There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
We have,
Based on a sample of 217 subjects, 53 of them developed nausea.
To test this claim, a hypothesis test is conducted using a significance level of 0.01.
The null hypothesis, denoted as H0, assumes that the true proportion of users who develop nausea is less than or equal to 20%, while the alternative hypothesis, denoted as Ha, assumes that the true proportion is greater than 20%.
If the test statistic, calculated from the sample data, falls in the rejection region, which is determined based on the significance level and the degrees of freedom, then the null hypothesis is rejected, and it can be concluded that there is sufficient evidence to support the alternative hypothesis.
In this case,
If the test statistic falls in the rejection region, it means that the evidence suggests that more than 20% of users of the pain drug develop nausea, and the claim that less than or equal to 20% of users develop nausea is not supported by the data.
Thus,
There is not enough evidence to support the claim that more than 20% of users develop nausea at a 0.01 significance level.
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Pls tell me just the answer
The domain of the function g(x) is given as follows:
B. All values of x such that x ≥ 0.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
The function for this problem is defined as follows:
[tex]g(x) = \sqrt{8x}[/tex]
The square root function assumes values that are greater than or equals to zero, hence the domain of the function is obtained as follows:
8x ≥ 0.
x ≥ 0.
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In a certain board game, a 12-sided number cube showing numbers 1-12 is rolled. In this game, a number cube must be rolled until a number 9 or higher appears.
Is it appropriate to use the geometric distribution to calculate probabilities in this situation?
O Yes, the geometric distribution is appropriate.
O No, since each trial is not independent of the other trials.
O No, because it is not looking for the first occurrence of success.
O No, since a success and failure on each trial cannot be defined.
Answer:
THE ANSWER IS (A)
Step-by-step explanation:
BECAUSE I JUST DID AT
The chief physician at a hospital wants to analyze the amount of time it takes two doctors to complete a particular surgical procedure. A sample of 35 of these procedures performed by Dr. McCoy were completed in a mean time of 60.3 minutes with a standard deviation of 4.3 minutes. A sample of 41 these procedures performed by Dr. Turk were completed in a mean time of 61.2 minutes with a standard deviation of 4.7 minutes. A claim is made that the mean time for Dr. McCoy (
ц1) is less than the mean time for Dr. Turk ц2
).
For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t =" before your answers. Round each of your answers to 3 places after the decimal point.
(a) Calculate the value of the test statistic used in this test.
Test statistic's value =
(b) Use your calculator to find the P-value of this test.
P-value =
Submit QuestionQuestion 9
The value of the test statistic used in this test is t = -2.168 and the P-value of this test is P-value is 0.034
To test whether the mean time for Dr. McCoy is different from the mean time for Dr. Turk, we can use a two-sample t-test with unequal variances. The test statistic for this test is given by:
t = (X₁ - X₂) / √(s₁²/n₁ + s₂²/n₂)
where X₁ and X₂ are the sample means, s₁ and s₂ are the sample standard deviations, and n₁ and n₂ are the sample sizes.
Plugging in the given values, we get:
t = (78 - 78.7) / √(2.3²/38 + 4.1²/33)
= -2.168
Therefore, the value of the test statistic used in this test is t = -2.168.
b) To find the P-value of this test, we need to use a t-distribution with degrees of freedom given by:
df = (s₁²/n₁+ s₂²/n₂)² / [ (s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1) ]
Plugging in the given values, we get:
df = (2.3²/38 + 4.1²/33)² / [ (2.3²/38)²/37 + (4.1²/33)²/32 ] ≈ 65.385
Using a t-distribution table or a calculator with t-distribution function, we find that the P-value for a two-tailed test with t = -2.168 and df = 65.385 is approximately 0.034.
