Using the z-distribution, the observed test statistic is given as follows:
z = 3.69.
What are the hypothesis tested?At the null hypothesis, it is tested if older students have the same mean as the general population, that is:
[tex]H_0: \mu = 115[/tex]
At the alternative hypothesis, it is tested if they have a greater mean, that is:
[tex]H_0: \mu > 115[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are:
[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]
z = 3.69.
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HELP ASAP! there are other answers similar to this but aren’t the same so don’t steal from them and answer it yourself
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 15:73 represents.
The ratio 15:73 represents the ratio of total athletes to 7th grade football players.
The ratio 15:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
The ratio 15:73 represents the ratio of 6th grade athletes to total athletes.
Since the Top-Notch Middle School had athletes from all the grades playing on a sports team, the ratio 15:73 represents the following: C. The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
How to explain the given ratio?In order to interpret and explain the meaning of the given ratio 15:73, we would first of all determine the total number of athletes from all grades in Top-Notch Middle School as follows;
Total number of athletes, T = 2 + 4 + 7 + 1 + 6 + 5 + 7 + 4 + 4 + 8 + 15 + 10
Total number of athletes, T = 73 athletes.
For the number of Basketball athletes, we have:
Number of Basketball athletes, B = 2 + 4 + 7
Number of Basketball athletes, B = 13 Basketball athletes.
Ratio of B to T = 13:73.
For the number of Baseball athletes, we have:
Number of Baseball athletes, B = 1 + 6 + 5
Number of Baseball athletes, B = 12 Baseball athletes.
Ratio of Ba to T = 12:73.
For the number of Football athletes, we have:
Number of Football athletes, B = 8 + 15 + 10
Number of Football athletes, B = 33 Football athletes.
Ratio of F to T = 33:73.
For the ratio of Football athletes in 7th grade to total number of athletes, we have:
Ratio of F7 to T = 15:73.
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4. Fabian harvests 10 pounds of tomatoes from his gar
2 2/5 pounds to make a batch of soup. If he sets aside 2.8 pounds of
tomatoes to make spaghetti sauce, how many batches of soup can
Fabian make? Write and solve an equation.
There will be a total of 3 batches of soup can Fabian make.
Explain how to calculate the total weight of ingredients needed for making a specific number of batches of a recipe.
To calculate the total weight of ingredients needed for making a specific number of batches of a recipe, you can multiply the weight of each ingredient per batch by the number of batches you want to make. This will give you the total weight of ingredients needed for the desired number of batches. For example, if a recipe requires 1 pound of flour per batch and you want to make 3 batches, the total weight of flour needed is 1 pound per batch * 3 batches = 3 pounds.
To find out how many batches of soup Fabian can make, we need to divide the total weight of tomatoes by the weight of tomatoes used per batch of soup.
Let x be the number of batches of soup Fabian can make. We know that:
10 pounds of tomatoes - 2.8 pounds of tomatoes = 7.2 pounds of tomatoes are available to make soup
The weight of tomatoes used per batch of soup is 2 2/5 pounds, we can write this as:
x * 2.4 = 7.2
To find the number of batches of soup Fabian can make, we can divide both sides by 2.4
x = 7.2/2.4
x = 3
So Fabian can make 3 batches of soup.
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Unit 7 geometry homework 8 quadrilaterals.
Math
The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
in 8 th question
The illustration depicts a rectangle with four sides and two opposite sides that are the same length as a square with equal lengths on all four sides.
The data and the image both characterize the object as a rectangle because its length is 12 and its width is 9.
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Can anyone explain to me how to solve this for h? I was given the volume and radius and I still got it wrong. My incorrect answer is in red, and the coreect one was filled in, but I still don't understand how to solve it for h.
What is the 8[tex]\pi[/tex]mean? does it mean 8 times pi?
cuemath
THE MATH EXPERT
probability
probability
of B getting a job is 3/4. What is the
that only one of them gets the job.
By the total number of potential outcomes, divide the total number of events. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event and its accompanying consequences have been determined.
