Answers
Answer:
[tex]\huge\boxed{x=15;\ y=4}[/tex]
Step-by-step explanation:
Proportion:
[tex]\dfrac{x}{18}=\dfrac{5}{6}\qquad|\text{cross multiply}\\\\(x)(6)=(18)(5)\\\\6x=90\qquad|\text{divide both sides by 6}\\\\\huge\boxed{x=15}[/tex]
[tex]\dfrac{y}{5}=\dfrac{12}{x}[/tex]
substitute x = 15:
[tex]\dfrac{y}{5}=\dfrac{12:3}{15:3}\\\\\dfrac{y}{5}=\dfrac{4}{5}\qquad|\text{cross multiply}\\\\(y)(5)=(5)(4)\\\\5y=20\qquad|\text{divide both sides by 5}\\\\\huge\boxed{y=4}[/tex]
Related Questions
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answers
3y= -18x -18
y= -6x - 6
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms. Statistical analysis of the output suggests that the resistances can be approximated by a normal distribution with known standard deviation of 0.005 ohms. We are interested in testing the hypothesis that the resistors conform to the specifications.
Requied:
a. Determine whether a random sample of 10 resistors yielding a sample mean of 0.152 ohms indicates that the resistors are conforming. Use alpha = 0.05.
b. Calculate a 95% confidence interval for the average resistance. How does this interval relate to your solution of part (a)?
Answers
Answer:
a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
Step-by-step explanation:
Question a:
The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.
At the null hypothesis, we test if this is the average resistance, that is:
[tex]H_0: \mu = 0.15[/tex]
We are interested in testing the hypothesis that the resistors conform to the specifications.
At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:
[tex]H_1: \mu \neq 0.15[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.15 is tested at the null hypothesis:
This means that [tex]\mu = 0.15[/tex]
Sample mean of 0.152, sample of 10, population standard deviation of 0.005.
This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]
[tex]z = 1.26[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.
Looking at the z-table, z = -1.26 has a p-value of 0.1038.
2*0.1038 = 0.2076
The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.
Question b:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.
The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.
The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.
5.04 X 10
200.8
504
H 5,044
J 50,400
K
none of these
Answers
Step-by-step explanation:
The answer to 5.04 × 10 eqauls 50.4 , but there are no answers choices that have exactly 50.4 , so the answer is none of these . I hope this helps you :)
Suppose the distributor charges the artist a $40.00 cost for distribution, and the streaming services pays $4.00 per unit. (Note: One unit = one thousand streams)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Formula: y = 40x + 4 (Graph Attached)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
After how many streams will you pay for the distributor charges? (Hint: this is where the line crosses the x-axis, round to the nearest thousand)
Answers
Answer:
356 streams
Step-by-step explanation:
From the graph, you will see that the line cross the x-axis at x = 8.8
Substitute into the expression y = 40x + 4
y = 40(8.8)+4
y = 352 + 4
y = 356
Hence the distributor charges will be paid for after 356 streams
Help! I need help with these two questions (10 points each!)
Answers
Answer:
see image...
the (x-h) shifts the curve left right (east west)
and the +k at the end shifts it up/down (north/south)
Step-by-step explanation:
The work of a student to solve a set of equations is shown:
Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z
Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3
In which step did the student first make an error?
Step1
Step 2
Step 3
Step 4
Answers
Step 2
−2y = 15 − 2z
should be
−2y = -30 + 4a
find the missing side length in the image below
Answers
Answer:
3/6=?/10
Step-by-step explanation:
multiply by together. ?=5
Buses on a particular route stop in front of De Anza College every 20 minutes between 3:00 p.m. and 1:00 a.m. The waiting times are equally likely. We asked the 33 people waiting at 6:45 p.m. how long they had been waiting, and then calculated the average wait time for those people.
The probability that the average wait time is no more than 15 minutes is:____.
a. 1.
b. 0. 7500.
c. 0. 7769.
d. 0.
The distribution of the average wait times is:
a. N(10 , 1. 0050).
b. U(0 , 20).
c. N(10 , 5.7735).
d. Exp (1 20).
Answers
Answer:
1. a. 1
2. a. N(10 , 1. 0050)
Step-by-step explanation:
The average time for the people waiting for the bus will be no longer than 15 minutes. There are 33 people who were observed and their waiting time did not exceed 15 minutes. The probability is therefore 1 for the wait time.
An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?
Answers
Answer:
The standard deviation of your weight over a day is of 1.1547 pounds.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b, and the standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.
This means that [tex]a = -2, b = 2[/tex]
What is the standard deviation of your weight over a day?
[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]
The standard deviation of your weight over a day is of 1.1547 pounds.
