Which is the area of a square with one side that measures 1 foot?

A) 1 square inch
B) 100 square inches
C) 144 square inches
D) none of the above

Step-by-step explanation:

V∝I

V=kI

36=k*8

k=36/8

k=4.5

a. V=4.5I

b. V=4.5*14

V= 63

c. 27=4.5I

I=27/4.5

I= 6

Answer:

P(A∪B) = 1/3

Step-by-step explanation:

Red  Garments = 1 red shirt + 1 red hat  + 1 red pairs of pants

Total Red Garments = 3

Green Garments =  1 green shirt + 1 green scarf + 1 green pairs of pants

Total Green Garments = 3

The total number of garments =  Total Red Garments + Total Green Garments:

3 + 3 = 6

Let A be the event that he selects a green garment

P(A) = Number of required outcomes/Total number of possible outcomes

P(A) =  3/6

Let B be the  event that he chooses a scarf

P(B) = 1/6

The objective here is to determine P(A or B) = P(A∪B)

Using the  probability set notation theory:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∩B) = Probability that a green pair of pant is chosen = P(A) - P(B)

= 3/6-1/6

= 2/6

P(A∪B) = 1/2 + 1/6 - 2/6

P(A∪B) = 2/6

P(A∪B) = 1/3

Answer:

in the khan academy answer is both A and B are dependent on each other.

Step-by-step explanation:

√(7^2) + (9^2)

=√(49) + (81)

=√(130)

=11.401754251

Answer:

a.

Probability of Diet Cola = 19/28

Probability of Lemonade = 4/28

Probability of Root Beer = 5/28

b. Theoretical Probability

Step-by-step explanation:

Given

Diet Cola = 19

Lemonade = 4

Root Beer = 5

Required

Probability the her next drink will be

- Diet Cola

- Lemonade

- Root beer

To calculate the probability of each of the above, first we need to calculate the total number of drinks she's had

Total = Diet Cola + Lemonade + Root Beer

Total = 19 + 4 + 5

Total = 28

The probability that her next drink can be any of the above can then be calculated.

This is calculated by dividing each outcome by the total; as follows;

Probability of Diet Cola = 19/28

Probability of Lemonade = 4/28

Probability of Root Beer = 5/28

This type of probability is referred to as theoretical probability because it makes predictions base on previous occurrence of events.

Answer:

166.67 in³

Step-by-step explanation:

If the top of the pyramid is at half of the height of 10 cm tall cube, the height of the pyramid (h) is 5 inches.

Assuming that the base of the pyramid is the same as the base of the cube, the volume of the square pyramid is given by:

[tex]V=\frac{1}{3}*B*h[/tex]

Where B is the area of the square base:

[tex]V=\frac{1}{3}*(10*10)*5\\ V=166.67\ in^3[/tex]

The volume of the square pyramid inside the cube is 166.67 in³.

Answer:

The retained earnings decreased by $1,020,600

Step-by-step explanation:

Given that Rayan Company has 420,000 shares of $ 10 par. Rayan then declared a 5% share dividend when the market price of the shares was $36 per share.

Let's calculate the shares issued as stock dividends below:

Issued shares = stock dividends * outstanding shares

= 5% * 420,000

= 21,000

21,000 shares were issued.

Let's calculate the stock dividends.

Stock dividends = issued shares * market price per share

= 21,000 * $36

= $756,000

Stock dividends is $756,000

Let's calculate the amount of cash dividends, since the company declared a $0.60 per share cash dividend after 3 months. We have:

Cash dividend = cash dividend per share * new number of shares.

= $0.60 * (420,000 + 21,000)

= $0.60 * 441,000

= $264,600

Cash dividends paid is $264,600

The find the decrease in retained earnings, we have:

Decrease in Retained earnings = cost of stock dividend + cash dividend.

= $756,000 + $264,600

= $1,020,600

Therefore, the retained earnings decreased by $1,020,600

Answer:

v = 18

Step-by-step explanation:

3v-9=45

Add 9 to each side

3v-9+9=45+9

3v = 54

Divide each side by 3

3v/3 = 54/3

v =18

Answer:

Step-by-step explanation:

Answer:

g(-9) = 1

Step-by-step explanation:

g(-9) is the value of the function at x = -9

Go over the x = -9 and go up until you hit the blue line

Read the value of y

g(-9) = 1

An outside angle is equal to the sum of the two opposite inside angles.

