How much running area is there?

R = 20 ft

I WILL MARK YOU BRAINLIEST AND GIVE 30 POINTS

Answer:

39 3/8 ft ^2

Step-by-step explanation:

To find the area of a rectangle, multiply the length times the width.

A = l*w

  = 7 1/2  * 5 1/4

Change the mixed numbers to improper fractions.

A = 15/2 * 21/4

    =315/8

Change back to a mixed number.

8 goes into 315 39 times with 3 left over.

 = 39 3/8

Answer:

(you can round to 39.4)

Step-by-step explanation:

Find the area of the rectangle shown

7 1/2 ft

5 1/4ft

7 1/2 = 7.5 ft

5 1/4 = 5.25 ft

Area = L x W

Area = 7.5 x 5.25

Area = 39.375

the answer is 6 minutes and 46 seconds

sinθ = t/o

cosθ = m/o

tanθ = t/m

cscθ = o/t

secθ = o/m

cotθ = m/t

Answer:

(a) 74.62

(b) 78.57

Step-by-step explanation:

.72 x 103.64 = 74.62

.72 x 109.13 = 78.57

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The area of the region in which the burro can graze will be 833 pi square feet.

Each interior vertex angle of a regular hexagon is (n - 2)·180°/n  =  (6 - 2)·180°o/6  =  120°

I'll break up the area into three sections.

There is one major section, going 150' along one side in a circular arc to 150' along the adjacent side.

Since the interior angle is 120°, the exterior angle will be 240°.

The area of this section will be:  (240°/360°)·pi·radius2  =  (2/3)·pi·1502  =  15,000 pi

Then, on each end, around the corner of the barn, the goat can go in a circular arc with radius = 50'.

This angle will be 60°, or one-sixth or a circle.

The area of each section will be (1/6)·pi·502  =  416 2/3 pi

Total area:  15,000 pi + 416 2/3 pi + 416 2/3 pi  =  833 1/3 pi square feet.

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Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

The possibility that experimental results are due to chance or some factor other than the experimental variable is measured by the p-value.

The p-value is a statistical measure that provides information about the likelihood of obtaining a particular result due to random chance or some factor other than the experimental variable. In experimental design, a null hypothesis is usually assumed, which states that there is no relationship between the independent and dependent variables. The p-value is then used to assess the strength of evidence against this null hypothesis.

A p-value is calculated based on the data obtained from an experiment and the assumptions of the statistical test used. It is a number between 0 and 1, and it represents the probability of obtaining a result as extreme or more extreme than what was actually observed, given that the null hypothesis is true.

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1. The z-scores are given as follows:

Due to the lower z-score, Joe had a better time.

2. The actual score is of 40.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

Considering the mean and the standard deviation for his distribution, and also that 15 seconds = 0.25 minutes, the z-score for Joe is obtained as follows:

Z = (19.75 - 22.5)/4

Z = -0.6875.

For Sara, the z-score is calculated as follows:

Z = (28.33 - 31.25)/6

Z = -0.49.

Joe had a better time, as his lower z-score means that a lower percentage of runners spent less time than him, that is, a lower percentage of runners ran faster than him.

For item 2, the actual score is calculated as follows:

-2 = (X - 50)/5

X - 50 = -10

X = 40.

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Film cameras allow a limited number of shots per role. 36 images can a photographer typically shoot on a roll. Thus, option A is the correct option.

The most cost-effective per shot is the roll, which typically yields 36 exposures. The 35mm format comes in a few different forms. On a roll of 35mm film, half-frame cameras may capture twice as many images at a smaller size.

Rolls of film typically have 24 or 36 exposures. The number of pictures you may take before loading a new roll may be limited as a result. However, some photographers view this as a benefit since it forces them to be more deliberate and exact when creating their images.

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Answer:

x15 y90 z13

Step-by-step explanation:

https://dlsfile.com/dd/MTQ1ODE5a3Bjd2hiaGxmXzM0MTMyNQ

When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).

We can conclude that there is not enough evidence to suggest that the distribution of blood types in hospital patients is different from that of the general population at a significance level of 0.10.

Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.

It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.

We have,

We need to perform a hypothesis test to determine if the distribution of blood types in hospital patients is the same as that of the general population.

