Answers
The test Statistic and the critical value is 20.692 and 15.308 respectively.
Given that,
Null and Alternative hypothesis,
Null hypothesis: H₀ = 5.7
and Alternative hypothesis: H₁ < 5.7
∴
Test Statistic =
x² = (n-1)s²/σ², where s is the standard deviation = 4.9 and n sample size = 29,
= 28 × 4.9² / 5.7²
= 20.692
The critical value of the left tailed test at significance level 0.025 and df = 28,
x²(critical) = x²(1-α), (n-1) = x²(0.975, 28)
= 15.308
Hence, the test Statistic and the critical value is 20.692 and 15.308 respectively.
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Related Questions
8 in.
8 in.
12 in.
Find the surface area of the rectangular prism.
Surface Area = [?] square inches
Answers
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
Substituting the given values, we get:
Surface Area = 2(8 in. x 8 in.) + 2(8 in. x 12 in.) + 2(8 in. x 12 in.)
Surface Area = 2(64 sq. in.) + 2(96 sq. in.) + 2(96 sq. in.)
Surface Area = 128 sq. in. + 192 sq. in. + 192 sq. in.
Surface Area = 512 sq. in.
Therefore, the surface area of the rectangular prism is 512 square inches.
What order do the fractions go
Answers
Answer:
ur image doesn't show the fractions they got cut off
A pet store increases the price of a bag of dog food by 5%
If the increase in price is $2.00, what is the new price for dog food?
Answers
Answer:
$42.00
Step-by-step explanation:
We can represent the given information as a ratio:
% of original price : price
5% : $2.00
Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.
5% : $2.00
↓ × 20 ↓ × 20
100% : $40.00
Now that we know the original price, we can add $2.00 to get the new price.
$40.00 + $2.00 = $42.00
The table shows Henry's savings over several weeks. If the pattern continues, what will Henry's savings be in Week 10? Tell how you know. Week Savings
Answers
Check the picture below.
Find the unit vector that has the same direction as the vector v. v = 5i - 3j
Answers
The unit vector that has the same direction as v is given by u = (5/√(34)) i - (3/√(34)) j
A vector is defined as a quantity that has both magnitude (length) and direction. In this case, the vector v is defined as v = 5i - 3j, where i and j are the unit vectors in the x and y direction, respectively.
To find the unit vector that has the same direction as v, we need to normalize v by dividing it by its magnitude. The magnitude of v is given by the Pythagorean theorem as:
|v| = √((5² + (-3)²)) = √(34)
So, the unit vector that has the same direction as v is given by:
u = v / |v| = (5/√(34)) i - (3/√(34)) j
This unit vector represents the direction of v with a magnitude of 1. We can interpret this as a scaling factor that can be applied to u to obtain vectors of different lengths that have the same direction as v. For example, a vector of length 10 that has the same direction as v would be given by 10u.
In summary, to find the unit vector that has the same direction as a given vector, we normalize the vector by dividing it by its magnitude. This results in a vector of magnitude 1 that points in the same direction as the original vector.
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Joyce works at Fortunato's Furniture. She is paid on commission. She receives 10% of her first $1,200 in sales and 15% of the balance of her sales. Last week she earned $950. What was the value of the furniture she sold? show your work.
Answers
The total value of the furniture sold by Joyce last week is A = $ 6,733.33
Given data ,
Let's call the value of the furniture Joyce sold "x".
She receives 10% commission on the first $1,200 of sales, which is $120:
Commission on first $1,200 = 0.1 * 1200 = 120
The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:
Remaining sales = x - 1200
She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:
Commission on remaining sales = 0.15 * (x - 1200)
Her total earnings from commission last week was $950. So we can write an equation:
Commission on first $1,200 + Commission on remaining sales = $950
Substituting the expressions we found for the two commissions, we get:
120 + 0.15(x - 1200) = 950
120 + 0.15x - 180 = 950
On simplifying the equation , we get
0.15x - 60 = 950
0.15x = 1010
x = 6,733.33
Hence , the value of the furniture Joyce sold last week was $6,733.33
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Pls help me with this question
Answers
The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.
