Jacob and Ali want to run from one corner of a football field to the opposite corner. The rectangular football field is 50 yards wide and 120 yards long. Jacob runs around the perimeter of the field, while Ali runs in a straight line through the middle of the field. How many more yards does Jacob run than Ali?

Answer:

The number is 226.

Step-by-step explanation:

Let the number be x.

Given:

The number is greater than two hundred twenty-five.

So we can say that;

[tex]x>225[/tex] equation 1

Also Given:

Her number is less than 2 hundreds,2 tens, and 7 ones.

Now we can say that 2 hundreds,2 tens, and 7 ones is equal to 227

So now the number is less than 227.

[tex]x<227[/tex] equation 2

From equation 1 and equation 2 we can say that;

[tex]225<x<227[/tex] equation 3

Also,

[tex]225<226<227[/tex] equation 4

Comparing equation 3 and 4 we get;

[tex]x=226[/tex]

Hence The number is 226.

Answer:

The sampling used is simple random sampling.

Step-by-step explanation:

Consider the provided information.

Types:

Here, randomly selected 60 customers, Thus, the sampling used is simple random sampling.

Answer:

See the plot below.

For this case we can consider as an outlier the value 8.0 since is far away from the other points

Step-by-step explanation:

For this case we can create the stem plot like this:

Stem      Leaf

 0      |     5 7

 1       |     1 2 2 3 3 5 5 7 7 8 9

 2      |     0 2 5 6 8 8 8

 3      |     5 8

 4      |     4 8 9

 5      |     2 5 7 8

 6      |

 7      |

 8      |    0

Notation : "1 |1 means 1.1 for example and 3|5 means 3.5"

By definition an outlier is "an observation that lies an abnormal distance from other values in a random sample from a population"

For this case we can consider as an outlier the value 8.0 since is far away from the other points

Answer:

(0.2599,0.3401)                                                

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 500

x = 150

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3[/tex]

Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]

Putting the values, we get:

[tex]0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)[/tex]

The 95% confidence interval is (0.2599,0.3401).

Answer:

B)temperature during the game on Saturday

Step-by-step explanation:

Answer:

The answer to your question is below

Step-by-step explanation:

Data

P (-5, 5)

Parallel to 6x - 5y - 9 = 0

Process

1.- Find the equation of the line

                  6x - 5y = 9

                       -5y = -6x + 9

                          y = -6/-5 x + 9/-5

                          y = 6/5 x - 9/5

slope = 6/5, as the lines are parallels, the slope is the same.

2.- Get the equation of the new line

                     y - y1 = m(x - x1)

                     y - 5 = 6/5 (x + 5)

                     y - 5 = 6/5x + 6

                          y = 6/5x + 6 + 5

                          y = 6/5x + 11                     Point-slope form

                   5y - 25 = 6(x + 5)

                   5y - 25 = 6x + 30

                   6x - 5y + 30 + 25 = 0

                  6x - 5y + 55 = 0                      General form

The equation of the line that passes through (-5,5) and is parallel to 6x - 5y - 9 = 0 can be written in point-slope form as y - 5 = (6/5)(x + 5) and in general form as -6x + 5y - 55 = 0.

To write an equation for the line that passes through the point (-5,5) and is parallel to the line 6x - 5y - 9 = 0, we first need to find the slope of the given line. By rewriting the equation in slope-intercept form (y = mx + b), we can identify the slope (m). The equation 6x - 5y - 9 = 0 can be rewritten as y = (6/5)x + 9/5, so the slope of the line is 6/5. Since parallel lines have the same slope, the slope of our new line is also 6/5.

Next, we use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (here (-5,5)) and m is the slope. Substituting these values into the equation gives us y - 5 = (6/5)(x + 5).

To express this in general form (Ax + By + C = 0), we rearrange the equation: multiply both sides by 5 to clear the fraction, resulting in 5(y - 5) = 6(x + 5), which simplifies to 5y - 25 = 6x + 30. Rearranging gives -6x + 5y - 55 = 0.

