Answer:
If a polynomial function has integer coefficients, then every rational zero will have the form pq p q where p p is a factor of the constant and q q is a factor
Step-by-step explanation:
Using synth. div. to check whether or not 7/2 is a root:
___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0
Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.
Please see question below in picture
It was Robin's birthday and she knew she was going to have a good day. She was driving to work, and when she turned on the radio, her favorite song was playing. Besides, the traffic light at the main intersection she crossed to get to work was green when she arrived, something that seemed to happen less than once a week. When she arrived at work, rather than having to search as she usually did, she found an empty parking space right in front of the building. Identify three random circumstances in the story, and give the possible outcomes for each of them. (Select all that apply.)
Answer:
1.Random circumstance: Color of traffic light when Robin approaches the main intersection. Possible outcomes: Traffic light is green when Robin arrives, or Traffic light is not green when Robin arrives.
2.Random circumstance: Song on the radio when first turned on. Possible outcomes: Robin's favorite song is playing, or Robin's favorite song is not playing.
4.Random circumstance: Nearest available parking space. Possible outcomes: Robin finds an empty parking space in front of the building, or Robin does not find an empty parking space in front of the building.
Step-by-step explanation:
A random circumstance is one whose outcome cannot be predicted because we either do not have the full details of the matter or it has not been confirmed yet by a reliable source. In the short description of events provided above;
1.The color of the traffic light is unpredictable because it is not under the control of the drivers but is automated.
2. Robin's favorite song playing on the radio is a random circumstance because she has no control over what song is played. So, she might as well have tuned in and it would be her least favorite song playing.
3. Robin driving into the office and finding the parking space empty is a random circumstance because it is not predictable. She might have come in and found the entire space filled.
One United Bank is the largest Black-owned bank in the United States which calculates simple interest using the following equation below.
I=prt
Solve the equation for r, the rate balance.
A. Ir=pt
B. Ipt=r
C. rI=pt
D. ptI=r
Answer:
WHat is it :(
Step-by-step explanation:
Answer:
Easy Question: I/pt=r
Step-by-step explanation:
You take the equation i=prt and you solve it out.
You divide the half "prt" by pt like this: prt/pt
You also do that to the other side "I"
You are left with I/pt=r and there it is!!
Need help on this ASAPPPPPPPP
Answer:
B
Step-by-step explanation:
We know that the blue triangle is the image as it has the ' on the letters. For example G'.
To first start off, you can look at any points to help solve this problem. I used the point H to help me solve this
Since we know that the black triangle is our old image we know the distance in x values between the black triangle to the blue is -2 as it moves to the left 2 times. (Note: it's going more into the negatives, if it were going to the right it would be positive)
Now we do the same to find our y values, and we see that y value for h on the black triangle goes up +1.
Now we know that the X goes to the left two times to get -2 and that the Y goes up once to get +1.
Hope this helps! :)
Answer:
b. (x - 2, y + 1)
Step-by-step explanation:
You can make that determination visually. However, if you need numbers...
Pick a point on the black triangle, let's say F(0, 0) and the corresponding point on the blue tirangle F(-2, 1)
(y₁ + y₂) / (x₁ + x₂) = (0 + 1) / (0 + (-2)) = 1 / -2
[tex]\frac{rise}{run}[/tex] = [tex]-\frac{1}{2}[/tex]
So, from the F(0,0) position move -2 to the left then up 1 to land on F(-2, 1).
This translated to (x - 2, y + 1)
At the Last Chance Filling Station, gas costs $1.60 a gallon. Trevor paid $32.00 to fill his tank. How many gallons of gas did he buy? a. Write an algebraic equation that represents the scenario. b. Solve to find the solution.
I know it’s 32/1.60=20 gallons
But how do you write the algebraic expression?
Answer:
1.60x=32.00
Step-by-step explanation:
Since you do not how much gallons of gas he bought you would use the variable x.
Answer:
1.60x=32
Step-by-step explanation:
A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.
Single Policyholders Married Policyholders
n1 = 500 n2 = 800
Number making claims = 95 Number making claims = 80
(a) Use a level of significance a = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
(b) Provide a 95% confidence interval for the difference between the proportions for the two populations.
