Answer:
12
Step-by-step explanation:
1:4 = 3:12
Answer:
12 cups of water
Step-by-step explanation:
The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12
A researcher studying the effect of price promotions on consumers' expectations makes up two different histories of the store price of a hypothetical brand of laundry detergent for the past year. Students in a marketing course are randomly assigned to view one or the other price history on a computer. Some students see a steady price, while others see regular promotions that temporarily cut the price. Then the students are asked what price they would expect to pay for the detergent.
Is this study an experiment? Why?A. Yes. Each subject is randomly assigned to a treatment.B. No. Each subject is randomly assigned to a treatment. C. Yes. Each subject is not randomly assigned to a treatment.D. No. Each subject is not randomly assigned to a treatment.
Answer:
A. Yes. Each subject is randomly assigned to a treatment
Step-by-step explanation:
In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.
In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.
6z+10=-2
pls answer'
i willmarke brainlest
Answer:
Step-by-step explanation: 6z=-2-10
6z= -12
z=-12/6
then z= -2
A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
you secure a mortgage to buy a house with a loan of $140,000 at 8.5% for 20 years. answer the following questions about that loan for the first two months of payments: a) what is the monthly payment? b)how much of the monthly payment goes toward interest when you submit your first payment? c)what is your balance after the first payment? d) how much of the monthly payment goes toward interest when you submit your second payment? e) what is your balance after the second payment?
Answer:
monthly payment $1214.951st month's interest $991.67balance after 1st payment $139,776.722nd month's interest $990.09balance after 2nd payment $139,551.86Step-by-step explanation:
The monthly interest rate is ...
[tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]
a) The monthly payment is given by the amortization formula:
A = Pr/(1 -(1+r)^-n)
where r is the monthly interest rate on a loan of amount P for n months.
A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95
The monthly payment is $1214.95.
__
b) The amount to interest is the product of the remaining principal and the monthly interest rate.
first month's interest = $140,000·0.0070833 = $991.67
__
c) The balance after the first payment is ...
new balance = $140,000 +991.67 -1214.95 = $139,776.72
__
d) The amount to interest for the second payment is computed the same way:
second month's interest = $139,776.72·0.00708333 = $990.09
__
e) The balance after the second payment is computed the same way:
new balance = $139,776.72 +990.09 -1214.95 = $139,551.86
Evaluate 16x^0 if x= -3
Answer:
16
Step-by-step explanation:
[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]
Hope this helps!
x = -3
[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]
Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]
the population of a country increased by 3%, 2.6%, and 1.8% in three successive years. what was the total percentage increase in the country's population over the three year period?
please tell me how u did it
Answer:
The total percentage increase in the country's population over the three year period is 7.6%.
Step-by-step explanation:
Let x be the original population of a country.
It is provided that the population increased by 3%, 2.6%, and 1.8% in three successive years.
Compute the population of the country after three years as follows:
[tex]\text{New Population}=\text{Origibal Population}\times I_{1}\%\times I_{2}\%\times I_{3}\%[/tex]
[tex]=x\times [1+\frac{3}{100}]\times [1+\frac{2.6}{100}]\times [1+\frac{1.8}{100}]\\\\=x\times 1.03\times 1.026\times 1.018\\\\=1.07580204\cdot x\\\\\approx 1.076\cdot x[/tex]
The new population after three years is 1.076 x.
Compute the total percentage increase in the country's population over the three year period as follows:
[tex]\text{Total Increase}\%=\frac{\text{New Population}\ -\ \text{Original Population}}{\text{Original Population}}\times 100[/tex]
[tex]=\frac{1.076x-x}{x}\times 100\\\\=0.076\times 100\\\\=7.6\%[/tex]
Thus, the total percentage increase in the country's population over the three year period is 7.6%.
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score 2 2 3 3 4 2 1 1 2 4 Husband's score 2 1 2 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)(1) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)(2) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)(3) What is the p-value? (Round your answer to four decimal places.)(4) Alpha (Enter an exact number as an integer, fraction, or decimal.)α =
Answer;
1) The t-distribution is most suitable for this problem.