Therefore, the P-value of this test is P-value = 0.034
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Help please 3rd times a charm
The amount that you would save in annual fuel expenses would be $9, 333. 32
The amount that you would have saved over the five years would be $52, 854.63
How to find the fuel savings ?The amount saved in fuel when using the hybrid is:
= Fuel usage by SUV - Fuel usage by Hybrid
= ( 30, 000 / 9 x 4 ) - ( 30, 000 / 30 x 4 )
= $9, 333.32
If you saved this amount as an annuity, it would come out to:
= ( 9, 333.32 / 12 ) x [ ( 1 + 0. 004333 ) ^ ( 12 x 5 ) - 1 ] / 0. 004333
= 777. 78 x 0. 2957 / 0. 004333
= $ 52, 854.63
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Two forces act at a point in the plane. the angles between the two forces are given. fidn the magnitude of the resultant force
The resultant between the two vectors is 21.17 lb
What is parallelogram law of vectors?Parallelogram law of vectors says that if two vectors acts on a point, the resultant of this vectors can be represented by the diagonal from the point of intersection.
R² = x²+y2+2xycos (tetha)
where x and y are the vectors
When x = 20.6 and y = 17.4
R² = 20.6²+17.4²+2(20.6)(17.4)cos 112.9
R² = 727.12+716.88cos 112.9
R² = 727.12 -278.95
R² = 448.17
R = √448.17
R = 21.17 lb
Therefore the resultant is 21.17lb
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(06.02 HC)
A person with type A blood can donate red blood cells to people with type A or type AB blood. About 31% of the U.S. population has type A blood. University High held a blood drive where 50 students donated blood.
Part A: What is the probability that exactly 17 of the students had type A blood? (5 points)
Part B: What is the probability that at least 17 of the students had type A blood? (5 points)
A) A probability of approximately 0.128 or 12.8% that exactly 17 students had type A blood.
B) There is a 93.0% chance that at least 17 students had type A blood in the blood drive held at University High.
Part A: To find the probability that exactly 17 of the 50 students had type A blood, we first need to calculate the probability of a single student having type A blood. Since about 31% of the U.S. population has type A blood, the probability of a student at University High having type A blood is also 31%.
We can use the binomial distribution formula to calculate the probability of exactly 17 students having type A blood in a sample of 50 students. The formula is:
P(X = x) = (n choose k) x pˣ x (1-p)ⁿ⁻ˣ
where P(X = x) is the probability of exactly x successes, n is the sample size (in this case, 50), p is the probability of success (31% or 0.31), (n choose k) is the binomial coefficient or the number of ways to choose k successes from n trials.
Plugging in the values, we get:
P(X = 17) = (50 choose 17) x 0.31¹⁷ x (1-0.31)⁵⁰⁻¹⁷ = 0.128 or 12.8%
Part B: To find the probability that at least 17 of the 50 students had type A blood, we need to calculate the probability of 17, 18, 19,...50 students having type A blood and then add those probabilities together. This is because "at least 17" means 17 or more students, so we need to consider all possibilities from 17 to 50.
Therefore, the probability of at least 17 students having type A blood is:
P(X >= 17) = 1 - P(X < 17)
where P(X < 17) is the probability of less than 17 students having type A blood. We can use the binomial distribution formula to calculate this probability as well:
P(X < 17) = P(X = 0) + P(X = 1) + ... + P(X = 16)
Again, this can be a tedious task to calculate manually. Instead, we can use a binomial calculator or a software program to find this probability.
Using a binomial, we find that the probability of less than 17 students having type A blood is approximately 0.070 or 7.0%. Therefore, the probability of at least 17 students having type A blood is:
P(X >= 17) = 1 - P(X < 17) = 1 - 0.070 = 0.930 or 93.0%
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What is the volume of this figure?
4, 8, 6, 2, 3
6x3 − 4x2 + 11, x + 3
The quotient of the long division of the polynomial (6x³ - 4x² + 11)/(x+3) is 6x² - 22x + 66.
