Riding your bike is good exercise. If your goal is to ride your bike a total of 140 laps around the block over the next 20 days, how many laps must you ride each day

Answer:

I think it's D also

Step-by-step explanation:

D is my best answer plus I don't think it would be negative and it would be a fraction

Answer:

x = 15; y = 17

Step-by-step explanation:

A line equals 180 degrees

7x + 7 and 4y form the full line

As such:

7x + 7 + 4y = 180

Another line formation is between 4y and 112

A line equals 180 degrees

4y + 112 = 180

180 = 180 so:

7x + 7 + 4y = 4y + 112

Isolate the variable x

Subtract 4y from both sides

7x + 7 + 4y - 4y = 4y - 4y + 112

7x + 7 = 112

Subtract both sides by 7

7x + 7 - 7 = 112 - 7

7x = 105

Divide both sides by 7

7x ÷ 7 ÷ = 105 ÷ 7

1x = 15

x = 15

If x = 15, plug this new information into the expression with both x and y variables

7(15) + 7 + 4y = 180

Pemdas says multiply first

105 + 7 + 4y = 180

Combine like terms

112 + 4y = 180

Subtract both sides by 112

112 - 112 + 4y = 180 - 112

4y = 68

Divide both sides by 4

4y ÷ 4 = 68 ÷ 4

1y = 17

y = 17

Check work:

7(15) + 7 + 4(17) = 180

Pemdas says multiply first

105 + 7 + 68 = 180

Combine like terms

112 + 68 = 180

180 = 180

This means the variable values are correct

The required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.

To determine the required sample size for desired confidence level and margin of error, we can use the formula for sample size calculation:

\(\[ n = \left(\frac{{Z^2 \cdot p \cdot (1-p)}}{{E^2}}\right) \]\)

Where:

\(\( n \)\) = required sample size

\(\( Z \)\) = Z-score corresponding to the desired confidence level (for 95% confidence, \(( Z = 1.96 \))\)

\(\( p \)\) = estimated proportion (0.5 can be used as a conservative estimate when the true proportion is unknown)

\(\( E \)\) = desired margin of error (5.8 percentage points)

Plugging in the values into the formula:

\(\[ n = \left(\frac{{1.96^2 \cdot 0.5 \cdot (1-0.5)}}{{0.058^2}}\right) \]\)

\(\( n \approx 385.9 \)\)

Since sample size must be a whole number, we round up to the nearest integer.

Therefore, the required sample size is approximately 386 to be 95% confident that the sample percentage is within 5.8 percentage points of the true population percentage.

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Answer:

311.2

Step-by-step explanation:

for these kind of problems its best to put it in a calculator to get a quick and accurate answer

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations, either the disk method or the shell method can be used.

When finding the volume of a solid generated by revolving a region around a line, we have two methods at our disposal: the disk method and the shell method.

1. Disk Method:

The disk method involves dividing the region into infinitesimally thin disks perpendicular to the axis of rotation. The volume of each disk can be calculated using the formula for the volume of a cylinder (V = πr^2h), where r represents the radius of the disk and h represents its height. By summing up the volumes of all the disks, we obtain the total volume of the solid.

2. Shell Method:

The shell method, on the other hand, involves dividing the region into infinitesimally thin cylindrical shells parallel to the axis of rotation. Each shell has a thickness of Δx, where x is the variable that defines the boundaries of the region. The volume of each shell is calculated by multiplying the height of the shell (given by the difference in the y-values of the two bounding curves) by the circumference of the shell (given by 2πx). By summing up the volumes of all the shells, we obtain the total volume of the solid.

Both methods yield the same result for the volume of the solid. The choice between the two methods depends on the shape of the region and the convenience of integrating with respect to either x or y.

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Answer:

Total number of stamps is 600

Number of stamps collected from Europe is 150

Number of stamps collected from America is 200

Step-by-step explanation:

1/3 of stamps collected are from America

1/4 of stamps collected are from Europe

While 250 stamps are from Africa and Asia

Now what this means is that the fraction remaining when we subtract the sum of 1/3 and 1/4 is what is equal to 250

Firstly, let’s say the total stamp is x

Now the fraction of x equal to 250 would be ;

1-1/3-1/4 = 1-(1/3 + 1/4) = 1-(7/12) = 5/12

Now, 5/12 of x = 250

5/12 * x = 250

5x = 12 * 250

5x = 3,000

x = 3,000/5

x = 600 stamps

Thus, the total number of stamps collected is 600

The number collected from America is 1/3 * 600 = 200

The number collected from Europe is 1/4 * 600 = 150

the pounds of apples you need for average price 1.84 is 3.84 pounds

what is an average and how to compute?