Let's set up the null and alternative hypotheses:

Null hypothesis:

The distribution of blood types in hospital patients is the same as that of the general population.

Alternative hypothesis:

The distribution of blood types in hospital patients is different from that of the general population.

We can use a chi-squared test to test the hypothesis.

First, we need to calculate the expected frequencies for each blood type based on the general population distribution:

Expected frequency of type A = 50 x 0.22 = 11

Expected frequency of type B = 50 x 0.28 = 14

Expected frequency of type O = 50 x 0.38 = 19

Expected frequency of type AB = 50 x 0.12 = 6

Next, we can calculate the chi-squared statistic:

\($\chi^2 = \frac{(11-11)^2}{11} + \frac{(9-14)^2}{14} + \frac{(24-19)^2}{19} + \frac{(6-6)^2}{6} = 2.84$\)

The degrees of freedom for the test is (4 - 1) = 3.

Using a chi-squared distribution table with 3 degrees of freedom and a significance level of 0.10, the critical value is 6.251.

Since the calculated chi-squared value (2.84) is less than the critical value (6.251), we fail to reject the null hypothesis.

Thus,

We can conclude that there is not enough evidence to suggest that the distribution of blood types in hospital patients is different from that of the general population at a significance level of 0.10.

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The fraction of 3.88888 will be \(3\frac{11111}{12500}\)

What is Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts.

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator

How to solve this problem?

The steps are as follow:

Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).

Step 2: Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Next, given that you have x decimal places, multiply numerator and denominator by 10x.

Step 3: Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

So the 3.88888 can be written as in fraction as following:

3.88888 = 388888/100000

dividing both num. and denominator ny 8

=(388888/8)/(100000/8)

=\(3\frac{11111}{12500}\)

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Let's x be equal to 3.88888...

Multiplying both sides of the equation by 10, we get 10x = 38.88888...

Subtracting the left sides of these equations, we get:

10x - x = 38.88888... - 3.88888...

9x = 35

Dividing both sides of this equation by 9, we get:

x = 35/9

Therefore, the decimal 3.88888... is equal to the fraction 35/9. Answer: A) 38/9 (reduced form of 35/9).

Answer:

275, 350, 450, 550, 675

Step-by-step explanation:

Arrange in order

275, 300, 450, 490, 675

range 275 to 675

median 450

mean 438

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

Raise 300 to 350

Raise 490 to 550

New set of prices

275, 350, 450, 550, 675

range 275 to 675     same

median 450     same

mean 460    increased

Answer:

One set of prices could be: {275,300,450,600,675}

Another set could be: {275,300,450,600,675}

There are many other solutions possible.

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

Explanation:

A = {450, 275, 675, 490, 300}

B = {275, 300, 450, 490, 675}

Set A is the original set of values in the order they were given to you. Set B is the sorted version of set A from smallest to largest.

The mean is found by adding up the values and dividing by 5 (because there are five items in the set).

The mean is (275+300+450+490+675)/5 = 2190/5 = 438. The shopkeeper wants to increase the mean to something larger, but keep the median and range the same.

The median is the middle most number. In set B, we can see that is 450. So the median is 450. We want to keep the median the same at 450.

The range is the difference in min and max

range = max - min = 675-275 = 400

We want to keep the range at 400

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

There are a number of ways to increase the mean, while keeping the median and range the same.

Let's say we keep the min and max the same. In order to increase the mean, we need to increase the 490 (second largest value) to something larger. Let's bump that up to 600 for instance.

Recomputing the mean gets us

(275+300+450+600+675)/5 = 2300/5 = 460

The old mean was 438 and the new mean is now 460. The mean has increased. This is due to the larger price pulling on the mean to get the mean to increase.

The median is still 450 because it's still in the direct middle of set C

C = {275,300,450,600,675}

The range is still the same as well because we haven't changed the min and max.

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

So one possible set could be

C = {275,300,450,600,675}

We could also have

D = {275,400,450,500,675}

The difference is that the 300 bumped to 400, and the 600 dropped to 500. You should find that the median and range are the same, while the mean is 460.

There are many possible solutions here.

The table and graph is mentioned below.

