Answer:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
Step-by-step explanation:
Info given
[tex]\bar X=54.6[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=9.2 represent the sample standard deviation
n=48 represent the sample size
Part a
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
The Confidence is 0.999 or 99.9%, and the significance is [tex]\alpha=0.001[/tex] and [tex]\alpha/2 =0.0005[/tex], and the critical value would be [tex]t_{\alpha/2}=3.51[/tex]
And replacing we got:
[tex]54.6-3.51\frac{9.2}{\sqrt{48}}=49.94[/tex]
[tex]54.6+3.51\frac{9.2}{\sqrt{48}}=59.26[/tex]
The confidence interval is given by (49.94, 59.26)
Which triangle’s area would be calculated using the trigonometric area formula?
Triangle E F D is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12.
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Triangle A B C is shown. The length of A B is 4 and the length of B C is 5. Angle B C A is 25 degrees.
Triangle X Y Z is shown. The length of Y Z is 4. Angle Z X Y is 29 degrees and angle X Y Z is 110 degrees.
Answer:
Triangle Q R P is shown. The length of Q R is 5 and the length of R P is 6. Angle Q R P is 40 degrees.
Step-by-step explanation:
The trigonometric formula refers the two sides length of the triangle and it also consists of included angle to find out the area
A = [tex]\frac{1}{2}[/tex] ab sin C
QPR contains two sides and the included angle
XYZ has one side and the two angles
DEF has only three sides
And, the ABC contains two sides but does not have the included angle
Based on the explanation above, the correct option is B
Answer: the second option aka B
Step-by-step explanation: The other person explained it and I'm just here to tell you they gave the correct and answer for edge 2020.
What is the length of the diagonal of the square shown below?
Answer:
It’s E
Step-by-step explanation:
The length of the diagonal of the figure considered is given by: Option E: 5√2
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Consider the figure attached below.
The triangle ABC is a right angled triangle as one of its angle is of 90 degrees.
Thus, we can use Pythagoras theorem here to find the length of the diagonal line AC.
Since it is given that:
|AB| = 5 units = |BC|, thus, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC| = \sqrt{5^2 + 5^2} = \sqrt{2 \times 5^2} = \sqrt{5^2} \times \sqrt{2} = 5\sqrt{2} \: \rm units[/tex]
We didn't took negative of root as length cannot be negative.
Thus, the length of the diagonal of the figure considered is given by: Option E: 5√2
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
Suppose ARB Bank is reviewing its service charges and interest payment policies on current accounts. Suppose further that ARB has found that the average daily balance on personal current accounts is GH¢350.00, with a standard deviation of GH¢160.00. In addition, the average daily balances have been found to follow a normal distribution;
What percentage of customers carries a balance of GH¢100 or lower?
What percentage of customers carries a balance of GH¢500 or lower?
What percentage of current account customers carries average daily balances exactly equal to GH¢500?
What percentage of customers maintains account balance between GH¢100 and GH¢500?
Answer:
5.94% of customers carries a balance of GH¢100 or lower.
82.64% of customers carries a balance of GH¢500 or lower.
0% of current account customers carries average daily balances exactly equal to GH¢500.
76.7% of customers maintains account balance between GH¢100 and GH¢500
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 350, \sigma = 160[/tex]
What percentage of customers carries a balance of GH¢100 or lower?
This is the pvalue of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 350}{160}[/tex]
[tex]Z = -1.56[/tex]
[tex]Z = -1.56[/tex] has a pvalue of 0.0594
5.94% of customers carries a balance of GH¢100 or lower.
What percentage of customers carries a balance of GH¢500 or lower?
This is the pvalue of Z when X = 500.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 350}{160}[/tex]
[tex]Z = 0.94[/tex]
[tex]Z = 0.94[/tex] has a pvalue of 0.8264
82.64% of customers carries a balance of GH¢500 or lower.
What percentage of current account customers carries average daily balances exactly equal to GH¢500?
In the normal distribution, the probability of finding a value exactly equal to X is 0. So
0% of current account customers carries average daily balances exactly equal to GH¢500.
What percentage of customers maintains account balance between GH¢100 and GH¢500?
This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 100.
From b), when X = 500, Z = 0.94 has a pvalue of 0.8264
From a), when X = 100, Z = -1.56 has a pvalue of 0.0594
0.8264 - 0.0594 = 0.767
76.7% of customers maintains account balance between GH¢100 and GH¢500
In the triangles below, m B = MZP and mZT = m J.
What is the length of PQ?
6
3
5
12
I can't solve it because it didn't have enough information
Outline the procedure for finding probabilities of any given compound events.