When two lines intersect, then their opposite angles are equal. Then the equation is given as,
m° + 66° + m° = 120°
Simplify the equation for m, then the value of 'm' is calculated as,
m° + 66° + m° = 120°
2m° = 120° - 66°
2m° = 54°
m° = 27°
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I AM GIVING ALOT OF POINTS BECAUSE I NEED THIS RIGHT NOW I HAVE ONE MINUTE LEFT
Town A is 7 feet below sea level and Town B is 692 feet above sea level. What is the difference in elevation between Town A and Town B?
A. 685 feet
B. 692 feet
C. 695 feet
D. 699 feet
Answers
Answer:
D)699
Step-by-step explanation:
Since Town A is 7 feet below sea level, you will need to add that to 692 instead of subtract.
692+7=699
Answer: D
Step-by-step explanation: 692+7=699
2.5.2 Test (CST): Transformations, Congruence, and Similarity, Part 1
Question 8 of 15
Which triangle makes this statement true?
ΔΑΒC =
B
16
90
T
34
AABC
28
Answers
The triangle that makes the statement true is Option A. ΔABC ≅ ΔRST
How is this so?For two triangle to be similar, they must have share the same angle size and sides that are related with a common ratio.
All the angles in Option A Δ RST are similar to those ΔABC.
Also note that
ST = 1/2 AB
SR = 1/2 BC and
RT = 1/2 AC
hence, the correct statement is:
ΔABC ≅ ΔRST
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Full Question:
See attached image.
Is this correct or incorrect …..
Answers
A zero has the same meaning as the vertex.
What is a vertex?The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.
The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.
Thus, a zero has the same meaning as the vertex.
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Come on guys help please
Answers
The scale factor from shape A to shape B is 3/4. The value of side w is 5.25 cm
What is an equation?An exponential equation is an expression that shows how numbers and variables using mathematical operators.
Scale factor is the ratio of the corresponding sides of two similar figures. Two figures are similar if the ratio of their corresponding sides are congruent.
From the figure:
Scale factor = Ratio of corresponding shape B side / Ratio of corresponding shape A side
Scale factor = 9/12 = 3/4
The scale factor is 3/4
To find w:
scale factor = w/7
3/4 = w/7
w = 5.25 cm
The value of side w is 5.25 cm
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Which graph represents the solution to X>1/2
Answers
Answer:
The graph that represents the solution to X > 1/2 is the graph where the line is vertical, passing through x = 1/2, and all the points to the right of this line are shaded. This is because the inequality X > 1/2 means that X can take any value greater than 1/2, but not including 1/2.
The city of Bangor, Maine has a scale model of Paul Bunyan nearly 30 feet tall. The model’s scale is 1:5. On the scale model, Paul Bunyan’s belt buckle is 12 feet from the ground. In real life, how far from the ground is Paul Bunyan’s belt buckle? The diameter of Paul Bunyan’s actual head is 9 inches. What is the diameter of the Paul Bunyan’s scale model head in feet?
Answers
The distance between of the belt buckle from the ground is 2.40 feet.
The diameter of the head is 3 3/4 inches.
What are the distance?A scale drawing is either an enlarged or reduced image of another image or object. A scale drawing is enlarged or reduced using a scale. A scale is a used to determine the ratio between the scale drawing and the original diagram.
The distance between of the belt buckle from the ground in real life would be greater than that of the scale drawing. Also, the diameter of the head would be larger in real life.
Distance between of the belt buckle from the ground = 12 / 5 = 2.40 feet
In order to determine the diameter of the scale head, first convert inches to feet.
1 inch = 1/12 feet
9/12 = 3/4 feet
Diameter of the scale head = 3/4 x 5 = 15/4 = 3 3/4 feet
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College Level Trigonometry any help will be appreciated
Answers
The angle between the beam and the 35 ft cable is 43 degrees
How to determine the angleTo determine the angle between the beam, we need to know all the trigonometric identities as well as their ratios.
We have the identities as;
secanttangentcosinecosecantcotangentsineAlso, their ratios are represented as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
sin θ = 65/95
divide the values
sin θ = 0. 6842
find the inverse
θ = 43 degrees
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a man left his home and drove along a certain road at the rate of 48 km/h. one hour later, his son left the same house and drove along the same road in the same direction at 72 km/h. in how many hours does the son overtake the father?
