At a coffee shop, the price of a cup of coffee increased from $1.20 to $1.44. What is the percent increase in the cost of the coffee?

Answer:

The distance is radical 520

Step-by-step explanation:

Answer:

a because a variable cannot be a variable

Answer:

x^2=y would a a function of x

Step-by-step explanation:

The total surface area of the given prism would be = 504

The formula that can be used to calculate the total surface area of a square prism = 2a² + 4a L

where a = 7

L = 14.5

Area = 2(7²) + 4 ( 7× 14.5)

= 2×49 + 4( 101.5)

= 98 + 406

= 504

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Answer:

x=17

Missing angles are 52 and 38.

Step-by-step explanation:

All triangles add up to equal 180 degrees. Using this information we can create an equation to help solve this problem. We are given one of the angles and the other 2 are shown as expressions, so the equation will look like 90+(2x+4)+(3x+1)=180. You can subtract 90 from both sides to simplify the equation to (2x+4)+(3x+1)=90. From here solve for x.

Combine the like terms

Next, subtract 5 from both sides

Then, divide both sides by 5

Then, plug in 17 for x in the expressions to find the missing angles. The top angle is 3(17)+1=52. The bottom angle is 2(17)+4=38.

Answer:

6/11 games

Step-by-step explanation:

Take the total number of wins, losses, and ties, and add them up to get the total number of games.

3+2+6=11

Then divide the wins by the number of games to get the fraction.

6/11

Using relations in a right triangle, it is found that the length of y is given by:

\(y = 2\sqrt{6}\)

The relations in a right triangle are given as follows:

The hypotenuse of both triangles is found as follows:

sin(60º) = 6/x.

\(\frac{\sqrt{3}}{2} = \frac{6}{x}\)

\(x = \frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)

\(x = 4\sqrt{3}\)

Hence length y is found as follows:

\(\cos{45^\circ} = \frac{y}{4\sqrt{3}}\)

\(\frac{\sqrt{2}}{2} = \frac{y}{4\sqrt{3}}\)

\(2y = 4\sqrt{6}\)

\(y = 2\sqrt{6}\)

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Answer:

24

Step-by-step explanation:

This a special right triangle with angle measures of 30° 60° 90°

The side length that sees angle measure 30° is represented with a, the one that sees 90° is represented by 2a and the one that sees 60° is represented by a√2

AC sees angle B which has an angle measure of 60

(6√2)×(√2) = 24

Answer:

y = 4

Step-by-step explanation:

6y - (4y - 12) = 20

Distribute;

6y - 4y + 12 = 20

2y + 12 = 20

Subtract 12 from both sides;

2y = 8

Divide both sides by 2;

y = 4

The mean (μ) for the given binomial distribution is 0.50.

To calculate the mean (μ) of a binomial distribution, we multiply the number of trials (n) by the probability of success in a single trial (π). Let's examine each scenario in detail:

a. When n = 5 and π = 0.10:

μ = 5 * 0.10

  = 0.50

For this binomial distribution, with 5 trials and a success probability of 0.10, the mean (μ) is 0.50. This means that, on average, we would expect to have 0.50 successes per trial.

b. When n = 3 and π = 0.40:

μ = 3 * 0.40

  = 1.20

In this case, the mean (μ) of the binomial distribution is 1.20. It indicates that, on average, there would be 1.20 successes per trial when there are 3 trials and a success probability of 0.40.

c. When n = 5 and π = 0.50:

μ = 5 * 0.50

  = 2.50

For a binomial distribution with 5 trials and a success probability of 0.50, the mean (μ) is 2.50. This means that, on average, we would expect to have 2.50 successes per trial.

d. When n = 3 and π = 0.80:

μ = 3 * 0.80

  = 2.40

In this scenario, the mean (μ) of the binomial distribution is 2.40. It suggests that, on average, we would expect to have 2.40 successes per trial when there are 3 trials and a success probability of 0.80.

