Consider the figure below.
Find the value of x.
Answer:
x = 5
Step-by-step explanation:
When two straight lines intersect, four angles are formed. The angles that are directly opposite of each other are equal. Since the angles are equal set the values equal to each other and solve for x.
5x - 5 = 2x + 10
5x - 5 - 2x = 2x + 10 - 2x
3x - 5 = 10
3x - 5 + 5 = 10 + 5
3x = 15
3x/3 = 15/3
x = 5
Bob uses a 20 foot ladder to paint a section of his house that is 16 feet high.
-
16 ft
Ladder
20 ft
80
Ground
Select all equations that can be used to solve for 0.
sin 0
12
20
cos
12
20
12
tan 8 =
20
O sin e
16
20
cos e
16
20
Answer:
Option (2) and Option (4)
Step-by-step explanation:
From the picture attached,
Length of ladder AC = 20 feet
Height of the highest point of the ladder from ground AB = 16 ft
By Pythagoras theorem,
AC² = BC² + AB²
BC² = AC² - AB²
BC = [tex]\sqrt{(20)^2-(16)^2}[/tex]
= [tex]\sqrt{400-256}[/tex]
= [tex]\sqrt{144}[/tex]
= 12
Now, Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}[/tex]
= [tex]\frac{16}{20}[/tex]
Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}[/tex]
= [tex]\frac{12}{20}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{16}{12}[/tex]
Therefore, Option (2) and Option (4) are the correct options.
The equation that should be used is option 2 and option 4.
Calculation of the equation:Since
Length of ladder AC = 20 feet
Height of the highest point of the ladder from ground AB = 16 ft
So here we apply the Pythagoras theorem,
AC² = BC² + AB²
BC² = AC² - AB²
So,
[tex]BC = \sqrt{(20)^2 - (16)^22}\\\\ = \sqrt{400 - 256}\\\\ = \sqrt{144}[/tex]
= 12
Now
Sin θ = 16\20
Cos θ = 12\20
tan θ = 16 \12
hence, The equation that should be used is option 2 and option 4.
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please help me asap
Answer:
-.51, .1/2, .42, 11/20
Answer:
-.51
-1/2
.42
11/20
The value of √ 8 is between which two integers?
a. 2 and 3
b. 3 and 4
c. 7 and 9
d. 49 amd 81
I have a question attached pls help
Answer:
10.35oz
Step-by-step explanation:
Cuz if you do the math 16 times 14 equals 224 and 15.5 times 10 equals 155 so if you minus 155 from 224 then you have 69 square inches which you multiply by 0.15 which thus gets you the answer 10.35
A professor of management has heard that seven students in his class of 49 have landed an internship for the summer. Suppose he runs into two of his students in the corridor. a. Find the probability that neither of these students has landed an internship. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. Find the probability that both of these students have landed an internship. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
Answer:
Total = 0.7321 (Approx)
Probability that both got internship = 0.0179 (Approx)
Step-by-step explanation:
1. First student not get internship = (49-7) / 49
First student not get internship = 42 / 49
Second student not get internship = (42-1) / (49-1)
Second student not get internship = 41 / 48
Total = [42 / 49][41 / 48]
Total = 0.7321 (Approx)
2. Probability that both got internship = 7C2/49C2
Probability that both got internship = (7)(6)/(49)(48)
Probability that both got internship = 0.0179 (Approx)
How does the digit 5 in the number 357 compare with the digit 5 in the number 465?
A) The digit 5 in the number 357 represents 1/10 as much as the digit 5 in the number 465.
B) The digit 5 in the number 357 represents 10 times as much as it represents in the number 465.
C)The digit 5 in the number 357 represents 100 times as much as it represents in the number 465.
D)The digit 5 in the number 357 represents the same amount as it represents in the number 465.
Answer:
Option B.
Step-by-step explanation:
In this problem, we need to compare digit 5 in the number 357 with the digit 5 in the number 465.
In 357, 5 is on the tens place while in 465 5 is in the ones place.
Place value of 5 in 357 is 50 and in 465 is 5 only.
For comparison, divide 50 by 5. So,
50/5 = 10
It means that the digit 5 in the number 357 represents 10 times as much as it represents in the number 465.
In 1 hr, a plane can travel 390 mi into the wind and 470 mi with the wind. Find the wind speed and the rate of the plane in still air.
The wind speed is mph.
The rate of the plane in still air
mph
Let w be the wind speed and p the plane's speed in still air.