Answer:
Explained below.
Step-by-step explanation:
A compound event is an event in which has possible outcomes more than one.
To determine the probability of compound events on has to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.
Examples of compound events are:
The events of roll a five using a 6-sided die .The number of favorable outcome is rolling a 5, is 1.
The total number of outcomes of rolling a die is 6.
Then the probability of rolling a 5 is 1/6.
The events of pulling a heart out of a standard deck of cardsThe number of favorable outcome of pulling a heart is 13.
The total number of outcomes is 52.
The probability of pulling a heart from a standard deck is 13/52 or 1/4.
Thus, the procedure is to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.
What is the solution to the equation a+5-2/3=9
Answer:
a= [tex]\frac{14}{3}[/tex]
a≈4.6
Step-by-step explanation:
a+5- [tex]\frac{2}{3}[/tex] =9
a+ [tex]\frac{15}{3} -\frac{2}{3}[/tex] =9
a+ [tex]\frac{13}{3}[/tex] =9
Subtract [tex]\frac{13}{3}[/tex] from both sides
a=[tex]\frac{14}{3}[/tex]
a≈4.6
Answer:
a
Step-by-step explanation:
(Please hurry)
Explain how to find the value of x
Answer:
96
Step-by-step explanation:
Exterior angles add up to 360
360 - 134-130 = 96
x = 96
Please answer this question for me thank you !! 20 Points !! Will give brainliest !!
Answer:
b
Step-by-step explanation:
In a parralel graph, the slopes would always be the same. The intercept in the answer is 2, showing that the coordinate points are (0,2)
Hope this helps!:)
Answer:
B) y = 2x + 2
Step-by-step explanation:
Firstly, you have to know that parallel lines have congruent slopes. That means that the slope of this line will be 2.
Next, make a point slope form of the equation:
y - y1 = m(x - x1)
y - 2 = 2(x - 0)
y - 2 = 2x - 0
Now, we can make it into slope intercept form.
y - 2 = 2x
y = 2x + 2
Hope this helps :)
In a random sample of high school seniors, the proportion who use text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it?
a. 1.5
b. 0.02
c. 0.78
d. 0.30
Answer:
b. 0.02
Step-by-step explanation:
The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. In this case, this will mean rejecting that the proportions are not significantly different.
Usually, a p-value is considered to be statistically significant when p ≤ 0.05.
From the answer options provided, alternative b. 0.02 is the only one that represents the difference in proportions to be statistically significant (there is only a 2% chance that the proportions are not significantly different).
Therefore, the answer is b. 0.02
How do I set up this problem. I'm lost
Answer:
the answer is 64 .
Step-by-step explanation:
basically i just divided 48 by 2.4 and got 20 .. so that means that 20 has to be the multiplied factor so i just multiplied 3.2 by 20 and got 64.
Simplify this equation x2-5x-36
Answer:
[tex]=\left(x+4\right)\left(x-9\right)[/tex]
Step-by-step explanation:
[tex]x^2-5x-36\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+4x\right)+\left(-9x-36\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9x-36\mathrm{:\quad }-9\left(x+4\right)\\=x\left(x+4\right)-9\left(x+4\right)\\\mathrm{Factor\:out\:common\:term\:}x+4\\=\left(x+4\right)\left(x-9\right)[/tex]
PLS HELP ME 10PTS
An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 7 feet tall and has a base with a circumference of 27.632 feet, what is the volume of the sculpture?
Answer: The volume of the sculpture is 141.84 cubic-feet
Step-by-step explanation: Please see the attachments below
Isaac is organizing a 5-kilometer road race. The safety committee
recommends having a volunteer every 1 of a kilometer and at
the finish.
| Are 10 volunteers enough?
Answer:
10 volunteers are more than recommendedStep-by-step explanation:
The recommended number of volunteers is five (5)
Since the the distance of the race is 5km,
and the safety committees recommends 1 volunteer per kilometre.
Hence ten (10) volunteers is more than enough
Complete the paragraph proof. Given: and are right angles Line segment A B is-congruent-to line segment B C Line segment B C is-congruent-to line segment A C Prove: Line A R bisects Angle B A C Triangles A B R and R C A share side R A. A line is drawn from point B to point C and intersects side A R at point P. It is given that and are right angles, and . Since they contain right angles, ΔABR and ΔACR are right triangles. The right triangles share hypotenuse , and reflexive property justifies that . Since and , the transitive property justifies . Now, the hypotenuse and leg of right ΔABR is congruent to the hypotenuse and the leg of right ΔACR, so by the HL congruence postulate. Therefore, ________ by CPCTC, and bisects by the definition of bisector.