What are the quotient of the polynomial?The quotient of the polynomial divided by a factor of x + 3 is determined by applying long division method as shown below;
6x³ - 4x² + 11 ÷ x + 3
6x² - 22x + 66
------------------------
x + 3 √ 6x³ - 4x² + 11
- (6x³ + 18x²)
-------------------------
-22x² + 11
- (-22x² - 66x)
-----------------------------
66x + 11
- (66x + 198)
---------------------------------
-187
Thus, the quotient of the long division of the polynomial is obtained as 6x² - 22x + 66.
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Find the quotient of the polynomial using long division
6x3 − 4x2 + 11/x + 3
The length of a picture frame is 7 inches more than the width. For what values of x is the perimeter of the picture frame greater than 150 inches?
Answers for these test question, thank you
The missing lengths of the following two triangles:
Case 1: x = 50 km
Case 2: x = 40 km
Case 3: Obtuse
Case 4: Acute
Case 5: Right
Case 6: m = 16, n = 8√3
Case 7: x = 3√2, y = 3
How to find the length of missing sides in a triangle
In this problem we must determine all missing lenghts in a triangle, this can be done by law of cosine:
x² = a² + b² - 2 · a · b · cos X
Where X is the angle opposite to side x.
Now we proceed to determine the missing lengths of the following two triangles:
Case 1
x = √[(14 km)² + (48 km)² - 2 · (14 km) · (48 km) · cos 90°]
x = 50 km
Case 2
x = √[(24 km)² + (32 km)² - 2 · (24 km) · (32 km) · cos 90°]
x = 40 km
In addition, we can determine if any triangle is acute, obtuse and right also by law of cosine:
cos X = - (x² - a² - b²) / (2 · a · b)
Case 3
cos X = - [(18 in)² - (12 in)² - (9 in)²] / [2 · (12 in) · (9 in)]
cos X = - 0.458 (Obtuse)
Case 4
cos X = - [(15 ft)² - (12 in)² - (14 in)²] / [2 · (12 in) · (14 in)]
cos X = 0.342 (Acute)
Case 5
cos X = - [(5 ft)² - (3 in)² - (4 in)²] / [2 · (3 in) · (4 in)]
cos X = 0 (Right)
Finaly, we determine the missing lengths of two right triangles by trigonometric functions:
sin θ = y / r
cos θ = x / r
tan θ = y / x
Now we find the missing lengths:
Case 6
m = 8 / cos 60°
m = 16
n = 8 · tan 60°
n = 8√3
Case 7
x = 3 / sin 45°
x = 3√2
y = 3 / tan 45°
y = 3
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and P (more than 2)
The probability P (4) and of getting more than 2 questions correct are 0.017 and 0.113 respectively.
The number of ways the student can answer each question is 4 (since there are 4 choices), so the probability of getting any one question correct by guessing is 1/4, and the probability of getting any one question wrong by guessing is 3/4.
We can use the binomial probability formula to find the probability of getting a specific number of questions correct out of the 10:
[tex]P(X = k) = ( ^kC _n) * p^k * (1-p)^(n-k)[/tex]
a) P(4) represents the probability of getting exactly 4 questions correct out of 10.
[tex]P(X = 4) = (^{10}C_4) * (1/4)^4 * (3/4)^{(10-4)} \approx 0.017[/tex]
So the probability of getting exactly 4 questions correct is approximately 0.017.
b) P(more than 2) represents the probability of getting 3, 4, 5, ..., or 10 questions correct out of 10. We can use the complement rule to find this probability:
P(more than 2) = 1 - P(X ≤ 2)
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\\= (^{10} C_0) * (1/4)^0 * (3/4)^{10}+ (^{10} C_1) * (1/4)^1 * (3/4)^9+ (^{10} C_2) * (1/4)^2 * (3/4)^8\\\approx 0.887[/tex]
So,
P(more than 2) = 1 - P(X ≤ 2) ≈ 1 - 0.887 ≈ 0.113
Therefore, the probability of getting more than 2 questions correct is approximately 0.113.
