What is the length of the shadow cast by a 12-foot lamp post when the angle of elevation of the sun is 60º? (to the nearest tenth)

She bikes 761.25 miles in all to and from her job in 29 weeks.

Step-by-step explanation:

Distance from her house = 2.625 miles

As this is the distance of one side, she covers same distance for coming back.

Total distance for one day = 2.625 + 2.625 = 5.25 miles

She goes to work for 5 days per week.

29 weeks = [tex]29*5 = 145\ days[/tex]

Total distance covered in 29 weeks;

Total distance = Distance for one day * Days in 29 weeks

[tex]Total\ distance=5.25*145=761.25\ miles[/tex]

She bikes 761.25 miles in all to and from her job in 29 weeks.

Keywords: multiplication, distance

Learn more about multiplication at:

#LearnwithBrainly

Answer:

The average rate of speed of the model airplane, per second is 18 feet.

Step-by-step explanation:

Given:

It took the model airplane 5 seconds to go 90 feet.

Now, to find the average rate of speed in feet per second.

So, in 5 seconds the airplane go to = 90 feet.

In 1 second the airplane go to = 90 ÷ 5 feet.

Therefore, by dividing 90 feet by 5 seconds we get = 18 feet.

Thus, the average rate of speed of the model airplane, per second is 18 feet.

The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:

y = [tex]e^{(ln(13)x)} - 7[/tex].

To find an exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6), we can use the general form of an exponential function:

[tex]y = A * e^{(kx)} + C[/tex]

where A is the initial value, k is the growth/decay rate, e is the base of the natural logarithm (approximately 2.71828), x is the independent variable, and C is the y-coordinate of the horizontal asymptote.

Step 1: Determine the value of C (the y-coordinate of the horizontal asymptote):

Since the asymptote is y = -7, we set C = -7.

Step 2: Use the given points to find A and k:

For point (0, -6):

-6 = A * e⁰ - 7

-6 + 7 = A

A = 1

For point (1, 6):

6 = 1 * [tex]e^{(k*1)[/tex] - 7

13 = [tex]e^{k[/tex]

Step 3: Solve for k:

Take the natural logarithm of both sides: ln(13) = k

Step 4: Write the exponential function:

The exponential function with a horizontal asymptote y = -7 that passes through the points (0, -6) and (1, 6) is:

y = [tex]e^{(ln(13)x)} - 7[/tex].

This function will have a horizontal asymptote at y = -7 and pass through the given points (0, -6) and (1, 6).

To learn more about exponential function click on,

https://brainly.com/question/32543068

#SPJ2

Answer:

Find the question in the attachment below.

Number of tickets sold on Saturday [tex]=6986[/tex]

Number of tickets sold over the days [tex]=9640[/tex]

Step-by-step explanation:

a.

Number of tickets sold on Saturday

Twice as many as the number of adult tickets [tex]=2\times 976= 1952[/tex]

Three times as many as the number of children's tickets [tex]3\times 1678=5034[/tex]

Total number of tickets sold on Saturday =[tex](1952+5034)=6986[/tex]

b.

Total number of tickets sold on Friday and Saturday

Summation of adult and children's ticket on both the days.

[tex]=(6986+976+1678)=9640[/tex]

So total tickets sold on Saturday is [tex]6986[/tex] and tickets sold on both days [tex]=9640[/tex]

Answer:D

Step-by-step explanation:

factorise 2x²-16x+32

x²-8x+16

(x-4)²

factorise 4x²-2x-20

2x²-x-10

2x²+4x-5x-10

2x(x+2)-5(x+2)

(2x-5)(x+2)

solving for (f/g)(x)

(x-4)²/(x+2)÷(2x-5)(x+2)/(x-4)²

(x-4)²/(x+2)*(x-4)²/(2x-5)(x+2)

(x-4)⁴/(2x-5)(x+2)²

Answer:

23 quarters and 12 dimes

Step-by-step explanation:

Answer:

About 158 students in the district participate in the school music program.

Step-by-step explanation:

394(2/5)=788/5=157.6

James has 55 dimes in the bag

Step-by-step explanation:

The given is:

We need to find how many dimes James has

Assume that the number of nickels is x and the number of

dimes is y in the bag

∵ There are x nickels in the bag

∵ There are y dimes in the bag

∵ There are 77 coins in the bag

∴ x + y = 77 ⇒ (1)

∵ 1 nickel = 5 cents

∴ The value of nickles in the bag = 5x cents

∵ 1 dime = 10 cents

∴ The value of dimes in the bag = 10y cents

∵ The total value of coins is $6.60

∵ 1 dollar = 100 cents

∴ $6.60 = 6.60 × 100 = 660 cents

∴ 5x + 10y = 660 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -770 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -110

- Divide both sides by -5

∴ x = 22

Substitute the value of x in equation (2) to find y

∵ 22 + y = 77

- Subtract 22 from both sides

∴ y = 55

∴ The number of dimes is 55

James has 55 dimes in the bag

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

Answer:

This is correct I did it on schoology

Step-by-step explanation:

Answer:

2114.7 people per square mile

Step-by-step explanation:

Population density can be calculated by dividing the total number of people by the area.

