What is the missing length of this rectangle?

Answer:

Mario's heart beats 112 times per minute.

To find out, we can use the following equation:

Heart rate = number of beats / time

Since we're given that Mario's heart beats 28 times in 1/4 minute, we can set up the equation like this:

Heart rate = 28 / 1/4

To divide by a fraction, we can multiply by its reciprocal:

Heart rate = 28 x 4/1

Heart rate = 112

Therefore, Mario's heart rate is 112 beats per minute.

Answer:

y = -6/5x + 36/5  (3rd choice down)

Step-by-step explanation:

Find the slope of the line by choosing 2 points ON THE LINE:  (1,6) and (6,0)

slope = m = Δy/Δx = (0-6) / (6-1) = -6/5

Now use the point (1,6) in the point-intercept form to find b, the y-intercept:

(y-y1) = m(x-x1)

y - 6 = -6/5(x - 1)

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

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

y = -6/5x + 36/5

quick answer:  the line slants down, therefore it has a negative slope;  the only choice with a negative slope is the 3rd one down

Based on the calculations, the rate of change for the function is equal to 5.

Mathematically, the rate of change for the function can be calculated by using this expression;

Rate of change = [½ ÷ ⅒]/[0 - (-1)]

Rate of change = 5/1

Rate of change = 5.

Rate of change = [5/2 ÷ ½]/[1 - 0]

Rate of change = 5/1

Rate of change = 5.

Rate of change = [125/2 ÷ 25/2]/[3 - 2]

Rate of change = 5/1

Rate of change = 5.

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An estimate of the observed value for y for x = 3.5 is 14.866. We rounded our answer to three decimal places, as instructed. It's worth noting that the regression line equation gives us a predicted value of y for any given value of x, based on the relationship between the two variables in the sample data.

To find an estimate of an observed value for y for x = 3.5, we can use the estimated regression line equation y = -5.399 + 5.790x. Plugging in x = 3.5, we get:
y = -5.399 + 5.790(3.5)
y = -5.399 + 20.265
y = 14.866
Therefore, an estimate of the observed value for y for x = 3.5 is 14.866. We rounded our answer to three decimal places, as instructed. It's worth noting that the regression line equation gives us a predicted value of y for any given value of x, based on the relationship between the two variables in the sample data. However, this predicted value may not be exactly equal to the actual observed value of y for that value of x, since there is always some level of variability and uncertainty in the data.

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a) the probability that someone's favorite activity is snowboarding given that they like winter is 0.286. This is option A

b) the probability that someone's favorite activity is sledding given that they don't like winter is 0.214. This is option C

a) Probability that someone's favorite activity is snowboarding given that they like winter

To find the probability that someone's favorite activity is snowboarding given that they like winter, we need to use conditional probability formula:

P(Snowboarding|Like winter) = P(Snowboarding and Like winter) / P(Like winter)

P(Snowboarding|Like winter) = 28/ (55 + 28 + 15)= 28/98= 0.2857 ≈ 0.286.

Therefore, the probability that someone's favorite activity is snowboarding given that they like winter is 0.286.

b) Probability that someone's favorite activity is sledding given that they don't like winter

To find the probability that someone's favorite activity is sledding given that they don't like winter, we need to use conditional probability formula:

P(Sledding|Don't like winter) = P(Sledding and Don't like winter) / P(Don't like winter)

P(Sledding|Don't like winter) = 15/ (33 + 22 + 15)= 15/70= 0.2142 ≈ 0.214

Therefore, the probability that someone's favorite activity is sledding given that they don't like winter is 0.214.

Hence, the answer are A and C respectively.

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The radius of the cylinder for maximum volume is r = 10/π

Given data:

To find the radius of the right circular cylinder with maximum volume among all cylinders for which the sum of the height and circumference is 30 centimeters, use optimization techniques.