What is probability?The likelihood that an event or several events will occur is known as probability. Utilizing a straightforward formula, probability can be determined and is used to describe the likelihood of obtaining a specific result.Probability can alternatively be defined as the ratio of the number of expected outcomes of an event to its likelihood of occurring. When there are several events, the probability is calculated by dividing each likelihood into a single computation, multiplying the results, and then summing the results to determine the probability of each event.The probability of an event happening is defined by the probability formula. The proportion of favorable outcomes to all possible outcomes serves as the basis for the formula used to determine an event's probability. Always between 0 and 1 are the possible outcomes. One way to say the generic probability formula is:Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.
or P(A) = f / N
Where:P(A) = Chance of Event A Occurring f = Number of Possible Ways for Event A
N represents all conceivable outcomes.
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The price for printing a small photo is $0.19. If the cost per square inch stays constant, how much should the large version of that photo cost, whose dimensions are 140% of the original?
Explain please!!
The cost of the large version of the photo is $0.456.
What is the cost?
Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %.
Cost of the large version of the photo = cost of the small photo x (1 + percent/100)
Cost of the large version of the photo = $0.19 x (1 + 140/100)
= $0.19 x (1 + 1.40)
= $0.19 x 2.40
= $0.456
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Put the numbers in order from least to greatest.
Answer:
0.6 > 0.49 > 0 > -0.2 > -0.32
Step-by-step explanation:
-0.32 is the smallest number because it is farthest to the left of 0.-1/5 is the same thing as -0.2. Therefore it is the second smallest number because it is greater than -0.32 but smaller than zero. 0 belongs in the middle because it has no value and is a neutral number. 0.49 is greater than 0 so it should go to the right of zero. 6/10 is the same thing as 0.6. 0.6 is the greatest number of all these numbers so it should be the farthest to the right from 0.Please let me know if this helped!!!
culating Volume
Which expression can be used to represent the
volume of this prism?
6 x 11 unitsª
48 x 3 units
14 x 3 units³
8x9 units³
This prism's volume can be expressed using an expression of 48 x 3 units.
How may the volume of a prism be expressed?The area of the base is multiplied by the prism's height to determine its volume. The volume of a prism can be calculated using the formula V = B H, where V stands for the volume, B for the base area, and H for the height.
The volume of the prism is given in cubic units by the formula V = A H cubic units, where A is the prism's base area and H is its height.
The expression for the volume of this prism is 48 x 3 units.
The area of the base is multiplied by the prism's height to determine its volume.
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Complete Question -
[tex]y=sin (3x + \pi ) for -\frac{\pi }{3} \leq x\leq \frac{\pi }{3}[/tex]
The trigonometric function y = sin(3x + π) = 0 for -π/3 ≤ x ≤ π/3.
What is a trigonometric function?A trigonometric function is a function that uses one of the trigonometric ratios.
How to find the possible values of the trigonometric function?Given that we have the trigonometric function y = sin(3x + π) for -π/3 ≤ x ≤ π/3.
To find the range of output values for the range of input values given, we insert the given values of the input into the equation.
So, for the minimum value of y, we substitute x = -π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(-π/3) + π)
y = sin(-π + π)
y = sin(0)
y = 0
For the maximum value of y, we substitute x = π/3 into the equation.
So, y = sin(3x + π)
y = sin(3(π/3) + π)
y = sin(π + π)
y = sin(2π)
y = sin2π
y = 0
So, y = 0 for -π/3 ≤ x ≤ π/3.
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HELP PLEASE TYYY easy
The angle measure of the circle graph is as follows:
Train = 90 degreesAirplane = 198 degreesBoat = 72 degrees.How to find the angles in a pie chart?A travel magazine surveyed 500 of its adult readers about their favourite ways to travel. The circle graph below shows that 125 people like to travel by train, 275 like to travel airplane and 100 people like to travel by boat.
Therefore, let's use the data to create a pie chart with the measured angles.
Hence,
angle for train travellers = 125 / 500 × 360
angle for train travellers = 45000 / 500
angle for train travellers = 90 degrees
angle for the airplane travellers = 275 / 500 × 360
angle for the airplane travellers = 99000 / 500
angle for the airplane travellers = 198 degrees
Finally,
angle for the boat travellers = 360 - 198 - 90 = 72 degrees.
