coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 in3/min. (a) how fast is the level in the pot rising when the coffee in the cone is 5 in deep?

Add the scale factor to the x- and y-coordinates of a point on a coordinate plane with the center of dilatation at the origin.

Given,

Dilation;

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

We have to dilate a figure with a center of dilation;

Dilations centered at the origin;

On the coordinate plane, figures can be enlarged. The centre of dilatation is frequently used to be the origin. The points in the picture can be found by multiplying the coordinates of the preimage's points by the scale factor when distorting a figure that is centered at the origin.

That is,

On a coordinate plane with the center of dilatation at the origin, multiply the point's x and y coordinates by the scale factor.

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The total number of frogs in the reservoir are 160.

What is Reservoir?

An enlarged lake behind a dam is a reservoir. Such a dam could be a man-made structure created to hold freshwater or it could be a natural formation.

Given:

Elanor wants to estimate the number of frogs in a reservoir.

She catches 90 frogs from the reservoir and marks them with a non-harmful dye.

Elanor then returns the frogs to the reservoir.

The next day she catches another 80 frogs and 10 of these are marked with the dye.

So on the first day the total frogs are 90.

On second day total frogs are 80 but 10 of them are dye, so the remaining are 70.

Therefore, the total frogs are 90 + 70 = 160.

Hence, the total number of frogs in the reservoir are 160.

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Option A and C have a proportional relationship.

What is proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

(a) Total cost of buying x avocados be p

 So, p = 4x

(b) Let the total amount a taxi driver earns be y

So, y = 3 + m

(c) Let the total number of toys be x

So, x = 2w

(d) Let the total amount a Gardner earns be c

So, c = 10 + 15r

Hence, option A and C have a proportional relationship.

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Answer: The area is 12

Step-by-step explanation:

P=2l+2w

We are given, 

P=40in

l=2w-4

Plug these into the first formula and solve for the dimensions,

length and width, of the rectangle:

 40=2(2w-4)+2w       Simplify

40=4w-8+2w

40=6w-8

48=6w

8=w OR the width is 8 in, therefore, 

the length is

l=2(8)-4

l=12 sq in

l= area

Answer: the volume of the figure is 792 ft³

Step-by-step explanation:

The volume of a shape V consists of the volume of a prism V1 and

the volume of the pyramid V2

9²+12²=15²

81+144=225

225≡225

Hence, figure base is а right triangle

So, V=V1+V2

[tex]\displaystyle\\V1=\frac{12*9}{2} *10\\\\V1=6(9)(10)\\\\V1=540\ ft^3\\[/tex]

[tex]\displaystyle\\V2=\frac{1}{3}(\frac{12*9}{2} )(24-10) \\\\V2=\frac{12(9)(14)}{6} \\\\V2=252\ ft^3[/tex]

[tex]V=540+252\\\\V=792\ ft^3[/tex]

The equation of the line that passes through the point (1,2) is y = 2x – 1with slope 1.

Using the point-slope form of the equation of a line, we can write the equation of a line that passes through the point (1,2) as:

y - 2 = m(x - 1)

Since the slope of the line is m, we can set m = 1 and solve for y:

y - 2 = 1(x - 1)

y - 2 = x - 1

y = x - 1 + 2

y = 2x – 1

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Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.

Dale and his dog walk for 5 miles.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given:

Dale and his dog walked for 1.25 hours at a speed of 4 miles per hour.

Since,

Distance = Speed x time

Here, speed = 4 miles per hour and

time is 1.25 hours

So,

Distance = 4 x 1.25

Distance = 5 miles

Hence, Dale and his dog walk for 5 miles.

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Answer: 8

Step-by-step explanation:

128 divided by 16 = 8 baseball cards on each page

8 Baseball card if the page takes the same number of baseball cards

Step-by-step explanation:

If the album as 16pages, and there are 128 baseball cards to share in each pages "equally", then it's going to be 128/16 which equals 8 in each pages

The required simplified value of the function when t= 3  is y = 36.8.

To Identify the initial amount a and the rate of decay r (as a percent) of the exponential functionⁿ.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given expression,
[tex]y=575(1-0.6)^t[/tex]
put t = 3
y=575(1-0.6)³
y = 36.8

Thus, the required simplified value of the function when t= 3  is y = 36.8.

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The equation that has no solutions are:

x + 6 =  5 + x

5 - 3x = -3x + 4

Options A and E are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

x + 6 =  5 + x

6 = 5

Which is not equal.