Let's denote the radius of the cylinder as r (in centimeters) and the height as h (in centimeters). The sum of the height and circumference is given as 30 centimeters:

h + 2πr = 30

From this equation, express the height in terms of the radius:

h = 30 - 2πr

Now, the volume V of a cylinder is given by the formula:

\(V = \pi r^2h\)

Substituting the expression for h:

\(V = \pi r^2(30 - 2 \pi r)\)

Expanding and simplifying:

\(V = 30 \pi r^2 - 2 \pi ^2r^3\)

To find the radius that maximizes the volume, find the critical points by taking the derivative of V with respect to r and setting it equal to zero:

\(\frac{dV}{dr} = 60\pi r - 6\pi^2r^2\)

Setting \(\frac{dV}{dr}\)  equal to zero and solving for r:

\(60\pir - 6\pi^2r^2 = 0\)

Dividing both sides by 6πr:

10 - πr = 0

πr = 10

r = 10/π

Hence, the radius of the right circular cylinder with maximum volume, given the constraint that the sum of the height and circumference is 30 centimeters, is 10/π centimeters.

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Answer:

3

Step-by-step explanation:

sin30=x/6

SOH CAH TOA

then reorganize and it is 6 (sin 30)= 3

As I cannot help you do your assignment since you didn't upload the questions, I can just give you the instructions.

I believe you are supposed to open the Student Guide that your cursor is hovering over (the boxed line in the picture) and then solve the problems (or do) the stuff inside. Then, you take a picture of your work/answers and upload that to the File Upload below.

The value of P(4<X≤12) is 0.45

The complete question is added as an attachment

To calculate P(4<X≤12), we use the following equation

P(4<X≤12) = P(4<X≤8) + P(8<X≤12)

From the histogram, we have:

P(4<X≤8) = 0.1

P(8<X≤12) = 0.35

So, we have:

P(4<X≤12) = 0.1 + 0.35

Evaluate

P(4<X≤12) = 0.45

Hence, the value of P(4<X≤12) is 0.45

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The bird is 25.23 feet away from Amanda and Jamie.

Given that:

Point A is Amanda's Position.

Point B is Jamie's position.

and Point C is Bird's position.

Thus,

C is the standing of Amanda and Jamie.

So, A = 55°

      B = 63°

and C = 25 feet.

Since, the sum of the angle measure of a Triangle.

Therefore,

    A +B +C = 180°

⇒  55° + 63° +C = 180°

⇒ 118° + C = 180°

⇒ C = 62°

Now,

By the Law of Sines:

     \(\frac{Sin\beta }{b} = \frac{Sin\alpha }{c}\)

⇒ C sin β = b sinα

⇒ b = c sinβ/ sinα

⇒ b = 25.23

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Answer:

90°

Step-by-step explanation:

\(10 + 3 + 7 = 20 \\ \frac{20}{20} = 180 \\ \frac{1}{20} = \frac{180}{20} \\ \frac{10}{20} = \frac{180}{20} \\ the \: largest \: angle = 90 \\ \)

Answer:

Step-by-step explanation:

a) 6305/65= 97

b) 94+94= 188

   306-188= 118

Answer:

a. 87 b. 59

Step-by-step explanation:

typing bc I need to have 20 letters

Answer:

149

Step-by-step explanation:

JUST TOOK TEST

Answer:

149

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

yes, the board is long enough

Step-by-step explanation:

5.5 in x 4 walls = 22 inches

The board is 24.5 in, so there is enough.

24.5 > 22, there is an extra 2.5 in left over.

Answer:

11 a.m

Step-by-step explanation:

The LCM of (30, 40) would be 120

So divide it by how many minutes in a hour to get 2 hours

so 2 plus 9 to get 11

The explanation of the cost of a sample college would be the fact that fees such as tuition would be paid, other essentials that are necessary for the learning and development of the student such as books are also needed.

Given that a state college cost yearly includes:

Therefore, assuming that a community college cost would be less than the cost of a state college:

Hence, to find the sample community college costs after 2 years would be $95,000.

The sample state college costs after 4 years would be $238,136.

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The critical value for this two-tailed test is 2.6759.

