Answer
15.8
Step-by-step explanation:
I’ll mark as brainliest.
Answer:
12 feet
Step-by-step explanation:
48 divided by 4 is 12 and 48 is the total area
Answer:
12 sq. ft.
Step-by-step explanation:
To find the area of a square (or rectangle) you multiply the length by the width.
To find the length of one side, when you have the area and one side, you divide the area by the side you have.
48 divided by 4 equals 12.
Hope this helps :)
please show work for both thank you!!
Answer:
a. x = 4.8989794855663561963945681494118 or 4.9 rounded
b. x = 8.6023252670426267717294735350497 or 8.6 rounded
Step-by-step explanation:
7² - 5² = x²
49 - 25 = x
49 - 25 = 24
√24 = 4.8989794855663561963945681494118
7² + 5² = x²
49 + 25 = x
49 + 25 = 74
√74 = 8.6023252670426267717294735350497
What is the probability of picking a 5 and then picking a 4?
I'm so confused pls help
Answer:
Step-by-step explanation:
Slope = 3.200/2.000 = 1.600
x-intercept = 5/8 = 0.62500
y-intercept = 5/-5 = 1/-1 = -1.00000
Find the value of x.
2x
20°
A. 80
B. 10
C. 35
O D. 45
Answer:
x = 10
Step-by-step explanation:
2x = 20°
x = 20/2
x =10
Answer:ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
Step-by-step explanation:
Create a step function for the following graph, be sure to watch holes in the graph. NEED HELP ASAP!
Answer:
See below
Step-by-step explanation:
This is a piece-wise function.
4, -4≤ x ≤ -2
f(x) = 2, -2 ≤ x < 2
-3, 2 ≤ x ≤ 4
Find the area of the triangle
The area is __yd^2
Answer:
13.5 yd²
Step-by-step explanation:
area = 1/2 ×4.5×6 = 13.5 yd²
Step-by-step explanation:
A=(base x height)/2
Base=6yd
Height=4.5yd
A=(4.5 x 6)/2 = 13.5yd^2
What are the solutions to the equation x2 + 4x – 12 = 0? O A. x = -6 and x = 2 O B. x= -4 and x= 3 O C. X=-3 and x = 4 D. x = -2 and x = 6
Answer:
the answer is A.
Fifteen students from Poppy High School were accepted at Branch University. Of those students, six were offered academic scholarships and nine were not. Mrs. Bergen believes Branch University may be accepting students with lower ACT scores if they have an academic scholarship. The newly accepted student ACT scores are shown here.
Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27
Part A: Do these data provide convincing evidence of a difference in ACT scores between students with and without an academic scholarship? Carry out an appropriate test at the α = 0.02 significance level. (5 points)
Part B: Create and interpret a 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship. (5 points)
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A:
Given:
Pooled sample size: [tex]n=15[/tex]
Sample size (with academic scholarships): [tex]n_1=6[/tex]
Sample size (no academic scholarships): [tex]n_2=9[/tex]
Population standard deviations: Unknown
Sample mean (with academic scholarships): [tex]\bar{x}=\frac{25+24+23+21+22+20}{6}=22.5[/tex]
Sample mean (no academic scholarship):[tex]\bar{x}=\frac{23+25+30+32+29+26+27+29+27}{9}=27.\bar{5}[/tex]
Sample standard deviation (with academic scholarships): [tex]s_1=1.7078[/tex]
Sample standard deviation (no academic scholarships): [tex]s_2=2.5868[/tex]
Degrees of freedom: [tex]df=n-2=15-2=13[/tex]
Significance level: [tex]\alpha =0.02[/tex]
Decide which test is most appropriate to conduct:
Therefore, we will conduct a 2-sample t-test assuming our conditions are satisfied.