The mean (μ) provides a measure of the central tendency or the average number of successes in a binomial distribution based on the given parameters.

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Answer:

\(f(x) = log_{2}(x - 3) - 2\)

\(f(7) = log_{2}(7 - 3) - 2\)

\(f(7) = log_{2}(4) - 2 \)

\(f(7) = 2 - 2 = 0\)

Answer:

See below

Step-by-step explanation:

g (h(6))   :

   h (6) =  3 ( 6^2) + 2 = 110

   then g (110) =   sqrt (110)

h (g(5))

    g(5) = sqrt 5

        then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

Answer:

B) t = l / pr

Step-by-step explanation:

l = prt

l / pt = t

Change from multiplication to division

=== Thanks ===

Answer:

82

Step-by-step explanation:

The number can only round up if the number after is 5 or greater.

Remember that a whole number cannot have any decimal points.

1. Look at the tenths place to determine whether to round up or down

2. 2 is less than five so the whole number would stay the same.

So, 82. 265 rounded to the nearest whole number would be 82

Answer:

82

Step-by-step explanation:

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

Step-by-step explanation:

((3×5)+4)/5=

19/5

The improper fraction is 19/5.

We have to convert \(3 \dfrac{4}{5}\)  it into an improper fraction.

To convert into an improper fraction calculation must be done in a single unit following all the steps given below.

                    \(= \dfrac{3 \times 5 + 4}{5}\)

                    \(=\dfrac{15+4}{5}\\\\=\dfrac{19}{5}\)

Hence, The improper fraction is 19/5.

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Stephen A. Douglas proposed the use of popular sovereignty to determine the issue of slavery in the Kansas-Nebraska scheme, allowing the residents of each territory to decide for themselves whether to permit slavery.

Stephen A. Douglas, a prominent politician and U.S. Senator, put forth the Kansas-Nebraska Act in 1854. The act aimed to organize the territories of Kansas and Nebraska, but it also ignited intense debates regarding the expansion of slavery into these regions. Douglas proposed that the issue of slavery in these territories should be decided by popular sovereignty, a principle that advocated for the residents of the territories to vote and determine their own stance on slavery.

Under this proposal, the residents of Kansas and Nebraska would have the authority to choose whether to allow or prohibit slavery within their borders. However, this plan effectively disregarded the Missouri Compromise of 1820, which had previously prohibited slavery in territories north of a certain latitude. As a result, the Kansas-Nebraska Act generated significant controversy and contributed to the deepening divisions between pro-slavery and anti-slavery factions in the United States, ultimately fueling tensions that would lead to the American Civil War.

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The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.

So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:

A'(-3, 3 - 4) = A'(-3, -1)

B'(0, 4 - 4) = B'(0, 0)

C'(-3, 0 - 4) = C'(-3, -4)

Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).

So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).

To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

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The amount of water rounded to the nearest hundred should be 100 liters.

Since The Grayson family got a new backyard swimming pool. When they tell their friends how much water it holds, they round the number to 51{,}10051,10051, comma, 100 liters.

So based on this, if there is 51 liters so it should be rounded to 100 liters

Therefore, we can conclude that The amount of water rounded to the nearest hundred should be 100 liters.

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The air is filled inside the balloon at the rate of 1600π cm³/sec.

The rate during which air is blown into the balloon is identical to the rate that the volume of a balloon grows.

Volume of the spherical balloon;

V = (4/3)πr³

Given is dr/dt = 4 cm/sec.

To calculate the volume change with respect to time.

dV/dt when r = 10 cm.

Differentiate V = (4/3)πr³ with respect to t.

d(V)/dt = (d/dt)(4/3)πr³

dV/dt = (4/3)π. 3r² dr/dt

dV/dt = 4πr² dr/dt

Put the values.

dV/dt = 4π(10)² .(4)

dV/dt = 1600π cm³/sec

Thus, air is filled inside the balloon at the rate of 1600π cm³/sec.

