Answer:
A manufacturing machine has a 40% defect rate. If 131 items are chosen at random, then:
The random variable, X=Number of 131 randomly selected items that are defective.Number of Items, n=131The point estimate of defective items, p=40%=0.4Solve the inequality.
-3(x-1) > -3x - 2
Answer:
all real x
Step-by-step explanation:
-3(x-1) > -3x - 2
Distribute
-3x +3> -3x -2
Add 3x to each side
-3x +3 +3x > -3x+3x - 2
3 > -2
This is always true so the inequality is true for all x
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Which statement is correct?
-Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
-Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
-Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
-Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
The correct answer is C. Mark’s method is correct because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Explanation:
To begin Mark should determine the rate of delivery (number of houses the carrier can deliver in 1 minute). This can be found by dividing the houses by the minutes (36 / 30 = 1.2 houses per minute). This means the 1.2 rate found by Mark is correct; also, in this case, it is important to clarify, the carrier will not deliver to 1.2 houses at the same time, but this is the delivery rate or number used to understand the relationship between the number of houses, and the time.
Moreover, you can use this rate, and multiply it by 7.5 and this will show you how many houses the carrier can deliver in this time (7.5 (minutes) x 1.2 (delivery rate) = 9 houses). Thus, the method is correct, and in it, 1.2 represents the unit rate, this is why even when it is not possible to deliver to 1.2 houses all the process is correct.
Answer:
c
Step-by-step explanation:
i took the test
Which value of k makes 5-k+12=16 a true statement? Choose 1 answer: Choice A) k=1 (Choice B) k=2 (Choice C) k=3 (Choice D) k=4
Answer:
A) k=1
Step-by-step explanation:
5-k+12=16
17-k=16
k=1
Answer:
k=1
Step-by-step explanation:
5-k+12=16
Combine like terms
17 - k = 16
Subtract 17 from each side
17-k-17 = 16-17
-k = -1
Divide by -1
k = 1
Given f(xl=x-7 and g(x)=x^2 find g(f(4))
Answer:
So we first need to solve for f(4) because thats what's inside g(_)
It should be 4-7 because I think its f(x)=x-7 you weren't very clear on it.
so that means that we need to solve for g(-3)
-3^2 = 9 because -3*-3 = 9
9 is answer
Find the constant of variation for the relation and use it to write and solve the equation.
if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4
Answer:
When x = 1 and z = 4, [tex]y=\frac{80}{9}[/tex]
Step-by-step explanation:
The variation described in the problem can be written using a constant of proportionality "b" as:
[tex]y=b\,\,x\,\,z^2[/tex]
The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":
[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]
Knowing this constant, we can find the value of y when x=1 and z=4 as:
[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]
what is the x-intercept of the line 10x-5y=40
Answer:
4
Step-by-step explanation:
The x-intercept occurs when y=0, if you think about it graphically. Plug y=o into your equation:
10x - 5(0) = 40
10x = 40 (divide each side by 10)
x=4
A mountain bike is priced at $413. If the sales tax is 6.5 percent, what is the cost to purchase the mountain bike? Round to the
nearest cent if necessary.
$26.85
$28.91
$437.78
$439.85
answer: D) 439.85
Step-by-step explanation:
we are given the price of the bike which is $413.
we are also given the sales tax which is 6.5%.
sales tax is added to the original price to give us our total. so in order to find the total cost we need to find what the 6.5% sales tax is and add it to our original price. to find the sales tax number in dollars we need to set up our formula. The easiest formula is to use a proportion. X is out of 413 = 6.5% is out of 100%. X/413=6.5/100. We can then cross multiply then divide. 6.5 times 413=2,684.5. then divide 2684.5÷100= 26.845.
we need to round up to the nearest cent since we are working with dollars and cents 26.85. 26.85 is 6.5% of the price of the bike which is 413. Now we just simply add the tax to the original price and we get the cost. 413+26.85=439.85
Answer: The answer is D) 439.85
Step-by-step explanation:
I WILLL GIVE BRAINLIEST ANSWER ASAP
Answer: 2ND ONE
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
5x+3=4x
5x-4x=-3
x=-3
Edit: Check by plugging in x = -3
5(-3)+3=4(-3)
-15+3=-12
-12=-12✅
f(x)<0 over (-∞, -3) and what other interval?
