what is an equation of the line that passes through the points (4,-6) and has a slope of -3
1) y = -3x + 6
2)y = -3x - 6
3)y = -3x + 10
4) y = -3x + 14
Answer:
1) y = -3x + 6
Step-by-step explanation:
1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute -3 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:
[tex]y+6 = -3(x-4)[/tex]
2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.
[tex]y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6[/tex]
So, the first option is correct.
Luna packed two chocolate bars for her trip. One s'mores uses 1/2 of a bar. If she has one s'mores a day, about how many days will the chocolates last?
Answer:
4 days.
Step-by-step explanation:
Each bar has 2 halves.
That means that in total, Luna has 4 halves, or, 4/2 parts.
If she uses half of a bar each day, then she will last 4 days.
An Internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the proportion of all customers who have experienced a service interruption. (0.080, 0.123) (0.873, 0.924) (0.076, 0.127) (0.102, 0.898)
Answer: a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).
Step-by-step explanation:
Let p be the population proportion of all customers who have experienced a service interruption.
Confidence interval for p:[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex], where [tex]\hat{p}[/tex] = sample proportion, n= sample size, z* = critical z-value.
Given: n = 540
[tex]\hat{p}=\dfrac{55}{540}=0.102[/tex]
z* = 1.96
The required confidence interval:
[tex]0.102\pm (1.96)\sqrt{\dfrac{0.102(1-0.102)}{540}}\\\\=0.102\pm (1.96)(0.013024)\\\\=0.102\pm$$0.02552704\\\\=(0.102-$$0.02552704, 0.102+0.02552704)\\\\\approx(0.076, 0.127)[/tex]
Hence, a 95% confidence interval for the proportion of all customers who have experienced a service interruption: (0.076, 0.127).
Mario is arranging unit cubes. He stacks all of the cubes to make a solid figure with no gaps.
What is the volume of the figure Mario creates?
a.9 units cube
b.10 units cubed
c.6 units cubed
d.4 units cubed
Answer:
4units
Step-by-step explanation:
because he stack 4 units in right side
what is 24 1/2 by 12 4/5?
Answer:
313.6
Step-by-step explanation:
24 1/2 * 12 4/5 = 1568/5 = 313 3/5
= 313.6
Hope I helped (p.s. maybe brainliest?)
Answer:
24 1/2 ÷ 12 4/5 = 1 117/128
Step-by-step explanation:
:))
The following MINITAB output presents the results of a hypothesis test for a population mean μ.
One-Sample Z : X
Test of mu = 73.5 vs not = 73.5
The assumed standard deviation = 2.3634
Variable N Mean StDev SE Mean 95% 01 Z P
X 145 73.2461 2.3634 0.1963 (72.8614, 73.6308) -1.29 0.196
A. Is this a one-tailed or two tailed test?
B. What is the null hypothesis?
C. What is the P-value?
D. Use the output to compute the P-value for the test of H0 : μ ≥ 73.6 versus H1 : μ < 73.6.
Answer:
A. This is a two tailed test.
B. H0: μ= 73.5
C. P-value= 0.196
D. The P-Value is 0.460172 for one tailed test .
Step-by-step explanation:
The given data is
Variable N Mean StDev SE Mean 95% 01 Z P
X 145 73.2461 2.3634 0.1963 (72.8614, 73.6308) -1.29 0.196
A. Is this a one-tailed or two tailed test?
This is a two tailed test because H0: μ= 73.5 against Ha: μ ≠ 73.5
B. What is the null hypothesis?
H0: μ= 73.5
C. What is the P-value?
P-value= 0.196
D. Use the output to compute the P-value for the test of H0 : μ ≥ 73.6 versus H1 : μ < 73.6.
For z= -1.29 the P-Value is 0.460172 for one tailed test .
The result is not significant at p < 0.05.
Use synthetic division to solve (2x3+4x2 – 35x+15) +(x-3). What is the quotient?
