Answer:
X=1 x=-9
Step-by-step explanation:
(x^2)+8x=9
(x^2)+8x-9=0
(x-1)(x+9)=0
x=1 x=-9
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits c= v+7. The variable v represents the number of visits to the art museum and the variable c represents the total cost of those visits. For a member of the art museum, what is the total cost of 10 visits?
Answer:
17
Step-by-step explanation:
the amount of visits given by the problem is:
[tex]v=10[/tex]
and we have that the equation that relates the number of visits with the total cost is:
[tex]c=v+7[/tex]
where [tex]c[/tex] is the total cost for [tex]v[/tex] number of visits.
We plug into this equation the known value of visitors:
[tex]c=10+7[/tex]
and we solve this expression:
[tex]c=17[/tex]
the total cost for 10 visitors is 17.
Can someone simplify
Answer:
Option (2). [tex]2\frac{1}{4}[/tex]
Step-by-step explanation:
The given expression is [[tex]-5\frac{1}{4}-(-7\frac{1}{2})[/tex]]
We can rewrite the fractions as,
[tex]-5\frac{1}{4}[/tex] = [tex]-(5+\frac{1}{4})[/tex]
[tex]-7\frac{1}{2}=-(7+\frac{1}{2})[/tex]
Now we will substitute the fractions in the expression,
[tex][-(5+\frac{1}{4})]-[-(7+\frac{1}{2})][/tex]
= [tex]-(5+\frac{1}{4})+(7+\frac{1}{2})[/tex]
= (-5 + 7) + [tex](-\frac{1}{4}+\frac{1}{2})[/tex]
= 2 + [tex]\frac{2-1}{4}[/tex]
= 2 + [tex]\frac{1}{4}[/tex]
= [tex]2\frac{1}{4}[/tex]
Therefore, Option (2). will be the answer.
Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of 40 lb and the terminal point of the vector is point P(1, 1, 0). The second force has a magnitude of 60 lb and the terminal point of its vector is point Q(0, 1, 1). Let F be the resultant force of forces F1 and F2.
(a) Find the magnitude (in pounds) of F. (Round the answer to one decimal place.)
(b) Find the direction of F.
Answer:
Step-by-step explanation:
The two force F1 and F2 are represented by vectors with initial points that are at the origin.
the terminal point of the vector is point P(1, 1, 0)
Therefore, the direction of the vector force is
[tex]v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j[/tex]
The unit vector in the direction of force will be
[tex]\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}[/tex]
The magnitude of the force is 40lb, so the force will be
[tex]F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)[/tex]
The terminal point of its vector is point Q(0, 1, 1)
Therefore, the direction of the vector force is
[tex]v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k[/tex]
[tex]\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}[/tex]
The magnitude of the force is 60lb, so the force will be
[tex]F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)[/tex]
The resultant of the two forces is
[tex]F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k[/tex]
The magnitude force will be
[tex]|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68[/tex]
to (1 decimal place)=55.7lb
b) The direction angle of force F
The angle formed by F and x axis
[tex]\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469[/tex]
The angle formed by F and y axis
[tex]\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=[/tex]
The angle formed by F and z axis
[tex]\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359[/tex]
A light bulb is programmed to turn on when the temperature in a terrarium is 72 F or cooler
Question:
Write an inequality to represent the situation.
A light bulb is programmed to turn on
when the temperature in a terrarium is
72°F or cooler.
Answer:
t ≤ 72⁰F
Step-by-step Explanation:
Given this situation, we can write an inequality to represent the temperature in a terrarium at which the light bulb is programmed to turn on as follows:
t ≤ 72⁰F
where, t is the temperature of the terrarium, the sign "≤" implies that at a temperature of 72⁰F and below (i.e. colder would mean temperature below 72⁰F), the light bulb should turn on, as programmed.
Invariably, the inequality "t ≤ 72⁰F" mean the light bulb would turn on if the temperature of the terrarium is less than or equals 72⁰F.
Linda earns $600 each week working her full time job. Her employer has a 16% tax deduction on all monies earned each week
Answer:
$504 a week
Step-by-step explanation:
Find the domain of the graphed function.
Answer:
A
Step-by-step explanation:
The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county’s residents are smarter than the national average and wants to use it (the intelligence of the residents) as a marketing tool to bring industries to the area. A researcher is hired to conduct a study to determine whether Smart County’s residents have, on average, higher Full Scale IQs than the population. A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105. After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average, the p-value of 0.0004 was obtained. Using a 0.05 significance level, what conclusion can be drawn from the data?
Answer:
Step-by-step explanation:
Hello!