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David has twenty dimes (d) and quarters (q). These coins total $2.75. How many of each type of coin does he have? • Write a systems of equations to model this scenario. • Show your work and state how many of each type of coin he has. Enter your systems of equations, your work, and your statement of how many of each type coin David has below.
David has 15 dimes and 5 quarters.
Given that, David has twenty dimes (d) and quarters (q). These coins total $2.75.
Establishing the system of equations,
d + q = 20
d = 20 - q.............(i)
0.1d + 0.25q = 2.75..........(ii)
Put eq(i) in eq(ii),
0.1(20-q)+0.25q = 2.75
2-0.1q + 0.25q = 2.75
0.15q = 0.75
q = 5
Put q = 5 in eq(i)
d = 20-5
d = 15
Hence, David has 15 dimes and 5 quarters.
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Manuel bought a car for 65% of the original price of $7,000. How much did he pay for the car
Manuel bought a car for 65% (percentage) of the original price of $7,000, he must have paid $4,550 for the car.
What is the percentage?The percentage is a number or ratio that represents a fraction of a whole number or the sum of ratios.
The percentage is computed by dividing one number by another and multiplying the result by 100.
The original price of the car = $7,000
The discount factor = 65% (1 - 35%) or 0.65
The discounted price = $4,550 ($7,000 x 0.65)
Thus, by implication, for receiving a discount of 35% (100% - 65%), Manuel paid $4,550 for the car.
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What is the x of a 68⁰? I’m in 8th grade learning about angels and basically adding them .
The complement and the supplement of an angle of 68º are given as follows:
Complement: 22º.Supplement: 112º.How to obtain the complement of an angle?When two angles are complementary, the sum of the measures of the angles is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.When two angles are supplementary, the sum of the measures of the angles is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.Hence the complement and the supplement of an angle of 68º are obtained as follows:
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José has a wedge-shaped piece of wood as shown in the diagram. José plans to paint the piece
needs.
3 in.
4 in.
5 in.
8 in.
Answer:
E. 108 in.²
Step-by-step explanation:
The piece of wood has the shape of a triangular prism.
SA = lateral area + area of the bases
SA = perimeter × height + 2 × bh/2
SA = (5 + 3 + 4) in. × 8 in. + 3 in. × 4 in.
SA = 108 in.²
Hurry up please
State the domain and range and tell if the graph is a function yes or no
What’s the domain and range?
The graph is a function: yes
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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a rectangular prism has 312 cubes. The cubes have an edge length of 1/5 cm. What is the volume of this rectangular prism?
Answer:
[tex] {( \frac{1}{5}) }^{3} (312) = \frac{312}{125} = 2.496[/tex]
The volume of this rectangular prism is 2.496 cubic centimeters.
The volume of the rectangular prism is 2.496 cubic centimeters.
If the rectangular prism has 312 cubes with an edge length of 1/5 cm, we may calculate the total volume by multiplying the number of cubes by the volume of each cube.
V = x3 gives the volume of a cube with edge length x. Because the edge length, in this case, is 1/5 cm, the volume of each cube is (1/5)3 = 1/125 cm3.
We multiply the number of cubes by the volume of each cube to determine the volume of the rectangular prism:
312 cubes (1/125 cm3/cube) = 2.496cm3 volume
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Round to the nearest tenth, then find the sum. 35.26 + 8.32 + 6.78 i will give 12 points pleas help me in in a test
Answer:
Step-by-step explanation:
35.26 rounded to 35.3
8.32 rounded to 8.3
6.78 rounded to 6.8
35.3 + 8.3 = 43.6
43.6 + 6.8 = 50.4
The answer is 50.4.
39.26 rounds to 35.3
8.32 rounds to 8.3
6.78 rounds to 6.8
When you add them together, you get 50.4.
Solve for a.
60°
a
60°
a = [? ]°
The value of a in the equation 60°a = [? ]° is dependent on the value of [? ].
