 + c = 180

c= 180 - 85

c= 95 degrees

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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By using Law of Sines, the side b and a when A = 37°, B = 49°,c=5, and A = 132", C = 23, b = 10 is b ≈ 4.09 and a ≈ 19.66 respectively.

To use the Law of Sines to solve for the missing side in an oblique triangle, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's solve each problem using the Law of Sines:

Find side b when A = 37°, B = 49°, c = 5.

We know angle A, angle B, and side c. We need to find side b.

b/sin(B) = c/sin(C)

b/sin(49°) = 5/sin(180° - 37° - 49°)

b/sin(49°) = 5/sin(94°)

Cross-multiplying:

b * sin(94°) = 5 * sin(49°)

b = (5 * sin(49°)) / sin(94°)

b ≈ 4.09

Therefore, side b ≈ 4.09 (rounded to the nearest hundredth).

Find side a when A = 132°, C = 23, b = 10.

We know angle A, angle C, and side b. We need to find side a.

a/sin(A) = b/sin(B)

a/sin(132°) = 10/sin(180° - 132° - 23°)

a/sin(132°) = 10/sin(25°)

Cross-multiplying:

a * sin(25°) = 10 * sin(132°)

a = (10 * sin(132°)) / sin(25°)

a ≈ 19.66

Therefore, side a ≈ 19.66 (rounded to the nearest hundredth).

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There are 126 number of ways for 8 men and 5 women to stand in a line such that no two women stand next to each other.

To determine the number of ways for 8 men and 5 women to stand in a line such that no two women stand next to each other, we can use the concept of permutations.

First, let's consider arranging the 8 men in a line. There are 8! (8 factorial) ways to arrange them.

Next, let's create spaces between the men where the women can stand.

Since no two women can stand next to each other, we need to distribute these spaces among the 8 men.

There are 9 spaces available: one at the beginning of the line, one at the end, and seven spaces between the men.

To ensure that no two women stand next to each other, we can choose 5 spaces out of the 9 available spaces for the women to occupy.

We can do this in (9 choose 5) ways, which is denoted as C(9, 5) or binomial coefficient.

The formula for the binomial coefficient is:

\(\[C(n, k) = \frac{{n!}}{{k! \cdot (n-k)!}}\]\)

In this case, we have:

\(\[C(9, 5) = \frac{{9!}}{{5! \cdot (9-5)!}} = \frac{{9!}}{{5! \cdot 4!}} = \frac{{9 \cdot 8 \cdot 7 \cdot 6}}{{4 \cdot 3 \cdot 2 \cdot 1}} = 126.\]\)

Therefore, there are 126 ways.

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Step-by-step explanation:

There are 7 fruits for every 4 vegetables.

If there are 28 fruits, the number of fruits have multiplied by 4. This means that the number of vegetables have multiplied by 4 as well.

=> 4 * 4 = 16 vegetables.

Hence there are 16 vegetables.

Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Answer:

-14/3

Step-by-step explanation:

this is a geometric series with r = -7/8

The infinite sum of geometric series with |r| < 1 is

We already have r, but we need to find a1 which is the first term of the series.

To find it, only plug in 1 for n, 10(-7/8) and this = -35/4

Now plug in r and a1 in the formula above:

\(\frac{-35/4}{1+7/8}\)

after simplifying it, you will get the infinite sum = -14/3

The equation to represent the hanger diagram is   5x - 2x = 21 - 12 and weight of 1 triangle in the hanger is 3 gram. .

In the question ,

it is given that ,

the the weight of one square is = 2 gram

the weight of one circle is = 3 gram

and the weight of one triangle is is = x gram

When the hanger is balanced , then weight on Left side =  weight on Right side

we see that left side have 2 triangles , 6 squares and 3 circles ,

and the Right side have 2 circle , 3 square and 5 triangle ,

So , the balanced equation for the hanger can be written as

2*x + 6*2 + 3*3 = 2*3 + 3*2 + 5*x

2x + 12 + 9 = 6 + 6 + 5x

2x + 21 = 12 + 5x

5x - 2x = 21 - 12

3x = 9

x = 3

Therefore , the equation is 5x - 2x = 21 - 12  and the weight of triangle is 3 grams .

The given question is incomplete , the complete question is

There is a hanger that is in balance. squares are worth 2 grams and circles are worth 3 grams, and triangles are x grams. write an equation to represent the hanger diagram and find the weight of 1 triangle .