122 = x + 24

X = 122 - 24

X = 98 degrees

Answer:

[tex] y =mx +b[/tex]

Where m is the slope and b the intercept.

Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:

[tex] y =5.5 x+ 10[/tex]

Wher y is the total cost and x the hours rented

Step-by-step explanation:

For this case we want to model the situation with a general equation given by:

[tex] y =mx +b[/tex]

Where m is the slope and b the intercept.

Using the information given the variable cost 5.5 per hour represent the slope and the fixed cost 10 represent the value of b and then our model would be given by:

[tex] y =5.5 x+ 10[/tex]

Wher y is the total cost and x the hours rented

Answer:

7098

Step-by-step explanation:

For this we need to identify the area of the garden entirely and subtract the area of the parallelogram getting our land of grass.

1) 65*110=7150

2) 13*4=52

3) 7150-52=7098

What's the question asking? 12a+15(18)?

Answer:

the answer is 3

Step-by-step explanation:

Answer:

  D. g(x) = f(x) - 5

Step-by-step explanation:

To move the intercept to -2, one needs to translate the function down by 5 or left by 5. The first translation (down 5) would result in ...

  g(x) = f(x) - 5 . . . . . . matches choice D

The second translation (left 5) would result in ...

  g(x) = f(x+5) . . . . doesn't match any available choice

Answer: g(x) = f(x) - 5

Step-by-step explanation:

just took this

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: pulse rate of a female adult. (beats/min)

Mean X[bar]= 74.0 beats/min

Standard deviation S= 12.5 beats/min

The lowest pulse rate is 36 beats/min

a)

The difference between the lowest pulse rate and the mean pulse for females is: 36 - 74= -38 beats/min

b)

To calculate how many standard deviations a value of the variable is from the mean, you have to subtract the mean from it and divide by the standard deviation:

(X-X[bar])/S= (36-74)/12.5= -3.04

The minimum pulse for female adults is -3.04 standard deviations away from the mean.

c)

The z score for 36 beats/min is -3.04

Considering the region of acceptance (-2; 2), the calculated value is below its lower limit, so you can conclude that the pulse rate 36 beats/min is significantly low.

I hope this helps!

Answer:

I'm assuming that the range means the smallest number to largest number which will be 10 to 54

Step-by-step explanation:

Let x represent 1st number, y represent 2nd number and z represent 3rd number

rest of the working is in the picture attached. hope you understand it!

Answer:

$70.00 +/- $4.43

= ( $65.57, $74.43)

Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Sample Mean x = $70.00

Standard deviation r = $17.50

Number of samples n = 60

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

$70.00+/-1.96($17.50/√60)

$70.00+/-1.96($2.259240285287)

$70.00+/-$4.428110959163

$70.00+/-$4.43

= ( $65.57, $74.43)

Therefore at 95% confidence interval (a,b) = ( $65.57, $74.43)

Answer:

The product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex] is [tex]\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex].

Step-by-step explanation:

A matrix is a rectangular arrangement of numbers into rows and columns.

Matrix multiplication refers to the product of two matrices.

The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one.

To find the product of [tex]\begin{pmatrix}3&-5\\ \:1&7\end{pmatrix}\begin{pmatrix}4&2\\ \:-4&2\end{pmatrix}[/tex]

[tex]\mathrm{Multiply\:the\:rows\:of\:the\:first\:matrix\:by\:the\:columns\:of\:the\:second\:matrix}\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=3\cdot \:4+\left(-5\right)\left(-4\right)\\\\\begin{pmatrix}3&-5\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=3\cdot \:2+\left(-5\right)\cdot \:2\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}4\\ -4\end{pmatrix}=1\cdot \:4+7\left(-4\right)\\\\\begin{pmatrix}1&7\end{pmatrix}\begin{pmatrix}2\\ 2\end{pmatrix}=1\cdot \:2+7\cdot \:2[/tex]

[tex]\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}3\cdot \:4+\left(-5\right)\left(-4\right)&3\cdot \:2+\left(-5\right)\cdot \:2\\ 1\cdot \:4+7\left(-4\right)&1\cdot \:2+7\cdot \:2\end{pmatrix}[/tex]

[tex]\mathrm{Simplify\:each\:element}\\\\\begin{pmatrix}3&-5\\ 1&7\end{pmatrix}\begin{pmatrix}4&2\\ -4&2\end{pmatrix}=\begin{pmatrix}32&-4\\ -24&16\end{pmatrix}[/tex]

Answer:

x = 1 and y = 1

Step-by-step explanation:

7(1) minus 3(1) = 4

and 2(1) minus 1 = 1

just try and guess a number and try to solve the problem with that number, if it isn't the answer then repeat.

