There insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.
Step 1: State the hypotheses:
- Null hypothesis (H0): The mean amount spent by a customer is equal to or greater than last year's mean ($52).
- Alternative hypothesis (H1): The mean amount spent by a customer is significantly less than last year's mean ($52).
Step 2: Set the significance level:
The significance level (α) is given as 0.10. This represents a 10% chance of rejecting the null hypothesis when it is true.
Step 3: Formulate the decision rule:
Since the alternative hypothesis is stating a decrease in the mean amount spent, we will conduct a one-tailed t-test and reject the null hypothesis if the test statistic falls in the critical region corresponding to the left tail of the t-distribution.
Step 4: Calculate the test statistic:
We need to calculate the t-statistic using the formula:
t = (sample mean - population mean) / (sample standard deviation / √(sample size))
Given data:
Population mean (μ) = $52
Sample mean (X) = $50
Sample standard deviation (s) = $11
Sample size (n) = 36
Plugging in the values:
t = ($50 - $52) / ($11 / √(36))
t = -2 / ($11 / 6)
t ≈ -1.0909
Step 5: Determine the critical value and make a decision:
Since the significance level is 0.10 and the test is one-tailed to the left, we need to find the critical t-value at a 0.10 significance level with degrees of freedom equal to (n - 1) = (36 - 1) = 35.
so, the critical t-value is -1.3104.
Since the calculated t-statistic (-1.0909) does not fall in the critical region (t < -1.3104), we do not have enough evidence to reject the null hypothesis.
Step 6: State the conclusion:
Based on the data and the hypothesis test, at the 0.10 significance level, there is insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.
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Show, using the Mean Value Theorem, that sin xsin y ≤ x − y| for all real numbers x and y. b) Prove, using a), that sinx is uniformly continuous on R.
Using the Mean Value Theorem, sin xsin y ≤ x − y| for all real numbers x and y, sinx is uniformly continuous on R.
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) where the derivative of the function is equal to the average rate of change of the function over [a, b].
Applying this theorem to the function f(x) = sin x on the interval [x, y], we can find a point c between x and y where the derivative of f(x) is equal to the average rate of change of f(x) over [x, y].
Since the derivative of sin x is cos x, we have cos c = (sin y - sin x) / (y - x). Rearranging the inequality, we get sin y - sin x ≤ cos c (y - x). Now, using the fact that |cos c| ≤ 1, we can rewrite the inequality as sin y - sin x ≤ |y - x|. Thus, sin xsin y ≤ x - y| for all real numbers x and y.
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A ship sails 9 km due West, then 5 km due South.
Find the bearing of the ship from its initial position.
Give your answer correct to 2 decimal places.
Answer:
10.29 km
Step-by-step explanation:
Given that,
A ship sails 9 km due West, then 5 km due South.
We need to find the distance of the ship from its initial position. Let the distance be d. We can find it as follows :
[tex]d=\sqrt{9^2+5^2} \\\\d=10.29\ km[/tex]
So, the required distance of the ship from its initial position is equal to 10.29 km.
Solve 5/4=x/12.
x=
Please help!
Answer: x=15
Step-by-step explanation:Step 1: Cross-multiply.
5
4
=
x
12
(5)*(12)=x*(4)
60=4x
Step 2: Flip the equation.
4x=60
Step 3: Divide both sides by 4.
4x
4
=
60
4
x=15
Answer:
x=15
If the number of bacteria in a colony doubles every 46 minutes and there is currently a
population of 150 bacteria, what will the population be 92 minutes from now?
bacteria
Answer: 608
Step-by-step explanation: multiply by 2
Does the nature of the data allow you describe the difference of the two medians as a multiple of the interquartile range? If so, what is the multiple?
Answer:
1/3
Step-by-step explanation:
From the figure, we know that the median of Amy is 40 and the median of Megan is 35.
Therefore the difference in their medians is = 40 - 35
= 5
We see that Q1 of Megan is 25 and Q3 is 40. Therefore, her interquartile range is given by Q3 - Q1 = 40 - 25
= 15
So, the difference of the medians is the multiple of the interquartile range.
So the multiple is = 5/15
= 1/3 (IQR of Megan)
Answer:
Yes, I can describe the difference of the two medians as a multiple of the interquartile range as shown below.
Step-by-step explanation:
The difference of the medians for the two data sets is 69 − 60 = 9. The interquartile ranges for the data sets are 9 ounces and 8 ounces.
This shows that the difference of the medians is about 1 times, or nearly equal to, the interquartile range of either data set.
