Answer:
B
Step-by-step explanation:
We want to find the point-slope equation of a line that passes through the points (-1, 4) and (8, -2).
Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's find the slope of the line first. We can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{-2-4}{8-(-1)}=\frac{-6}{9}=-\frac{2}{3}[/tex]
We can choose (-1, 4) as our point. So, (x₁, y₁) = (-1, 4).
Substitute:
[tex]\displaystyle y-(4)=-\frac{2}{3}(x-(-1))[/tex]
Simplify:
[tex]\displaystyle y-4=-\frac{2}{3}(x+1)[/tex]
Therefore, our answer is B.
what is the distance between point M and point provide an exact answer
What is the value of x to the nearest tenth ?
Answer:
4.7 to nearest tenth.
Step-by-step explanation:
By Pythagoras:
8^2 = x^2 + 6.5^2
x^2 = 8^2 - 6.5^2
x^2 = 64 - 42.25 = 21.75
x = √21.75
= 4.6637
$250 is invested in an account earning 6.8% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer:
36123.5994797
Suppose a large consignment of televisions contained 11% defectives. If a sample of size 237 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large consignment of televisions contained 11% defectives.
This means that [tex]p = 0.11[/tex]
Sample of size 237
This means that [tex]n = 237[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.11[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.11*0.89}{237}} = 0.0203[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
P-value of Z when X = 0.11 + 0.03 = 0.14 subtracted by the p-value of Z when X = 0.11 - 0.03 = 0.08. So
X = 0.14
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.14 - 0.11}{0.0203}[/tex]
[tex]Z = 1.48[/tex]
[tex]Z = 1.48[/tex] has a p-value of 0.9306
X = 0.08
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.08 - 0.11}{0.0203}[/tex]
[tex]Z = -1.48[/tex]
[tex]Z = -1.48[/tex] has a p-value of 0.0694
0.9306 - 0.0694 = 0.8612
0.8612 = 86.12% probability that the sample proportion will differ from the population proportion by less than 3%
What would be the answer to this problem
Answer:
1
Step-by-step explanation:
When you multiply two quantities under a root, it is just like normal multiplication. 2*18 is 36, which is the perfect square of six. Since this number can be expressed as p/q (where p and q are integers; the values here are 6 and 1), it is rational.
Find the exact value
Answer:
Step-by-step explanation:
[tex]sin({\alpha\over{2}})=\pm\sqrt{{1-cos(\alpha)\over{2}}}\Rightarrow sin({30\over{2}})=+\sqrt{{1-{\sqrt{3}\over{2}}\over{2}}}={\sqrt{{2-\sqrt{3}}}\over{2}}[/tex]
[tex]cos({\alpha\over{2}})=\pm\sqrt{{1+cos(\alpha)}\over{2}}=+\sqrt{{1+{\sqrt{3}\over{2}}\over{2}}}={\sqrt{{2+\sqrt{3}}}\over{2}}[/tex]
substituting we get:
[tex]tg(15)=\sqrt{{2-\sqrt{3}}\over{2+\sqrt{3}}}[/tex]
Identify the hypotheses and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular
Answers:
hypothesis = two lines intersect at right anglesconclusion = the two lines are perpendicular=================================================
Explanation:
Any conditional statement is of the form "If P, then Q"
P is the hypothesis, which is the initial set up to lead to the conclusion Q
As an example, the sentence "If it rains, then it gets wet on the road" has P = "it rains" as the hypothesis and Q = "it gets wet on the road" as the conclusion.
-------------
In short, the format is "If hypothesis, then conclusion".
What is the midpoint of the segment shown below? (1,2) (1, -5)
A. (1, - 3/2)
B. (2, - 3/2)
C. (1,-3)
D. (2, -3)
9514 1404 393
Answer:
A. (1, - 3/2)
Step-by-step explanation:
The coordinate of the midpoint is the average of the endpoint coordinates.
M = (A +B)/2
M = ((1, 2) +(1, -5))/2 = (1+1, 2-5)/2 = (2, -3)/2
M = (1, -3/2) . . . . . matches choice A
Answer:
A. (1, - 3/2)
Step-by-step explanation:
Mr. Gonzales has only $55.00 to spend at a clothing store. He wants to buy a shirt that costs $30, including tax, and some bracelets that cost $5
including tax Write an equation to determine x, the maximum number of bracelets Mr. Gonzales could buy
Can someone please help me?
