1.
The ratio of width to length of Jerry's poster is 2 ft:4 ft. If the width of the poster is reduced to
6 inches, what is it's length?
A.
1 in
0.1 in
C. 12 in
D. 24 in

Step-by-step explanation:

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Step-by-step explanation:

Hope it's helpful for you

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Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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Answer:

\(\frac{6}{10}\)

Step-by-step explanation:÷

convert 0.7 to a fraction so \(\frac{7}{10}\)

and convert the mixed number to a fraction \(\frac{7}{6\\}\)

now divide them

\(\frac{7}{10}\) ÷  \(\frac{7}{6\\}\)

\(\frac{7}{10}\) x \(\frac{6}{7}\)

so 7 and 7 cancel out so 1 over 10 and 6 over 1 now multiply and you get

6 over 10

:)

Answer:

Phase shift: -90(90 to the left)

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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3. If x = 4, x2 = 16

This statement can be written as x = 4 → x2 = 16. It is true because if x is 4, then x2 is 16 by the definition of squaring.

The converse of this statement is x2 = 16 → x = 4. It is false because there are two possible values of x that satisfy x2 = 16, namely 4 and -4. A counterexample is x = -4.

4. If one angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle.

This statement can be written as one angle of a quadrilateral is a right angle → the quadrilateral is a rectangle. It is false because there are quadrilaterals with one right angle that are not rectangles, such as trapezoids or kites. A counterexample is a trapezoid with one right angle.

The converse of this statement is the quadrilateral is a rectangle → one angle of a quadrilateral is a right angle. It is true because all rectangles have four right angles by definition.

5. If a triangle is equilateral, then it has three equal angles.

This statement can be written as a triangle is equilateral → it has three equal angles. It is true because all equilateral triangles have three equal angles of 60 degrees by definition.

The converse of this statement is it has three equal angles → a triangle is equilateral. It is true because if a triangle has three equal angles, then they must be 60 degrees each, and therefore the triangle must be equilateral by definition.

Out of the 225 people surveyed, 135 said they shop online, 27 said they always get their order delivered, and 54 said they had loyalty cards.

To calculate the number of people who said they shop online, we can use the percentage given. If 60% of the 225 people surveyed said they prefer to shop online, we can find the number by multiplying the total number of people surveyed by the percentage:

Number of people who shop online = 225 * 0.60

Number of people who shop online = 135

Therefore, 135 people said they shop online.

To find the number of people who have shopping delivered, we need to calculate 20% of the number of people who shop online:

Number of people with shopping delivered = 135 * 0.20

Number of people with shopping delivered = 27

Hence, 27 people said they always get their order delivered.

Now let's calculate the number of people who had loyalty cards. First, we need to find the number of people who said they go in-store to shop. This is 40% of the total surveyed:

Number of people who go in-store to shop = 225 * 0.40

Number of people who go in-store to shop = 90

Out of these 90 people, only 60% said they had loyalty cards:

Number of people with loyalty cards = 90 * 0.60

Number of people with loyalty cards = 54

Therefore, 54 people said they had loyalty cards.

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Step-by-step explanation:

A

this is the combination of a 4×6 rectangle and a 2×2 square. nothing is excluded.

so, the area is

(6-2)×6 + 2×2 = 4×6 + 4 = 24 + 4 = 28 cm²

B

this is the area of the large 8×5 rectangle minus the area of the small 2×3 rectangle.

so the area is

8×5 - 3×2 = 40 - 6 = 34 cm²

C

Basically the same thing as for B. large rectangle minus smaller rectangle.

so, the area is

15×10 - 9×6 = 150 - 54 = 96 cm²

D

the area of a triangle is

baseline × height / 2

or baseline here is 2×8, and the height is 5

so we get the area

2×8 × 5 / 2 = 8×5 = 40 cm²

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We should know that a circle is a set of points on a circle that are equal from a fixed point

The standard form for finding the equation of a circle is expressed as;

(x-a)² + (y-b)² = b=r²

where; (a, b) is the center of the circle

r is the radius of the circle

Given the following

Diameter = 12 units

radius = 12/2 = 6 units

If the center lies on the y-axis, the center will be at (0, 3)

Therefore, Substituting into the formula, we will have (x-0)² + (y-3)² = 6² which is equivalent to x²+ (y-3)² = 36

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Answer:

$135

Step-by-step explanation:

We Know

A gold chain is sold for $635 at a gain of 27% on the sale price.

Find the profit.

Let's W be wholesale.

W = 635/1.27 = $500

Profit = 635 - 500 = $135

So, the profit is $135

Answer:

x=5 and y=-2

Step-by-step explanation:

The given system of equations are :

7x +y = 33  ....(1)

-7x + 6y = -47 ....(2)

We need to find the solution of the given equations.

Adding equation (1) and (2) we get :

7x +y + (-7x) +6y = 33+(-47)

7y = -14

y = -2

Put the value of y in equation (1).

7x +(-2) = 33

7x-2=33

7x=33+2

7x = 35

x = 5

Hence, the solution of the above equations are x=5 and y=-2

Answer:

3a + 2b + 4c = D

D = Amount Spent

Step-by-step explanation:

Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.0262

It goes like tens, hundreds, thousands, ten thousands

Answer:

Decrease of 28.6%.

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

Decrease of 15%

1 - 15/100 = 1 - 0.15 = 0.85

Decrease of 16%

1 - 16/100 = 1 - 0.16 = 0.84

Both:

0.85*0.84 = 0.714

Change:

The initial percentage is 100% = 1.

0.714 - 1 = -0.286

Negative, so a decrease

The answer is a decrease of 28.6%.

Answer:

\(\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\), \(\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\), \(\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\)

Step-by-step explanation:

We proceed to derive each expression by rule of chain. Let be \(w = \ln (x+2\cdot y + 3\cdot z)\), \(x = r^{2}+t^{2}\), \(y = s^{2}-t^{2}\) and \(z = r^{2}+s^{2}\):

\(\frac{dw}{dr} = \frac{\frac{dx}{dr}+2\cdot \frac{dy}{dr} +3\cdot \frac{dz}{dr} }{x+2\cdot y + 3\cdot z}\)

\(\frac{dx}{dr} = 2\cdot r\)

\(\frac{dy}{dr} = 0\)

\(\frac{dz}{dr} = 2\cdot r\)

\(\frac{dw}{dr} = \frac{8\cdot r}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}\)

\(\frac{dw}{dr} = \frac{8\cdot r}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\) (1)

\(\frac{dw}{ds} = \frac{\frac{dx}{ds}+2\cdot \frac{dy}{ds} +3\cdot \frac{dz}{ds} }{x+2\cdot y + 3\cdot z}\)

\(\frac{dx}{ds} = 0\)

\(\frac{dy}{ds} = 2\cdot s\)

\(\frac{dz}{ds} = 2\cdot s\)

\(\frac{dw}{ds} = \frac{10\cdot s}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}\)

\(\frac{dw}{ds} = \frac{10\cdot s}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\) (2)

\(\frac{dw}{dt} = \frac{\frac{dx}{dt}+2\cdot \frac{dy}{dt} +3\cdot \frac{dz}{dt} }{x+2\cdot y + 3\cdot z}\)

\(\frac{dx}{dt} = 2\cdot t\)

\(\frac{dy}{dt} = -2\cdot t\)

\(\frac{dz}{dt} = 0\)

\(\frac{dw}{dt} = -\frac{2\cdot t}{(r^{2}+t^{2})+2\cdot (s^{2}-t^{2})+3\cdot (r^{2}+s^{2})}\)

\(\frac{dw}{dt} = -\frac{2\cdot t}{4\cdot r^{2}-t^{2}+5\cdot s^{2}}\) (3)

Answer:

x = 7.5

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and equals:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, subtract 2x from both sides of the equation:

10x (-2x) = 2x (-2x) + 60

10x - 2x = 60

8x = 60

Next, isolate the variable, x. Divide 8 from both sides of the equation:

(8x)/8 = (60)/8

x = 60/8

x = 7.5

x = 7.5 is your answer.

~

Answer:

45

Step-by-step explanation:

You are given only one space. Note that the term 6 shows up on both sides. Therefore, it is implying that you need to multiply the other two terms together. Do so:

9 x 5 = 45

45 is your answer.

~

15 it was rigth  in khan academy if u got the letter one its A

The circumference of the fountain will be 43.98 square feet. Thus, the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let d be the diameter of the circle. The circumference of the circle will be given as,

C = πd units

The diameter of the circular fountain is 14 feet. Then the circumference is calculated as,

C = π x 14

C = 43.98 square feet

Thus, the correct option is A.

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Answer:

B

Step-by-step explanation:

Standard deviation is the average distance away from the mean, thus B is correct

Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

Answer: There is no solution.

Answer:

There is no solution

Step-by-step explanation:

Answer:

-0.8+0.7+0.4+0.3=-0.1+0.5

Answer:

6 units

Step-by-step explanation:

Volume of square pyramid is

  1/3    *  base area  *  height

For the first pyramid

  70  =  1/3  *  base  *  6

   base = 35

For the second pyramid

 70 = 1/3  * 35 * h

 h = 6  

The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."

To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:

8b + 5 = 9

To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:

Subtract 5 from both sides to get rid of the constant term:

8b + 5 - 5 = 9 - 5

8b = 4

Divide both sides of the equation by 8 to solve for b:

8b/8 = 4/8

b = 1/2

Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:

8(1/2) + 5 = 9

4 + 5 = 9

Both sides of the equation are equal, confirming that b = 1/2 is the solution.

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The Variables (a) Gender is Categorical , (b) Alcohol can be either Categorical or Quantitative and (c) Height is Quantitative .

We can identify the type of each variable as categorical or quantitative.

(a) Gender: This variable is categorical, as it describes a characteristic that can only take on a limited number of values (e.g., male or female).

(b) Alcohol: Without additional information , it is not clear whether this variable is categorical or quantitative.

If the data set only includes information about whether an individual drinks alcohol or not, then this variable is categorical. If the data set includes information about how much alcohol an individual consumes, then this variable would be quantitative.

(c) Height: This variable is quantitative, as it represents a numerical measurement of a continuous variable.

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The given question is incomplete , the complete question is

Identify and classify the variable(s) you will use. here is the list of variables in the data set.  

(i) identify the variable as either categorical or quantitative.

the variables are (a) Gender , (b) Alcohol , (c) Height .