The variable "X: Full scale IQ score of an adult" follows a normal distribution with mean μ= 100 and standard deviation σ= 15
The claim is that the county's residents are smarter than the national average, symbolically: μ > 100
To test this a researcher took a sample of n=100 residents that took the test and recorded an average of X[bar]= 105
The hypotheses are:
H₀: μ ≤ 100
H₁: μ > 100
α: 0.05
p-value: 0.0004
Using the p-value approach, the decision rule is as follows:
p-value ≤ α, reject the null hypothesis.
p-value > α, do not reject the null hypothesis.
The p-value is less than the significance level so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the average full-scale IQ score of the Smart County residents is higher than the national average.
I hope this helps!
Scores on a certain IQ test are knownto have a mean of 100. A random sample of 43 students attend a series of coaching classes before taking the test. Let \small \mu be the population mean IQ score that would occur if every student took the coaching classes.The classes are successful if \small \mu > 100 . A test is made of the hypothesis \small H_{0}:\mu = 100 versus \small H_{1}:\mu > 100
Consider three possible conclusions :
(i) The classes are successful
(ii) The classes are not successful
(iii) The classes might not be successful.
Part 1
Assume that the classes are successsful but the conclusion is reached that the classes might not be successful. Which type of error is this?
Part 2
Assume that the classes are not successful. It is possible to make a type II error? Explain.
_______(Yes, No) , a type II error _____(is, is not) possible. The classes are not successful when the null hypothesis is______(true, false).
Answer:
Part 1
Type II error
Part 2
No ; is not ; true
Step-by-step explanation:
Data provided in the question
Mean = 100
The Random sample is taken = 43 students
Based on the given information, the conclusion is as follows
Part 1
Since it is mentioned that the classes are successful which is same treated as a null rejection and at the same time it also accepts the alternate hypothesis
Based on this, it is a failure to deny or reject the false null that represents type II error
Part 2
And if the classes are not successful so we can make successful by making type I error and at the same time type II error is not possible
Therefore no type II error is not possible and when the null hypothesis is true the classes are not successful
A company produces steel rods. The lengths of all their steel rods are normally distributed with a mean of 155.1-cm and a standard deviation of 2.2-cm. For shipment, 11 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm.
Answer:
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm
P(155.6 < x⁻ < 156.2) = 0.174 cm
Step-by-step explanation:
Given sample size 'n' = 11 steel rods
Mean of the Population = 155.1 cm
Standard deviation of the Population = 2.2 cm
Given x⁻ be the random variable of Normal distribution
Let x₁⁻ = 155.6 cm
[tex]Z_{1} = \frac{x^{-} _{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{155.6-155.1}{\frac{2.2}{\sqrt{11} } } = 0.7541[/tex]
Let x₂⁻ = 156.2 cm
[tex]Z_{2} = \frac{x^{-} _{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{156.2-155.1}{\frac{2.2}{\sqrt{11} } } = 1.659[/tex]
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm.
P(x⁻₁ < x⁻ <x⁻₂) = P(Z₁ < Z <Z₂)
= P(Z <Z₂) - P(Z<Z₁)
= 0.5 +A(1.629) - (0.5 +A(0.7541)
= A(1.629) - A(0.7541)
= 0.4474 - 0.2734
= 0.174
Conclusion:-
The probability that the average length of a randomly selected bundle of steel rods is between 155.6-cm and 156.2-cm = 0.174
The U.S. Department of Transportation provides the number of miles that residents of the75 largest metropolitan areas travel per day in a car. Suppose that for a simple randomsample of 50 Buffalo residents the mean is 22.5 miles a day and the standard deviation is 8.4 miles a day, and for an independent simple random sample of 40 Boston residents themean is 18.6 miles a day and the standard deviation is 7.4 miles a day.a. What is the point estimate of the difference between the mean number of miles thatBuffalo residents travel per day and the mean number of miles that Boston residentstravel per day?b. What is the 95% confidence interval for the difference between the two populationmeans?
Answer:
a. The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88
b. The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)
Step-by-step explanation:
a. According to the given data we have the following:
Buffalo residents mean=22.5
Standard deviation=8.4
n=50
Boston residents mean=18.6
Standard deviation=7.4
n=40
Hence, the point estimate is the difference of the means=22.5-18.6=3.9
The standard error=√((s1∧2/n1)+((s2∧2/n2))=√((8.4∧2/50)+(7.4∧2/40))=1.67
Therefore, the difference of miles=n1+n2-2=50+40-2=88
The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residentstravel per day is 88.
b. The critical value of t at 95% confidence level and DoF=88 is 1.987
The interval:(x1-x2)+ (critical value* std error)
=3.9-(1.987*1.67),3.9+(1.987*1.67)
Difference between mean=(0.58171,7.21829)
The 95% confidence interval for the difference between the two population means is (0.58171,7.21829)
What’s the correct answer for this?