Answer:

Don't worry friend! I am here to help you!

Step-by-step explanation:

I tried answering as many questions as I could, but the ones I didn't answer, I didn't know how to solve.

Please understand that I am here to help you and others on brainly!

I hope this makes you feel better!

- sincerelynini

Answer:

Step-by-step explanation:

(a) R2 does not determine the level of correlation between two variables in statistics but rather it is used to determine the level of variance in a dependent variable that is explained by an independent variable. It is also known as coefficient of determination.

Pearson's correlation coefficient (r) will better explain a direct relationship between a country's literacy rate and life expectancy and the value obtained will better explain option a

(b) The slope of the line can predict an improvement in life expectancy but cannot guarantee this improvement. And as such, the use of the word "will" suggests a form of guarantee which is wrong in interpreting slopes.

Answer: [tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]

Step-by-step explanation:

Let x be the equal sides of the triangle .

The , the third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So , The perimeter of triangle would be  x+x+(x+113)= 3x+113 --------(1)

Since , it is given that the perimeter of triangle is 525. -----(2)

So from (1) and (2) , we have

[tex]3x+113=525\\\\ 3x=525-113=412\\\\ x=\dfrac{412}{3}=137\dfrac{1}{3}[/tex]

Then, third side = [tex]137\dfrac{1}{3}+113=250\dfrac{1}{3}\ cm[/tex]

Hence , the sides of a triangle  are:[tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]

Answer: 1 16/45, 1 16/45, 2 31/45

Step-by-step explanation:

Say x is the equal side of the triangle.

The third side would be x+113 cm.

The perimeter is the sum of all sides of a triangle.

So, the perimeter of the triangle would be  x+x+(x+113)= 3x+113

Since the triangle's perimeter is 5 2/5, 3x + 1 1/3 = 5 2/5.

1 1/3 is 1 5/15. 5 2/5 is 5 6/15. 5 6/15 - 1 5/15 = 4 1/15.

This means 3x = 4 1/15.

4 1/15 = 61/15

3x = 61/15

To make 3x into x, you can multiply it by 1/3.

3x*1/3 is x. 61/15*1/3 = 61/45.

x = 1 16/45 because 61/45 = 1 16/45.

The longer side is x + 1 1/3 so you have to add 1 1/3 to 1 16/45 which is

2 31/45.

So, the sides are 1 16/45, 1 16/45 and 2 31,45.

Answer:

Step-by-step explanation:

Let x represent the average speed of flight 725.

Flight 725 left New York at 10:28 a.m. flying north.

Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. This means that the speed of flight 245 is

3x - 120

At 1:06 p.m. they are 1,030 kilometers apart. This means that total distance travelled by both planes would be 1030

Between 10:28am and 1:06pm, the number of hours would be 2hr 38 minutes = 2 + 38/60 = 2.63 hours

Distance = speed × time

Total distance travelled by flight 725 = x × 2.63 = 2.63x

Between 11:18am and 1:06pm, the number of hours would be 1hr 48 minutes = 1 + 48/60 = 1.8 hours

Distance = speed × time

Total distance travelled by flight 245 = x × 1.8 = 1.8(3x - 120)

5.4x - 216 + 2.63x = 1030

8.03x = 1030 + 216 = 1246

x = 1246/8.03 = 155 kph

Answer:

0.33

Step-by-step explanation:

So we find the difference between the price of milk at 6 storms and the price of milk at 3 storms.

3.88 - 2.89= 0.99

Then we divide the difference by 3 to find the average rate of change for each storm between 3 to 6.

0.99 ÷3= 0.33

So the answer is 0.33.

The average rate of change from 3 to 6 storms is 0.33

A correlation exists as a statistical measurement that expresses the extent to which two variables are linearly related (suggesting they change together at a constant rate). It's a familiar tool for defining simple relationships without making a statement about cause and effect.

