Answers
Answer: The two roots are x = 3/2 and x = -2
=========================================================
Explanation:
You have the right idea so far. But the two numbers should be 3 and -4 since
3*(-4) = -123+(-4) = -1The -1 being the coefficient of the x term.
This means you need to change the -3x and 4x to 3x and -4x respectively. The other inner boxes are correct.
---------
Refer to the diagram below to see one way to fill out the box method, and that helps determine the factorization.
If we place a 2x to the left of -2x^2, then we need an -x up top because 2x*(-x) = -2x^2
Then based on that outer 2x, we need a -2 up top over the -4x. That way we get 2x*(-2) = -4x
So we have the factor -x-2 along the top
The last thing missing is the -3 to the left of 3x. Note how -3*(-x) = 3x in the left corner and -3*(-2) = 6 in the lower right corner.
We have the factor 2x-3 along the left side.
---------
The two factors are (2x-3) and (-x-2) which leads to the factorization (x+3)(-x+2)
The last thing to do is set each factor equal to 0 and solve for x
2x-3 = 0 solves to x = 3/2 = 1.5-x-2 = 0 solves to x = -2The two roots are x = 3/2 and x = -2
Related Questions
36 apples cost $6. How many apples can you buy for $1?
Answers
Answer: you can buy 6apples for$1
Step-by-step explanation: you divide 36 by 6 and get 6 so it’s 6apples.
help please. I cant figure it out and it’s hard.
Answers
Answer:
The student is comparing the different heart rates due to the temperature. The independent variable is the Temperature and the dependent variable is the beats of the heart from the larva.
Suppose that $2000 is invested at a rate of 4%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 5 years. Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Answer:
Step-by-step explanation:
A = P(1+r/n)^ nt
A = 2000(1+.04/2)^(5*2)
A = [tex]2000(1.02)^{10}[/tex] = $2437.99
(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice president, and secretary of state are chosen randomly from the adults in the country, with each adult having an equal chance to be assigned each of the 3 jobs. What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130
Answers
Answer:
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Step-by-step explanation:
To solve this question, we need to use the binomial and the normal probability distributions.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Probability the president will have an IQ of at least 107.5
IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]
This probability is 1 subtracted by the p-value of Z when X = 107.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{107.5 - 100}{15}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 probability that the president will have an IQ of at least 107.5.
Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 100}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?
0.3085 probability that the president will have an IQ of at least 107.5.
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Independent events, so we multiply the probabilities.
0.3082*0.0451 = 0.0139
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Study the adjoining figure and then explain why x = y
Answers
Answer:
Step-by-step explanation:
y is the remote exterior angle. The remote exterior angle has the strange property that it is equal to the two remote interior angle. The two remote interior angles are the two, neither of which is the supplement of the exterior angle
So y = x/2 + x/2 which are marked as being opposite equal angles.
1/2 x + 1/2 x = x
y by substitution is = x /2 + x/2
y = x
In a marketing survey, a random sample of 1020 supermarket shoppers revealed that 268 always stock up on an item when they find that item at a real bargain price.
a. Find a 95% confidence interval for p?
b. What is the margin of error based on a 95% confidence interval?
Answers
Answer:
a) 95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.
b) Margin of error = 0.0270.
Step-by-step explanation:
a)
[tex]\hat{p}[/tex] = point estimate of p [tex]= 268/1020 =0.2627[/tex]
[tex]\hat{q}= 1 - 0.2627 = 0.7373[/tex]
[tex]SE = \sqrt{\hat{p}\hat{q}/n}\\\\=\sqrt{0.2627\times 0.7373/1020}=0.0138\\\alpha = 0.05[/tex]
From Table, critical values of [tex]Z= \pm1.96[/tex] ,
Lower limit
[tex]= \hat{p} - Z SE\\ = 0.2627 - (1.96 X 0.0138) \\ = 0.2627 - 0.0276 \\ = 0.236[/tex]
upper limit = 0.2627 + 0.0276
= 0.2903
Correct option:
95% of the confidence intervals created using this method would include the true proportion of shoppers who stock up on bargains.
b) Margin of error =Z SE
= 1.96 X 0.0141
= 0.0270.
Given that events A and B are independent with P(A) = 0.55 and P(B) = 0.72,
determine the value of P(AB), rounding to the nearest thousandth, if necessary.
Answers
Answer:
Step-by-step explanation:
For independent events,
P(AB)=P(A)orP(B)
= P(A)uP(B)
=P(A)×P(B)
= 0.55×0.72
P(AB)=0.396
Write an equation for the line with passing through ( -2, 9) and ( 1, 0)
Answers
Answer:
[tex]y=-3x+3[/tex]
Step-by-step explanation:
We start by finding the slope of the line, which is given by the formula:
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.
