The null hypothesis is that the true average amount left is equal to 10% of the advertised net contents. In In another case of true average amount is less than 10% of the advertised net contents.
Hence, we will utilize one-tailed t-test with a significance level of 0.05 to test this hypothesis.
The sample mean of the five tubes is (0.51+0.63+0.42+0.5+0.37)/5 = 0.486 ounces.
The sample standard deviation is √(((0.51-0.486)² + (0.63-0.486)² + (0.42-0.486)² + (0.5-0.486)² + (0.37-0.486)²)/4) = 0.107 ounces.
The t-statistic is calculated as
(mean sample - hypothe -sized mean)/( standard deviation sample/√( size sample))
= (0.486 - 0.6)/(0.107/√(5))
= -3.06.
The p-value for this test is 0.0249 which is less than our significance level of 0.05.
Therefore, we reject the null hypothesis and conclude that there is evidence that the true average amount left in a tube of toothpaste is less than 10% of the advertised net contents.
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Tasha has a gift card to buy tickets to the movie theater. The initial value of the gift card is $120 . The function M(x)=120-12x represents the amount of money, M , in dollars, that is still left on the gift card after purchasing x movie tickets at a cost of $12 each.
Complete the statements.
The value of is 60/-60 which is viable/not viable in terms of the given context.
The solution to the linear function M(x) = 180 is of x = -5.
What is a Linear Function Equation?The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.
In this problem, the function is defined as follows:
M(x) = 120 - 12x.
M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.
The domain of the situation is given as follows:
x ≥ 0. {discrete}
As the number of tickets cannot assume negative neither decimal values.
The equation is:
M(x) = 180.
The solution is calculated as:
120 - 12x = 180
12x = -60
x = -60/12
x = -5.
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What is the domain of h?
A coordinate plane. The x- and y-axes both scale by one. The graph of the function h starts at the point negative seven, negative three and has a line segment to negative four, zero. Then it increases at a non linear rate to zero, four and decreases at a non linear rate to four, zero. A line segment connects four, zero to seven, negative three, which is plotted on the graph.
Choose 1 answer:
Choice A: -7 ≤ x ≤ 7
Choice B: -3 ≤ x ≤ 4
Choice C: The x-values -7, -4, 0, 4, and 7
Choice D: The x-values -3, 0, and 4
Answer:
The domain of h is
[tex] - 7 \leqslant x \leqslant 7[/tex]
Choice A is correct.
Answer:
c
Step-by-step explanation:
Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Thus, we may estimate that there were 557 principals present at the meeting.
Explain about the Proportion:A mathematical comparison of two numbers is called a percentage. These figures frequently serve as a comparison between various objects or individuals. Take the scenario where you entered a crowded room as an example.
We can forecast how many principals will attend the conference according to the data supplied.In a room with 70 individuals in total and 52 principals, the ratio of principals to attendees would be as follows:52/70 = 0.743 or 74.3%
Applying this ratio to the total number of attendees, we can extrapolate the proportion of principals at the conference, assuming that it is reflective of the conference as a whole:
Total principals at conference = Proportion of principals x Total number of attendees
Total principals at conference = 0.743 x 750
Total principals at conference ≈ 557
As a result, we may estimate that there were 557 principals present at the meeting.
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What is the smallest rational number:
The smallest rational number among all the given numbers is equal to 0.2345678.
The rational number are equal to,
-√5 , (1/4), √25 , -√27 , 0.2345678
First simplify each of the given numbers we have,
√5 is an irrational number,
so it is not rational.
1/4 is a rational number.
√25 = 5,
which is a rational number.
-√27 = -3√3,
which is an irrational number, so it is not rational.
0.2345678 is a rational number.
Arrange the rational number in ascending order to get the smallest rational number .
Value of 1/4 = 0.25
0.2345678 < 0.25 < 5
Therefore, the smallest rational number among the given options is 0.2345678.
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Estimate the difference. 9 1/2 - 1 6/7
8 1/2
7 1/2
7
8
Answer:
1 6/7 is about 2, so 9 1/2 - 1 6/7 is about
7 1/2.
A population has a mean μ=71 and a standard deviation Ï=20. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=249.
The mean and standard deviation of a sampling distribution of sample means with sample size 249 are 71 and approximately 1.267 respectively when the population has a mean of 71 and standard deviation of 20.
