The equation of the polynomial is f ( x ) = -13.5 ( x + 2 )²( x - 3 )
Given data ,
The equation of degree 3 polynomial function with real coefficients
And , zeros x = - 2 with multiplicity 2 and x = 3 with multiplicity 1
where function passes through the point (1, 54)
If a polynomial function has a zero x = a with multiplicity k, then the factor (x - a)^k appears in its factored form.
Therefore, a degree 3 polynomial function with zeros x = -2 with multiplicity 2 and x = 3 with multiplicity 1 can be written in factored form as:
f(x) = a(x + 2)²(x - 3)
where a is a constant factor. To find the value of a, we use the fact that the function passes through the point (1, 54):
f(1) = a(1 + 2)²(1 - 3) = 54
a(-1)²(-2) = 54
-4a = 54
Divide by -4 on both sides , we get
a = -13.5
Hence , the equation of the degree 3 polynomial function with the given zeros and passing through the point (1, 54) is f ( x ) = -13.5 ( x + 2 )²( x - 3 )
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PLS HELP I WILL MARK AS BRAINLIST IF SHOW WORK
4 Mr. Qureshi writes 4s = 56 and {13, 14, 15) on the board. Tell if each value in the
set is a solution of the equation. Show your work
The solution is: the value of s is:
s = 8
Explanation:
The initial equation is:
4s - 28 = 4
So, to solve for s, we can add 28 to both sides:
4s - 28 + 28 = 4 + 28
4s = 32
Finally, we can divide both sides by 4:
4s/4 = 32/4
s = 8
So, the value of s is 8
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complete question:
What is the value of s for the equation 4s-28=4
For the right triangle below, find sec exact (not decimal approximations):
p.s. No calculator allowed. IGNORE what I wrote.
The exact value of sec(θ) is 8√(39)/39.
Given information:
In a right triangle,
Perpendicular side = 5, Hypotenuse side = 8.
Then to find exact secθ:
We can use the definition of secant, which is the reciprocal of cosine:
sec(θ) = 1/cos(θ)
In a right triangle, the cosine of an angle is equal to the adjacent side length divided by the hypotenuse length. Therefore, we first need to find the length of the adjacent side of the angle θ.
Let's label the sides of the right triangle as follows:
the hypotenuse side is H, with a length of 8
the perpendicular side is P, with a length of 5
the base side (adjacent to the angle theta) is B
Using the Pythagorean theorem, we can find the length of the base side B:
B² + P² = H²
B² + 5² = 8²
B² + 25 = 64
B² = 64 - 25
B² = 39
B = √(39)
Now we can use the cosine function to find cos(theta):
cos(θ) = B/H
cos(θ) = √(39)/8
Finally, we can find sec(θ) by taking the reciprocal of cos(θ):
sec(θ) = 1/cos(θ)
sec(θ) = 8/√(39) x √(39)/√(39)
sec(θ) = 8√(39)/39
Therefore, the exact value of sec(θ) is 8√(39)/39. This is the simplified form of the expression and cannot be further reduced because the square root of 39 is not a perfect square.
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Pls help me I will mark the brainliest
The most specific correct name for this figure is a trapezoid.
A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.
An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.
A parallelogram has opposite sides parallel. >>> This figure is not a parallelogram.
A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.
A spinner with four equal sections of blue, green, yellow, and red is spun 100 times. It lands on blue 14 times, green 10 ten times, yellow 8 times, and red 68 times. What is the relative frequency of landing on green? Express your answer as a percent.
IS is tangent to circle O at point I. If m∠=111∘m∠HIS=111 ∘ , find m⌢m IZH⌢
Answer:
222
Step-by-step explanation:
111 * 2
alternate segment theorem
gathmath
IZH = 2 * HIS
Mario buys a shirt for $28.95 and a pair of socks for $4.29. He gives the clerk at the store two 20 bills. How much change should Mario receive?
The revenue generated by a company manufacturing lawn mowers is R= -0.5x^2+91x, where x represents the number of mowers produced. The cost to produce the mowers is C= 38x+300,where x is the number of mowers produced.
Find the profit polynomial (Hint: Profit = Revenue - Cost) that describes the total profit generated by the company manufacturing lawn mowers based on the number of mowers produced.
--------------------------
Give the profit earned if 53 mowers are sold. ------------
add work please
The profit earned if 53 mowers are sold is $1104.50.
To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = (-0.5x^2 + 91x) - (38x + 300)
P(x) = -0.5x^2 + 53x - 300
So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.
To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:
P(53) = -0.5(53)^2 + 53(53) - 300
P(53) = -0.5(2809) + 2809 - 300
P(53) = -1404.5 + 2509
P(53) = 1104.5
Therefore, the profit earned if 53 mowers are sold is $1104.50.