[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]
Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):
[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]
If two standard, six-sided die were rolled and the numbers that turned up on each were added together, which of the following would be the probability their sum would be equal to 4?
Answers
Answer:
3/36 or 8.333
Step-by-step explanation:
the way you get it is write all the possibilities and that how you get 3/36
what is the approximate surface area of a cylinder with a radius of 3 inches and a height of 10 inches?
1. 30in^2
2. 87in^2
3. 217in^2
4. 245in^2
Answers
Curved surface = 2pi x r x h = 2 x 3.1 x 3 x 10 = 186
2 ends = 2 x (Pi x r x r) = 2 x 3.1 x 3 x 3 = 55.8
Total area = 186 + 55.8 = 242in^2 approximately
These two polygons are similar. In the spaces below, enter the values of a, b, m
Answers
Given:
The two polygons are similar.
To find:
The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].
Solution:
We know that the corresponding side of similar figures are proportional. So,
[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]
[tex]1.25=\dfrac{5.39}{a}[/tex]
[tex]a=\dfrac{5.39}{1.25}[/tex]
[tex]a=4.312[/tex]
Similarly,
[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]
[tex]1.25=\dfrac{5.83}{b}[/tex]
[tex]b=\dfrac{5.83}{1.25}[/tex]
[tex]b=4.664[/tex]
We know that the corresponding angles of similar figures are congruent and their measures are equal. So,
[tex]m\angle C=99.2^\circ[/tex]
[tex]m\angle D=149^\circ[/tex]
Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].
Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide. He will use 1-foot square tiles. He has two different types of tile: plain and hand-painted. Plain tiles cost $0.79 per tile. Hand-painted tiles cost $5.00 per tile. What is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $200?
Answers
Answer:
The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
Step-by-step explanation:
Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:
10 x 15 = 150
150 x 0.79 + 0 x 5 = 118.5
130 x 0.79 + 20 x 5 = 202.7
131 x 0.79 + 19 x 5 = 198.49
Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
Plzzz help me please ??
Answers
A. 4/7 Answer:
B. 60/7 or (8 and 4/7)
Step-by-step explanation:
A. 4 divided by 7 is the same as 4/7
B. 4/7 • 15/1= 60/7
Decide which project the most profitable is by:
(a) Determining the NPV at a discount rate of 6.5%. (8 marks)
(b) The IRR. ?
Answers
Answer:
Project A :
NPV : $703,888.64
IRR : 44.882%
Project B:
NPV : $5,241.26
IRR : 49.662%
Project B is more profitable
Step-by-step explanation:
The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.
The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.
Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64
The IRR of project A is : 44.882%
The NPV for Project B is : $5,241.26
The Internal rate of return (IRR) : 49.662%
From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.
3. The simple interest on $6,000 for 4 years is $1,680. *
Answers
I=. p r t
1,680=(3000)(r)(8). Multiplying
1,680= 24,000r Divide both sides by 24,000
0.07= r
So, the percentage is (0.07)(100)= 7%...
Well, Anita, I am glad to help out... Don't forget to rate my answer:)
I need help with #1 . Please help. I have to show all work so please explain
Answers
Answer:C=10
Step-by-step explanation:
Follow along with the picture below
The formula for this type of problem is a^2+b^2=c^2
We know that 6=a and 8=b so we fill in the formula and square them
we then add the two values we got which get us to 100=c^2
we want to get rid of that square with we square root bothe sides and get c and the square root of 100 is 10.
So C=10
PLEASE HELPPPPPPPP MEEE PLEASE!
Answers
Answer:
Root Multiplicity
-4 2
-1 2
2 1
5 3
---------------------------
y = a(x + 4)²(x + 1)²(x - 2)(x - 5)³
find "a" using point (0, 20000)
20000 = a(0 + 4)²(0 + 1)² (0 - 2)(0 - 5)³
20000 = a(16)(1)(-2)(-125)
20000 = a (4000)
a = 20000/4000
a = 5
y = 5(x + 4)²(x + 1)²(x - 2)(x - 5)³
what is 1+544 please somone tell me or i wikl fail mah test qwq
Answers
Answer:555
Step-by-step explanation:
Answer:
545
Step-by-step explanation:
you are just adding one
544+1=
Find the missing coordinates.