We know that, if the population has mean [tex]=\mu[/tex] and standard deviation [tex]=\sigma[/tex] and if the sampling distribution has sample size of n then
mean of the sampling distribution will be [tex](\mu_{\bar{x}})=\mu[/tex]
and the standard deviation of sampling distribution will be [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}[/tex]
Here in this problem,
Mean of the population [tex](\mu)[/tex] = 71
Standard Deviation of the population [tex](\sigma)[/tex] = 20
And the sample size of the sampling distribution (n) = 249
So, the mean of sampling distribution [tex](\mu_{\bar{x}})=\mu[/tex] = 71
Standard Deviation of sampling distribution [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{249}} \approx 1.267[/tex] (Correct up to three decimal places)
Hence, the mean and standard deviation of the sampling distribution of sample means with sample size 249 are 71 and 1.267 (approximately) respectively.
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monthly sales are independent normal random variables with mean and standard deviation a. find the probability that exactly of the next months have sales greater than 100. b. find the probability that the total of the sales in the next
Answer: We can use the properties of the normal distribution to solve both parts of this problem.
a) The number of months with sales greater than 100 is a binomial random variable with parameters n = the number of months and p = the probability of a single month having sales greater than 100. Since each month is an independent normal random variable, we can use the standard normal distribution to find this probability. Let X be the number of months with sales greater than 100. Then:
X ~ Binomial(n, p)
where n is the number of months and p is given by:
p = P(X_i > 100) = P(Z > (100 - a) / a)
where Z is a standard normal random variable.
Using the binomial probability formula, the probability of exactly k months having sales greater than 100 is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
So the probability of exactly 3 months having sales greater than 100 is:
P(X = 3) = (n choose 3) * p^3 * (1 - p)^(n - 3)
= (12 choose 3) * P(Z > (100 - a) / a)^3 * [1 - P(Z > (100 - a) / a)]^(12 - 3)
b) The total sales in the next 12 months is a normal random variable with mean 12a and standard deviation sqrt(12)a. Let Y be the total sales in the next 12 months. Then:
Y ~ Normal(12a, sqrt(12)a)
The probability of the total sales being greater than some value x can be found by standardizing Y and using the standard normal distribution:
P(Y > x) = P((Y - 12a) / (sqrt(12)a) > (x - 12a) / (sqrt(12)a))
= P(Z > (x - 12a) / (sqrt(12)a))
where Z is a standard normal random variable. So the probability of the total sales in the next 12 months being greater than 1500 is:
P(Y > 1500) = P(Z > (1500 - 12a) / (sqrt(12)a))
Step-by-step explanation:
How do you find the legs of a 45-45-90 triangle if you know the length of the hypotenuse?
Each leg of the triangle has a length of 5√(2) units
Since the triangle is 45-45-90, each of the two legs has the same length, which we'll call x. By the Pythagorean theorem, we know that:
x² + x² = h²
Simplifying this equation, we get:
2x² = h²
To solve for x, we can divide both sides by 2 and then take the square root:
x = h / √(2)
This tells us that each leg of a 45-45-90 triangle is equal to the hypotenuse divided by the square root of 2.
Let's say you have a 45-45-90 triangle with a hypotenuse of length 10. To find the length of each leg, you would use the formula:
x = h / √(2)
Substituting h = 10, we get:
x = 10 / √(2)
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √(2):
x = (10 / √(2)) * (√(2) / √(2))
= 10√(2) / 2
= 5√(2)
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The bases of a right prism are parallelograms with sides a=10 cm, b=6 cm. The altitude of the parallelogram towards side a is ha = 3 cm. Find the surface area of the parallelepiped if the height of the prism is h=12 cm.
The solution is, the surface area of the parallelepiped is:444 cm²
Here, we have,
Area of parallelogram = a*h
= 10*3
= 30 ,
there are 2 such parallelograms in the prism
2 faces are rectangles with sides 12 and 6 ,
Area of this face is 12*6=72, there are 2 such faces
we have,
2 faces are rectangles with sides 12 and 10
Area of this face is 12*10=120,
there are 2 such faces
the surface area of the parallelepiped is:
2*30+2*72+2*120
= 444 cm²
Hence, The solution is, the surface area of the parallelepiped is:444 cm²
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A company is designing a new cylindrical water bottle. The volume of the bottle will be 220 cm cubed 3. The height of the water bottle is 8. 9 cm. What is the radius of the water bottle? Use 3. 14 for π
The radius of the cylindrical water bottle is approximately 2.34 cm.
