Answer:
− 3 x + 1
Step-by-step explanation:
Answer: -3x + 1
Step-by-step explanation: I know Math O_O
A 17 feet ladder is placed against a building. The bottom of the ladder is 15 feet away from the building. How many feet high is the top of the ladder?
7 feet
12 feet
8 feet
15 feet
Answer:
[tex]8 \ feet[/tex]
Step-by-step explanation:
In this situation, one is given the following information. A ladder is leaning against a wall and has a measure of (17) feet. The bottom of the ladder is (15) feet away from the wall. One can infer that the wall forms a right angle with the ground. Thus, the triangle formed between the ground, ladder, and wall is a right triangle. Therefore, one can use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle. The parameter (c) represents the hypotenuse or the side opposite the right angle. In this case, the legs are the ground and wall, and the hypotenuse is the ladder. Substitute this into the formula a solve for the height of the wall.
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex](ground)^2+(wall)^2=(ladder)^2\\\\(15)^2+(wall)^2=(17)^2\\[/tex]
Simplify,
[tex](15)^2+(wall)^2=(17)^2\\\\225+(wall)^2=289[/tex]
Inverse operations,
[tex]225+(wall)^2=289\\\\(wall)^2=64\\\\wall=8[/tex]
William has been contracted to paint a school classroom. The classroom is 20 m long, 15 m wide and 5 m high. There are four windows (2m by 3m) and a door (2m by 1m). Determine the cost of painting the ceiling at N$ 6.50/m²
Answer:
Step-by-step explanation:
l -> length
b -> width
h -> height
Find the area of four walls and ceiling. then subtract the area of four windows and a door form that area.
Area of four walls + ceiling = 2( lh + bh) +lb
= 2*(20*5 + 15*5) + 20*15
= 2( 100 + 75) + 300
= 2* 175 + 300
= 350 +300
= 650 sq m
Area of window = 2 *3 = 6 sq.m
Area of four windows = 4*6 = 24 sq.m
Area of door = 2 * 1 = 2 sq.m
Area of four walls excluding 4 windows and door = 650 - 24 - 2 = 624 sq.m
Cost of painting = 624 * 6.50
= $ 4056
Answer: 1950 dollars to paint the ceiling only (ignoring the walls)
The cost to paint the walls only is 2106 dollars.
The cost to paint the walls and ceiling is 4056 dollars.
==================================================
Explanation:
It seems a bit strange how your teacher mentions the windows and doors, but then asks about the ceiling only. Perhaps this is a red herring, but I'm not sure.
Anyway, to directly answer the question, we'll need to find the area of the ceiling first. The ceiling is a rectangle of dimensions 20 m by 15 m, so its area is 20*15 = 300 square meters.
Since paint costs 6.50 dollars per square meter, the total cost for the ceiling alone is 6.50*300 = 1950 dollars
If your teacher only cares about the ceiling, then you can stop here (and ignore the next section below).
---------------------------
If you wanted to find the cost to paint the walls, then we need to find the area of the walls.
For now, ignore the windows and door. Two opposite walls have area of 20*5 = 100 m^2 each. That accounts for 2*100 = 200 m^2 of wall area so far.
The other pair of opposite walls have area 15*5 = 75 m^2 each. That's another 2*75 = 150 m^2 of wall area.
In all, the total wall area without considering the windows or door is 200+150 = 350 m^2.
Now we consider the windows. Each window is 2 m by 3 m, yielding an area of 2*3 = 6 m^2. Four such windows have a total area of 4*6 = 24 m^2.
The door is 2 m by 1 m, so its area is 2*1 = 2 m^2
We'll subtract the wall area and the combined window+door areas to get
wallArea - windowArea - doorArea = 350-24-2 = 324
So after accounting for the windows and door, the amount of wall to paint is 324 m^2, which leads to a cost of 6.50*324 = 2106 dollars.
Therefore, painting the walls and ceiling gets us a total cost of 1950+2106 = 4056 dollars
This section is entirely optional if your teacher only cares about the ceiling.
What is the domain of this function y= 1/ square root 2-x
Answer:
Domain:
( − ∞ , 2 ] , { x | x ≤ 2 }
Range:
[ 0 , ∞ ) , { y | y ≥ 0 }
If the domain of a function that is rotated 90 degrees counter-clockwise is (0, 0), (3, 5), (-1, 4), what is the range?
