Find the slope: (0,5) and (1,2)​

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer:

These are instructions for finding the product of two binomials. by, means multiplied by. Say we want to find the product ( x – 3)(2x + 1).

...

step 1: Square the First Term,

step 2: Double the Product of the 2 terms ,

step 3: Square the Last Term. So to find (x – 5)² : square x, multiply 2 times x times – 5, square (– 5)

Step-by-step explanation:

Answer:

picture #1 - 50.27 square units

picture #2 - 113.10 square units

picture #3 - 380.13 square units

Step-by-step explanation:

picture #1 - area = πr^2 -> π*4^2 = 50.27 square units

picture #2 - area = πr^2 -> π*6^2 = 113.10

picture #3 - area = πr^2 -> π*11^2 = 380.13

Answer:

23 cm = 0.23 m or  9.055118 inches

Step-by-step explanation:

The fudge factory will need 181.25 cups of sugar to complete this order.

To calculate the total amount of sugar needed to complete the order, we will multiply the amount of sugar required per batch by the number of batches for each type of fudge and then sum up the results.

For caramel fudge:

Sugar required per batch = 6.25 cups

Number of batches = 20

Total sugar for caramel fudge = 6.25 cups/batch * 20 batches = 125 cups

For chocolate chip fudge:

Sugar required per batch = 6.25 cups

Number of batches = 7

Total sugar for chocolate chip fudge = 6.25 cups/batch * 7 batches = 43.75 cups

For lemon fudge:

Sugar required per batch = 6.25 cups

Number of batches = 2

Total sugar for lemon fudge = 6.25 cups/batch * 2 batches = 12.5 cups

To find the total amount of sugar needed to complete the order, we add up the sugar requirements for each type of fudge:

Total sugar needed = 125 cups + 43.75 cups + 12.5 cups = 181.25 cups

Therefore, the fudge factory will need 181.25 cups of sugar to complete this order.

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The given vector field f(x,y) = 39x^2y^2i + 26x^3yj is conservative.

The vector field f(x,y) is given by:
f(x,y) = 39x^2y^2i + 26x^3yj

To check if the vector field is conservative, we need to verify if the curl of the vector field is zero. The curl of a 2D vector field is defined as:

Curl(f) = (∂(26x^3y) / ∂x) - (∂(39x^2y^2) / ∂y)

Calculate the partial derivative with respect to x for the second component (j):

∂(26x^3y) / ∂x = 78x^2y

Calculate the partial derivative with respect to y for the first component (i):

∂(39x^2y^2) / ∂y = 78x^2y

Subtract the second derivative from the first derivative:

Curl(f) = 78x^2y - 78x^2y = 0

Since the curl of the vector field f(x,y) is 0, the vector field is conservative.

The correct question should be :

Determine whether or not the vector field given below is conservative.

f(x,y) = 39x^2y^2i + 26x^3yj

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Analyzing the characteristics of respondents and non-respondents can provide insights into potential biases and help address any discrepancies.

The survey results are at risk for a type of bias known as non-response bias. Non-response bias occurs when a subset of individuals chosen to participate in a survey does not respond, leading to potential differences between the respondents and non-respondents. In this case, the employees in the human resources department who were hired in the past two years are required to respond to the questionnaire within five days.

Non-response bias can arise due to various reasons. Some employees may choose not to participate in the survey because they are dissatisfied or unhappy with their job, leading to a skewed representation of employee satisfaction. On the other hand, employees who are highly satisfied or have positive experiences may be more motivated to complete the survey, leading to an overrepresentation of their views. This can result in an inaccurate picture of overall employee satisfaction within the department.

To minimize non-response bias, the manager could consider implementing strategies such as reminders, follow-ups, or incentives to encourage higher response rates.

Additionally, analyzing the characteristics of respondents and non-respondents can provide insights into potential biases and help address any discrepancies.