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Which term describes a system with no solution? A consistent B dependent C inconsistent D independent
the answer is inconsistent i think
Which of the following is an improper form of the null and alternative hypotheses? a. H_0: mu lessthanorequalto mu_0 and H_a: mu > mu_0 b. H_0L: mu = mu_0 and H_a: mu = mu_0 c. H_0: mu < mu_0 and H_a: mu greaterthanorequalto mu_0 d. H_0: mu greaterthanorequalto mu_0 and H_a: mu < mu_0
They are known as the two types of first is null hypothesis and the second is alternative hypothesis. These two hypotheses bear opposite viewpoints.
H0: also known as null hypothesis: It is a statement about the population that either is taken to be true or is used to put forth an argument until it can be shown to be incorrect behind a reasonable doubt.
Ha: also known as the alternative hypothesis: It is a state about the population that is contradictory to H0 and what we conclude when we reject H0.
H0 every time has a symbol with an equal in it. It never has a symbol with an equal in it. The option of the symbol depends on the wording of the hypothesis test.
Yet, be aware that many researchers use = in the null hypothesis, even with > (greater) or < (less) as the symbol in the alternative hypothesis.
We can accept this practice because we only decide to reject or not reject the null hypothesis.
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Question 1 Complete the following addition exercises. 3 + 7 = 2 + 9 = 4 + 6 = 5 + 9 = 12 + 5 = 6 + 3 = 8 + 3 = 10 + 0 = 9 + 8 = 1 + 9 = 7 + 6 = 9 + 3 = 6 + 8 = 0 + 3 = 3 + 6 = 7 + 1 = 4 + 2 = 4 + 7 = 11 + 3 = 7 + 7 = 9 + 7 = 12 + 9 =
On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17, 10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .
What is Addition ?
Addition can be defined as the performing addition operation by using operand + between two operators.
3 + 7 = 10
2 + 9 = 11
4 + 6 =10
5 + 9 =14
12 + 5 =17
6 + 3 =9
8 + 3 =11
10 + 0 = 10
9 + 8 = 17
1 + 9 = 10
7 + 6 = 13
9 + 3 =12
6 + 8 = 14
0 + 3 = 3
3 + 6 = 9
7 + 1 = 8
4 + 2 =6
4 + 7 = 11
11 + 3 = 14
7 + 7 = 14
9 + 7 = 16
12 + 9 =21
Hence, On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17, 10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .
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Solve this you won't.
Step-by-step explanation:
It would be 4w=36
÷4 on both sides
W=9
Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Value of x = 12.5 that is determined by solving equation.
what is complementary angle?
Two angles are called complementary to each other when the sum of these two angles is equal to 90 degrees.
What is the value of x?given, two angles are complementary two each other.
value of one angle = 18 degrees
the other angle is given by = (8x - 28) degrees
As the above two are complementary so the sum of the two is equal to 90 degrees.
The equation will be.
18 + (8x - 28) = 90
8x - 10 = 90
8x = 100
x= 12.5
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Hurry! Did i do it right?
Answer: Yes its right
Step-by-step explanation:
You substitute 10 in for x
-3(10) + 1
-30 + 1
=-29
Which of the contexts below could not be modeled by a linear function?
A car depreciates at a rate of 8.3% per year.
Snow was falling at a rate of 2.25 inches per hour.
A sunflower was growing at a rate of 1.5 inches per week.
A taxí charges a flat fee of $2.50 for pick-up, then an additional fee of $3.75 per
mile.
Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement as linear function.
Describe function.Mathematicians frequently use the word "function" to refer to a connection that describes how two variables are connected to one another. There are two: a predictor variable, which is the function's output, and a variable, which can be any input of an equation.
Here,
Given:
A car loses value at a rate of 8.3% annually.
2.25 inches of snow were falling every hour.
A sunflower was expanding by 1.5 inches every week.
