Write an equation to represent this scenerio
You are about to take a major assessment, and each question is one two types. Multiple-choice questions are worth 2 points each, and short-response questions are worth 4 points each. The assessment is worth 100 total points. Let x represent the number of multiple-choice questions, and let y represent the number of short-response questions.

The water level is rising at a rate of 0.0764 cm per second.

Using implicit differentiation, it is found that the water level is rising at a rate of 0.0764 cm per second.

The volume of a cone of radius r and height h is given by:

V = πr²h/3

Applying implicit differentiation, the rate of change is given by:

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

In this problem:

The radius is constant, thus dr/dt = 0

Height of 5 cm and radius of 3 cm, thus h = 5, r=3.

Water poured at a rate of 2 cm³/s, thus dV/dt = 2

Then

dV/dt = 2πr/3 dr/dt + πr²/3 dh/dt

2 = 25π/3 dh/dt

dh/dt = 6/25π

dh/dt = 0.0764

The water level is rising at a rate of 0.0764 cm per second.

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The distance traveled by light in 1 minute = 18 million kilometers and the distance traveled by light in 1 second = 0.3 million kilometers.

We are given that -

The distance traveled by light in 10 minutes = 180 million km.

Now we have to find the distance traveled by light in 1 minute.

Using the unitary method, we get -

Distance traveled by light in 1 min = 180000000 / 10

Distance traveled by light in 1 min = 18 million kilometers

Now we have to find the distance traveled by light in 1 second.

We know that 1 minute= 60 seconds,

Thus, In 60 seconds light travels a distance of = 18 million kilometers. (from above)

therefore, in 1 second light would travel a distance of = 18 million / 60

                                                                                         = 0.3 million km

Hence, the distance traveled by light in 1 second = 0.3 million kilometers.

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The complete question is -

Light travels about 180 million kilometers in 10 minutes. How far does it travel in one minute? How far does it travel in one second?

The given population is 10%.

If the 10 % condition is met, a binomial distribution can be used to approximate the number of successes in a simple random sample. The 10% condition requires that the sample represents less than 10% of the population. Despite the fact that the sample size is far too tiny in comparison to the population, it is reasonable to infer that the trials of occurrences are independent. This suggests that the sample size n must be smaller than 10% of the population size N in this situation.

According to the 10% condition, sample sizes shouldn't exceed 10% of the population. Check the condition whenever samples are involved in statistics to make sure your findings are reliable. If you want to employ a typical normal model, some statisticians contend that a condition of 5% is preferable to a condition of 10%.

Hence we get the required answer.

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Answer: x = 14

Step-by-step explanation:

3x+9x-5=163

12x-5=163

12x=163+5

12x=168

x=14

y=6x+6 is the equation of the tangent line to the curve at point (0,6)

In order to fing the equation of tangent of any graph we need 2 things.

i . A point on the graph at which tangent need to be drawn.

ii . Slope a line on that point.

solpe of line = [tex]y^'[/tex]  =[tex]\frac{d(y)}{dx}[/tex]

=> d(6[tex]e^xcosx[/tex])/dx

in order to differentiate the above equation we have to use by parts

=> 6([tex]e^xcox-e^xsinx[/tex])

finding the slope at point(0,6)

[tex]y^'[/tex] = 6*(1*1-1*0)

=>6

so slope is 6

now equation of line with slope 6 and point (0,6)

=> y-6 = 6(x-0)

=> y = 6x+6

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Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.

In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).

A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

The graph is given below:

h (x) = (f + g) (x)

The function h(x) can be written as

h (x) = f (x) + g (x)

Different x values must be taken into account in order to graph h (x).

h (0) = f (0) + g (0) = 2 - 1 = 1

h (1) = f (1) + g (1) = 3 + 0 = 3

h (2) = f (2) + g (2) = 1 + 0.5 = 1.5

h (3) = f (3) + g (3) = 2 + 0 = 2

So the graph of the h(x) is given below:

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sample consists of 87 subjects, with 71 successes.the test statistic, rounded to 2 decimal places ,Test statistic = (71/87) = 0.81

To calculate the test statistic, you need to divide the number of successes by the total number of subjects in the sample.

In this case, the number of successes is 71 and the total number of subjects is 87.

Therefore, the test statistic is calculated a

s 71/87 = 0.81

which can be rounded to two decimal places. The result of the calculation is that the test statistic is 0.81.

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Store D provides the best value, with the lowest price per donut at $0.24.

To determine which store has the best deal, you should compare the price per donut at each store.

At Store A, the BOGO offer means that you can buy one dozen donuts for the regular price of $6.35 and get a second dozen for free. This means that you are paying $6.35 for 2 dozen donuts, or $0.27 per donut.

At Store B, a dozen donuts cost $3.35, or $0.28 per donut.

At Store C, a dozen and a half donuts cost $6.50, or $0.26 per donut.

At Store D, if you buy 2 dozen donuts at $3.70 each and receive a 25% discount, you will pay $3.70 × 2 × (1 - 0.25) = $5.77 for 2 dozen donuts, or $0.24 per donut.

Thus, based on these prices, Store D is the best deal, as it has the lowest price per donut at $0.24.

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Answer: $43.43

Step-by-step explanation:

Take 9.65 times 4.5 = $ 43.425

Round up; we will get the answer $43.43

if it is not possible to obtain a list of all elements in a population, this is a; group of answer choices  finite population statistic

It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.  

Its sampling distribution of the "x bar" should also be naturally independent of the random sample, that is usually distributed.

We consider the population as endless if the sampling size is at least 20 times greater than the sample size.

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Answer:

here is the answer with proper steps.