The company designing the water bottle has given us the volume of the bottle, which is 220 cm³, and the height of the bottle, which is 8.9 cm. We can use the formula for the volume of a cylinder to relate the radius, height, and volume of the water bottle. The formula is:
Volume of a cylinder = π × radius² × height
We are given the volume of the cylinder as 220 cm³ and the height as 8.9 cm, so we can substitute these values into the formula to get:
220 = π × radius² × 8.9
To solve for the radius, we need to isolate it on one side of the equation. We can start by dividing both sides by π × 8.9:
220 ÷ (π × 8.9) = radius²
Now, we can take the square root of both sides to find the value of the radius:
√(220 ÷ (π × 8.9)) = radius
Using 3.14 for π, we can simplify the expression to get:
radius ≈ 2.34 cm
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a classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats in the back what is the probability that that the first student who enters the room will be assigned to the front row
The probability that the first student who enters the room will be assigned to the front row is 4/15.
What is probability?The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.
given that ,
A classroom is arranged with 8 seats in the front row 10 seats in the middle row and 12 seats
The total number of seats in the classroom is 8 + 10 + 12 = 30.
There are thirty seats to choose from because there is only one student entering the room.
However, we want to determine the likelihood that the student will be assigned to one of the eight seats in the front row.
Therefore, the probability of assigning the front row to the first student who enters the room is:
P(front row) = 8/30
Simplifying this fraction gives:
P(front row) = 4/15
As a result, there is a probability of 4/15, or roughly 0.267, that the first student who enters the room will be assigned to the front row.
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Kendrick attends a private school where he must wear a uniform. Last year, the price of the uniform was $52. This year's uniform price was $65. What is the percent of increase in the cost of the uniform?
The percent increase in the cost of the uniform from last year to this year is 25%.
What is the percent of increase in the cost of the uniform?To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.
The difference between this year's price and last year's price is:
$65 - $52 = $13
The original price (last year's price) is $52.
So the percent increase in the cost of the uniform is:
percent increase = (difference / original price) x 100
percent increase = ($13 / $52) x 100
percent increase = 0.25 x 100
percent increase = 25%
Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.
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Ryan has 2,000 grams of Flerovium-289, which has a half life of 30 seconds. Use
the formula y = ab* to figure out how much Flerovium-289 you will have after
5 minutes. (Hint: x is the the total number of half lives in 5 minutes)
(.5)_
a.) 62.5 grams
b.) 1.95 grams
c.) 353.55 grams
d.) 1,000 grams
y =____
A woman decides to have children until she has her first girl or until she has four children, whichever comes first. Let X = number of children she has. For simplicity, assume that the probability of a girl is .5 for each birth.a. Write the simple events in the sample space. Use B for boy and G for girl. For instance, one simple event is BG, because the woman would stop having children once she has a girl.b. Find the probability for each of the simple events in the sample space.c. Find the probability distribution function for X.d. Draw a picture of the probability distribution function for X.
For the experiment of birth of children,
a) Sample space is S = { G, BG, BBG, BBBG, BBBB}.
b) The probability for each of the simple events in the sample space, 0.5, 0.25, 0.125, 0.0625 and 0.0625.
c) The probability distribution function for X is 0.5, 0.25, 0.125, 0.0625 and 0.0625.
d) The table form of probability density function is present in above figure.
We have a woman who decides to have children until she has first a baby girl or until she has four children, which event occurred.
a) Sample space is S = { G, BG, BBG, BBBG, BBBB} where G and B represents the birth of baby boy and baby girl.
b) Since, birth become independent so P( B) = P( G) = 0.5. Using multiplcation rule, the probability for each of the simple events, P( G) = 0.5
P( BG) = P( B) P(G) = 0.25
P( BBG) = P(B)× P(B)× P(G) = 0.125
P( BBBG) = P(B)× P(B)× P(B) ×P(G)
= 0.0625
P( BBBB) = P(B)× P(B)× P(B) ×P(B)= 0.0625
c) Let X be a variable such that it denotes number of children. So, X can take value from set { 1,2,3,4}.