2) Test statistic = 2.356
3) p-value = 0.0214
4) Alpha = 5% = 0.05
5) The p-value is greater than the significance level at which the test was performed, meaning that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Step-by-step Explanation:
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
To conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife, we first take the difference in the respomses of wives and husbands
x = (wife's score) - (husband's score)
Wife's score 2 2 3 3 4 2 1 1 2 4
Husband's score 2 1 2 3 2 1 1 1 2 4
Difference | 0 | 1 | 1 | 0 | 2 | 1 | 0 | 0 | 0 | 0
To use the hypothesis test method, we have to make sure that the distribution is a random sample of the population and it is normally distributed.
The question already cleared these two for us that this sample size is randomly selected from the population and each variable is independent from the other.
The question also already explained that the distribution is assumed to be normally distributed.
1) The distribution to use for this test is the t-distribution. This is because the sample size isn't very large and we have no information about the population mean and standard deviation.
For any hypothesis testing, we must first define the null and alternative hypothesis
Since we want to investigate whether the husbands are happier, that the mean difference is negative, that is less than 0,
The null hypothesis, which normally counters the claim to be investigated, would be that there isnt evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness isn't less than 0, that it is equal to or greater than 0.
And the alternative hypothesis, which usually confirms the claim to be tested, is that there is significant evidence to conclude that the husbands are happier in dual couple marriages. That is, the mean difference in happiness is less than 0.
Mathematically, if μ is the mean difference in happiness of wives and husbands,
The null hypothesis is represented as
H₀: μ ≥ 0
The alternative hypothesis is represented as
Hₐ: μ < 0
2) To obtain the test statistic, we need the mean and standard deviation first.
Mean = (sum of variables)/(number of variables) = (5/10) = 0.5
Standard deviation = σ = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = 6(0 - 0.5)² + 3(1 - 0.5)² + (2 - 0.5)² = 1.5 + 0.75 + 2.25 = 4.5
σ = √(4.5/10) = 0.671
we compute the t-test statistic
t = (x - μ)/σₓ
x = sample mean difference = 0.50
μ = 0
σₓ = standard error of the sample mean = (σ/√n)
where n = Sample size = 10,
σ = Sample standard deviation = 0.671
σₓ = (0.671/√10) = 0.2122
t = (0.50 - 0) ÷ 0.2122
t = 2.356
3) checking the tables for the p-value of this t-statistic
Degree of freedom = df = n - 1 = 10 - 1 = 9
Significance level = 5% = 0.05
The hypothesis test uses a one-tailed condition because we're testing only in one direction.
p-value (for t = 2.356, at 0.05 significance level, df = 9, with a one tailed condition) = 0.021441 = 0.0214
4) Alpha = significance level = 5% = 0.05
5) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.0214
0.0214 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the husbands are happier in dual couple marriages.
Hope this Helps!!
How can you convert the Heun’s Method into the Implicit Heun’s Method? Show an example
Answer:
Heun's method is also known by its other name called Modified Euler methods. This method is used in computational or mathematical science.
Step-by-step explanation:
Euler method is the method that is also pronounced in two similar stages such as Runge- Kutta methods. This method has been named after Dr. Heun.
This method is used for the solution of ordinary differential equations with its given values. There is some method to calculate this method. The improved Runge Kutta methods are also called the Butcher tableau method, the other methods are also called the Ralston methods.
Please help. I’ll mark you as brainliest if correct . I don’t understand this math problem. Thank you .
Answer:
That can be factored as
(x -1 (1/3) ) * ( x +3) * (x -4/5)
and the zeroes are located at:
x = 1.33333333... x = -3 and x = .8
Step-by-step explanation:
Answer:
[tex]\boxed{\sf \ \ \ f(x)=(x+3)(5x-4)(3x-4) \ \ \ }[/tex]
Step-by-step explanation:
We need to factorise the following function
[tex]f(x)=15 x^3+13 x^2-80 x+48[/tex]
-3 is a trivial solution, we can notice that f(-3)=0
so we can factorise by (x+3)
let s note a, b and c real and let s write
[tex]f(x)=15 x^3+13 x^2-80 x+48=(x+3)(ax^2+bx+c)[/tex]
[tex](x+3)(ax^2+bx+c) = ax^3+bx^2+cx+3ax^2+3bx+3c=ax^3+(b+3a)x^2+(3b+c)x+3c[/tex]
let s identify...
