Answer:
(7-2x)3 =9-10x
x= -3
Step-by-step explanation:
we let the number to be x.
twice a number=2x is decreased by 7 that is to say 7-2x, is multiplied by 3, we have (7-2x)3.
the result is 9 less than 10times the number which is =9-10x.
so bringing all these together we have;
(7-2x)3=9-10x.
what is the number?
solving, we have:
(7-2x)3=9-10x
21-6x=9-10x
21-9= -10x+6x
12= -4x
dividing both sides by -4 we have our number
x= -3.
for proof we can substitute x=-3 into the equation.
21-6(-3) =9-10(-3)
21+18=9+30
39=39
There is a 0.9986 probability that a randomly selected 30 year old male lives through the year (based on data from the US department of Health and Human Services). A Fidelity life insurance company charges $161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit. If a 30 year old male purchases the policy, what is his expected value?
Answer:
a) Surviving the year: $ -161. Not surviving: 99,839.
b) 0.9986 * -161 + (1-0.9986) * 100000 = -20.7746
c) As the expected value is negative from the male's perspective, it is positive from the insurance company's perspective. So as the number of people purchasing this insurance becomes large, the company's profit will converge to an average value of 20.7746 per male. So the company is indeed profitting.
Which operation should you perform last in the expression 32 + 2?
Answer:
Step-by-step explanation:
Adding the numbers because that is the only step. Making it the last operation.
Suppose an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000. Assume that a random sample of 500 households in Michigan is taken. Then, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be:
Answer: 0.0179
Step-by-step explanation:
We know that , the standard error of the sampling distribution of sample proportion (p) is given by :-
[tex]S.E.=\sqrt{\dfrac{p(1-p)}{n}}[/tex]
where , n= sample size
Let p be the proportion of households who have incomes in excess of $60,000 .
As per given , we have
p= 20% = 0.20
n= 500
Then,
[tex]S.E.=\sqrt{\dfrac{0.20(1-0.20)}{500}}=\sqrt{\dfrac{0.20\times0.80}{500}}\\\\=\sqrt{0.00032}\\\\=0.01788854382\approx0.0179[/tex]
Hence, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 is 0.0179.
The standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be 0.0179.
Calculation of the standard error:Since an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000.
So here the standard error should be
[tex]\sqrt (.2\times (1-.2)\div 500) \\\\= 0.0179[/tex]
Hence, the standard error should be 0.0179.
Learn more about sample here: https://brainly.com/question/9222927
A professor notices that more and more students are using their notebook computers in class, presumably to take notes. He wonders if this may actually improve academic success. To test this, the professor records the number of times each student uses his or her computer during a class for one semester and the final grade in the class (out of 100 points). If notebook computer use during class is related to improved academic success, then a positive correlation should be evident. Given the following data, test whether notebook computer use and grades are related at a .05 level of significance.
State the conclusions for this test using APA format. First, describe the correlation coefficient in words and give the value of r. Then give the value of R2 and describe (in words) the effect size using the coefficient of determination. Finally, is there a significant relationship?
Answer:
Step-by-step explanation:
The hypothesis being tested is:
H0: ρ = 0
Ha: ρ ≠ 0
Pearson's r is -0.140.
The critical r-value is 0.404.
Since 0.140 < 0.404, we cannot reject the null hypothesis.
Therefore, we cannot conclude that notebook computer use and grades are related.
Pearson's r is -0.140. It means that there is a weak negative relationship between notebook computer use and grades.
The coefficient of determination is 0.020. 2% of the variation in the model is explained.
The relationship is not significant.
Notebook Computer Use Final Grade for Course
30 86
23 88
6 94
0 56
24 78
36 72
10 80
0 90
0 82
8 60
12 84
18 74
0 78
32 66
36 54
12 98
8 81
18 74
22 70
38 90
5 85
29 93
26 67
10 80
r² = 0.020
r = -0.140
Std. Error = 11.996
n = 24
k = 1
ANOVA table
Source SS df MS F p-value
Regression 63.6652 1 63.6652 0.44 0.5129
Residual 3,165.668 22 143.8940
Total 3,229.333 23
Please help I will mark you a brainliest
Answer:
[tex]sin\;60 =\frac{\sqrt{3} }{2}[/tex]
At a time denoted as t=0, a student carrying a new flu virus comes back to an isolated campus that has a fixed number of 1000 people. Determine a differential equation for the number of people x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it. (Please use k as the proportional constant.)