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Answer:

π radians

Step-by-step explanation:

*view photo*

The value of \(\( f'(1) \)\)for the function \(\( f(x) = 2x^2 - 2x + 4 \)\) can be found by taking the derivative of \(\( f(x) \)\) with respect to \(\( x \)\) and evaluating it at \(\( x = 1 \).\)

To find \(\( f'(x) \),\) we differentiate each term of \(\( f(x) \)\) separately using the power rule for differentiation. The derivative of \(\( 2x^2 \) is \( 4x \)\) (the coefficient is multiplied by the exponent, and the exponent is decreased by 1), the derivative of \(\( -2x \) is \( -2 \)\) (the coefficient remains unchanged since the exponent is 1), and the derivative of the constant term 4 is 0. Therefore, \(\( f'(x) = 4x - 2 \).\)

To find \(\( f'(1) \),\) we substitute \(\( x = 1 \)\) into the expression for \(\( f'(x) \). \( f'(1) = 4(1) - 2 = 4 - 2 = 2 \).\)

Therefore, \(\( f'(1) = 2 \).\)

Given the function \(\( f(x) = 2x^2 - 2x + 4 \),\) we need to find its derivative \(\( f'(x) \).\) The power rule states that the derivative of \(\( x^n \) is \( nx^{n-1} \).\) Applying this rule, we differentiate each term of the function separately.

The derivative of \(\( 2x^2 \)\) is obtained by multiplying the coefficient 2 by the exponent 2 and then decreasing the exponent by 1, resulting in \(\( 4x \).\) The derivative of \(\( -2x \)\) is obtained by applying the power rule for the exponent 1, which gives us \(\( -2 \).\) Since the constant term 4 does not contain any variable, its derivative is 0.

Combining these derivatives, we obtain \(\( f'(x) = 4x - 2 \).\)

To find \(\( f'(1) \),\) we substitute \(\( x = 1 \)\) into the expression for \(\( f'(x) \).\) This gives us \(\( f'(1) = 4(1) - 2 = 4 - 2 = 2 \).\)

Therefore, \(\( f'(1) = 2 \),\) which represents the slope of the function \(\( f(x) \)\) at the point \(\( x = 1 \).\)

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The addition inequality 37 + x ≥ 42 can be used to determine how much taller William must be to ride the coaster, where x represents the additional height he needs to meet the height requirement.

To write an addition inequality to determine how much taller William must be to ride the coaster, we first need to convert his height to inches. Since he is 3 feet 1 inch tall, his height is (3 x 12) + 1 = 37 inches.

Let x be the amount of additional height William needs to ride the roller coaster. The inequality can be written as:

37 + x ≥ 42

This inequality ensures that William's total height after adding x must be greater than or equal to the required height of 42 inches to ride the roller coaster.

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Answer: 15, and 44 are integers.

Step-by-step explanation: For 15 to be an integer, 15 has to be a whole number. Furthermore, for 15 to be an integer, you should be able to write 15 without a fractional or decimal component. 15 is a whole number that can be written without a fractional component, thus 15 is an integer, as well as 44.

1)  XY' + Z + X'Z' + YZ'

2) equation 2 is correct.

3) equation 3 is incorrect .

1)

Simplifying algebraically,

XY' +Z+ (X' + Y)Z'

So,

XY' + Z + X'Z' + YZ'

2)

D(A + B)(A + B')C

Simplifying,

(AD + DB) (A + B')C

Further,

ADC + AB'CD + ABCD + BB'CD

ACD + ABCD + AB'CD

= ACD

Thus equation 2 is correct .

Hence proved .

3)

(a + b)(b + c)(c + a) = f1

Simplifying further,

abc + ab + bc + ac = f1

Let f2 = (a'+ b')(b' + c')(c' + a')

Simplify further,

f2 = a'b'c' + a'b' + b'c' + a'c'

Here,

f1 ≠ f2

Thus we disprove equation 3 .

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The sum of squares explained (SSE) is 56. The answer is (b) 56.

The sum of squares is a statistical measure of deviation from the mean. It is also known as variation. It is calculated by adding together the squared differences of each data point. To determine the sum of squares, square the distance between each data point and the line of best fit, then add them together.

The sum of squares  of the regression equation (SST) is the sum of the squares of the difference between each observed value of the dependent variable and the mean  of the dependent variable. This can be expressed as:

SST = SSR + SSE

where SSR is the regression sum of squares (explained sum of squares) and SSE is the residual sum of squares (unexplained sum of squares).

We get that SST = 81 and SSR = 25. Therefore, we can solve for SSE as:

SSE = SST – SSR

SSE = 81-25

SSE = 56

Therefore, the explained sum of squares  (SSE) is 56. The answer is (b) 56.

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K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

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The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

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Answer:

Quadrant IV

Step-by-step explanation:

The measure of the angle ABC from the diagram is equivalent to 78 degrees.

We need to find <ABC

Let us produce BA to meet PR at point G.

It is given that BG || PQ

Thus, <RGB and <QPR are corresponding angles.

This shows that <RGB = <QPR since they are corresponding angles.

On the other hand, <QPR = 102 degrees and <ABC are <RGB consecutive interior angles, then:

<ABC + <RGB = 180

<ABC + 102 = 180

<ABC = 180 - 102

<ABC = 78 degrees

Hence the measure of the angle ABC from the diagram is 78 degrees.

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Answer:

Step-by-step explanation:

3x-5-(4x+1) =

3x-5-4x-1 =

Now combine like terms

-x-6

The number of different sequences of crabapple recipients that are possible in a week are 14,641.