O (-2.4, - 1.1)
O (-3, - 1.1)
O (-1.1, 2)
O (-1.1, 0.9)
Answer:
Option (4). (-1.1, 0.9)
Step-by-step explanation:
In a graph of any function, values of f(x) are represented by the values on the y-axis for the different input values on x-axis.
For the given graph, values of f(x) are less than zero.
That means interval in which the values of the function are negative for the different values of x.
Negative values of the given function are in the intervals (-∞, -3), (-1.1, 9).
Therefore, from the given options, Option (4) will be the answer.
Answer is (-1.1,0.9)
Step-by-step explanation:
Homework: Section 1.2 Applications Linear
Score: 0 of 1 pt
8 of 10 (7 complete)
1.2.31
How many quarts of pure antifreeze must be added to 4 quarts of a 10% antifreeze solution to obtain a 20% antifreeze solution?
quart(s) of pure antifreeze must be added.
(Round to the nearest tenth as needed)
Answer:
q = 0.5 quarts of 100% antifreeze
Step-by-step explanation:
q = quarts of pure antifreeze
Set this up as a weighted combination of the mixtures.
(100%)(q) + (10%)(4) = (20%)(q + 4)
100q + 40 = 20(q + 4)
5q + 2 = q + 4
4q = 2
q = 0.5 quarts of 100% antifreeze
I need help pleaseeee help meee
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
Express the following ratio in its simplest form.
4:12
Answer:
1:3
Step-by-step explanation:
divide 4 ...............
.............
ps: idk the explanation
The point A (-7,5) is reflected over the line x = -5, and then is reflected over the line x= 2. What are the coordinates of
A?
o (7, 19)
O (10,5)
(7,5)
(10, 19)
Answer:
(7, 5) is the final reflection of the point.
Step-by-step explanation:
We are given point A(-7, 5) which is first reflected over the line [tex]x= -5[/tex].
The minimum distance of the point A(-7, 5) from the line [tex]x= -5[/tex] is 2 units across the horizontal path (No change in y coordinate).
Point A lies 2 units on the left side of the line [tex]x= -5[/tex].
So, its reflection will be 2 units on the right side of [tex]x= -5[/tex].
Let its reflection be A' which has coordinates as (-5+2,5) i.e. (-3, 5).
Now A'(-3, 5) is reflected on the line [tex]x=2[/tex].
The minimum distance of the point A'(-3, 5) from the line [tex]x=2[/tex] is 5 units across the horizontal path (No change in y coordinate).
Point A' lies 5 units on the left side of the line [tex]x=2[/tex].
So, its reflection will be 5 units on the right side of [tex]x=2[/tex].
Let its reflection be A'' which has coordinates as (2+5, 5) i.e (7, 5) is the final reflection of the point..
Please find attached image.
(7, 5) is the final reflection of the point.
A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24).
(a) How many selections result in all 4 workers coming from the day shift? What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)
The probability that all 4 selected workers will be from the day shift is, = 0.0198
The probability that all 4 selected workers will be from the same shift is = 0.0278
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
To solve this question properly, we will need to make use of the concept of combination along with set theory.
What is Combination?In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.