Answer:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]
Step-by-step explanation:
Total Number of People on Campus =1000
Let the number of people who have contracted the flu =x(t)
Therefore, the number of people who have not contracted the flu =1000-x(t)
Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.
[tex]\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)][/tex]
Introducing the proportional constant k, we obtain:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)][/tex]
At t=0, there was no infected on the campus, therefore the initial condition is given:
[tex]x(0)=0[/tex]
Therefore, a differential equation for the number of people x(t) who have contracted the flu is:
[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]
A box has a volume of 22 1/2 in³. Find the length of the box!
Answer:
Length = 2.823 in (to 3 decimal places)
Step-by-step explanation:
assuming that the box is a cubic box:
volume of box = [tex]22\frac{1}{2}[/tex] in³ = 22.5 in³
volume = Length × Length × Length = (Length)³
∴ (Length)³ = 22.5
∴ Length = ∛(22.5)
using the calculator punch ∛(22.5), and the answer is:
∴ Length = 2.823 in (to 3 decimal places)
¿Pueden ser complementarios un ángulo agudo y un ángulo obtuso?
Answer:
No porque si sumas los dos el resultado es más de 90 grados.
Step-by-step explanation:
Ashley and Robbin bought identical backpacks at different stores. Ashley’s backpack originally cost $65 and was discounted 25%. Robbin’s backpack originally cost $75 and was on sale for 30% off of the original price. Which backpack is the better buy? Explain.
Answer:
Ashley’s backpack is the better buy.
Step-by-step explanation:
You have to calculate the price that was paid for each backpack after the discount was applied.
Ashley’s backpack: $65*0.25= $16.25
Final price= $65-$16.25= $48.75
Robbin's backpack: $75*0.3= $22.5
Final price= $75-$22.5= $52.5
According to this, the backpack that is the better buy is the one that Ashley bought because after the discounts were applied it cost $48.75 and Robbin's backpack cost $52.2 which means that Ashley's backpack was cheaper.
Please answer this correctly
Answer:
3.00
Step-by-step explanation:
3.14 is rounded to 3.00
Answer:
141.3 m²
Step-by-step explanation:
V= πr²h
V=3.14*(6/2)²*5= 141.3 m²
If f(x) = 2x2 - 5 and g(x) = 3x + 3, find (f - g)(x).
A. 3x – 2x2 - 2
B. 2x2 – 3x - 2
C. 2x2 – 3x-8
D. - x² – 8
Answer:
2x^2 -3x -8
Step-by-step explanation:
f(x) = 2x^2 - 5
g(x) = 3x + 3,
(f - g)(x)= 2x^2 - 5 -(3x + 3)
Distribute the minus sign
(f - g)(x)= 2x^2 - 5 -3x - 3
Combine like terms
= 2x^2 -3x -8
A park in the shape of quadrilateral PQRS is bordered by four sidewalks. Find the measure of each
exterior angle of the park.
15z=
7z=
7z=
11z=
Answer:
135°, 63°, 63°, 99°
Step-by-step explanation:
Find attached the diagram used in solving the question.
We would use formula for sum of interior angles to get each exterior angle.
From the diagram, we added additional variables to be able to solve for sum of interior angles.
Sum of angle on a straight line = 180°
a° +15z° = 180°
b° +7z° = 180°
c° +7z° = 180°
d° +11z° = 180°
Where a,b,c and d are interior angles
Sum of interior angles = 180(n-2)
n = number of sides
For quadrilateral, n= 4
a°+b°+c°+d° = 180(n-2)
180-15z +180-7z+180-7z+180-11z = 180(4-2)
720-40z = 180(2)
720 - 360 = 40z
z = 360/40
z = 9
Each exterior angle:
15z = 15×9 = 135°
7z = 7×9 = 63°
7z = 7×9 = 63°
11z = 11×9 = 99°
Please answer this correctly without making mistakes
Answer:
1st one, I think so. I'm pretty positive
Answer:
1st Option (4 Blocks)Step-by-step explanation:
So, in this image, there are 6 blocks in total!