In Mrs. Crabapple's British literature class, there are 11 students, and she gives out a crabapple at the beginning of each of the 4 class meetings per week.
To determine the number of different sequences of crabapple recipients, we will calculate the number of possibilities for each class meeting and multiply them together. Since she can pick any of the 11 students for each class, there are:
11 possibilities for the first class,
11 possibilities for the second class,
11 possibilities for the third class, and
11 possibilities for the fourth class.
So, the total number of different sequences of crabapple recipients in a week is:
11 * 11 * 11 * 11 = 11^4 = 14,641 different sequences.

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Answer:

7 bows

Step-by-step explanation:

I will assume that the numbers are \(1\frac{1}{4}\) and \(8\frac{3}{4}\). To find the answer, we can do:

\(8\frac{3}{4} / 1\frac{1}{4}\\ = \frac{35}{4} / \frac{5}{4} \\= \frac{35}{4} * \frac{4}{5}\\= \frac{35}{5}\)

= 7 bows

Answer:

58.43%

Step-by-step explanation:

The first thing we must do is calculate the probability of when both are equal, that is, take out two cookies of the same type, since we can calculate that they are not equal by means of their complement:

The probability that they are equal is:

P (plain, plain) = (12/20) (11/19)

= 132/380

P (chocolate, chocolate) = (5/20) (4/19)

 = 20/380

P (currant, currant) = (3/20) (2/19)

= 6/380

The final probability would be the sum of these:

P (equal) = 132/380 + 20/380 + 6/380

P (equal) = 158/380

P (equal) = 0.4157

The probability that they are different is the opposite of the probability that they are equal, that is, the complement. Therefore, the probability that they are different is:

P (different) = 1 - 0.4157

P (different) = 0.5843

In other words, the probability would be 58.43%

Answer:

if you need a clearer version or a paper showing work lmk:)

Answer:

0: 3.00

1: 3.49

2: 3.98

3: 4.47

4: 4.96

5: 5.45

10: 7.90

Step-by-step explanation:

The general formula is y=0.49x+3.00 because 0.49 is the rate and 3.00 is the flat charge. Plug in the number of cans in x and solve.

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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The point where the x and y values intersect is the location of the point on the Cartesian coordinate plane.

What are coordinates ?

In mathematics, coordinates refer to a set of values that locate the position of a point or an object in space. They are usually represented as ordered pairs or triplets, depending on the dimensionality of the space being considered.

To use ordered pairs to represent location on a Cartesian coordinate plane, you can follow these steps:

Draw the x-axis and y-axis of the Cartesian coordinate plane. The x-axis is the horizontal axis, and the y-axis is the vertical axis.

Choose a point on the plane as your reference point, called the origin. The origin is usually denoted by the ordered pair (0,0).

Determine the location of a point on the plane by using an ordered pair of numbers (x,y). The first number in the pair, x, represents the horizontal position of the point on the x-axis, and the second number, y, represents the vertical position of the point on the y-axis.

Locate the point on the plane by finding the intersection of the x and y values. Start from the origin and move along the x-axis to the right if x is positive or to the left if x is negative. Then move along the y-axis upward if y is positive or downward if y is negative.

For example, the ordered pair (3,2) represents a point that is 3 units to the right of the origin and 2 units upward from the origin. Similarly, the ordered pair (-2,-5) represents a point that is 2 units to the left of the origin and 5 units downward from the origin.

Therefore, The point where the x and y values intersect is the location of the point on the Cartesian coordinate plane.

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Given :

Teresa is going to make 3 batches of cookies.

She needs 3/4 milk for each. Her measuring cup only holds 1/4 gallon.

To Find :

How many times will she need to fill up.

Solution :

Amount of milk need per batch, A = 3/4 gallon.

Measuring cup only holds, m = 1/4 gallon.

Number of times she need to fill up,

n = A/m = (3/4)/(1/4) = 3

Now, number of batches are three.

So, number of time she need to fill up in three batch.

\(N = n \times 3 \\\\N = 3 \times 3 \\\\N = 9\)

Therefore, this is the required solution.

Answer:

x = 3

Step-by-step explanation:

Answer:

x=27

Step-by-step explanation:

Step-by-step explanation:

You have to expand the expression, then evaluate the power, next, use the properties of radicals, then you simplify the roots.

Answer:

There is no unique solution to this problem.

There are infinitely many solutions to this problem.

Step-by-step explanation:

Let B denotes broccoli crop

Let S denotes spinach crop

Last year, he grew 6 tons of broccoli per acre and 9 tons of spinach per acre, for a total of 93 tons of vegetables.

Mathematically,

6B + 9S = 93        eq. 1

This year, he grew 2 tons of broccoli per acre and 3 tons of spinach per acre, for a total of 31 tons of vegetables.

Mathematically,

2B + 3S = 31

2B = 31 -  3S

B = (31 -  3S)/2      eq. 2

Substitute eq. 2 into eq. 1

6B + 9S = 93

6[(31 -  3S)/2] + 9S = 93

3(31 -  3S) + 9S = 93

93 - 9S + 9S = 93

- 9S + 9S = 93 - 93

0 = 0

Therefore, there is no unique solution to this problem.

Which means that there are infinitely many solutions to this problem.