Identify the rate, base, and percent in each statement. Place them in
the correct columns to complete the table.
1) 25 is 25% of 100
2) 15 is 25% of 60
318 is 20% of 90
4) 18 is 30% of 60
5) 20% of 150 is 30
What it is rate?
What it is base?
What it is percentage?

Answer:  114,510,000

Delete the commas if needed.

============================================

Explanation:

The given number is 114,509,772

The 0 is in the ten thousandths place value. Just to the right of it is 9, which fits the criteria of "5 or larger". So we'll bump the "509" up to "510". Everything to the right of 9 will be replaced with zeros.

That's how we go from 114,509,772 to 114,510,000

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

Put another way:

Temporarily ignore the 114 up front and focus on the remaining portion 509,772

This number can be verbalized as "509 thousand" in an approximate sense. The 772 at the end means it's much closer to 510 thousand than it is to 509 thousand. That's why the 509 bumps up to 510.

Therefore, we have 509,772 round to 510,000

Overall, we have 114,509,772 round to 114,510,000

Answer:

the first answer is correct

Step-by-step explanation:

y=118x=118

Answer: I'm not really sure what the question is but the volume is 224

Step-by-step explanation:

The shape of the distribution of the sample mean time is normal.

The standard error of the mean time is 0.5.

The percentage of the sample means that would be greater than 31.25 seconds is 0.621%.

The percentage of the sample means that would be greater than 28.25 seconds is 99.977%.

The percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds is 99.357%.

Given the following data:

Mean = 30.

Standard deviation = 2.

Sample = 16 ads.

What is a normal distribution?

A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data far from the mean.

a. The shape of the distribution of the sample mean time is normal.

b. To calculate the standard error of the mean time, we would apply this formula:

Standard error = 0.5.

c. To calculate the percentage of the sample means that would be greater than 31.25 seconds:

P(Z>2.5) = 0.621%.

d. To calculate the percentage of the sample means that would be greater than 28.25 seconds:

P(Z>2.5) = 99.977%.

e. To calculate the percentage of the sample means that would be greater than 28.25 but less than 31.25 seconds:

P(-3.5<Z<2.5) = 99.357%.

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Answer: Option A

Step-by-step explanation:

The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:

t = -1.4789

P-value = 0.173292

Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.

With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.

A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.

Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.

To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.

Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.

To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:

Mean difference = (0.30 - 0.07) / 10 = 0.023

Standard deviation = 2.967

t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394

The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.

Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:

Thus, the correct option is D.

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b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

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One solution: (6,2)

Systems of equations are a set of equations that share variables.

Number of Solutions

There are multiple ways to find the number of solutions to a system of equations. Firstly, if 2 lines are parallel, then there will never be a point that satisfies both equations. This means that there will be no solutions. If 2 equations create the same line, then there will be infinitely solutions. Lastly, if there are 2 linear lines that are not parallel or the same, then they will have exactly one solution.

Solving Systems of Equation

The solution to a system of equations is the point that makes both equations true. When looking at a graph, the solution to a system of equations will be where the lines intersect. In this question, the lines intersect at (6,2). This means the solution to the system of equations is (6,2).

Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

Answer:

66.67%

Step-by-step explanation:

To find the probability, divide 4 by 6, since there are 4 numbers less than 5, out of 6 in total.

4/6

= 0.6667

So, the probability is approximately 66.67%

The red car is actually traveling at a speed of 45 feet per second.

What is the concept of related rates and how does it apply to this problem?

Related rates is a calculus topic that deals with finding the rate of change of one variable with respect to another variable. In this problem, the distance between the police car and the red car is decreasing at a constant rate, and we need to find the speed of the red car. The key is to set up an equation that relates the variables involved and differentiate it with respect to time, using the chain rule. This allows us to find the rate of change of the variables with respect to time, and then solve for the desired rate of change.

Calculating the actual speed of the red car :

Let's call the distance between the police car and the red car "d" and the speed of the red car "v". We want to find [tex]dv/dt[/tex], the rate of change of v with respect to time.

From the problem statement, we know that [tex]dd/dt = -75[/tex] feet per second, since the distance between the cars is decreasing at a rate of 75 feet per second.

To find [tex]dv/dt[/tex], we need to use the Pythagorean theorem to relate d and v. We have a right triangle with legs of length 30 and 160, and hypotenuse d. Using the Pythagorean theorem, we get:

[tex]d^2 = 30^2 + 160^2[/tex]

[tex]d= \sqrt{(30^2 + 160^2)} =161.24[/tex] feet

Now we take the derivative of both sides of this equation with respect to time:

[tex]2\times\d(dd/dt) = 0.5\times(2d)\times(dv/dt)[/tex]

[tex]dd/dt = -75[/tex]

[tex]d = 161.24[/tex]

Substituting these values, we get:

[tex]2(161.24)(-75) = 0.5(2(161.24))(dv/dt)[/tex]

Simplifying and solving for [tex]dv/dt,[/tex] we get:

[tex]dv/dt = (-2)(161.24)(-75)/(2(161.24))[/tex]

[tex]dv/dt = 45[/tex] feet per second

Therefore, the red car is actually traveling at a speed of 45 feet per second.