List null and alternate hypotheses:
[tex]H_o:\mu_1=\mu_2[/tex] -> There's no difference in ACT scores between students with and without an academic scholarship
[tex]H_a:\mu}_1\neq\mu_2[/tex] -> There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
Determine the value of the test statistic:
We will use the formula [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }[/tex] to compute the test statistic [tex]t[/tex]. Therefore, the test statistic is [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }=\frac{27.\bar{5}-22.5}{\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9} } }=4.5592[/tex]
Calculate the p-value:
Because the test is two-sided, [tex]p=2tcdf(4.5592,1e99,13)=2(0.0003)=0.0006[/tex]
Interpret p-value and conclude test:
Given our significance level is [tex]\alpha =0.02[/tex], since [tex]p<\alpha[/tex], we reject the null hypothesis and conclude that there is significant evidence that suggests that there is a difference in ACT scores between students with and without an academic scholarship (it's more likely that the alternate hypothesis is true)
Part B:
The formula for a confidence interval for the difference in 2 population means is [tex]CI=(\bar{x}_1-\bar{x}_2)\pm t^*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/tex] where [tex]\bar{x}_1-\bar{x}_2[/tex] is the difference of the 2 sample means and [tex]t^*[/tex] is the critical score for the desired confidence level.
The critical score for our 98% confidence interval would be [tex]t^*=invT(0.99,13)=2.6503[/tex]
Therefore, our 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is [tex]CI=(27.\bar{5}-22)\pm 2.6503\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9}}}=[2.6167,8.4944][/tex]
This means that we are 98% confident that the true difference in the ACT scores between students with and without an academic scholarship is contained within the interval [tex][2.6167,8.4944][/tex]
The evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
How to perform two sample t-test?If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.
Let we have:
[tex]\overline{x}_1[/tex] = mean of first sample[tex]\overline{x}_2[/tex] = mean of second sample[tex]s_1[/tex] = standard deviation of first sample[tex]s_2[/tex] = standard deviation of second sample.Then, the value of t-test statistic is obtained as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]
If the level of significance is [tex]\alpha[/tex], then as we have:
the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex], the critical value of t is found to be [tex]t_{\alpha/2}[/tex], then if we get:
[tex]|t| < t_{\alpha/2}[/tex]null hypothesis
and if we get [tex]|t| > t_{\alpha/2}[/tex] null hypothesis, and thus, accept the alternate hypothesis.
For this case, we want to test if there is
Thus, we form the hypotheses as:
Null hypothesis: There's no difference in ACT scores between students with and without an academic scholarship
or: [tex]H_0: \mu_1 = \mu_2[/tex]
Alternative hypothesis: There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
or [tex]H_1: \mu_1 \neq \mu_2[/tex]
where we have:
[tex]\mu_1[/tex] = population mean score of ACT of students having academic scholarship[tex]\mu_2[/tex] = population mean score of ACT of students having no academic scholarshipFor this case, we evaluate the mean and standard deviation as:
Sample 1: Academic scholarship: 25, 24, 23, 21, 22, 20Sample size = [tex]n_1 = 6[/tex]
Mean = sum of all observation/ number of observations = 135/6 =22.5
Thus, standard deviation = [tex]s_1 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_1})^2}} = \sqrt{\dfrac{17.5}{6}} \approx1.71[/tex]
Sample 2: No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27Sample size = [tex]n_2 = 9[/tex]
Mean = sum of all observation/ number of observations = 248/9 ≈27.56
Thus, standard deviation = [tex]s_2 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_2})^2}} \approx \sqrt{\dfrac{60.22}{9}} \approx 2.59[/tex]
The t-test statistic is evaluated as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}} = \dfrac{22.5 -27.56}{\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}}} \approx -4.56[/tex]
Degree of freedom = [tex]n_1 + n_2 - 2 = 6 + 9 - 2 = 13[/tex]
Level of significance = 0.02 = 2%
The critical value of t is found to be [tex]t_{0.02/2} =2.65[/tex]
Thus, we get: [tex]|t| \approx 4.56 > 2.65 =t_{\alpha/2}[/tex]
Thus, we may reject the null hypothesis.
That means, there is enough evidence of a difference in ACT scores between students with and without an academic scholarship at 0.02 level of significance.