To solve this example use this rule :

Δx/Δy

x exists the amount that changed. so Δx=0,99.

The storm stands to 3 to 6 so find the difference for x: for the 3rd and 6th members of the table... 3.88-2.89=0.99

Now,

0.99/Δy

Because require to find from 3 to 6, Δy=3,

When finding both, rate of change with :

0.99/3=0.33.

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Answer: Its True

Step-by-step explanation:

The statement is true because the Percentages are preferred and also they are easier to compare than counts.

Answer:

89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6      

Step-by-step explanation:

We are given a normally distributed data.

We have to find the percentage of data that lies within the range  z = − 1.6 and z= 1.6

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

[tex]P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%[/tex]

89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6

Final answer:

Approximately 89.04% of data points fall within 1.6 standard deviations of the mean in a normally distributed set, calculated using the empirical rule and Z-table for the standard normal distribution.

Explanation:

To find the percentage of data points that fall between z-scores of -1.6 and 1.6, we use the properties of the standard normal distribution. Based on the empirical rule (also known as the 68-95-99.7 rule), we know that approximately 68% of data points lie within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean in a normal distribution.

Since our z-scores are between -1 and 2, we will look at the percentages for these intervals. Typically, a z-score of 1.6 would correspond to a value between the percentages for 1 and 2 standard deviations from the mean. Using a Z-table or standard normal distribution curve calculator, we find that a z-score of 1.6 gives us approximately 0.4452 (or 44.52%) to the left of the z-score and 0.4452 to the right. Therefore, the total area between -1.6 and 1.6 is 2 × 0.4452, which is approximately 0.8904 (or 89.04%). Thus, approximately 89.04% of the data points will fall within 1.6 standard deviations from the mean in a normally distributed data set.

Final answer:

After 100 days, there will be approximately 7.18 bacteria present.

Explanation:

To determine the number of bacteria that will be present after 100 days, we need to calculate the exponential growth of the bacteria. The bacteria reproduce at a rate of 4% per day, which means the population will double every 25 days (since 100 divided by 4 is 25).

To calculate the final population, we can use the formula N = N₀ * [tex](1 + r/100)^t[/tex], where N is the final population, N₀ is the initial population, r is the growth rate, and t is the time in days.

In this case, the initial population is 2 (assuming there are initially only two bacteria), the growth rate is 4%, and the time is 100 days.

Plugging in these values,

we get [tex]N = 2 * (1 + 4/100)^{100} = 2 * (1.04)^{100}[/tex]nal population of approximately 7.18 bacteria. Therefore, there will be approximately 7.18 bacteria present after 100 days.

Answer:

x=11

Step-by-step explanation:

[tex]\frac{5x}{3x-3} =\frac{44}{24} =\frac{11}{6} \\33x-33=30x\\33x-30x=33\\3x=33\\x=11[/tex]

Answer:

[tex]MG=56\ units[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem we have that

∆EGF~∆EML

so

[tex]\frac{EG}{EM}=\frac{EF}{EL}[/tex]

substitute the given values

[tex]\frac{5x+2}{16}=\frac{126}{28}[/tex]

solve for x

[tex]5x+2=\frac{126}{28}(16)[/tex]

[tex]5x+2=72\\5x=70\\x=14[/tex]

[tex]EG=5x+2=5(14)+2=72\ units[/tex]

step 2

Find MG

we know that

[tex]MG=EG-EM[/tex]

substitute

[tex]MG=72-16=56\ units[/tex]

Answer:

[tex]a=-6[/tex]

Step-by-step explanation:

Line 1:  (1, a) and (5, −2)

slope of the   line is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-a}{5-1} =\frac{-2-a}{4}[/tex]

Line 2:  (2, 8) and (−5, a + 7)

slope of the   line is

[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{a+7-8}{-5-2} =\frac{a-1}{-7}[/tex]

when the lines are parallel then slopes are equal

[tex]\frac{a-1}{-7} =\frac{-2-a}{4}[/tex]

cross multiply it

[tex]4(a-1)=-7(-2-a)[/tex]