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The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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Therefore , the solution of the given problem of angles comes out to be  the engraved angle ACB is 16 degrees in size.

Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.

Here,

A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:

=> Angle ACB = 32 / (1/2)

=> ACB = 16 degree angle

As a result, the engraved angle ACB is 16 degrees in size.

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Answer:

x = 0

Step-by-step explanation:

9x - 7 = -7

Add 7 to both sides.

9x - 7 + 7 = -7 + 7

9x = 0

Divide both sides by 9.

9x/9 = 0/9

x = 0

Answer:

x=0

Step-by-step explanation:

The calculated area of the composite figure is 129 square units

Given that we have

A composite figure

To find the area of a composite figure, you can break it down into smaller, simpler shapes whose areas you can calculate. Then you can add up the areas of these shapes to get the total area of the composite figure.

The area is then calculated as

Area = Trapezoid + Rectangle + Parallelogram + Triangle

Using the dimensions from the graph, we have

Area = 1/2 * (12 + 6) * 4 + 6 * 10 + 3 * 7 +  1/2 * 6 * 4

Evaluate

Area = 129

Hence, the area is 129 square units

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Answer:60

Step-by-step explanation:

30x2=60

Answer:

Each tile would be 8.5 in

Step-by-step explanation:

Area of parallelogram is A=bh, so 4.25*2= 8.5

Answer:

  (a)  Figure 3

  (b)  66.2 meters per second

Step-by-step explanation:

You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.

The fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.

The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.

The speed is estimated by the equation of the curve of best fit as ...

  y = 0.6x² +2.1x +11

A slight rearrangement can make this easier to evaluate:

  y = (0.6x +2.1)x +11

For x=8, the value of y is ...

  y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2

The predicted speed at 8 seconds is 66.2 meters per second.

Answer: brainliest ?

The correct answer is: The data is dependent, because the hours of video streaming in January and July occurred in the same households.

This is because the data collected is related to the same households and not different people. The same households were monitored during both January and July, which means that any changes in the video streaming hours during those months are likely due to factors within those households, such as changes in habits, routines, or available free time.

If the data were independent, then it would mean that the hours of video streaming in January and July were not related or influenced by any factors from the other month. For example, if the data were collected from two completely different sets of households, then it would be considered independent because there would be no connection or influence between the households in January and July. However, this is not the case in the given scenario, so the correct answer is that the data is dependent.

Step-by-step explanation:

hope its help <:

The statement which best describe the correct null and alternative hypotheses, the test statistic, and conclusion at a significance level of 0.05 is:

D. H₀: μ₁ = μ₂ H₁: μ₁ < μ₂.

test statistic, t = -1.5625.

conclusion: fail to reject the null hypothesis μ₁ = μ₂.

Based on the information provided, the appropriate null hypothesis and alternative hypothesis would be represented by the following mathematical expression:

H₀: μ₁ - μ₂ ≤ 0; μ₁ = μ₂

H₁: μ₁ - μ₂ < 0; μ₁ < μ₂.

For the critical value, we have:

Critical probability (p*) = 1 - α

Critical probability (p*) = 1 - 0.05

Critical probability (p*) = 0.9500.

Based on the distribution table for probabilities, a value that corresponds to 0.9500 can be calculated as follows;

Zα = 1.6 + 0.05 = 1.65.

For an upper-tailed test, the critical value is given by;

Z_{critical} = 1.65.

Therefore, if Z_{test} > 1.65; reject null hypothesis (H₀) and if Z_{test} < 1.65; fail to reject null hypothesis (H₀).

Next, we would determine the test statistic:

[tex]Z_{test} = \frac{116 -121 -0}{\sqrt{\frac{16^2}{50} +\frac{16^2}{50} } } \\\\Z_{test} = \frac{-5}{\sqrt{\frac{256}{50} +\frac{256}{50} } }\\\\Z_{test} = \frac{-5}{\sqrt{10.24} }[/tex]

Z_{test} = -5/3.2

Z_{test} = -1.5625

In conclusion, we would fail to reject null hypothesis (H₀) since a Z_{test} of -1.5625 is less than a Z_{critical} of 1.65.

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Therefore , the solution of the given problem of percentage comes out to be 15 customers per hour make up the unit cost. 15 clients per hour, to be exact.

A number or statistic that is stated as an amount of 100 is referred to as "a%" in statistics. The forms "pct," "pct," or "pc" are additionally uncommon. The common way to indicate it is with a representation "%," though. The ratio to the total sum is flat, and there are no indicators. Percentages are actually integers because they almost always add up to 100. To suggest that a number indicates a percentage, either the word "fraction" or a representation for percentage (%) must come before the number.

Here,

We must divide the overall number of customers by the number of hours in order to determine the unit rate (in customers per hour).

There are 120 total clients.

There are 8 hours in all.

Unit rate is equal to the sum of all clients times the number of hours.