In mathematics, a graph is a visual representation of a set of objects, often referred to as vertices or nodes, and the connections or edges that exist between them. Graphs are used to represent a wide range of mathematical concepts, such as functions, equations, and data sets.

A graph can be thought of as a collection of points or vertices that are connected by lines or edges. The way these vertices and edges are arranged can convey important information about the relationships between the objects being represented.

Graphs can be classified into different types, such as directed or undirected graphs, weighted or unweighted graphs, and cyclic or acyclic graphs. They can also be used to model real-world systems, such as social networks, transportation systems, and computer networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

               0                 $75.00

               10                 $95.00

               20                 $115.00

               30                 $135.00

               40                 $155.00

               50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

                0                 $5.75

                10                 $60.75

                20                 $115.75

                30                 $170.75

                40                 $225.75

                50                 $280.75

b) On the same set of axes, the graph is attached below.

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Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished.

In mathematics, a graph is a picture of a collection of things, also known as vertices or nodes, and the links or edges that join them. Numerous mathematical ideas, including functions, formulae, and data sets, are represented by graphs.

A collection of vertices or points linked by lines or edges is referred to as a graph. The arrangement of these vertices and edges can reveal crucial details about the connections between the things being represented.

Different kinds of graphs, including directed and undirected graphs, weighted and unweighted graphs, and cyclic and acyclic graphs, can be distinguished. Additionally, they can be used to simulate real-world systems like computer networks, transit systems, and social networks.

a)Table for Members:

Number of Movies (n) Cost (C1)

0                 $75.00

10                 $95.00

20                 $115.00

30                 $135.00

40                 $155.00

50                 $175.00

Table for Non-members:

Number of Movies (n) Cost (C2)

0                 $5.75

10                 $60.75

20                 $115.75

30                 $170.75

40                 $225.75

50                 $280.75

b) On the same set of axes, the graph is attached below.

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Answer:

1073.45 in²

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The equation to solve for the area of a circle is:

But wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:

Now that we know this, we can insert 37 in for the diameter:

So, the radius of the circle is 18.5 inches.

Inserting 18.5 into the expression for the radius:

Using 3.14 for pi:

Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².

Answer:

8/21

Step-by-step explanation:

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Using percentages we know that 62% or 62 students out of 100 students prefer biology.

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage.

When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100.

Thus, the proportion refers to a component per 100.

The word percent denotes a percentage of 100. It is represented by the symbol "%."

So, according to the given situation:

34 females enjoy biology

Do boys enjoy biology?

It is 34%≤

Then,

27% favor chemistry

10% favor physics.

The calculation would be:

27 + 11 = 38

100 - 38 = 62

Therefore, using percentages we know that 62% or 62 students out of 100 students prefer biology.

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Correct question:

100 students are interviewed to see which of biology, chemistry or physics they prefer.72 of the students are girls. 34 of the girls like biology best. 11 of the boys prefer physics. 24 out of the 27 who prefer chemistry are girls. What percentage of the students prefer biology?

By solving the system of equations using both methods we get ,

Both graph intersects at (9,6). So A=9 and B=6

By substitution method we got A=9 and B=6

Given :

If a nurse has 20% alcohol solution and 70% alcohol solution, but needs 15 liters of a 40% alcohol solution

We are already given with 2 equations

\(A + B = 15\\0.20A + 0.70B = 6\)

Lets graph both the equations

While graphing we use variables   x  and y

Lets take A as x  and B as y

\(x + y = 15\\0.20x + 0.70y = 6\)

Lets graph first equation

\(x+y=15\\y=-x+15\\slope =-1\\y intercept = 15\)

Graph the above equation using slope and y intercept

Now we graph the second equation

\(0.20x + 0.70y = 6\\+ 0.70y = -0.20x+6\\y=-\frac{2}{7} x+\frac{6}{0.7} \\slope =-\frac{2}{7} \\y intercept is \frac{6}{0.7}\)

Graph is attached below

Both the lines intersects at (9,6)

A is 9  and B is 6

Now we solve using substitution method

\(0.2A+0.7B=6\\2A+7B=60\\2A=60-7B\\A=\frac{60-7B}{2}\)

Substitute it in first equation

\(\frac{60-7B}{2}+B=15\\\frac{2\left(60-5B\right)}{2}=15\cdot \:2\\60-5B=30\\-5B=-30\\B=6\)