The probability of a girl child is for each birth = 0.5
Therefore, P( X = 1) = { only 1 girl} = P( G)
= 0.5
P(X = 2) = { one boy and one girl } = P( BG) = P(B) P(G) = 0.25
P( X = 3) = { two boys one girl } = P( BBG) = 0.125
P( X = 4) = { three boys one girl or four all boys } = P( BBBG) + P( BBBB) = 0.0625 + 0.0625
= 0.125
So, the above values of probability distribution function for random variable X.
d) A table form picture of the probability distribution function for X is present in above figure. Hence, the required table is known.
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a) option 4-t test for one mean.
b) Null hypothesis: μ_Shadyside - μ_Oakland <= 0 (Mean monthly rent of apartments in Shadyside is not higher than in Oakland).
Alternative hypothesis: μ_Shadyside - μ_Oakland > 0 (Mean monthly rent of apartments in Shadyside is higher than in Oakland).
a) The most appropriate statistical test for this scenario would be (vi) test for two independent means, also known as two-sample t-test. This test is used to compare the means of two independent samples to determine if they are significantly different from each other. In this case, we are comparing the mean monthly rent of apartments in Shadyside and Oakland, and we have two independent samples.
b) The appropriate hypotheses for the two-sample t-test are as follows:
Null hypothesis: The mean monthly rent of apartments in Shadyside is equal to the mean monthly rent of apartments in Oakland.
Alternative hypothesis: The mean monthly rent of apartments in Shadyside is greater than the mean monthly rent of apartments in Oakland.
Symbolically, the null hypothesis can be represented as H0: µ1 = µ2, where µ1 and µ2 represent the population means of monthly rent in Shadyside and Oakland, respectively.
The alternative hypothesis can be represented as Ha: µ1 > µ2, indicating that the population mean of monthly rent in Shadyside is greater than the population mean of monthly rent in Oakland
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Does tripling the length of time for the investment double the interest earned with
compound?
No, tripling the length of time for the investment does not double the interest earned with compound interest.
Explaining if tripling the length double the interestWhen interest is compounded, the interest earned depends not only on the length of time, but also on the interest rate and the number of compounding periods.
For example, if an investment of $100 earns 5% annual interest compounded annually for 1 year, the interest earned would be:
Interest = $100 x 0.05 = $5
If the same investment is compounded for 2 years instead of 1, the interest earned would be:
Interest = $100 x (1 + 0.05)^2 - $100 = $10.25
As we can see, doubling the length of time for the investment does not double the interest earned with compound interest.
The interest earned depends on the interest rate and the number of compounding periods as well.
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One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?
The container can contains 3,000 pounds of chemicals.
How many pounds can the container hold?One cubic foot of a chemical weighs 50 pounds which means 1 ft³ of chemical = 60 pounds
We must find how many pounds in the container whose dimension 6 ft, 4 ft and 2.5 ft. So, the l = 6 ft, b = 4 ft and h = 2.5 ft.
Volume of box = L*B*H
Volume of box = 6 x 4 x 2.5
Volume of box = 60 ft³
From 1 ft³ of chemical = 60 pounds; then, the 50 ft³ of chemical will be:
= 50 x 60
= 3,000 pounds
Full question "One cubic foot of a chemical weighs 60 pounds. How many pounds of the chemical can a container with the dimensions shown hold? The base is 6, the width is 4, and the height is 2.5"
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In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?
Answer:
21.5
Step-by-step explanation:
1. Line the numbers from least to greatest:
20, 20, 21, 22, 23, 26
2. cross off one from one side then the other
(ex: 20, 20, 21, 22, 23, 26 --> 20, 21, 22, 23 --> 21, 22)
3. the number left is the median, but if there are 2 numbers left do step 4 and 5
4. find the middle of the 2 numbers (ex: 21 and 22's middle is 21.5)
5. The middle of the those 2 numbers is the median (which in this case is 21.5)
a circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 79 cm long. 1/360th of the circumference of the circle is 0.5 cm long. what is the measure of this angle in degrees?
The measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
Since 1/360th of the circumference of the circle is 0.5 cm long, the circumference of the circle is 360 times longer, or 180 cm long.
The arc subtended by the angle is 79 cm long, which is a fraction of the entire circumference. To find the angle in degrees, we need to convert the arc length to an angle measure using the formula:
angle measure = (arc length / circumference) x 360 degrees
Substituting the values we know, we get:
angle measure = (79 cm / 180 cm) x 360 degrees
Simplifying the fraction, we get:
angle measure = 1.9833 x 360 degrees
Rounding to the nearest degree, we get:
angle measure ≈ 713 degrees
Therefore, the measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.