Answer:
third and last one
Step-by-step explanation:
im pretty sure those are the answers i used a graphing calculator.
9514 1404 393
Answer:
C and E
Step-by-step explanation:
The rules of exponents apply:
(a^b)(a^c) = a^(b+c)
__
[tex]200(10^x)=20\cdot10^1\cdot10^x=\boxed{20(10^{x+1})}\\\\=2\cdot10^2\cdot10^x=\boxed{2(10^{x+2})}[/tex]
These match the 3rd (C) and last (E) choices.
The lines shown below are parallel. If the green line has a slope of -3/7, what is
the slope of the red line?
A. -3/7
B. 7/3
C. -7/3
D. 3/7
Find the length of side x in
Answer: x=3
Step-by-step explanation:
from figure
=>tan45= x/3
=>x= 3tan45
=>x=3
Answer:
Step-by-step explanation:
here hypotenuse is x
since it is an isosceles triangle the other side of the triangle also must 3.
using pythagoras theorem
a^2 + b^2 = c^2
3^2 + 3^2 = x^2
9 + 9 = x^2
18 = x^2
[tex]\sqrt{18} = x[/tex]
If P dollars is deposited in an account paying R percent annual interest, approximate the amount in the account after x years.
P = $1600, R = 8%, x = 16
The amount in the account after 16 years is approximately
Answer: $3648
Step-by-step explanation:
Firstly, we have to calculate the interest which will be:
= Principal × Rate × Time
= $1600 × 8% × 16
= $1600 × 0.08 × 16
= $2048
Therefore, the amount in the account after 16 years will be:
= Principal + Interest.
= $1600 + $2048
= $3648
What’s the answer to this? I need to do this for extra credit and I have no idea what this is
9514 1404 393
Answer:
20
Step-by-step explanation:
As with any evaluation problem, take it step by step according to the order of operations.
The first thing you need to do here is compute a#b.
The given definition can be simplified a bit for evaluation purposes:
a#b = a²b -ab² = ab(a -b)
Then for a=3 and b=-2, you have ...
(3)#(-2) = (3)(-2)(3 -(-2)) = -6(5) = -30
Now, you are in a position to evaluate the expression you're asked for.
[tex]\dfrac{(a\#b)^2}{15-(a\#b)}=\dfrac{(-30)^2}{15-(-30)}=\dfrac{900}{45}=\boxed{20}[/tex]
Suppose aggressive behavior is the dependent variable in a regression model and the other variables are independent variables. Is there evidence of extreme Multicollinearity
Answer and explanation:
Multicollinearity happens when multiple independent variables are correlated and therefore it is hard to determine which independent variable has the most impact or is most significantly affecting the dependent variable. This could be a source of confusion as the coefficients become less reliable.
Extreme multicollinearity occurs when there is exaggerated standard errors or increased variance of coefficient estimates.
What is the radius of the quarter if the area is about 452.16 square millimeters ? Use 3.14 for pi. Do not label. Do not round.
Answer:
Step-by-step explanation:
Im not sure but i think
452.16/3.14.= 3.14r^2/3.14
144(square root sign) = squarw root sign r^2)
12=r
An airplane travels 240 miles in 3 hours with the wind. The return trip against the wind takes 4 hours. What is the wind speed and the speed of the airplane in still air?
Answer:
Let p = the speed of the plane
and w = the speed of the wind
It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. So we set up a system of equations.
600mi3hr=p−w600mi2hr=p+w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation. I'll solve for x in the first equation:
200mph = p - w
Add w to both sides:
p = 200mph + w
Now we can substitute the x that we found in the first equation into the second equation so we can solve for w:
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
Divide by 2:
50mph = w
So the speed of the wind is 50mph.
Now plug the value we just found back in to either equation to find the speed of the plane, I'll plug it into the first equation:
200mph = p - 50mph
Add 50mph on both sides:
250mph = p
So the speed of the plane in still air is 250mph.
Answer:
140miles/hour
Step-by-step explanation:
Speed of airplane + speed of wind
=240miles/3 hours + 240miles/4 hours
=80miles/hour +60miles/hour
= 140miles/hour
According to a study by the Alliance of American Insurers, it costs more than three times the original purchase price in parts and labor to reconstruct a wrecked Chevrolet. Explain the reasons for this large discrepancy in terms of the processes used to assemble the original car and those required to reconstruct the wrecked car.