The little guy standing in front would only be able to see the bottom two cubes, along with the top two, making 4 blocks in total! :3
#SpreadTheLove <3
A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. A new study provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01?
What are the null and alternative hypotheses?
Answer:
Null hypothesis H0: p = 0.01
Alternative hypothesis Ha: p < 0.01
Step-by-step explanation:
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 the case above;
The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.
H0: p = 0.01
The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.
Ha: p < 0.01
write the equation of a line that is perpendicular to the given line and that passes through the given point. -3x - 6y = 17; (6, 3)
Answer:
Y=2x-9
Step-by-step explanation:
Is this right ? Anyone ?
Answer:
yes this right, it depends on what one tho
Step-by-step explanation:
Darío buys applesauce cups for a family reunion. He needs 23 cups, and he buys them in packs of 6. How many packs does Dario need?
Answer:
He needs four packs.
Step-by-step explanation:
6*4=24 there is 23 so he will need 4 packs in total.
Answer:
4 packs
Step-by-step explanation:
3 packs only gives him 18 and he needs atleast 23. The closest number that meets 23 is 24. It takes 4 packs of 6 to get 24.
What general conclusions can be drawn when you compare salaries with education levels?
Answer:
typically, careers that require higher education levels pay higher salaries than those that require a high school diploma.
Find the indicated probability. The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week
Given Information:
Mean weekly salary = μ = $490
Standard deviation of weekly salary = σ = $45
Required Information:
P(X > $525) = ?
Answer:
P(X > $525) = 21.77%
Step-by-step explanation:
We want to find out the probability that a randomly selected teacher earns more than $525 a week.
[tex]P(X > 525) = 1 - P(X < 525)\\\\P(X > 525) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 525) = 1 - P(Z < \frac{525 - 490}{45} )\\\\P(X > 525) = 1 - P(Z < \frac{35}{45} )\\\\P(X > 525) = 1 - P(Z < 0.78)\\\\[/tex]
The z-score corresponding to 0.78 from the z-table is 0.7823
[tex]P(X > 525) = 1 - 0.7823\\\\P(X > 525) = 0.2177\\\\P(X > 525) = 21.77 \%[/tex]
Therefore, there is 21.77% probability that a randomly selected teacher earns more than $525 a week.
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.7, 2.2, 1.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.78 then go for 0.08 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
An economist wants to test if there is any difference in income between Escambia county and Miami-Dade county in Florida. To do this, she collects random samples of residents from both these counties. The information collected from these samples is tabulated below. Assume that both the populations are normally distributed with equal population variances.
Escambia County (Population 1) Miami-Dade County (Population 2)
n 1 = 11 n 2 = 15
x ¯ 1 = 36,700 x ¯ 2 = 34 ,700
s 1 = 7800 s 2 = 7375
Set up the null and alternative hypotheses to test the economist’s claim.
a) H_0 : μ1- μ2 is less than or equal to 0 versus H_a: is μ1- μ2 greater than 0b) H_0 : μ1 <μ2 versus H_a: is μ1 is greater than or equal to μ2c) H_0 : μ1 is not equal to μ2 versus H_a: is μ1 is equal to μ2d) H_0 : μ1- μ2 is greater than or equal to 0 versus H_a: is μ1- μ2 is less than 0e) H_0 : μ1- μ2 = 0 versus H_a: is μ1- μ2 not equal t0 0
Answer:
Yo
Step-by-step explanation:
Write down the 1st term in the sequence given by: T(n) = n2 + 3
Answer:
5
To find the first term
T(1)=(1×2)+3
=2+3
=5
A test was made of H0: μ1 = μ2 versus H1: μ1 < μ2. The sample means were and the sample standard deviations were and and the sample sizes were and Is H0 rejected at the 0.05 level? (Hint: First compute the value of the test statistic.)
Answer:
Step-by-step explanation:
Hello!
