Answer:
You would either need to complete the square, use the quadratic equation, or another method because when reduced by the common factor, the constant term c is prime which means that it is only divisible by one and itself. Because the possible rational factors determined by c do not add up to the b term, it cannot be factored.
Explanation:
3x² + 24x - 15 = 0
3(x² + 8x - 5) = 0
[find the greatest common factor between each term and move the coefficient outside of the expression; in this case it's 3 since 3 fits into numbers 3, 24, and -15 so that it cannot be reduced further]
Then you can either use the box or pq method (since a is 1) to find working factors.
x² + bx + c → (x + p)(x + q).
p + q = b.
pq = c.
In this case with 3(x² + 8x - 5), b is 8 and c is -5.
This means we need two numbers that add up to 8 and multiply to -5.
Since -5 is prime, our only options are ±1 for p and ∓5 for q. This is because these are the only factors which multiply to -5.
1 + -5 = -4 ≠ 8
-1 + 5 = 4 ≠ 8.
Since we cannot find rational solutions, this cannot be factored, and so we must use another method.
Due to manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 24 pk. Suppose that two cans are randomly selected from the 24-pk.
a) Determine the probability that both contain diet soda.
b) Determine the probability that both contain regular soda.
c) Determine the probability that exactly one is diet and exactly one is regular.
I'm not knowledgeable about how to write this out to solve it? Please help?
Hope this helps you If you need any more help let me know in the comments
PLEASE HELP
determine the intercepts of the line
x intercept (__ , __)
y intercept (__ , __)
Answer:
i think y=2 and x=-7
Step-by-step explanation:
Alice has $90 to spend on
new clothes. She wants to buy
some shirts for $20 each. If
she has a coupon for $10 off
her total purchase, how many
shirts can she buy?
Answer:
5
step by step explanation:
if she gets $10 off of her purchase that means she would have a little extra money to another shirt
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.
r1(t) = t^2, 8t − 15, t^2
r2(t) = 11t − 30, t^2, 13t − 40
t=
Answer:
Step-by-step explanation:
[tex]r_1(t) = < t^2 , 8t-15,t^2> \\ \\ r_2(t) = < 11t-30, \ t^2 , \ 13t-40> \\ \\ at \ r_1 = r_2 \\ \\ t^2 = 11t - 30 , \ \ \ \ \ \ \ \ \ \ \ \ 8t - 15 = t^2 , \ \ \ \ \ \ \ \ \ t^2 = 13t -40 \\ \\ t^2 - 11t + 30\ \ \ \ \ \ \ \ \ \ \ \ t^2 -8t + 15 , \ \ \ \ \ \ \ \ \ \ \ \ t^2 -13t + 40 \\ \\ t^2 -8t-3t + 30=0 \ \ \ \ \ \ t^2 - 2t -4t + 15=0 \ \ \ \ \ \ t^2 - 1t - 13t + 40 =0[/tex]
[tex](t-6)(t-5) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-3) \ \ \ \ \ \ \ \ \ \ \ (t-5)(t-8)[/tex]
[tex]\mathbf{The \ common \ value \ of \ t \ = \ 5}[/tex]
What is 5x5+34-10 pls need help
At Central Theatre, the cost of a matinee movie is under $5.50. The cost of a
popcorn is exactly $2.25. Write an inequality for the possible total cost, c, of a
movie and popcorn. Show your work.
Answer:
5.50 + 2.25 ≥ c
Step-by-step explanation
Movie = 5.50
Popcorn = 2.25
C = The total cost
5.50 + 2.25 = C
which set of measurements would NOT creat a triangle?
A) 3in,8in,6in
B) 14in,6in,20in
C)11in,12in,22in
D)9in,8in,16in
MADD (Mother's Against Drunk Drivers) wishes to estimate the proportion of adult drivers that have run at least one red light in the last month. A poll is conducted on a simple random sample of adult drivers and it is found that out of 1251 adult drivers, 641 of them have run at least one red light in the last month. You will be finding a 90% confidence interval for the fraction of adult drivers that run at least one red light in the last month.
Check that the normality assumptions are met?
Interpret the confidence interval obtained.
Answer:
Normality assumptions are met.
The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Out of 1251 adult drivers, 641 of them have run at least one red light in the last month.
This means that [tex]n = 1251, \pi = \frac{641}{1251} = 0.5124[/tex]
Normality assumptions:
We need that: [tex]n\pi[/tex] and [tex]n(1-\pi)[/tex] are 10 or greater. So
[tex]n\pi = 1251*0.5124 = 641[/tex]
[tex]n(1-\pi) = 1251*0.4876 = 610[/tex]
So the normality assumptions are met.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 - 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.4892[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5124 + 1.645\sqrt{\frac{0.5124*0.4876}{1251}} = 0.5356[/tex]
The 90% confidence interval for the proportion of adult drivers that run at least one red light in the last month is (0.4892, 0.5356). The interpretation is that we are 90% sure that the true proportion of all adult drivers than ran at least one red light in the last month is between these bounds.
