If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints? Alternative Text A. 48 ft2 B. 64 ft2 C. 96 ft2 D. 112 ft2
Answers
The total surface area that she paints will be 96 square feet. Thus, the correct option is C.
What is the area of the rectangle?Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,
Area of the rectangle = L × W square units
Given that:
Length, L = 12 ft
Width, W = 8 ft
The area of the rectangle is given as,
A = 12 x 8
A = 96 square feet
Thus, the correct option is C.
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The missing diagram is given below.
Related Questions
Find the measure of x
A. x=2
B. x = 6
C. x=8
D. X=10
Answers
Answer:
x = 6º
Step-by-step explanation:
120º = 15(x + 2)
120 = 15x + 30
15x = 120 - 30
15x = 90
x = 90/15
x = 6º
The measure of x is 6°, which corresponds to option B: x = 6, using the property of parallel lines.
We can observe that the given lines are parallel cut by a transversal.
So, the angles 120° and 15(x + 2) are alternate exterior angles which are equal.
So, 120° = 15(x + 2)
To find the value of x:
1. Start by isolating the variable x on one side of the equation.
Subtract 30 from both sides to move the constant term to the other side:
120° - 30° = 15(x + 2) - 30°
2. Simplify the equation:
90° = 15(x + 2)
3. Now, divide both sides of the equation by 15 to solve for x:
(90°) / 15 = (15(x + 2)) / 15
4. Calculate:
90° / 15 = 6°
So, x = 6°.
Therefore, the correct answer is: B. x = 6.
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Triangle ABC has vertices at A(-5, 4), B(4, 1), and C(1, -8). Choose the terms below which correctly describe this triangle:
Answers
Answer:
An ISOSCELES TRIANGLE
Step-by-step explanation:
Given a triangle ABC with vertices at A(-5, 4), B(4, 1), and C(1, -8), to know the type of triangle this is, we need to find the three sides of the triangles by taking the distance between the points.
Distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
For side |AB|:
A(-5, 4) and B(4, 1)
|AB| = √(4-(-5))²+(1-4)²
|AB| = √9²+3²
|AB| = √90
For side |BC|
B(4, 1), and C(1, -8)
|BC| =√(1-4)²+(-8-1)²
|BC| = √3²+9²
|BC| = √90
For side |AC|:
A(-5, 4) and C(1, -8).
|AC| = √(1-(-5))²+(-8-4)²
|AC| = √6²+12²
|AC| = √36+144
|AC| = √180
Based on the distances, it is seen that side AB and BC are equal which shows that two sides of the triangle are equal. A triangle that has two of its sides to be equal is known as an ISOSCELES TRIANGLE. Therefore the term that correctly describes the triangle is an isosceles triangle.
What is the volume of a prism with base 32inches squared and height of 8
Answers
Answer:
V =256 in^3
Step-by-step explanation:
The volume of a prism is given by
V = Bh where B is the area of a base and h is the height
V = 32 * 8
V =256 in^3
The sum of 20.7 and a number is 50.5. Which equation could you use to solve the problem? What should you do to each side of the equation to isolate the variable? What is the solution of the equation?
Answers
Answer:
Which equation could you use to solve the problem?
✔ g + 20.7 = 50.5
What should you do to each side of the equation to isolate the variable?
✔ Subtract 20.7 from each side.
What is the solution of the equation?
✔ 29.8
Step-by-step explanation:
An equation that could be used to solve this word problem is 20.7 + x = 50.5.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In order to solve this word problem, we would assign a variable (x) to the unknown number and then translate the word problem into algebraic equation as follows:
20.7 + x = 50.5
Subtract 20.7 from each side:
20.7 - 20.7 + x = 50.5 - 20.7
x = 50.5 - 20.7
x = 29.8.
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A random sample of size 13 is selected from men with hypertension. For each person, systolic blood pressure was measured right before and one hour after taking the medicine. The mean reduction of the blood pressures was 10.1 and the standard deviation of the difference was 11.2. Test if there is sufficient evidence to conclude that the hypertension medicine lowered blood pressure. What is the value of the test statistic (round off to second decimal place)
Answers
Answer:
Yes, hypertension drugs lowers blood pressure.
Step-by-step explanation:
Claim: The hypertension medicine lowered blood pressure.
The null and alternative hypothesis is
H0:\mu_{d}\geq 0
H1:\mu_{d}< 0
Level of significance = 0.05
Sample size = n = 13
Sample mean of difference = \bar{d} = 10.1
Sample standard deviation of difference = s_{d} = 11.2
Test statistic is
t=\frac{\bar{d}}{s_{d}/\sqrt{n}}
t = ((10.1) / (11.2 /squre root of 13)) = 3.251
Degrees of freedom = n - 1 = 13 - 1 = 12
Critical value =2.179( Using t table)
Test statistic | t | > critical value we reject null hypothesis.
In Conclusion: The hypertension medicine lowered blood pressure
what’s the value of x?
Answers
Answer:
D
Step-by-step explanation:
Answer:
x = 29.1m
Step-by-step explanation:
X= 71 x =
Y = y = 28.2 m
Z = z = 20.9 m
[tex]x^{2} = y^{2} + z^{2} - 2yz cos x\\(28.2 )^{2} + (20.9)^{2} - 2(28.2 )(20.9) cos (71)\\795.24 + 436.81 - 1178.76cos(71)\\1232.05 - 1178.76 cos (71)\\{1232.05-383.767}\\\\\sqrt{x^{2} } = \sqrt{1232.05 - 383.767}\\ x = 29.1[/tex]
Four red candies and three green candies can be combined to make many different flavors. Flavors are different if the percent red is different, so 3 red / 0 green is the same flavor as 2 red / 0 green; and likewise 4 red / 2 green is the same flavor as 2 red / 1 green. If a flavor is to be made using some or all of the seven candies, how many different flavors are possible
Answers
Answer:
11
Step-by-step explanation:
:):
How many times can a 9/2 yard line be divided into 3- inch segment?
a.45 times
b.54 times
c.64 times
d.84 times
Answers
Answer:
54 times
Step-by-step explanation:
1 yard = 3 feet
[tex]9/2 * 3 = 27/2 ft = 13.5 ft[/tex]
1 ft = 12 inches
[tex]13.5*12=162[/tex] inches
162 / 3 = 54 times
B is the answer.
A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. There is no fire There is a fire (b) Define Type I and II errors. A smoke detector sounds an alarm when there is no fire A smoke detector does not sound an alarm when there is a fire (c) In this case, which type of error has the more severe consequences
Answers
Answer:
(a) H₀: There is no fire vs. Hₐ: There is a fire.
(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
(c) In this case, type II error has the more severe consequences.
Step-by-step explanation:
It is provided that a hotel installs smoke detectors with adjustable sensitivity in all public guest rooms.
(a)
The hypothesis can be defined as follows:
H₀: There is no fire.
Hₐ: There is a fire.
(b)
A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).
In this case a type I error will be committed if we conclude that there is a fire and the smoke detector sounds an alarm, when in fact there is no fire.
In this case a type II error will be committed if we conclude that there is no fire and the smoke detector does not sounds an alarm, when in fact there is a fire.
(c)
In this case, type II error has the more severe consequences.
Concluding that there is no fire as the smoke detector did not sound an alarm, when in fact there is a fire, will cause casualties and is harmful for the health of the guests.
Guests would not be alert about the fire as there was not any alarm, and many may loose their lives because of this.
The null hypothesis is 'There is no fire', the alternative hypothesis is 'There is a fire'. A Type I error would be sounding an alarm when there is no fire (rejecting the null hypothesis when it is true), a Type II error would be not sounding an alarm when there is a fire (failing to reject the null hypothesis when it is false). The more severe consequence would be due to a Type II error, as it could result in unrecognized danger.
Explanation:In this scenario, the null hypothesis would be 'There is no fire' and the alternative hypothesis would be 'There is a fire'. In terms of type I and II errors, a Type I error would occur if the smoke detector sounded an alarm when there is no fire, or in other words, rejecting the null hypothesis when it is in fact true. A Type II error would occur if the smoke detector does not sound an alarm when there is a fire, meaning failing to reject the null hypothesis when it is in fact false.
Considering the consequences of these errors, a Type II error would be more severe in this scenario, as it could lead to a serious danger not being recognized, potentially resulting in damage or harm.
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Mary made $1,850 last month. A 25% deduction was subtracted from her pay. What was her deduction?
Answers
Answer:$462.50
Step-by-step explanation:multiply $1,850 by .25 to get your answear
each shape is divided into equal parts. select the shapes that show thirds. mark all that apply
Answers
Answer:
Triangle,Circle,Square, 3 cubes
Step-by-step explanation:
How many times greater is 70 million than 4 million?
Answers
Answer:
66 million
Step-by-step explanation:
4 million on 70 million is 66 million
Answer:
17.5
Step-by-step explanation:
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can i please get brainliest
8300 dollars is placed in an account with an annual interest rate of 6.5%. How much
will be in the account after 14 years, to the nearest cent?
Answers
Answer:
(About) 20043.46 after 14 years
Step-by-step explanation:
~ Let us apply a compound interest formula not through substituting values, but through a similar way of following this formula ~
1. First let us assign the values:
interest ⇒ 6.5 percent ( % ), principle number - start value ⇒ $ 8300, time ⇒ 14 years
2. Now let us convert interest ⇒ decimal form: 0.065
3. Add 1 to this value 0.065 ⇒ 1 + 0.065 = 1.065
4. Now let us take 1.065 exponentially to the power of itself 14 times, or in other words to the power of time ( 14 years ): 1.065^ 14 = 2.414874185.......
5. Multiply this infinite number by the principle number P, or most commonly known as the start value: 2.414874185....... * 8300 ⇒
(About) 20043.46 after 14 years
Using the formula for compound interest and substituting accordingly, the given investment grows to approximately 18,108.80 dollars after 14 years.
Explanation:To solve this, we'll use the formula for compound interest, which is P(1 + r/n)^(nt), where P is the principle amount (initial investment), r is the annual interest rate, n is the number of times that interest is compounded per unit t, and t is the time the money is invested for.
In this case, P = 8300 dollars, r = 6.5/100 = 0.065 (we need the rate in decimal form), n = 1 (since the interest is given annually), and t = 14 years.
Substitute these values into the formula:
A = 8300(1 + 0.065/1)^(1*14) which simplifies to A = 8300(1.065)^14.
Using a calculator, A ≈ 18,108.80 dollars. So, after 14 years, the account will have approximately 18,108.80 dollars.
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Todos los días, Luna utiliza 12 regaderas de medio litro para regar su jardín. ¿Cuántos litros de agua utiliza al día?
Answers
The question in English:
Every day Luna uses 12 half-liter watering cans to water her garden. How many liters of water does she use per day?
Answer:
Español:
Luna utiliza 6 litros de agua al día.
¡Espero que esto ayude!
English:
Luna uses 6 liters of water a day.
Hope this helps!
The amount water used by Luna is equivalent is 6 liters.
What is water?Water is a tiny molecule. It consists of three atoms : two of hydrogen and one of oxygen. Water molecules cling to each other because of a force called hydrogen bonding.
Given is that every day, Luna uses 12 half-liter watering cans to water her garden.
The amount water used by Luna is equivalent to -
A{w} = 1/2 x 12
A{w} = 6 liters
Therefore, the amount of water used by Luna is equivalent is 6 liters.
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{Question in english -
Every day, Luna uses 12 half-liter watering cans to water her garden. How many liters of water she use per day?}
The amount of chill is _ times the amount of cream cheese
Answers
Answer:
6 Chili / 3 cream cheese = 2 Timeschilli compared to cream cheese.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
There are 6 for chilli and 3 for cream cheese.
3 *2 is 6, there fore it is 2 times as much
Hope this is helpful! :)
If g(x) = x square - 2x + 11, find g(-2)
Answers
Answer:
g(-2) = 19
Step-by-step explanation:
g(x) = x ^2 - 2x + 11,
Let x= -2
g(-2) = (-2)^2 -2(-2) +11
= 4 +4 +11
=19
Answer:
-2
Step-by-step explanation:
Which hypotheses are being tested by the chi-square test? The distribution of gender is different for the three different goals. The null hypothesis is that the most important goal is the same for each gender, and the alternative is that the means differ. The distribution of most important goals is different for men and women. The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Answers
Answer:
The null hypothesis is that the most important goal and gender are independent, and the alternative is that they are dependent.
Step-by-step explanation:
Chi Square test is used to test relationship between categorical (nominal) variables of a population. Eg : Testing men & women for any attribute, lets say empathy
Null Hypothesis states that there is no relationship between the attribute & categorical variable, they are independent.Alternate Hypothesis states that there is relationship between the attribute & categorical variable, they are dependent.Eg : Null hypothesis states that there is no difference of empathy level in men & women. Alternate Hypothesis states that there is difference of empathy level in men & women.
One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Answers
Answer:
It would take 7.62 minutes for the third conveyor belt alone to do the same job
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this question:
First conveyor: Rate of 1/9.
Second: Rate of 1/11.
Third: Rate of 1/x.
Total: 1/3
So
[tex]\frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}[/tex]
[tex]\frac{11x + 9x + 99}{99x} = \frac{1}{3}[/tex]
[tex]\frac{20x + 99}{99x} = \frac{1}{3}[/tex]
[tex]3(20x + 99) = 99x[/tex]
[tex]60x + 297 = 99x[/tex]
[tex]39x = 297[/tex]
[tex]x = \frac{297}{39}[/tex]
[tex]x = 7.62[/tex]
It would take 7.62 minutes for the third conveyor belt alone to do the same job
Consider the graph of the quadratic function y = 2(x + 3)2 – 3 with two real zeros. What number can be added to the right side of the equation to change it to a function with one real zero?.
Answers
Answer: 3
Step-by-step explanation:
Answer: I am pretty sure it is 3 but I apologize if it is incorrect.
Step-by-step explanation:
For what values of x is x2-36=5x true?
A. -9 and -4
B. -4 and 9
C. 4 and -9
D. 9 and 4
Answers
Answer:
B. -4 and 9
Step-by-step explanation:
First, you want to get the equation to equal 0.
[tex]x^{2} - 36 = 5x[/tex] subtract 5x from both sides to make the equation equal to 0.
[tex]x^{2} -5x - 36 =0[/tex]
Now you are going to want to factor the equation
Find factors that add up to 5
[tex](x+4)(x-9)[/tex] I used 4 and 9 because they multiply to be 36, since 36 is negative that means that one of the numbers has to be negative. I made 9 negative because when you add 4 it equals 5.
Make both equations equal to 0
[tex]x+4=0[/tex]
[tex]-4[/tex] [tex]-4[/tex] subtract 4 from both sides to get x alone
[tex]x = -4[/tex]
[tex]x-9=0[/tex]
[tex]+9[/tex] [tex]+9[/tex] add 9 to both sides to get x alone
[tex]x=9[/tex]
Answer:
B. -4 and 9
Step-by-step explanation:
move the 5x over and factor to get (x-9)(x+4)=0, set both of the expressions equal to zero, and solve, pretty much you just fator and flip the signs. Hope this helps!
Point A is at (3,-8) and point M is at (5,-2.5).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answers
Answer:
B(7, 3)
Step-by-step explanation:
The formula for the unknown endpoint is ...
B = 2M -A
B = 2(5, -2.5) -(3, -8) = (2·5 -3, 2(-2.5)+8)
B = (7, 3)
Answer:
b 7,3
Step-by-step explanation:
What is the volume of the prism?
in.3.
I need help
Answers
Answer:
18
Step-by-step explanation:
Answer: V ≈ 18
Step-by-step explanation: To get the volume of a prism, we have to follow the method. We have to use V = L * H * W.
First, let's turn 2 [tex]\frac{1}{4}[/tex] into a decimal.
We must divide the numerator by the denominator using long division.
1 ÷ 4 = 0.25 = 2.25
Now, let's use V = L * H * W.
2.25 * 4 = 9 * 2 = 18
The volume is 18, I hope this helps!
Is 3 a solution for -3(x-7+2)=16? If not, find at least one solution
Answers
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x= -1/3
Decimal Form:
x= -0.3 repeating
Brainliest?
Answer:wym by soulution?
Step-by-step explanation:
A researcher has collected the following sample data. The mean of the sample below is 5.
3 , 5 , 12 , 3 , 2
Find the coefficient of variation
Answers
Answer:
The coefficient of variation is 72.66%
Step-by-step explanation:
Data : 3 , 5 , 12 , 3 , 2
We are given that The mean of the sample is 5.
Formula of standard deviation =[tex]\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}[/tex]
Substitute the values :
[tex]\sigma = \sqrt{\frac{(3-5)^2+(5-5)^2+(12-5)^2+(3-5)^2+(2-5)^2}{5}}=3.633[/tex]
Coefficient of variation=[tex]\frac{\sigma}{\mu} \times 100=\frac{3.633}{5} \times 100 =72.66\%[/tex]
Hence The coefficient of variation is 72.66%
The coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
Recall:
Coefficient of variation = Standard deviation / mean x 100%Given, the following data:
3 , 5 , 12 , 3 , 2Mean is given as: 5We are not given the standard deviation.
First, find the standard deviation of the data set, using the formula, [tex]\mathbf{SD = \sqrt{\frac{\sum (x - \bar{x}) }{n} } }[/tex]
Thus:SD = [tex]\sqrt{\frac{66}{5} } = \sqrt{13.2}[/tex]
SD = 3.633
Next, find the coefficient of variation:
Cov. = 3.633/5 x 100 = 72.7%
Therefore, the coefficient of variation of the data set, 3 , 5 , 12 , 3 , 2, is: 72.7%
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"We keep tossing a fair coin n = 10^6 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? I also want the numerical value. 5. We rand
Answers
Answer:
Check the explanation
Step-by-step explanation:
Let [tex]X_{i}[/tex] be the indicator random variable that takes the value 1 if the ith coin is the first coin in a sequence of 19 consecutive heads.
For any sequence of length 19, the starting coin can be from toss i ,
such that i is between 1 and n - 19+1
Thus the number of such sequences is
Kindly check the attached image below for the step by step explanation to the question above.
In a random sample of 7 residents of the state of California, the mean waste recycled per person per day was 1.5 pounds with a standard deviation of 0.58 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of California. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
CI(99%) = ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
Critical value z(at 99% confidence) = z(0.005) = 2.58
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 1.5
Standard deviation r = 0.58
Number of samples n = 7
Confidence interval = 99%
Critical value z(at 99% confidence) = z((1-0.99)/2)
z(0.005) = 2.58
Substituting the values we have;
1.5+/-2.58(0.58/√7)
1.5+/-2.58(0.2192)
1.5+/-0.565536
1.5+/-0.57
= ( 0.93 , 2.07)
Therefore at 99% confidence interval (a,b) = ( 0.93 , 2.07)
For every truck a police officer encounters she writes down T, for every car C, for every van V, and for every vehicle that is not a car, truck or van O (for "other"). Estimate the probability that the next vehicle the police officer encounters is not a car, truck, or van.
T T T C V O O V C T T C C C C C C V O
Answers
Answer:
5 = T
8 = C
3 = V
3 = O
which means its other because it said it is not a car, truck or van so its other meaning O
O = other
Answer: O
Step-by-step explanation: Theirs really nothing to it just pay attention to the hint :)
Answer:
3/19
Step-by-step explanation:
Gradpoint
Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. Net growth rate was computed by comparing the initial and final abundance of G. semen in the experiment, with a negative value indicative of a decrease in abundance. Here are the findings:Number of D. magna grazers 1 2 3 4 5 6Net growth rate of G. semen −1.9 −2.5 −2.2 −3.9 −4.1 −4.3Using the above information, software tells us that the least-squares slope is b = −0.5286 with standard error SEb = 0.1059.(a) What is the t statistic for testing H0: β = 0? (Round your answer to two decimal places.)t = (b) How many degrees of freedom does t have?df = Use this table to approximate the P-value of t against the one-sided alternative Ha: β > 0 (as the grazers would be expected to reduce algal growth).0.001 < P < 0.00250.0025 < P < 0.005 0.005 < P < 0.0100.010 < P < 0.0200.020 < P < 0.025(c) What do you conclude? (Use α = 0.05.)There is strong evidence that the population slope β is negative.There is not enough evidence to conclude that the population slope β is negative.
Answers
Answer:
Step-by-step explanation:
Hello!
To study if the biomass of Gonyostomum semen can be controlled by grazing zooplankton species the research team examined the relationship between:
Y: Net grow rate of G. semen in a test tube.
X: Number of D. magna grazers introduced in test tubes.
Since they are testing the relationship between two variables, i.e. how one variable affects the other, the researchers made a linear regression analysis and estimated the slope of the regression:
The point estimate of the slope: b= -0.5286
Standard deviation of the slope: Sb= 0.1059
n= 6 test tubes.
a)
For the hypotheses:
H₀: β = 0
H₁: β ≠ 0
The formula for the t-statistic is:
b)
The statistic has n-2 degrees of freedom.
So in this case you are working with a Student's t with 6-2= 4 degrees of freedom.
c)
Considering a one-sided alternative hypothesis H₁: β > 0, the calculated value of the statistic under the null hypothesis doesn't change, what change is the direction and size of the rejection region. In item a, the hypotheses had a two-tailed rejection region, for this item the rejection region is one-tailed to the right. This means that you'll reject at hight values of the statistic. The p-value is also one-tailed and you'll find it in the right tail of the distribution (That's why it's positive):
P(t₄≥4.99)= 1 - P(t₄<4.99)
Looking at the t-table. For this distribution, the value of 4.99 is between the t values that accumulate P(t₄<4.604)= 0.995 and P(t₄<7.173)= 0.999 of probability, so it will be between:
1 - 0.995= 0.005
and
1 - 0.999= 0.001
Using the given table and considering the value is closer to 4.064 than 7.173, the p-value will be approximate:
0.00025 < P < 0.005
The p-value is less than the significance level, α: 0.05, so the decision is to reject the null hypothesis. You can conclude that the population slope is not negative (β > 0)
⇒There is not enough evidence to conclude that the population slope β is negative.
I hope you have a SUPER day!
The answers are: a) The t statistic is approximately -4.99. b) the degrees of freedom are 4. c) There is strong evidence that the population slope β is negative.
(a) The t statistic for testing the null hypothesis H0: β = 0 is calculated using the formula:
t = (b - 0) / SEb
Where:
b = slope coefficient = -0.5286
SEb = standard error of the slope coefficient = 0.1059
Substitute the values into the formula:
t = (-0.5286 - 0) / 0.1059 ≈ -4.99
So, the t statistic is approximately -4.99.
(b) The degrees of freedom for the t statistic can be calculated using the formula:
df = n - 2
Where n is the number of data points, which is the number of observations (in this case, the number of Daphnia grazers), minus 2 for the two estimated coefficients (intercept and slope).
Given that there are 6 data points:
df = 6 - 2 = 4
So, the degrees of freedom are 4.
we see that the P-value falls between 0.001 and 0.0025. Therefore, we can approximate the P-value as:
0.001 < P < 0.0025
(c) Using α = 0.05 as the significance level, we compare the P-value to α. Since the P-value is less than α (0.0025 < 0.05), we reject the null hypothesis.
Therefore, the conclusion is: There is strong evidence that the population slope β is negative. In other words, based on the provided data and statistical analysis, it can be concluded that there is strong evidence that an increase in the number of Daphnia magna grazers is associated with a decrease in the net growth rate of Gonyostomum semen, indicating that the grazers are likely reducing the algal growth.
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How is the graph of y =(x-1)2 - 3 transformed to produce the graph of y = 5(X+4)??
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.
The graph is stretched vertically by a factor of 3, translated left 5 units, and translated up 3 units
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units
The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units
Answers
Answer:
The graph is translated left 5 units, compressed vertically by a factor of 5, and translated up 3 units.Step-by-step explanation:
The initial function is
[tex]y=(x-1)^{2} -3[/tex]
The transformed function is
[tex]y=5(x+4)^{2}[/tex]
Notice that the first function represents a parabola with vertex at (1, -3), and the secong function represents a parabola with vertex at (-4, 0). That means the function was shifted three units up and 5 units to the left. Additionally, the function was compressed by a scale factor of 5, because that's the coffecient of the quadratic term.
Therefore, the right answer is the first choice.
Answer:
A.
Step-by-step explanation:
The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
what is equivalent to 601/2
Answers
Answer:
as a mixed number: 300 1/2 (reduced or equivalent)
as a decimal: 300.5 (reduced or equivalent)
as a percentage: 30,050% (reduced or equivalent)
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
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