Answer:
<BAR ≅<CAR
Step-by-step explanation:
Just took the test
Answer:
A edg 2020
Step-by-step explanation:
In a grinding operation, there is an upper specification of 3.150 in. on a dimension of a certain part after grinding. Suppose that the standard deviation of this normally distributed dimension for parts of this type ground to any particular mean dimension LaTeX: \mu\:is\:\sigma=.002 μ i s σ = .002 in. Suppose further that you desire to have no more than 3% of the parts fail to meet specifications. What is the maximum (minimum machining cost) LaTeX: \mu μ that can be used if this 3% requirement is to be met?
Answer:
Step-by-step explanation:
Let X denote the dimension of the part after grinding
X has normal distribution with standard deviation [tex]\sigma=0.002 in[/tex]
Let the mean of X be denoted by [tex]\mu[/tex]
there is an upper specification of 3.150 in. on a dimension of a certain part after grinding.
We desire to have no more than 3% of the parts fail to meet specifications.
We have to find the maximum [tex]\mu[/tex] such that can be used if this 3% requirement is to be meet
[tex]\Rightarrow P(\frac{X- \mu}{\sigma} <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{0.002} )\leq 0.03[/tex]
We know from the Standard normal tables that
[tex]P(Z\leq -1.87)=0.0307\\\\P(Z\leq -1.88)=0.0300\\\\P(Z\leq -1.89)=0.0293[/tex]
So, the value of Z consistent with the required condition is approximately -1.88
Thus we have
[tex]\frac{3.15- \mu}{0.002} =-1.88\\\\\Rrightarrow \mu =1.88\times0.002+3.15\\\\=3.15[/tex]
If (-2, y) lies on the graph of y=3x, then y=
1/9
0-6
hi
if reduce equation of line is y = 3x
and if x = -2 so y = 3*-2 = -6
if y=5x what happens to the value of y if the value of x doubles
Answer:
[tex] y = 5x[/tex]
And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:
[tex] y_f = 5(2x) = 10x[/tex]
And if we find the ratio between the two equations we got:
[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]
So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2
Step-by-step explanation:
For this case we have this equation given:
[tex] y = 5x[/tex]
And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:
[tex] y_f = 5(2x) = 10x[/tex]
And if we find the ratio between the two equations we got:
[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]
So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2
What’s the correct answer for this question?
Answer: choice D 1/2
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
so
1/6=1/3*p(A)
p(A)=1/2
please hurry I’ll make brainiest
A marble is thrown off of a balcony, towards the ground, from a height
of 18 feet above ground level, with a velocity of 4.5 feet per second.
Which function could be used to model the height of the marble, after
t seconds?
Answer:
Option (3)
Step-by-step explanation:
A stone has been thrown off towards the ground from a height [tex]h_{0}[/tex] = 18 feet
Initial speed of the stone 'u' = 4.5 feet per second
Since height 'h' of a projectile at any moment 't' will be represented by the function,
h(t) = ut - [tex]\frac{1}{2}(g)(t)^2[/tex] + [tex]h_{0}[/tex]
h(t) = 4.5t - [tex]\frac{1}{2}(32)t^2[/tex]+ 18 [ g = 32 feet per second square]
h(t) = 4.5t - 16t² + 18
h(t) =-16t² + 4.5t + 18
Therefore, Option (3) will be the answer.
Please answer this correctly
Answer:
Stem | Leaf
13 | 4 9 9
16 | 0 2 3 6
Step-by-step explanation:
134, 139, 139
160, 162, 163, 166
I NEED HELP WITH THIS PLEASE HELP ME
Answer:
156 minutes
Step-by-step explanation:
So we need to create an equation to represent how Frank's phone company bills him
I will denote "y" as the total for his billI will denote "x" as the number of minutes Frank usesSo the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"
They then charge $0.06 for every minute he talks, this will be our "slope"
Combining everything into an equation, we have: y = 0.06x + 8
Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value
y = 0.06x + 8 → y - 8 = 0.06x → [tex]x=\frac{y-8}{0.06}[/tex] Then plugging in our y value we get [tex]x=\frac{17.36-8}{0.06}=\frac{9.36}{0.06}= 156[/tex]Frank used up a total of 156 minutes
SELECT THE EQUIVALENT EXPRESSION
(6^-4 x 8^-7)^-9
A. 6^36•8^63
B. 1/6^13•8^16
Answer:
A
Step-by-step explanation:
Calculate the products in the multiple choice and see if any equal the product in the problem.