Holly works at a garage.
Mr Bakir brings his car in for a service.
He also buys 2 tyres and a battery.
Holly has this list of costs
• service £110
• tyres £49.99 each
• battery £89
She uses this list to start to work out the bill for Mr Bakir.
Holly also has to charge 20% VAT on the costs to work out the total bill.
Work out the total bill. (You MUST show your working in the box below)
(4 Points)
Combine like terms
x + 10x-30= -8
Answer: x=2
Isolate the variable by dividing each side by the factors that don't contain variables.
Consider an angle with a measure of θ=225∘.
Sketch a diagram representing the situation.
Determine the measure of the reference angle for this angle.
_______°
Now, determine the exact values of the following expressions. Your answers should include fractions and square roots, and not decimal values.
cos(θ)=
sin(θ)=
tan(θ)=
Answer:
cos 225° = [tex]-\frac{\sqrt{2} }{2}[/tex]
sin 225° = [tex]-\frac{\sqrt{2} }{2}[/tex]
tan 225° = 1
Step-by-step explanation:
I cannot sketch a diagram, but a 225° angle is a 3rd quadrant angle and the reference angle is 45° (225 - 180 = 45)
cos and sin are negative in the 3rd quadrant and the tan is positive
cos 225° = - cos 45° = [tex]-\frac{\sqrt{2} }{2}[/tex]
sin 225° = -sin 45° = [tex]-\frac{\sqrt{2} }{2}[/tex]
tan 225° = tan 45° = 1
In 1960 sociologists studied a random sample of 1,018 families that consisted of a husband, a wife, and at least one child. Of those families, 5.8 percent reported that the wife was the primary wage earner of the family. In 2011 the study was replicated with a random sample of 1,013 families that consisted of a husband, a wife, and at least one child. Of those families, 22.3 percent reported that the wife was the primary wage earner of the family. Which of the following represents a 99 percent confidence interval for the difference between the proportions of families that consisted of a husband, a wife, and at least one child from 1960 to 2011 that would have reported the wife as the primary wage carner? (0.223)(0.777) (0.058) (0.942)
(A) (0.223-0.058) 1.96L03 ) (223-0058) ±196 1.013 1 1.018
(B) (0.223-0058) 226(07,(0580942 1,013 1,018
(C) (0.223-0058)2.576, (02230772)(0.45810942 (0.058)(0.942) 1,018
(D) (0.223-0.058) t2.326, 2,031 1,013 1.018
(E) (0.223-0058)?2.57612031(1.013 +1.18
Answer:
(0.223 - 0.058) ± 2.576 * sqrt[((0.223)(0.777))/1018 - ((0.058)(0.942))/1013]
Step-by-step explanation:
Given that :
P1 = 22.3% = 0.223
q1 = 1 - P1 = 1 - 0.223 = 0.777
Sample size, n1 = 1018
P2 = 5.8% = 0.058
q2 = 1 - P2 = 1 - 0.058 = 0.942
Sample size, n2 = 1013
Confidence level, Zcritical at 99% = 2.576
Using the relation :
(P1 - P2) ± Zcritical * Sqrt[(P1q1/n1 + P2q2/n2)
(0.223 - 0.058) ± 2.58 * sqrt[((0.223)(0.777))/1018 - ((0.058)(0.942))/1013]
ILL GIVE BRAINLESTTTTT
Answer:
11/6 - 5/6 = 6/6
Step-by-step explanation:
Maurice Luken deposited $3,021 in a savings account that paid 5.5 percent interest
compounded daily. How much interest did he earn in 31 days?
9514 1404 393
Answer:
$14.14
Step-by-step explanation:
The amount of interest earned is ...
I = P((1 +r/365)^n -1) . . . . interest on principal P at annual rate r compounded daily for n days
I = 3021(1 +0.055/365)^31 -1) ≈ 14.14
$14.14 in interest is earned in 31 days.
Which of the following describes volume? I. the amount of frosting on a cake II. the amount of space in a sock drawer III. the distance between two cities IV. the amount of fabric needed to cover a couch cushion
A. II
B. III
C. IV
D. I
Answer:2
Step-by-step explanation:
To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35models of Make A and 35 models of Make B. The mean braking distance for Make A is 41feet. Assume the population standard deviation is 4.6 feet.The mean braking distance for Make B is 45feet. Assume the population standard deviation is 4.3 feet.At alphaequals0.10,can the engineer support the claim that the mean braking distances are different for the two makes of automobiles
Answer:
There is sufficient evidence to support the claim.