Answers
Answer:
The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.
Step-by-step explanation:
Father:
speed = 48 km/h
distance = d
time = t
Son:
speed = 72 km/h
distance = d
time = t - 1
speed = distance/time
distance = speed × time
Father:
d = st
d = 48t
Son:
d = st
d = 72(t - 1)
d = 48t
d = 72(t - 1)
48t = 72(t - 1)
48t = 72t - 72
72 = 24t
t = 3
The son overtakes the father 3 hours after the father started driving which is 2 hours after the son started driving.
what proportion of observation is greater than 7?
Answers
The proportion of observations greater than 7 is 0.25 or 25%.
How to solveFor this question, we need to identify the number of observations higher than 7.
After inspecting the dataset, 25 values can be seen that are greater than 7.
Then, the proportion of observations greater than 7 can be calculated as follows:
proportion = number of observations greater than 7 / total number of observations
proportion = 25 / 100
proportion = 0.25
Therefore, the proportion of observations greater than 7 is 0.25 or 25%.
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Suppose we have a dataset of 100 observations, where each observation is a continuous variable. What proportion of the observations in the dataset are greater than 7?
Will mark brainliest.
Answers
Applying the inscribed angle theorem, the missing measures are:
measure of arc TR = 106°
measure of arc TL = 74°
m∠L = 50°
m∠R = 37°
m∠RTV = 37°
Here, we have,
The Inscribed Angle Theorem
Measure of an inscribed angle = half the measure of the arc it intercepts
Central angle = measure of intercepted arc
We are given the following:
LR and TV are diameters of the circle O.
m∠TOR = 106° (central angle)
Find measure of arc TR:
measure of arc TR = m∠TOR
measure of arc TR = 106°
Find measure of arc TL:
measure of arc TL = 180° - m∠TOR
measure of arc TL = 180° - 106°
measure of arc TL = 74°
Find m∠L:
m∠L = ½(measure of arc TR)
m∠L = ½(106°)
m∠L = 50°
Find m∠R:
m∠R = ½(measure of arc TL)
m∠R = ½(74°)
m∠R = 37°
Find m∠RTV:
m∠RTV = ½(measure of arc RV)
m∠RTV = ½(180 - 106)
m∠RTV = ½(74)
m∠RTV = 37°
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complete question:
Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =
Jake plays basketball. He kept track of the number of free throws he made per game. On your own paper, make a histogram or dot plot of Jake's data and then use that to describe the shape of the data.
9, 8, 15, 17, 18, 19, 10, 18, 17, 18, 18, 11, 12, 15, 16, 17, 17, 18, 17
Answers
```
9
8
1 5
2 0
3 0
4 0
5 0
6 1
7 0
8 3
9 0
10 1
11 1
12 1
13 0
14 0
15 2
16 1
17 5
18 4
19 1
```
From the dot plot, we can see that the data is roughly symmetric with a peak at around 17 free throws made per game. There is a slight skewness towards the upper end of the range, with more data points above the mean than below it. Overall, the data appears to be fairly normally distributed, with no major outliers.
Analysis of Jake's free-throw data shows that it is positively skewed, indicating that he most frequently scores around 17-18 points per game, with fewer games with lower scores.
Explanation:To visualize and understand Jake's free-throw data, we can create a histogram. First, we'll list the range of shots made per game. These are: 8, 9, 10, 11, 12, 15, 16, 17, 18, and 19. Then, for each number, count how many times it occurs in the data set. The distribution could look something like this:
8: •9: •10: •11: •12: •15: ••16: •17: •••••18: ••••19: •Based on this distribution, the shape of the data is positively skewed, with most of the data clustered around 17-18 points per game, and fewer games with lower scores.
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I need help with this please
Answers
Answer:
a. 830.380
Step-by-step explanation:
3 × [tex]\frac{1}{10}[/tex] is [tex]\frac{3}{10}[/tex]. This is the same as .3 when it's written in decimal form.
The first place on the right side of the decimal is the 'tenths' place. The second spot on the right side of the decimal is the 'hundredths' place.
Like this:
hundreds tens ones . tenths hundredths thousandths
All of the answers have the 830 in them. The only difference between the answers is the .380, .308, .038, .083. Once you see you have 3/10 (which is said three-tenths, which is .3) you can eliminate the last two answers, c and d. Then check the hundredths place. You have 8/100 (which is said eight-hundredths, which is .08) then you can eliminate b and find your answer, a.
