An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 28 feet up. The ladder makes an angle of 60° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.

Answer: -3.5

Step-by-step explanation:

Daily wage of James is $64.

Students should follow these steps to solve any word puzzle:

1. Read the problem: Students should first give the problem a quick once-over.

2. Highlight facts: After reading the issue through one more, students should underline or highlight crucial information, such as crucial numbers or words that indicate an operation.

3. Visualize the issue; you might find it useful to create a picture or a diagram.

By developing pertinent images, students can begin to visualize either simple or more complicated problems.

4. Identify the operation(s): Identify the operations that must be carried out. Is it division, multiplication, or addition?

James earns a total of $448 in a week, and he work 8 hours day.

Let his daily wage be x

As daily wage of James is X

In a week there are 7 days

Therefore, 7×X = $448

X = [tex]\frac{448}{7} = 64[/tex]

So, daily wage of James is $64.

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Answer:

Step-by-step explanation:

1/5 (1/3) + 1/15 = 1/15 + 1/15

                      = 2/15

The expression that represents the perimeter of the frame is (8x+24) inches. Option C

From the question, we are given that dimensions of the photograph is 5 inch × 7 inchIt is given that the dimensions of the frame are 2x inches larger than the dimensions of the photograph. Thus, the dimensions of the frame is (2x+5) inches × (2x+7) inches.

Since, the frame is in rectangular shape. Perimeter of a rectangle = 2(Length + Width)

= 2(2x+5+2x+7)

= 2(4x+12)

= 8x+24 inches.

Thus, the perimeter of the frame is represented by the expression (8x+24) inches.

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Answer:

Step-by-step explanation:

Rounding to 1 sig fig:

12 becomes 10

478 becomes 500 (that hurts)

Multiply

10 x 500 = 5000

[Actual value of 12 x 478 is 5736. The reason the estimated value is lower is due to the fact that going from 12 to 10 was a reduction of 17%, while going from 478 to 500 was an increase of only 5%]

Answer:

N=3. you get this by using the proportion 6/N=1/1/2.

The function has been shifted down by 8 units.

Here given the function,

y = x

Required that,

Find the transformation that results in: y = x - 8

When a function f(x) is shifted by b units, the new function g(x) is defined as g(x) = f(x) - b.

In this instance:

y = x

b = 8

As a result, the new function is:

y = x - b

8 should be substituted for b.

y = x - 8

Hence, the function is shifted 8 units downward,

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The required length of the right rectangular prism is 18 in whose volume is 540 cu. in

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in form. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its form. A rectangular prism may be found in everyday objects like a geometry box, notebooks, diaries, and rooms.

Rectangular prism characteristics

There are two categories into which rectangular prisms can be divided. These are:

A rectangular prism is a prism with rectangular bases. A right rectangular prism is a prism with six rectangle-shaped faces with angles that are all right angles.

Vertices of a rectangular prism = 8

Edges of a rectangular prism = 12

Faces of a rectangular prism= 6 (including bases)

total volume of the prism = 540 cubic inches.

Width = 6 in

Height = 5 in

We know volume is length * breadth* height

⇒ 540 = 5*6* length

⇒length = 18 in

The required length of the right rectangular prism is 18 in.

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The required, bike is the fastest among all the vehicles.

Unit conversion is defined as the conversion of units of the same identity through various methods such as, meters in kilometers and centimeters in kilometers.

1.
In 5 seconds skateboard traveled 90 feet.

SInce 1 feet = 30.48 centimeter
90 feet = 2743.2 centimeter

2.
In 5 seconds scooter traveled 1,020 inches
Since 1 inch = 2.54 centimeter,
1020 inches = 2590.8 centimeter

3.
In 5 seconds  bike traveled 4800 centimeters

4.
In 5 seconds go-kart traveled 0.03 kilometers

Since, 1  kilometers = 100000 centimeter

0.03  kilometers = 3000 centimeter

Now compare all the distances which one has the higher distance will be the fastest,
Bike > go-kart > skateboard > scooter.