Answer:
i dont know hun i am very sorry
Step-by-step explanation:
What is 75% of eight
Answer:
6
Step-by-step explanation:
.....................
Answer:
6
Step-by-step explanation:
pecentage calculator.what is 75 percent of 8?=6
what is the area of the triangle in centimetres Square?
Answer:
Step-by-step explanation:
either do 23 x23
or
23 x 16 ( do this first )
please help if you can
The scale is 5/4
Because:
Let's take
20/16 = 5/4
20/16 = 5/4
15/12 = 5/4
Answer:
5/2 or 5:2 ratio is the reduced fraction from the scale factor A to B.
HELP PLEASEEEEEEEE !!!
Joe made 5 loaves of banana bread.
If one serving is 1/5
loaf, how many servings does
Justine have?
T
Answer:
5 divided by 1/5
5 x 5/1 = 25, he has 25 servings.
- Susan drives north on the 405 Freeway at 50
miles per hour. Two hours after Susan
passes under Westminster Blvd, Maria
enters the 405 Freeway at Westminster Blvd
and heads north at 60 miles per hour. If both
cars maintain their average speeds, how long
will it take Mary to catch up with Susan?
Answer:
If both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.
Step-by-step explanation:
Since Susan drives north on the 405 Freeway at 50 miles per hour, and two hours after Susan passes under Westminster Blvd, Maria enters the 405 Freeway at Westminster Blvd and heads north at 60 miles per hour, if both cars maintain their average speeds, to determine how long will it take Mary to catch up with Susan the following calculation must be performed:
Hour 1 = 50
Hour 2 = 100
Hour 3 = 150 - 60
Hour 4 = 200 - 120
Hour 5 = 250 - 180
Hour 6 = 300 - 240
Hour 7 = 350 - 300
Hour 8 = 400 - 360
Hour 9 = 450 - 420
Hour 10 = 500 - 480
Hour 11 = 550 - 540
Hour 12 = 600 - 600
Therefore, if both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.
Find the sum 14+8+2+...+(−274)+(−280)
Answer:
Sn=−6650
Step-by-step explanation:
HELP NEEDED IMMEDIATE PLEASE AND THANKS :)
Answer:
OMGGGG wanna work on this together I need this question too
Which first step most directly leads to the solution of the equation below?
x^2 – 16 = 65
A. Add 16 to both sides of the equation.
B. Add -x^2 to both sides of the equation.
C. Rewrite the left-hand side as (x - 4)(x+4)
D. Rewrite the left-hand side as (x - 4)^2
Faisal tries to solve
(x + 2)(x - 7) = 0
Here is his working.
(x + 2) = 0
or
(x - 7) = 0
Answer
x = 2
or
x=7
Give a reason why his answer is wrong.
Answer:
He should have subtracted 2 from each side to find the solution for x+2 =0
Step-by-step explanation:
(x + 2)(x - 7) = 0
Using the zero product property
x+2 = 0 x-7=0
x+2-2=0-2 x-7+7=0+7
x = -2 x=7
He should have subtracted 2 from each side to find the solution for x+2 =0
Step-by-step explanation:
the steps he took are correct but the answer of x is somehow wrong because
(x+2)=0
x = -2
and not x = 2
alguien me lo puede de hacer
Answer:
..........
Step-by-step explanation:
[tex]\pi[/tex]
What is the equation of the line graphed below?
Answer: [tex]y=-\frac{1}{3}x[/tex]
Step-by-step explanation:
From the origin we can see to get to the point plotted we have to go down 1 and right three giving us the slope [tex]\frac{-1}{3}[/tex]
These are in the form of y=mx+b
b is the y-intercept and m is the slope
since the y-intercept is 0 b is 0 and isn't need leaving us with y=mx
We can put our slope into the equation giving us the answer in C
The required equation of the line is that passing through the point (3, -1) is y = -x/3.
Given that,
To determine the equation of the line that passes through the origin and a point (3, -1).
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Since the line passes from the origin and a point (3, -1)
So, the slope of the line is given by,
m = (y₂ - y₁) / (x₂ - x₁)
Substitute the respective values in the above equation,
m = -1 + 0 / 3 - 0
m = -1/3,
Now the point-slope form of the equation of a line is,
y - y₁ = m (x - x₁)
Substitute the respective values in the above equation,
y + 1 = -1/3 (x - 3)
y = -x/3
Thus, the required equation of the line is that passing through the point (3, -1) is y = -x/3.
Learn more about slopes here:
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