Simplify the expression 7a^-5b^3
Answers
Answer: To simplify the expression 7a^⁻⁵b^3, we can use the negative exponent property, which states that a^⁻ⁿ = 1/aⁿ. Applying this property to the variable a gives us:
7a^⁻⁵b^3 = 7(1/a⁵)b^3
We can also simplify b^3 to get the final answer:
7a^⁻⁵b^3 = 7b^3/a⁵
Therefore, the simplified expression is 7b^3/a⁵.
Please help me answer this question
Answers
(1/8)× - 2 5/7 subtracted from 3 1/4x + 7 1/14
31/4× +71/14 - (1/8 × - 2 5/7)
31/4 × - 1/8 x + 7 1/14 + 2 10/14
3 1/8 × + 9 11/14 ANSWER A. is correct
Ryan delivers flowers to two customers. He drives for 12 minutes at an average speed of 40 miles per hour to reach his first customer. He drives for 15 minutes at an average speed of 60 miles per hour second customer. during the 27 minutes, how many miles did he drive?
Answers
Ryan drove 23 miles during the 27 minutes.
To discover the total distance Ryan drove during the 27 mins, we want to first calculate the distance he drove to reach every consumer and then add the ones distances collectively.
For the first customer, Ryan drove for 12 minutes at an average pace of 40 miles per hour:
Distance = speed × timeDistance = 40 × (12/60) (changing minutes to hours)Distance = 8 milesFor the second customer, Ryan drove for 15 mins at an average velocity of 60 miles consistent with hour:
Distance = speed × timeDistance = 60 × (15/60) (converting mins to hours)Distance = 15 milestherefore, the entire distance Ryan drove in the course of the 27 mins is:
Total distance = distance to first customer + distance to 2nd consumerTotal distance = 8 + 15Total distance = 23 milesSo, Ryan drove 23 miles during the 27 minutes.
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4
A gasoline pump delivers 4 gallons of
gas per minute. How many minutes will
it take to fill a gas tank that holds
16 gallons?
2
min
14
Answers
If a gasoline pump delivers 4 gallons of gas per minute, proportionately, it will take it 4 minutes to fill a gas tank that holds 16 gallons.
What is proportion?Proportion refers to the ratio of one unit or quantity compared to another unit or quantity.
Proportions are represented as fractional values using decimals, fractions, and percentages.
The time it takes the gasoline pump to deliver 4 gallons = 1 minute
Proportionately, to deliver 16 gallons, the time = 4 minutes (16 ÷ 4)
Thus, using proportional relationships, to deliver 16 gallons, the gasoline pump will take 4 minutes.
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What is the correct sequence for these steps in CADD, which describe how to draw a square whose diagonal length is provided?
enter the coordinates to specify the center of the square
define the number of sides
select the inscribed option
enter the radius value of the circle as half the length of the diagonal
select the Polygon command
enter the desired distance between the corners of the square
Answers
1. Select the Polygon command
2. Define the number of sides
3. Select the inscribed option
4. Enter the radius value of the circle as half the length of the diagonal
5. Enter the coordinates to specify the center of the square
6. Enter the desired distance between the corners of the square
By following these steps in order, you will be able to draw a square whose diagonal length is provided.
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 7 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.
A) H0: p > 0.0007 H1: p ? 0.0007
B) H0: p = 0.0007 H1: p > 0.0007
C) H0: p < 0.0007 H1: p ? 0.0007
D) H0: p = 0.0007 H1: p < 0.0007
Answers
The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
We have,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
This means that the true proportion of male fireflies unable to produce light is greater than or equal to 7 in ten thousand.
The alternative hypothesis in symbolic form is Ha: p < 0.0007
This means that the true proportion of male fireflies unable to produce light is less than 7 in ten thousand.
Thus,
The null hypothesis in symbolic form is H0: p ≥ 0.0007
The alternative hypothesis in symbolic form is Ha: p < 0.0007
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A certain circle can be represented by the following equation.
x^2+y^2-4x+12y-24=0
What is the center of the circle?
