The height of the wall if A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall, is 5.81 feet.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine, cosine, and tangents are their names and acronyms (tan).
Given:
A repairman leans the top of an 8 ft ladder against the top of a stone wall, the base of the ladder is 5.5 ft from the wall,
Calculate the height of the wall as shown below,
Assume the height of the wall is x then,
x² + base² = ladder height²
x² + 5.5² = 8²
x² = 64 - 30.25
x² = 33.75
x = √33.75
x = 5.81 ft
Thus, the height of the wall is 5.81 feet.
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Circumference is 4 what is the radius and area of the circle
What is the slope of this line?
how do i solve 3 (2y-4)=8y+9-9y
a triangle with an area of 202.5 has a height that measures 15 find its base
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Jack needs to save $125 to go to a concert. He has saved $35. He makes $7.50 an hour at his job. With x representing the number of hours, which equation and solution can be used to show how many hours Jack must work in order to have enough money to go to the concert?
A. 125x + 35 = 750; x = 5.75
B. 35x + 125 = 750; x = 18
C. 7.5x + 35 = 125; x = 12
D. 35−7.5x=125;x=6
Which of the binomials below is a factor of this trinomial ? X^2 + x + 12
Two numbers multiply to be -15 and adds to be 2 what are the numbers?
Graph the data from the table below. Describe the parent function as linear, square root, cube root, cubic, or quadratic.
Solving for Circumference of a Penny A penny is 1.9 cm wide. What is the circumference of a penny? Approximate using mc001-1.jpg = 3.14 and round the answer to the nearest tenth if necessary.
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
To find the circumference of a penny, we use the formula for the circumference of a circle:
Circumference = π * diameter
Since the penny's width is given (which is the same as the diameter), we can plug in the values:
Circumference = 3.14 * 1.9 cm
Now, calculate the circumference:
Circumference ≈ 5.966 cm
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
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Diane is baking cookies. She bakes four dozen sugar cookies, three dozen butter cookies, and two dozen chocolate chip cookies. She gives away 2 dozen sugar cookies, 2.5 dozen butter cookies, and 1.5 dozen chocolate chip how many cookies does she have left? ( Give an exact number of cookies).
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Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain
A) The two line plots are attached.
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= {4, 4, 0, 0, 0, 2, 2, 4}
RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= {4, 2, 0, 0, 0, 0, 2, 4}
Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
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What method could have been used to collect the data?
there are 54 people at the party. 18 of them are wearing red, what percent of them are not wearing red
There are 54 people at the party.
18 people are wearing red which means that 36 people are not wearing red
54 - 18 = 36
The fraction [tex]\frac{36}{54}[/tex] represents the 36 people at the party that are wearing no red. We can find what percent of the people at the party are not wearing red by turning [tex]\frac{36}{54}[/tex] into a percent.
[tex]\frac{36}{54}[/tex] can be reduced to [tex]\frac{2}{3}[/tex] by dividing both the numerator and denominator by the greatest common factor of 36 and 54.
2 ÷ 3 = 0.667
0.667 × 100 = 66.67%
Therefore, 66.67% of the people at the party are not wearing red
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The original price for a clothes washer and dryer is $999. Which coupon is a better deal? A) SAVE 20% ON ANY WASHER/DRYER COMBO B) SAVE $200 ON ANY WASHER/DRYER COMBO C) SAVE $75 PLUS 5% OFF ON ANY WASHER/DRYER COMBO D) SAVE $50 PLUS 20% OFF ON ANY WASHER/DRYER COMBO
Which measure is equivalent to 2.5 liters? A)2.5 mL B)250 mL C) 2500 mL D)25,000 mL
we know that
[tex] 1L=1000mL [/tex]
we are given 2.5L
so, to find 2.5L into mL, we will have to multiply both sides by 2.5
[tex] 2.5*1L=2.5*1000mL [/tex]
now, we can simplify it
[tex] 2.5L=2500mL [/tex]
so, option-C.............Answer
Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all faces of the ramp with plywood, how much plywood will he need?
96 square feet
144 square feet
156 square feet
168 square feet
Answer:
C) 156
Step-by-step explanation:
What do you call a person who makes face all day long
A clockmaker is the answer
The diameter of a circular placemat is 15 inches. Devon wants to sew a border of lace around the placemat. If the lace he wants is sold by the foot, how many feet of lace will he need to purchase?
What conclusions can you make about numbers in scientific notation with negative exponents?
The sum of the ages of two people is 32. The difference is their ages is 4. What is the age of the younger person ?
Mitch does not know the correct answer to two multiple choice questions. The choices are A,B,C, and D. If Mitch just guesses, what is the probability that Mitch will guess both answers correctly?
Final answer:
Mitch has a 1/16 probability of guessing both multiple-choice answers correctly when randomly guessing among four options.
Explanation:
If Mitch guesses on two multiple-choice questions with choices A, B, C, and D, the probability of guessing both correctly is calculated as follows: The probability of correctly guessing one question is 1/4 (since there are 4 possible choices, and only one is correct). To find the probability of guessing both correctly, we multiply the probabilities of each independent event. Thus, the probability of guessing the first question correctly AND the second question correctly is 1/4 × 1/4 = 1/16.
Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How much change will Mrs. Sloan receive if she gives the cashier $20.00.
a. $14.45 b. $5.55 c. $12.55 d. $7.45
Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (1,2). A. Y=2x^2. B. Y=2(x-1)^2. C. Y=x^2. D. Y=(x+1)^2+1
The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]
The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.
In this case, the vertex is (0, 0), so h = 0 and k = 0.
Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].
Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:
[tex]2 = a(1)^2[/tex].
Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]
So, the correct answer is A. [tex]Y = 2x^2.[/tex]
7.Kristy baked 18 cookies. She took 2/3 of the cookies to work. How many cookies did she NOT take to work? 4 6 8 12
write the worlds as an algebraic expression. the width plus twelve. how do i do it?
the number of people who attended the spring festival is 799 more than 8 thousands. how many people attended the festival?
In this question, we are given the information about total number of people but in word equation.
We are given that, 799 more from 8 thousand attend the festival.
When we are given more, we add the number to the number from which it is more.
Here, we will add 799 to 8,000 in order to calculate total number of people who attended the festival
Thus, total number of people who attended the festival = 8,000 people + 799 people = 8,799 people.
A probability close to 1/2 indicates a chance event is ________ to occur
Likely, unlikely, or neither likely nor unlikely
Please help
solve the exponential equation
[tex] {10}^{ - x} = {7}^{4x} [/tex]
Solve the system of equations. y = 7x + 43 y = 2x + 13 a. ( -6, 1) c. ( 6, 1) b. ( 6, -1) d. No solution