Answer:
first option
Step-by-step explanation:
Given 2 secants to a circle from an external point, then
The product of the external part and the whole of one secant is equal to the external part and the whole of the other secant, that is
PQ(RP) = PS(TP)
Which line is parallel to the line that passes through the points (1, 7) and (-3, 4)? A. B. C. D.
Answer:
hope this helps you
G
What is the value of f(x) when X=-3?
f(x)=-2x-3
f-3)=
Answer:
f(-3)=3
Step-by-step explanation:
We know that f(x)=-2x-3. In order to find f(-3), we simply need to substitute x with -3.
Thus, we have:
=-2(-3)-3
=6-3
=3
Answer:
3
Step-by-step explanation:
f(x)=-2x-3
Let x=-3
f(-3)= -2(-3) -3
= 6-3
= 3
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.7-in and a standard deviation of 1.1-in.In what range would you expect to find the middle 50% of most head breadths
Answer:
[tex] 6.7 -0.674 *1.1 =5.96[/tex]
[tex] 6.7 +0.674 *1.1 =7.44[/tex]
Step-by-step explanation:
Let X the random variable that represent the head breadths of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(6.7,1.1)[/tex]
Where [tex]\mu=6.7[/tex] and [tex]\sigma=1.1[/tex]
We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
The critical values that accumulates 0.25 of the area on each tail we got:
[tex] z_{crit}= \pm 0.674[/tex]
And if we solve x from the z score we got:
[tex] x = \mu \pm z \sigma[/tex]
And replacing we got:
[tex] 6.7 -0.674 *1.1 =5.96[/tex]
[tex] 6.7 +0.674 *1.1 =7.44[/tex]
One hundred ople were surveyed
about their favorite flower. Of these,
20 people say their favorite flower is
the tulip. What fraction of the people
say their favorite flower is NOT the
tulip? Explain your answer.
Answer:
4/5
Step-by-step explanation:
Since there are 100 people, and 20 people say their favorite flower was the tulip, we can make a fraction of the people who like tulip.
20/100=2/10=1/5
There are the people who's favorite flower is tulip. However, the question asks what fraction of the people say their favorite flower is NOT tulip.
Take 1 as the entire people surveyed, and subtract:
1-1/5= 4/5
Therefore 4/5 of the people surveyed says their favorite flower is NOT tulip.
On March 1, 2022, Carla Vista Co. acquired real estate, on which it planned to construct a small office building, by paying $79,000 in cash. An old warehouse on the property was demolished at a cost of $8,000; the salvaged materials were sold for $1,660. Additional expenditures before construction began included $1,160 attorney’s fee for work concerning the land purchase, $4,400 real estate broker’s fee, $8,660 architect’s fee, and $13,800 to put in driveways and a parking lot. (a) Determine the amount to be reported as the cost of the land.
Answer:
Cost of the land = $90,900
Step-by-step explanation:
Cash Paid for the construction = $79,000
Cost of demolition of the old warehouse = $8,000
Salvage (i.e Proceeds from the salvaged materials) = $1,660
Additional Expenditure before construction began
Attorney's fee = $1,160
Real estate broker's fee = $4,400
Architect's fee = $8,660 ( Note that this will be capitalized to building cost)
Driveways and parking lot = $13,800 ( Note that this is capitalized to land improvements)
Sum of additional expenditure = Attorney's fee + Real estate broker's fee
Sum of the additional expenditure = 1160 + 4400
Sum of the additional expenditure = $5,560
Cost of the land = Cash paid + cost of demolition + Additional expenditure - salvage
Cost of the land = 79000 + 8000 + 5560 - 1660
Cost of the land = $90,900
Answer:
Amount to be reported as the cost of the land = $ 91,400
Step-by-step explanation:
Payment of Real Estate= $ 79,000
Building Demolished $ 8000
Gains on Sale of materials = ($1660)
Attorney’s fee for work concerning the land purchase, $1160
Broker's fee $4,400
Amount to be reported as the cost of the land = $ 91,400
Broker's fee is included in the purchase of land . Gains on the sale of salvaged materials is deducted from the cost of land because it is of the building demolished. Architect's fee is not also included in the cost of land but in the construction costs.
Which triangle is congruence postulate can be used to prove that
Answer:
HL
Step-by-step explanation:
Both triangles are right triangles as shown by the right angle marks in the figure.
Two corresponding legs are congruent as shown.
The diagonal is congruent to itself, and it is the hypotenuse of both right triangles.
