A 4-pint carton of frozen yogurt costs $10.52. What is the price per quart?

Answer:

-8/27

Step-by-step explanation:

The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

Answer:

64:343

Step-by-step explanation:

The ratio of the volume of the small pyramid to the volume of the large pyramid is equal to the cube of the ratio of their corresponding linear dimensions.

In this case, the ratio of the heights is 4/7, so the ratio of the volumes is (4/7)^3 = 64/343.

Therefore, the ratio of the volumes of the two pyramids is 64:343.

Here is a more detailed explanation:

The volume of a pyramid is given by the formula:

V = ⅓*Bh

where V is the volume, B is the area of the base, and h is the height.

Since the two pyramids are similar, the ratio of their areas is equal to the square of the ratio of their corresponding ki linear dimensions.

In this case, the ratio of the heights is 4/7, so the ratio of the areas is (4/7)^2 = 16/49.

Therefore, the ratio of the volumes of the two pyramids is:

(1/3) * (16/49) * (4/7) = 64/343

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.

1 meter is equal to 39.37 inches.

To convert the units, we can set up the following conversion factor:

1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²

Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:

Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²

Acceleration in in/s² ≈ 15222.7568 in/s²

Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

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Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.

A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.

The initial velocity of the rocket = 156 ft./s upwards

The given equation of the rocket is: h = 156·t - 16·t²

The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:  

h = 60 = 156·t - 16·t²

156·t - 16·t² - 60 = 0

4·(39·t - 4·t² - 15) = 0

Therefore: \(39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0\)

39·t - 4·t² - 15 = 0

-4·t² + 39·t - 15 = 0

From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;

\(x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:

\(t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}\)

Therefore, when the height of the rocket is 60 feet, the times are: \(t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35\) and \(t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40\)

The times when the height of the rocket is 60 feet, the times are:

t ≈ 9.35 s, and t ≈ 0.40 s

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The table representing the exact values of y from the function is attached below.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.

The given function is of the form y = 2x .

Now let us find the respective values of y for the given values of x.

At x = -2

y = 2x = 2 × (-2) = -4

At x = -1

y = 2x = 2 × (-1) = -2

At x = 0

y = 2x = 2 × (0) = 0

At x = 1

y = 2x = 2 × (1) = 2

At x = -2

y = 2x = 2 × (2) = 4

Therefore the table to represent this y-values of the function is \(\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}\)\(\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}\)attached below.

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Answer:

Step-by-step explanation:

The ratio is given:

Let each equal part be x, then we have:

Total number of counters:

Step-by-step explanation:

Let,

Blue counter = 9x

Red counter = 6x

Yellow counter = 3x

Given,

9x = 6x + 6

9x - 6x = 6

3x = 6

x = 6/3

x = 2

Now,

Total number of counter = 2(9) + 2(6) + 2(3)

=> 18 + 12 + 6

=> 36

Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Answer:

the polygon is a trapezoid

Step-by-step explanation:

(1, −1), (4, −1), the two points having the same y coordinate they make a horizontal line

(−1, −3), (7, −3) the two points having the same y coordinate they make another horizontal line

All horizontal lines are parallel.

The shape is a trapezoid because it has one pair of parallel lines.

Answer:

A = 76

Step-by-step explanation:

Formula of the area of a triangle: \(A=\frac{h*b}{2}\)

Formula of a rectangle: \(A=l*w\)

So starting with the triangle...You know that the height of the triangle is 7, and the base of the triangle is 8 because the base of the rectangle is the same as the triangle's base...

Now using the formula of the triangle...

A = \(\frac{7*8}{2}\)

= 28

Now find the area of the whole retangle...The length of the rectangle is 13 because 7+6=13; the width is 8

Now using the formula of the rectangle...

A = \(13*8\)

= 108

Now that you have the areas of both the triangle and the retangle...Do subtraction to find the shaded area...

\(108 - 28 = 76\)

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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Answer:

Step-by-step exi  i dont know but thanks for the points sorry

Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.

Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:

x0 = a

x1 = a + (b - a)/n

x2 = a + 2(b - a)/n

...

xn = b

The width of each subinterval is (b - a)/n.

We can then use these points to define the upper sum and lower sum as follows:

Upper sum = ∑ (b - a)/n * max(f(x))

Lower sum = ∑ (b - a)/n * min(f(x))

where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.

To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.

Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.

For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.

In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer: 31.25%

Step-by-step explanation:

Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%

Answer:

it could help you so you don't have to count on your fingers

Step-by-step explanation:

5 divided by 2

5 times 2 = 10

so your answer would be 2

Answer:

Step-by-step explanation:

Judging by the context, you are looking for the angle x of a triangle, where the other two angles are 76 and 49. The sum of a triangle's angles is always 180, so

76 + 49 + x = 180

125 + x = 180

x = 55

Answer:

The method of moment (MOM) estimator as:  \(\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}\)

\(\overline X = \dfrac{4}{9}\)

\(\mathbf{\hat {\theta} =\dfrac{16}{25} }\)

Step-by-step explanation:

From the question, the correct format for the probability density function is:

\(fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.\)

where θ > 0 is an unknown parameter.

(a) The MOM estimator can be calculated as follows:

\(E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx\)

\(E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx\)

\(E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0\)

\(E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }\)

suppose E(X) = \(\overline X\)

Then;

\(\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }\)

\(\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}\)

\(\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}\)

making \(\dfrac{1}{\sqrt{\theta}}\) the subject of the formula, we have:

\(\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1\)

\(\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}\)

\(\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}\)

squaring both sides, we have:

The method of moment (MOM) estimator as:  \(\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}\)

b) If the observations are \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}\)

Then,

\(\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}\)

\(\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}\)

\(\overline X = \dfrac{\dfrac{8}{6}}{3}\)

\(\overline X = \dfrac{8}{6} \times \dfrac{1}{3}\)

\(\overline X = \dfrac{8}{18}\)

\(\overline X = \dfrac{4}{9}\)

Finally, the point estimate of the estimator \(\theta\) is

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\dfrac{16}{25} }\)

The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

Step-by-step explanation:

I assume you want to simplify this.

Use distributive property:

x^2+4x−32 should be your answer.

Answer:

x^2+4x-32

Step-by-step explanation:

(x-4)(x+8)=x^2+8x-4x-32

x^2+4x-32

Answer:

Sol Levin needs to sell 49 pairs shoes on Saturday.

Step-by-step explanation:

29 x 6 = 174

(22 x 3) + 28 + 31 + x = 174

66 + 28 + 31 + x = 174

94 + 31 + x = 174

125 + x = 174

(125 - 125) + x = (174 - 125)

x = 49