Answer:
Its 111ft. tall if thats what your asking.
Step-by-step explanation:
100+11=111
The answer is: [tex]83.66^\circ[/tex]. The angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].
To solve the problem, we need to find the angle of elevation that the ladder makes with the ground when it is resting on top of the hook and ladder truck. We are given that the ladder is 100 feet long and its base is 11 feet from the ground.
We can use trigonometry to solve for the angle of elevation (θ). The tangent of the angle of elevation is the ratio of the opposite side (height from the ground to the top of the ladder) to the adjacent side (the distance from the base of the ladder to the point on the ground directly below the top of the ladder).
Let's denote:
- The length of the ladder as [tex]\( L \)[/tex], which is 100 feet.
- The distance from the base of the ladder to the point on the ground directly below the top of the ladder as [tex]\( d \)[/tex], which is 11 feet.
- The height from the ground to the top of the ladder as [tex]\( h \)[/tex].
Using the Pythagorean theorem, we can find [tex]\( h \)[/tex]:
[tex]\[ h^2 + d^2 = L^2 \][/tex]
[tex]\[ h^2 + 11^2 = 100^2 \][/tex]
[tex]\[ h^2 = 100^2 - 11^2 \][/tex]
[tex]\[ h^2 = 10000 - 121 \][/tex]
[tex]\[ h^2 = 9879 \][/tex]
[tex]\[ h = \sqrt{9879} \][/tex]
[tex]\[ h \approx 99.39 \text{ feet} \][/tex]
Now, we can find the angle of elevation using the tangent function:
[tex]\[ \tan(\theta) = \frac{h}{d} \][/tex]
[tex]\[ \theta = \arctan\left(\frac{h}{d}\right) \][/tex]
[tex]\[ \theta = \arctan\left(\frac{99.39}{11}\right) \][/tex]
[tex]\[ \theta \approx \arctan(9.03545455) \][/tex]
[tex]\[ \theta \approx 83.66^\circ \][/tex]
Therefore, the angle of elevation that the ladder makes with the ground is approximately [tex]\( 83.66^\circ \)[/tex].
The final answer is:
[tex]\[ \boxed{83.66^\circ} \][/tex]
The complete question is:
A 100 ft ladder rests on top of a hook and ladder truck with its base 11 feet from the ground. When the angle of elevation of the ladder is 81°, how high up the building will the ladder reach?
A cylindrical jar's lid has a radius of 4 inches. If the volume is 351.68 in , approximately what is the height of the jar?
Answer:
7 inches
Step-by-step explanation:
The volume of a cylinder is calculated using
[tex]V = \pi {r}^{2}h[/tex]
where r =4 inches is the radius and V=351.68 is the volume.
To find the height of the jar, we substitute these values and solve for h.
[tex]351.68 = 3.14 \times {4}^{2} \times h[/tex]
[tex]351.68 = 50.24h[/tex]
Divide both sides by 50.24 to get:
[tex]h = \frac{351.68}{50.24} [/tex]
h=7 inches
Therefore the height of the jar is 7 inches
The minor arc measures of circle Z are shown in the figure.
Circle Z is shown. Radii Z Y, Z X, Z W, Z V, Z U, and Z T are shown. The arc measure of Y X is 71 degrees, the arc measure of X W is 32 degrees, the arc measure of W V is 71 degrees, the arc measure of V U is 78 degrees, the arc measure of U T is 54 degrees, and the arc measure of T Y is 54 degrees.
Use the drop-down menus to complete each statement.
Answer:
Part 1) Option a. TZY
Part 2) Option c. YZX
Step-by-step explanation:
The question is as following and see the attached figure
The minor arc measures of circle Z are shown in the figure.
Use the drop-down menus to complete each statement.
1) Angle UZT is congruent to angle _____
2) Angle VZW is congruent to angle____
Answer choices
1) a. TZY, b. XZW, c. VZW
2) a. UZV, b. TZY, c. YZX
===============================================
Solution:
Part 1) Angle UZT is congruent to angle______
From the attached figure, we can deduce that:
∠UZT = 54°
∠TZY = 54°
So,
∠TZY = ∠UZT ⇒ both angles are congruent.