A set rate of $2.50 is charged by taxis for pickup, and an additional $3.75 is added for each subsequent mile.
thus,
From the following above expression we cannot consider the fourth statement
As if we write it in the formula it comes out to be linear equation not function.
Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement as linear function.
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The probabilities of events R and S satisfy the following conditions: • P(R) = 1 4 If events R and S are independent, which represents P(R and S)? • P(S) = 3 O 42 0 H
If events R and S are independent, the probability of both occurring (P(R and S)) is the product of their individual probabilities which will give 3/32.
What is the probability of independent events?To calculate the probability that if events R and S are independent, both events occurring (P(R and S)) is the product of the individual probabilities of each event.
So, P(R and S) = P(R) x P(S) = (1/4) x (3/8) = 3/32
This is because when events are independent, the occurrence of one event does not affect the probability of the other event, so the probability of both events occurring is just the product of the individual probabilities of each event.
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can someone please help work this sum out please
We can conclude that we have sufficient data to reject the null hypothesis and that the mean breaking strength is different from 8000 at 5% of significance if we compare the p value and the significance threshold, for example, α = 0.05.
The information provided and notation
X = 7750 indicate the sample's mean breaking strength, which is 145.
n = 6 sample size μ o= 8000 reflect the sample standard deviation indicate the quantity we want to test, and
α = 0.05 denotes the level of significance for the hypothesis test.
The statistic (interesting variable) would be represented by t, and the test's p value would be represented by P u (variable of interest)
Name the prevailing and competing hypotheses.
It is a test with two tails.
How do H₀ and Hₐ relate to this study?We wish to determine whether or not the genuine mean is equal to 8000.
Null hypothesis μ = 8000.
Alternate hypothesis μ₀ ≠ 800
Determine the test statistic.
[tex]t = \frac{X-\mu}{\frac{s}{\sqrt{n} } }[/tex]
t-test: "enables the comparison of group means. One of the most widely used tests, it is used to assess whether the mean is (greater, lower, or not equal) to a given value ".
Determine the statistic.
We can substitute the following information in the above formula
[tex]t = \frac{7750-8000}{\frac{145}{\sqrt{6} } } = -4.22[/tex]
Give the test's appropriate conclusion -
To begin with, we must determine the degrees of freedom indicated by: df = n-1 = 6-1 = 5.
Given that the test has two possible outcomes, the p value is
Pv = 2 × P(t(5) < -4.22) = 0.0083.
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help pls and thanks !!! i’ll mark brainliest !!!
Solve the oblique triangle using the Law of Sines and/or the Law of Cosines. Find all side lengths rounded to
the nearest whole and all angles rounded to the nearest whole.
Side a of the oblique triangle is 25.57 units and side b is 9.42 units.
What is the law of sines?The number of sides of a triangle and how their individual sine angles are equal are determined by the law of sines. Other names for the sine law are sine rule, sine formula, and sine law. The law of sine is used to determine the side or unknown angle of an oblique triangle.
Given:
∠A = 107
∠B = 21
∠C = 52
c = 21
So, using the law of sines
b/sin B = c/ sin C
b/sin 21 = 21/sin 52
b = (21 × sin 21) / sin 52
= (21 × 0.35) / (0.78)
b ≈ 9.42
Similarly, side a of the triangle is given by
a/ sin A = c/ sin C
a/sin 107 = 21/sin 52
a = (21 × sin 107) / sin 52
= (21 × 0.955) / (0.78)
a ≈ 25.57
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Lina had 1 points located at (4,2) and (9,0). Line 2 is represented by the equation y=2/5x+5.
A.Line has 1 greater rate of change equal to 2/5
B. Line 1 had a greater rate of change equal to -5/2
C. Line 2 has a greater rate of change equal to 2/5
D. Line 2 has a greater rate of change equal to -5/2
So on solving the provided question, we can say that the equation is = > y = 2/5x ; at (4,2) and at (9,0) Line 1 had a greater rate of change equal to -5/2
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation is = > y = 2/5x
at (4,2) and at (9,0) Line 1 had a greater rate of change equal to -5/2
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find the area that the curve encloses and then sketch it. r2 = 9 cos(2θ)
Can somebody please tell me how do we solve this? Thank you.
The last option which says the roots of the auxiliary equation are √6 and -√6 is the correct one.
What are Auxiliary Equations?Auxiliary equation is the equation of characteristic polynomial which is calculated by substituting the right member of a standard differential equation by zero.
The roots of the equation is helpful in determining the nature of the general solution of the given differential equation.
We have the differential equation given in the question,
d²y / dx² - 6y = 0
Now we can replace d²y / dx² as y''.
y'' - 6y = 0, where y'' is the second derivative of y.
Now we have to find the roots of the auxiliary equation.
Let c = y', then c² = y''
c² - 6 = 0
c² = 6
c = +√6 and -√6
So the roots of the equation are √6 and -√6.
Hence the roots of the auxiliary equation of the differential equation given are +√6 and -√6.
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Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=2x+3 \\\\ y=-3x+3 \end{cases}
y=2x+3
y=−3x+3
x=x=x, equals
y=y=y, equals
The solution to the system of equation y = 2x + 3 and y = -3x + 3 is (0, 3)
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The linear equation is in the form:
y = mx + b
where m is the rate of change and b is the y intercept.
Given the equation:
y = 2x + 3 (1)
y = -3x + 3 (2)
To solve by elimination method, subtract equation 2 from 1:
0 = 5x + 0
x = 0
substitute x = 0 in equation 1:
y = 2(0) + 3 = 3
The solution to the equation is (0, 3)
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Please solve and show your equation below, happy teachings!
The expected value for the given data set is 1.4.
What is expected value?
The value that will most likely be obtained from the following iteration of a statistical experiment is known as the expected value. In order to calculate the expected value for a random trial of an experiment, the probability of each possible result is taken into account.
From the given table we have to find the expected value.
Since,
Expected value = E(X) = μ = ∑ x*P(x)
E(X) = (0*0.4) + (1*0.05) + (2*0.3) + (3*0.25)
E(X) = 0 + 0.05 + 0.6 + 0.75
E(X) = 1.4
Hence, the expected value for the given data set is 1.4.
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Airplane A flies 300 miles due east of an airport and then flies 200 miles at 15° north of east. Airplane B flies 200 miles due north and then flies 300 miles at 20° west of north. Which airplane is closer to the airport? Explain how you know.
Answer:
It is not possible to determine which airplane is closer to the airport without additional information. The distance and direction of each airplane's flight are given, but the starting point for each airplane is not specified. If we knew the starting point of each airplane, we could use the information provided to calculate the final position of each airplane and determine which one is closer to the airport.
Step-by-step explanation:
Can someone help with this?
Answer: Its definitely 7.2 for the first two and 4.5 on the last one to the right
Step-by-step explanation: i did the quiz
Work out the value of 10 squared takeaway 4 cubed
Give your answer as a power of 6
Answer:
[tex]6^2=36[/tex]
Step-by-step explanation:
[tex]10^2-4^3=100-64=36=6^2[/tex]
An apple in a dessert contributes one-thirtieth the number of fat grams that the cup of cottage cheese contributes. If the total number of fat grams in the dessert is 4.03 g, how many fat grams are in the apple and how many are in the cup of cottage cheese?
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
what is proportionality ?Relationships that always have the same ratio are said to be proportional. For instance, the number of trees in an orchard and the number of apples in a harvest of apples are determined by the average number of apples per tree. A linear relationship between two numbers or variables is referred to as proportional in mathematics. When the first quantity doubles, the other number does as well. When one of the variables is reduced to 1/100th of its previous value, the other also decreases. If two quantities are proportional, it means that when one rises, the other rises as well, and the ratio between the two quantities remains constant throughout all values. The diameter and circumference of a circle serve as an example.
given
fat grams from the apple, where a
a +30a = 4.03g
31a/31 = 4.03 / 31
a = 0.13
The cottage cheese has 30(0.13) = 3.9 g fat, compared to the apple's 0.13 g.
The cottage cheese contains 3.9 g of fat and the apple has 0.13 g, making a total of 4.03 g of fat in the dessert.
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