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6. Suppose the object hits the top of a tree that is 44 feet above the
ground. Write and solve an equation that allows you to find how many
seconds after being dropped that this occurs.
According to the Equation, the provided question's conclusion is that the object strikes the top of the tree in roughly 4 seconds.
What is Equation?An equation is a mathematical statement that demonstrates the equality of two expressions and is typically denoted by the equals symbol (=). Equations can be used to solve issues and make predictions as well as to express a wide variety of mathematical relationships.
The formula for the distance travelled by an object under constant acceleration can be used to solve this issue:
d = 1/2 * g * t²
where:
The distance travelled is d.
Gravitational acceleration (g) is around 32.2 feet per second squared.
T is the passing of time
Since the object is being dropped in this scenario, we know that its initial height is 0 feet and its ending height is 44 feet. For the duration of the trip, we may construct the following equation:
The required time is t seconds.
h(t) = 44
Simplifying:
-16t² + 300 = 44
16t² = 300 - 44
t² = 256/16
t² = 16
When both sides are squared:
t = 4 seconds
The time it takes for the object to strike the tree's top is therefore 4 seconds.
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The complete question is,
Let's say the object lands 44 feet above the ground, at the top of a tree. You may calculate the number of seconds after being dropped by writing and solving an equation.
10. Jill's bank statement shows a balance of $539.22. Checks outstanding were #841 for $29.67, #843 for $89.02, and #844 for $9.76. A $130 deposit was outstanding. Reconcile Jill's bank statement.
Answer:
Step-by-step explanation:
539.22 dollars
A store sells pajamas in two sizes.
• The child size is for people less than `60` inches tall.
• The adult size is for people `60` inches tall or more.
Juan’s height is `145` centimeters.
Would he fit the child or adult size
What is the answer
he would fit the child size
his height is 145cm and we want to convert it into inches so the formula is
length/2.54=
145cm/2.54=57.08in
so juan is 57.08 inches, so he fits the child size.
Let's take a collection of any three 'high mountains of Nepal' and answer following questions. a) Is it a well-defined collection? Give reason. b) Is it a set? Give reason. c) Let's express it as a well-defined collection.
The collection of "high mountains of Nepal" is subjective and not well-defined, it may or may not be a set depending on the criteria specified, and to express it as a well-defined collection.
a) It is not a well-defined collection because the term "high mountains of Nepal" is subjective and does not have a clear definition. What one person considers high might be different from what another person considers high.
b) It is not necessarily a set, depending on how the collection is specified. If the collection is specified using clear criteria (such as mountains over a certain height), then it could be a set.
However, if the collection is just described using vague language like "high mountains of Nepal," then it is not necessarily a set.
c) In order to articulate it as a precise collection, we may define a precise standard for what constitutes a "high mountain of Nepal." As an illustration, we could say that any peak in Nepal that rises higher than 7,000 meters qualifies as a high mountain there.
With this precise definition, we could then pinpoint a trio of Nepalese mountains.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
one fifth
12
one twelfth
Nicholas splits 27 green markers equally into 9 cups. He then splits 18 yellow markers equally into the same 9 cups. How many markers are in each cup?
There are 5 markers in each cup
How to calculate the number of markers in each cup?Nicholas splits 27 green markers equally into 9 cups
Hence the number of green markers in one cup is
= 27/9
= 3
He then spilt 18 yellow markers equally into the same 9 cups
The number of yellow markers in one cup is
= 18/9
= 2
The total number of markers in each cup is
= 3 + 2
= 5
Hence there are 5 markers in each cup
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a random sample of 50 medical school applicants at a university has a mean raw score of 31 on the multiple choice portions of the medical college admission test (mcat). a student says that the mean raw score for the school's applicants is more than 30. assume the population standard deviation is 2.5. use a 1% level of significance. is there enough evidence to support the student's claim?
There is enough proof that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01, therefore we reject the null hypothesis.
The null hypothesis H0: μ ≤ 30 mean raw score for the school's applicants is less than or equal to 30 and the alternative hypothesis Ha: μ > 30
We can utilize a one-tailed t-test since we don't know the population standard deviation and our sample size is less than 30. The test statistic is evaluated
t = (x' - μ) / (s / √n)
here
x'= sample mean = 31,
μ = hypothesized population mean = 30,
s = standard deviation = 2.5,
n = sample size = 50.
t = (31 - 30) / (2.5 / √50)
= 3.16
Applying t-distribution table with degrees of freedom (df) = n - 1 = 49 and a significance level of α = 0.01, we find that the critical value is
t-critical = 2.404.
