Answer:
A) Yes. At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.
B) P-value = 0.001
C) The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the mean water temperature is significantly below 100 °F.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=9.
The sample mean is M=98.
The standard deviation of the population is known and has a value of σ=2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2}{\sqrt{9}}=0.667[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{98-100}{0.667}=\dfrac{-2}{0.667}=-3[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-3)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.
The critical value for this left-tailed test is zc=-1.645.
The null hypothesis would be accepted if the test statistic is higher than zc=-1.645. For a normal distribution with the parameters of the null hypothesis (μ=100, σ=2), this would correspond to a value of:
[tex]X=\mu+z\sigma/\sqrt{n}=100+(-1.645)\cdot 2/\sqrt{9}=100-1.1=98.9[/tex]
This means that if we get a sample of size n=9 and mean bigger than 98.9, we will failed to reject the null hypothesis.
If the true mean is 104 °F, the probability of getting a sample mean over 98.9 for this sample size can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{98.9-104}{2/\sqrt{9}}=\dfrac{-5.1}{0.6667}=-7.65\\\\\\P(M>98.9)=P(z>-7.65)=1[/tex]
The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.
please help! the number of candies consumed varies inversely with the number of children present
Answer:
The answer is
210 candiesStep-by-step explanation:
Let n represent the number of children
Let c represent the number of candies
The above variation is written as
[tex]c = \frac{k}{n} [/tex]
when n = 12 c = 140
So we have
[tex]140 = \frac{k}{12} [/tex]
Cross multiply
That's
k = 1680
So the formula for the variation is
[tex]c = \frac{1680}{n} [/tex]
when n = 8
[tex]c = \frac{1680}{8} [/tex]
c = 210
Therefore there are 210 candies consumed when there are 8 children
Hope this helps you
Expand and simplify (4x+3)(2x-5)
Answer:
4x(2x-5)+3(2x-5)
8x^2-20x+6x-15
8x^2-14x-15
Can somebody help me with this question?
Answer:
86 yd
Step-by-step explanation:
the area of the shaded region is 2924 yd²
let b the doted side next y :
the area of the total triangle is :
A = (y+b)*68/2 = 2924+ b*68/2
[tex]\frac{(y+b)*68}{2}[/tex] = [tex]\frac{b*68}{2}[/tex] + 2924 [tex]\frac{68*(y+b-b)}{2}[/tex] = 2924 68*y/2 = 2924 68y = 2*2924 y= (2*2924)/68 y= 86 ydg A catering service offers 7 %E2%80%8b Appetizers, 9 main%E2%80%8B courses, and 5 desserts. A banquet committee is to select 2 %E2%80%8b Appetizers, 8 main%E2%80%8B courses, and 4 desserts. How many ways can this be%E2%80%8B done
Answer:
945 ways
Step-by-step explanation:
Total
Number of Appetizers = 7Number of main courses = 9Number of desserts =5Required Selection
Number of Appetizers = 2Number of main courses = 8Number of desserts =42 Appetizers out of 7 can be selected in [tex]^7C_2[/tex] ways
8 main courses out of 9 can be selected in [tex]^9C_8[/tex] ways
4 desserts out of 5 can be selected in [tex]^5C_4[/tex] ways
Therefore, the number of ways this can be done
[tex]=^7C_2 \times ^9C_8 \times ^5C_4[/tex]
=945 ways
Which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) − 3x
Answer:
it has no solution.
hope it helps..
Answer:
D. the equation has infinitely many solutions
6x+15=6x+15 ❤️Solve the equation correctly to get brainliest and thanks! :)❤️
Answer:
Hey there!
6x+15=6x+15
Subtract 15 on both sides
6x=6x
Divide by 6 on both sides
x=x
Thus, x can be any number and there is an infinite amount of solutions.
Hope this helps :)
Jerry has a miniature model of a boat. He knows that the model is 3 3/4 inches wide and 5 1/2 inches long. What is the actual length of the boat if the actual width is 15 feet
Answer:
22 feet
Step-by-step explanation:
Change 15 feet into inches using the conversion
1 foot = 12 inches, thus
15 ft = 15 × 12 = 180 inches
scale factor = 180 ÷ 3.75 = 48
Thus the actual dimensions of the boat are 48 times the model.
actual length = 48 × 5.5 = 264 inches = 264 ÷ 12 = 22 feet
Find the value of x geometry
Answer:
x = 22
Step-by-step explanation:
Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22
What is the serving of coffee? 1 quart, 1 ml, or 1 c
What is the degree measure of an arc 4 ft. long in a circle of radius 10 ft.? 72° 60° 57.6°
Measure of an arc = ( intercepted angle/ full circle) x circumference
4 ft =( intercepted angle/360) x (2 x 10 x pi)
4 = intercepted angle /360 x 62.8
Divide both sides by 62.8
4/62.8 = intercepted angle/360
Multiply both sides by 360
Intercepted angle = (4/62.8) x 360
Angle = 22.93 degrees
Answer:
22.9 degrees
Step-by-step explanation:
The degree measure (in radians) can be found using the following formula.