23,896 people ÷ 11.3 square miles

≈ 2114.7 people per square mile    (rounded number)

Your answer is one decimal place off.

To calculate the total number of homes in Lora's community, the number of flyers distributed (630) is divided by the percentage of homes that received flyers (35%), resulting in a total of 1800 homes.

To find the total number of homes in Lora's community, we need to set up a proportion where the number of flyers delivered represents 35% of all homes. Since Lora distributed flyers to 630, that is 35% of the total homes. Using the percentage formula:

Total Homes = Distributed Flyers / Percentage of Homes

So, in this case, it would be:

Total Homes = 630 / 0.35

Dividing 630 homes by 0.35 (35% as a decimal) gives us:

Total Homes = 1800

Therefore, there are 1800 homes in Lora's community.

Answer:

The values are x = 0° or x = 60°

Step-by-step explanation:

Given:

[tex]\cos x + \frac{1}{\sqrt{3} }\times \sin x = 1[/tex]

Let it be in the form of

[tex]a\cos x + b\sin x = 1[/tex] such that

a = 1

[tex]b=\frac{1}{\sqrt{3} }[/tex]

We have

[tex]\sqrt{(a^{2}+b^{2} )}=\sqrt{(1^{2}+(\frac{1}{\sqrt{3} }) ^{2} )}\\=\sqrt{\frac{4}{3}}\\=\frac{2}{\sqrt{3} }[/tex]

Now, Dividing both the side by [tex]\frac{2}{\sqrt{3} }[/tex] we get

[tex]\frac{\sqrt{3} }{2}\cos x + \frac{1}{2}\sin x =\frac{\sqrt{3} }{2}\\[/tex]

We Know

[tex]\sin 60 =\frac{\sqrt{3} }{2}\\and\\\cos 60 = \frac{1}{2}[/tex]

Now by replacing with above values we get

[tex]\sin 60\times \cos x + \cos 60\times \sin x = \frac{\sqrt{3} }{2}\\[/tex]

Also we have formula

[tex]\sin A\times \cos B + \cos A\times \sin B = \sin (A+B)[/tex]

By applying the above Formula we get

[tex]\sin (60+x)=\frac{\sqrt{3} }{2}\\[/tex]

Also ,

[tex]\sin (60)=\frac{\sqrt{3} }{2}\\and\\\sin (120)=\frac{\sqrt{3} }{2}[/tex]

Comparing we get

 60 + x = 60   or  60 + x = 120

∴ x = 0°               ∴ x = 120 - 60 = 60°    

Therefore, the values are x = 0° or x = 60° i.e between 0° to 360°

The number of adults = 41

The number of children = 97

Step-by-step explanation:

Let x be the number of adults and

y be the number of children

then according to the given conditions

[tex]x+y = 138\ \ \ Eqn\ 1\\11x+4y = 839\ \ \ Eqn\ 2[/tex]

From equation 1:

x = 138-y

Putting in equation 2

[tex]11(138-y)+4y = 839\\1518-11y+4y = 839\\1518 -7y = 839\\-7y = 839-1518\\-7y = -679\\[/tex]

Dividing both sides by -7

[tex]\frac{-7y}{-7} = \frac{-679}{-7}\\y = 97[/tex]

Putting y = 97 in equation 1

[tex]x+ 97 = 138\\x = 138-97\\x = 41[/tex]

Hence,

The number of adults = 41

The number of children = 97

Keywords: Linear equations variables

Learn more about linear equations at:

#LearnwithBrainly

Answer:

The cabinet is longer by 1/12 foot.

Step-by-step explanation:

3/4 x 3/3 = 9/12

2/3 x 4/4 = 8/12

The inverse is: {(3,5), (4,-2), (-2,7)}

Step-by-step explanation:

In the inverse of a function, the output becomes input and the input becomes output i.e. the functions is reversed.

Given function is:

[(5,3) (-2,4) (7,-2)]

The order of elements in ordered pairs will be reversed. The second elements will be on first place and first element will be on second place.

So,

The inverse is: {(3,5), (4,-2), (-2,7)}

Keywords: Functions, inverse

Learn more about functions at:

#LearnwithBrainly

The inverse of the given function (5,3), (-2,4), (7,-2) is (3,5), (4,-2), (-2,7).

The inverse of a function is created by swapping each input-output pair.

For the given function with ordered pairs (5,3), (-2,4), and (7,-2), we can find the inverse by switching each pair's coordinates. This yields the inverse ordered pairs (3,5), (4,-2), (-2,7). Remember that the inverse function only exists if the original function is bijective, meaning each output is paired with exactly one input.

Answer:

p=11 packets were purchased

Step-by-step explanation:

30+11p=151

11p=121

then

121/11

so

p=11

Hope I understood the question :/

Answer:

Step-by-step explanation:

I believe the correct answer is that Andrew's Math Teacher purchased 11 packets of 10 tests each, meaning that the total number of test would be 110. I got this by subtracting the $30 entrance fee from the $151. After doing this we are left with $121. I then divided the $121 by the cost per packet and I was left with 11 packets. Since every packet contains 10 tests I multiplied that by the number of packets to get the final answer... 110 tests purchased.