What is the radius of the circle?
Answers
Radius: 8
A coordinate plane. The x- and y-axis each scale by one. The graph of a line goes through the points negative seven, negative three, and negative two, four. Both points are plotted.
A coordinate plane. The x- and y-axis each scale by one. The graph of a line goes through the points negative seven, negative three, and negative two, four. Both points are plotted.
Write an equation that represents the line.
Use exact numbers.
Answers
An equation that represents the line: y = (7/5)x + 34/5
We know that the formula for the two point form of equation of line is:
(y - y₁)/(y₂ - y₁) = (x - x₁)(x₂ - x₁)
Here, the graph of a line goes through the points (-7, -3) and (-2, 4)
Let us assume that (x₁, y₁) = (-7, -3)
(x₂, y₂) = (-2, 4)
Using above formula the equation of the line would be,
(y - y₁)/(y₂ - y₁) = (x - x₁)(x₂ - x₁)
(y - (-3))/(4 - (-3)) = (x - (-7))(-2 - (-7))
(y + 3)/(4 + 3) = (x + 7)(-2 + 7)
(y + 3) / 7 = (x + 7) / 5
y + 3 = (7/5)x + (7/5)7
y + 3 = (7/5)x + (49/5)
y = (7/5)x + (49/5) - 3
y = (7/5)x + 34/5
This equation represents the line.
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A cable network offers members a Basic plan for $7.88 per month. For $3.00 more per month, the cable network offers a Standard plan, which includes HD movies. During one week, 330 new subscribers paid a total of $3110.40 for their plans. How many Basic plans and how many Standard plans were purchased?
Answers
A cable network offers members a Basic plan for $7.88 per month. For $3.00 more per month, the cable network offers a Standard plan, which includes HD movies, there were 140 Basic plans purchased.
Let x be the number of Basic plans and y be the number of Standard plans.
From the problem, we know that:
- The cost of a Basic plan is $7.88 per month
- The cost of a Standard plan is $7.88 + $3.00 = $10.88 per month
- There were a total of 330 new subscribers
- The total amount paid for plans was $3110.40
We can set up a system of equations to represent the problem:
x + y = 330 (equation 1: the total number of plans is 330)
7.88x + 10.88y = 3110.40 (equation 2: the total amount paid for plans is $3110.40)
To solve for x and y, we can use elimination method. Multiplying equation 1 by 7.88 and subtracting it from equation 2, we get:
(7.88x + 10.88y) - (7.88x + 7.88y) = 3110.40 - (7.88 * 330)
3y = 570.48
y = 190
So there were 190 Standard plans purchased. To find the number of Basic plans, we can substitute y = 190 into equation 1:
x + 190 = 330
x = 140
Therefore, there were 140 Basic plans purchased.
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Alewuya invests $19,000 at 3% simple interest for 1 year. How much is in the account at the end of the 1 year period?
Answers
At the conclusion of the year, Alewuya's account had $19,570 in it.
To calculate the amount in Alewuya's account at the end of 1 year, we can use the formula for simple interest:
I = Prt
where I is the interest earned, P is the principal (the amount invested), r is the interest rate as a decimal, and t is the time in years.
In this case, P = $19,000, r = 0.03, and t = 1. Plugging these values into the formula, we get:
I = ($19,000)(0.03)(1) = $570
So Alewuya earned $570 in interest over the 1 year period. To find the total amount in the account at the end of the period, we add the interest to the principal:
$19,000 + $570 = $19,570
Therefore, there is $19,570 in Alewuya's account at the end of the 1 year period.
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Previous
Save and complete later
Solve: 9x In x + x = 0
(Use calculator for x and round the answer to 3 decimal places)
Next
Don
Answers
The value of x in the equation 9x In x + x = 0 is x = 0.895
Calculating the value of x in the equationFrom the question, we have the following parameters that can be used in our computation:
9x In x + x = 0
To calculate the value of x, we start by dividing through the equation by x
So, we have the following representation
9 In x + 1 = 0
Subtract 1 from both sides of the equation
This gives
9 ln x = -1
Divide both sides by 9
ln x = -1/9
So, we have
x = e^(-1/9)
Evaluate the exponent
x = 0.895
Hence, the solution to the equation is x = 0.895
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