Thus, Bike is the fastest vehicle.

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The speed of the cyclist in miles per hour is 16 miles per hour

The speed of an object is the rate of change of the object's distance over time

From the question, we have the following parameters that can be used in our computation:

A cyclist rides 8 miles in 30 minutes.

The parameters in the above statement can be further expressed as

Distance = 8 miles

Time = 30 minutes

This means that the distance is 8 miles and the time taken to cover the distance is 30 minutes

Convert the minutes to hour

So, we have

Time = 0.5 hour

The speed of the cyclist in miles per hour is then calculated as

speed = 8 miles/0.5 hour

Evaluate the quotient

speed = 16 miles/hour

Hence, the cyclist' speed is 16 miles/hour

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24 fluid ounces of juice in number cups is 3 cups.

Given that, Shen drank 24 fluid ounces of juice.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

From table, 1 cup = 8 fluid ounce

So, 24/8

= 3 cups

Therefore, 24 fluid ounces of juice in number cups is 3 cups.

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Answer:

558

Step-by-step explanation:

93 times 600 divided by 100 equals 558

In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be "x"  the price per pound for grapefruit, "y" the price per pound for oranges.

We know that Steve buys 2 pounds of grapefruit and 3  of oranges for $7.20.

This means that the sum of the products of 2x and 3y is $7.20. Then, we can write this equation to represent it

                                2x + 3y = 7.20

Kennedy buys 4 pounds of grapefruit and 2 pounds of oranges for $8.80.

This means that the sum of the products of  4x and 2y  is $8.80. Then, we can write this equation to represent this

                  4x + 2y = 8.80

Therefore, we get that the system of equations that models the situation is

           { 2x + 3y = 7.20

            { 4x + 2y = 8.80

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Answer:

Step-by-step explanation:

so first 48+9e

then add 34

take away

The coordinates of points C are (4,1).

The coordinates of the points D are (3, 2) respectively.

y = mx + c. Conversely,is the formula of coordinate that help to find  satisfy to the equation y = mx + c is always lie on the line with the gradient m and y-intercept of c.

If the point C is divides AB in the ratio 2:3, then the coordinates of C are;

Xc=2(1)+3(6)/2+3

Xc=2+18/5

Xc=20/5 = 4

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

Yc=8-3/5

Yc=5/5 = 1

The coordinates of points C are (4,1).

If the point D divides the  AC in the ratio 3:2, then the coordinates of D are-

Xc= 3(1)+2(6)/3+2

Xc=3+12/5

Xc=15/5 = 3

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

Yc=12-2/5

Yc=10/5=2

The coordinates of the point D are (3, 2).

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Las soluciones de las ecuaciones lineales por propiedades algebraicas se listan a continuación:

7) x = 7

8) x = 16 / 7

9) x = - 1 / 4

10) x = 1 / 5

En este caso tenemos cuatro casos de ecuaciones lineales, cuya variable x debe ser despejada mediante propiedades algebraicas. A continuación, se procede a determinar las soluciones correspondientes a cada expresión:

Caso 7:

2 · (x - 1) - 5 = 14 - x

2 · x - 2 - 5 = 14 - x

2 · x - 7 = 14 - x

3 · x = 21

x = 7

Caso 8:

15 · x + 10 = 6 · x - 2 · (x - 7) + 3 · (1 - x)

15 · x + 10 = 6 · x - 2 · x + 14 + 3 - 3 · x

15 · x + 10 = x + 17

14 · x = 32

x = 32 / 14

x = 16 / 7

Caso 9:

x + 3 · (x - 1) = 6 - 4 · (2 · x + 3)

x + 3 · x - 3 = 6 - 8 · x - 12

4 · x - 3 = - 6 - 8 · x

12 · x = - 3

x = - 1 / 4

Caso 10:

6 - 3 · (x + 1) = 4 · x + 2 · (1 - x)

6 - 3 · x - 3 = 4 · x + 2 - 2 · x

3 - 3 · x = 2 · x + 2

- 5 · x = - 1

x = 1 / 5

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Answer:

A

Step-by-step explanation:

A stem and leaf plot is a way of representing data (it might be helpful to look up a video—the organic chemistry tutor has a good one).