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COVID Vaccines As of March 2022, in the United States, 127 million people aged 12 years and older have been vaccinated for COVID (the first full sequence plus one booster) and 38 million have not (Source: How to Compare COVID Deaths for Vaccinated and Unvaccinated People - Scientific American). For those vaccinated, there have been an average of 261 deaths per week and for those who have not, there have been an average of 383 deaths per week. Assume that those data are correct for the past week (so the proportion of vaccinated deaths is 261/127,000,000 and unvaccinated is 383/38,000,000).
1. Which group can be considered the placebo group? Why is it important to have a placebo group? What other factors are important in designing a study like this?
2. What are the conditions that must be met to perform a hypothesis test comparing the vaccinated to the placebo group? Were they met?
3. Regardless of your answer in Part 2, test the hypothesis that the vaccine was effective in reducing the number of deaths from COVID. Use = 0.01 and make sure you state your null and alternative hypotheses and write a sentence stating your conclusion
This question involves statistical analysis and hypothesis testing, and the provided information does not contain all the necessary information to answer the questions fully and accurately. However, I can provide some general guidance on hypothesis testing and the factors to consider when designing a study.
It is not appropriate to refer to the vaccinated group as the placebo group. A placebo group is a group that receives a treatment that is inactive or does not contain the active ingredient being tested, while the treatment group receives the active treatment. In the case of the COVID vaccine, the treatment group is the group that received the vaccine, while the control group would be the group that did not receive the vaccine. In this scenario, it is important to have a control group to compare the effectiveness of the vaccine to the effectiveness of no intervention.
Other important factors to consider when designing a study include sample size, randomization, blinding, and the choice of outcome measures. These factors help to reduce bias and ensure that the results are generalizable to the target population.
To perform a hypothesis test comparing the vaccinated group to the control group, the following conditions must typically be met: the samples are independent, the samples are randomly selected from their respective populations, and the samples are normally distributed (or the sample size is large enough, typically n > 30). Additionally, the variances of the two populations should be assumed to be equal unless there is strong evidence to the contrary.
Assuming the conditions for performing a hypothesis test are met, the null hypothesis (H0) is that there is no difference in the number of deaths from COVID between the vaccinated group and the unvaccinated group, while the alternative hypothesis (Ha) is that the vaccine is effective in reducing the number of deaths from COVID. A two-sample t-test can be used to test whether the means of the two groups are significantly different. If the p-value is less than the significance level (alpha) of 0.01, the null hypothesis can be rejected in favor of the alternative hypothesis, and it can be concluded that the vaccine is effective in reducing the number of deaths from COVID.
Once again, please note that the information provided may not be sufficient to provide an accurate analysis of this question, and further information may be necessary to perform an appropriate hypothesis test and draw meaningful conclusions.
Rewrite the equation below so that it does not have fractions
Step-by-step explanation:
First thing to solve expression, use the Reverse-Inverse PEMDAS
PEMDAS is order of operations where
we
evaluate parethiss first
then exponents
then multiplication/division(which ever comes first while reading left to right )
then addition and subtraction(which ever comes first while reading left to right)
We will go in reverse to solve for x.
Are there any addition and subtraction.
Yes, there is addition when we add 4, therefore we do the Inverse and subtract 4 from both sides
[tex] - \frac{4}{9} x = \frac{2}{3} - 4[/tex]
[tex] - \frac{4}{9} x = \frac{2}{3} - \frac{4}{1} [/tex]
Use Butterfly Method to simplify
[tex] - \frac{4}{9} x = \frac{ - 10}{3} [/tex]
Is there any multiplication or division happening to our variable of interest
Yes, there is multiplication happening as our variable is being multiplied by -4/9.
To get rid of this, we do the Inverse and divide by -4/9 on both sides.
Divide by -4/9 is the sames as multiplying by -9/4
[tex]x = \frac{ - 10}{3} \times - \frac{9}{4} = \frac{15}{2} [/tex]
So our answer is 15/2
Marcela's grocery bills for three months were
$75, $87, and $25. To add the bills mentally,
Marcela thought:
"75 + 87 + 25 = 75 + 25 + 87"
What property did Marcela use?
Answer:
Marcela used the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:
For any three numbers a, b, and c, (a + b) + c = a + (b + c)
For example: (2 + 3) + 4 = 2 + (3 + 4) = 9
So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.
how many dozen is he left with?
Answer:
1.75
Step-by-step explanation:
convert to fraction
What is the standard form of the line that passes through the points (-4, 6) and (0, -7)?
