If polynomial function vanishes at
x
=
a
, then
(
x
−
a
)
must be one of its factors.
Thus
(
x
−
7
)
,
(
x
−
4
−
√
6
)
and
(
x
−
4
+
√
6
)
are factors of the required polynomial.
The simplest polynomial that satisfies this is
(
x
−
7
)
(
x
−
4
−
√
6
)
(
x
−
4
+
√
6
)
=
(
x
−
7
)
{
(
x
−
4
)
−
√
6
}
{
(
x
−
4
)
+
√
6
}
=
(
x
−
7
)
{
(
x
−
4
)
2
−
6
}
=
(
x
−
7
)
(
x
2
−
8
x
+
16
−
6
)
=
(
x
−
7
)
(
x
2
−
8
x
+
10
)
Evaluate the Expression when x = 6 and y = 5.
(x - 1) + (y - 1)
Answer:
9
Step-by-step explanation:
Tasha needs to walk 7/10 miles to school. She has already walked 3/5 mile. How much farther does Tasha need to walk? Answer in simplified form, if needed.
Answer:
1/10
Step-by-step explanation:
We are to determine the difference between the miles walked Tasha already and the total number of miles to school
[tex]\frac{7}{10} - \frac{3}{5}[/tex]
[tex]\frac{7-6}{10}[/tex] = [tex]\frac{1}{10}[/tex]
The results of a series of surveys revealed a population with a mean of 4.73 and a standard deviation of 0.865. If each survey has a sample size of 200, which value falls within the interval where 95% of the sample means occur? A. 4.88 B. 4.63 C. 4.91 D. 4.55
Answer:
4.63
Please give me brainliest, I really need it.
The value of 4.63 falls within the interval (4.66, 4.791) where 95% of the sample means occur option (B) is correct.
What is a confidence interval for population standard deviation?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
[tex]\chi^2_{\alpha/2, \ n-1} and \chi^2_{1-\alpha/2, \ n-1}[/tex] are the constant based on the Chi-Square distribution table.
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
It is given that:
Mean of the population x = 4.73
Standard deviation s = 0.865
Sample size n = 200
The interval where 95% of the sample means occur:
Lower limit = 4.73 - 0.865/√200
Lower limit = 4.66
Upper limit = 4.73 + 0.865/√200
Upper limit = 4.791
The interval = (4.66, 4.791)
Thus, the value of 4.63 falls within the interval (4.66, 4.791) where 95% of the sample means occur option (B) is correct.
Learn more about the confidence interval here:
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HELP HELP PLEASE!! D:
Determine the missing side length!!
PLEASE NO CAP!!
Answer:
missing side length = 9
Step-by-step explanation:
[tex]c^{2} = a^{2} + b^{2}[/tex]
a = 6
b = 7
c = missing side
[tex]c^{2} = 6^{2} + 7^{2}[/tex]
[tex]c^{2} = 36 + 49[/tex]
[tex]c^{2} = 85[/tex]
[tex]\sqrt{c^{2} } = \sqrt{85}[/tex]
[tex]c = 9.219 = 9[/tex]
Determine the y intercept (8gtade
4.
In a certain state, license plates have 2 letters followed by 5 digits. How many different license plates
are possible if
a) digits and letters can be repeated?
b)
digits and letters cannot be repeated?
Answer: A) 26_ 26 10_10_10_10_10 = 67,600,000
B) 26_25 10_9_8_7_6 = 19,656,000
Step-by-step explanation: A) There's exactly 26 letters in the Alphabet and it wants us to repeat it, so write 26_26. Since it's also asking for a 5 digits, write 10 five times because there's only 10 digits; 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Multiply the Numbers all-together which is equals 67,600,000.
B). Again, since the License plate has 2 letters, write the Number twice. However it cannot be repeated, so write 26_25. As for the 5 digits write the Number 5 times, but it also can't be repeated, so write 10_9_8_7_6 (Use commas if you want). Then Multiply the Numbers all-together which equals 19,656,000.
Maria is solving this number riddle by using guess and check: Fifteen less than a number is twelve.
Based on the riddle, which statements must be true? Check all that apply.
Answer:
27
Step-by-step explanation:
x-15=12
x=15+12
x=27
Answer:
27
Step-by-step explanation:
The sanctuary takes out a $12,500 loan to renovate its gift shop. At 5%
simple interest, how much would the sanctuary need to pay back in total after 10 years?
Answer:
20361.18283
Step-by-step explanation:
p(1+r/100)n
12500(1+5/100)power 10
i hope this answer helps a little bit.
What is the domain of the function?
Answer: -6 ≤ x < 4
Step-by-step explanation:
Open circles on a graph mean that that point is not included
Filled in circles on a graph mean that that point is included
As a result, the end point (-6, -6) is included while (4, 8) is not
The domain is all possible x-values so the graph can be anywhere from:
-6 ≤ x < 4
Note that there are no possible values for the x-value of 4
A company negotiator claims that only 35% of union members will support a strike, but a union rep believes that the true percentage is greater and runs a hypothesis test. What are the hypothesis statements for this situation?
