One angle of a right triangle measures 51 degrees. What is the measure of the other small angle?

Answer:

radius=7

diameter =2×radius

d=2×7

diameter=14

Answer:

Hello!

The answer is-

Radius: 7

Diameter: 14

Step-by-step explanation:

Diameter:

2*(radius)

d=2(7)

Diameter is 14

Step-by-step explanation:

work is shown and pictured

[tex]g(x)=4(x+1)-2[/tex]

[tex]g(x)=4x+4-2[/tex]

[tex]g(x)=4x+2[/tex]

Image attached below for graph.

Step-by-step explanation:

Hope this helps

Hope this is correct

Answer:

F = 95°

Step-by-step explanation:

[tex]C=\frac{5}{9}(F-32)[/tex] is the formula to convert Fahrenheit to Celsius

If we have C = 35, we just need to plug in this number to its corresponding variable and then solve for F

Answer:

work is shown and pictured

Answer: x<3

Step-by-step explanation:

Answer: 8.059

Explanation: It's the digit times the column heading.

Answer:

-The total area of a Rectangular Prism:

[tex]A = 366[/tex] [tex]in^{2}[/tex]

Step-by-step explanation:

-To find the total area of a rectangular prism, you need this formula:

[tex]A = 2(l \cdot w + l \cdot h + w \cdot h)[/tex]

[tex]l =[/tex] Length

[tex]w =[/tex] Width

[tex]h =[/tex] Height

-Apply the length, width and height for the formula:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]l =[/tex] 11 in

[tex]w =[/tex] 8 in

[tex]h =[/tex] 5 in

-Then, solve for the area:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]A = 2(88 + 55 + 40)[/tex]

[tex]A = 2(143 + 40)[/tex]

[tex]A = 2 \times 183[/tex]

[tex]A = 366[/tex]

So, the total area would be [tex]366[/tex] [tex]in ^{2}[/tex].

Answer:

A rectangle is a 2 dimensional figure, it is in a plane, so it has two faces, and yes, they are equals.

Answer:

[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]

And we can use the probability mass function and we got:

[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]

And replacing we got:

[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]

Step-by-step explanation:

Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:  

[tex]X \sim Binom(n=4, p=0.72)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X \geq 1)[/tex]

And we can use the complement rule and we got:

[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]

And we can use the probability mass function and we got:

[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]

And replacing we got:

[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]

Answer:

a. 65  seats

b. $422.50

Step-by-step explanation:

We have the following two functions:

8 * x, {0 <= x <= 50}

x * (8 - 0.1 * (x - 50)), {x> 50}, solving we have:

-0.1 * x ^ 2 + 13 * x, {x> 50}

Now we derive both functions and we are left with:

8, {0 <= x <= 50}

-0.2 * x + 13 {x> 50}

we cannot equal to 0 the first function that is equal to 0, because it would be inconsistent, therefore we equal the second function to 0:

-0.2 * x + 13 = 0

0.2 * x = - 13

x = -13 / -0.2

x = 65

Now, test for increasing and decreasing on the intervals (0.65) and (65, infinity)

p '(60) = -0.2 * (60) + 13 = 1

since this value is positive the profit is increasing on (0.65)

p '(70) = -0.2 * (70) + 13 = -1

becuase this value is negative the profit is decreasing on (65, infinity)

Therefore 65 seats are needed to maximize profit

The maximum value would be:

P (65) = 0.1 * (65 ^ 2) + 13 * 65 = 422.5

That is, the maximum value is $ 422.50

Answer:

(0,2)

Step-by-step explanation:

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)

Answer:

A. Only the mode makes sense since the data is nominal.

Step-by-step explanation:

Hello!

The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.

The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.

Possible values of Phenotype codes:

1= smooth-yellow

2= smooth-green

3= wrinkled-yellow

4= wrinkled-green

The absolute frequencies for each phenotype are:

f(1)= 3

f(2)= 4

f(3)= 6

f(4)= 1

n= 14

a) Mean:

X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36

The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.

b) Median:

To determine the value that corresponds to the median you have to calculate its position:

For even samples the position is:

PosMe= n/2= 14/2= 7

Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.

Me= 2= smooth-green.

c) Mode:

The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow

Md= 3= wrinkled-yellow

d) Midrange: (1 + 4)/2= 2.5

e)

As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.

I hope this helps!