Answer: HL
A pile of earth removed from an excavation is a cone measuring 12 ft high and 30 ft across its base. How many trips will it take to haul away the
earth using a dump truck with a capacity of 9 cubic yards?
trips =
Answer:
12 trips
Step-by-step explanation:
Given;
Dimension of cone shapef pile of earth;
height h = 12 ft = 4 yards
diameter d = 30 ft = 10 yards
radius r = d/2 = 10/2 = 5 yards
The volume of a cone V;
V = (1/3)πr^2 h
Substituting the given values;
V = (1/3) ×π × 5^2 × 4 cubic yards
V = 104.72 cubic yards
Given that a dump truck have a capacity of 9 cubic yards.
Vc = 9 cubic yards
Number of trips it will take is;
N = Volume of earth pile/truck capacity
N = V/Vc
Substituting the values;
N = 104.72/9
N = 11.64
N ≈ 12 trips
Therefore, the truck will make 12 trips
A certain disease only affects men 20 years of age or older. The chart shows the probability that a man with the disease falls in the given age group. What is the probability that a randomly selected man with the disease is not between the ages of 55 and 64
Answer:
0.68
Explanation:
The question is incomplete without the tables. Find attached the table used in solving the question.
group 20-24 25-34 35-44 45-54 55-64 65-74 75+ respectively
Probability 0.004 0.006 0.14 0.29 0.32 0.17 respectively
This is a probability of complementary events. The sum of the two complementary events = 1
Hence, the probability of selecting a man with the disease that is not between the ages of 55 and 64 + the probability of selecting a man with the disease that is between the ages of 55 and 64 = 1
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1- probability of selecting a man with the disease is between the ages of 55 and 64
Let Pr(between 55 and 74) = probability of selecting a man with the disease is between the ages of 55 and 64
From the table, Pr(between 55 and 74) = 0.32
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 1 - 0.32
The probability of selecting a man with the disease is not between the ages of 55 and 64 = 0.68
What is the value of -2(5) + 3?
Answer:
-2 (5) + 3
- 10 + 3
= -7
You are a state inspector for the Division of Weights and Measures. Your responsibility is to be sure the net weight found on all containers is correctly reflected on the label (note: the label is a claim). You are inspecting ABC Company who makes dry dog food in boxes and bags. The boxes you are checking indicate a net mean weight of 32 ounces. You check a sample of 200 boxes and found the average content to be 31.7 ounces. The standard deviation allowed for this type of product is 2.2 ounces. Can you conclude at a .02 level of significance that the boxes of dog food are being under filled
Answer:
No. There is not enough evidence to support the claim that the boxes of dog food are being under filled (P-vaue=0.027).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the boxes of dog food are being under filled.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=32\\\\H_a:\mu< 32[/tex]
The significance level is 0.02.
The sample has a size n=200.
The sample mean is M=31.7.
The standard deviation of the population is known and has a value of σ=2.2.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2.2}{\sqrt{200}}=0.156[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{31.7-32}{0.156}=\dfrac{-0.3}{0.156}=-1.928[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.928)=0.027[/tex]
As the P-value (0.027) is bigger than the significance level (0.02), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the boxes of dog food are being under filled.
The number of points that Shira scored each basketball game so far this season is shown on the dot plot. A number line going from 1 to 13. 2 dots are above 2. 1 dot is above 3. 1 dot is above 5. 2 dots are above 7. 3 dots are above 9. 6 dots are above 11. 1 dot is above 12. Which statement must be true according to the dot plot?
The according to the dot plot, the true statement is: the data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
What is Left-Skewed Data Distribution?A data distribution that is left-skewed is negatively skewed. This means that the long tail goes in the negative direction of the number line, with most of the values being concentrated on the right side.
The dot plot given is left-skewed, which means it is negatively-skewed.
Therefore, the according to the dot plot, the true statement is:
The data is left-skewed and shows Shira never scored fewer than 2 points or more than 12 points in a game
Learn more about left-skewed data on:
https://brainly.com/question/3252860
Answer:
c
The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
Step-by-step explanation:
swag
Joann's entire office is moving to a new location. She is helping to fill two moving vans with boxes. The large van can hold up to 15 boxes. The large van can hold up to 25 boxes. There are 800 boxes that must be moved. How many trips will the two vans need to take to transport all of the boxes to the new location?
Answer:
20 trips
Step-by-step explanation:
How many arrivals were much more delayed than others (i.e., positive outliers with z-score of time difference > 3)? (e) How many flights arrived much earlier than scheduled compared to others (i.e., negative outliers with z-score of time difference < -3)?
