A roofer props a ladder against a wall so that the top of the ladder reaches a 20 foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is 46 degrees, what is the length of the ladder to the nearest foot?

No, it is not always necessary to rename the whole number part of a mixed number when subtracting a fraction from it. Whether renaming is required depends on the specific subtraction problem and the desired form of the result.

Let's consider an example to illustrate this. Suppose we have the mixed number 3 1/4 and we want to subtract 1/2 from it.

Method 1: Without Renaming the Whole Number

We can directly subtract the fractions without renaming the whole number part:

3 1/4 - 1/2 = 3 - 1/2 + 1/4 = 2 1/4

In this case, we did not need to rename the whole number part, and the result is expressed as a mixed number.

Method 2: Renaming the Whole Number

Alternatively, we can rename the whole number part by borrowing 1 from the whole number:

3 1/4 - 1/2 = 2 + (3/4 - 1/2) = 2 + 1/4 = 2 1/4

In this case, we chose to rename the whole number part, but it was not necessary to obtain the same result.

Both methods yield the same result, 2 1/4, but the decision to rename the whole number part depends on personal preference or specific requirements for the form of the answer.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

y = 172.973

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

0.74y = 128

Step 2: Solve for y

Step 3: Check

Plug in y into the original equation to verify it is a solution.

Here we see that 128 does indeed equal 128.

∴ y = 172.973 is a solution of the equation.

Add £48.28 to £142 so you get £190.28

AnswerAnswerAnswerAnswer:

190.28

Step-by-step explanation:

£142 + 34% = £142 x 1.34 = 190.28

Answer:

The length of side EF is 10 units.

If there is any specific measurement for each unit, multiply 10 by the measurement amount.

Answer:

10 units

Step-by-step explanation:

The side of EF is 10 units

The side of DE is 10 units

The side of DF is about 14.1 units

Answer: A

Step-by-step explanation:

pretty sure :)

Using the continuity concept, it is found that the function that is continuous at x = 18 is given by:

\(f(x) = \frac{(x - 18)^2}{x}\)

A function f(x) is continuous at x = a if it is defined at x = a, and:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

In this problem:

In the fourth function:

\(f(18) = 36\)

\(\lim_{x \rightarrow 18^-} f(x) = 18^2 \neq 36\)

Hence also not continuous.

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To determine an expression in terms of m and l for the moment of inertia of the masses about axis a, we need some additional information about the configuration of the masses and the axis.

The moment of inertia depends on the distribution of masses relative to the axis of rotation. It is a measure of an object's resistance to rotational motion. The formula for the moment of inertia varies depending on the specific shape and distribution of masses.

If you can provide more details about the arrangement of masses and the axis of rotation, I can help you derive the expression for the moment of inertia in terms of m and l.

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This type of departmentalization groups activities based on common functions or tasks, ensuring that employees with similar skills and expertise are grouped together to handle specific responsibilities.

In a government organization where public service responsibilities are divided into activities for employees, children, and the disabled, functional departmentalization would be suitable. This approach organizes the organization based on common functions or tasks performed.

Each department would focus on a specific area of public services, such as employee services, child welfare, and services for the disabled. Within each department, employees with relevant expertise and skills in those areas would be grouped together. This enables specialization and allows the organization to efficiently address the unique needs and requirements of each group.

Functional departmentalization facilitates effective coordination, communication, and resource allocation within the organization, ensuring that services are provided in a targeted and specialized manner to meet the diverse needs of employees, children, and the disabled.

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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0

Step-by-step explanation:

bob:fred

5. : 2

0. :0

bob is older than fred with 3 years so when bob was born the fred didn't even exist

but im not sure

The ratio of the surface area of the two similar solids is 16:25. Option D, 16:25, is the correct answer .To find the ratio of the surface areas of two similar solids

We can make use of the correspondence between their corresponding edge lengths. We can suppose that the solids have lengths of 4x and 5x, where x is a constant, given that the ratio between the lengths of their edges is 4:5.

The square of an object's edge length determines its surface area. Therefore, the square of the ratio of their edge lengths will be the ratio of their surface areas.

The ratio of their surface areas will now be calculated.

Edge length ratio is 4:5.

Ratio of surface areas = (4:5)^2 = 16:25

The two identical solids' surface areas therefore have a 16:25 ratio. 16:25 in Option D is the right response.

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Answer:

9 x 7 = 63 <---- Parallelogram

10 x 6.8 = 68, 68 divided by 2 = 34 <------- Triangle

13 + 15 = 28, 28 x 6 = 168, 168 divided by 2 = 84 <------- Trapezoid

The trapezoid has the greatest area.

Formula of trapezoid:

B1(base 1) + B2(base 2) x H (height) x 1/2 (basically dividing by 2)

Formula of triangle:

B(base) x H(height) x 1/2 (basically dividing by 2)

Formula of Parallelogram:

B(base) x H(height)

The correct answer is C. This is because the shaded part, the y, is less than the line, so it would be <, but the line is not dotted, so then it would be less than or equal to.

The probability that all three events will happen is 0.01536.

Let A, B and C be the three independent events, such that

P(A) = 0.2

P(B) = 0.24

P(C) = 0.32

The probability that all three events will happen can be calculated using the formula:

P(A ∩ B ∩ C) = P(A) × P(B) × P(C)

Now, substituting the values, we get:

P(A ∩ B ∩ C) = 0.2 × 0.24 × 0.32

= 0.01536

Therefore, the probability that all three events will happen is 0.01536.