the terms in [tex]x^3[/tex]
15 = a
the terms in [tex]x^2[/tex]
13 = b + 3a
the terms in x
-80 = 3b+c
the constant terms
48 = 3c
so it comes, c=48/3=16, a = 15, b = 13-3*15=13-45=-32
so [tex]f(x)=(x+3)(15x^2-32x+16)[/tex]
[tex]\Delta=32^2-4*15*16=64[/tex]
so the roots of [tex](15x^2-32x+16)[/tex] are
[tex]\dfrac{32-8}{15*2}=\dfrac{24}{30}=\dfrac{12}{15}=\dfrac{4}{5}[/tex]
and
[tex]\dfrac{32+8}{15*2}=\dfrac{40}{30}=\dfrac{20}{15}=\dfrac{4}{3}[/tex]
so [tex]f(x)=(x+3)(5x-4)(3x-4)[/tex]
the zeros are -3, 4/5, 4/3
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at time t hours is given by a function A(t) and the amount in Vat B is given by B(t). The two vats contain the same amount of water at t=0. You have a formula for the rate of flow for Vat A and the amount in Vat B: Vat A rate of flow: A(t)-3t2+24t-21 Vat B amount: B(t)-2t2+16t+40
(a) Find all times at which the graph of A(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum of A(t) smaller t= 1 gives a local minimum larger t= 7 l maximum
(b) Let D(t)-B(t)-A(t). Determine all times at which D(t) has a horizontal tangent and determine whether each gives a local maximum or a local minimum. (Round your times to two digits after the decimal.) xgives a Select x gives a Select smaller t- larger t=
(c) Use the fact trruntain the same amount of water at ta0 to find the formula for A(), the amount in Vat A at time t Enter a number
(d) At what time is the water level in Vat A rising most rapidly? t- hours
(e) what is the highest water level in Vat A during the interval from t=0 to t=10 hours? gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t-0 to t-10 hours? gallons per hour
(g) How much water flows into VatA during the interval from t=1 to t-8 hours? gallons
Note: The first file attached contains the clear and complete question
Answer:
a) The times at which the graph of A(t) has horizontal tangent are t = 1 and t = 7
A(t) has a local maximum at t=7
A(t) has a local minimum at t=1
b) The times at which the graph of D(t) has horizontal tangent are t = 1.59 and t = 7.74
D(t) has a local maximum at t=1.59
D(t) has a local minimum at t=7.74
c) A(t) = (-t^3) + 8(t^2) -21t + 40
d) The water level in vat A is rising most rapidly at t = 4 hrs
e) 138 gallons
f) 18 gallons per hour
g) 98 gallons
Step-by-step explanation:
For clarity and easiness of expression, the calculations are handwritten and attached as files below.
Each step is neatly expressed and solutions to each part of the question are clearly written
A box is filled with 6 red cards, 8 green cards and 4 blue cards what is the probability that the card is not green that is chosen
Answer:
10/18
=5/9
pls mark as brainliest
Answer:
5/9
Step-by-step explanation:
6 red cards, 8 green cards and 4 blue cards = 18 total cards
not green cards = 6 red+ 4 blue = 10 cards
P( not green) = number not green / total
= 10/18
=5/9
Please answer this correctly without making mistakes
Answer:
The perimeter is 26 yards
Step-by-step explanation:
Area of rectangle = A= l x w
1st rectangle = 6 x 5 = 30 yards squared
2nd rectangle= 10 x 3 = 30 yards squared
perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction Solve the proportion for x. After using cross products, the proportion becomes the equation . Isolate the variable by dividing both sides of the equation by . x = .
Answer:
StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction
Solve the proportion for x.
After using cross products, the proportion becomes the equation
✔ 4x = 10
.
Isolate the variable by dividing both sides of the equation by
✔ 4
.
x = ✔ 2.5
.
The value of x is 2.5 for the given proportion.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
The proportion is given in the question, as follows:
4/2 = 5/x
Using cross-product, the proportion becomes the equation as:
4x = 2 × 5
4x = 10
Divide by 4 into both sides of the above equation,
x = 10/4
x = 2.5
Thus, the value of x is 2.5 for the given proportion.