1. Angle UZT is congruent to angle TZY
===========================================
Part 2) Angle VZW is congruent to angle_____
From the attached figure, we can deduce that:
∠VZW = 71°
∠YZX = 71°
So,
∠YZX = ∠VZW ⇒ both angles are congruent
2. Angle VZW is congruent to angle YZX
Answer: correct answer is TZY for first one and YZX for second
Step-by-step explanation:
Just chose those and got it correct :)
Population in Millions
World: 7,691
Canada: 37.4
What percent of the 2019 world population lives in Canada? Round the percentage to three decimal places.
Answer:
0.486% of world population lives in Canada.
Step-by-step explanation:
Given: World Population= 7691 million.
Canada Population= 37.4 million.
Now, finding the percentage of world population lives in Canada.
[tex]Population\ percentage= \frac{Canada\ population}{World\ population} \times 100[/tex]
⇒ [tex]Population\ percentage= \frac{37.4}{7691} \times 100[/tex]
⇒ [tex]Population\ percentage= 0.00486\times 100[/tex]
∴ [tex]Population\ percentage= 0.486\%[/tex]
Hence, 0.486% of world population lives in Canada.
What is the final amount if 943 is decreased by 13% followed by a further 6% decrease?
Give your answer rounded to 2 DP.
The final amount after a 13% decrease followed by a further 6% decrease from 943, rounded to two decimal places, is 771.19.
Explanation:To calculate the final amount after sequential percentage decreases, you first apply the initial percentage decrease to the original amount, then apply the second percentage decrease to the new, lower amount.
Here’s how you can do it step by step:
Calculate the first decrease of 13%: 943 × 0.13 = 122.59Subtract the first decrease from the original amount: 943 - 122.59 = 820.41Calculate the second decrease of 6% on the new amount: 820.41 × 0.06 = 49.2246Subtract the second decrease from the new amount: 820.41 - 49.2246 = 771.1854The calculator answer is 771.1854, but since we want the answer rounded to two decimal places, we must look at the third decimal place. Since the digit in the thousandths place (5) is greater than or equal to 5, we round up giving us a final answer of 771.19.
You are on your way to work. You drive 3.9 miles to a gas station and buy gas. Your workplace is 1.39 miles from the gas station. What is the distance of your commute to work?
Your commute is
( ?????) Miles.
Answer:
Approx. 5.3 miles
Step-by-step explanation:
Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 4 to 2. Tia
wants to sell a total of 54 apples and oranges. How many apples should she sell?
A.
52 apples
B. 36 apples
C. 9 apples
D. 32 apples
Answer:
[tex]\large \boxed{\text{B. 36 apples}}[/tex]
Step-by-step explanation:
Let a = the number of apples
and o = the number of oranges
You have two conditions:
[tex]\begin{array}{lrcl}(1) & \dfrac{a}{o} & = & \dfrac{4}{2} \\\\(2) & a+ o & = & 54\\\end{array}[/tex]
Solve the equations for a
[tex]\begin{array}{rcll}2a & = & 4o & \text{Multiplied each side of (1) by 2o}\\\(3) \,2a - 4o& = & 0 &\text{Subtracted 4o from each side}\\a + o & = & 54& \text{This is equation (2)}\\(4) \, 4a +4o& = &216&\text{Multiplied each side by 4} \\6a& = &216&\text{Added (3) and (4)} \\a & = &\mathbf{36}&\text{Divided each side by 6} \\\end{array}\\\text{Tia should sell $\large \boxed{\textbf{36 apples}}$}[/tex]
The sum of four and three multiplied by the quotient of four and two
Answer:
14
Step-by-step explanation:
4+3=7
4/2=2
7•2=14
Sam invests $6000 in an account that pays interest of 4.5% per year.
a) How much interest would he earn each year?
b) How much would he have in his account at the end of the first year?
He would earn an interest of $270 each year and at the end of the first year he would have $6270 in his account.
Step-by-step explanation:
Step 1: Given details are Principal Amount (P) = $6000, Rate of Interest (R) = 4.5% and time (T) = 1 yearStep 2: Calculate simple interest by using the formula SI = PRT/100⇒ SI = 6000 × 4.5 × 1/100
⇒ SI = 60 × 4.5 = $270
Step 3: Calculate the amount he would receive at the end of an year by using the formula, A = P + SI⇒ A = 6000 + 270
⇒ A = $6270
Two people bought a 13-inch sandwich to share. How many inches of sandwich does each person get if they split it evenly? Choose the correct answer from the choices below.