A. H0: p < 0.35; Ha: p = 0.35
B. H0: p = 0.35; Ha: p < 0.35
C. H0: p > 0.35 ; Ha: p = 0.35
D. H0: p = 0.35; Ha: p > 0.35
Answer:
[tex](d)[/tex] [tex]H_o: p = 0.35[/tex] [tex]H_a: p > 0.35[/tex]
Step-by-step explanation:
Given
[tex]\mu = 35\%[/tex]
Required
The hypothesis statements
First claim: 35% will support a strike.
This represents the null hypothesis
[tex]H_o: p = 0.35[/tex]
Second claim: A greater percentage will support the strike.
This represents the alternate hypothesis
[tex]H_a: p > 0.35[/tex]
In the triangle MSA, MS = 17 and MA = 8. What is the value of angle S, to the nearest degree?
Answer:
B. 28 degrees
Step-by-step explanation:
Which expressions represent the product of a variable and a coefficient? Choose 3 answers: Choose 3 answers: (Choice A) A 11c11c11, c (Choice B) B \dfrac{1}{2}t 2 1 tstart fraction, 1, divided by, 2, end fraction, t (Choice C) C 5\cdot 105⋅105, dot, 10 (Choice D) D j\cdot 4j⋅4j, dot, 4
Question:
Which expression represents the product of a variable and coefficient?
Choose 3 answers
(A) 11c
(B) 1/2 t
(C) 5•10
(D) j•4
Answer:
(A) 11c
(B) 1/2 t
(D) j•4
Step-by-step explanation:
Required
Expression for variable and coefficient product
In algebra:
A coefficient can be anything (number of alphabets). However, a variable is always represented with an alphabet
Having said that:
Analyze each of the options
(A) 11c
Here, we have:
[tex]Variable = c[/tex]
[tex]Coefficient = 11[/tex]
(B) 1/2 t
Here, we have:
[tex]Variable = t[/tex]
[tex]Coefficient = 1/2[/tex]
(C) 5•10
Here, 5 and 10 are not variables
(D) j•4
Here, we have:
[tex]Variable = j[/tex]
[tex]Coefficient = 4[/tex]
So, the correct options are: (A), (B) and (D)
Answer:
A
B
D
Step-by-step explanation:
Pretty sure
Anyone know the answer to this ?
Answer:
no srry
Step-by-step explanation:
At Home Depot, Johnny bought 3 rose bushes and 7 flats of petunias for a total of $114.75. Rosie bought 2 rose bushes and 6 flats of petunias for a total of $89.50. How much does a rose bush cost? How much does a flat of petunias cost?
Answer:
a rose bush cost $15.5 , a flat of petunias cost $9.75
Step-by-step explanation:
Let $x be the cost of rose bush and $y be the cost of a flat of petunias cost
3x + 7y = 114.75
2x + 6y = 89.5
x = 31/2 , y = 39/4
A right triangle has side lengths of 0.6 meter and 0.8 meter. What is the length of the hypotenuse? Round to the nearest tenth.
A. 0.1 meter
B. 0.5 meter
C. 1.0 meter
D. 4.8 meters
Use the Pythagorean theorem since you are working with a right triangle:
a^2+b^2=c^2a2+b2=c2
The legs are a and b and the hypotenuse is c. The hypotenuse is always opposite the 90° angle. Insert the appropriate values:
0.8^2+0.6^2=c^20.82+0.62=c2
Solve for c. Simplify the exponents (x^2=x*xx2=x∗x ):
0.64+0.36=c^20.64+0.36=c2
Add:
1=c^21=c2
Isolate c. Find the square root of both sides:
\begin{gathered}\sqrt{1}=\sqrt{c^2}\\\\\sqrt{1}=c\end{gathered}1=c21=c
Simplify \sqrt{1}1 . Any root of 1 is 1:
c=c= ±11 *
c=1,-1c=1,−1
What is the data range of the data below 625, 638, 619, 677, 638, 659
Answer:
58
Step-by-step explanation:
The range is the difference between the highest and the lowest numbers in the number set.
The highest number in this set is 677 and the lowest number is 619.
677 - 619 = 58
You can buy 3 CDs for $36.00. Assuming these rates are proportional, what would be the cost of 5 CDs?
Answer:
$60
Step-by-step explanation:
36 / 3 = $12 for a single CD
12 * 5 = $60 for 5 CDs
4) Find the length of each side. Please help ASAP. I NEED it. I’m begging you!!
Which number, when raised to the power of 5, equals 2?
Answer:
1.148698
Step-by-step explanation:
The number that will be equal to 2 when raised to the power of 5 is 1.1487.
When raising a particular number to the power of another, It implies that we are multiplying that particular number in the number of places with which the power is being raised.