A. (0, 0), (5, 3), (4, -1)
B. (0, 0), (5, -3), (4, 1)
C. (0, 0), (-3, -5), (1, -4)
D. (0, 0), (-5, 3), (-4, -1)
Answer:
the answer is B. (0,0) (5,-3) (4,1)
please mark me brainlist
Step-by-step explanation:
Answer:
Your answer is
Step-by-step explanation:
Your answer is B.(0, 0), (5, -3), (4, 1)
I want to find the inverse for the following function, but I think there is a mistake. Identify the first mistake in the following process. Explain how to fix the mistake.
Answer:
Step-by-step explanation:
The only mistake is in the last line. You need to replace the y by x, So:
f-1(x) = (x - 4)/-8
It's usual to put the negative on the top so it becomes
-(x -4)/8
- and we can simplify this a bit more to give
f-1(x) = (4 - x)/5
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers. If the operator is correct, what is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Answer:
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 9% of the phone calls are wrong numbers.
This means that [tex]p = 0.09[/tex]
Sample of 448
This means that [tex]n = 448[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{448}} = 0.0135[/tex]
What is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%?
More than 9% + 3% = 12 or less than 9% - 3% = 6%. Since the normal distribution is symmetric, these probabilities are the same, so we find one of them and multiply by 2.
Probability it is less than 6%
P-value of Z when X = 0.06. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0135}[/tex]
[tex]Z = -2.22[/tex]
[tex]Z = -2.22[/tex] has a p-value of 0.0132
2*0.0132 = 0.0264
0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%
Choose all that apply:
1.Circle A and circle A', have the same circumference.
2.The radii of circle A and circle A', have the same lengths.
3. Points A and A', are both on the xxx-axis.
4. None of the above
Answer:
Step-by-step explanation:
1. Circle A and circle A', have the same circumference. (Yes)
2. The radii of circle A and circle A', have the same lengths. (Yes)
3. .... (No)
4. ... (No)
There are eggs in a dozen. If a farmer's chickens produce an average of dozen eggs in a month, how many eggs are reported per month?
Complete Question:
There are 12 eggs in a dozen. If a farmer's chickens produce an average of 423 dozen eggs in a month, how many eggs are reported per month?
Answer:
The eggs reported per month are:
= 5,076 eggs.
Step-by-step explanation:
a) Data and Calculations:
A dozen eggs = 12 pieces of eggs
Average of dozen eggs produced in a month = 423
Therefore, the eggs that are reported per month should average 5,076 (12 * 423)
b) The arrangement or measurement of eggs in dozens makes it easier to calculate the number of eggs produced in the farm each period. The result is obtained by multiplying the average of dozen eggs produced by 12.
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Answer:
b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2
c)CI 95 % = ( 0.00002 ; 0.09998)
Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.
Recent Sample
Sample size n₁ = 1000
Number of events of people with financial fitness more than fair
x₁ = 410
p₁ = 410/ 1000 = 0.4 then q₁ = 1 - p₁ q₁ = 1 - 0.4 q₁ = 0.6
Sample a year ago
Sample size n₂ = 1200
Number of events of people with financial fitness more than fair
x₂ = 420
p₂ = 420/1200 p₂ = 0.35 q₂ = 1 - p₂ q₂ = 1 - 0.35 q₂ = 0.65
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
CI 95 % then significance level α = 5% α = 0.05 α/2 = 0.025
To calculate p-value:
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ 0.4*0.6/1000 + 0.65*0.35/1200
SE = √ 0.00024 + 0.000189
SE = 0.021
z(s) = ( p₁ - p₂ ) / SE
z(s) = ( 0.4 - 0.35 )/0.021
z(s) = 0.05/ 0.021
z(s) = 2.38
We find p-value from z-table to be p-value = 0.00842
Comparing
p-value with α/2 = 0.025
α/2 > p-value
Then z(s) is in the rejection region for H₀. We reject H₀
CI 95 % = ( p₁ - p₂ ) ± 2.38*SE
CI 95 % = ( 0.05 ± 2.38*0.021 )
CI 95 % = ( 0.05 ± 0.04998)
CI 95 % = ( 0.00002 ; 0.09998)
CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate
The domain of the function f(x)=-x3+4
Answer:
Domain= {x:x £|R}
|R=any real number
What is the following product? Assume x>0 and y>0 v5x^8y^2•v10^3•v12y
Answer:
[tex]10x^{5}y \sqrt{6xy}[/tex]
Step-by-step explanation:
(sec theta - tan theta)²
Answer:
(sec θ - tan θ)²
= sec² θ –2 sec θ tan θ + tan² θ
For a popular Broadway music the theater box office sold 356 tickets at $80 a piece275 tickets at $60 a piece and 369 tickets at $ 45 a piece. How much money did the box office take in?