Answer:
a
The determination is
There is sufficient to conclude that proportion of the single policy
b
The 95% confidence interval is [tex] 0.0498 < p_1 - p_2 < 0.1302 [/tex]
holders is difference from the proportion of married policy holders
Step-by-step explanation:
From the question we are told that
The sample size for single policy holders is [tex]n_1 = 500[/tex]
The number of single police holders making claim is k = 95
The sample size for married policy holders [tex]n_2 = 800[/tex]
The number of double police holders making claim is u = 80
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the
normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 \ne p_2[/tex]
The sample proportion of single police holders making claim is
[tex]\r p_ 1 = \frac{k}{n_1}[/tex]
=> [tex]\r p_ 1 = \frac{95}{500}[/tex]
=> [tex]\r p_ 1 = 0.19[/tex]
The sample proportion of married police holders making claim is
[tex]\r p_ 2 = \frac{u}{n_2}[/tex]
=> [tex]\r p_ 2 = \frac{80}{800}[/tex]
=> [tex]\r p_ 2 = 0.1[/tex]
Generally the pooled sample proportion is mathematically represented as
[tex]\r p = \frac{k + u}{n_1 + n_2}[/tex]
=> [tex]\r p = \frac{95 + 80}{500 + 800}[/tex]
=> [tex]\r p = 0.1346 [/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\r p_1 - \r p_2 }{ \sqrt{ \r p (1 - \r p )* [\frac{1}{n_1} + \frac{1}{n_2} ]} }[/tex]
=> [tex]z = \frac{0.19 - 0.1 }{ \sqrt{0.1346 (1 - 0.1346 )* [\frac{1}{500} + \frac{1}{800} ]} }[/tex]
=>[tex]z = 4.6256 [/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2* P(Z >4.6256 )[/tex]
From the z table [tex]P(Z >4.6256 ) = 0 [/tex]
[tex]p-value = 2* 0 = 0[/tex]
From the calculation we see that the p-value < [tex]\alpha[/tex] so the null hypothesis is rejected
Hence there is sufficient to conclude that proportion of the single policy holders is difference from the proportion of married policy holders
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{ \frac{\r p_1 (1 -\r p_1)}{n_1} + \frac{\r p_2 (1 -\r p_2)}{n_2} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.19 (1 -0.19)}{500} + \frac{ 0.1 (1 - 0.1)}{800} }[/tex]
=> [tex]SE =0.0205012[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 *0.0205012 [/tex]
=> [tex]E = 0.0402035[/tex]
Generally the 95% confidence level is mathematically represented as
[tex]\r p_1 - \r p_2 - E < p_1 - p_2 < \r p_1 - \r p_2 + E[/tex]
=> [tex]0.19 - 0.10 -0.0402035 < p_1 - p_2 < 0.19 - 0.10 + 0.0402035 [/tex]
=> [tex]0.09 -0.0402035 < p_1 - p_2 < 0.09 + 0.0402035 [/tex]
=> [tex] 0.0498 < p_1 - p_2 < 0.1302 [/tex]
What is 6(4p - 2) + 2 (5p + 2)
Answer:
34p -8
Step-by-step explanation:
6 (4p- 2) + 2 (5p + 2)
24p - 12 + 2 (5p +2)
24p - 12 + 10p + 4
34p -8
What are the coordinates of the y-intercept of the function y=|6x-5|-4
Answer: (0,1)
Step-by-step explanation:
Hope this helps
What is -3.2 + (1 1/2) + (-2)
Answer:
-3.7
Step-by-step explanation:
-3.2 + 1.5 -2 = -3.7
Answer:
-5/2
Step-by-step explanation:
-6+11/2+(-2)
-12+11+(-4)/2
-5/2
-3x + 31 < 25 can anyone help me do this please
Answer:
x > 2
Step-by-step explanation:
Pull out like factors :
-3x + 6 = -3 • (x - 2)
Divide both sides by -3
Remember to flip the inequality sign:
Solve Basic Inequality :
Add 2 to both sides
x > 2
Answer:
x > 2Step-by-step explanation:
-3x + 31 < 25
subtract -31 from both sides:
-3x + 31 - 31 < 25 - 31
simplify:
-3x < -6
reverser the inequality:
3x > 6 divide 3 on both sides
x > 2
Write an equation that represents this comparison sentence.
24 is 4 times as many as 6
Answer:6 x 4 = 24
Step-by-step explanation:
im not sure what was so hard
Answer:
4x6=24 its just you multiply the two smallest numbers
please solve 2x+3=x−4
a) Isaac and his sister plan to surprise their parents by buying them each a pair of shoes.
They agree that Isaac will pay 68% of the price since he receives a greater
allowance. Use an estimation strategy to determine how much Isaac will pay if the
total bill is $97.65. Show the step-by-step process you used to solve the problem.
THIS IS WHAT I GOT EM I RIGHT OR WRONG !!
$97.65 x .68 = 66.402 (rounded)
Isaac will pay $66.40
Answer:
percentage formula
Step-by-step explanation:
if it is 68% on 97.65 dollar the 97.68x 68%/100
Shop Mart bought 47 crates of cereal. In each crate, there are a dozen boxes of cereal. How many boxes of cereal did Shop Mart buy? Answer the question below and remember to label your answer!
Answer:
564 Boxes Of Cereal
Step-by-step explanation:
You take 47 (# of crates), and 12 (# of items in a dozen) and multiply them.. to get 564
f (x) = 4x + 7. Find the inverse of f(x).
O A. f-1 (x) = -74
OB. f-'(x) = 7 - 4x
O c. f-1(x) = 11
O D. f ? (x) = 4x – 7
Anybody please ? I suck at math !
