Answer:
[tex]-210[/tex]
Step-by-step explanation:
We have the function:
[tex]f(x)=x^3-2x^2-51x-108[/tex]
And we want to find the remainder when it is divided by [tex](x-2)[/tex].
We can use the Polynomial Remainder Theorem, where if we have a function [tex]f(x)[/tex] divided by a binomial [tex](x-a)[/tex], then our remainder will be [tex]f(a)[/tex].
Here, our divisor is [tex](x-2)[/tex], so our a is 2.
Therefore, our remainder will be [tex]f(2)[/tex]. Let's substitute this for x. This yields:
[tex]f(2)=(2)^3-2(2)^2-51(2)-108[/tex]
Evaluate. Do the exponents:
[tex]f(2)=8-2(4)-51(2)-108[/tex]
Multiply:
[tex]f(2)=8-8-102-108[/tex]
Subtract:
[tex]f(2)=-210[/tex]
So, our remainder is -210.
And we're done!
Which table represents a linear function?
957x8=
how much does it equal too?
Answer:
7656
Step-by-step explanation:
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The product will be 7656.
The sum of a twice a number and three is 15. What is the number?
Answer:
The answer is 6. Does that help?
Which of the following equations is equivalent to 4(6p – 3) = 26?
A: 10p – 1 = 26
B:24p – 12 = 26
C: 10p – 7 = 26
D: 24p – 3 = 26
Answer:
B. 24p - 12 = 26
For both 4(6p – 3) = 26 and 24p - 12 = 26, [tex]p = \frac{19}{12}[/tex]
I hope that this helps you!
Answer:
B:24p – 12 = 26
Step-by-step explanation:
3. A new process has been developed for applying pho toresist to 125-mm silicon wafers used in manufac turing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstroms x 1,000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002. a. Test the hypothesis that mean thickness is 13.4 x 1,000 A. Use a = 0.05 and assume a two-sided alternative. b. Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness is normally distributed.
Answer:
a
The null hypothesis is [tex]H_o : \mu = 13.4000[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 13.4000[/tex]
The null hypothesis is rejected
b
The 99% confidence level is [tex]13.3930 < \mu < 13.3994 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 10
The population mean is [tex]\mu = 13.4 000 \ angstroms[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The sample data is
13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{13.3987+ 13.3957\cdots +13.4002 }{10}[/tex]
=> [tex]\= x = 13.3962 [/tex]
Generally the sample standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }[/tex]
=> [tex]\sigma =0.0039 [/tex]
The null hypothesis is [tex]H_o : \mu = 13.4000[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 13.4000[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }[/tex]
=> [tex]z = 3.08[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2P( z > 3.08)[/tex]
From the z-table [tex]P(z > 3.08)= 0.001035[/tex]
So
[tex]p-value = 2* 0.001035[/tex]
[tex]p-value = 0.00207[/tex]
So from the obtained value we see that
[tex]p-value < \alpha[/tex]
Hence the null hypothesis is rejected
Consider the b question
Given that the confidence level is 99% then the level of significance is
[tex]\alpha = (100 -99)\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{0.0039}{\sqrt{10} }[/tex]
=> [tex]E = 0.00318[/tex]
Generally the 99% confidence interval is mathematically represented as
[tex]13.3962 - 0.00318 < \mu < 13.3962 + 0.00318 [/tex]
=> [tex]13.3930 < \mu < 13.3994 [/tex]
A line passes to the points(
(8,-1) and (-4,2)
What is the y-intercept of this line?
-4
-1
1
4
The cost of a computer declined by
$5.75 per day for 9 days. What was the
total change in price after the 9 days?
Answer:
the answer is 51.75
Step-by-step explanation:
What you do is take 5.75 and multiply it by 9 and that's your answer
0.47
× 3.2. Help me please
Answer:
1.504
Step-by-step explanation:
HELP!!!! Additive Identify property stuff!!!!
Answer:
i am pretty sure it is F
Step-by-step explanation:
Answer:f?
Step-by-step explanation:
Which statement is true?
O A. The absolute value of 3 is -3.
OB. The opposite of 7 is 7.
O C. The absolute value of 5 is equal to the opposite of 5.
O D. The opposite of -4 is
equal to the absolute value of -4.
Answer:
D. The opposite of -4 is equal to the absolute value of -4.
Step-by-step explanation:
A biologist observed a population of bacteria that grew at a rate expressed by the exponential equation
f(t) = 256e0.06111)
where t is in minutes. How long will it take the population to reach 5 times its initial value?
Round to two decimal places and do not include "t =" in your answer.
Answer:
It will take 26.34 minutes for the population to reach 5 times its initial value
Step-by-step explanation:
Exponential Growing
The population of bacteria grows at a rate expressed by the equation:
[tex]f(t)=256e^{0.06111t}[/tex]
Where t is in minutes.