Answer:
6.5
Step-by-step explanation:
13/2 = 6.5 inches or 6 1/2 inches
Answer:
6 2/4ths
Step-by-step explanation:
If a polynomial function f(x) has roots 4 - 131 and 5, what must be a factor of f(x)?
Answer:
(x - 4), (x + 131), and (x - 5) must all be factors of f(x).
Step-by-step explanation:
HELPPP....PLEASE...........
Answer:
9 1/3, 12 1/2, 14 3/4
Step-by-step explanation:
I assume the formula you’re working with is A=b*h since nothing says otherwise...
((Patio 1))
So you have your area (147) and your base (15 3/4), now you need to plug them in, which should look like this:
147= 15 3/4*h
You need to isolate your h in order to get the missing number, so you should divide both sides by 15 3/4 OR 63/4 ((15*3—>60+3=63))
Dividing by a fraction is the equivalent of multiplying by its reciprocal... so
147 * 4/63 = 588/63 which can be simplified to 84/9 once both the numerator and denominator are divided by 7
In mixed number for it is 9 3/9 which simplified becomes 9 1/3
You solve the other similarly
find the area of the shape shown below
Answer: 42 units squared
Step-by-step explanation:
3x7=21
3x7=21 divided by 2 = 10.5 + 10.5 = 21 so,
21+21=42
Hope it helps
Answer:
34.5 units^2
Step-by-step explanation:
The square is A = bh.
A = 7 * 3 = 24.
The triangle is A = 0.5bh.
A = 0.5 * 7 * 3 = 0.5 * 21 = 10.5.
24 + 10.5 = 34.5 units^2.
I am interested in a new van that costs $32,500. The salesman says he will give it to me for $27,950. What is the percent discount he is giving me?
Answer:
The salesman is giving you a 14% discount
Step-by-step explanation:
Do 27950/32500 to get 0.86
Then do 1-0.86=0.14
Multiply by 100 to get 14%
Hope this helped!
Can you divide a number with a fraction
Answer:
yes
Step-by-step explanation:
yesAnswer:
yes you can
Step-by-step explanation:
if its a number put it as a fraction put a one number the number your divining and divide and if it's a improper fraction turn in into a mixed number :)
VERY VERY VERY VERY VERY URGENT!!?!!???
These triangles are similar.
True
False
Answer:
True
Step-by-step explanation:
Evaluate the function. F(x)=3/x-1/. F(-3)
perimeter of a triangle formula
Side 1 + side 2 + side 3 = perimeter
Step-by-step explanation:
You add all three side lengths
Twenty-four hundredth in decimal notation
Answer:
0.24
Step-by-step explanation:
Twenty-four hundredths = 24/100 = 24×(1/100) = 24×0.01 = 0.24
_____
Both 24/100 and 0.24 are pronounced "twenty-four hundredths."
Answer:
0.24
Step-by-step explanation:
If you say hundredths with ths it means that the number is at the right side the decimal point. so that means twenty four hundredths is at the right side of the decimal point so the answer will be 0.24 hundredths.
There are 180 calories in 3 scoops of vanilla ice cream. How many calories are in 7 scoops.
Answer:
420 calories
Step-by-step explanation:
180 / 3 = 60 calories
60 x 7 =420 calories
-4/3x-3=1/3x+3/4 solve for X
Answer:
-9/4
Step-by-step explanation:
-4/3x-3=1/3x+3/4
-4/3x-1/3x-3=3/4
-5/3x=3/4+3
-5/3x=3/4+12/4
-5/3x=15/4
x=(15/4)/(-5/3)
x=(15/4)(-3/5)
x=-45/20
simplify
x=-9/4
Della Ahkta has a whole life policy for $50,000. She pays an annual premium rate of $13.47 per
$1,000. When she signed her insurance contract she chose to use the annual dividend to reduce the
annual premium. When she gets a notice that her insurance premium is due, she is notified that her
policy has paid an annual dividend of $27.94. What amount will Della need to send the insurance
company to pay the balance due on the annual premium?
Answer:
645.56
Step-by-step explanation:
50000/1000 13.37=673.50
673.50
-27.94
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The student council at Princeton High School is making T-shirts to sell for a fundraiser, at a price of $11 apiece. The costs, meanwhile, are $9 per shirt, plus a setup fee of $140. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
Selling shirts will cover the $ in costs.
To cover costs, the student council needs to sell 70 T-shirts, which will cover the $770 in costs.