Answer:

x = 25

Step-by-step explanation:

The two interior angles equal the exterior angle.

6x - 12 = 3x + 2x + 13  Combine like terms

6x - 12 = 5x + 13  Subtract 5x from both sides of the equation

6x -5x - 12= 5x - 5x + 13

x - 12 = 13  Add 12 to both sides of the equation

x - 12 + 12 = 13 + 12

x = 25

True. Adjusted R2 is always less than or equal to R2 in the multiple regression model.

A statistical method called regression links a response variable with one or more independence (explanatory) variables. A regression model can demonstrate whether changes in any or all of the independent variable are related to changes in the dependent variable.

Regress, from which the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a simpler and more significant model in this manner. Forecasting, time series modeling, and determining the causal connection between variables are the three basic applications of regression analysis.

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=(2x2 −2xz+z ^2 )(2x−z)(z)

I would like to construct a 95% confidence interval with a 4% margin of error. We don't have an estimate for the percentage, so we use a conservative estimate.

This is the minimum sample size, so we need to round up to 601. The larger the sample, the more confident the responses truly represent the population.

This shows that for a given confidence level, the confidence interval gets smaller as the sample size increases. At least 1450 samples from each group are required.

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The value of first quartile of the given data set is 2.5

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

Given is a data set,

According to the data,

The lower quartile is between 0 and 2.5, which under 25% of the data.

Hence, The value of first quartile of the given data set is 2.5

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The equivalent equation is 2x - 3 = 4. Option A

An equivalent expressions are simply described as algebraic expression that have the same solution(s) but differ in the arrangement of their values.

These expressions are known to work in the same way but look different.

Two algebraic expressions are said to be equivalent, when the expressions have the same value when plugged in the same value(s) for specific variable(s).

From the information given, we have;

(6x-9) = 12

expand the bracket

6x - 9 = 12

Find the common factors

2x - 3 = 4

Hence, the equation is 2x -3 = 4

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The congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.

What is congruence theorem?

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.

The figure, in this case a triangle, is congruent if and only if the corresponding sides and angles are equal in measurement. In this case we have BC being common to both triangles. Thus, one pair of corresponding sides is equal. Next, we have another pair of corresponding sides that are equal, AC and DC. Lastly, we have the included angles being equal to each other. Thus, the congruence theorem that would best prove the congruence of the triangles is SAS that is Side-Angle-Side.

Complete question: Triangles ABC and DBC have the following characteristics: BC is a side of both triangles ∠ACB and ∠DCB are right angles AC ≅ DC Which congruence theorem can be used to prove △ABC ≅ △DBC?

AAS

SSS

HL

SAS

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An angle is formed when two straight lines or rays meet at a common endpoint.

The common point of contact is called the vertex of an angle. The word angle is from a Latin word that means ‘angulus,’ meaning “corner.”

There are many examples of an angle, such as cloth hangers, arrowheads, scissors, etc.

Symbol of Angle:

The symbol ∠ represents an angle. Angles are measured in degrees (°) using a protractor.

For example, 45 degrees is represented as 45°

Parts of Angles:

Vertex: A vertex is a corner of an angle, a point where two lines/sides meet.

Arms: The two sides of the angle, joined at a common endpoint.

Initial Side: It is also known as the reference line, a straight line from where an angle is drawn.

Terminal Side: The side up to which the angle measurement is done.

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Answer:

<E=180-60=120

t=60 degrees

u=8

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Answer:

------------------------------------------------

Complete the square as follows:

Step-by-step explanation:

The equations of axes of ellipse:

y

+

3

=

0

&

x

−

2

=

0

Plot the axes of ellipse. Specify the center

(

2

,

−

3

)

, vertices & focii on the corresponding axes. Draw a free hand curve passing through the vertices & the points of intersection of ellipse with coordinate axes to get graph.

Answer:

y – 5 = m(x – 6)

Step-by-step explanation:

using y =mx +c as our guide line

Step 1 : identification of coordinates

(6,5) ;x1= 6,y1 = 5

step 2 : applying the formula

y – y1 = m(x – x1)

y – 5 = m(x – 6)

3 15/8 = 39/8 = 4 7/8

2 13/6 = 25/6 = 4 1/6

1.shade 3 full 8/8 circles 2. Shade 15 little slices in the rest 3. You done with the first one 1. Shade 2 full 6/6 circles 2. Shade 13 more little slices in the rest 3. TADAAA you done

Step-by-step explanation:

If new automobile prices are roughly regularly distributed, with a mean of $17,000 and a standard deviation of $500, then it means that the majority of the prices paid for the car will fall within a certain range.

Specifically, approximately 68% of the prices paid will be within one standard deviation of the mean, which in this case would be between $16,500 and $17,500.

Approximately 95% of the prices paid will be within two standard deviations of the mean, which would be between $16,000 and $18,000. And approximately 99.7% of the prices paid will be within three standard deviations of the mean, which would be between $15,500 and $18,500. This demonstrates that the prices paid for the cars are generally consistent, with only a tiny percentage deviating from the mean and standard deviation-defined range.

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Answer:

---------------------------------------------

Given:

Divide the number of inches by the time to get the rate of snowfall:

Answer:

[tex]y=-\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Parallel means same slope.

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]5=-\frac{2}{3} (-6)+b[/tex]

5 = 4 + b

b = 1

[tex]y=-\frac{2}{3}x+1[/tex]

Answer: y = 14.50x + 2.99

Step-by-step explanation:

The equation is y = mx + b

y is the total cost and x is the number of shirt

We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope

The 2.99 shipping fee is the y-intercept

So our equation is

y = 14.50x + 2.99