Answer:
d) 0.135% of total arrivals were much more delayed than others.
e) 0.135% of total flights arrived much earlier than scheduled compared to others.
Step-by-step explanation:
With the question not totally complete, we will solve the available parts as well as possible.
d) How many arrivals were much more delayed than others (i.e., positive outliers with z-score of time difference > 3)?
P(z > 3)
Using the normal distribution table
P(z > 3) = 1 - P(z ≤ 3) = 1 - 0.99865 = 0.00135 = 0.135% of total arrivals were much more delayed than others.
e) How many flights arrived much earlier than scheduled compared to others (i.e., negative outliers with z-score of time difference < -3)?
P(z < -3)
Using the normal distribution table
P(z < -3) = 0.00135 = 0.135% of total flights arrived much earlier than scheduled compared to others.
Hope this Helps!!!
Compare 2/6 and 5/8 using benchmark number. Which number can you use to compare these fraction
Answer:
5/8 is about 1/2. 2/6 is about 0.
Step-by-step explanation: 2/6 is about 0 because 2 is close to 0. If the numerator is close to 0 and the denominator is not close to 0 then the benchmark is going to be 0. If the numerator is about half of the denominator then the benchmark is going to be 1/2. If the numerator and denominator is close to each other than the benchmark is going to be 1.
If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem. (x + 2)(x + 60) (x – 2)(x – 60) (x – 10)(x + 2)(x + 6) (x + 10)(x – 2)(x – 6)
Answer:
Step-by-step explanation:
A
All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,
⇒ (x - 10) (x + 6) (x + 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = x³ - 2x² - 68x - 120
Here, We have;
⇒ f (-2) = 0
Hence, This function have a factor (x + 2).
Now, After divide the function f (x) = x³ - 2x² - 68x - 120 by (x + 2), we get;
⇒ ( x³ - 2x² - 68x - 120 ) ÷ (x + 2)
⇒ x² - 4x - 60
⇒ (x - 10) (x + 6)
Hence, All the factors of the function f (x) = x³ - 2x² - 68x - 120 are,
⇒ (x - 10) (x + 6) (x + 2)
Learn more about the mathematical expression visit:
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#SPJ2
The complete question is this,
If f(–2) = 0, what are all the factors of the function f (x) = x cubed minus 2 x squared minus 68 x minus 120? Use the Remainder Theorem. (x + 2)(x + 60) (x – 2)(x – 60) (x – 10)(x + 2)(x + 6) (x + 10)(x – 2)(x – 6)
Angle θ is in standard position and ( 4 , 4 ) is a point on the terminal side of θ. What is the exact value of sec θ sec 0 in simplest form with a rational denominator?
Answer:
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Angle θ is in standard position and (4,4) is a point on the terminal side of θ.
[tex]\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}[/tex]
Now, secant is the inverse of cosine.
Therefore:
[tex]\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}[/tex]
Antonio has a CD-player that holds six CDs. He puts six different
CDs in the player and the CD player randomly plays a song from
any of the CDs. What is the probability that the CD player will
play the first song from the first CD and the first song from the
sixth CD?
Answer:
1/6
Step-by-step explanation:
There are 6 CD
P( song from 6th ) = number of CD's that are 6th/ total
= 1/6
A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 21 newly graduated law students. Their scores give a sample standard deviation of 68 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60.
(a) What is the level of significance?
(b) Find the value of the chi-square statistic for the sample. (Use 2 decimal places.) What are the degrees of freedom?
Answer:
Step-by-step explanation:
From the information given :
The null hypothesis [tex]H_o : \sigma = 60[/tex]
The alternative hypothesis [tex]Ha : \sigma \neq 60[/tex]
Given that:
the sample size n = 21
sample standard deviation s = 68
population standard deviation σ = 60
a) The level of significance [tex]\alpha =0.01[/tex]
b) The chi-square statistics can be calculated as:
[tex]\bar X = \dfrac{(n-1)s^2}{\sigma^2}[/tex]
[tex]\bar X = \dfrac{(21-1)68^2}{60^2}[/tex]
[tex]\bar X = \dfrac{(20)4624}{3600}[/tex]
[tex]\bar X = 25.69[/tex]
The degree of freedom is :
= n - 1
= 21 - 1
= 20
What is the volume of the sphere in the diagram? with a diameter of 3
Answer:
Given diameter: r = d / 2 , Given area: r = √[A / (4 * π)] , Given volume: r = ³√[3 * V / (4 * π)] , Given surface to volume ratio: r = 3 / (A/V) .
Step-by-step explanation:
So, do that!
Answer:
36pi
Step-by-step explanation:
i already did it and it was correct.