Answer:
C. f(x) = x - 7 all over 4
Step-by-step explanation:
NB: Let f(x) = y
Exchange X and Y
Make y the subject
f(x) = 4x + 7
y = 4x + 7
x = 4y + 7
x - 7 = 4y
x - 7 all over 4 = 4 ÷ 4
y = x - 7 all over 4
alice sold 3 more than 2 times the number of magazines Josh sold. Alice sold a total of 27 magazines. How many magazines does Josh sell?
Answer: 12
Step-by-step explanation:
you can check this by doing this 12 x 2 = 24 + 3 = 27
To reduce laboratory costs, water samples from five public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.007 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from five public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Answer:
Step-by-step explanation:
Given that:
The numbers of the possible public swimming pools are 5
From past results, we have 0.007 probability of finding bacteria in a public swimming area.
In the public swimming pool, the probability of not finding bacteria = 1 - 0.007
= 0.993
Thus;
Probability of combined = Probability that at least one public
sample with bacteria swimming area have bacteria
Probability of combined sample with bacteria = 1 - P(none out of 5 has
bacteria)
Probability of combined sample with bacteria = 1 - (0.993)⁵
= 1 - 0.9655
= 0.0345
Thus, the probability that the combined sample from five public swimming areas will show the presence of bacteria is 0.0345
From above, the probability that the combined sample shows the presence of bacteria is 0.0345 which is lesser than 0.05.
Thus, we can conclude that; Yes, the probability is low enough that there is a need for further testing.
Unit 1 Cumulative Assessment
Multiple Choice
Let f(x) = x2 and g(x) = x - 6. What is f-g?
a
A. X²-6
B. x2 - 36
O
C. x2 - 12x - 36
D. x2 - 12x + 36
someone please help I’m so confused
Answer:
80 - 12 - 5f
Step-by-step explanation:
You have a total of eighty seeds in all.
Minus the twelve seeds Demi planted.
The number of friends she gave seeds to is unclear.
To find out how many seeds she gave you'd have to
multiply five by the number of friends.
It's is all being subtracted from the total.
Hope this helps. ;)
What is the product?
-4.2.(-9)
O –72
0 -11
O 72
0 144
help me with this question please
What is the retail price of a shirt that has a wholesale price of $12 and is marked up by 60 percent?
$7.20
$19.20
$31.20
$72.00
Answer: 19.20
Step-by-step explanation: What I did was figure out what 10% of 12 was (1.2) then multiplied it by 6 which was 7.2. Then I added that to 12 and got 19.2.
Let me know if this was helpful! :D
Answer:
19.20
Step-by-step explanation:
I just did this and payed attention during the lesson.
A bicyclist rides ⅕ mile in 1/65 hour. Write this as a unit rate.
Answer:
13 ml per hr
Step-by-step explanation:
1/5mi=1/65hr
65/5mi=hr
13mi hr
The bicyclist rides 13 miles per hour
I HOPE THIS WORKS FOR YOU!
Answer:
(1/13)(mile/hour)
Step-by-step explanation:
Simplify this rate of change:
⅕ mile 1 mile
---------------- = --------------- = (1/13)(mile/hour)
(1/65) hour (65/5) hr
2. CARS It took Lisa 85 minutes to wash three cars. She spent x minutes on each car and 10 minutes
putting everything away.
Solve 3x + 10 = 85 to find how long it took to wash each car.
(5 Points)
10
25
50/2
50-25
help meeeeee please
If it's a rectangle:
perimeter = 2F+10g
Area=g(4F+4g)
Step-by-step explanation:
Perimeter = 2×(l+b)
Area= l×b
What is the slope of a line perpendicular to the line is question is 3x-3y=54? fully reduce your answer. (it’s not 1)
Answer:
-1
Step-by-step explanation:
Has to be the opposite
Can someone please help, ty!! (Will mark brainliest)
Step-by-step explanation:
y-1=-4/7*(x-(-4))
7(y-1)=-4(x+4)
7y-7=-4x-16
7y+4x=-16+7=-9
so is the first one
Answer:
7y+4x=-9
Step-by-step explanation:
y=-4/7 x +b
1=-4/7 (-4)+b
b=1-16/7
b=7-16/7
b=-9/7
7y=-4x-9
7y+4x=-9
evaluate y 9-(-9) =?
Answer: 18
Step-by-step explanation:
when there is a in front of an expression in parentheses change the sign of each term in the expression. 9+9=18 so ANSWER 18
I NEED AN ANSWER ASAP (photo)
Answer:
C
Step-by-step explanation:
A, B, and D equal -4, while C equals 4.
A positive number times/divided by a negative number (or vice versa) is a negative number. A negative number times/divided by a negative number (or vice versa) is a positive number.
I need help on this!!!
Step-by-step explanation:
3 tickets = $16.50
1 tickets = $16.50/3
= $5.5
2 tickets = $2×5.5
= $11.00