Find out A by replacing B with 6

\(A=\frac{60-7\cdot \:6}{2}\\A=9\)

So, A is 9  and B is 6 using substitution method

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Answer:

(a) No solution

(b) Infinitely many solution

(c) No solution

(d) Infinitely many solution

Step-by-step explanation:

Solving (a):

\(2x + 10y = 9\) --- (1)

\(3x + 15y = 13\) --- (2)

Multiply (1) by 1.5

1.5 * [\(2x + 10y = 9\)]

\(3x + 15y = 13.5\) --- (3)

Subtract 2 and 3

\(3x - 3x + 15y - 15y = 13.5 - 13\)

\(0 = 0.5\)

The above is false; Hence, the system has no solution

Solving (b):

\(2x + 8y = 5\) --- (1)

\(3x + 12y = 7.5\) -- (2)

Multiply 1 by 1.5

1.5 * [\(2x + 8y = 5\)]

\(3x + 12y = 7.5\)

Subtract 2 and 3

\(3x - 3x + 12y - 12y = 7.5 - 7.5\)

\(0 = 0\)

The above implies that the system has infinitely many solutions

Solving (c):

\(y = 3 - x\)

A second equation is required to solve for (c)

Solving (d):

\(5x - 8y = -1\) --- (1)

\(-\frac{5}{2}x+ 4y = \frac{1}{2}\) --- (2)

Multiply (2) by 2

\(-5x + 8y = 1\) --- (3)

Add 1 and 3

\(5x - 5x -8y + 8y = -1 + 1\)

\(0 = 0\)

The above implies that the system has infinitely many solutions

Answer:

3 : 15 : 2

Step-by-step explanation:

Let cranberry juice = x,

3/4 + 1/10 + x = 1

x = 3/20

Ratio = cranberry : apple : orange

= 3/20 : 3/4 : 1/10

= 3 : 15 : 2 (Times everything with 20)

Answer:

x = 6

Step-by-step explanation:

Verticle angles are formed when two lines intersect. The angles opposite each other are congruent, those angles are called vertical angles.

Using this knowledge, one can say;

3x + 2= 20

Use inverse oeprations to solve for "x"

3x + 2 = 20

     -2       -2

3x = 18

/3      /3

x = 6

Answer:

the product of the decimal equivalents of all discount in the series

Step-by-step explanation:

OUT of  35 spins   4 + 15 + 3  = 22   were blue or green or purple

 22/35 probability  = 63%

Answer:

20 hours

Step-by-step explanation:

2 yards = 5 hours

ratio of 2:5

and so 2x4 = 8

so do the same to the 5

8 yards in 20 hours

Answer:

Chris can mow 8 yards in 20 hours.

Step-by-step explanation:

Chris can mow 2 yards in 5 hours. That means the ratio between his amount of yards and the time it takes to mow them is 2:5. In order to figure out how long it takes him to mow 8 yards we need to find the unit rate. In this situation, the unit rate would represent how long it takes Chris to mow 1 yard. In order to find the unit rate we need to divide. 2/2 is 1 which is the number we're trying to get to. According to distributive property, what you do to one side you also have to do to the other. That menas we divide 5 by 1 as well. That gives us 2.5. This means that in 2.5 hours Chris can mow 1 yard. We can check our work by doing the opposite of division, multiplication. 1 x 2 = 2. 2.5 x 2 = 5. Everything adds up. Now that we hav our unit rate we do the same thing except with 8 instead of 5 hours. Just plug the numbers in, it's easy and fun when you understand the formula. 1 x 8 = 8. 2.5 x 8 = 20. Chris can mow 8 yards in 20 hours. To check our work we do the oppistite. Divide instead of multiply. 20/ 8 =2.5. 8/8 = 1. It adds up correctly. Hope this helps!  :)

Answer:

Rhana buys a skateboard for which the original price is $130.oo and an in-line skates with an  original price of $ 290.00. Pedro buys a baseball glove for which the original price is $160.00  and in- line skates with an original price of $210.00. There is also a 5% tax on the sale of all  sporting goods. Who spent less money at the sporting goods store?

Step-by-step explanation:

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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