John's average on all three tests, assuming a score of S on the third test, would be

(82 + 98 + S)/3

He wants the average to be at least 88, so solve the inequality:

(82 + 98 + S)/3 ≥ 88

82 + 98 + S ≥ 264

180 + S ≥ 264

S ≥ 84

So John needs to obtain a grade of at least 84 on the third test to get the average he wants.

The score on his third test is 84 so that his average is at least 88 given first two grades 82 and 98. This can be obtained by using the formula to find average.

Average of observations is the ratio of sum of observations to total number of observations.

Grade of first test=82

Grade of second test = 98

let grade of third test be x

Average of the grades = [tex]\frac{82+98+x}{3}[/tex] ≥ 88

[tex]\frac{180+x}{3}[/tex] ≥ 88 ⇒ x ≥ 246-180 ⇒ x ≥ 84

Hence we can say that the score on his third test is 84 so that his average is at least 88 given first two grades 82 and 98.

Learn more about averages here:

brainly.com/question/19004665

#SPJ2

Answer:

rounded to 3 decimal places ...

Step-by-step explanation:

The function can be put into vertex form:

  h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2

  h(t) ≈ -4.92(t -1.79776)^2 +590.90122

The value of h(t) is zero for ...

  t = √(590.90122/4.92) +1.79776 ≈ 12.75686

For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...

  0 ≤ t ≤ 12.75686

The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.

The range is 0 ≤ h(t) ≤ 590.90122.

_____

Alternate interpretation of the question

The function h(t) is defined for all values of t, so that could be considered the domain.

The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.

Answer:

a) 6

b) 10

Step-by-step explanation:

a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.

b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!

Answer:

First we need to calculate 1 part.

Calculate big part first

13*15 = 195

7*12 = 84

195+84=279

279

279 is answer

Answer: 279 yd^2

Step-by-step explanation:

Separate this into two separate rectangles: the larger top rectangle (13 yd x 15 yd) and the smaller bottom rectangle (12 yd x 7 yd).

area of rectangle 1 + area of rectangle 2 = total area of figure

b1(h1) + b2(h2) = total area

13(15) + 7(12) = total area

195 + 84 = total area

279 yd^2 = total area

Answer:

a. [tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c.  the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e.  86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability  density function can now be determined as :

[tex]f_X(x) = \dfrac{1}{B-A}A<x<B[/tex]

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x) = \dfrac{1}{12-8.5}8.5<x<12[/tex]

[tex]f_X(x) = \dfrac{1}{3.5}8.5<x<12[/tex]

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

[tex]F(x) = \dfrac{x-A}{B-A}[/tex]

[tex]F(10) = \dfrac{10-8.5}{12-8.5}[/tex]

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

[tex]P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (12-11)[/tex]

[tex]P(X\geq11) = {\dfrac{1}{3.5}} (1)[/tex]

[tex]P(X\geq11) = 0.2857[/tex]

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

[tex]P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)[/tex]

[tex]P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.2857* (2)[/tex]

[tex]P(9.5 \leq X\leq11.5) =0.5714[/tex]

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

[tex]P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)[/tex]

[tex]P(X \geq 9) = {\dfrac{1}{3.5}}(3)[/tex]

[tex]P(X \geq 9) = 0.2857*}(3)[/tex]

[tex]P(X \geq 9) = 0.8571[/tex]

NOW; The Number of iPad  that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

Answer:

16

Step-by-step explanation:

We can find x using tan 40° which can be represented as x/20. tan 40° is also equal to about 0.8 so that means x / 20 = 0.8 and x = 16.

Answer:

2

Step-by-step explanation:

the vertical axis would be h, the plant's height, and the horizontal axis would be m, the number of months. This would make statement 2 the only valid statement.

statement 1: Incorrect, as the vertical axis is the height

statement 2: correct, as h depends on m

statement 3: incorrect, as the domain is the horizontal and represents the number of months

statement 4: incorrect, as h = f(m)

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

Answer:

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Step-by-step explanation:

We have the standard deviation for the population, so we can use the normal distribution. If we had the standard deviation for the sample, we would have to use the t-distribution.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.8}{2} = 0.1[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.5 = 0.9[/tex], so [tex]z = 1.282[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.282*\frac{6}{\sqrt{21}} = 1.68[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 30 - 1.68 = 28.32 characters.