Θ=S/r
where S is the arc length and r is the radius.
We know the arc length is 4 feet and the radius is 10 feet. Substitute the values into the formula.
Θ= 4/10
Θ= 0.4
The measure is 0.4 radians.
Convert radians to degrees using the following formula.
Θ * 180/π
We know that Θ= 0.4 , so we can substitute it in.
0.4 * 180/π
0.4 * 57.2957795
22.9183118
Round to the nearest tenth. The 1 in the hundredth place tells us to leave the 9 in the tenth place.
22.9
The angle measure is about 22.9 degrees.
can someone pleaseee help me??
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answer: (a) [tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
(b) A = $1680.67
(c) t = 9.99 years
(d) A = $1689.85
Step-by-step explanation:
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex] where
A is the amount accrued (balance)P is the principal (original/initial amount)r is the interest rate (convert to a decimal)n is the number of times compounded per yeart is the number of yearsa) Given: P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]
b) Given: P = 900, r = 7% = 0.07, n = quarterly = 4, t = 9
[tex]A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4(9)}\\\\\\A = 900\bigg(1+\dfrac{0.07}{4}\bigg)^{36}[/tex]
A = 1680.67
c) Given: A = 1800, P = 900, r = 7% = 0.07, n = quarterly = 4
[tex]1800=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\2=\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2=ln\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2 = 4t\ ln\bigg(1+\dfrac{0.07}{4}\bigg)\\\\\\\dfrac{ln\ 2}{4\ ln\bigg(1+\dfrac{0.07}{4}\bigg)}=t\\\\\\\bold{t=9.99}[/tex]
d) [tex]A=Pe^{rt}[/tex]
Given: P = 900, r = 7% = 0.07, t = 9
[tex]A=900e^{0.07(9)}\\\\\\A=900e^{.63}\\\\\\\bold{A=1689.85}[/tex]
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
3. Find the measure of x.
a 18°
b. 54°
C 126
d. 45
Answer:
18 degrees
Step-by-step explanation:
The triangle is an iscoceles right triangle.
The angles in a triangle add up to 180.
90+2y (iscoceles) =180
2y=90
y=45
So the angles of the right triangle are 45. However, you have to take away 27 because you are solving for only a part of 45. 45-27=18
Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=x8+3y+xy.
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the partial derivatives indicated Assume the variables are restricted to a domain on which the function is defined. z=[tex]x^{8}[/tex]+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
a) Zx b) Zy
In differentiation, if y = axⁿ, y' = [tex]nax^{n-1} \ where \ n\ is\ a\ constant[/tex]. Applying this in question;
Given the function z = x⁸+[tex]3^{y}[/tex]+[tex]x^{y}[/tex]
[tex]Z_x = \frac{\delta z}{\delta x} = 8x^{7} + 0 + yx^{y-1} \\\frac{\delta z}{\delta x} = 8x^{7} + yx^{y-1} \\[/tex]
Note that y is treated as a constant since we are to differentiate only with respect to x.
For Zy;
[tex]Z_y = \frac{\delta z}{\delta y} =0+ 3^{y} ln3 + x^{y}lnx \\\frac{\delta z}{\delta y} = 3^{y} ln3 + x^{y}lnx } \\[/tex]
Here x is treated as a constant and differential of a constant is zero.
Which of the following is a secant on the circle below?
DE is secant on the circle below.
What is Secant?A secant line is a straight line that twice intersects a circle.
We have a diagram of circle.
As, Either a secant or a tangent will arise from the circle's junction.
A secant is a line that intersects a circle twice. The relationship between the circle and the line that intersects it is explained by this idea.
Again from the figure CA and CE intersect circle at B and D.
It can also represented that the AB and DE intersects at a point C.
So, the secant line that intersects the circle twice.
Learn more about Secant here:
https://brainly.com/question/14348796
#SPJ7
plz answer question in screen shot
Answer: 342.32
Step-by-step explanation: sin(25) = h/a
Sin(25)= h/27
27*sin(25) = h
b*h = area
In the xy-plane, what is the y-intercept of the graph of the equation y=V4-?
O a. 2
O b.4
O c. 16
O d. There is no y-intercept.
Answer:
D
Step-by-step explanation:
There isn't enough information to find a y-intercept.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n)
Answer:
[tex]V(n) = 575000(0.7)^{n}[/tex]
Step-by-step explanation:
The value of the machine after n years is given by an exponential function in the following format:
[tex]V(n) = V(0)(1-r)^{n}[/tex]
In which V(0) is the initial value and r is the yearly rate of depreciation, as a decimal.