So,

It has no solutions.

-2(x - 3) = -2x + 6

-2x + 6 = -2x + 6

This has many solutions.

4 - 4x = 3x + 2

4 - 2 = 3x + 4x

2 = 7x

x = 2/7

This has one solution.

4(x + 1) = 3(x + 2)

4x + 4 = 3x + 6

4x - 3x = 6 - 4

x =  2

This has one solution.

5 - 3x = -3x + 4

5 - 4 = -3x + 3x
1 = 0

This has no solutions.

Thus,

x + 6 =  5 + x and 5 - 3x = -3x + 4 are the equations that have no solutions.

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Standard deviation of the sampling distribution of the sample mean is 50.

We were asked to determine the mean of the sampling distribution of the sample mean. The mean score for a standardized exam is 400, the standard deviation is 50, and we have a random sample of 25 students. You take a sample of 25 students in total. You will obtain a sample average of X after averaging that sample. Take 70 student samples, then compute the mean.

The sampling distribution of the sample mean is the term used to describe how the mean varies from sample to sample. The question being posed here is, what is the mean of the sampling distribution of sample means?

Regardless of how the population distribution is shaped, the mean of sample averages is always the same as the mean of the population.

The sample mean is 400.

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured. Whether the data is being treated as a population unto itself or as a sample of a larger population will affect the standard deviation calculation formula.

So standard deviation of sample mean is also same as it is for random sample that is 50.

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Draw a drawing in the scale factor of 5 / 1 then drawn drawing is said to be in ratio and get enlarge 5 times to the scale drawing.

As given in the question,

Given scale ratio is equal to 5 / 1.

Let us consider scale drawing is in the scale ratio of 1cm  : 3m

It means we have

Therefore, scale factor of 5 / 1 used to draw a drawing is said to be in ratio to  enlarge or small the given picture.

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There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.

The intersection locations of all the aforementioned equations can be found using graphic solutions to a system of equations.

Only when the equations have an intersection point can a system of two or more equations be solved.

According to the given information

A set of equations including

4x - 10y = 4 and 2x + 5y = - 2... (ii).

Now, when we multiply equation(i) by 2, we get

- 4x + 10y = - 4. (iii).

Adding (ii) and (iii) now gives us,

0x + 0y = 0.

Since 0 = 0, these coincident lines have an infinite number of solutions.

There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.

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Answer: 11

Step-by-step explanation:

I think sorry

Answer:

9

Step-by-step explanation:

The rationale underlying the use of projective personality tests, such as the Rorschach test and the thematic apperception test, is that they reveal the subjects' personalities by eliciting responses to vague, ambiguous stimuli.

The rationale underlying the use of projective personality tests, such as the Rorschach test and the Thematic Apperception Test, is that they can reveal a person's unconscious thoughts, feelings, and motivations. These tests use vague and ambiguous stimuli, such as inkblots or pictures, and ask the person to describe what they see or make up a story about the stimuli. The person's responses are believed to reflect their underlying personality traits and psychological conflicts.

The theory is that when faced with ambiguous stimuli, people project their own thoughts, feelings, and motivations onto the stimuli, revealing their unconscious processes.

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After a comparison of females and males on the number of hours of a day that the subject watched the TV.

The hypotheses of a significance test to analyze whether the population means differ for females and males would be as follows:

(a) H0: μ1 = μ2 (the population means are equal for females and males)

Ha: μ1 ≠ μ2 (the population means are not equal for females and males)

(b) In order to conduct the significance test, we would need to calculate the t-statistic and the P-value. However, the question does not provide the necessary information to do so (e.g. sample means, standard deviations, sample sizes). Without this information, we cannot conduct the significance test and interpret the P-value.

(c) Without conducting the significance test, we cannot conclude anything about whether there is a gender difference in TV watching.

(d) Similarly, without conducting the significance test and calculating the confidence interval, we cannot determine whether the confidence interval would contain 0 or not.

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If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean then the minimum sample size that should be taken is 83.

Given:

the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels.

if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean

what is the minimum sample size that should be taken = ?

population standard deviation (σ) = 94

margin of error (E) = 17

for 90% confidence interval Zα/2 = 1.645

formula:

sample size (n) = [ zα/2 × σ/E]²

sample size (n) = [1.645×94/17]²

sample size (n) = 82.7

sample size (n) ≈ 83

Hence we get the required answer.