Plz help
Need answers ASAP
Answers
Answer:
1. cube
2. square pyramid
4. cone
5. cube
2. Square Pyramid
4. Cone
5. Cube
What is the surface area of a cube with a side length of 6 m?
156 m2
300 m2
216 m2
360 m2
Answers
Answer:
216 m²
Step-by-step explanation:
Surface area of a cube = 6a², when a = length of one side
so,
6a²
= 6×6²
= 6×36
= 216 m²
Answered by GAUTHMATH
Answer:
216 m²
Step-by-step explanation:
Does this appear to be a regular polygon? Explain using the definition of a regular polygon.
Answers
Answer:
yes it is. a polygon is any closed shape with at least 3 connected lines (eg. triangle, square, pentagon, hexagon, heptagon, octagon, etc)
Step-by-step explanation:
HELP!!!!
Please help me!!
I need help!!
HELP!!!!
Answers
Answer:
Pretty sure it's A
Step-by-step explanation:
The x outside the parenthesis means that there's an x intercept at (0,0) and (x-3) means there's another one at (3,0)
The median age (in years) of the U.S. population over the decades from 1960 through 2010 is given by
f(t) = −0.2176t3 + 1.962t2 − 2.833t + 29.4 (0 ≤ t ≤ 5)
where t is measured in decades, with t = 0 corresponding to 1960.
(a) What was the median age of the population in the year 1970?
(b) At what rate was the median age of the population changing in the year 1970?
(c) Calculate f ''(1).
Answers
Considering the given function, we have that:
a) 28.31 years.
b) 0.3382 years a decade.
c) 2.6184.
What is the function?The median age of the U.S. population in t decades after 1960 is:
f(t) = -0.2176t³ + 1.962t² - 2.833t + 29.4.
1970 is one decade after 1960, hence the median was:
f(1) = -0.2176 x 1³ + 1.962 x 1² - 2.833 x 1 + 29.4 = 28.31 years.
The rate of change was is the derivative when t = 1, hence:
f'(t) = -0.6528t² + 3.924t - 2.933
f'(1) = -0.6528 x 1² + 3.924 x 1 - 2.933 = 0.3382 years a decade.
The second derivative is:
f''(t) = -1.3056t + 3.924
Hence:
f''(1) = -1.3056 x 1 + 3.924 = 2.6184.
More can be learned about functions at https://brainly.com/question/25537936
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Calculate the sum and enter it below.
-4 + 16
Answer here
Answers
Adding a negative number to a positive number is like subtracting
Answer:
12
Step-by-step explanation:
because 16 + -4 is like 16-4 which is 12
terms are there. Divide 51 into three parts in AP so that the largest exceeds the smallest by 10.
Answers
The first three terms of the Arithmetic Progression are 12, 17 and 22.
For an ARITHMETIC PROGRESSION, AP ;
First term = a
Second term = a + d
Third term = a + 2d
Where, d = common difference ;
If third term exceeds smallest by 10 ;
Third term - first term
a + 2d - a = 10
2d = 10
d = 10/2
d = 5
Sum of the three terms :
a + (a + d) + a + 2d = 51
3a + 3d = 51
d = 5
3a + 3(5) = 51
3a + 15 = 51
3a = 51 - 15
3a = 36
a = 12
The AP would be:
First term, a = 12
Second term, a + d = 12 + 5 = 17
Third term = a + 2(d) = 12 + 10 = 22
Therefore , the first three terms of the AP are :
12, 17 and 22
Learn more about ARITHMETIC PROGRESSION :
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Find the largest factor of 2520 that is not divisible by 6.
Answers
Solve for x then measure to find A
Answers
Answer:
[tex]125 \: \: degrees[/tex]
Step-by-step explanation:
As the 2 lines are parallel
<A = <B ( Alternative Angles)
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]
[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]
<A=6x+5
=6×20+5
=120+5
=125
<B=4x+45
=4×20+45
=80+45
=125
it is alternate angle they are equal each other
<A = < B
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]
Manish writes the functions g(x)= 3 sqrt -x - 72 and h(x) = -(x + 72)^3
Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?