Hence as the products calculated in choice A equal that in the problem;the answer is A
Zed went to the store and bought a bag of chips. He estimated there would 1 point
be 350 chips in the package, but realized there were only 210 chips in that
package. What was his percent error?'
Answer:
66.67%
Step-by-step explanation:
They do not say that I estimate a value of 350 chips but in reality there were 210 chips in total, we have that the error formula is:
Percentage error (%) = (estimated value - actual value) / actual value × 100 (in absolute value)
replacing:
Percentage error (%) = | 350 - 210 | / 210 × 100
Percentage error (%) = 140/210 * 100
Percentage error (%) = 66.67
Which means that the percentage error is 66.67%
Expansion Numerically Impractical. Show that the computation of an nth-order determinant by expansion involves multiplications, which if a multiplication takes sec would take these times:
n 10 15 20 25
Time 0.004 sec 22 min 77 years 0.5.109years
Answer:
number of multiplies is n!n=10, 3.6 msn=15, 21.8 minn=20, 77.09 yrn=25, 4.9×10^8 yrStep-by-step explanation:
Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...
mpy[n] = n·mp[n-1]
mpy[2] = 2
So, ...
mpy[n] = n! . . . n ≥ 2
__
If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...
10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10
Then the larger matrices take ...
n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min
n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years
n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years
_____
For the shorter time periods (less than 100 years), we use 365.25 days per year.
For the longer time periods (more than 400 years), we use 365.2425 days per year.
Nam owns a used car lot. He checked the odometers of the cars and recorded how far they had driven. He
then created both a histogram and a box plot to display this same data (both diagrams are shown below).
Which display can be used to find how many vehicles had driven more than 200,000 km (kilometers)?
Choose 1 answer:
Answer:
a histogram
Step-by-step explanation:
You can count easily from hiistogram how many vehicles had driven more than 200,000 km (kilometers) and that's not the case with the box plot
The mean family income for a random sample of 600 suburban households in Loganville shows that a 95 percent confidence interval is ($43,100, $59,710). Alma is conducting a test of the null hypothesis H0: µ = 42,000 against the alternative hypothesis Ha: µ ≠ 42,000 at the α = 0.05 level of significance. Does Alma have enough information to conduct a test of the null hypothesis against the alternative?
Answer:
[tex] 43100 \leq \mu \leq 59710[/tex]
And for this case we want to test the following hypothesis:
Null hypothesis: [tex] \mu =42000[/tex]
Alternative hypothesis: [tex] \mu \neq 42000[/tex]
For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000
Step-by-step explanation:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And for this case the 95% confidence interval is already calculated as:
[tex] 43100 \leq \mu \leq 59710[/tex]
And for this case we want to test the following hypothesis:
Null hypothesis: [tex] \mu =42000[/tex]
Alternative hypothesis: [tex] \mu \neq 42000[/tex]
For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000
Answer: Yes, because $42,000 is not contained in the 95% confidence interval, the null hypothesis would be rejected in favor of the alternative, and it could be concluded that the mean family income is significantly different from $42,000 at the α = 0.05 level
Step-by-step explanation:
took the test
8 cm
10 cm
The surface area of the above figure is
A. 816.8 cm2
B. 879.6 cm2
C. 565.5 cm2
D. 1131.0 cm
Hi there u have not given us the figure please correct the answer and I will send my answer.Is it a cylinder cuboid cube or?
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.
Answer:
There are two complex roots.
Step-by-step explanation:
When the discriminant is a negative number, the parabola will not intersect the x-axis. This means that there are no solutions/two complex solutions.
If a triangle has sides that are 21 and 6 what is the range for third side x?
Enter your answer without spaces in range format.
Example: 1<x<3
Answer:
15<x<27
Step-by-step explanation:
Rule for the sides of a triangle:
The sum of the two smallest sides of a triangle must be greater than the biggest side.
In this question:
Sides of 6, 21 and x. We have to find the range for x.
If 21 is the largest side:
Two smallest are 6 and x.
x + 6 > 21
x > 21 - 6
x > 15
If x is the largest side:
Two smallest and 6 and 21. So
21 + 6 > x
27 > x
x < 27
Then
x has to be greater than 15 and smaller than 27. So the answer is:
15<x<27
if you’re good with permutations in math 30 help out with this easy question
In how many ways can five boys and three girls sit in a row such that all boys sit together?
a) 4800
b) 5760
c) 2880
d) 1440
Answer:
2880
Step-by-step explanation:
Consider the 5 boys to be 1 group. The boys and 3 girls can be arranged in 4! ways.
Within the group, the boys can be arranged 5! ways.
The total number of permutations is therefore:
4! × 5! = 2880