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Answer: 135

Step-by-step explanation:

dutch chocolate: 107.5

country vanilla: 142.5

sweet coconut: 65

espresso: 50

107.5 + 142.5 + 65 + 50 = 365

500 - 365 = 135

cake batter sounds good

Answer:

Cone volume formula

To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h

Step-by-step explanation:

Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

One student, Kyle, hasn't taken his final exam yet, but his marks in the first five categories are 90, 79, 82, 70, and 85. This problem requires determining the weighted mean for Kyle before the final exam and comparing it to the unweighted mean.

To calculate the weighted mean for Kyle before the final exam, we need to multiply each category's mark by its corresponding weight, sum them up, and divide by the total weight. For Kyle, the weighted mean would be calculated as follows:

Weighted Mean = (Knowledge × 25% + Application × 20% + Thinking × 10% + Culminating Project × 15% + Final Exam × 15% + Communication × 15%) / (Total Weight)

However, since Kyle hasn't written his final exam yet, we can exclude the Final Exam mark and its weight from the calculation. The weighted mean would then be:

Weighted Mean = (90 × 25% + 79 × 20% + 82 × 10% + 70 × 15% + 85 × 15%) / (25% + 20% + 10% + 15% + 15%)

To find the difference between the weighted mean and the unweighted mean, we need to calculate the unweighted mean by simply taking the average of the marks in the first five categories:

Unweighted Mean = (90 + 79 + 82 + 70 + 85) / 5

By comparing the weighted mean and the unweighted mean, we can evaluate how much the inclusion of weights for different categories affects Kyle's overall mark.

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A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.

Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.

Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.

Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.

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According to the vertical angles theorem, m∠1 = 117°.

Based on the corresponding angles theorem, m∠2 = 117°.

The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.

When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.

Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.

Therefore:

m∠1 = 117° [vertical angles theorem]

Angles 1 and 2 are corresponding angles. Therefore:

m∠2 = m∠1

Substitute

m∠2 = 117° [corresponding angles theorem]

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Answer: C

Step-by-step explanation: The slope is -5/4 and the y intercept is -1

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below, keeping in mind that the y-intersect is when the graph intersects the y-axis, so

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{5 }{ 4 } \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \qquad \begin{array}{llll} y=-\cfrac{5}{4}(~~x-(-1)~~) \\\\ {\Large \begin{array}{llll} y=-\cfrac{5}{4}(x+1) \end{array}} \end{array}\)

Answer:

y = 1250 - .22t

The supplementary angles are 60 degrees and 120 degrees

Two angles are said to be supplementary when their measure add up to 180 degrees.

Therefore, if x and y are supplementary angles,

x + y = 180

x represent the degree measure of the​ angle's supplement.

The measure of the angle is two times greater than its supplement.

Therefore, the algebraic expression of the angles is as follows:

x + 2x = 180

3x = 180

divide both sides by 3

3x / 3 = 180 / 3

x = 60

Therefore, the supplementary angles are 60 degrees and 120 degrees.

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Answer:

$4,499.46

Step-by-step explanation:

after year 1 $4160, after Year 2 $4326.40, after 3 years $4499.46

Answer:

5

Step-by-step explanation:

If you put this in a calculator it comes back with 4.79583... decimals forever.  Rounding to the nearest integer gives 5.

Answer:

5

Step-by-step explanation:

√23 : 4.795831523 whose nearest integer is 5 .

Hence, the nearest number is 5.

Rhett will pay approximately $4,800 in interest on the 10-year $7,500 Federal Direct Unsubsidized Loan. Rhett will pay approximately $4,800 in total interest on this loan.

When Rhett decides to capitalize the interest on the loan, it means that instead of making interest payments while he is in college, the accrued interest is added to the principal balance. As a result, the interest starts accruing on the new higher principal balance.

The interest rate on the loan is 6.4%. To calculate the total interest paid, we need to determine the total accrued interest over the loan period. The loan has a 10-year term, and Rhett will begin making payments six months after graduation. This means the interest accrues for 10 years and six months.