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The existing power plant in West Fremont can produce 96,000,000 kWh of electrical energy in a year.

The existing power plant in West Fremont has a capacity of 12 megawatts (MW) and can operate at full capacity for 8,000 hours/yr.

This means that the plant can produce 12 MW x 8,000 hours = 96,000 megawatt hours (MWh) of electrical energy in a year.

This energy can be further converted to 96,000 MWh/1,000 kWh/MWh = 96,000,000 kilowatt hours (kWh) of electrical energy in a year.

Therefore, the existing power plant in West Fremont can produce 96,000,000 kWh of electrical energy in a year.

The town currently pays $0.10 per kWh of energy, which means it would cost $9,600,000 to purchase this energy from the electric utility.

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The greatest possible mass of the rock to two decimal places is 86.34 g

Since the mass of the piece of rock is 86.3 g, correct to the nearest 0.1 g. Thus, the actual mass of the rock  in 2 decimal places could be between 86.25 g and 86.34 g.

To find the greatest possible mass of the rock, we need to round up to the higher end of the range of the mass of the rock.

Therefore, the greatest possible mass of the rock to two decimal places is 86.34 g

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Answer:

distance between (F,G) and (H,J) = 9.02

distance between (F,H) and (G,J) = 3.8

distance between (F,J) and (G,H) = 3.8

Step-by-step explanation:

Distance between (F,G) and (H,J)

d=√(7.2−3.9)2+(10.6−2.2)2

d=√(3.3)2+(8.4)2

d=√10.89+70.56

d=√81.45

d=9.024965

Distance between (F,H) and (H,J)

d=√(2.2−3.9)2+(10.6−7.2)2

d=√(−1.7)2+(3.4)2

d=√2.89+11.56

d=√14.45

d=3.801316

Distance between (F,J) and (G,H)

d=√(2.2−3.9)2+(7.2−10.6)2

d=√(−1.7)2+(−3.4)2

d=√2.89+11.56

d=√14.45

d=3.801316

Hope this helps a lot!!

Answer:

y is 100degrees

it is correct answer

The equations can be solved in the following manner. As shown below.

The equations can be solved in the following manner. As shown below.

1.  Multiplication Property of Equality

10a + 35b = 0, 21a - 35b = 217            

2.  Addition Property of Equality

31a = 217

3.  Division Property of Equality

a = 7

4.  Substitution Property of Equality

2(7) +7b = 0

5.  Simplify

14 + 7b = 0

6.  Subtraction Property of Equality

7b=-14

7.Division Property of Equality

b= -2

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11812.5 Jamaican dollars is equivalent to $135

The conversion rate is given as:

$1 = JA 87.50

Multiply both sides of the conversion rate by 135

135 * $1 = JA 87.50 * 135

Evaluate the product

$135  = JA 11812.5

Hence, 11812.5 Jamaican dollars is equivalent to $135

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Step-by-step explanation:

To add integers on the number line, you move forward, and you face right (the positive direction) when you add a positive number. As with positive numbers, to add negative integers on the number line, you move forward, but you face left (the negative direction) when you add a negative number.

Answer:

1

Step-by-step explanation:

To find the median number of musical instruments played, we first need to arrange the data in ascending order:

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3

Next, we count the total number of responses, which is 15. Since 15 is an odd number, the median will be the average of the middle value.

The middle value is 1

Hence, the median number of musical instruments played is 1.

Answer:

Step-by-step explanation:

a right angle contains 90° (always)

according to the question

x+3+x-1+x+1=90

3x3=90

x=87

x=29

Answer:

2 and 2/3 for the first question

-1/8 for the second one

-1/5 for the third one

ive never done this type of question or maybe it was too long ago for me to remember but out of this answer choices i would guess that its the last one

this is 3

Step-by-step explanation:

you add the numerators which is the top number in order to get 2 and 2/3rds

you subtract 5 from 4 to get -1/8

same situation as the last one, subtract 15 from 11 to make it a negative 4/20 and then simplify that by dividing it by four to get 1/5th

this one i dont understand or remember how to do very well but if i had to guess its the last answer choice

this one you add 3/4 plus 1/4 in order to get 4/4 or rather 1, so basically its asking what 1+1+1 is which is 3

Answer:

m∠GFT = 142°

Step-by-step explanation:

∠GFT and ∠DFT are supplementary.

m∠GFT + m∠DFT = 180

7f + 163 + 6f + 56 = 180

13f + 219 = 180

13f = -39

f = -3

m∠GFT = 7f + 163 = 7(-3) + 163 = -21 + 163 = 142

Answer:

The clock face is divided into sixty equal parts, each minute. The minute hand is located on the 20 minute mark at 6:20, the hour hand located between the 30 minute mark and the 35 minute mark. When the minute hand goes all sixty minutes, the hour hand only moves five, so to figure out the location of the hour hand, we look at how much the hour has progressed, in this case 20 minutes, or one third of the hour. So the minute hand has moved one third of the way through the hour, so has the hour hand moved one third of the way through the five minutes, or, five thirds of a minute, which is one and two thirds minute, one minute forty seconds. That puts the hour hand at thirty minutes plus one minute and forty seconds—at 31min 40sec—which is 11min 40sec farther than the minute hand.

Step-by-step explanation:

Answer:

the odds against Zahra climbing to the top are,

B. 4:1

Step-by-step explanation:

Since she has climbed 7 times in 28 attempts,

the probability of a successful climb is,

P = 7/28

P = 1/4

So, the odds against Zahra climbing to the top are 4:1

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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Answer:

If you were to attach the shape, I could help.