Ax+4y= -7
B
4x+y=-7
13x + 4y = -28
D-4x+y=-28
30960995
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]
what is the median for 31,35,28,31,37
Answer:
31
Step-by-step explanation:
Answer:
The median is the middle value in a set of numbers. To find the median for the given set of numbers 31, 35, 28, 31, and 37, we first need to arrange them in numerical order: 28, 31, 31, 35, 37.
Since there are an odd number of values in this set, the median is simply the middle value which is **31**.
MARK AS BRAINLIEST, I DID EXPLANATION AND TOOK A LOT OF TIME!
Suppose a star has a luminosity of 8.0×1026 watts
and an apparent brightness of 1.5×10−12 watt/m2
. How far away is it? Give your answer in both kilometers and light-years.
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
We have,
We can use the inverse square law to find the distance to the star:
Luminosity / (4π(distance)²) = Apparent brightness
Rearranging this formula to solve for the distance, we get:
distance = √(Luminosity / (4π (Apparent brightness)))
Plugging in the given values, we get:
distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))
Simplifying this expression, we get:
distance = 3.04 × 10^{20} meters
Converting this distance to kilometers, we get:
distance = 3.04 × 10^{17} kilometers
To convert this distance to light-years, we divide by the speed of light in kilometers per year:
distance = (3.04 × 10^{17}) / (9.46 × 10^{12})
Simplifying this expression, we get:
distance = 32.2 light-years
Therefore,
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
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-3*10^2t=-28 Solve the equation for
t
Express the solution as a logarithm in base-
10
The solution for t is t = log(28/3) / 2, the Logarithm in base-10.
The equation -3 * 10^(2t) = -28 for t, the exponential term and then take the logarithm of both sides. Let's go through the steps:
Step 1: Divide both sides of the equation by -3:
(10^(2t)) = -28 / -3
Step 2: Simplify the right-hand side:
(10^(2t)) = 28/3
Step 3: Take the logarithm of both sides using base-10 logarithm (log):
log(10^(2t)) = log(28/3)
Step 4: Apply the power rule of logarithms to bring down the exponent:
2t * log(10) = log(28/3)
Step 5: Since log(10) = 1, we have:
2t = log(28/3)
Step 6: Divide both sides of the equation by 2:
t = log(28/3) / 2
Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.
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HELP! PLEASE final math problem I need this done by tomorrow please!!!
22. An electronics store makes $125 profit on every iPhone it sells and $100 on every Android it sells.
The store owner wants to make a profit of at least $500 a day selling DVD players and CD players.
a. Write an inequality to describe the situation.
x=iPhone y=Android
____x ______ ____y ____ _______
(125/100) (≤ / ≥) (500/125)
-rearrange so y is the answer
Answer: y ≥ (5/4)x - 1, where x represents the number of iPhones sold and y represents the number of Androids sold.
Step-by-step explanation:
Adam graphs f(x) = x2 and g(x) = 3x2. Which of the following is NOT the same for the graphs of functions f and g?
The different features for the graphs of f(x) and g(x) is given as follows:
C. y-value when x = 5.
How to find the numeric value of a function at a point?To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The numeric value for the function f(x) at x = 5 is given as follows:
f(5) = 5² = 25.
The numeric value for the function g(x) at x = 5 is given as follows:
g(5) = 3 x 5² = 75.
Missing InformationThe options are given as follows:
A. location of the vertex
B. axis of symmetry
C. y-value when x = 5
D. direction parabola opens
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Select the correct answer. Which equation represents a circle with center Z (-3,5) and a radius of 4 units? A. (x − 3)2 + (y + 5)2 = 4 B. (x − 3)2 + (y + 5)2 = 16 C. (x + 3)2 + (y − 5)2 = 4 D. (x + 3)2 + (y − 5)2 = 16
The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x + 3)² + (y - 5)² = 16
We have to given that;
In a circle,
Center = (- 3, 5)
Radius = 4
Since, The standard form of equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) = center
And, r is radius
Here, Center = (- 3, 5)
Radius = 4
Hence, The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x - (- 3))² + (y - 5)² = 4²
⇒ (x + 3)² + (y - 5)² = 16
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find the value of x such that line L and M are parrle
Answer:
3x+10+5x+18=180
8x+28=180
8x= 152
x=19
Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 3 units right and 4 units up
B. shifted 3 units right and 2 units up
C. shifted 2 units right and 3 units up
D. shifted 2 units right and 4 units up
Twenty-two people have hair 2.5 inches long and twenty-eight people have hair 5.7 inches long. What is the average hair length of all the people detailed? A. 4.29 B. 5.10 C. 4.92 D. 4.57
Answer:
A. 4.29
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the total numbers present.