[tex]4a-4=14+7a[/tex]

subtract 4a from both sides

[tex]-4=14+3a[/tex]

[tex]-18=+3a[/tex]

divide both sides by 3

[tex]a=-6[/tex]

Answer:

[tex]x^{4}[/tex] + 3x² - 4

Step-by-step explanation:

Note that complex zeros occur in conjugate pairs

If 2i is a zero then - 2i is a zero

The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are

(x - 1), (x + 1), (x - 2i) and (x + 2i)

The polynomial is expressed as the product of the factors, thus

f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs

     = (x² - 1)(x² - 4i²) → i² = - 1

     = (x² - 1)(x² + 4) ← distribute

     = [tex]x^{4}[/tex] + 4x² - x² - 4

     = [tex]x^{4}[/tex] + 3x² - 4

Answer:

48 liters

Step-by-step explanation:

You should multiply the number of containers by the number of liters in each container.

12 x 4 = 48

Pam brought 48 liters of water to the soccer game.

Answer:

The regular price of the car is $13,000.

Step-by-step explanation:

i) let the price of the van Andy and Diane want to buy be $x.

ii) they get $5,500 for their present car

iii) they also make a down payment of $2,300.

iv) therefore $x = $0.4x + $5,500 +  $2,300

   therefore $0.6x = $7,800

therefore $x = $[tex]\frac{7800}{0.6}[/tex] = $13,000

The regular price of the car is $13,000.

Final answer:

Carol has 10 green cubes in the box. After adding 12 more red cubes, she ends up with 32 red cubes.

Explanation:

To solve this problem, we can use the concept of ratios and equations. First, we know that the initial ratio of red to green cubes is 2:1. Let's represent the number of red cubes as 2x and green cubes as x. We then are told that Carol adds 12 more red cubes and the ratio becomes 4:5. If we let the number of green cubes remain as x, we have that the new number of red cubes is 2x + 12.

We can set up the following proportion to represent the new situation:

(2x + 12) / x = 4 / 5

By cross-multiplying, we can solve for x to find the quantity of green cubes:

5(2x + 12) = 4x

10x + 60 = 4x

6x = 60

x = 10

Therefore, there are 10 green cubes in the box (as x represents the number of green cubes).

To find out how many red cubes are there in the end, we add 12 to the initial amount of red cubes (2 times the number of green cubes):

Initial red cubes = 2x = 2(10) = 20

Final red cubes = 20 + 12 = 32 cubes

So, Carol has 32 red cubes in the end.

Answer: she has 16 dimes and 48 nickels

Step-by-step explanation:

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of dimes that she has in her wallet.

Let y represent the number of nickels that she has in her wallet.

she has three times as many nickels as she does dimes. This means that

y = 3x

the total value of the coins is $4.00. This means that

0.1x + 0.05y = 4 - - - - - - - - - - - 1

Substituting y = 3x into equation 1, it becomes

0.1x + 0.05 × 3x = 4

0.1x + 0.15x = 4

x = 4/0.25 = 16

y = 3x = 3 × 16

y = 48

Answer:

Siham ran for 305 minutes

Step-by-step explanation:

Let

Siham Ran for time = X

Siham Ran for time = X-60

According to given condition

X + (X-60) = 670

X + X - 60 = 670

2X = 670-60

2X = 610

X = 610/2

X = 305

So Siham ran for 305 minutes only

Answer:

side length is [tex]\frac{20\sqrt{3} }{3}[/tex] feet

Step-by-step explanation:

An equilateral triangle has a height of 10 feet.  the height of the triangle is the perpendicular bisector to the base

so it forms a two right angle triangle

the triangle formed is a 30-60-90 degree triangle

the diagram is attached below

Let x be the side if the equilateral triangle

sin(theta)=opposite by hypotenuse

[tex]sin(60)=\frac{10}{x}[/tex]

[tex]\frac{\sqrt{3}}{2} =\frac{10}{x}[/tex]

cross multiply

[tex]\sqrt{3} x=20[/tex]

[tex]x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}[/tex]

The length of the side of an equilateral triangle with a height of 10 feet is approximately 11.54 feet. This is determined by applying the properties of a 30-60-90 triangle which is a half of an equilateral triangle.