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For each of the sequences below, find a formula that generates the sequence. (a) 4, 10, 16, 22, 28, 34, 40, . . . (b) 5, 15, 45, 135, 405, . . . (c) 10, 20, 10, 20, 10, 20, 10
Answer:
[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]
Step-by-step explanation:
[tex]6(1)-2=4[/tex]
[tex]6(2)-2=10[/tex]
[tex]5 \times 3^{(3)-1}=45[/tex]
[tex]5 \times 3^{(4)-1}=135[/tex]
[tex]5(-1^{(5)}+3)=10[/tex]
[tex]5(-1^{(6)}+3)=20[/tex]
a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)
b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹
c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is an = 10 + 10 * ((n + 1) % 2)
(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.
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MTH 154 - DOBM
Homework: Homework 4B
Score: 0 of 1 pt
22 of 27 (21 complete)
V Score: 777
4.B.63
* Question H
Use the appropriate compound interest formula to compute the balance in the account afte
stated period of time
$14,000 is invested for 6 years with an APR of 5% and quarterly compounding.
Answer:
$18,862.91
Step-by-step explanation:
The appropriate formula is ...
A = P(1 +r/n)^(nt)
where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Filling in the numbers and doing the arithmetic, we get ...
A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91
The balance after 6 years will be $18,862.91.
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 89.4% of all their rugby balls have the correct shape. If exactly 6 of the 10 have the right shape, should the company stop the production line?
1)Yes as the probability of six having the correct shape is not unusual
2)NO. as the probability of six having the correct shape is unusual
3)Yes as the probability of six having the correct shape is unusual
4) No. as the probability of six having the correct shape is not unusual
Solution:
If exactly 6 of the 10 have the right shape, it means that the probability of success for the sample is
6/10 = 0.6
Expressing the probability in terms if percentage, it becomes
0.6 × 100 = 60%
Over time, the company has found that 89.4% of all their rugby balls have the correct shape. It means that the probability of success for the population is 89.4%
Comparing both probabilities, the probability of only 6 having the right shape is unusual. Therefore, the correct option is
3)Yes as the probability of six having the correct shape is unusual
image 30 points) math
Answer:
[tex]\pi =\frac{C}{d}[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]\pi =\frac{C}{d}[/tex]
Answer:
I'm not 100%sure but i'm think that it is c
Step-by-step explanation:
Hope this helps! May have gotten it wrong really sorry if I did
a student in greece discovers a pottery bowl that contains 29% of its original amount of C-14
Answer:
The age of the pottery bowl is 12,378.7 years
Step-by-step explanation:
The amount of C-14 after t yeas is given by the following equation:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which N(0) is the initial amount and k is the decay rate.
In this question, we have that:
[tex]k = 0.0001[/tex]
So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
Age of the pottery bowl:
29% of its original amount of C-14. So we have to find t for which N(t) = 0.29N(0). So
[tex]N(t) = N(0)e^{-0.0001t}[/tex]
[tex]0.29N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.29[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.29}[/tex]
[tex]-0.0001t = \ln{0.29}[/tex]
[tex]t = -\frac{\ln{0.29}}{0.0001}[/tex]
[tex]t = 12378.7[/tex]
The age of the pottery bowl is 12,378.7 years
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Answer:
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 185
Standard deviation = 26
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?
133 = 185 - 2*26
So 133 is two standard deviations below the mean.
By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133
p = 0.05*0.5 = 0.025
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Use the triangle shown on the right to complete the statement:
_____ (75*)=14.1/x
Answer: cos
2nd part: Use the equation shown to solve for the value of x. Round to the nearest tenth.
cos(75*)=14.1/x x=14.1/cos(75*)
Answer: 54.5 in
Answer:
Step-by-step explanation:
The answer is 54.5 on edg
For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
What is right angle triangle property?In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.
[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.
Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,
[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]
Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.
For the second part, we need to find the value of x. Thus solve the above equation further as,
[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]
Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.
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Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? A: x^2 + 8x – 308 = 0 B: x^2 – 8x + 308 = 0 C: x^2 + 8x + 308 = 0 D: x^2 − 8x − 308 = 0
Answer:
A
Step-by-step explanation:
The smaller negative integer is x.
The larger one is x+8, since they are 8 units apart.