The formula for calculating combination can be expressed as:
[tex]\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}[/tex]
From the parameters given:
Workers employed on the day shift = 10Workers on swing shift = 8Workers on graveyard shift = 6A quality control consultant is to select 4 of these workers for in-depth interviews:
Using the expression for calculating combination:
(a)
The number of selections results in all 4 workers coming from the day shift is :
[tex]\mathbf{(^n _r) = (^{10} _4)}[/tex]
[tex]\mathbf{=\dfrac{(10!)}{4!(10-4)!}}[/tex]
= 210
The probability that all 5 selected workers will be from the day shift is,
[tex]\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}[/tex]
[tex]\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}[/tex]
(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:
P( all 4 selected workers will be) [tex]\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}[/tex]
where;
[tex]\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}[/tex]
[tex]\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}[/tex]
P( all 4 selected workers is:)
[tex]\mathbf{=\dfrac{210+70+15}{10626}}[/tex]
The probability that all 4 selected workers will be from the same shift is = 0.0278
(c)
The probability that at least two different shifts will be represented among the selected workers can be computed as:
[tex]= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}[/tex]
[tex]=1 - \dfrac{210+70+15}{10626}[/tex]
= 1 - 0.0278
= 0.9722
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
(d)
The probability that at least one of the shifts will be unrepresented in the sample of workers is:
[tex]P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0[/tex]
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
Learn more about combination and probability here:
https://brainly.com/question/9465501
https://brainly.com/question/25870256
Solve the inequality 2(4x-3)>-3(3x)+5
Answer:
48x>+2
Step-by-step explanation:
a circle with circumference 20 has an arc at 72 central angle. what is the length of the arc
Answer:
4 units
Step-by-step explanation:
[tex] \because \: l = \frac{ \theta}{360 \degree} \times c \\ \\ \therefore \: l = \frac{72 \degree}{360 \degree} \times 20 \\ \\ \therefore \: l = \frac{72 \degree}{18\degree} \\ \\ \therefore \: l = 4 \: units[/tex]
Find the equation of the line passing through the point (4,−1) that is parallel to the line 2x−3y=9 Find the slope of the line 2x−3y=9. Use a forward slash (i.e. "/") for all fractions (e.g. 1/2 for 12). m=____ What would the parallel slope be? m=______ Use the slope to find the y-intercept of the parallel line. b= _____
Answer:
Step-by-step explanation:
2x - 3y = 9
-3y = -2x + 9
[tex]y=\frac{-2}{-3}x + \frac{9}{-3}\\\\y=\frac{2}{3}x-3\\[/tex]
Parallel lines have same slope.So,
Slope m = 2/3
(4 , -1)
Equation: y - y1 = m(x - x1)
[tex]y-[-1]=\frac{2}{3}(x - 4)\\\\y+1=\frac{2}{3}*x - \frac{2}{3}*4\\\\y+1=\frac{2}{3}x-\frac{8}{3}\\\\y=\frac{2}{3}x-\frac{8}{3}-1\\\\y=\frac{2}{3}x-\frac{8}{3}-\frac{3}{3}\\\\y=\frac{2}{3}x-\frac{11}{3}[/tex]
b = -11/3
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
Want Brainliest? Get this Correct The x-values in the table for f(x) were multiplied by -1 to create the table for g(x) What is the relationship between the graphs of the two functions? A. They are reflections of each other across the y-axis B. They are reflections of each other across the x-axis C. The graphs are not related D. They are reflections of each other over the line x = y
Answer:
Option (A).
Step-by-step explanation:
We choose a point from table of f(x), that is (-2, -31)
1). If this point is reflected across x-axis, rule to be followed,
(x, y) → (x, -y)
That means y coordinate of the point gets changed with opposite notation.
If (-2, -31) is reflected over the x-axis,
(-2, -31) → (-2, 31) ----------(1)
2). When a point is reflected over the y-axis,
Rule to be followed,
(x, y) → (-x, y)
(-2, -31) → (2, -31) ----------(2)
3). When a point is reflected over the line y = x
Rule to be followed,
(x, y) → (y, x)
(-2, -31) → (-31, -2) -----------(3)
By comparing f(x) and g(x) we find the relation between the functions as,
f(-2, -31) → g(2, -31)
Rule between the functions f and g matches with the rule number (2).
Therefore, function 'f' has been reflected across y axis to get the function 'g'.
Option (A) will be the answer.
Answer for (12x+5)x-7x+2
Answer:
(12x2-2x+2)
Step-by-step explanation:
(12x)(x)+(5)(x)+-7x+2
12x2+5x+-7x+2
(12x2)+(5x+-7x)+(2)
12x2+-2x+2
4x and 16y are like terms.