The problem is asking to solve for the side (s) of an equilateral triangle given the height (h). An equilateral triangle can be divided into two 30-60-90 right triangles. In such a triangle, the ratio between the hypotenuse (which is the side of the equilateral triangle) and the longer leg (which is half of the height) is 2:√3. Therefore, if the height is 10 feet, then the side length would be (2/√3)*h.

Step 1: Recognize that the triangle is a 30-60-90 triangle.

Step 2: Apply the ratio between the sides in a 30-60-90 triangle, 2:√3.

Step 3: Multiply the height by 2/√3 to get the length of one side which equals about 11.5 feet.

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Answer:

The answer to your question is 12 monitors

Step-by-step explanation:

Data

v = monitors weighing 25 lb

f = monitors weighing 40 lb

Total weight = 680 lb

Total monitors = 20

Process

1.- Write equations

         v + f = 20          ------------------ (l)

       25v + 40f = 680  -----------------(II)

2.- Solve the system by elimination

Multiply equation l by -25

       -25v -  25f  = - 500

        25v + 40f =    680

          0    + 15 f = 180

Solve for f

                       f = 180 / 15

                       f = 12

3.- Find the value of v

          v + 12 = 20

          v = 20 - 12

          v = 8

4.- Conclusion

      There are 12 monitors weighing forty lb

       There are 8 monitors weighing 25 lb

Answer:

yo is ya boi Nick you already know what it is yeah big daddy nick

Answer:

3. Test Statistic

A test statistic is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

The numerical quantity computed from the data of a sample and used in reaching a decision on whether or not to reject the null hypothesis is called; 3.Test statistic.

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The model shown in the graph describes a piece rate. Correct option is D.

Let us take a point (3, 60) in the given graph.

The function which model this is y=kx.

Let us plug in y as 60 and x as 3.

60=3k

Divide both sides by 3:

k=20

So, y=20x.

The model is proportional function, if the x value increases then y value increases.

Similarly, if x value decreases the y value decreases.

Hence, the model shown in the graph describes a piece rate. option D is correct.

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Answer:

Hourly pay without a bonus

Step-by-step explanation:

I just took the test

Answer:

a) The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.

b) For this case we can use the z score formula again:

[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]

[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]

For this case we want this probability:

[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]

So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%

Step-by-step explanation:

The empirical rule, also referred to as "the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)". The empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

For this case we know that the body temperatures for a group of heatlhy adults represented with the random variable X follows this distribution:

[tex] X \sim N(\mu =98.38F, \sigma=0.48 F)[/tex]

Part a

For this case we can use the z score formula to measure how many deviations we are within the mean, given by:

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

If we find the z score for the values given we got:

[tex] z_1= \frac{99.57-98.38}{0.48}=2.479[/tex]

[tex] z_2= \frac{97.05-98.38}{0.48}=-2.771[/tex]

The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.

Part b

For this case we can use the z score formula again:

[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]

[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]

For this case we want this probability:

[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]

So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%

Answer:

Step-by-step explanation:

In our triangle, angles E + F + G = 180 degrees.  If angle E is 4 times the measure of F, and G is 18 less than E, then

F is x,

E is 4x, and

G is 4x - 18

Add these all together and set the sum equal to 180:

x + 4x + 4x - 18 = 180

Combining like terms:

9x - 18 = 180 and

9x = 196 so

x = 22

That means that

F = 22,

E = 4(22) = 88 and

G = 4(22) - 18 = 88 - 18 = 70

Since 22 + 88 + 70 do in fact equal 180 you can be fairly certain that your answer is correct! (It is correct...trust me!)