Explanation:
To solve for a in the equation 60°a = [? ]°, we need to isolate a on one side of the equation. We can do this by dividing both sides of the equation by 60°:
60°a / 60° = [? ]° / 60°
This simplifies to:
a = [? ]° / 60°
Since we don't have the value of [? ]°, we cannot determine the exact value of a. However, we can simplify the expression by canceling out the ° units:
a = [? ] / 60
Therefore, the value of a is dependent on the value of [? ].
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when its comes to interest,most CDs will allow which of the following options?
a. Unlimited withdraws of interest
b. Periodic interest payout
c. loans against principal
d. Withdrawal of principal
When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.
A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.
However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.
While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.
Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.
So, correct option is B.
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Determine each lengths in right triangle ABC.
BD———>
AB———>
The missing parts of the triangle are
BD = 8
AD = 8 sqrt(2)
How to find the missing partsThe missing part BD of the figure is solved using similar triangles
The expression is as follows
h / 8 = 8 / h
h^2 = 8 x 8
h^2 = 64
h sqrt = (64)
h = 8
Solving for AB we use Pythagoras theorem
AB^2 = h^2 + 8^2
AB^2 = 8^2 + 8^2
AB = sqrt(64 + 64)
AB = sqrt (128)
AB = 8 sqrt (2)
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X
-2
-1
01
2
3
-2
0
7
What is the rate of change for the interval between 0
and 2 for the quadratic equation as f(x)=2x²+x-3
represented in the table?
O
5
10
The rate of change for the interval between 0 and 2 for the quadratic equation is 10.
What is the change in interval of the quadratic equation?
A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms that are raised to the power of two.
The general form is;
ax² + bx + c = 0
Where;
x is the variablea, b, and c are constantsThe rate of change for the interval between 0 and 2 for the quadratic equation is calculated as;
f(2) - f(0) = 7 - (-3)
= 7 + 3
= 10
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Solve the following for θ, in radians, where 0≤θ<2π.
−7cos2(θ)+3cos(θ)+7=0
Select all that apply:
1.77
0.48
1.4
3.77
2.99
2.51
Answer:3.77
2.51 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
-7u^2 + 3u + 7 = 0
Multiplying both sides by -1, we get:
7u^2 - 3u - 7 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 7, b = -3, and c = -7. Substituting these values, we get:
u = (3 ± sqrt(9 + 196)) / 14
u = (3 ± 5sqrt(5)) / 14
Therefore, either:
b) The Median and Mode of the following wage distribution are known to be $33.5 and $34 respectively. Three frequency values from the table are, however, missing. Find the missing values. Wages (in $) 0-10 10- 20 20 - 30 30 - 40 40-50 50 - 60 60-70 Frequencies (f) 10 10 ? ? ? 6 4 230
The frequencies based on the information are are 100, 40, and 6.
How to explain the frequencyIn the formula of the median, we have to calculate cumulative frequencies and have to use cumulative frequency of the interval previous to the median class. Also, in the formula of mode, frequencies are used and not the cumulative frequencies.
140 - y = 100
y = 40
substituting y and x in equation 1 is:
x + y + z = 146
100 + 40 + z = 146
z = 6
Therefore, the missing frequencies are 100, 40, and 6.
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a principal data about the distance, in miles that his teachers and bus drivers live from the school, the box plots below show these data. based on the box plots, which statement is true?
Option C is the true statement from the data that has been gathered and shown in the image
How to get the true statementThe interquartile range exemplifies the "dispersion" or width of a set [1] by determining the difference between the top quartile (the 25% highest) and lower quartile (the 25% lowest). In reference to the provided picture:
- The bus drivers' interquartile range is 10, represented by subtracting their distance's lowest point (10) from the highest (20).
20 - 10 = 20
- Similarly, the teachers' interquartile range is 15, which stems from finding the difference between their lowest distance (15) and highest distance (30).
30 - 15 = 15
Therefore, comparing both ranges reflects that the bus drivers have an interquartile range of distances that is 5 miles smaller than the one for the teachers. Consequently, we opt for option C.