The column on the left shows the first digit of each number, and the column on the right is the different ones place digits.

Take the number 31. It would go at the bottom, where the 3 (from the tens place) is in the left column and the 1 (from the ones place) is in the right column.

3 would be in the first row as 03.

You have three nines in your list of data, and only A has three nines.

I hope this helps!

Answer:

Step-by-step explanation:

To estimate the distance across the gorge, Jamal can use the following steps:

First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.

Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:

AC^2 = YA^2 + YC^2

He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:

AC^2 = 500^2 + 327^2

AC^2 = 250000 + 107649

AC^2 = 357659

AC = √357659

AC ≈ 597.56 ft

Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:

distance across gorge = XA + AY

distance across gorge = AC + YA + YC

distance across gorge = 597.56 ft + 500 ft + 327 ft

distance across gorge ≈ 1424.56 ft

This is Jamal's estimate of the distance across the gorge.

Answer:

To find the growth rate for a country with a population of 11,000,000, 320,000 births, and 650,000 deaths, you need to first calculate the natural increase in the population by subtracting the number of deaths from the number of births: 320,000 - 650,000 = -330,000. This means that there are 330,000 more deaths than births in this country.

To calculate the growth rate, you need to divide the natural increase by the total population and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (-330,000 / 11,000,000) * 100 = -3.0%. This means that the population is decreasing at a rate of 3.0% per year.

To find the growth rate for a country with 60,000 births, 50,000 deaths, 20,000 immigrants, and 10,000 emigrants, you need to first calculate the natural increase in the population by subtracting the number of deaths from the number of births: 60,000 - 50,000 = 10,000. Then, you need to add the number of immigrants to this number to get the total increase in the population: 10,000 + 20,000 = 30,000. Finally, you need to subtract the number of emigrants from this number to get the net increase in the population: 30,000 - 10,000 = 20,000.

To calculate the growth rate, you need to divide the net increase in the population by the total population and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (20,000 / 20,000,000) * 100 = 0.1%. This means that the population is increasing at a rate of 0.1% per year.

Belgium has a growth rate of 0.1%, which means that its population is increasing by 0.1% per year. To find out how many years it will take for the population to double, you need to divide the growth rate into the number 100. Since 100 / 0.1 = 1000, it will take 1000 years for Belgium's population to double if it continues to grow at a rate of 0.1% per year.

Libya is doubling its population every 19 years, which means that its population is increasing by 100% every 19 years. To find the growth rate, you need to divide the population increase (100%) by the number of years it takes for the population to double (19 years) and multiply by 100 to express the result as a percentage. In this case, the growth rate would be: (100 / 19) * 100 = 5.26%. This means that Libya's population is increasing at a rate of 5.26% per year.

Step-by-step explanation:

Answer:

La notación científica es una forma de escribir números muy grandes o muy pequeños de manera más compacta y legible. En la notación científica, se mueve el punto decimal de un número hasta que tenga una sola cifra a la izquierda del punto y luego se multiplica el número resultante por 10 elevado a una potencia de 10.

Por ejemplo, para escribir 621,000 en notación científica, podemos mover el punto decimal tres lugares a la derecha para obtener el número 6.21. Luego, podemos multiplicar este número por 10 elevado a la potencia de 3 (10^3), lo que da 6.21 x 10^3 = 6.21 x 1000 = 621,000.

Entonces, en notación científica, 621,000 se escribe como 6.21 x 10^3.