Sum of numbers: Instead of having to write out 2.5 twenty-two times and 5.7 twenty-eight times, we can remember that adding 2.5 twenty-two times is the same as multiplying 2.5 and 22 while adding 5.7 twenty-eight times is the same as multiplying 5.7 and 28. Thus, our numerator for the average is (2.5 * 22) + (5.7 * 28)
Total number of people: We know that there are 50 people in all since 22 + 28 = 50. Thus, our denominator for the average is 50
Average: We divide our numerator by our denominator and simplify to find our average:
Average = ((2.5 * 22 + (5.7 * 28)) / 50
Average = (55 + 159.6) / 50
Average = 214.6 / 50
Average = 4.292
Average = 4.29
Thus, the average and our answer is A. 4.29
Use the internet to identify a major league ballpark in which the distance from home plate to the center field fence and the height of the center field fence require that a ball hit 2 feet above the ground will necessitate an angle of elevation less than .86 degrees to just clear the center field fence. what is the name and location of the major league ballpark that you identified? what is the distance from home plate to the center field fence and what is the height of the center field fence in the ballpark? What is the angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground? Round to the nearest hundredth of a degree.
We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.
How to find the angle of elevation?The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.
Thus, to solve for the angle of elevation, we can use the following equation:
tan θ = (y - h) / d
Where:
θ is the angle of elevation
y is the height of the fence
h is the height of the ball
d is the distance to the fence.
tan θ = (8 - 2) / 409
tan θ = 0.602
θ = [tex]tan^{-1}[/tex] (0.602)
θ = 0.85°
The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.
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A fisherman catches three different fish. The first fish weighs 2.02 pounds, the second weighs 2.20 pounds, the third weighs 2.2 pounds.
Do all three fish weigh the same? Explain.
Answer:
No
Step-by-step explanation:
2.20 and 2.2 are the same
but 2.02 is not the same as the others
The pie below is cut into 8 equal slices. Shade 1/2 of this pie.
well, here is your pie...
Help pls! ( Don’t mind this text)
The value of the expression 10 ÷ 40 using the long division method will be 0.25.
The expression is given below.
10 ÷ 40
Division means the separation of something into different parts, sharing of something among different people, places, etc.
The division is given below by the long division method. Then
40 ) 100 ( 0.25
- 80
200
- 200
0
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6. (15 points) Metal bar costs $3 per meter and wooden bar costs $2 per meter. If we have $6000 to
purchase both type of bars, what is the maximum area we can enclose at this cost?
the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.
How to determine the maximum area we can enclose at this costLet's assume we purchase x meters of metal bars and y meters of wooden bars. The cost equation can be expressed as:
3x + 2y = 6000 (total cost equation)
We want to maximize the area, which is given by the equation:
Area = x * y
To solve this problem, we can use the method of substitution or elimination. Let's use substitution.
From the total cost equation, we can express x in terms of y:
x = (6000 - 2y) / 3
Now we can substitute this value of x into the area equation:
Area = [(6000 - 2y) / 3] * y
Simplifying further:
Area = (6000y - 2y^2) / 3
The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
In this case, a = -2 and b = 6000, so:
y = -6000 / (2 * -2) = 1500
Substituting this value of y back into the cost equation, we can find the corresponding value of x:
x = (6000 - 2 * 1500) / 3 = 1000
Therefore, with a budget of $6000, we can purchase 1000 meters of metal bars and 1500 meters of wooden bars, resulting in the maximum area.
Area = x * y = 1000 * 1500 = 1,500,000 square meters
So, the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.
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Deena buys a hat for $8 and a coat for $75. She gives the cashier five $20 bills to pay for the items.
How much change does Deena get back?
Answer:
$17
Step-by-step explanation:
5(20) - (8 + 75)
= 100 - 83
= 17.
Deena will get $17 back
10. Mr. Brown bought a car for commuting to
work and completing errands. He found
that he traveled an average 1,100 miles per
month, with a standard of 100 miles. About 95% of the data lies in which interval
To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.
Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:
- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.
Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.
Therefore, the interval within which about 95% of the data lies is:
1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles
So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).
d = 5t + 20
your answer is there so i'll be on my way, Have a nice day!!
Ana estimated the mass of an object to be 54 grams. The actual mass of the object was 45 grams. What was the percent error in Ana’s estimate.
Answer:
20%
Step-by-step explanation:
percent error = (estimated value - real value)/(real value) × 100%
percent error = (54 - 45)/(45) × 100%
percent error = 0.2 × 100%
percent error = 20%
Building A is 165 feet tall and Building B is 210 feet tall. If the angle of depression from the top of Building B to the top of Building A is 52°, how far apart are the buildings?
help please