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PLEASE HELP HURRY FAST PLEASE THANK YOU!
4. Find the rational roots of x^4+5x^3+7x^2-3x-10=0
A. -2,1
B. 2,1
C. -2,-1
D. 2,-1
5. Find all the zeros of the equation 3x^2-4=-x^4
A. 1,2i
B. -1,-2i
C. 1,-1,2i,-2i,0
D. 1,-1,2i,-2i
6. What is a polynomial function in standard form with zeros 1,2,-2, and -3?
A. x^4+2x^3+7x^2-8x+12
B. x^4+2x^3-7x^2-8x+12
C. x^4+2x^3-7x^2+8x+12
D. x^4+2x^3+7x^2+8x+12
7. Which correctly describes the roots of the following cubic question.
x^3-3x^2+4x-12=0
A. three real roots, each with a different value
B. one real root and two complex roots
C. three real roots, two of which are equal in value
D. two real roots and one complex root
8. What is the solution of 5^3x=900. Round your answer to the nearest hundredth
A. 1.24
B. 1.41
C. 4.23
D. 0.69
9. x= 1,2,4,6,8,10,11 y= 0,-1,0,4,8,9,8 <--- Table is right here
Which of the following questions best represents the regression line for the data given in the table above.
A. y=x+2
B. y=2x-2
C. y=-x-2
D. y=x-2
10. Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation, write a function to model it. ---> Table x= 2,5,12,20 y= 30,12,5,3
A. direct variation; y=15x
B. inverse variation; y=60/x
C. direct variation; y=2x+2
D. neither
11. A drama club is planning a bus trip to New York City to see a Broadway play. the cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 55 people go on the trip. Round your answer to the nearest cent if necessary
A. $48.00
B. $12.50
C. $24.00
D. $33.00
12. What is the simpler form of the radical expression? 4sqrt2401x^12y^16
A. 49|x^9|y^16
B. 49x^9|y^16|
C. 7|x^3|y^4
D. 7x^3|y^4|
13. Simplify. 125^1/3
A. 125
B. 5
C. 25
D. sqrt125
14. Graph the function. y=sqrtx+3
15. An initial population of 293 quail increases at an annual rate of 6%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?
A. f(x)=(293 x 1.06)^x; 930
B. f(x)=293(0.06)^x; 379
C. f(x)=293(1.06)^x; 370
D. f(x)=293(6)^x; 190
16. Evaluate the logarithm
log3 2187
A. 5
B. 6
C. 7
D. -7
17. Estimate the value of the logarithm to the nearest tenth
log4 22
A. 2.2
B. 0.4
C. -0.7
D. 3.2
18. Solve 1n 4 + 1n (3x)=2. Round your answer to the nearest hundredth
A. 1.13
B. 0.18
C. 1.41
D. 0.62
19. Write an equation for the translation of y= 4/x that has the asymptotes x=7 and y=6.
A. y= 4/x-6 +7
B. y= 4/x+7 +6
C. y= 4/x-7 +6
D. y= 4/x+6 +7
20. What is the graph of the rational function?
y=(x-5)(x-3)/(x+4)(x-4)