Average is mean value of a dataset. to compute average first add all the elements of dataset and divide it by the number of elements in the dataset.

apple costs $1.49 per pound and grapes sell for $1.75 per pound.

Also We need total 10 pounds of mixed fruit

Let the amount of apples in pounds be x and amount of grapes in pound be y

Hence, x+y=10               (1)

And the average price per pound is $1.84

Hence the price of 10 pounds is $18.4

1.49x+1.75y=18.4                (2)

Solving the equation simultaneously

x=3.84 pounds and y=6.16 pounds

Hence we will need 3.84 pounds of apples

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The probability of an event is a measure of the likelihood that the event will occur. In this case, the event is "randomly selecting a gold coin from the box."

If the probability of selecting a gold coin, denoted as P(gold coin), is 50%, it means that if you were to randomly select an item from the box, there's a 50% chance that the item you select will be a gold coin.

In other words, if you were to repeat the process of randomly selecting an item from the box many times (under the same conditions), about half of the time you would expect to draw a gold coin. This is assuming that after each draw, the item is replaced back into the box, so the conditions remain the same for each draw.

Remember that probability is a theoretical measure, and actual results can vary, especially if the number of draws is small. But as the number of draws increases, the proportion of times you draw a gold coin should get closer and closer to 50%.

This is a simplified explanation, and the actual process of conducting a two-sample t-test involves additional steps and considerations, such as checking assumptions, calculating degrees of freedom.

It's important to note that this is a simplified explanation, and the actual process of conducting a two-sample t-test involves additional steps and considerations, such as checking assumptions, calculating degrees of freedom, and interpreting the p-value associated with the test statistic.

The test statistic t is a commonly used statistic in hypothesis testing when comparing two sample means using a two-sample t-test. It measures the difference between the means of two groups relative to the variability within each group.

In the context of comparing the drinking habits of students at university 1 and university 2, the test statistic t would be calculated based on the data collected from both groups. The specific formula for calculating the t-statistic depends on the assumptions made about the data and the type of t-test being performed (e.g., equal variance assumption or unequal variance assumption).

Once the test statistic t is calculated, it is compared to a critical value from the t-distribution with degrees of freedom determined by the sample sizes of the two groups. The critical value is based on the desired level of significance (e.g., 0.05 or 0.01) and determines the cutoff point for determining whether the difference between the means is statistically significant.

If the absolute value of the calculated t-statistic is larger than the critical value, it indicates that there is significant evidence to suggest that students at one university drink more than students at the other university. On the other hand, if the t-statistic is smaller than the critical value, it suggests that there is not enough evidence to conclude a significant difference in drinking habits between the two universities.

It's important to note that this is a simplified explanation, and the actual process of conducting a two-sample t-test involves additional steps and considerations, such as checking assumptions, calculating degrees of freedom, and interpreting the p-value associated with the test statistic.

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Answer:

14/20

Step-by-step explanation:

There are 20 squares altogether and there are only 14 shaded in so it 14/20.

Answer:

Your answer is 105km travelled in 7 hours.

Step-by-step explanation:

Divide 150km by 10 to find the amount of km travelled in 1 hour. Then multiply that answer by 7.

Answer:

y = -2/7

Step-by-step explanation:

8^(y+2) = 2^4/4^(2y)

you want to on both sides so you can solve for the exponents

8= 2^3

4= 2^2

2^3y+6 = 2^4/2^(4y)

2^(3y+6) = 2^(4-4y)

3y + 6 = 4 - 4y

7y = -2

y = -2/7

The samples of size n = 2 that can be drawn from this population is 28

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

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

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

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Answer:

12 x 12 = 144

Step-by-step explanation:

12 times by 12 is 144

Answer:

If the left column is the width then the length is 45

If the right column is width then the length is 7.2

Step-by-step explanation:

ratios

This means that function of (x²+ 1) will give 1/(x²+ 1). To  get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give;

f(x) = 1/x

How do you define a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given h(x) = 1/(x²+ 1) and g(x) = x²+ 1. If h(x) = f(g(x)) then;

1/(x²+ 1) = f(x²+ 1)

f(x²+ 1) = 1/(x²+ 1)

This means that function of (x²+ 1) will give 1/(x²+ 1). To  get f(x), we will simply replace x²+ 1 in the function f(x²+ 1) with x to give output ;

f(x) = 1/x

Hence the function of x i.e f(x) is 1/x

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Answer:

Given that ,

738 students wore red while 162 students wore green.

Therefore , total number of students ,

\(\dashrightarrow \: 738 + 162 \\ \dashrightarrow \: 900\)

Now , 738 students out of 900 wore red.