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Answer:

4x+14

Step-by-step explanation:

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By replacing the value of x by 4 the answer to the given Algebraic Expression is 10

What is an Algebraic Expression?

The concept of algebraic expressions is to represent numbers using letters or alphabets without providing their real values. In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

All we have to do to solve the following problem is to replace x by 4

3(4+4)(4+1)/(4+2)(4-2)

(3*8*5)/(6*2)

10

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Answer:Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

Step-by-step explanation:

Answer:

( -4 , 1 )

Step-by-step explanation:

Answer: -4

(Hope I'm correct :D )

Step-by-step explanation:

Easy, let's start with what we know to find the slope. To find the slope you do:

(y2-y1)/(x2-x1)

For this equation then, we do:

(-2 - 2)/ (-5 - (-6)) Which simplifies to:

-4/1

= -4

So the slope is -4.

Parallel slope intercept form is a form of linear equation that describes a line parallel to a given line with slope m.

The equation for a line parallel to the line with equation y = mx + b is y = mx + b + c, where c is any constant.

1. Start with the equation of the original line in slope-intercept form, y = mx + b

2. To make a parallel line, add a constant c to the y-intercept, so the equation is y = mx + b + c

3. That's it! You now have an equation for a parallel line in slope-intercept form.

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Various linear equations in different forms are : horizontal and vertical line equations, An equation for a line in point-slope form, Linear equation in two-point form, the line's slope-intercept form equation, intercept form 

and standard form.

1) Equation of a Vertical Line : x = k , where k is a constant.

2) Equation of a Horizontal Line: y = k , where k is a constant.

3) Form of a Point Slope: y - y1 = m (x - x1).

If the slope m and a point (x1, y1) through which the line travels are known, the point-slope form is helpful.

4) Form of the slope-intercept, y = mx + b

If the slope m and the y-intercept (0, b) are known, the slope-intercept form is helpful.

5) Standard form: a x + b y = c , where a, b and c are constants.

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The fraction of people that preferred lunch is of:

30%.

The three options are given as follows:

The sum of the fractions of each of these options is of:

100%.

10 of the respondents preferred breakfast, and there were 50 people, hence the fraction that preferred breakfast is of:

10/50 x 100% = 20%.

Then the fractions in this problem are given as follows:

Thus the missing fraction, which is the fraction of people that prefer lunch, is obtained as follows:

50 + 20 + x = 100

70 + x = 100

x = 30%.

(as the sum of the three fractions is of 100%, as they represent all the possible outcomes).

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The image of (- 4, 4) by rotation is equal to (4, - 4).

In this problem we get the coordinates of the point and we are asked to find the coordinates of its image by rotation about the origin. The rotation rule is described below:

x' = x · cos θ - y · sin θ

y' = x · sin θ + y · cos θ

Where:

First, write the coordinates of the point:

P(x, y) = (- 4, 4)

Second, use the rotation formula to find its image:

x' = - 4 · cos 180° - 4 · sin 180°

x' = 4

y' = - 4 · sin 180° + 4 · cos 180°

y' = - 4

The point (4, - 4) is the image by rotation of the point (- 4, 4).

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The Square-1 is a Cubic twisty puzzle.

It is similar to the 3x3 Rubik's cube, but due to the way the pieces are cut and designed can shapeshift. It is even governed by the WCA, and uniquely the only shapeshifting puzzle in the WCA.

It's probably the hardest WCA puzzle to learn how to solve due to the restrictions in its turning and its unique design.Square-1 became an official WCA event in 2007. It is a shape-shifting puzzle with a middle slice that you can use to interchange pieces.

X-Man Volt has long been the best square-1 on the market. However, Yu-Xin has rolled out a new budget square-1, which is fully magnetic.

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Answer:

A’ (5,2) B’ (2,1) and C’ (1,3)

Step-by-step explanation:

When we reflect a point (x,y) over x-axis, we get (x,-y)

A ( 2,5) becomes (2,-5)

B (1,2) becomes (1,-2)

C ( 3,1) becomes (3,-1)

Then we proceed to rotate 90 degrees counterclockwise about the origin

(x,y) becomes (-y,x)

(2,-5) becomes (5,2)

(1,-2) becomes (2,1)

(3,-1) becomes (1,3)

Answer:

There are 400 Students.

Point-slope form: y - 13= -3(x + 8)

Slope-intercept form: y = -3x - 11