O A. True
O B. False
Here is rectangle A. Block A. Rectangle B is ¹/₅ longer than A Block B. Rectangle C is ¹/₃ longer than B Block C. The total length of all three rectangles is 133 cm. How much longer is rectangle C than B?
Answer:
Rectangle C is 14 cm longer than B
Step-by-step explanation:
Let x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,
Therefore the length of rectangle B is:
[tex]x+\frac{1}{5}x[/tex]
Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:
[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]
The total length of all three rectangles is 133 cm.
Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm
[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]
Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]
Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B
A student is interested in becoming an actuary. The student knows that becoming an actuary takes a lot of schooling and will have to take out student loans and wants to make sure the starting salary will be higher than $55,000/year. The student takes a random sample of 30 starting salaries for actuaries and finds a p-value of 0.0392. Use α = 0.05.
a. Choose the correct hypotheses.
H0:μ≠55,000 H1:μ=55,000
H0:μ>55,000 H1:μ≤55,000
H0:μ<55,000 H1:μ≥55,000
H0:μ=55,000 H1:μ>55,000
H0:μ=55,000 H1:μ≠55,000
H0:μ=55,000 H1:μ<55,000
b. Should the student pursue an actuary career?
No, since we can reject the null hypothesis
No, since we can reject the claim
Yes, since we can reject the claim
Yes, since we can can reject the null hypothesis
Answer:
a) H0:μ=55,000 H1:μ>55,000
b) Yes, since we can can reject the null hypothesis
Step-by-step explanation:
a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For this case;
Null hypothesis is that the starting salary will be equal to $55,000/year.
H0:μ=55,000
Alternative hypothesis is that the starting salary will be greater than $55,000/year.
H1:μ>55,000
b) Decision Rule;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
For this case;
P-value = 0.0392
α = 0.05
Since P-value < 0.05, we can reject null hypothesis.
Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.
- Yes, since we can can reject the null hypothesis
Jeff rear-ended a car on his way to work and damaged his vehicle. He drove his car to the local body shop for an
estimate of the cost to repair his car. Jeff has a $500 deductible. The local body shop provided an estimate of $3725,
How much will Jeff have to pay?
A $3225
B $3725
C $4225
D $500
Answer:
A $3225
Step-by-step explanation:
Total = $3725
Dectuable = Able to be deducted
$3725 - $500 = $3225
A completely randomized design Group of answer choices has one factor and one block. has one factor and one block and multiple values. can have more than one factor, each with several treatment groups. has only one factor with several treatment groups.
Answer:
C. can have more than one factor, each with several treatment groups.
Step-by-step explanation:
A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.
Completely randomized design has found application in agricultural and environmental researches.
A family of five rents a kayak and splits the total time, k, equally. Each family member spent less than 25 minutes kayaking. Which values can be used to complete the math sentence below so that it accurately represents the situation?
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Edg.
Answer:
k ÷ 5 < 25
Step-by-step explanation:
Simplify the following expression and then write down the coefficient of x²: x² + x² + x² + x²
Answer:
The expression is 4x² and coefficient is 4.
Step-by-step explanation:
All have the same variables, x², so you add up together :
[tex] 1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2} [/tex]
[tex] = 4 {x}^{2} [/tex]
"How much room is there to spread frosting on the cookie?" Clare says, "The radius of the cookie is about 3 cm, so the space for frosting is about 6 cm." Andre says, "The diameter of the cookie is about 3 inches, so the space for frosting is about 2.25 sq. in."
A. Is this question talking about area or circumference? Pick one. Why?
B. Which person is most likely correct, Clare or Andre? Why?
Answer:
(a)Area
(b)Andre is Right
Step-by-step explanation:
(a)Frost is spread on the surface of a cookie, therefore the question is talking about the area of the circular cookie.
(b)
Andre says, "The diameter of the cookie is about 3 inches, so the space for frosting is about 2.25 sq. in
Area of a Circle[tex]=\pi r^2[/tex]
Radius =Diameter/2 =3/2=1.5 Inches
Therefore, Space for frosting on the cookie
[tex]=\pi *1.5^2\\=2.25\pi$ in^2[/tex]
Andre is right.
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