We need to know when the population will reach 5 times its initial value. The initial value can be determined by setting t=0:
[tex]f(0)=256e^{0.06111\cdot 0}=256\cdot 1=256[/tex]
Now we find the time when the population is 5*256=1,280. The equation to solve is:
[tex]1,280=256e^{0.06111t}[/tex]
Dividing by 256:
[tex]e^{0.06111t}=1,280/256=5[/tex]
Taking natural logarithms:
[tex]ln\left(e^{0.06111t}\right)=ln5[/tex]
Applying the logarithm properties:
[tex]0.06111t=ln5[/tex]
Solving for t:
[tex]t=ln5/0.06111=26.34[/tex]
It will take 26.34 minutes for the population to reach 5 times its initial value
What is the answer to 2+2-3+5=
Answer:
6
Step-by-step explanation:
add,subtract
0.315 ___ 0.615 what sign do i put
Answer:
Less than - hope it helpssssss
Step-by-step explanation:
A contractor cut 28 feet of wire into sections that were feet long. How many pieces of wire did the contractor have?
Answer:
its 6
Step-by-step explanation
How would I solve number six?
Answer:
Angle ABC is equal to 130.4°
Step-by-step explanation:
When an angle is bisected, it is divided into two equal parts, so if BD bisects ∠ABC, then the two angles that add up to it, ∠ABD and ∠DBC, must be equivalent.
We know that ∠ABD equals 65.2, so that must mean that ∠DBC also equals 65.2.
Here is our equation:
∠ABC=∠ABD+∠DBC
After substituting, we will get
∠ABC=65.2+65.2=130.4
130.4° is the measure of ∠ABC.
SOLVE AND JUSTIFY RIGHT ANSWER GETS BRAIN
Answer:
y is more than or equal to -1 5/23
HELP What is the slope of the line that contains points (-6, -6) and (-3, 1)?
Find the first of three consecutive even integers if the sum of the first and second is 15 less than 3 times the third.
Answer:
First even integer: 6
Step-by-step explanation:
Inequalities
Assume x is the first even integer. The next integer is x+2, and the last integer ix x+4.
The condition states that the sum of the first and the second number is 15 less than three times the third. This takes us to the inequality:
[tex]x+x+2<3(x+4)-15[/tex]
Operating:
[tex]2x+2<3x+12-15[/tex]
Subtracting 2 and 2x:
[tex]0<3x+12-15-2x-2[/tex]
Simplifying:
[tex]0<x-5[/tex]
Solving:
x>5
There are infinitely many solutions. For example, for x=6 (first even number into the solution interval):
First integer: 6
Second integer: 8
Third integer: 10
There are other solutions, like 20,22,24 but the first set is 6,8,10.
HELPPPP ASAPPP
6(1+r)^3n
find the value of r?
Answer:
5 possibly.
Step-by-step explanation:
If you can give me the answer to the equation I could give you a more accurate answer.
Please help me on this question ASAP if you do ill give you brainliest!
Answer:
7. 2/3 8. 1 1/13 9. 1 3/5 10. 1 17/19 11. 1 16/19 12. 22.63 13. 4 20/39 14.2 16 /145 15. 1 25 /62
Step-by-step explanation:
Which of the following shows the equation solved for y?
2x + 6y = -12
Answer:
Here it goes -0.333
What expression is 8/12 eual to?
Answer:
8/12 = 2/3
Step-by-step explanation:
Sally started with $100 and is saving for a new Uggs. The first month she had $124, the next month $148, and by the third month she had $172 saved. Write an explicit rule to represent how much she saves each month.
An = 100n + 24
An = 24n + 124
An = 124n + 24
An = 24n + 100
What is the correct fraction and decimal form of 10-4?
Answer:
0.0001
Step-by-step explanation:
10^-4 = 0.0001
What are the roots of the polynomial equation x cubed minus 7 x = 6 x minus 12? Use a graphing calculator and a system of equations. –6, 6 –4, 1, 3 –3, –1, 4 1, 3
Answer:
-4, 1, 3 (B)
Step-by-step explanation:
im taking the test right now and its right.
The roots of the polynomial equation, x³ -7x = 6x -12 are; -4, 1 , 3.
Roots of Polynomial equationsThe Polynomial equation given; x³ -7x = 6x -12 can be rewritten as;
x³-13x+12 = 0By testing factors of 12, we can obtained the first factor, (x -1); from x= 1
When the polynomial is divided by long division method and factorised, the factors are; (x+4) (x -3) (x -1).
Read more on roots of Polynomial;
https://brainly.com/question/2833285
What is the remainder when you divide
(2x^3– 5x – 7) by (x + 2) ?
Answer:
this is the remainder.
mean median mode 20, 22, 23, 25, 26, 26, 32
Answer:
mode: 26 median: 25
Step-by-step explanation:
mode: because mode is what appears most, and thats 25
median: is what is in the middle so we cross some numbers off and we get 25
please mark brainliest
Dante rode his bike a mile in 5 minutes. At that rate, how many miles can he ride in an hour?
Answer:
Step-by-step explanation:
direct proportion
1mile in 5 minutes
xmiles in 60 minutes
cross multiply
60/5=12 miles
Answer:
12 miles
Step-by-step explanation:
1×12=12 a clock has 60 minutes per hour 60÷5=12 12×1=12
Helpppppp pleasssseeeeee
Answer:
the last one is not part of the proof, because it's not SSS it's SAS.
Answer:
D
Step-by-step explanation:
it is incorrect the answer is SAS
4. How many ones is in the number 500? *
(10 Points)
500 ones
50 ones
5 ones
Answer:
500 ones hope this helps