So , percentage of students who wore red ,

\(\dashrightarrow \: \frac{738}{9\cancel{00}} \times \cancel{100} \\ \\ \dashrightarrow \: \cancel\frac{738}{9} \\ \\ \dashrightarrow \: 82\%\)

hope helpful :-;

Answer:

d = 2\(\sqrt{3}\)

Step-by-step explanation:

\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(3-9)^2+(6-2)^2} \\d= \sqrt{(-6)^2+(4)^2} \\d= \sqrt{(36)+(16)} \\d= \sqrt{52} \\d=2 \sqrt{13}\)

The length of the curve x = 1/3 √y (y − 3)  is 64/3.

The distance between two point along a segment of a curve is known as the arc length.

The equation of the curve is given by:

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) between point  x =a to x = b is given by:  

\(\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx\)

 √1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 * \(y^\frac{3}{2}\) - \(y^\frac{1}{2}\)

Let's find the first derivative of x.

dx/dy = 1/3. 3/2.  \(y^\frac{1}{2}\)- 1/2 .  \(y^\frac{1}{2}\)

dx/ dy = 1/2 ( \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))

(dx/dy)^2= 1/4 (  \(y^\frac{1}{2}\) - \(y^\frac{-1}{2}\))^2

= 1/4(y + \(y^-^1\)-2)

1 + {f′(x)}2 = 1 + 1/4(y +\(y^-^1\)-2)

= 1/4 y + 1/4\(y^-^1\)+ 1/2

1 + {f′(x)}2= 1/4 (y + \(y^-^1\) + 2)

√[1 + {f′(x)}2] = 1/2 (  \(y^\frac{1}{2}\) +  \(y^\frac{-1}{2}\))

Length of curve  is given by:  

25

∫   \(\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }\) dy

16

= \(\left \{ {{y=25} \atop {x=16}} \right.\) [\(y^\frac{3}{2}\)/3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

So the length of the curve is 64/3

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As per the curve the derivative of the curve and integrating it over the interval 1 <= t <= 4.

A curve is a geometric shape defined by a set of points. It can be represented mathematically by a function that maps points in space to a real number.

In this case, the curve is defined by the function r(t) = (7t², 8t², 2√2t²),for 1 <= t <= 4.

The parameter t is not an arc length parameter, as it does not represent the distance along the curve. Instead, it represents the position along the curve at a particular time.

To determine whether a curve uses arc length as a parameter, we need to calculate the arc length of the curve and compare it to the value of the parameter.

If the parameter is equal to the arc length, then the curve uses arc length as a parameter. In this case, the parameter t is not equal to the arc length of the curve, so the curve does not use arc length as a parameter.

Complete Question:

Determine whether the following curve uses arc length as a parameter. If not, find a description that uses arc length as a parameter r(t) = (7t², 8t², 2√2t²), for 1 less than or equal to t less than or equal to 4.

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If in  triangle ABC, EG = x inches and BG = (5x - 12) inches, the length of EB is 7x - 12 inches.

In triangle ABC, the centroid G is the point of intersection of the three medians AD, BE, and CF. We are given that EG = x inches and BG = (5x - 12) inches. We need to find the length of EB.

We can use the fact that the centroid G divides each median in the ratio of 2:1. Let M be the midpoint of AC, and let N be the midpoint of BC. Then, we have:

BE/EN = 2/1

Using this proportion, we can solve for EB as follows:

BE/EN = 2/1

BE/(BN + EN) = 2/1

BE/((5x - 12)/2 + x) = 2/1 (substituting BN = (5x - 12)/2 and EN = x)

BE/(7x/2 - 6) = 2/1

BE = 2(7x/2 - 6)

BE = 7x - 12

In conclusion, we can use the fact that the centroid divides each median in the ratio of 2:1 to find the length of EB in triangle ABC. We can solve for the unknown using a proportion and the lengths of the medians that pass through it.

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Complete question is:

Answer:

12

Step-by-step explanation:

i got it right

Answer:

s=16

Step-by-step explanation:

3x16=48

48/4=12

12-4=8

Mrs Morraine bought some chocolates. At first, she gave Neighbour A 60% of the The final remainder after giving to Neighbour B and taking back 50 chocolates is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50) = 410.

To solve this problem without using algebra, we can follow the given steps and keep track of the chocolates at each stage.

Step 1: Mrs Morraine initially had some chocolates (unknown number).

Step 2: She gave Neighbour A 60% of the chocolates and an additional 40 chocolates. This means Neighbour A received 60% of the chocolates, and the remaining chocolates were reduced by 40.