Answer:
Step-by-step explanation:
356 * 80 = 28 480
275 * 60 = 16 500
369 * 45 = 16 605
sum = $ 61 585
What is the Value of the expression 1/4(c cubed + d squared) when c = -4 and d = 10
Answer: 9
Step-by-step explanation:
[tex]\frac{1}{4} (c^{3}+d^{2})[/tex]
c = -4d = 10Substitute in the values into the expression:
[tex]\frac{1}{4} ((-4)^{3}+10^{2})\\\\=\frac{1}{4}(-64+100)\\\\=\frac{1}{4}(36)\\\\=\frac{36}{4} =9[/tex]
DO THIS AND ILL MARK! PLEASE
Answer:
Sin = 7/25
Cos = 24/25
Tan = 7/24
Step-by-step explanation:
The ratio for sin is opposite/hypotenuse, cos is adjacent/ hypotenuse, and tan is opposite/ adjacent.
the cost of 7 shirts is $63. find the cost of 5 shirts
1. $35
2. $45
3. $52
4. $70
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW!!!
9. Suppose y varies inversely with x, and y = 49 when x = 1/7. What is the value of x when y = 7?
a. 14
b. 2
c. 1
d. 7
10. Suppose y varies inversely with x, and y = 5 when x = 3. What is the inverse variation equation that relates x and y?
a. y = 3/x
b. y = 5/x
c. y = 15/x
d. y = 15x
9514 1404 393
Answer:
9. c. 1
10. c. y = 15/x
Step-by-step explanation:
The equation for inverse variation can be written as ...
y = k/x
The value of k can be determined from given values of x and y. Multiply by x to get ...
k = xy
Solving for x, you get ...
x = k/y
___
9. k = (1/7)(49) = 7
x = k/y = 7/7
x = 1
__
10. k = (3)(5) = 15
y = 15/x
45 is what percent of 78?
Answer:
35.1
Step-by-step explanation:
45×78/100 that's 100% correct
Jamal opens a savings account with a starting balance of $200 and plans to
deposit $75 each week after opening the account. His savings over time is
represented by the graph below. How would this graph change if Jamal
decided to deposit $100 each week instead?
the graph would steeper, meaning more savings over time
The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 millimeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters. Round your answer to four decimal places.
Answer:
69.14% probability that the diameter of a selected bearing is greater than 84 millimeters
Step-by-step explanation:
According to the Question,
Given That, The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 millimeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters.
In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σwe have μ=87 , σ=6 & X=84
Find the probability that the diameter of a selected bearing is greater than 84 millimetersThis is 1 subtracted by the p-value of Z when X = 84.
So, Z = (84-87)/6
Z = -3/6
Z = -0.5 has a p-value of 0.30854.
⇒1 - 0.30854 = 0.69146
0.69146 = 69.14% probability that the diameter of a selected bearing is greater than 84 millimeters.Note- (The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X)
use the figure below to find the answer. find y.
9514 1404 393
Answer:
y = 7√2
Step-by-step explanation:
We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(45°) = 7/y
y = 7/sin(45°) = 7/(1/√2)
y = 7√2
__
Additional comment
In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...
x = 7
What is the solution to the system of linear equations?
(-3,0)
(-3,3)
(0,2)
(3,1)
Which ordered pair (a, b) is the solution to the given system of linear equations? 3a+b= 10 -4a-2b=2
(1,7)
(3, 1)
(11, -23)
(23, -11)
Hello,
answer C (11,-23)
[tex]\left\{\begin{array}{ccc}3a+b&=&10\\-4a-2b&=&2\end{array}\right.\\\\\\\left\{\begin{array}{ccc}6a+2b&=&20\\-4a-2b&=&2\end{array}\right.\\\\\\\left\{\begin{array}{ccc}3a+b&=&10\\2a&=&22\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&11\\b&=&10-3*11\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&11\\b&=&-21\end{array}\right.\\[/tex]
Answer: C. (11,-23)
Step-by-step explanation:
help e please i’ll give brainliest
Answer:
363,000,000
..........