=> Unit rate: 120 / 8

=>  Rate per unit: 15

Consequently, 15 customers per hour make up the unit cost. 15 clients per hour, to be exact.

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Answer: 6 tablespoons

Answer:

5.5 hours

Step-by-step explanation:

Volume of a cylinder = π(d/2)²h

V = (3.14)(8/2)²(1.2) = 60.288 m³

fill rate = 11 m³/hr

time to fill the pool = (60.288 m³)(1 hr/11 m³) = 5.48 hr ≈ 5.5 hrs

Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 and c = - [tex]\frac{1}{2}[/tex] , then

y = 3x - [tex]\frac{1}{2}[/tex] ← equation of line

As a ladybug on the outer surface of the Klein bottle, there is no direct path to the inside. However, you can travel along a specific type of curve called a "cross-cap curve" to reach the inside. and using topology.

To do this, start by moving along the outer surface of the Klein bottle until you reach the point directly opposite to your starting position. Then, imagine folding the surface of the bottle in half along a line that runs through this point.

This folding will create a new surface that intersects with the original surface of the bottle along a cross-cap curve. Follow this curve until you reach the inside of the Klein bottle, where the special gentleman bug is waiting for you.

It's important to note that the Klein bottle is a non-orientable surface, which means that there is no "inside" or "outside" in the traditional sense. However, the concept of inside and outside can still be useful for navigation purposes.

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Answer: D

Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis

To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.

The image undergoes a reflection at y=-3, Option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.

In the given figure the above image is original and it is flipped to form the image which is below the x axis.

In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

Hence, the image undergoes a reflection over y axis which is at y=-3.

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Answer:

Try using the Symbolab calculator.

Step-by-step explanation:

Thats what I usually use and it works

a. The total length of cloth required to make shirts for 15 students is 345 meters.

b. At least 23 meters of cloth to make one shirt

c. The length of cloth required for one shirt in decimal form is 23.00 meters.

d. 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

What is total length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

(a) Total cloth required = 15 × 23 meters = 345 meters

Therefore, the total length of cloth required to make shirts for 15 students is 345 meters.

(b) Number of shirts = 9.5 meters ÷ 23 meters/shirt ≈ 0.413

Therefore, only 0 shirts can be made from a piece of cloth 9.5 meters long. We need at least 23 meters of cloth to make one shirt.

(c) 23 meters = 23.00 meters

Therefore, the length of cloth required for one shirt in decimal form is 23.00 meters.

(d) Number of shirts = 36.25 meters ÷ 23 meters/shirt ≈ 1.576

The amount of cloth left over after making 1 shirt is:

Cloth left over = 36.25 meters - 23 meters = 13.25 meters

Therefore, 13.25 meters of cloth is left after making 1 shirt from a piece of cloth that is 36.25 meters long.

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Answer:

Step-by-step explanation:

The eighth grade class has a more consistent time spent on math homework. This can be seen in the histogram, which shows that the eighth grade class has a peak at 20 minutes.

Consistent refers to something that remains unchanged or is regular and dependable over time. It is a dependable and steady quality or state. Consistency is important in many areas of life, from professional and personal relationships to commitments and expectations. Consistent behavior is sometimes a sign of reliability, trustworthiness, and dependability.

Consistent actions are important for maintaining relationships and for achieving goals. Consistency helps to create stability, reliability, and predictability. Without consistency, it would be difficult to know what to expect from people and situations.

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Mr. Sullivan's class typically spends more time on math homework, as the mean of their sample is slightly higher than that of Mrs. Farrington's class.

Spend is an action that involves exchanging money for goods, services, or other items of value. When someone spends money, they take money out of their account or wallet and use it to purchase something.

Mrs. Farrington's class has a more consistent time spent on math homework, as the range of the sample is smaller than that of Mr. Sullivan's class.
For Mr. Sullivan's class:
The mean of the sample is 11.6, so the mean of the population is expected to be 11.6 as well. The standard deviation of the sample is 3.41. Therefore, the expected standard deviation of the population is 3.41.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.79 and 14.41 minutes on math homework.
95% of the population is expected to spend between 5.38 and 17.82 minutes on math homework.
99.7% of the population is expected to spend between 1.97 and 21.23
minutes on math homework.
Therefore, we can expect approximately 82 (68% of 120) students in Mr. Sullivan's class to spend between 9 and 12 minutes on math homework.

For Mrs. Farrington's class:
The mean of the sample is 11 and the standard deviation is 2.87. Therefore, we can expect the mean and standard deviation of the population to be 11 and 2.87, respectively.
Using the 68-95-99.7 rule, we can calculate the following:
68% of the population is expected to spend between 8.26 and 13.74 minutes on math homework.
95% of the population is expected to spend between 5.39 and 16.61 minutes on math homework.
99.7% of the population is expected to spend between 1.72 and 19.48 minutes on math homework.
Therefore, we can expect approximately 68 (68% of 100) students in Mrs. Farrington's class to spend between 9 and 12 minutes on math homework.

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Answer:

Step-by-step explanation:

104.4 divided by 4 = 26.1