Mrs. Everett, the P.E. teacher, is pairing off students to race against each other. Antonio can run 8 meters per second, and Devin can run 9 meters per second. Mrs. Everett decides to give Antonio a head start of 50 meters since he runs more slowly. Once the students start running, Devin will quickly catch up to Antonio. How long will that take?
Write a system of equations, graph them, and type the solution.

The principles of integration were formulated independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century, who thought of the area under a curve as an infinite sum of rectangles of infinitesimal width.

A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). Double integrals are the integrals of a function of two variables over an area in R2 (the real-number plane).

The double integral of a positive function with two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function with one variable represents the area of the region between the graph of the function and the x-axis.

A multiple integral will produce hypervolumes of multidimensional data if there are more variables.

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For the given normally distributed data, the number of children have height greater than 116 is given by 79.

Using normally distribution we have,

Z = ( X - µ ) / σ

Here,

Mean 'µ' = 110

Standard deviation 'σ' = 6 cm

n = 500

Number of children with height greater than 116 cm

P (x > 116) = 1 - P (x < 116)

For,

P( X < 116 )  

⇒ P[ (X - μ) / σ > (116 - 110)/ 6 )

⇒ P( Z < 6 / 6 )

⇒ P( Z < 1 )

Using the value from normal distribution table we have:

P (Z< 1) = 0.8413

⇒P (x > 116) = 1 - 0.8413

⇒P (x > 116) = 0.1587

Number of children with height greater than 116 is :

= 0.1587 × 500

= 79.35

= 79 ( approximately )

Therefore, the number of children have the height greater than 116 cm is equal to 79.

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If vanilla cake has a diameter of 8 inches and chocolate cake has a diameter of 10 inches , then the circumference of vanilla cake is 25.12 inches and of chocolate cake is  31.4 inches .

The Circumference(C) of the circle can be found using formula: C = 2×π×r and r is the radius of the circle.

For the Vanilla cake, the diameter is 8 inches ;

and So , radius is = 8/2 = 4 inches.

The , Circumference of vanilla cake is = 2×π×4 = 8×3.14 inches.

= 25.12 inches .

For Chocolate cake, diameter is 10 inches ;

and radius is = 10/2 = 5 inches.

So , Circumference of chocolate cake is = 2×π×5 = 10×3.14 inches.

= 31.4 inches .

Therefore , To the nearest tenth, circumference of  vanilla cake is 25.13 inches and circumference of chocolate cake is 31.42 inches.

The given question is incomplete , the complete question is

A vanilla cake has a diameter of 8 inches. A chocolate cake has a diameter of 10 inches. What is the circumference the top surfaces of the two cakes to the nearest tenth? Use 3. 14 for π .

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The statement "If we subtract 25 from a number, the result is 17" represented by the equation x - 25 = 17.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

The given verbal statement is "If we subtract 25 from a number, the result is 17"

Now we have to convert to algebraic equation.

we subtract 25 from a number = x - 25

this is equal to 17

So,  If we subtract 25 from a number, the result is 17 means

x - 25 = 17

Therefore, the answer is x - 25 = 17.

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The complete question is:

Which equation represents this statement "If we subtract 25 from a number, the result is 17"?

(a) x − 17 = 25

(b) x − 25 = 17

(c) x + 17 = −25

(d) x − 17 = −25

Actor Albert Brook changed his surname to Albert Einstein to avoid sharing it with another well-known Al. Option C

In 1921, Albert Einstein received the Physics Nobel Prize in honor of his contributions to theoretical physics, particularly the creation of the law of the photoelectric effect. Despite moving to Switzerland in 1895 and giving up his German nationality the following year to become a citizen of the County of Württemberg, Einstein was born within the boundaries of the German Empire.

He enrolled in the program for teaching diplomas in physics and mathematics at the Swiss Federal University of Technology School in Zürich in 1897 as a 17-year-old, and he completed it in 1900.

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The number of customers when there are 576 towers will be 12.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Based on the information, it should be noted that the number of phone is proportional to the number of customers

The constant of proportionality will be:

= 252 / 5.25

= 48

Therefore, the customers when there are 576 towers will be:

= 576 / 48

= 12

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The estimate of the product expression is 0.12

From the question, we have the following parameters that can be used in our computation:

3.71 * 0.296

From the question, the numbers are to be rounded to the place of its leftmost nonzero digit.

So, when the numbers are rounded, we have

4 * 0.3

Evaluate the product

This gives

0.12

Hence, the solution is 0.12

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Answer:

-5

Step-by-step explanation:

Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:

2 - 7 (from B-A)

= -5

The value of {n} for which the given equation holds true is

n = ±√2.125..

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

A quadratic function is of the form -

f(x) = ax² + bx + c

Given is the function as -

f(n) = 8n² - 17

Put f(n) = 0. Solving, we get -

8n² - 17 = 0

8n² = 17

n² = 17/8

n = ±√17/8

n = ±√2.125

Therefore, the value of {n} for which the given equation holds true is

n = ±√2.125.