Answers
Answer:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 3\sqrt x - 72[/tex]
[tex]h(x) = -(x +72)^3[/tex]
Required
Show that they are inverse functions
For g(x) and h(x) to be inverse, then:
[tex]g(h(x)) = h(g(x))[/tex]
We have:
[tex]g(x) = 3\sqrt x - 72[/tex]
Replace x with h(x)
[tex]g(h(x)) = 3\sqrt{h(x)} - 72[/tex]
Substitute value for h(x)
[tex]g(h(x)) = 3\sqrt{-(x +72)^3} - 72[/tex]
Similarly;
[tex]h(x) = -(x +72)^3[/tex]
Replace x with g(x)
[tex]h(g(x)) = -(g(x) +72)^3[/tex]
Substitute value for g(x)
[tex]h(g(x)) = -(3\sqrt x - 72 +72)^3[/tex]
Recall that:
[tex]g(h(x)) = h(g(x))[/tex]
So:
[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]
Its c
explanation:
on edge
I need to know the answer ASAP thank you
Answers
Answer:
Step-by-step explanation:
Quick Test
7. After 12% discounts, the price of a car is RM 44,000. What is the original price?
A. RM 52,800
B. RM 38,720
C. RM 49,280
D. RM 50,000
8. Find the interest on RM 2,800 if the rate is 5% for 4 years.
A. RM 500
B. RM 660
C. RM 460
D. RM 560
9. Find the net price of an item with a list price of RM 80.00 and a trade discount of 12%
A. RM 69.50
B. RM 57.70
C. RM 70.50
D. RM 70.40
10. The price of a hard drive is RM 215. If Andrew is given 6% discounts, find the mark down
amount.
A. RM 202.10
B. RM 86.00
C. RM 129.00
D. RM 12.90
Answers
Answer:
number 7 the answer is 50,000
) Express the prime number 43 as the difference of two squares?
Answers
Step-by-step explanation:
The prime 43 appears in the sixth twin-prime pair 41, 43. As a sum of four or fewer squares: 43 = 32 + 32 + 52 = 12 + 12 + 42 + 52 = 32 + 32 + 32 + 42. ... As a difference of two squares: 43 = 222 − 212.
which of the following are solutions to the quadratic equation below? x^2+7x=8
Answers
Answer:
x = -8, 1
Step-by-step explanation:
Hi there!
[tex]x^2+7x=8[/tex]
Move 8 to the other side:
[tex]x^2+7x-8=8-8\\x^2+7x-8=0[/tex]
Now, we can ask ourselves: what two factors of -8 add to 7? Those two numbers would be 8 and -1. Knowing this, factor:
[tex](x+8)(x-1)=0[/tex]
Because of the zero product property (that states that if the product of two numbers is 0, then one of the numbers must be equal to 0), we can find the solutions to the quadratic by setting each term equal to 0:
[tex]x+8=0\\x=-8[/tex]
[tex]x-1=0\\x=1[/tex]
Therefore, the solutions of the quadratic are -8 and 1.
I hope this helps!
how many degrees are there in the angle made by the heart hand and the minute hand of a clock when it is 9 o'clock
Answers
both angles are 90 degrees
find the surface area of the triangular prism below.
Answers
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
This table shows how many male and female students attended two different
movies.
What is the probability that a randomly chosen person from this group is male
and attended an action movie?
Round your answer to two decimal places.
Action
Drama
Total
Mala
105
124
229
Female
99
151
250
Total
204
275
479
A. 0.11
B. 0.43
Ο Ο Ο Ο
C. 0.22
D. 0.52
Answers
Answer:
Male & action movie among a group of total 479
Step-by-step explanation:
We only choose male from action movie category so:
p = 105/ 479 = 0.22
The probability that a randomly chosen person from this group is male and attended an action movie will be 0.22. Then the correct option is C.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
This table shows how many male and female students attended two different movies.
Action Drama Total
Mala 105 124 229
Female 99 151 250
Total 204 275 479
Then the probability that a randomly chosen person from this group is male and attended an action movie will be
Favorable event = 105
Total event = 479
Then the probability will be
P = 105 / 479
P = 0.219
P ≈ 0.22
Then the correct option is C.
More about the probability link is given below.
https://brainly.com/question/795909
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If a $6 per unit tax is introduced in this market, then the new equilibrium quantity will be
Answers
Answer:
soory i dont know just report me if you angry
In a survey conducted at a pet store, 150 customers were asked if they owned
birds or fish. The survey data are shown in the relative frequency table.
Answers
Answer:
12% percent of fish in own
The % of people surveyed own fish is 12%.
To find the % of people surveyed own fish.
What is relative frequency?Relative frequency refers to the percentage or proportion of times that a given value occurs within a set of numbers, such as in the data recorded for a variable in a survey data set.
Given that:
In a survey conducted at a pet store, 150 customers were asked if they owned birds or fish.
By the data on the table:
Total (own fish) = 0.04 + 0.08 = 0.12
So, own fish = 0.12
=12/100= 12%
So, 12% of the people surveyed own fish.
Learn more about relative frequency here:
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Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
Answers
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
Read more about equations at:
https://brainly.com/question/2396830
Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Answers
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