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9514 1404 393

Answer:

  ∠B = 41°

Step-by-step explanation:

Step 1: Recognize that ∠B and ∠A are "remote interior angles" with respect to the exterior angle at C. Hence their sum will be equal to the measure of the exterior angle.

Step 2. Compute angle B as the difference between the exterior angle at C and the interior angle at A:

  113° - 72° = ∠B = 41°

Answer:

3x-8y-16  = 0

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Average Rate of change of given function \(h(x)=-x^2-6x+17\) is 2

Step-by-step explanation:

We are given function: \(h(x)=-x^2-6x+17\) (considering x is missed)

We need to find average rate of change  of the function over the interval \(- 6 < x < -2\).

\(x_{1} = -6\\x_2 =-2\)

Formula used to find average rate of change is: \(Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}\)

Finding f(x₁) and f(x₂)

\(We \ have \ x_1=-6\\h(x_1)= -x^2-6x+17\\h(x_1)=-(-6)^2-6(-6)+17\\h(x_1)=-36+36+17\\h(x_1)=17\)

\(We \ have \ x_2=-2\\h(x_2)=-x^2-6x+17\\h(x_2)=-(-2)^2-6(-2)+17\\h(x_2)=-4+12+17\\h(x_2)=25\)

Putting values in the formula of average rate of change

\(Average \ Rate \ of \ Change =\frac{h(x_2)-h(x_1)}{x_2-x1}\\h(x_2)=25, h(x_1)=17, x_1 =-6 \ and \ x_2=-2\\Average \ Rate \ of \ Change =\frac{25-17}{-2-(-6)}\\Average \ Rate \ of \ Change =\frac{8}{4}\\Average \ Rate \ of \ Change =2\)

So, Average Rate of change of given function \(h(x)=-x^2-6x+17\) is 2

Answer:

b. The total sum of the money was $330

Step-by-step explanation:

#b

∵ A sum of money is divided among John, Paul, and Robert

∵ The ratio of the shares of John, Paul, and Robert is 2: 4: 5

→ Multiply the ratio of each share by x

∴ The share of John = 2x

∴ The share of Paul = 4x

∴ The share of Robert = 5x

→ Find their sum

∴ The sum of the money = 2x + 4x + 5x = 11x

∵ The sum of the money is divided equally among them

→ That means dividing the sum by 3 to find the share of every one

∵ The sum of the money = 11x

∴ The share of every one = \(\frac{11x}{3}\) = \(\frac{11}{3}\)x

∴ The share of John is larger by $50

→ That means the difference between his shares is 50

∵ \(\frac{11}{3}\)x - 2x = 50

∴ \(\frac{5}{3}\)x = 50

→ Divide both sides by \(\frac{5}{3}\)

∴ x = 30

→ Substitute it in the sum of the money to find it

∵ The sum of the money = 11(30)

∴ The sum of the money = $330

∴ The total sum of the money is $330

Comparing the two results, we see that the diagonal of prism P is longer than the diagonal of prism Q. Therefore, prism P has a longer diagonal.

What is diagonal ?

A diagonal is a straight line that connects any two non-adjacent vertices (corners) of a polygon or a three-dimensional shape, such as a rectangular prism. In a rectangular prism, the diagonal is the line that passes through the solid connecting two opposite corners of the rectangular base and extending to the opposite corners of the rectangular top face. The length of the diagonal can be found using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the length, width, and height of the rectangular prism.

To determine which rectangular prism has a longer diagonal, we need to calculate the length of the diagonal for each prism using the Pythagorean theorem, and then compare the results.

For prism P with height 15, length 3, and breadth 4, the length of the diagonal can be calculated as:

√(15² + 3² + 4²) = √(225 + 9 + 16) = √(250) = 5*√(10)

For prism Q with height 5, length 4, and breadth 12, the length of the diagonal can be calculated as:

√(5² + 4²+ 12²) = √(25 + 16 + 144) = √(185)

Comparing the two results, we see that the diagonal of prism P is longer than the diagonal of prism Q. Therefore, prism P has a longer diagonal.