Explanation:To solve the student council's problem, we need to find the number of T-shirts that must be sold so that the total revenue equals or exceeds the costs associated with making the T-shirts. Let's define x as the number of T-shirts to be sold. The total revenue from selling the T-shirts at $11 apiece can be represented as 11x. The costs consist of a setup fee of $140 and $9 per shirt, so the total cost is 9x + 140. To determine when the revenue will cover the costs, we can set up the following equation:
11x = 9x + 140
Solving this equation for x, we subtract 9x from both sides:
2x = 140
Then divide both sides by 2:
x = 70
Therefore, the student council needs to sell 70 T-shirts to cover their costs, which will be $770 ($11 per shirt multiplied by 70 shirts).
if the interior angle ofa regular polygon is 162° how many sides does it have
Answer:
20 sides.
Step-by-step explanation:
The exterior angle = 180 - 162 = 18 degrees.
Since the sum of the exterior angles = 360 degrees the number of sides
= 360 / 18
= 20 sides.
Mary took out a student loan for $15000 at 4% simple interest. How much interest will she pay in 10 years? suppose she paid it off in 8 years instead of 10 years. how much would she save in interest?
Answer:$1200
Step-by-step explanation:
erin makes $18 an hour. she works 40 hours a week. she found an apartment for $1,000 a month. Should erin rent the apartment?
Answer:
Based on her monthly income YES
Step-by-step explanation:
18 × 4 = $720 a week and 720 × 4 = $2,880 a month
The rent for the apartment is $1,000 if Erin rent this place she will have an extra =1,880 for her living expenses after she pays for the rent so there would be no problem of her renting the place.
Marco buys a certain brand of shampoo from a supplier at 7.25 dollars per bottle .He sells it at a markup of 25 percent. What is the markup .
Final answer:
Marco buys shampoo at $7.25 per bottle and sells it with a 25% markup, making the markup $1.81 per bottle. The selling price, therefore, is $9.06 per bottle.
Explanation:
The question is about calculating the markup applied by Marco on a bottle of shampoo. Marco buys the shampoo at $7.25 per bottle and sells it at a markup of 25 percent. The markup is calculated based on the cost price of the product. In this case, to find the markup amount, we use the formula: Markup = Cost Price * Markup Percentage. So, the markup on each bottle of shampoo is $7.25 * 0.25 = $1.81. Therefore, Marco applies a $1.81 markup on each bottle of shampoo.
To determine the selling price, one can add the markup to the cost price, which would be $7.25 + $1.81 = $9.06. This is Marco's selling price per bottle after applying the 25 percent markup.
What is 7 3/8 + 3 1/4?
Answer:
10 5/8
Step-by-step explanation:
1/4 = 2/ 8
7 3/8 + 3 1/4 = 7 3/8 + 3 2/8
7 3/8 + 3 2/8 = 10 5/8
Answer:
10.675
Step-by-step explanation:
How many times does 5 go into 236
Answer:
47.2
Step-by-step explanation:
236/5
47.5
47.2
Step-by-step explanation:
Because,
= 236/5
= 47.2
Therefore, 47.2 tines 5 goes into 236.
How is the Distributive Property used to simplify operations with scientific notation
Answer:
See explanation
Step-by-step explanation:
Let a,b, and c be real numbers.
The distributive property says that:
[tex]a(b + c) = ab + ac[/tex]
Assuming we want to simplify:
[tex]10(5*10^{-1}+150*10^{-3})[/tex]
We apply the distributive property to get:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10[/tex]
We can now use rules of exponents to simplify further:
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2}x {10}^{2} [/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5*1+1.50*10^{-2 + 2}[/tex]
[tex]10(5*10^{-1}+150*10^{-3}) = 5+1.50*10^{0} = 6.5 \times {10}^{0} [/tex]
Mary has 15 points with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there
Answer:
The number of nickel coins is 10 and the number of quarter coins is 5
Step-by-step explanation:
The correct question is
Mary has 15 coins with the total value of $1.75 if the coins are nickels and quarters how many of each kind are there
Let
x ----> the number of nickel coins
y ----> the number of quarter coins
Remember that
[tex]1\ nickel=\$0.05[/tex]
[tex]1\ quarter=\$0.25[/tex]
we know that
Mary has 15 coins
so
[tex]x+y=15[/tex] -----> equation A
The total value of the coins is $1.75
so
[tex]0.05x+0.25y=1.75[/tex] ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (10,5)
therefore
The number of nickel coins is 10 and the number of quarter coins is 5