Using the formula for compound interest, we can calculate the total interest as follows:

Principal = $7,500

Interest Rate = 6.4% = 0.064

Time = 10.5 years

Total Interest = Principal *\((1 + Interest Rate)^Time\) - Principal

Plugging in the values:

Total Interest =\($7,500 * (1 + 0.064)^10.5 - $7,500\)

≈ $4,800

Therefore, Rhett will pay approximately $4,800 in total interest on this loan if he chooses to capitalize the accrued interest before making payments.

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.

Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:

Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.

If 35 pepperoni pizzas were ordered, the total number is found as follows:

7x/30 = 35

7x = 30 x 35

x = 30 x 5

x = 150 pizzas.

2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:

2/25 x 150 = 2 x 6 = 12 pizzas.

The cheese fraction is given by:

10/30.

Hence, out of 360 pizzas, the number is given by:

10/30 x 360 = 10 x 12 = 120 cheese pizzas

The mushroom fraction is given by:

8/30.

Hence, out of 360 pizzas, the number is given by:

8/30 x 360 = 8 x 12 = 96 mushroom pizzas

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Answer:

Step-by-step explanation:

Given

To find

Solution

Answer: 20

Answer:

c

Domain: x>=-3

Range: y<=-2

Step-by-step explanation:

Domain is all of the x values.  Range is all of the y values.  The negative infront of the square root makes the graph go down.  The three after the x shifts the graph to the right 3.  The -2 on the outside shifts the graph down two.  When the graph is looked at it is very easy to tell what the doamin and range is.

Answer:

x = -8

Step-by-step explanation:

The triangle is isosceles so the two angles are equal

Equation :

65 = x + 73

Subtract 73 from both sides

-8 = x

Check:

65 = -8 + 73

65 = 65

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

q(x, θ) = x(1) − θ is a pivotal quantity, and its distribution is the same as the distribution of x(1).

A pivotal quantity is a function of the data and the unknown parameters whose distribution does not depend on the unknown parameters. In other words, the distribution of the pivotal quantity remains the same under different values of the parameters.

To show that q(x, θ) = x(1) − θ is a pivotal quantity, we need to show that its distribution does not depend on the unknown parameter θ. To do so, let's consider the distribution of q(x, θ):

P(q(x, θ) ≤ t) = P(x(1) − θ ≤ t)

= P(x(1) ≤ t + θ)

= F(x(1); t + θ)

where F(x(1); t + θ) is the cumulative distribution function of x(1).

Since the distribution of x(1) does not depend on θ, we can see that the distribution of q(x, θ) does not depend on θ either. Therefore, q(x, θ) is a pivotal quantity.

Furthermore, since q(x, θ) is a pivotal quantity, we can find its distribution by looking at the distribution of x(1). Therefore, the distribution of q(x, θ) is the same as the distribution of x(1).

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The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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The value of x is 4√6. The value of y is 4√2.

What are similar triangles?

If two triangles have the same ratio of corresponding sides and an equal pair of corresponding angles, they are similar. When two or more figures have the same shape but differ in size, they are referred to as similar figures.

Consider △ABC:

Height = AC = x, Hypoteneous = BC = 4+8 = 12.

Consider △ADC:

Height = DC = 8, Base = AD = y, Hypoteneous =  AC = x

Consider △ABD:

Height = AD = y, Base = 4.

The triangle ABC is similar to ADC, and ABC is similar to ABD. Since all have one right angle and one angle is common.

The ratio of the corresponding sides of similar triangles is constant.

Consider △ABC and △ADC:

AC/DC = BC/AC

x/8 = 12/x

x² = 12×8

x = 4√6.

Since ABC is similar to ADC and ABC is similar to ABD. Then ADC is similar to ABD.

Consider △ADC and △ABD:

DC/AD = AD/BD

8/y = y/4

y² = 4×8

y = 4√2

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The value of x/w is 1/3.

...........

The volume is increasing at a rate of 784 * pi cubic inches per second.

The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.

We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.

dV/dt = (4/3) * pi * 3r^2 * dr/dt

Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:

dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec

So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.

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Answer:

9

Step-by-step explanation:

48 / 4 = 12

12 - 3 = 9

Check Work

9 + 3 = 12

12 * 4 = 48