For Genivieve, the multiple is 1:
9 = m(9)
m = 1
For Mindy, the multiple is 1.125:
9 = m(8)
m = 1.125
(This is the answer on edumentum)
Write a word problem for 1/3 X 2/3 . Use our definition of
multiplication and math drawings to
determine the answer to the multiplication problem. Explain
clearly.
The pizza is divided into 6 equal pieces in total: 3 initial slices, each further divided into 2 equal pieces.
A pizza is cut into 3 equal slices. Each slice is then cut into 2 equal pieces. How many pieces of pizza are there in total?
To solve this problem, we can use our definition of multiplication. Multiplication is repeated addition. In this case, we are repeatedly adding 2 to itself 3 times. This gives us 2 + 2 + 2 = 6. Therefore, there are 6 pieces of pizza in total.
We can also use math drawings to solve this problem. Here is a math drawing that shows how to find the product of 1/3 * 2/3:
The first row of the math drawing shows 1/3 of a pizza. The second row shows 2/3 of a pizza. The third row shows the product of 1/3 * 2/3. As you can see, the product is 6 pieces of pizza.
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What is the difference between a leg and a hypotenuse?
Answer:
Legs - the sides that form the right angle of a right triangle.
Hypotenuse - the side opposite the right angle of a right triangle.
Step-by-step explanation:
Every triangle has 3 sides.
Certain special triangle have specific names assigned to their sides.
A right triangle has one right angle and two acute angles. The two sides that form the right angle of a right triangle are called legs. The third side of the right triangle is called hypotenuse. The hypotenuse is opposite the right angle and does not help form the right angle.
PLEASE ANSWER THIS ASAP I WILL GIVE YOU 5 STARS AND BRAINLIEST
Answer:
1. d
2. c
3. b
4. f
5. a
6. e
Step-by-step explanation:
Good Luck
Can someone plz help me
Answer:
54 sq ft
Step-by-step explanation:
6ft x 3 ft = 18 sq ft
9 ft x 4 ft = 36 sq ft
18 sq ft + 36 sq ft = 54 sq ft
The choices should be in sq ft, not in sq cm
The value of area in sq cm would be far greater than the value of area in sq ft.
The population of a city is 100,000 and the annual growth rate is of 4.2%. Write an equation to model the population y after x years.
Answer:
y= 100,000*(1.042^x)
Step-by-step explanation:
Giving the following information:
Present Value= 100,000 people
Growth rate (g)= 4.2% per year
To calculate the future value (y) of the in any given year (x), we need to use the following formula:
y= PV*(1 + g)^x
y= 100,000*(1.042^x)
For example, for 5 years:
y= 100,000*1.042^5
y= 122,839.66 = 122,839
NEED HELP!! 50 points!!!
Answer: 3, The initial velocity of the rocket
Answer:
the initial velocity of the rocket
Step-by-step explanation:
3x-y=2
x+2y=3
elimination method
Answer:
x=1 and y=1
Step-by-step explanation:
see attachment
HELP ME I NEED HELP!!!
Answer: B
Step-by-step explanation:
4.2 / 0.25 = 21
0.4 · 21 = 8.4
8.4 + 2.5 = 10.9
Use the standard normal distribution to find P(Z < -2.33 or z > 2.33). Select one: O 9809 .7888 .0198 O 0606
The probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198.
How to find the probabilitiesTo find the probability P(Z < -2.33 or Z > 2.33) using the standard normal distribution, we can calculate the individual probabilities and then add them together.
Using a standard normal distribution calculator
The value for P(Z < -2.33) is approximately 0.0099.
P(Z < -2.33), which is approximately 0.0099.
we can add the two probabilities together
P(Z < -2.33 or Z > 2.33) = P(Z < -2.33) + P(Z > 2.33)
= 0.0099 + 0.0099
= 0.0198
Therefore, the probability P(Z < -2.33 or Z > 2.33) is approximately 0.0198
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(2x+1)^2+4x(x-1)-3+3(-4x^2
Answer:
−4x2−2
Step-by-step explanation:
The center and a point on a circle are given. Find the circumference to the nearest tenth.
center:(2, 2);
point on the circle: (−6, 5)
The circumference is about ?
Answer:
Circumference ~ 53.4
Step-by-step explanation:
Use the distance formula to get the radius of the circle. The radius is about 8.5. Now put 8.5 into the formula 2(pi)r for the Circumference. Rounding to the nearest tenth the answer is 53.4
A population of values has a normal distribution with 4 = 31.3 and o random sample of size n = 62. 18.4. You intend to draw a What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means?
The standard deviation of the distribution of sample means is approximately 2.331.