A company buys a machine for $575,000 that depreciates at a rate of 30% per year.
This means, respectively, that: [tex]V(0) = 575000, r = 0.3[/tex]. So
[tex]V(n) = V(0)(1-r)^{n}[/tex]
[tex]V(n) = 575000(1-0.3)^{n}[/tex]
[tex]V(n) = 575000(0.7)^{n}[/tex]
What is the Square root of 42?
Answer:
the square root is 6.48
Answer:
≈6.48
Step-by-step explanation:
[tex]\sqrt{42}=\\6.4807407...[/tex]
If you multiply it by itself, it will equal 42. (Or you can just use a calculator)
Ryan called each school in the district to determine whether or not they have a recycling program. What is true about Ryan’s data collection?
Answer:
A. Ryan conducted a survey where he asked about qualitative data.
Step-by-step explanation:
Surveys when carried out on people as the subjects are meant for the purpose of extracting some specific information from them. Observational studies involve close monitoring of the subject under evaluation. Quantitative data mainly deal with numbers and figures obtained from measurements or calculations. Qualitative data on the other hand is basically descriptive in nature and could sometimes be quite detailed.
Ryan's data collection would require a yes or no answer from the schools involved, and this information is descriptive or qualitative in nature. It also does not involve observation or close monitoring as he relies on the information provided by the school.
Answer: A
Step-by-step explanation:
Have a nice day
A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl
Answer: 7/8
Step-by-step explanation:
Let the boy is letter B and the girl is letter G.
So the possible outcomes are as follows below
BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
SO the number of possible outcomes is 8
The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7
So the probability, that family with 3 kids has at least 1 girl is
P(number of girls >=1)= 7/8
What is the area of this composite shape? Enter your answer in the box. in²
Answer:
53 in.
Step-by-step explanation:
to find the area u do 8 times 6 and 1/2 2(5)
triangle = 1/2bh
rectangle = bh
hope this helps
i need this asap guys im giving brainliest
An aquarium is in the shape of a rectangular prism. How much water will it take to fill the aquarium if the dimensions are 2ft by 4ft by 3ft? 12 cubic feet 24 cubic feet 36 cubic feet 8 cubic feet
Answer:
24 cubic feet.
Step-by-step explanation:
What we need to do here, is to find the volume of the aquarium.
The Aquarium is a rectangular prism.
The volume of a rectangular prism is length*width*height (we just multiply the dimensions together)
2*4*3=8*3=24
The volume of the aquarium is 24 cubic feet, and therefore 24 cubic feet of water is required to fill the tank.
Answer:
Hello! :) The answer will be under “Explanation”
Step-by-step explanation:
The answer will be 24 cubic feet.
Work:
LxWxH
(Length,Width,Hight)
So you the question is asking about volume, we need to do the formula (length,width, and hight)
Now we have to multiply
2x4=8
8x3=24
So the answer will be 24 cubic feet.
Hope this helps! :)
what is 8/5plus 2x?please answer this for me
Please help ASAP thanks in advance
Answer:
Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)
Step-by-step explanation:
Select the correct answer from each drop-down menu. The given equation has been solved in the table.
Answer:
1). SUBTRACTION property of equality
2). MULTIPLICATION property of equality
Step-by-step explanation:
Step 2:
When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.
[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]
Here 5 has been subtracted from both the sides.
Therefore, SUBTRACTION property of equality was applied.
Step 4:
If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.
[tex]4\times \frac{x}{4}=4\times (18)[/tex]
Here 4 has been multiplied to both the sides.
Therefore, MULTIPLICATION property of equality was applied.
2x + (-2x) when simplified is: ?
Answer:
Hello!
___________________
2x + (-2x) = 0
Step-by-step explanation: Simplify the expression.
Hope this helped you!
Can anyone help me with the question I attached below?
Answer:
The range in the average rate of change in temperature of the substance is from a low temperature of -22 ºF to a high of 16 ºF.
Step-by-step explanation:
Sine function is a bounded function whose range is between -1 and 1. The lowest average rate of change in temperature occurs when sine function is equal to 1 and the highest when this function is equal to -1. Then, the minimum and maximum average rate of changes in temperature are:
Minimum
[tex]f_{min} = -19 -3[/tex]
[tex]f_{min} = -22[/tex]
Maximum
[tex]f_{max} = 19-3[/tex]
[tex]f_{max} = 16[/tex]
The range in the average rate of change in temperature of the substance is from a low temperature of -22 ºF to a high of 16 ºF.
Which of the following statements about trapezoids is true?
O A. Opposite angles are equal
B. One pair of opposite sides is paralel.
C. Opposite sides are equal
O D. Both pairs of opposite sides are parallel
Answer:
B
Step-by-step explanation:
Trapezoids have only one pair of parallel lines.