The mean absolute deviation is a measure of variation in a dataset, not its center. It helps indicates how spread out the data is from the mean value.

The mean absolute deviation is not a measure of center,instead, it is a measure of variation. The center of a data set is typically represented by measures like the mean, median, or mode. These describe the common, central value in the dataset.

Conversely, the mean absolute deviation is a statistical tool used for understanding the dispersion or variation in a set of values. It gives an average of the absolute differences between each data point and the mean of the data set. This helps identify how spread out the data is from the mean.

https://brainly.com/question/32035745

#SPJ12

Answer:

[tex]\displaystyle y = \frac{4}{5}x[/tex]

B. x 1 3 4 5

y 50 150 200 250

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{0 + 24}{0 + 30} = \frac{24}{30} = \frac{4}{5} \\ \\ y = \frac{4}{5}x[/tex]

We can write the equation from here, since both the x-intercept and y-intercept are at the origin.

_______________________________________________

Now, all you have to do is input each value into the function to confirm their authenticities. Once you do this, you WILL arrive at answer choice B).

I am joyous to assist you anytime.

Answer:

D. Subtraction property of equality; n = 15

Step-by-step explanation:

Given equation that shows the cost of n basketballs uniforms,

C = 40n + 260

According to the question,

Total cost = $ 860,

⇒ 40n + 260 = 860

Using subtraction property of equality, subtract 260 on both sides,

⇒ 40n = 860 - 260

⇒ 40n = 600

Using division property of equality, divide both sides by 40.

⇒ n = [tex]\frac{600}{40}[/tex] = 15.

Hence, 15 uniforms were purchased.

i.e. Option D is correct.

Answer:

5 hours  was Aaron at the sitter

Explanation:

Cost of baby sitting for the first hour: 10

Cost of baby sitting for additional hour= 12

Total cost of babysitting= 58

Since the cost of first hour is 10

Hence  the remaining cost after first hour

= 54-10

=48

Which means 1 hour  is consumed in the first hour

Now to calculate the remaining hours for every additional hour

= [tex]\frac{48}{12}[/tex]

=4 hours

Hence the total hour Aaron was with the sitter

= 1 hour + 4 hours

= 5 hours

Answer:

2

Step-by-step explanation:

Answer:

120 gallons per hour.

Step-by-step explanation:

Between 1:30 P.M. and 1:50 P.M., 40 gallons of water leaked into a boat.

We know, the (1: 50 P.M. - 1: 30 P.M.) = 20 minutes.

So, the time span is of 20 minutes and the amount of water leaked into is 40 gallons.

Therefore, the amount of water that will leak into the boat in 60 minutes is [tex]\frac{40 \times 60}{20} = 120[/tex] gallons.

So, the rate in gallons per hour of the leaking water is 120 gallons per hour. (Answer)

Answer:

The graph of g(x) = –2 · 10x is stretched vertically and reflected across the x-axis.

Step-by-step explanation:

Answer:

D. The graph of g(x) = –2 · 10x is stretched vertically and reflected across the x-axis.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a(c + b) = d          // We multiply a by c and b (addition is distributive)

ac  +  ab = d        // We let the c addend in the left

ac = d - ab          // We divide by a

c = (d - ab) / a

Answer: Hi Hi I know this is like a year late but I would like to be able to help future people with this question.

The correct answer is: c=d+ab/a (B)

Isolate the variable by dividing each side by factors that don't contain the variable.

I really hope this helps people, have a happy halloween :D

Answer:

26

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

7.88

Step-by-step explanation:

Answer: 7,88

Explanation

Answer:

1/4

Step-by-step explanation:

The number of kids who brought their lunches is 3/7 of 84.

3/7 of 84 = 3/7 * 84 = 3/7 * 84/1 = (3 * 84)/(7 * 1) = 252/7 = 36

36 kids brought their lunches.

9 of the 36 kids got a slice of pizza.

The fraction is 9/36 = 1/4

Answer: 1/4

Answer:

The numbers are 23 and 24

Step-by-step explanation:

Let

x ----> the first positive consecutive integer

x+1 ----> the second positive consecutive integer

we know that

The product of the two consecutive positive integers is 552

so

The algebraic expression that represent this situation is

[tex]x(x+1)=552[/tex]

Convert to expanded form

[tex]x^2+x-552=0[/tex]

Solve the quadratic equation by graphing

The roots of the equation are

[tex]x_1=-24[/tex] ----> the number cannot be negative

[tex]x_2=23[/tex]

see the attached figure

therefore

[tex]x=23\\x+1=24[/tex]

The numbers are 23 and 24

To find two consecutive positive integers whose product is 552, set up the equation x(x + 1) = 552, expand and solve the quadratic equation.

To find two consecutive positive integers whose product is 552, we can set up the equation x(x + 1) = 552, where x represents the smaller integer.

Expanding the equation, we get x^2 + x - 552 = 0. This is a quadratic equation, and we can solve it by factoring or using the quadratic formula.

Factoring the quadratic equation, we find that (x - 23)(x + 24) = 0. So the two consecutive positive integers are 23 and 24.