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{Question in english -

HELPPPPP with this math. Problem i doing-

8n² − 17.}

The scatter plot for the randomly selects 12 students is illustrated below.

The term called scatter plot in math is defined as a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

Here we have know that the statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade.

Here we know that the number of samples is 12.

And here we have each student's total is recorded along with their final grade.

Then the scatter plot for the following table of data is illustrated on the diagram.

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The unknown side BC is 2.33 units.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

A right triangle ABC.

∠ACB is a right angle.

∠ABC is twenty-five degrees.

The side AC is unknown.

Side BC is five units.

Now,

AC = x

BC = 5 units

Tan 25° = AC/BC

Tan 25° = x/5

0.47 = x/5

x = 5 x 0.47

x = 2.33

Thus,

Side BC is 2.33 units.

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Dimensions of the lower floor with the given volume of 2380 cubic feet are given by : length = 34feet, width = 7feet, and height = 10 feet.

Let us consider 'y' be the width of the barn.

Lower floor with horse stall which was extends 5 feet from both the sides.

Width after having horse stall = x - 10

Barn's length is twice the barn's width

Length = 2x

Height is 7 feet less than the barn's width = x - 7

Volume = 2380 cubic feet

⇒Length × width × height = 2380

⇒ ( 2x ) (x -10 ) (x -7 ) = 2380

⇒(2x² -20x)(x-7) = 1190

⇒2x³ -34x² +140x -2380 =0

⇒ x = 17 , √70i, -√70i

x can not be imaginary.

⇒ x = 17feet ( approximately)

Required dimensions are:

Length : 2x = 34feet

Width : x -10 = 7 feet

Height : x - 7 = 10 feet

Therefore, for the given volume the required dimensions are 34feet, 7 feet , and 10 feet.

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Answer:

for any two points in the interval, a change in x results in a zero change in f(x)

Step-by-step explanation:

Answer:

The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the line has a slope of 5 and passes through the point (-1,1) we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1)

The point (-1,1) can be plugged into the equation:

y - 1 = 5(x + 1)

By simplifying and re-arranging the equation, we get:

y = 5x + 6

So the equation of the line that passes through the point (-1,1) and has a slope of 5 is: y = 5x + 6

Answer:

y = 5x+6

Step-by-step explanation:

Using the slope-intercept form of a line

y = mx+b  where m is the slope and b is the y-intercept

y = 5x+b

Substitute the point into the line.

1 = 5(-1) +b

1+5 = b

6=b

The equation is

y = 5x+6

The sine of the angle theta is 1/2√3

From the question, we have the following parameters that can be used in our computation:

0 < θ < 90 and cosθ= 1/2

The above parameter mean that

sin(θ) = √(1 - cos²(θ))

substitute the known values in the above equation, so, we have the following representation

sin(θ) = √(1 - 1/2²)

This gives

sin(θ) = √(3/4)

Take the square roots

sin(θ) = 1/2√3

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Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

The equation that can be used to determine the total cost of renting shoes at both locations is:

total cost = fixed cost + variable cost

Total cost of renting at Bowler World = $5 + $1.1x

Total cost of renting at Lucky Spares = $3 + $1.50x

Where

x = number of games played

In order to determine the number of games that would make the cost equal in both locations, the following steps would be taken:

$5 + $1.1x = $3 + $1.50x

Combine similar terms

$5 - $3 = $1.50x - $1.1x

$2 = $0.40x

Divide both sides of the equation by $0.4

x = 2 / 0.4

x = 5 games

Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50

The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.

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Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.

However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).

By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.

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Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

The null hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is less than or equal to 57%. The alternative hypothesis is that the proportion of chips that do not fail in the first 1000 hours of their use is greater than 57%.

To test this, you would use a one-sample proportion test. The test statistic is calculated using the sample proportion (60%) and the hypothesized proportion (57%) and the sample size (800).

You would then compare the calculated test statistic to the critical value from a z-table (using a two-tailed test and a 0.02 level of significance) to determine whether or not to reject the null hypothesis.

Since the sample proportion (60%) is greater than the hypothesized proportion (57%), it is likely that there is sufficient evidence to support the company's claim.

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The probability that a random sample of 40 adults would have a mean of at least 7 marshmallows is 0.1943

We know that the formula for the z-score:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To find: the probability that a random sample of 40 adults would have a mean of at least 7 marshmallows.

This is nothing but the p-value of Z when X = 7

Here the number of marshmallows an adult can fit in their mouth is skewed right with a mean of 6. 5 and a standard deviation of 0. 58

So, mean μ = 6.5

standard deviation σ = 0.58

Also, n = 40,

x = 7,

By central limit theorem,

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{7-6.5}{0.58}\\\\z=\frac{0.5}{0.58}\\\\z = 0.86[/tex]

z = 0.86 has p value 0.1943

Thus, the required probability is 0.1943

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The probability of Sasha scoring at least one six is 11/36, and the probability of Sasha scoring no sixes is 25/36.

The total number of outcomes in which there is at least one 6 are:

(6,6), (6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

So there are 11 cases in which at least one six appears in two die rolls.