The mean of the distribution of sample means, also known as the sampling distribution mean, is equal to the population mean. In this case, the population mean (μ) is given as 31.3. Therefore, the mean of the distribution of sample means is also 31.3.
The standard deviation of the distribution of sample means, also known as the standard error, can be calculated using the formula:
Standard Error = Population Standard Deviation / √(Sample Size)
In this case, the population standard deviation (σ) is given as 18.4, and the sample size (n) is 62. Plugging these values into the formula, we get:
Standard Error = 18.4 / √(62)
Standard Error ≈ 2.331
Therefore, the standard deviation of the distribution of sample means is approximately 2.331.
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please answer asap
i will mark brainliest
Solve for x and find the missing angle measurement.
Answer: x=17 and 98
Step-by-step explanation:
Those two angles are supplementary so just add them together and make it equal to 180.
Rewrite the equation below in Graphing Form:
2.
y = x2 8x + 31
Answer:
y=x^28x+31
Step-by-step explanation:
Answer: y= x 4 − 6 y = 1 x − 2
Step-by-step explanation:
What is the image of (-1, 7) after a reflection over the line y = x?
Answer:
(7, - 1 )
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(- 1, 7 ) → (7, - 1 )
please help ·ω· pppppppllllllllllllllleeeeeeeeeeaaaaaaaassssssssseeeeeeeeee????
Answer:
x=49
Step-by-step explanation:
help ASAP ill give brainliest
Answer:
9 students is the correct answer :(
Is the triangle with leg lengths of 8 mm and 8 mm and a hypotenuse of length 12 mm a right triangle?
Answer:
No
Step-by-step explanation:
Use the Pythagorean Theorem to check on this.
Does 8^2 + 8^2 = 12^2? Does 64 + 64 = 144? NO. So this is not a right triangle.
Name the coordinates of P if P(0, 4) is rotated 180°
Answer:
P'(0, -4)
Step-by-step explanation:
when a coordinate (x, y) is rotated by 180 degrees, the resulting coordinate will be (-x, -y). Note that each coordinate is negated when rotated about 180 degrees
Given the coordinate P (0, 4). When rotated by 180 degrees, the resulting coordinate will be at P'(0, -4)
Yarely ordered a skateboard. There was a discount of 40% and the original price is
$60. What is the sale price?
4h + 6 = 30
h =___?
Im in 7th grade and I really need help
Answer: h = 6
explanation:
first u get h by itself
4h + 6 = 30
subtract 6 from both sides
4h = 24
divide by 4 on both sides
h = 6
Answer:h=3/13
Step-by-step explanation: Subtract 6 from both sides of the equation 4h+6-6=30h-6 you simplify 4h=30h-6. Subtract 30h from both sides of the equation then you get -26h=-6 then you divide both sides of the equation by the same term -26h/-26=-6/-26 and your answer is 3/13.
Simplify 3.(9.).
A. 3x
B. 27x
C. 9x
D. 2 + 7x
i think your answer is B. 27x
Trucking is considering whether to expand its service. The expansion requires the expenditure of $10,500,000 on new service equipment and would generate annual net cash inflows from reduced costs of operations equal to $3,500,000 per year for each of the next 9 years. In year 9 the firm will also get back a cash flow equal to the salvage value of the equipment, which is valued at $0.9 million. Thus, in year 9 the investment cash inflow totals $4,400,000. Calculate the project's NPV using a discount rate of 7 percent.
If the discount rate is 7 percent, then the project's NPV is
If the discount rate is 7 percent, then the project's NPV is $13,950,300.
Total expenditure = $10,500,000
Cost of operations = $3,500,000
Time = 9 years
Cash inflows = $4,400,000.
Calculating the present value (PV) of the annual net cash inflows -
[tex]PV = Cash inflow / (1 + Discount rate)^n[/tex]
[tex]PV = $3,500,000 / (1 + 0.07)^1 + $3,500,000 / (1 + 0.07)^2 + ... + $3,500,000 / (1 + 0.07)^9[/tex]
[tex]PV = $3,500,000 * [1 - (1 + 0.07)^-9] / 0.07[/tex]
= $24,450,300
Calculating the present value of the investment -
[tex]= $4,400,000 / (1 + 0.07)^9[/tex]
= $2,835,607
Calculating NPV -
NPV = PV of cash inflows - Initial investment cost
= $24,450,300 - $10,500,000
= $13,950,300
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Please answer correctly! I will mark you as Brainliest!
Multiply the length by width by the height/3
7 x 6 x 8/3 = 112 in^2
The answer is 112 in^2
Answer:
112
Step-by-step explanation:
please help me with this question