Now, the 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is calculated as:
[tex]CI = (\overline{x}_1 - \overline{x}_2) \pm t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}\\\\CI = -5.06 \pm 2.65(\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}})\\\\CI \approx -5.06 \pm 2.65 \times 1.11\\CI \approx -5.06 \pm 2.94\\CI \approx [-5.06 - 2.94, -5.06 + 2.94] = [-7.00, -2.14][/tex]
Thus, the evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
Learn more about two sample t-test here:
https://brainly.com/question/16285453
What value of x makes AD|| EH
Answer:
x = 3
Step-by-step explanation:
92 - 8x = 68
-8x = -24
x = 3
The two angles mentioned in the problem, if AD || EH, are congruent because they are corresponding angles.
Jacob bought some supplies for his lemonade stand. He purchased lemons for $4.85, sugar for $3.16, containers for $18. Taxes were included in all the prices. How much money did Jacob spend on all his purchases?
Answer:
26.01
Step-by-step explanation:
What is the surface area? 17 ft 16 ft 17 ft 19 ft 15 ft
Answer:
1,317,840
17×17=289×16=4,624×19=87,856×15=1,317,840
The midpoint of AB is M(5,-2). If the coordinates of A are
(6,-5), what are the coordinates of B?
Answer:
The coordinates of point B are (4,1)
Step-by-step explanation:
The easiest way of solving and explaining this question would to go by steps from each point. From point A to the midpoint, we go 1 left on the x axis from 6->5 and 3 up on the y axis from -5->-2. You then repeat these steps again to go from the midpoint to B. (5-1,-2+3) = (4,1)
solve for 5 + 6f > 8f -7
linear inequalities
Answer:
5+6f>8f-7
5+7>8f-6f
12>2f
6>f
f<6
Step-by-step explanation:
Simplify the expression. x4y−4z−2x2y−2z4 y2x2z6 the fraction with numerator y squared and denominator x squared z to the 6th power x2y2z6 the fraction with numerator x squared and denominator y squared z to the 6th power x2y2z6 the fraction with numerator x squared y squared and denominator z to the 6th power y2z6x2
Given:
Consider the given expression is:
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\dfrac{x^4y^{-4}z^{-2}}{x^2y^{-2}z^4}[/tex]
By using the quotient property of exponents, we get
[tex]=x^{4-2}y^{-4-(-2)}z^{-2-4}[/tex] [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]
[tex]=x^{2}y^{-4+2}z^{-6}[/tex]
[tex]=x^{2}y^{-2}z^{-6}[/tex]
By using negative exponent property, we get
[tex]=\dfrac{x^{2}}{y^{2}z^{6}}[/tex] [tex]\left[\because a^{-n}=\dfrac{1}{a^n}\right][/tex]
The simplified form of the given expression is [tex]\dfrac{x^{2}}{y^{2}z^{6}}[/tex].
Therefore, the correct option is B.
9 is what percent of 60
Answer:
15%
Step-by-step explanation:
[tex]\frac{9}{60} = \frac{3}{20}[/tex]
[tex]\frac{3}{20} = 0.15\\[/tex]
[tex]0.15 = 15%[/tex]
Answer:
if it's given 60,
so 1%=6
so 15/10=9
so answer is 1.5
Which statements about the system are true? Select two options.
y=x-4
3y - x= -7
The system has one solution.
The system consists of parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations represent the same line.
Save and Exit
Next
Submit
Mark this and return
Answer:
system has 1 solution at (2.5, -1.5)
Step-by-step explanation:
y = x - 4 this equation has a slope of 1 and a y-intercept of -4
3y - x = -7 this equation has a slope of 1/3 and a y-intercept of -7/3
which ones out of the three are no solution?
1. 10 + 6x = 15 + 9x – 3x
2. 11 + 3x – 7 = 6x + 5 – 3x
3. 11 + 3x – 7 = 6x + 5 – 3x
Answer: I'm going to say 3
Step-by-step explanation:
Find the value of X. If necessary write in radical form
Answer:
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\6^{2} +7^{2} =x^{2} \\\sqrt{85} = x[/tex]
Answer:
sqrt(85) =x
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + 7^2 = x^2
36+49 = x^2
85 = x^2
Take the square root of each side
sqrt(85) = sqrt(x^2)
sqrt(85) =x
What kind of solution is this? Prove it.