The equation would be:
x*(x+8)=308
Let's simplify it by distributing.
x^2+8x=308
Subtract 308 from both sides.
x^2+8x-308=0
Therefore, the answer would be A.
According to a recent census, 16% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which has a random sample of 437 county residents, and found that 44 of those surveyed are of Hispanic origin.Randomization condition:Choose the correct statement.Select one:a. The 437 county residents were a voluntary response sample of all county residents.b. The 437 county residents is a systematic response sample of all county residents.c. The 437 county residents were a random sample of all county residents.
Answer:
Option C is correct.
The 437 county residents were a random sample of all county residents.
a) If p is the proportion of Hispanics in the county,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.35
b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.
c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
Test statistic = -4.09
p-value = 0.000043
d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.
Step-by-step explanation:
According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.
a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).
Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).
The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).
Mathematically,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.16
b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.
Hence, the model of this test is two-tailled, one-proportion test.
And the major conditions for an hypothesis test is that
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.
- The sample must be a normal distribution sample or approximate a normal distribution.
The conditions to check this is that
np ≥ 10
and
np(1-p) ≥ 10
p = sample proportion = (44/437) = 0.101
np = 437×0.101 = 44 ≥ 10
np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10
The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.
c) So, we compute the t-test statistic
z = (x - μ)/σₓ
x = sample proportion = 0.101
μ = p₀ = The proportion we are comparing against = 0.16
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 437
σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144
z = (0.101 - 0.16) ÷ 0.0144
z = -4.093 = -4.09
checking the tables for the p-value of this z-statistic
Degree of freedom = df = n - 1 = 437 - 1 = 436
Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)
The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).
p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043
The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
d) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.000043
0.000043 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.
Hope this Helps!!!
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
What is 80,000,000,000,000 in standard form (80 billion)
Answer:
8x10^13
Step-by-step explanation:
multiply (5 4/7) times (- 2 2/5)
Answer: -13.37
Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.
Select the number line model that matches the expression |8 - 1|
Answer:
Option B is correct
Step-by-step explanation:
Original expression is |8 - 1| = 7 = distance between number 1 and number 8
=> Option B is correct
Hope this helps!
The number line model that matches the expression |8 - 1| which is correct option(B)
What is the graph?The graph can be defined as a pictorial representation or a diagram that represents data or values.
What is the expression?The expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given the expression as |8 - 1|,
The value of the expression would give us 7. Meaning that the distance between coordinate 8 and 1 is 7 units.
The graphs given models the expression, |8 - 1|.
Option A, would match |-8 -1| = 5 units
Option B, would match |8 - 1| = 7 units.
Therefore, the answer is option (B).
Learn more about graph here :
https://brainly.com/question/16608196
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A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
A cylindrical tank has a radius of 2 m and a height of 9 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.)
Answer:
3,325,140 Joules
Step-by-step explanation:
Work done by the pump = Force applied to pump * distance covered by the water.
Since Force = mass * acceleration due to gravity
Force = (density of water * volume of the tank) * acceleration due to gravity
F =ρVg
Workdone = (ρVg )* d
Given ρ = 1000kg/m³, g = 9.8m/s², d = 3m
[tex]V = \pi r^{2}h\\V = \pi (2)^{2} *9\\V = 36 \pi \\V =113.10m^{3}[/tex]
Workdone by the pump = 1000 * 113.10 * 9.8 * 3
Workdone by the pump = 3,325,140Joules
What’s the correct answer for this question?
Answer:
what's the question?
it's not showing
Answer:
C.
Step-by-step explanation:
To find the perimeter, we'll use the distance formula
Distance Formula = √(x₂-x₁)²+(y₂-y₁)²
Finding Distance of AB
|AB| = √(-2+5)²+(3+1)²
|AB| = √25
|AB| = 5
Now For BC
|BC| = √(6+2)²+(-3-3)²
|BC| = √(8)²+(-6)²
|BC| = √100
|BC| = 10
FOR CA:
|CA| = √(-5-6)²+(-3+1)²
|CA| = √125
Perimeter of Triangle = 10 + 5 + √125
= 15 + √125
2. What is the sum of 4 tens and 6 tens?
Answer:
100
Step-by-step explanation:
4 tens + 6 tens = 10 tens = 10*10 = 100