Step 3: Mrs Morraine then had a remainder of chocolates after giving to Neighbour A.

Step 4: She gave Neighbour B 25% of the remaining chocolates and took back 50 chocolates because Neighbour B had too many chocolates.

Step 5: Mrs Morraine was left with 410 chocolates.

Now, let's calculate the answers step by step:

Step 1: Mrs Morraine initially had some chocolates (unknown number).

Step 2: She gave Neighbour A 60% of the chocolates and an additional 40 chocolates.

Let's assume Mrs Morraine had x chocolates initially. Neighbour A received 60% of x, which is 0.6x. And the remaining chocolates reduced by 40, so we have x - (0.6x + 40) chocolates remaining.

Step 3: Mrs Morraine then had a remainder of chocolates after giving to Neighbour A.

The remainder after giving to Neighbour A is x - (0.6x + 40).

Step 4: She gave Neighbour B 25% of the remaining chocolates and took back 50 chocolates.

Neighbour B received 25% of the remainder, which is 0.25 * (x - (0.6x + 40)), and Mrs Morraine took back 50 chocolates. So, the new remainder is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50).

Step 5: Mrs Morraine was left with 410 chocolates.

The final remainder after giving to Neighbour B and taking back 50 chocolates is (x - (0.6x + 40)) - (0.25 * (x - (0.6x + 40)) + 50) = 410.

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To determine the equation of a circle, we need the coordinates of its center and the length of its radius. In this case, the center of the circle is (4, 6), and the radius is 5.

The general equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle, and r is the radius.

Using the given information, we can substitute the center coordinates (4, 6) into the equation and the radius value of 5:

\((x - 4)^2 + (y - 6)^2 = 5^2\)

Simplifying further:

\((x - 4)^2+ (y - 6)^2= 25\)

Therefore, the equation of the circle is:

\((x - 4)^2+ (y - 6)^2 = 25.\)

This equation represents all the points (x, y) that are exactly 5 units away from the center (4, 6). The squared terms (x - 4)² and (y - 6)² account for the distance between the point (x, y) and the center (4, 6). The radius squared, 25, ensures that the equation includes all the points lying on the circle with a radius of 5 units.

By substituting the given values of the center and the radius into the general equation, we obtain the specific equation of the circle.

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The standard deviation of the given discrete distribution, considering it's formula, is of 1.195.

Researching this problem on the internet, the distribution is given by:

Hence the mean is given by:

E(X) = 0.56(1) + 0.23(2) + 0.11(3) + 0.05(4) + 0.03(5) + 0.02(6) = 1.82.

The standard deviation is:

\(\sqrt{V(X)} = \sqrt{0.56(1-1.82)^2+0.23(2-1.82)^2+0.11(3-1.82)^2 + \cdots + 0.02(6-1.82)^2} = 1.195\).

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Answer:

No a triangle CAN’T have 2 obtuse angles. I dont know about the drop down menus since I can’t see the choices but there can’t be 2 obtuse angles in a triangle. I can guess two of them anyway

The second drop down one is “greater”

The last option is 180

Im not sure about he first since dropdowns aren’t presented

Valerie needs to add an additional 0.45 pounds of nuts to the scale to get the amount that she needs.

To find the number of pounds of nuts that need to be added to the scale, we need to find the difference between the amount of nuts that Valerie needs and the amount that is currently on the scale.

First, let's convert all the fractions to decimals to make the calculations easier:

3 4/5 pounds of nuts = 3 + 4/5 = 3.8 pounds

3 1/5 pounds = 3 + 1/5 = 3.2 pounds

3/20 pound = 3/20 = 0.15 pound

Now, let's subtract the weight of the container and the current amount of nuts on the scale from the amount of nuts that Valerie needs:

3.8 pounds - 0.15 pound - 3.2 pounds = 0.45 pound

This means that Valerie needs to add an additional 0.45 pounds of nuts to the scale to get the amount that she needs.

To solve the problem, we converted all the fractions to decimals and subtracted the weight of the container and the current amount of nuts on the scale from the amount of nuts that Valerie needs.

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Answer:

4.69 in

Step-by-step explanation:

By sine rule:

\( \frac{ \sin \: 23 \degree}{a} = \frac{ \sin \: 90 \degree}{12} \\ \\ \frac{ \sin \: 23 \degree}{a} = \frac{1}{12} \\ \\ a = 12 \: \sin 23 \degree \\ \\ a = 12 \times 0.3907311285 \\ \\ a = 4.68877354 \\ \\ a \approx 4.69\: in\)

Answer:

a1 = 3

a2 = 3 + 2 = 5

a3 = 5 + 2 = 7

a4 = 7 + 2 = 9