Hypotheses:
H₀: μ₁ = μ₂
H₁: μ₁ < μ₂
α: 0.05
Using the following sample information:
Sample 1
n₁= 15
X[bar]₁= 10
S₁= 4
Sample 2
n₂= 27
X[bar]₂= 8
S₂= 7
This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:
[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*16+26*49}{15+27-2} }= \sqrt{\frac{1498}{40} } = 6.119= 6.12[/tex]
[tex]t= \frac{(10-8)-0}{6.12*\sqrt{\frac{1}{15} +\frac{1}{27} } }= 1.01[/tex]
The p-value of this test is 0.1593
To decide using the p-value approach you have to use the following rule:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.
Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.
I hope this helps!
Select the correct answer.
What is 22% of 50?
OA.
44
OB.
28
Oc.
22
OD.
11
Answer:
11
Step-by-step explanation:
Which expression is equal to 5y^3÷5y^-2
Answer:
[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]
Step-by-step explanation:
[tex]5y^3/5y^-2[/tex]
as 5 is both in numerator and denominator it will get cancelled so we have now expression
[tex]y^3/y^-2[/tex]
we will use law of indices wherein if there is
[tex]a^x/a^y = a^(x-y)[/tex]
which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept
here power in numerator is 3 and power in denominator is -2
hence we will be subtracting -2 from 3
[tex]y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5[/tex]
Thus,
[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]
Rebecca needs a box with a rectangular base of 36 cm2 and a volume of 180 cm3,
What would be the height of this box?
Answer:
Height h = 5 cm
Step-by-step explanation:
Given;
Volume of box V = 180 cm^3
Base area of box A = 36 cm^2
Height = h
Volume = base area × height
height = volume/base area
h = V/A
Substituting the values;
h = (180cm^3)/(36cm^2)
Height h = 5 cm
The National Center for Educational Statistics surveyed 5400 college graduates about the lengths of time required to earn their bachelors degrees. The mean is 5.4 years and the standard deviation is 1.9 years. Based on this sample, construct a 90% confidence interval for the mean time required by all college graduates
Answer:
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
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 = 1.645*\frac{1.9}{\sqrt{4500}} = 0.04[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.
The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.
The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.
A recent study reported that 73% of Americans could only converse in one language. A random sample of 130 Americans was randomly selected. What is the probability that 100 or fewer of these Americans could only converse in one language?
Answer:
Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.
Step-by-step explanation:
We are given that a recent study reported that 73% of Americans could only converse in one language.
A random sample of 130 Americans was randomly selected.
Let [tex]\hat p[/tex] = sample proportion of Americans who could only converse in one language.
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, p = population proportion of Americans who could only converse in one language = 73%
[tex]\hat p[/tex] = sample proportion = [tex]\frac{100}{130}[/tex] = 0.77
n = sample of Americans = 130
Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77)
P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.77-0.73}{\sqrt{\frac{0.77(1-0.77)}{130} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.08) = 0.8599
The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.
What are the excluded values? x = -3; z = 0 y = -5; z = 0 y = 0; z = -5 none of the above
Answer:
y = 0; z = -5
Step-by-step explanation:
Excluded values are ones that make the fraction "undefined." That will be the case when the denominator is zero.
When y = 0, the denominator is zero.
When z = -5, the denominator is zero.
Excluded values are y = 0; z = -5.
Answer:
-5
Step-by-step explanation:
A random sample of a specific brand of snack bar is tested for calorie count, with the following results: Assume the population standard deviation is σ and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars.
Answer:
The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).
Step-by-step explanation:
The question is incomplete:
"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."
We start by calculating the mean of the sample:
[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is know and is σ=24.
The sample mean is M=146.
The sample size is N=9.
As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]
The z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]
The 95% confidence interval for the population mean is (130.32, 161.68).
The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153. After analyzing the data to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average, the p-value of 0.0099 was obtained. Using a 0.05 significance level, what conclusion can be drawn from the data?
Answer:
Step-by-step explanation:
The null hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is less than or equal to the national average: u ≤ 150
The alternative hypothesis: Mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average: u > 150
Since the p-value of 0.0099 was gotten which is less than the significance level of 0.05, we reject the null hypothesis and conclude that actually there is a statistically significant evidence to prove that the mean verbal reasoning GRE score of the engineering graduate students at the technical university is greater than the national average