Flying against the wind, the plane has velocity
p - w = 390 mi/h
and flying with it, it has
p + w = 470 mi/h
Add the two equations together to eliminate w and solve for p :
(p - w) + (p + w) = 390 mi/h + 470 mi/h
2p = 860 mi/h
p = 430 mi/h
Subtract them to eliminate p and solve for w :
(p - w) - (p + w) = 390 mi/h - 470 mi/h
-2w = -80 mi/h
w = 40 mi/h
XYZ, Inc. manufactures the same product in two of their plants, a Northern facility and a Southern facility. Customers who purchase from XYZ, Inc. are encouraged to return their products if they are defective. The probability that a customer returns his/her purchased product given that it was manufactured in the Southern facility is 0.15. The Southern facility produces 40% of the products. It has been recorded that 8% of the customers return their product. What is the probability that a product has been manufactured in the Southern facility if it has been returned to XYZ, Inc.
Answer: = 0.75
Step-by-step explanation:
given that;
P ( returned product / southern fac.) = 0.15
probability of being manufactured in Southern facility P(S) = 40% = 0.40
so probability of being manufactured in norther facility P(N) = 0.60
probability of product being returned =P(R) =0.08
therefore P(RnS) = P(S) * P(R|S)
= 0.40 * 0.15
= 0.06
so now the probability that a product has been manufactured in the Southern facility if it has been returned to XYZ
= P(S|R) = P(RnS)/P(R)
= 0.06 /0.08
= 0.75
Simplify 7(x + 3). what is the answer
Answer: x = ( -3)
Step-by-step explanation:
7 ( x+3 ) = 7x + 21
7x = -21
7x ÷ 7 = -21÷7
X = ( -3)
need help for geometry please
Answer:
C TSU=LMN
Step-by-step explanation:
When naming a shape with points you name from top to bottom, but since in order for it to be equal with the other triangle you'd flip it and then name it that way.
C = ΔTSU=ΔLMN
Step-by-step explanation:
They are flipped, simply look at the how many lines it has in the middle and follow them. TSU goes through 1 line, and 2 lines. LMN goes through 1 line, and 2 lines as well.
What is the solution to the following equation? (4 points)
5(2x − 6) + 20 = 10
9
5
3
2
Answer:
2
explanation:
5(2(2)-6)+20=10
5(4-6)+20=10
5(-2)+20=10
-10+20=10
10=10
The square root of 281961?
Answer:
531
Step-by-step explanation:
Answer:
531
Step-by-step explanation:
531 x 531 = 281961
35=-5/8x solve for x
By going through the problem, we can find that the answer is that x=-56.
EDIT: if i'm being honest i just used a calculator to do this lol
try web2.0calc.com, its what i use
Evaluate each expression.
|10|
|-7| - 5
1 + |7|
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
|10| = 10
|-7| - 5 = 2
1 + |7| = 8
Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?
Answer: C
Step-by-step explanation:
Answer:
Figure C
Step-by-step explanation:
PLEASE HELP!!!!
Use the table below to match the slopes to the lines.
Answer: Check out the filled out chart below.
Row 1: 1/4, 1/4, -4
Row 2: -2, -2, 1/2
Row 3: 3, 3, -1/3
=========================================
Explanation:
Parallel lines have equal slopes. So if the original line has slope 1/4, then any parallel line will also have slope 1/4. The only thing different is the y intercept.
Perpendicular slopes multiply to -1 assuming neither line is vertical. For row 1, the perpendicular slope is -4 which multiplies with the original slope 1/4 to get -1.
Put another way, the perpendicular slope is the negative reciprocal of the original slope. For row 2, the perpendicular slope is 1/2 because we flip the fraction and the sign for the original slope -2 = -2/1
One month also rented 5 movies and 3 video games for a total of $31 the next month he rented 7 movies and 9 video games for a total of $71 find the rental cost for each movie and each video game
Answer:
V = 5.75, M = 0.45
Step-by-step explanation:
5M + 3V = 31
7M + 9V = 71
5M = 31 - 3V
M = (31 - 3V) / 5
7((31 - 3V) / 5) + 9V = 71
(217 - 21V)/5 + 9V = 71
43.4 - 4.2V + 9V = 71
4.8V = 27.6
V = 5.75
5M + 3(5.75) = 31
5M = 2.25
M = 0.45
PLS ANSWER ASAPPPPPPPPPPPPPP
Answer:
5/14
Step-by-step explanation:
(5/4)(7/2)
Multiply the numerators with the denominators.