From the given information:
Let the unknown number be x;SO;
x⁵ = 2We will need to determine the fifth root of 2 in order to eliminate the power of 5 in x.
i.e
[tex]\mathbf{ \sqrt[5]{x^5}=\sqrt[5]{2} }[/tex]
[tex]\mathbf{ x=\sqrt[5]{2} }[/tex]
x = 1.1487
Therefore, we can conclude that the number that will be equal to 2 when raised to the power of 5 is 1.1487.
Learn more about the square root here:
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In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found that 80% of those who had a college degree voted in the last presidential election, whereas 56% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.)
Answer:
A. 8%
B. 39.6%
C. 58.4%
D. 41.6%
Step-by-step explanation:
Computation to determine the probability of eligible voter selected at random
First step is to Draw up a contingincy table which will include Rows = Degree/No degree
and Columns= Vote/Not vote
..............Vote..No vote
Degree 80...20...100
(80%*100=80)
(100-80=20)
No Degree 504..396..900
(1000-100=900)
(56%*900=504)
(504-900=396
Totals 584..416...1000
(80+504=584)
(20+396=416)
(900+100=1,000)
Summary
..............Vote..No vote
Degree 80...20...100
No Degree 504..396..900
Total Totals 584..416...1000
A. Calculation to determine the probability of The voter had a college degree and voted in the last presidential election.
P = 80/1,000
P=0.08*100
P=8%
Therefore the probability of The voter had a college degree and voted in the last presidential election will be 8%
B. Calculation to determine the probability of The voter did not have a college degree and did not vote in the last presidential election.
P =396/1000
P=0.396*100
P=39.6%
Therefore the probability of The voter did not have a college degree and did not vote in the last presidential election will be 39.6%
C. Calculation to determine the probability if The voter voted in the last presidential election.
P = 584/1,000
P=0.584*100
P=58.4%
Therefore the probability if The voter voted in the last presidential election will be 58.4%
D. Calculation to determine the probability if The voter did not vote in the last presidential election.
P = 416/1000
P=0.416*100
P=41.6%
Therefore the probability if The voter did not vote in the last presidential election will be 41.6%
A race takes 3 hours to complete. If the
bikers were traveling at a constant speed, and
traveled 45 miles, how fast were the bikers
traveling?
Answer:
Speed is equals to distance divided by time
ie
45 ÷ 3
you get 15 miles per hour
Answer:
15 miles per hour
Step-by-step explanation:
Speed = distance travelled / time taken
= 45 / 3
=15
Convert each of the following into fraction
(a)
32%
Answer:
8/25
Step-by-step explanation:
So 32% is essentially 32/100 now we can divide that even more so now we have 16/50(we divided it in half) but we can divide that again, so now we have 8/25 :)
rename 11/5 as a mixed answer
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
11 goes into 5 two times, but we are left with a remainder of 1.
So, we can say that the mixed number would be [tex]2\frac{1}{5}[/tex].
Solve the equation:
3/4x = 12
Enter the answer in the box. Enter your numerical answer in the box, do not include words or spaces.
Answer:
3/4x=12
3=4x*12
3=48x
3/48x=1/16
x=1/16
Ronnie wants to buy rosebushes he has $150 and each bus cost $11 right and solve an equality to find how many roses bushes he can buy and still have at least $95
Answer: 5 Rosebushes
Step-by-step explanation: if they required $95 at least, then you take $150 - $95 and you get $55
- Each rosebushes is $11 so you take 55/11= 5
The circumference of a tree trunk is 50 ft
Answer:
So the length will be the same as the length of the torso
Write a unit rate for the situation. Situation: 150 students in 6 classrooms Unit rate: __ students per classroom
Ted Stamos rented a minivan for 4 days for $88.00 per day plus $0.20 a mile for all miles
over 200. He drove 75, 120, 85, and 140 miles on the days rented. He paid a CDW fee of
$18.50 per day and $61.83 for gasoline. What is the (a) total cost, and (b) cost per mile?
Step-by-step explanation:maybe try diciding
The Cougars basketball team sold tins of flavored popcorn as a fundraiser. The players competed for prizes to see who could sell the most tins. This box plot shows the results.
Popcorn tins sold
What fraction of the players sold between 8 and 16 popcorn tins?
Answer:
1/2 percent
Step-by-step explanation:
If you look at the box, the middle number is 12 or since its the middle "1/2"
so the fraction would be 1/2, hope this helped.
The fraction of the players sold between 8 and 16 popcorn tins 1/2 percent.
We have given that,
The players sold between 8 and 16 popcorn tins,
If you look at the box, the middle number is 12, or since it's the middle 1/2.
What is the fraction?
Fractions represent equal parts of a whole or a collection. Fraction of a whole When we divide a whole into equal parts, each part is a fraction of the whole.
So the fraction would be 1/2, hope this helped.
The fraction of the players sold between 8 and 16 popcorn tins 1/2 percent.
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Help me please is this right