The upper end of the interval is the sample mean added to M. So it is 30 + 1.68 = 31.68 characters.

The 80% confidence interval for the population mean is between 28.32 characters and 31.68 characters.

Answer:

Step-by-step explanation:

2(f^4)^2/8(f^12)

2/8= 1/4

f^16/f^12

f^(16-12)= f^4

f^4/4 is the solution

Answer:

P = 62.5 %

Step-by-step explanation:

Of means multiply and is means equals

P * 48  = 30

Divide each side by 48

P = 30/48

P = .625

Change to percent form

P = 62.5 %

Answer:

62.5%

Step-by-step explanation:

30 is 62.5% of 48 since:

30÷48=0.625

0.625×100=62.5%

Answer:

Option D.

Step-by-step explanation:

If a line passing through two points, then the equation of line is

[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It is given that  Line f(x) passes through points (-4, 0) and (-3, 1).  So, equation of line f(x) is

[tex](y-0)=\dfrac{1-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=1(x+4)[/tex]

So, function f(x) is

[tex]f(x)=(x+4)[/tex]    ...(1)

Line g(x) passes through points (-4, 0) and (-3, -3).  So, equation of line f(x) is

[tex](y-0)=\dfrac{-3-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=-3(x+4)[/tex]

So, function g(x) is

[tex]g(x)=-3(x+4)[/tex]    ...(2)

Using (1) and (2), we get

[tex]g(x)=-3f(x)[/tex]    ...(3)

It is given that

[tex]g(x)=kf(x)[/tex]     ...(4)

On comparing (3) and (4), we get

[tex]k=-3[/tex]

Therefore, the correct option is D.

Answer:

The selection probability to be assigned to each of the package designs is 0.20

Step-by-step explanation:

Firstly, we need to assume that one design is just as likely to be selected by a consumer as any other design

so the probability of selecting any of the design is same and that is 1/5 = 0.20

Thus, what we are trying to say is that each of the package designs have an equal selection probability of 0.20

Answer:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Class width = 12.375

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Step-by-step explanation:

The first option is correct.

Parameter because the value is a numerical measurement describing a characteristic of population.

Parameter is a measure that describes the entire population.

Statistic basically describes a sample of the population.

From the given information , the entire 1700 professors at a college is the population and only  35 % own a television is a characteristic, called parameter, of population.

Another objective we are to find here is:

Use the given minimum and maximum data entries, and the number of classes, to find the class width, .

Class width = Maximum - Minimum /No of classes

Given that :

Maximum = 120

Minimum = 21

number of classes = 8

Then;

Class width = 120 - 21 /8

Class width = 12.375

From the given information :

B. 21.34, 47, 60, 73, 86, 99. 112 is the lower class limit

Answer:

To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 93, \sigma = 16[/tex]

How fast does a man have to run to be in the top 1% of runners?

The lower the time, the faster they are. So the man has to be at most in the 1st percentile, which is X when Z has a pvalue of 0.01. So he has to run in at most X seconds, and X is found when Z = -2.327. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.327 = \frac{X - 93}{16}[/tex]

[tex]X - 93 = -2.327*16[/tex]

[tex]X = 55.768[/tex]

To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.

Answer:

Step-by-step explanation:

Hello!

The statistical model predicts the appraised value of houses in a section of the county East Meadow (Y) in relationship with the number of rooms of the house (X)

For a sample of n=64 houses the simple linear regression was estimated:

^Y= 74.80 + 24.93X

Range of X: 5 - 11

Range of Y: 160 - 300 ($ thousands of dollars)

Interpretation of the estimates of the y-intercept and the slope

y-intercept:

74.80 thousand dollars is the estimated average value of a house in a section of the county East Meadow when the house has zero rooms.

Slope:

24.93 [tex]\frac{thousand dollars}{rooms}[/tex] is the modification of the estimated average value of a house in a section of the county East Meadow when the number of rooms increases on one.

I hope this helps!

Answer:

1. Experimental

2. Correlational

3. Experimental.

Step-by-step explanation:

1. Experimental.

Researches are interested on finding the effects of music on a test.

2. Correlational

Researchers are interested on finding the correlation of the gender and cognition from different samples

3. Experimental

The Researcher wants to know the effects of bedroom light.

Answer: the answer is linear pair

Step-by-step explanation:

Answer:

Linear pair postulate

Step-by-step explanation: