A score of 120 is one standard deviation below the mean of 150 on a test with a standard deviation of 30.
Explanation:The score that is 1 standard deviation below the mean is found by subtracting the standard deviation from the mean. In the context of this normal distribution of test scores, with a mean of 150 and a standard deviation of 30, we calculate the score one standard deviation below the mean as follows:
Score = Mean – Standard Deviation = 150 – 30 = 120
This calculation indicates that a score of 120 is one standard deviation below the mean on this test.
A restaurant has 10 sodas that come in 12 different cup sizes. How many different drinks can you order?
Answer:
There are 120 different drinks that you can order.
Step-by-step explanation:
You have 10 options of soda for which you can choose.
For each options, there are 12 different cup sizes.
12*10 = 120
So there are 120 different drinks that you can order.
The Florida Panhandle has almost 60 different types of habitats. Based on this fact, which statement best describes the Florida Panhandle?
Adidad
Answer:
A wide variety of life exists in Florida Panhandle
Step-by-step explanation:
A habitat is the natural environment in which organisms lives. We have three types of habitat which include aquatic, terrestrial and arboreal. These habitats contains different organisms.
Florida Panhandle having almost sixty different types of habitats means more organisms living in this place. This translates to a wide variety of life existing in Florida Panhandle.
The statement that best describes the Florida Panhandle based on the fact that it has almost 60 different types of habitats is that it is a region with high biodiversity and a variety of ecosystems.
The presence of nearly 60 distinct habitats in the Florida Panhandle indicates a rich tapestry of ecological systems. Biodiversity refers to the variety of life in the world or in a particular habitat or ecosystem. This includes the different species of plants, animals, and microorganisms, the genetic differences among them, and the ecosystems in which they occur. A high number of habitats suggests that the area supports a wide range of species that have adapted to the different environmental conditions present in these habitats.
Ecosystems are communities of living organisms in conjunction with the nonliving components of their environment (things like air, water, and soil), interacting as a system. These ecosystems can range from coastal marshes and estuaries to longleaf pine forests and freshwater springs. Each habitat type provides unique resources and living conditions, which in turn support different types of organisms.
The Florida Panhandle's diverse habitats likely result from its geography, climate, and history. The region may include coastal areas, wetlands, forests, and other landscapes, each with its own set of habitats. This diversity is crucial for the overall health of the environment, as it allows for a greater number of species to thrive and for ecological processes to function effectively. It also provides opportunities for recreation, research, and education, and it underscores the importance of conservation efforts to protect these valuable natural resources.
In summary, the high number of habitats in the Florida Panhandle is indicative of its ecological richness and the importance of conserving this diversity for environmental health and human enjoyment."
Todd has $124 in his checking account. He wrote two checks for $13.96 and $21.67 and transferred
$14 into his checking from his savings.
What is his new balance?
Answer:
$[tex]74.37[/tex]
Step-by-step explanation:
To figure out how much is left in his checking account, simply subtract the amount he took out.
[tex]124 -13.96 = 110.04[/tex]
[tex]110.04 - 21.67 =88.37[/tex]
[tex]88.37 - 14= 74.37[/tex]
$[tex]74.37[/tex] is left in his checking account.
Answer:
$102.37
Step-by-step explanation:
Todd has $124 to begin with
He writes two checks (subtract) $13.96 & $21.67
Then he removes $14.00 from his savings & places it into his Checking. (Adding) it to his checking account balance
$124-13.96-21.67+14 = $102.37
What is the area of the parallelograms?what is the square unit ?
Answer:
35 units^2.
Step-by-step explanation:
Area = base * altitude
= 7 * 5.
Answer:
35 sq. un.
Step-by-step explanation:
The Intuition for why the area of a parallelogram is A=bh (area = base x height)
The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.
Have a great day!
the second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence.
Answer:
3/4
Step-by-step explanation:
We know a geometric sequence has the formula: a_n = a_1 * r^(n-1)
a_2 = 20
a_4 = (45/4)
so... a_2 = a_1* r^(2-1) = 20
and a_4 = a_1* r^(4-1) = (45/4)
a_1 * r = 20
a_1* r^3 = (45/4)
a_1 = 20/r
(20/r) * r^3 = (45/4)
20 * r*r = 45/4
r*r = 45/80 = 9/16
r = 3/4 or r = -3/4 it must be positive.
common ratio is r = 3/4
A certain vehicle emission inspection station advertises that the wait time for customers is less than 8 minutes. A local resident wants to test this claim and collects a random sample of 64 wait times for customers at the testing station. She finds that the sample mean is 7.43 minutes, with a standard deviation of 3.6 minutes. Does the sample evidence support the inspection station's claim? Use the alphaequals0.005 level of significance to test the advertised claim that the wait time is less than 8 minutes.
Final answer:
The sample evidence does not support the inspection station's claim that the wait time is less than 8 minutes.
Explanation:
To test the claim that the wait time at the vehicle emission inspection station is less than 8 minutes, we can conduct a hypothesis test using the sample data provided. The null hypothesis (H0) is that the mean wait time is greater than or equal to 8 minutes, and the alternative hypothesis (Ha) is that the mean wait time is less than 8 minutes.
We need to calculate the test statistic, which is the t-value. The formula to calculate the t-value is:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Using the given data, we can plug in the values:
t = (7.43 - 8) / (3.6 / sqrt(64))
Calculating this gives us a t-value of -1.248.
Next, we need to determine the critical value at a significance level of 0.005. Since the alternative hypothesis is that the mean wait time is less than 8 minutes, we will use a one-tailed test and find the critical value from the t-distribution table. At a significance level of 0.005 and 63 degrees of freedom (64 - 1), the critical value is -2.650.
Finally, we compare the test statistic to the critical value. If the test statistic is less than the critical value, we reject the null hypothesis. In this case, -1.248 is greater than -2.650, so we fail to reject the null hypothesis. This means that the sample evidence does not support the inspection station's claim that the wait time is less than 8 minutes at a significance level of 0.005.
Which of the following statements about ANOVA completely randomized design is correct? a. The ANOVA test assumes that the sampled populations are normally distributed. b. The ANOVA test assumes that the sampled populations have a common variances . c. The ANOVA test assumes that the samples are randomly and independently selected from their respective populations. d. All of these. e. None of these.
Answer:
d. All of these.
Step-by-step explanation:
Analysis of variance (ANOVA) is used in statistics to determine the difference between the mean of two groups. A completely randomized design implies that samples are randomly assigned to either a treatment group or a placebo group during the experiment. For example, if 40 people are selected to test the effect of an analgesic, four groups could be designed- Groups A, B, C, and D. Groups A, B, and C, can be given different amounts of the drug and Group D, given a placebo. This is an example of a randomized design because the participants were randomly assigned to the groups.
For an ANOVA test to exhibit complete randomized design, we assume that the sample populations are normally distributed, and also have the same variances. We also assume in this design, that samples are randomly and independently selected from their respective populations.
grammium-the metal billings used to make the statuettes-is a mixture of aluminum and zinc. each atom of aluminum has 13 protons. that's 3 more than 1/3 the number, z, of protons in an atom of zinc. write and solve an equation to find z
kitchen tiles cost £2.75 each
work out the total cost for 62 tiles
Answer:
170.5
Step-by-step explanation:
2.75x62=170.5 hope this helps
Lee and Maya are collecting leaves for an art project. Lee collect 24/100 of the tiral number of leaves needed. Maya collects 4/10 of the total number of leaves needed. What fraction of tge total number of leaves did they collect altogether?
Answer:
The fraction of the total number of leaves did they collect altogether is [tex]\frac{16}{25}[/tex]
Step-by-step explanation:
This question can be solved by a sum of fractions.
Lee collect 24/100 of the tiral number of leaves needed.
Maya collects 4/10 of the total number of leaves needed.
What fraction of the total number of leaves did they collect altogether?
This is the sum of 24/100 and 4/10.
The lesser common multiple between 100 and 10 is 100. So
[tex]\frac{24}{100} + \frac{4}{10} = \frac{24 + 10*4}{1001} = \frac{64}{100}[/tex]
We can simplify by four
The fraction of the total number of leaves did they collect altogether is [tex]\frac{16}{25}[/tex]
Final answer:
Lee and Maya have collected 64/100 or 64% of the total number of leaves needed for their project when we add Lee's 24/100 and Maya's 40/100 together.
Explanation:
Lee has collected 24/100 of the leaves, and Maya has collected 4/10 of the leaves for their art project. To find out what fraction they have collected altogether, we need to add the two fractions. However, before we can do that, we need to make sure the fractions have the same denominator.
Since 4/10 can be simplified to 40/100, we now have a common denominator of 100. Adding the two fractions together:
Lee's leaves: 24/100
Maya's leaves: 40/100
Total leaves collected: 24/100 + 40/100 = 64/100
Therefore, Lee and Maya have collected 64/100 of the total number of leaves needed for their project.
What is the exact decimal equivalent of 7/12
Conduct a test at the alphaequals0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2. The sample data are x 1 equals 122, n 1 equals 244, x 2 equals 137, and n 2 equals 311.
Answer:
There is not enough evidence to reject the null hypothesis.
Step-by-step explanation:
(a)
The hypothesis can be defined as follows:
H₀: p₁ - p₂ ≤ 0 vs. Hₐ: p₁ - p₂ > 0.
(b)
The test statistic is defined as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
The information provided is:
n₁ = 244
n₂ = 311
x₁ = 122
x₂ = 137
Compute the sample proportions and total proportions as follows:
[tex]\hat p_{1}=\frac{x_{1}}{n_{1}}=\frac{122}{244}=0.50\\\\\hat p_{2}=\frac{x_{2}}{n_{2}}=\frac{137}{311}=0.44\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{122+137}{244+311}=0.47[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.50-0.44}{\sqrt{0.47(1-0.47)[\frac{1}{244}+\frac{1}{311}]}}\\\\=1.41[/tex]
The test statistic value is 1.41.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level α = 0.05.
Compute the p-value as follows:
[tex]p-value=P(Z>1.41)\\=1-P(Z<1.41)\\=1-0.92073\\=0.07927\\\approx 0.08[/tex]
*Use a z-table.
The p-value of the test is 0.08.
p-value = 0.08 > α = 0.05
The null hypothesis will not be rejected at 5% significance level.
Thus, there is not enough evidence to reject the null hypothesis.
Please help and get these points
Answer:
y = 15x
Step-by-step explanation:
The biggest giveaway here is the other answers have + a whole number at the end of the equation. We would see this + as a y-intercept on the graph.
Since our line had no y-intercept and starts from zero, y =15x can be used to represent the graph shown
Another way to know this is to look at the points marked on the line. There is a point at (2, 30). By plugging these co-ordinated into y = 15x we get 30 = 30, which makes sense
Answer:
y=15x
Step-by-step explanation:
because the y-intercept is 0, y=15x is the only choice that has y intercept 0
(9/3)+4(6-7)
Simplify the expression
Answer:
7
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
(9/3)+24-28
(3)+(-4)
-1
The radius of a circle is measured at 15.6cm. The actual radius is 15.3cm. Find, to the nearest percent, the percent error in the measurement of the radius.
Answer:
[tex]Percentage\hspace{3}error\approx 1.96\%[/tex]
Step-by-step explanation:
The error percentage is a measure of how inaccurate a measurement is, standardized based on the size of the measurement. It can be easily calculated using the following formula:
[tex]Percentage\hspace{3}error=|\frac{v_A-v_E}{v_E} | \times 100[/tex]
Where:
[tex]v_A=Approximate\hspace{3}value\\v_E=Exact\hspace{3}value[/tex]
Therefore, according to the data provided by the problem:
[tex]v_A=15.6\\v_E=15.3[/tex]
The percentage error is:
[tex]Percentage\hspace{3}error=|\frac{15.6-15.3}{15.3}| \times 100 = 1.960784314\%\approx 1.96\%[/tex]
If y varies directly as x and y = 15 when x = 5,what is the value of y when x = 6? a. 5 b. 36 c. 9 d. 18
never mind its D
How is the graph of y = (x minus 1) squared minus 3 transformed to produce the graph of y = one-half (x + 4) squared?
The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.
The graph is translated left 5 units, compressed horizontally by a factor of One-half, and translated down 3 units.
The graph is stretched horizontally by a factor of One-half, translated left 5 units, and translated down 3 units.
Answer:
A) The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
Step-by-step explanation:
Edg 2020
It follows from the task content that the transformation required to produce the graph is; The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
What set of transformations are required to produce the graph?It follows from the task content that initial equation is; y = (x-1)² - 3 while the transformation produced; y = (1/2)(x+4)².
It therefore follows that upon translation leftwards by 5 units, the (x-1) term becomes (x+4).
And finally, upon compression vertically by a factor of One-half, and translation upwards 3 units. The transformed form of the graph is obtained.
On this note, the required transformations are as indicated above.
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What is the value of x
Answer: The answer is b
Step-by-step explanation:
The answer is b due to the exterior angle theorem which is 1 exterior angles = 2 interior angles on the opposites sides
so the eqaution is
105= 67+x
and x + 38 which is b
Answer:
C. 33
Step-by-step explanation:
use a protractor in the future
Scott reads 11 pages of a book each day.
How many pages will he read in 7 days?
Answer:
Scott will read 77 pages in 7 days.
Step-by-step explanation:
7x11=77
You randomly draw a lane number for a 100-meter race. Then your friend randomly draws a
Lane number for the same race. Are these events independent or dependent?*
Answer:
Dependent
Step-by-step explanation:
Because you and your friend are in the same race, the lane number your friend will get is affected by your random draw.
Lane number for the same race is a dependent Event.
What is Independent and Dependent variable?An easy way to think of independent and dependent variables is, when you're performing an experiment, the independent variable is what you change, and the dependent variable is what changes because of that. The independent variable can alternatively be viewed as the cause, and the dependent variable as the result.
We have,
A lane number for a 100-meter race.
Here, Lane number for same race is dependent Quantity.
As, You and a friend are competing in the same race.
Then, your random draw will determine which lane number your friend will receive.
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A study was conducted to investigate the effectiveness of hypnotism in reducing pain. An SRS of 8 subjects was randomly selected, and the pain level was recorded for each one, with a lower score indicating less pain. After the subjects were hypnotized, their pain level was recorded again. The researchers calculated the difference in the pain level for each subject, calculated as After – Before. Assume the differences follow an approximately normal distribution, with the following sample statistics: Is pain, on average, lower after hypnotism? Test at a 1% significance level. a. The assumptions for this test are not met because the sample size is too small. b. Yes, the p-value is less than 0.01, so there is sufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. c. Yes, the p-value is greater than 0.01, so there is sufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. d. No, the p-value is less than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism. 3 points Save Answer
Answer:
e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism.
Step-by-step explanation:
Hello!
The study's objective is to test if hypnotism reduces pain.
A sample of n=8 subjects was taken and the pain level was recorded in each subject before and after being hypnotized.
The variable of interest was determined by calculating the difference of pain level after - before hypnosis. This is a paired sample test and the variable can be determined as:
Xd: Difference between pain level felt after hypnosis and pain level felt before hypnosis of a subject.
The sample average and standard deviation obtained were:
Xd= -3
Sd= 3
And the variable is presumed to be approximately normal.
An approximately normal distribution is enough to conduct a paired sample t-test.
If the claim is that hypnosis reduces pain, then the average pain level after hypnosis should be less than the average pain level before hypnosis, then the average difference is expected to be negative, symbolically: μd < 0
The test will be one-tailed and so will be the p-value.
Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
So first step is to calculate the value of the statistic under the null hypothesis and then you can calculate the p-value.
H₀: μd ≥ 0
H₁: μd < 0
[tex]t_{H_0}= \frac{X_d-Mu_{d}}{\frac{S_d}{n} }= \frac{-0-0}{\frac{3}{\sqrt{8} } } = -2.828= -2.83[/tex]
The DF of the t-test are n-1= 7
Then you can calculate the p-value as:
P(t₇≤-2.83)= 0.0127
The level of the test is α: 0.01
The decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value > α the decision is to not reject the null hypothesis.
Correct option: e. No, the p-value is greater than 0.01, so there is insufficient evidence at the 0.01 level to conclude that pain levels are lower after hypnotism.
I hope this helps!
The chickens at Colonel Thompson’s Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights in the following ranges. 33. More than 1700 g 34. Less than 1950 g 35. Between 1750 and 1900 g 36. Between 1600 and 2000 g 37. More than 2100 g or less than 1550 g 38. Find the smallest and largest weights for the middle 95% of the chickens.
Answer:
Kindly go through the explanation for all the answers required
Step-by-step explanation:
Values gotten from the question are: mean= 1850
standard deviation= 150
Z= \frac{x- \mu }{\sigma }
33) X= 1700
P(X>1700)=P( \frac{x- \mu }{\sigma }>\frac{1700-1850}{150})=P(Z>-1)
P(X>1700)=P(Z>-1)=1- P(Z\leq -1)=0.8413
34) X= 1950
P(X<1950)=P( \frac{x- \mu }{\sigma }<\frac{1950-1850}{150})=P(Z<0.6667)=0.7475
35) X1= 1750 and X2= 1900
P(1750\leq X\leq 1900)=P( \frac{1750-1850}{150}\leq \frac{x- \mu }{\sigma }\leq \frac{1900-1850}{150})=P(-0.6667\leq Z\leq 0.333)
P(1750\leq X\leq 1900)=P(-0.6667\leq Z\leq 0.333)=0.3781
36) X1= 1600 and X2= 2000
P(1600\leq X\leq 2000)=P( \frac{1600-1850}{150}\leq \frac{x- \mu }{\sigma }\leq \frac{2000-1850}{150})=P(-1.6667\leq Z\leq 1)
P(1600\leq X\leq 2000)=P(-1.6667\leq Z\leq 1)=0.7936
37) X1= 1550 and X2= 2100
P(1550> X> 2100)=P( \frac{1550-1850}{150}> \frac{x- \mu }{\sigma }> \frac{2100-1850}{150})
P(-2>Z>1.6667)=P(Z\leq -2)+(1-P(Z<1.6667))=0.02275+(1-0.9522)=0.0705
38) 95% Confidence interval:Critical value: Z(0.05/2)= 1.96
CI: \mu \pm Z*\sigma =>1850\pm 1.96*150
CI: 1850\pm 294=>(1850-294,1850+294)=>(1556,2144)
The smallest weight= 1556
The largest weight= 2144
Run a multiple regression where the dependent variable is ratings and the independent variables are star and fact. Use data from CBC only. CBC Management has several questions: Which has more impact on a movie’s rating: Being fact-based or having one star? How much does each of these factors change the ratings? How well does this regression analysis explain the ratings? Justify your answers referring to the relevant figures. Are either, both, or neither of the independent variables significantly related to the ratings at 95% confidence? Justify your answers referring to the relevant figures.
Answer:
See explaination
Step-by-step explanation:
See attachment for diagram
The r value is 0.373 (low). This implies a weak correlation between the dependent and independent variables for this sample.
The overall p- value for the regression model is 0.0017. This implies that at least one of the two independent variables (x1 or x2) in the model is significant predictor of the dependent variable y.
p- values for the both "Fact" and "Star" are < 0.05. This means both the independent variables are significant predictors of the "Rating" at 95% confidence level. The variable "Fact" is significant at 99% level of confidence also. This means the rating viewers award to a movie depends upon both the storyline (fact or Fiction) and the presence or absence of stars.
Expected rating for a fact based movie with no stars = 1.7991(1) + 1.2586(0) + 12.5685 = 14.37
Expected rating for a fiction based movie with a star = 1.7991(0) + 1.2586(1) + 12.5685 = 13.83
So, one may expect a fact based movie without any stars to get better ratings than a fiction based movie with one star.
Domain of {(-5, 4), (-4, -1), (-2, 1), (0, 4), (1,3)}
Answer:
{-5, -4, -2, 0, 1}
Step-by-step explanation:
The domain is the list of first numbers of the ordered pairs. That list is shown above.
in the figure below. AB is a diameter of circle P.
What is the arc measure of AD in degrees?
Answer:
m Arc AD = 43°
Step-by-step explanation:
The question is missing a diagram. Find attached the diagram of the question.
Given:
AB is a diameter of circle P
Solution:
From the diagram,
∠ADP = 7x+1
∠BPC = 9x-7
∠CPD = 90° (the symbol of right angle is drawn)
∠m Arc APB = 180° (sum of angles on a straight line or sum of angle in a semi circle)
∠APD + ∠CPD + ∠BPC = 180°
(7x+1)° + 90° + (9x-7)° = 180°
7x+1 + 90 + 9x-7 = 180
Collect like terms
7x+9x = 180 - 90 + 7 -1
16x = 96
x = 96/16
x = 6
Insert the value color x in ∠APD
∠APD = 7(6) + 1
∠APD = 43°
m Arc AD = ∠ APD
m Arc AD = 43°
Therefore arc measure of AD in degrees = 43°
The edges of three squares are joined together to form a right triangle with legs of lengths r and sand a hypotenuse of length t. What must be true?
1) The perimeter of Square T is equal to the sum of the perimeters of Square R and Square S.
2) The area of Square T is four times the area of Square R.
3) The perimeter of Square T is four times the perimeter of Square R.
4) The area of Square T is equal to the sum of the areas of Square R and Square S.
The area of Square T is equal to the sum of the areas of Square R and Square S.
Is the area of the square and circle the same?The area of a square is the same as the area of a circle. The perimeters of the circle and square are in the ratio. The area of a square is the same as the area of a circle. The perimeters of the circle and square are in the ratio.
How do you find the area?To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
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rewrite the equation by completing the square x^2+x-72=0
Answer:
(x + 1/2) ² = 289/4
Step-by-step explanation: I answered this correctly
The solutions to t[tex]x^2 + x = 72[/tex]he equation [tex]x^2 + x - 72[/tex] = 0 are x = 8 and x = -9.
To rewrite the quadratic equation[tex]x^2 + x - 72[/tex] = 0 by completing the square, we follow these steps:
Step 1: Move the constant term to the other side of the equation:
[tex]x^2 + x = 72[/tex]
Step 2: Take half of the coefficient of the x-term (which is 1) and square it. Add this value to both sides of the equation:
[tex]x^2 + x + (1/2)^2 = 72 + (1/2)^2\\x^2 + x + 1/4 = 72 + 1/4[/tex]
Step 3: Rewrite the left side as a perfect square:
[tex](x + 1/2)^2 = 289/4[/tex]
Step 4: Take the square root of both sides:
x + 1/2 = ± √(289/4)
Step 5: Solve for x:
x + 1/2 = ± 17/2
x = -1/2 ± 17/2
x = (-1 + 17)/2 or x = (-1 - 17)/2
x = 16/2 or x = -18/2
x = 8 or x = -9
The solutions to the equation [tex]x^2 + x - 72[/tex] = 0 are x = 8 and x = -9.
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A pole that is 12 feet tall casts a shadow that is 9 feet long. At the same time of day, how long is the shadow cast by a tree that is 45 feet tall?
Final answer:
To find the length of the shadow cast by the tree, calculate the scale factor between the pole and its shadow, then multiply this factor by the height of the tree to get the length of the tree's shadow.
Explanation:
To find the length of the shadow cast by the tree:
Calculate the scale factor between the pole and its shadow: 12 feet pole casts a 9 feet shadow, so the scale factor is 12/9 = 4/3.
Multiply this scale factor by the height of the tree: 45 feet x 4/3 = 60 feet shadow cast by the 45 feet tall tree.
Which expression has the same value as the one below?
10 +(-3)
The scores of individual students on the American College Testing (ACT), college readiness assessment, have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students
Answer:
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\sigma = 6, n = 36[/tex]
Then, by the Central Limit Theorem:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{6}{\sqrt{36}}[/tex]
[tex]s = 1[/tex]
The standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students is 1.