How many ways are there to assign four jobs to 7 employees if no employee can be given more than one job
Answer:
35ways
Step-by-step explanation:
Given the following
Total employees = 7employees
Number of tasks to be assigned = 4task
The number of ways this can be done is expressed as 7C4
7C4 = 7!/(7-4)!4!
7C4 = 7!/3!4!
7C4 = 7*6*5*4!/6*4!
7C4 = 35ways
Hence this can be done in 35ways
Fifteen dozen eggs were needed for baking four wedding cakes. The first cake
needed one dozen eggs, and each successive cake needed twice as many eggs as the
previous cake. How many eggs were used to make the fourth cake?
Answer:
96 eggs
Step-by-step explanation:
A dozen is equal to 12 eggs, so 15 dozen is equal to 180 eggs
(Because 15*12 = 180)
We already know how many eggs are required for the 1st cake: 12 eggs.
Then it says "each successive cake needs twice as many eggs as the previos cake".
(Successive means the cake directly after the previous cake)
Here's how we find the number of eggs needed for the 2nd cake:
The 1st cake needed 12 eggs, and because the 2nd cake is directly after the 1st cake, we are going to need two times the amount of 12 eggs.
This equation represents the above scenario:
12*2 = 24
So we need 24 eggs for the 2nd cake.
Now we repeat this process for the 3rd cake, finding twice the amount of eggs from the 2nd cake to find the amount of eggs needed for the 3rd cake:
24*2 = 48
And we repeat it once more for the 4th cake, using the eggs from the 3rd cake:
48*2 = 96
So here's the list of how many eggs are required for each of the cakes:
1st cake: 12
2nd cake: 24
3rd cake: 48
4th cake: 96
If you add all the eggs from each of the cakes, you will get 180, which is the number of eggs needed for all four cakes. So our answer is correct.
Hope this helps (●'◡'●)
19. The sum of a number m and a number n, multiplied by ninety-one 20. Forty-one times the difference when six is subtracted from a num- bera 21. A number r divided by the difference between eighty-three and ten 22. The total of a number p and twelve, divided by eighteen 23. The product of a number c and three more than the sum of nine and twelve 24. The sum of a number y and ten, divided by the difference when a number x is decreased by five. I need to convert all of them into expressions. PLEASE HELP.
Answer:
Step-by-step explanation:
19.
The numbers are m and n
Sum of m and n = m + n
Sum is multiplied by 91 = 91 x ( m + n )
20.
Let the number be = m
Six subtracted from the number = m - 6
41 times the difference = 41 x ( m - 6)
21.
Let the number be = r
Difference between 83 and 10 = 83 - 10 = 73
[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]
22.
Total of p and 23 = p + 12
[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]
23.
The product of c and 3 = 3c
Sum of 9 and 12 = 21
Product is more than Sum = 3c + 21
24.
Sum of y and 10 = y + 10
Number x decreased by 5 = x - 5
[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]
Write the formula of the function y whose graph is shown.
Answer:
This looks like the graph of [tex]f(x)=\frac{1}{x}[/tex] ! That's a reciprocal graph.
Craig made a mobile using geometric shapes including triangles shaped as shown. For what value of X and Y can you use a triangle congruence theorem to show that the triangles are congruent? Which triangle congruence theorem can you use? Explain.
.
.
.
May you also show the work? Please help. Thank you.
Answer:
x = 3
y = 8
Step-by-step explanation:
In the given triangle FGH,
m∠F + m∠G + m∠H = 180° [Triangle sum theorem]
60° + 90° + m∠H = 180°
m∠H = 30°
If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.
m∠F = m∠T
7y + 4 = 60°
7y = 56
y = 8
GH ≅ UV
8x - 12 = 12
8x = 24
x = 3
Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.
What is the AAS Congruence Theorem?According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.
Thus, by the AAS theorem, we have:
8x - 12 = 12
8x = 12 + 12
8x = 24
x = 3
Also,
7y + 4 = 60
7y = 60 - 4
7y = 56
y = 8
Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.
Learn more about AAS congruence theorem on:
https://brainly.com/question/3168048
Simplify this algebraic expression.
y-3/3 +12
O A. y-11
O B. y + 13
O c. y-5
O D. y+ 11
Answer:
D
Step-by-step explanation:
[tex]y - \frac{3}{3} + 12[/tex]
[tex]y - 1 + 12[/tex]
[tex]y + 11[/tex]