21. What are the points of discontinuity?
y=(x-3)/x^2-12x+27
A. x=4,x=9,x=1
B. x=-9,x=-3
C. x=-9,x=-3,x=-1
D. x=9,x=3
22. What is the quotient 6-x/x^2+2x-3/x^2-4x-12/x^2+4x+3 in simplified form? State any restrictions on the variable.
23. Simplify the complex fraction x+3/ 1/x+1/x+3
A. x^2/2x+3
B. x^2/2x
C. x^2/x+3
D. x^2+2x+3/2x+3
24. Simplify the difference
x^2-x-56/x^2+6x-7 - x^2+2x-15/x^2+9x+20
A. x-71/(x-1)(x+4)
B. 2x^2-8x-29/(x-1)(x+4)
C. -8x-35/(x-1)(x+4)
D. -35/(x-1)(x+4)
25. Solve the equation 1/x-3+1/x+5=1/3
A. x=1,x=7
B. x=3,x=-5
C. x=-3,x=1
D. x=-3,x=7
Answer:Find the rational roots of x^4+5x^3+7x^2-3x-10=0
To find the rational roots of a polynomial, we use the Rational Root Theorem, which states that if a polynomial has rational roots, then they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In this case, the constant term is -10, and the leading coefficient is 1. The factors of 10 are ±1, ±2, ±5, and ±10, and the factors of 1 are ±1. Therefore, the possible rational roots are:
±1, ±2, ±5, ±10
We can test each of these roots by synthetic division or long division to see if they are actually roots of the polynomial. After trying these roots, we find that only -2 and 1 are roots. Therefore, the answer is A. -2,1.
Find all the zeros of the equation 3x^2-4=-x^4
We can rewrite the equation as x^4+3x^2-4=0. To find the zeros of this equation, we can use the Rational Root Theorem as in the previous question, except that now the factors of the constant term -4 are ±1, ±2, and ±4. The factors of the leading coefficient 1 are ±1. Therefore, the possible rational roots are:
±1, ±2, ±4
Testing these roots, we find that the only roots are x=1, x=-1, x=2i, and x=-2i. Therefore, the answer is D. 1,-1,2i,-2i.
What is a polynomial function in standard form with zeros 1,2,-2, and -3?
If a polynomial has roots a, b, c, and d, then it can be written as (x-a)(x-b)(x-c)(x-d). To put it in standard form, we need to expand this expression:
(x-a)(x-b)(x-c)(x-d) = x^4 - (a+b+c+d)x^3 + (ab+ac+ad+bc+bd+cd)x^2 - (abc+abd+acd+bcd)x + abcd
Substituting the given values of a, b, c, and d, we get:
(x-1)(x-2)(x+2)(x+3) = x^4 + 2x^3 - 7x^2 - 8x + 12
Therefore, the answer is B. x^4+2x^3-7x^2-8x+12.
Which correctly describes the roots of the following cubic equation.
x^3-3x^2+4x-12=0
We can use the Rational Root Theorem again to find the possible rational roots of the polynomial. The factors of the constant term -12 are ±1, ±2, ±3, ±4, ±6, and ±12, and the factors of the leading coefficient 1 are ±1. Therefore, the possible rational roots are:
±1, ±2, ±3, ±4, ±6, ±12
Testing these roots, we find that none of them are roots of the polynomial. Therefore, the answer is B. one real root and two complex roots.
What is the solution of 5^3x=900. Round your answer to the nearest hundredth
We can solve for x by taking the logarithm of both sides with base 5:
log5(
Step-by-step explanation:
The answers to all parts are shown below.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
1. x⁴ + 5x³ + 7x² -3x - 10 = 0
= (x-1)(x+2)(x² + 4x + 5)
Thus, the rational roots are 1 and -2.
2. 3x² -4 = - x⁴
x⁴ + 3x² -4 = 0
(x-1)(x+1)(x² + 4) =0
Thus, the zeroes are 1, -1, -2i, +2i.
3. We can write the zeroes as
p(x)=(x-1)(x-2)(x+2)(x+3).
So, p(x) = x⁴ + 2x³ -7x² -8x +12
4. x³ -3x² +4x- 12=0
(x-3)(x²+4) =0
x= 3, -2i, 3i
5. x= 1,2,4,6,8,10,11
y= 0,-1,0,4,8,9,8
So, equation of line
(y- 0) = (-1-0)/(2-1)(x-1)
y = -1(x-1)
y + x +1=0
6. x= 2,5,12,20 and y= 30,12,5,3
k = 30/2
k = 15
So, the relationship is y= 15x.
7. cn = constant(k)
n= 44
then, c= 30/44 = 0.68
and, k = 44 x 0.68
k = 30
So, c = 1.5 dollars per person.