5*2=10
4*7=28
10/28 = 5/14
What is this?
Multiply.
14.3 X 6.2
Answer:
88.66
Step-by-step explanation:
14.3 * 6.2
88.66
One hundred clothing stores go out of business. This will
the supply of clothes at each price level.
A. increase
B. decrease
Answer:
A increase, because less stores means more people going to the other ones, which means more money for the owners, which means if they raise the proces, people still need cloths sothey will still buy
Step-by-step explanation:
Consider the diagram below.
Answer:
<a = 61
<b + <c = 90
carlita made 2 kinds of lemonade for her friends to enjoy at a fall celebration. After the celebration, she had 6.8 liters of pink lemonade left over and 10.2 liters of yellow lemonade left. About how many more liters of yellow lemonade were leftover to the nearest liter
Answer:
17 liters of pink lemonade
PLEASE HELP RN!!!! 15 POINTS I NEED ANSWERS
Given: m_Am_B=mZB+m2C
Prove: m_C=m_A
Write a paragraph proof to prove the statement
Answer:
We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.
Step-by-step explanation:
Thats the exact answer.
Which expression represents the distance between 1.8 and 9.4 on the number line?
Answer:
the distance between 1.8 & 9.4=9.2
Five friends share three pizzas that cost $12.75 each. How much does each friend pay?
Answer:
each friend paid $7.65
Step-by-step explanation:
(3*12.75)/5
38.25/5
7.65
Answer:
2.25
Step-by-step explanation:
Write an expression for “four less than six times a number m”
Need answer ASAP 10 due 5 min
Answer:
4-6x
Step-by-step explanation:
let the number be =x
4-6x
The mathematical expression is,
⇒ 6m - 4
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
“four less than six times a number m”
Now,
Since, The algebraic expression is,
“four less than six times a number m”
Hence, We can formulate the mathematical expression as;
⇒ 6 × m - 4
⇒ 6m - 4
Thus, The mathematical expression is,
⇒ 6m - 4
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Assume a normal distribution and that the average phone call in a certain town lasted 7 min, with a standard deviation of 1 min. What percentage of the calls lasted less than 6 min?
Answer:
16%
Step-by-step explanation:
First, find the z-score.
z = (x − μ) / σ
z = (6 − 7) / 1
z = -1
Use a chart, a calculator, or the empirical rule to find the probability.
Using the empirical rule:
P(Z < -1) = 0.5 − 0.34
P(Z < -1) = 0.16
The percentage is 16%
How do I calculate a percentage between two numbers?To calculate the share between two numbers, divide one variety by way of the opposite and multiply the end result by way of one hundred, e.g. (30 / 75) * 100. This indicates what percent the first number is of the second one, in the example - 30 is 40% of 75.
In mathematics, a percent is more than a few or a ratio expressed as a fragment of 100. It is regularly denoted using the percentage signal, "%", although the abbreviations "pct.", "pct" and from time to time "pc" also are used. A percentage is a dimensionless number; it has no unit of size.
First, discover the z-rating.
z = (x − μ) / σ
z = (6 − 7) / 1
z = -1
Use a chart, a calculator, or the empirical rule to discover the chance.
using the empirical rule:
P(Z < -1) = 0.5 − zero.34
P(Z < -1) = 0.16
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You borrow 529$ from your parents to buy a mountain bike. Your parents are not charging you interest, but they want to be repaid as soon as possible. You can afford to repay them $20 per week. How long will it take you to repay your parents
A group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths (stones that form in the colon of horses) and diet. They decided to conduct a survey of the feeding practices for horses admitted to the veterinary hospital. To obtain a random sample of the 5000 horses that had been admitted to the hospital over the last 10 years, the veterinarians sequentially assigned numbers (starting with 0001) to the horses, in order of admittance. They then picked a random starting point and decided to sample every hundredth horse to get a random sample of 50 horses. This procedure corresponds to:
Answer:
Systematic Sampling
Step-by-step explanation:
The procedure corresponds to systematic sampling because Systematic sampling is a method of probability sampling whereby sample members from a larger population are selected in order of a random starting point but in a fixed, periodic interval.
Now, in the question we are told that they picked a random starting point and decided to sample every hundredth horse to get a random sample of 50 horses. Since random starting point in corresponds to Systematic Sampling.
Another reason why it's a systematic sampling is because they sampled every hundredth horse and therefore not all the samples were considered.