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1. The expected number of sales is 6.45, which corresponds to option C. 2. The probability of making exactly 10 sales is approximately 1.72%, which corresponds to option B.

Sales refer to the process of selling goods or services in exchange for money or other forms of payment. It is a critical function of most businesses, as it is directly tied to generating revenue and profits.

The sales process typically involves several steps, including identifying potential customers, making contact with them, presenting the product or service, negotiating the terms of the sale, and closing the deal. Effective sales techniques can vary depending on the industry, product or service being sold, and the target audience, but typically involve building rapport, addressing customer needs and concerns, and highlighting the value proposition of the product or service.

1. The expected number of sales can be found using the formula E(sales) = n × p, where n is the number of calls and p is the probability of success. Here, n = 129 and p = 0.05. Thus,

\(E(sales) = 129 \times 0.05 = 6.45\)

Therefore, the expected number of sales is 6.45, which corresponds to option C.

2. The number of sales follows a binomial distribution with parameters n = 129 and p = 0.05. The probability of making exactly 10 sales can be found using the binomial probability formula:

\(P(X = 10) = (n $ choose $ X) \times p^X \times (1-p)^{(n-X)}\)

where (n choose X) =\(\frac{ n!}{ (X! \times (n-X)!)}\) is the binomial coefficient. Plugging in the values, we get:

\(P(X = 10) = (129 $ choose $ 10) \times 0.05^{10} \times 0.95^{119}\)

Using a calculator or software, we find:

P(X = 10) ≈ 0.0172

Therefore, the probability of making exactly 10 sales is approximately 1.72%, which corresponds to option B.

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Step-by-step explanation:

Divide 72 by 8:

72 / 8 = 9.

y is 9 times greater than x.

Divide 63 by 9:

63 / 9 = 7.

When y = 63, x = 7.

Answer:Therefore, the range is 32 and the standard deviation is approximately 10.523 for the given data set.

Step-by-step explanation:To calculate the range and standard deviation for the given data set {40, 65, 33, 46, 55, 50, 61}, we can follow these steps:

Step 1: Find the range.

The range is calculated by subtracting the minimum value from the maximum value in the data set.

Range = Maximum value - Minimum value

Range = 65 - 33

Range = 32

Step 2: Calculate the mean.

The mean is calculated by summing up all the values in the data set and dividing by the total number of values.

Mean = (40 + 65 + 33 + 46 + 55 + 50 + 61) / 7

Mean = 350 / 7

Mean = 50

Step 3: Calculate the deviation for each value.

Deviation is calculated by subtracting the mean from each value in the data set.

Deviation for 40 = 40 - 50 = -10

Deviation for 65 = 65 - 50 = 15

Deviation for 33 = 33 - 50 = -17

Deviation for 46 = 46 - 50 = -4

Deviation for 55 = 55 - 50 = 5

Deviation for 50 = 50 - 50 = 0

Deviation for 61 = 61 - 50 = 11

Step 4: Square each deviation.

Squared deviation for -10 = (-10)^2 = 100

Squared deviation for 15 = 15^2 = 225

Squared deviation for -17 = (-17)^2 = 289

Squared deviation for -4 = (-4)^2 = 16

Squared deviation for 5 = 5^2 = 25

Squared deviation for 0 = 0^2 = 0

Squared deviation for 11 = 11^2 = 121

Step 5: Calculate the variance.

Variance is calculated by summing up all the squared deviations and dividing by the total number of values.

Variance = (100 + 225 + 289 + 16 + 25 + 0 + 121) / 7

Variance = 776 / 7

Variance ≈ 110.857

Step 6: Calculate the standard deviation.

The standard deviation is the square root of the variance.

Standard Deviation ≈ √110.857

Standard Deviation ≈ 10.523