Answer: Use the app: photomath

Step-by-step explanation:

Answer:

B and C.

Step-by-step explanation:

just divide going all the way down starting from the number 4th spot. and if you get the same number each time, its exponential

Answer:

b) 9

Step-by-step explanation:

9 squared + 40 squared = 41 squared, which follows Pythagorean theorem.

The triangle is missing, so i have attached it.

Answer:

1)sin(α) = 4/7

2)cos(β) = 4/7

3)tan(α) = 4/√33

4)cot(β) = 4/√33

5)sec(α) = 7/√33

6)csc(β) = 7/√33

Step-by-step explanation:

(1) sin(α)

From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.

Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7

2) cos(β)

Cosine of an angle = adjacent side/hypotenuse.

In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7

3)tan(α)

tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.

Using the pythagoras theorem,

Adjacent side = √(7² - 4²)

Adjacent side = √(49 - 16)

Adjacent side = √33.

Thus, tan(α) = 4/√33

4) cot(β)

cot of an angle is the reciprocal of tangent of same angle.

The adjacent side to β is 4 while the opposite is √33.

So, tan(β) = (√33)/4

cot(β) = 1/tan(β)

cot(β) = 1/[(√33)/4]

cot(β) = 4/√33

5)sec(α)

sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.

Thus, sec(α) = 1/cosα = 7/√33.

6) csc(β)

Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.

Thus, csc(β) = 1/sin(β) = 7/√33

Answer:

(3,2)

Step-by-step explanation:

The solution of lines on a coordinate plane is its intersection point. In this case its (3,2)

Answer:

[tex]k=\frac{-cp+4r}{p}[/tex]

Step-by-step explanation:

[tex]r=p/4(c+k)[/tex]

[tex]\frac{r}{p/4} =c+k[/tex]

[tex]\frac{r}{p/4} -c=k[/tex]

[tex]-cp+4r=kp[/tex]

[tex]\frac{-cp+4r}{p} =k[/tex]

Answer:I believe it's C

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order for a line to have no y-intercept, it must be parallel to the y-axis. Its equation will be of the form ...

  x = constant.

If the x-intercept is (3, 0), then we must have constant = 3.

__

In order for a line to have no x-intercept, it must be parallel to the x-axis. Its equation will be of the form ...

  y = constant.

If the y-intercept is (0, -4), then we must have constant = -4.

__

The equation of line m is x = 3.

The equation of line n is y = -4.

the one that has 65 and 54, 3rd one

Answer:

Triangle three(bottom left corner)

Step-by-step explanation:

We know one angle must be 61, as it is given. The other angle can be found by subtracting 126 from 180.

So 180-126 = 54

So the two angles we are looking for are 61 and 54.

However none of the triangles have that those numbers, so we must find the third side. Using that the sum of the angles must be 180,

180-61-54 = 65

So the third angles must be 65

So now we look for the triangle that has 2 of the following: 65, 54, 61

Triangle 3 fits this.

Answer:

Range = {5, 8, 11}

Step-by-step explanation:

On the function f(x) = 3x + 2

For the first domain, when x = 1, f(x) = 3(1) + 2 = 3 + 2 = 5

For the second, when x = 2, f(x) = 3(2) + 2 = 6 + 2 = 8

For the third domain, when x = 3, f(x) = 3(3) + 2 = 9 + 2 = 11

Answer: B

Step-by-step explanation:

To find the answer, you add the two equations together

Answer:

A. x - 3

Step-by-step explanation:

Set it up like this:

(3x - 2) - (2x + 1)

Combine like terms:

3x - 2 - 2x - 1

3x - 2x = x

-2 - 1 = -3

Put it together:

x - 3