Answer: Its 130 degrees

Algebraic expressions -1/3(-3m+6-12+15m) and 2(1-2m) are equivalent as they give same expression of simplifying.

What are equivalent algebraic expressions?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

According the given question:

The given algebraic expressions in variable m are -1/3(-3m + 6- 12 + 15m) and 2(1 - 2m)

Simplifying 1st expression

-1/3(-3m + 6- 12 + 15m)

-1/3(-3m) -1/3(6) -1/3(-12) -1/3(15m)

m - 2 + 4 - 5m

-4m + 2 is the simplified form

Similarly simplifying 2nd expression

2(1 - 2m)

2 - 4m

Clearly both the algebraic expressions are same when simplified.

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The distance that Peter rode more than Lauren is 398 m  .

In the question ,

it is given that ,

before stopping the distance that Peter rode is = 1km = 1000 m .

the distance that Lauren rode is = 602 m .

the difference in the distance can be calculated using the formula ,

So , the difference in the distance is = (distance rode by Peter) - (distance rode by Lauren) .

Substituting the values from above ,

we get ,

= 1000 - 602

on further simplification,

we get ,

= 398 m

Therefore , Peter rode 398m farther than Lauren .

The given question is incomplete , the complete question is

Peter rode her bike 1 km before stopping. Lauren rode 602 m before stopping. How many meter farther did Peter ride than Lauren ?

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The percentage of the 30 minute television show's air time that is spent on commercials.

Given that  12 minutes  out of 30 minutes are commercials. This indicates that the fraction would be

[tex]\frac{12}{30}[/tex]

This fraction can be converted into percentage as follows:

Use division to convert the fraction to a decimal:

[tex]\frac{12}{30} = 12 \div 30 = 0.4\\[/tex]

Multiply by 100 to get percent value:

[tex]0.4 \times 100 = 40\%[/tex]

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. So, a part per hundred is what the percentage refers to. Per 100 is what the word percent means. The sign "%" is used to indicate .

Finding the fraction of a whole in terms of 100 in refers to calculating percentage. A percentage can be found in one of two ways:

a) use the unitary approach.

b) by changing the fraction's denominator to 100.

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary approach.

The percentage of the 30 minute television show's air time that is spent on commercials.

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The number of oil changes that Will and Owen would each have done is 6 oil changes respectively.

The number of hours it would take both Will and Owen is equal to 4 hours.

In order to write a system of equations to describe this situation, we would assign variables to the number of hours per oil change and number of oil changes respectively, and then translate the word problem into algebraic equation as follows:

Since Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour, we have;

y = 2x + 4     .....equation 1.

Since Owen just came on shift, and can finish 3 oil changes every hour, we have;

y = 3x     .....equation 2.

Next, we would determine the number of hours per oil changes they both would have each completed by equating equation 1 and equation 2 as follows;

3x = 2x + 4

3x - 2x = 4

x = 4 hours.

For the number of oil changes for Will, we have;

y = 2(4) + 4

y = 12 oil changes.

For the number of oil changes for Owen, we have;

y = 3(4)

y = 12 oil changes.

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The required solution of the nonlinear equation is (4, 13) and (2, 1).

Given that,
To solve the nonlinear system of equations for real solutions. y =x²-3, 6x-y=11.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
y =x²-3  - - - - - [1]

6x-y=11
From equation 1,
6x -x² + 3 = 11
x² - 6x + 8 = 0
x = 4, and 2

Substitute this x's in equation 1
That gives for the above x's,
y = 13 and 1

Thus, The required solution of the nonlinear equation is (4, 13) and (2, 1).

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Options B, C and D are the situations it is appropriate to use a sample.

Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method.  The sample is chosen by a random method as every subject in the sample is assigned a number.

Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searching people and collecting data from them.

Therefore, options B, C and D are the situations it is appropriate to use a sample.

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Answer:

B,C,D

Step-by-step explanation: