a measurement of 1/2" = 1" is the same scale as a ratio of ?

Answer: 17.7

Step-by-step explanation:

\(tan x = \frac{7}{22} \\tan x = .318181\\inverse tan of .3181818= 17. 65\)

We solve as follows:

-12x - 2y = 30

2(-4x + y = -5)

---------------------

-12x -2y = 30

-8x + 2y = -10

--------------------

-20x = 20 => x = -1

Now we replace the value of x in one of the original equations to solve for y, that is:

-4(-1) + y = -5 => 4 + y = -5 => y = -9

So, the solution is the point (-1, -9).

Answer:

60 = 2² x 3 x 5

Step-by-step explanation:

Prime Factorization is finding which prime numbers multiply together to make the original number.

A Prime Number is a whole number (integer) greater than 1 that cannot be made by multiplying other whole numbers.

Prime numbers: 2, 3, 5, 7, 11, 13, 17 etc.

Therefore, 60 = 2 x 2 x 3 x 5 = 60

We can write this using exponents as 2 x 2 = 2²

Therefore, 60 = 2² x 3 x 5

Answer: Pi multiplied by the diameter of the circle

Step-by-step explanation:

Answer:

The formula for finding the circumference of a circle is \(C = 2\pi r\). You substitute the radius of the circle for \(r\) and multiply it by \(2\pi\).

The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

27.27% of the students with scolarship are seniors.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has scolarship

Event B: Is a senior

15% are senior, and of those, 40% have scolarship. So

\(P(A \cap B) = 0.15*0.4 = 0.06\)

Probability of a scolarship:

15% of 40%(seniors)

30% of 25%(juniors)

20% of 25%(sophmores).

10% of 35%(freshmen). So

\(P(A) = 0.15*0.4 + 0.3*0.25 + 0.2*0.25 + 0.1*0.35 = 0.22\)

Percentage:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.22} = 0.2727\)

0.2727*100 = 27.27%

27.27% of the students with scolarship are seniors.

Answer:

1*32, 2*16, 4*8, 8*4, 16*2, 32*1

Step-by-step explanation:

Answer:

e^2v/2a^3y^7

Step-by-step explanation:

Answer:

9

In order to find the answer, you need to count. 1297, 1 is in the tenth place,  2 in is the hundredth place, 9 is in the thousandth place, and so on.

Answer: 9  ( EXPERT VERIFIED! )

Step-by-step explanation: 3.1297- tenths, hundredths then thousandths, so the decimal goes 3 places to the right.

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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Answer:

30 : 36

45 : 54

60 : 72

Answer: 4(4b - 5)(b + 5)

Step-by-step explanation:

All have a common factor of 4

4(4b^2 + 15b - 25)

--------------------------------------------------------------------------------------------------------------

Now you need to find two numbers that:

a) multiply to -100 (the a term * the c term = 4 * -25)

b) add to 15 (the b term)

After a little thinking, we can determine that the two numbers are:

20 and -5

--------------------------------------------------------------------------------------------------------------

Now we can rewrite the middle term as 20b - 5b (notice how it still equals 15b)

4(4b^2 + 20b - 5b - 25)

--------------------------------------------------------------------------------------------------------------

4((4b^2 + 20b) + (-5b - 25))

Group the terms (associative property)

--------------------------------------------------------------------------------------------------------------

Take out a common factor from each

4(4b(b + 5) - 5 (b + 5))

--------------------------------------------------------------------------------------------------------------

Now we can factor by grouping

4(4b - 5)(b + 5)

--------------------------------------------------------------------------------------------------------------

Answer/Step-by-step explanation:

The reasons for the stated numbered angles that are congruent to the given angles are written in the parentheses as follows:

7. <7 ≅ 65° (alternate interior angles)

<4 ≅ 65° (corresponding angles)

<1 ≅ 65° (vertical angles)

8. <4 ≅ 51° (alternate interior angles)

<5 ≅ 51° (corresponding angles)

<7 ≅ 51° (vertical angles)

9. <1 ≅ 120° (corresponding angles)

<3 ≅ 120° (alternate angles)

Answer:

6.75 gallons lost in 1 hour.

Step-by-step explanation:

1 US gallon = 128 ounces.

12 ounces takes 50 seconds.

x ounces takes 3600 seconds (which is 1 hour)  Cross multiply

12 * 3600 = 50 x

43200 = 50 x                Divide by 50

43200 / 50 = x

864 oz = x

So in 1 hour 864 ounces were lost.

Now there are 128 ounces in a gallon

1 gallon /128 ounces = x / 864        Cross multiply

864 * 1 / 128 = x

6.75 = x

There are 6.75 gallons in 1 hour

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

If you have the coordinates of two points, you can use the distance formula to find the length of the line segment between them. The distance formula is:

\(d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

where:

And to find a perimeter add all the sides as the perimeter is the sum of all sides of the shape or object.

Perimeter: Sum of all sides

Area : Length * breadth or base*height for rectangle

Answer:

i think its 3.5 years

Step-by-step explanation:

Answer:

x/2 = 1/2x

Step-by-step explanation:

# of paintbrushes/ 2 piles = 1/2 # of paintbrushes

Answer:

x/2

Step-by-step explanation:

Since Lucy is taking the paintbrushes, x, and splitting them into 2 equally sized groups we can assume that this IS 1/2 the size of the original group.

We can show this claim by simply doing this equation: x/2, since she is splitting them into 2 groups that are equally sized, we are just dividing x by two.

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Answer:

779 kg

Step-by-step explanation:

5,000 g = 5 kg, 784 - 5 = 779

The solution of the expression is,

⇒ x = - 1 and x = 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Solve the expression,

x² – 3x − 2 = x + 3

Now, We can simplify as;

x² – 3x − 2 = x + 3

x² – 3x − 2 - x - 3 = 0

x² - 4x - 5 = 0

x² - 5x + x - 5 = 0

x (x - 5) + 1(x - 5) = 0

(x + 1) (x - 5) = 0

x = - 1

x = 5

Thus, The solution of the expression is,

⇒ x = - 1 and x = 5

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Answer:

Step-by-step explanation:

Let's use algebra to solve the problem.

Let's say Daniel's age now is "D".

According to the problem, Kevin's age is 3 times as old as Daniel:

K = 3D

And four years ago, Kevin was 5 times as old as Daniel:

K - 4 = 5(D - 4)

We can substitute the first equation into the second equation:

(3D) - 4 = 5(D - 4)

Simplifying:

3D - 4 = 5D - 20

Subtracting 3D from both sides:

-4 = 2D - 20

Adding 20 to both sides:

16 = 2D

Dividing by 2:

D = 8

So Daniel is currently 8 years old.

To find Kevin's age, we can substitute D = 8 into the first equation:

K = 3D = 3(8) = 24

So Kevin is currently 24 years old.

Answer:  Daniel's age = 8

Step-by-step explanation: Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel. How old is Daniel now?

Kevin's age = 24 Daniel's age = 8.

The mean value theorem is used to link the average rate of change and the derivative of a function.

The value of V is 8.

The givenparameters are:

Mean value theorem states that:

If  [a,b] and

(a,b),

Then there is a point c in (a,b), such that:  

From the question, we understand that: f is differentiable

This means that:

avethat:

The equation becomes

Cross mltiply

o both side

From the question, we have:

By comparisons;

Hence, the value of V is 8.

Answer:

Computing the sum of $5.89 and $1.45 we get: $7.34

Step-by-step explanation:

We need to explain, how can we compute the sum of $5.89 and $1.45?

Computing the sums of dollar amounts is same as computing the sum of simple decimal expressions. Each value will be added to its corresponding values and we will get the answer.

Computing the sum of $5.89 and $1.45

\(\:\:\:\:\:\$ \:\:5.89\\+\$ \:\:1.45\\------\\\:\:\:\:\:\$ \:\:7.34\)

So, we will start adding from right side, 9 will be added with 5 and we get 14, 1 will be given carry and 8 will be added by 4 and add the carry we get 13, 1 will be given carry and 1 will be added by 5 and add the carry we get 7

So, Computing the sum of $5.89 and $1.45 we get: $7.34

1a. The percentage total return is -19.56%

1b. The dividend yield is 2.42%.

1c. The capital gains yield is -21.98%.

2a. The arithmetic average annual return on large-company stocks in nominal terms is 14.5%.

2b. The arithmetic average annual return on large-company stocks in real terms is 9.67%.

3a. The real return on long-term government bonds is 3.195%

3b. The real return on long-term corporate bonds is 3.291%

In Financial accounting, the percentage total return (P) can be calculated by using this formula;

P = [(Ending price - Initial price) + Dividend] ÷ Initial price

P = [(71 - 91) + 2.20] ÷ 91

P = -0.1956 or -19.56%

1b. For the dividend yield, we have:

Dividend yield = Dividend ÷ Initial price

Dividend yield = 2.20 ÷ 91

Dividend yield = 0.0242 or 2.42%

1c. For capital gains yield, we have:

Capital gains yield = (Ending price - Initial price) ÷ Initial price

Capital gains yield = (71 - 91) ÷ 91

Capital gains yield = -0.2198 or -21.98%.

Part 2.

a. The arithmetic average of annual return on large-company stocks in nominal terms is equal to 14.5%.

b. For arithmetic average annual return in real terms, we have:

(1 + 0.145) = (1 + r)(1 + 0.044)

r = (1.145/1.044) - 1

r = 9.67%

Part 3.

a. For real return on the long-term government bonds, we would apply Fisher equation:

(1 + i) = (1 + r)(1 + h)

Where:

(1 + 0.066) = (1 + r)(1 + 0.033)

1 + r = 1.066/1.033

r = 3.195%

b. For real return on long-term corporate bonds:

(1 + 0.067) = (1 + r)(1 + 0.033)

1 + r = 1.067/1.033

r = 3.291%

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