To conduct a two-tailed test at the 0.01 level of significance with a sample of 55 observations, we use the t-distribution because the population standard deviation is unknown. The critical value is determined by dividing the significance level (0.01) by 2 to account for both tails of the distribution. This gives an alpha level of 0.005. Using the degrees of freedom for a sample of size 55 (54 degrees of freedom), we find the corresponding critical value from a t-distribution table or calculator. In this case, the critical value is approximately 2.6759 when rounded to four decimal places.Since the population standard deviation is unknown, we'll use the t-distribution instead of the standard normal distribution. The degrees of freedom for a sample of size 55 is 54. Using a t-distribution table or a statistical calculator, the critical value for an alpha level of 0.005 and 54 degrees of freedom is approximately 2.6759 (rounded to four decimal places).

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9514 1404 393

Answer:

  499 1/3 miles

Step-by-step explanation:

Let m represent the number of miles the car can travel on 14 gallons. We assume distance is proportional to gas usage, so ...

  m/14 = 107/3

Multiplying by 14, we have ...

  m = 14(107/3) = 1498/3 = 499 1/3

The car can travel 499 1/3 miles on a full tank of gas.

Answer:

10

Step-by-step explanation:

The highest exponent determines the degree of a polynomial.

Answer:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

(x+13)²+(y-9)²=36you can write this equation too

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

(x-1)²+(y+1)²=121

you can write this equation too

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

3.

centre (h,k)=(3,1)

radius (r)=4units.

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-3)²+(y-1)²=4²

(x-3)²+(y-1)²=16 is a required equation.

4.

centre(h,k)=(4,-2)

radius (r)=3

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-4)²+(y+2)²=3²

(x-4)²+(y+2)²=9

you can write this equation too

Answer:

Whatever he just answered

Step-by-step explanation:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

(x+13)²+(y-9)²=36you can write this equation too

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

(x-1)²+(y+1)²=121

you can write this equation too

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

3.

centre (h,k)=(3,1)

radius (r)=4units.

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-3)²+(y-1)²=4²

(x-3)²+(y-1)²=16 is a required equation.

4.

centre(h,k)=(4,-2)

radius (r)=3

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-4)²+(y+2)²=3²

(x-4)²+(y+2)²=9

you can write this equation too

Answer:  Choice A

s = 10k + 6(5)

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

Reason:

k = number of adults

10k = cost for all the adults (at $10 per ticket)

5 = number of children

6(5) = cost for all the children ($6 per ticket)

10k + 6(5) = total cost for all adults and children

s = total cost in dollars

s = 10k+6(5)

The equation of the parallel lines will be y = 0.8x and y = 0.8x - 3.2.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The intercepts of the line are (0, -3.2) and (4, 0). Then the equation of the line is given as,

y + 3.2 = [(0 + 3.2) / (4 - 0)](x - 0)

y = 0.8x - 3.2

The equation of the other parallel line that passes through the origin will be given as,

y = 0.8x

The equation of the parallel lines will be y = 0.8x and y = 0.8x - 3.2.

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Answer:

90, 86, and 92 are three options

Step-by-step explanation:

Step-by-step explanation:

\( {x}^{2} - 12x + 36 = 90 \\ {x}^{2} - 12x - 54 = 0 \\\)

Let a=1, b=-12, c=-54

Use formula

\( \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \)

You will get

\(x = 6 + 3 \sqrt{10} \\ x = 15.48683298 \\ or \\ x = 6 - 3 \sqrt{10} \\ x = - 3.48683298\)

Answer:

x = 6 + 3\(\sqrt{10}\)

Step-by-step explanation:

if you 'un-foil' the equation \(x^{2}\) - 12x + 36 = 90 you will get the following:

(x - 6)^2 = 90

take the square root of each side and you will get the following:

x - 6 = \(\sqrt{90}\)

Add 6 to each side

x = 6 + \(\sqrt{90}\)

simplify \(\sqrt{90}\) to be \(\sqrt{9}\) x \(\sqrt{10}\)  which equals 3 \(\sqrt{10}\)

Final answer:  6 + 3\(\sqrt{10}\)

The measure of variation is the average distance between each data entry and the mean of the data set is mean absolute value deviation. Option D

The mean absolute deviation of a dataset is simply described as the average distance that exists between each given data point and the absolute mean.

This value gives us information about the variability in a dataset.

The steps in determining the value is;

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Answer:

-13/20

Step-by-step explanation:

-0.65=-65/100

=13/20