The total number of outcomes can be discovered through the multiplication principle. There are 6 numbers (numbers 1–6) on the first die and the same 6 numbers on the second die, so there are a total of 36 possible outcomes.

The probability of at least one six-in-two die roll is 11/36.

The total number of outcomes in which there is no 6 are:

(5,1), (5,2), (5,3), (5,4), (5,5), (4,1), (4,2), (4,3), (4,4), (4,5), (3,1), (3,2), (3,3), (3,4), (3,5), (2,1), (2,2), (2,3), (2,4), (2,5), (1,1), (1,2), (1,3), (1,4), (1,5).

So there are 25 cases in which no six appear in two die rolls.

The total number of outcomes can be discovered through the multiplication principle. There are 6 numbers (numbers 1–6) on the first die and the same 6 numbers on the second die, so there are a total of 36 possible outcomes.

The probability of no six-in-two die roll is 25/36.

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the probability that at least one of the events A and B occurs is 0.72.

What is probability ?

Probability is a measure of the likelihood of an event occurring. It is typically expressed as a decimal or fraction between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain.

The probability that event A occurs is 0.3 and the probability that event B does not occur is 0.4. To find the probability that at least one of the events A and B occurs, which states that the probability of an event occurring is equal to 1 minus the probability of it not occurring.

We can find the probability that neither event A nor event B occurs by multiplying the probability of event A not occurring (1-0.3 = 0.7) by the probability of event B not occurring (0.4). The probability that neither event A nor event B occurs is 0.7*0.4 = 0.28.

To find the probability that at least one of the events A and B occurs, we subtract the probability that neither event occurs from 1.

P(A or B) = 1 - P(neither A nor B) = 1 - 0.28 = 0.72

So the probability that at least one of the events A and B occurs is 0.72.

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The factored form of the expression -9x^³ - 12x² - 4x is given as follows:

A. -x(3x + 2)².

The expression for this problem is defined as follows:

-9x^³ - 12x² - 4x.

The exponents of the expression are given as follows:

3, 2 and 1.

The lowest exponent is of:

1.

Simplifying the lowest exponent, the expression is given as follows:

-x(9x² + 12x + 4)

The inner expression can be obtained with the square of the sum, as follows:

9x² + 12x + 4 = (3x + 2)².

Meaning that the simplified expression is of:

-x(3x + 2)².

Which is option A.

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A varied group of volunteers is frequently better able to function as a team since having a variety of viewpoints and personalities helps facilitate collaboration.

Diversity in volunteering refers to both the individuals participating and the opportunities offered. Regardless of ethnicity, gender, religion, sexual orientation, or other characteristics, volunteering should be a process that welcomes participation from people with a variety of backgrounds and talents.

People can learn from one another as a result of diversity, which introduces new ideas and experiences. Better problem-solving results from incorporating many ideas and perspectives. Working in diverse teams fosters innovation and encourages dialogue. Our culture benefits from variety as well.

Any employee, regardless of gender, race, age, ethnicity, physical ability, sexual orientation, religion, or other characteristic, has the same rights and opportunities in a diverse workplace.

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The required inequality to show how many refrigerators and how many pianos the truck could carry is  300x + 425y ≤ 7300.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have,

A truck that can carry no more than 7300 lb is being used to transport refrigerators and upright pianos.

Let x be the number of refrigerators in the truck and y be the number of pianos in the truck.

Then

300x + 425y = 7300

At x = 11 and y = 9

300(11) + 425(9)

= 7125 ib

So, the truck will not overload.

Inequality will we

300x + 425y ≤ 7300

Thus, required inequality is 300x + 425y ≤ 7300.

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Answer:

Answer in image

Step-by-step explanation:

Using the y-intercept, we can graph our first point at (0,5) the y-intercept. Then from there we can use the slope to continue to plot points. (This is a negative graph by the way based off of the slope -3/4).

-Hope this helped

What Meg needs to find is the whole and what Steve needs to find is the part.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

a/b * 100

(in percentage)

Since Meg already knows the part and the percent which is 10 and 33% respectively, then it means that what she needs to find is the whole which is the total number of dogs she saw.

Steve already knows the whole which is 12 dogs and the percent which is 50% and as such what he will need to do now is to find the part that makes up the percentage part.

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Answer:

the answer is b

Step-by-step explanation:

The weight of a randomly selected pack of gum that has a z-score of 3.11, is 54.6 grams. So, the right option is D.

A Z-score can be used to calculate how much the data deviates from the mean. It shows how frequently the data is either above or below the mean. According to the formula,

Z = (X - μ)/σ

where, Z is the Z-score, X is the data point, μ is the mean and σ is the standard variable.

Z = 3.11, σ = 2.4, μ = 47.1

Z = (X - μ)/σ

Now putting the value

3.11 = (X - 47.1)/2.4

Multiply by 2.4 on both side

X - 47.1 = 3.11 X 2.4

X - 47.1 = 7.464

Add 47.1 on both side, we get

X = 54.564 grams

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The complete question is:

The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3.11?

39.6 grams

44.7 grams

49.5 grams

54.6 grams

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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