Answers
Answer:
1) (2, 1)
2) (2, -2)
3) (-1, -1)
4) (-5, -5)
Answer:
1. Pairs A(2, 5), B(6, 5), and C(6, 1)
missing coordinate is (2,1)
2. Pairs A(2, 3), B(7, 3), and C(7, -2)
missing coordinate is (2,-2)
3. Pairs A(-5, -1), B(1, -1), and C(1, -5)
missing coordinate is (-5,-5)
4. Pairs A(-1, 4), B(7, 4), and C(7, -1)
missing coordinate is (-1,-1)
Hope this is correct!! Have a nice day!!<3
Consider randomly selecting a single individual and having that person test drive different vehicles. Define events , , and by Suppose that , , , , , and . What is the probability that the individual likes both vehicle
Answers
Answer:
[tex]P(A_1\ n\ A_2) = 0.40[/tex]
Step-by-step explanation:
Let:
[tex]A_1 \to[/tex] An Individual likes vehicle 1
[tex]A_2 \to[/tex] An Individual like vehicle 2
[tex]P(A_1) = 0.55[/tex]
[tex]P(A_2) = 0.65[/tex]
[tex]P (A_1\ u\ A_2 ) = 0.80[/tex]
Required
[tex]P(A_1\ n\ A_2)[/tex] --- probability that both vehicles are liked by the individual.
This is calculated as:
[tex]P(A_1\ n\ A_2) = P(A_1) + P(A_2) - P(A_1\ u\ A_2)[/tex]
So, we have:
[tex]P(A_1\ n\ A_2) = 0.55 + 0.65 - 0.80[/tex]
[tex]P(A_1\ n\ A_2) = 0.40[/tex]
A student solves for v
Which statement explains how to correct the error that was made?
The subtraction property of equality should have been applied to move m to the other side of the equation.
O The multiplication property of equality should have been applied before the division property of equality.
The division property of equality should have been applied to move the fraction to the other side of the equation.
The square root property should have been applied to both complete sides of the equation instead of to select variables.
Answers
Answer:
D (The square root property should have been applied to both complete sides of the equation instead of to select variables)
Step-by-step explanation:
On edge 2021
Find the measure of theta to the nearest tenth helpppp pleaseeee
Answers
Answer:
54.3°
Step-by-step explanation:
sinθ=opposite/hypotenuse
sinθ=26/32
sinθ=0.8125
θ=54.3°
The average marks for 25 students in a mathematics was was 48.
what was the total marks scored by the students?
Answers
Answer:
total of the data points = 1200
Step-by-step explanation:
The 'average' of a data set is the total of the data points divided by the number of data points.
Here:
total of the data points
---------------------------------- = 48
25
Multiplying both sides of this equation by 25 yields:
total of the data points = 1200
Find the volume V and surface area S of a
rectangular box with length 2 meters, width 6 meters,
and height 9 meters.
Answers
Answer:
Surface area add together all 6 sides = 24+36+108=168m^2
Volume L x W x D = 2 x 6 x 9 = 108 m ^3
Step-by-step explanation:
2 x 6 = 12
12 x 2 = 24 base and top
2 x 9 = 18
2 x 18 = 36 identical pair sides
6 x 9 = 54
2 x 54 = 108 identical pair sides
Surface area add together all 6 sides = 24+36+108=168m^2
Volume L x W x D = 2 x 6 x 9 = 108 m ^3
Just keep in mind these formulas:
Volume of rectangular prism:
Length • width • height
Surface Area of a rectangular prism:
2 (lw + hl + hw)
Where l is height, w is width, and and h is height.
Hope this absolutely helps! Have a nice day
A (non-zero) number multiplied by zero equals zero, whereas a non-zero number divided by zero is undefined.
a. True
b. False
Answers
If a triangle has angles of X+2, 2x, and 55. What are the three angle
measurements?
Answers
Answer:
41, 43 and 82
Step-by-step explanation:
hope it may help you
For a rock concert a rectangular field of size 100 m by 50 m was reserved for the
audience.
The concert was completely sold out and the field was full with all the fans standing.
Which one of the following is likely to be the best estimate of the total number of people
attending the concert?
2000
5000
20000
50000
100000
Answers
Answer:
5000
Step-by-step explanation:
but this depends upon how much room each person needs
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.
Which equation can be used to find m, the midpoint of the two numbers?
(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99
Answers
Answer:
[tex]m {}^{2} - 100 = - 99[/tex]
Step-by-step explanation:
Set up the binomial.
[tex](m - 10)[/tex]
[tex](m + 10)[/tex]
Multiply the binomial.
[tex](m - 10)(m + 10) = - 99[/tex]
Apply difference of squares rule
[tex](p + q)(p - q) = p {}^{2} - q {}^{2} [/tex]
[tex]m {}^{2} - 100 = - 99[/tex]
Answer: m^2-100=-99
Step-by-step explanation:
Set up the binomial.
(m-10)
(m+10)
Multiply the binomial.
(m-10)(m+10)=-99
Apply difference of squares rule
(p+q)(p-q) = p2-q2
Answer: m^2-100=-99
How to calculate raw score from standard score and percentile rank?
Answers
Answer:
Step-by-step explanation:
Bro i dont know what the x is tbh