8. 125¹/³
= (5³)¹/³
= 5
9. y = 293(1.06)⁴ = 370
10. log₃ 2187
= log₃ 3⁷
= 7
11. log₄ 22
= 2.29
12 . y= 4/x
The new equation is y = 4/(x - 7) + 6.
13. (6-x)/ (x² + 2x - 3) / (x² -4x- 12)/ (²x² + 4x + 3)
= - (x+1)/ (x+1)(x+2)
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I NEED THIS NOW 40 POINTS!!!!!!
Question 1 Part C (4 points): Showing the steps of your work, factor the polynomial from part B completely.
18x^3 + 6x^2y - 9x^2 - 3xy
(I already know the answer: 3x(3x + y) (2x − 1) I just need the work on how to get to the answer)
The polynomial 18x^3 + 6x^2y - 9x^2 - 3xy when factored completely is (6x^2 - 3x)(3x + y)
Factoring the polynomial completely.From the question, we have the following parameters that can be used in our computation:
18x^3 + 6x^2y - 9x^2 - 3xy
Factoize the expression
So, we have
6x^2(3x + y) - 3x(3x + y)
Factor out 3x + y
So, we have
(6x^2 - 3x)(3x + y)
Hence, the solution is (6x^2 - 3x)(3x + y)
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As seen in the diagram below, Arun is building a walkway with a width of x feet to go around a swimming pool that measures 15 feet by 7 feet. If the total area of the pool and the walkway will be 713 square feet, how wide should the walkway be?
The walkway around the swimming pool should be 8 feet wide.
Calculating the width of the walkwayFrom the question, we are given:
Length of the pool (l) = 15 feet
Width of the pool (w) = 7 feet
width of walkway (X) = X feet
Total Area = Area of pool and walkway = 713 square feet
Let's derive equation for the pool and walkaway combined:
length of the pool and walkway = 15 + 2X [walkway is on both sides]
width of the pool and walkway = 7 + 2X
Total Area = (length x width) of the pool and walkway
713 = (15 + 2X) x (7 + 2X)
713 = 15(7 + 2X) + 2X(7 + 2X)
713 = 105 + 30X + 14X + 4X²
713 = 105 + 44X + 4X²
Rearrange the equation
4X² + 44X + 105 = 713
Collect like terms and express in a proper quadratic equation
4X² + 44X - 608 = 0
Dividing both sides by 4, we get
X² + 11X - 152 = 0
Solve this equation quadratically
X = [tex]\frac{-b \± \sqrt{b^{2} - 4ac}}{2a}[/tex]
where
a = 1
b = 11
c = -152
Plug in the value into the equation
X = [tex]\frac{-11 \± \sqrt{11^{2} - 4(1)(-152)}}{2(1)}[/tex]
X = [tex]\frac{-11 \± \sqrt{121 + 608}}{2(1)}[/tex]
X = [tex]\frac{-11 \± \sqrt{729}}{2}[/tex]
X = [tex]\frac{-11 \± 27}{2}[/tex]
X = [tex]\frac{-11 + 27}{2}[/tex] or [tex]\frac{-11 - 27}{2}[/tex]
X = [tex]\frac{16}{2}[/tex] or [tex]\frac{-38}{2}[/tex]
X = 8 or -19
But since the width of the walkway cannot be negative, the only valid solution is therefore:
X = 8
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A line has a slope of 3 and y-intercept of -4. Write its equation in slope- intercept form.
Answer:
y=mx + b
Step-by-step explanation:
y=3x-4
3 is the slope and -4 is the y intercept
Tell whether each table represent If it does, identify the constant of 1. X y 2 18 5 45 7 63
Yes, the table represents a proportional relationship.
The constant of proportionality is equal to 9.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using the data points contained in the table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 18/2 = 45/5 = 63/7
Constant of proportionality, k = 9.
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Complete Question:
Tell whether each table represent a proportional relationship. If it does, identify the constant of proportionality.
1. X y 2 18 5 45 7 63