The calculated t-value (3.16) is greater than our critical value (2.404), we reject the null hypothesis since there is enough evidence to support the student's claim that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01.
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What is the solution to the following graph? PLEASE HELP ITS URGENT!!!
The solution shown in the graph is (-4, 0)
What is the solution of the graph?Here we have a system of equations graphed, the solutions of the system are all the points where the graphs of the functions (lines in this case) do intercept.
Then, in this case the solution is where the lines red and blue intercept, that happens at the point (-4, 0).
So that is the solution of the system of equations.
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One angle of a parallelogram measures 37°. What are the measures of the other three angles in the parallelogram?
The measures of the other two angles in the parallelogram are both 143 degrees.
what is a parallelogram?A parallelogram is a quadrilateral with two sides that are parallel to one another. A parallelogram has equal-length opposite sides and equal-length opposite angles. The internal angles that are extra to the transversal on the same side. A parallelogram's total interior angles add up to 360 degrees.
A parallelogram is formed by the junction of two parallel lines, and its opposite angles are equal.
Then, there are two 35 degree angles. Two further angles that are equivalent are noted: A parallelogram's angles add up to 360 degrees. Following that, x+x+37+37=360
2x=360-74
2x=286
x=143.
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find the antiderivative:x/square root of x
The antiderivative of f(x) = x/√x is [tex](2/3)x^{3/2} + C[/tex],
where C is the constant of integration.
To find the antiderivative of the given function.
The function is: f(x) = x/√x
First, let's rewrite the function in a more convenient form for integration:
f(x) = x / √x
[tex]= x / x^{1/2}[/tex]
[tex]= x^{1 - 1/2}[/tex]
[tex]= x^{1/2}[/tex]
Now, let's find the antiderivative using the power rule for integration:
∫[tex]x^{1/2} dx[/tex]
To apply the power rule, we need to add 1 to the exponent and then divide by the new exponent:
Antiderivative = [tex](x^{(1/2) + 1)) / ((1/2) + 1} ) + C[/tex]
Antiderivative =[tex](x^{3/2/ 3/2} + C)[/tex]
Finally, multiply by the reciprocal to simplify the expression:
Antiderivative = [tex](2/3)x^{3/2} + C.[/tex].
An antiderivative, also known as an indefinite integral, is a function that, when differentiated, yields a given function. In other words, an antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).
For example, if f(x) = 2x, then an antiderivative of f(x) would be F(x) = x^2 + C,
where C is a constant of integration.
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A useful computational shortcut for the ANOVA test is expressed asa. dfw = dfb + SST
b. SSB SSW-SST
c. SST = SSB/SSW
d. SSW SST-SSB
The correct answer is (b). SSB = SST - SSW
The ANOVA (analysis of variance) test is a statistical method used to compare the means of two or more groups. One useful computational shortcut for this test is expressed as SSB = SST - SSW, where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
The useful computational shortcut for the ANOVA test is expressed as:
SSB = SST - SSW
where SSB is the sum of squares between groups, SST is the total sum of squares, and SSW is the sum of squares within groups.
Option (b) is the closest, but it has a typo. It should be:
SSB = SST - SSW
Therefore, the correct answer is (b).
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The useful computational shortcut for the ANOVA test is SSW = SST - SSB
therefore,option d. SSW = SST - SSB is correct.
ANOVA (Analysis of Variance) is a statistical test used to analyze differences between group means.
The test involves partitioning the total variation into two components:
variation between groups (SSB, sum of squares between) and variation within groups (SSW, sum of squares within).
The total sum of squares (SST) represents the overall variability in the dataset.
The computational shortcut for ANOVA states that the sum of squares within groups (SSW) can be calculated by
subtracting the sum of squares between groups (SSB) from the total sum of squares (SST).
So, SSW = SST - SSB.
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1.572 × 108 troy oz of silver were used in the United States in 1980. How manykilograms is this? (1 troy oz = 31.1 g)A) 4.89 × 106 kg D) 4.89 x 1012 kgB) 4.89 kg E) 5.05 × 10 3 kgC) 5.05 × 10 6 kg