Step-by-step explanation:
Given
[tex]\alpha = 0.10[/tex]
Make A
[tex]\bar x_1 = 41[/tex]
[tex]\sigma_1= 4.6[/tex]
[tex]n = 35[/tex]
Make B
[tex]\bar x_2 = 45[/tex]
[tex]\sigma_2 = 4.3[/tex]
[tex]n = 35[/tex]
First, we state the null and alternate hypothesis
[tex]H_0 : \mu_1 = \mu_2[/tex]
[tex]H_1 : \mu_1 \ne \mu_2[/tex]
Next, calculate test statistic:
[tex]z = \frac{(\bar x_1 - \bar x_2)-(\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}[/tex]
[tex]z = \frac{(41- 45)-0}{\sqrt{\frac{4.6^2}{35}+\frac{4.3^2}{35}}}[/tex]
[tex]z = \frac{-4}{\sqrt{0.6046+0.5283}}[/tex]
[tex]z = \frac{-4}{\sqrt{1.1329}}[/tex]
[tex]z = \frac{-4}{1.0643}[/tex]
[tex]z = -3.7583[/tex]
The critical value at [tex]\alpha = 0.10[/tex] is: [tex]\±1.282[/tex]
[tex]-3.7583 < -1.282[/tex]
So, we reject [tex]H_0[/tex]
This implies that; there is sufficient evidence to support the claim.
4
Which of the following is a function?
А
B
C
D
Answer:
B)
Step-by-step explanation:
A function is when every input has one output.
Easiest way is to do the "vertical line test" and "horizonal line test."
Basically you draw a vertical line and a horizontal line.
If either line passes through more than one point, then it is not a function.
The only one that passes them is B, the line.
Answer:
B
Step-by-step explanation:
A function is when every input has one output.
Easiest way is to do the "vertical line test" and "horizonal line test."
Basically you draw a vertical line and a horizontal line.
If either line passes through more than one point, then it is not a function.
The only one that passes them is B, the line.
In terms of x, what are the dimensions of a rectangle whose area is represented by the
expression 49x2 - 16?
Please help
True or False: x is the same/equal to 1x
Answer:
Yes
Step-by-step explanation:
Because you're multiplying by 1 so it stays the same value
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
they all go straight across
Step-by-step explanation:
Answer:
Go across from each
Step-by-step explanation:
The number line is 0 to 1 true or false 2/8 is close to 0
Answer:
True
Step-by-step explanation:
from the scale 0-1, 2/8 is closer to 0 because you round 2 down to 0, which gives you 0.
Zach bought a video game that was 30% off. He paid $40 for the video game. How much was the game ORIGINALLY? (40 is the AMOUNT PAID so what Percent was me use to match that PART?)
Answer:
57.14$
Step-by-step explanation:
70/100 ( Remember 30% off so only paid 70% of original price) = 40/x ( 40$ is the price paid, x is the unknown original price)
70 = 40
100 X
40×100 = 4,000
4,000÷ 70X = 57.14
Factor the algebraic expression.
12a +9
Answer:
110
Step-by-step explanation:
because you have to add the number
9
On a field trip, there are 3 adults for every 45 students. Which graph models a relationship with
the same unit rate?
А
с
101
9
10
9
8
7
7
6
5
4
b
6.
5
4
3
2
3
2
1
0
30
60
90 120 150
30
60 90 120 156
B
D
10T
9
8
10
9
6
5
Answer:
I believe the answer is C
Find cos (P)
Q
74
70
P
24
R
A.
37
12
В.
35
37
C.
12
Answer:
cos P = 71.09
Step-by-step explanation:
cos = [tex]\frac{adajcent}{hypotenuse}[/tex]
cos P = [tex]\frac{24}{74}[/tex]
cos P = 0.324
cos-1 of 0.324 is 71.09
cos P = 71.09
Please help, I’ve looked everywhere and haven’t found any answers!
Answer:
m = 4 + (2n)/(3)
Step-by-step explanation:
Move all terms that contain m to the right side and solve it.
POV: you procrasiant a lot and dont pay attention on online school and ur failing ur classes, so now ur on brainly, just me?
also someone pls answer my other question will make brainliest!
Answer:
its true i cant pay attention in class cuz its boring but im
not failing it thank god
Answer:
sameeee but im currently not failing, lets hope it stays like that ;-;
Step-by-step explanation:
im smart
Can some one please help me with this math assignment . I would be really grateful
What is the answer to
2x squared?
Answer:
it’s just 2x^2
it’s not factorable
Can someone please help meeee I’m desperateeee
Answer:
Step-by-step explanation:
1)(-3x+10)(50-x)=180
-4x+60=180
-4x=120
x=-30
2)6x+2+2x=90
8x=88
x=11
larger angle: 68°
3) a=3x°
4)(7x-5)=-2x+22
9x=27
x=3
DBE=16°
5)(x-39)=2x-59)
x=20