3+8x=8x+3
3=3
0=0
Answer:
all real numbers
Step-by-step explanation:
3 + 8x = 8x + 3
Subtract 8x from both sides.
3 = 3
Since 3 = 3 is a true statement, the solution is
x = all real numbers
Every number is a solution of this equation.
Big brutus pizza had two deals on pizza the first was $6 for a cheese pizza plus $3 for each topping the second deal was $20 per cheese pizza and 1 dollar per topping wat is the x and y
Answer:
[tex]x = 7[/tex] --- toppings
[tex]y = 27[/tex] ---- amount
Step-by-step explanation:
Given
[tex]y \to\ amount[/tex]
[tex]x \to\ topping[/tex]
The first deal is:
[tex]y = 6 + 3x[/tex]
The second is:
[tex]y = 20 + x[/tex]
Required
The value of x and y [for which both deals are equal]
We have:
[tex]y = 6 + 3x[/tex]
[tex]y = 20 + x[/tex]
Equate both
[tex]y=y[/tex]
So, we have:
[tex]6 + 3x = 20 + x[/tex]
Collect like terms
[tex]3x - x = 20 - 6[/tex]
[tex]2x =14[/tex]
Divide by 2
[tex]x = 7[/tex]
Substitute [tex]x = 7[/tex] in [tex]y = 20 + x[/tex]
[tex]y = 20 + 7[/tex]
[tex]y = 27[/tex]
A rolled up sleeping bag and shaped like a cylinder with a radius of 5" and a volume of 1727.9 cubic inches. What is the height of the road up sleeping bag?
Answer:
I think the height is 22.
Find the square roots of the following numbers. Give the steps correctly.
\sqrt {19.9 }
Please give me the answer .
Answer:
the sqare root of 19.9 is 4.46094160464
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 63 manufacturing companies located in the Southwest. The mean expense is $50.63 million and the standard deviation is $11.48 million. Is it reasonable to conclude the sample data are from a population that follows a normal probability distribution?
Answer:hi
Step-by-step explanation:
Hi
The area of a rectangular window is 8526 cm?
If the length of the window is 98 cm, what is its width?
Answer:
87cm
Step-by-step explanation:
Length x width = area
98 x width = 8526
width=8526/98
width=87
Which expression is NOT equal to 28?
A (9+ 25 = 5) 2
B.3-4x2) - 11x7
C.42= 6 + 28 = 4
D. 7* [8-(2-4 * 2)]
I
Answer:
You need the legnth of x
Step-by-step explanation:
Answer:
C.42= 6 + 28 = 4 is the answer
A sound wave is given by the
following equation:
y = 6 sin(324pi t)
where t = time in seconds
How many cycles will occur
between t= 3 and t = 5.5 seconds?
Answer:
405 cycles
Step-by-step explanation:
We have the equation:
y = 6*sin(324*π*t)
For the properties of the sin function, we know that the period is 2π.
So between:
Sin(x) and Sin(x + 2*pi)
we have a cycle.
between:
Sin(x) and Sin(x + 6*pi)
we have 3 cycles.
and so on.
Now we want to find how many cycles will occur between t = 3 s, and t = 5.5 seconds
Between these times, the difference in the argument of the sin function is:
324*π*5.5 - 324*π*3 = 324*π*(5.5 - 3) = 324*π*2.5
Now, the number of cycles that we will have between these times is equal to the number of times that "2*π" is in 324*π*2.5
That number is just the quotient between 324*π*2.5 and 2*π
N = (324*π*2.5)/(2*π) = (324*2.5)/(2) = 405
There are 405 cycles between 3 seconds and 5.5 seconds.
$(x^2-4x+2)^{x^2-5x+2} = 1.$
;PPP
Please help ASAP I need helppppoñ
5 cm
What is the surface area of the cube?
A. 25 cm?
B. 70 cm
C.125 cm?
D. 150 cm?
E. 200 cm
Answer:
Step-by-step explanation:
Answer:
D. 150 cm²
[tex]area = 5 \times 5 \\ = 25 \: {cm}^{2} [/tex]
= 25 × 6 sides
= 150 cm²