O 2x2–2x-29+
102
X+ 3
102
O 2x2 - 2x-29+
X-3
2x + 10x2 - 6x
2x2 + 10x-5
Given:
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
To find:
The quotient by using the synthetic division.
Solution:
We have,
[tex](2x^3+4x^2-35x+15)\div (x-3)[/tex]
Here,
Dividend = [tex](2x^3+4x^2-35x+15)[/tex]
Divisor = [tex]x-3[/tex]
The coefficient of dividend are [tex]2, 4, -35, 15[/tex]. Write the coefficients of the dividend on the top row and we need to use 3 as divisor for synthetic division. The synthetic division is show below:
[tex]3 | 2\quad \quad 4\quad \quad -35\quad \quad 15\\\quad{}\quad{} \quad \quad \ 6\quad \quad \ \ \ 30\quad -15\\\overline{\quad 2\quad \quad 10\quad \quad -5\quad \quad 0\ \ \ }[/tex]
The bottom row represents the coefficients of quotient but the last element of bottom row is the remainder.
Degree of dividend is 3 and degree of division is 1. So, the degree of quotient must be [tex]3-1=2[/tex].
The quotient is [tex]2x^2+10x-5[/tex] and the reminder is 0.
Therefore, the correct option is D.
Answer: divisor: x+4, dividend: 2x^3+11x^2+18x+9, quotient: 2x^2+5x+3
Step-by-step explanation:
Find the value of x in this figure.
50
40
30
60
Answer:
the answer isnt right just trying to see if anyone else knows it
Step-by-step explanation:
-12 + 45
25 + -77
Theres more in pic
Answer
|-12|+|45|=|12|+|45|= 12+45=57
Step-by-step explanation:
When you take the absolute value of a negative number it is the same thing as taking as a positive number. The absolute value is just that number. Once you teach the absolute value of each number perform the operation given In the problem.
WILL MAKE BRAINLIEST!!!
write the equation given the slope and y-intercept
1.) m= 1, b=2
2.) m= 1/4, b=0
3.) m= -3, b= 0.5
4.) m= 0.2, b=0.8
Katrina is rolling a six-sided number cube.
1) Determine the probability Katrina will roll a number equal to or less than 2.
2) Determine the probability Katrina will roll a number greater than 2.
Answer:
Step-by-step explanation:
1. 1 or 2 so 2 options
2 out of 6 is 33%
2. 3 or 4 or 5 or 6 so 4 options
4 out of 6 is 66%
The product of 1and 3/4 is ____________ 3/4.
Answer:
https://youtu.be/cqF6M25kqq4
Step-by-step explanation:
Pls answer just the answer
Answer:
588000
Step-by-step explanation:
if i am wrong pls tell me cause i think there's a different answer gl g
Answer:
$103,421.88
Step-by-step explanation:
Given:
P = 70000
r = 0.05
n = 1
t = 8
Work:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=70000(1+\frac{0.05}{1} )^{1*8}\\\\A=70000(1.05)^8\\\\A=103421.88[/tex]
Which city has a higher median?
The correct answer is Arcadia
Let me explain why...
The median is the number that's in-between the other 2 numbers so for Millersburg the median around 200ish but the median for Arcadia is is exactly 240.This means that Arcadia is your answer
Hope you have an amazing day <3
-Yo MaMa
An apartment complex developer is considering building apartments in College Town, but first wants to do a market study. A sample was selected of monthly rent values ($) for 80 studio apartments in College Town with sample mean of 498.76. (Based on past experience, the developer assumes a known value of s = $65 for the population standard deviation.)
a. Develop a 98% confidence interval for the mean monthly rent for all studio apartments in this city.
b. Suppose the apartment developer wants a 98% confidence interval estimate of the population mean with a margin of error of E = $15. What sample size is needed?
Answer:
a. The 98% confidence interval for the mean monthly rent for all studio apartments in this city is between $481.85 and $515.67
b. A sample size of 102 is needed.
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{65}{\sqrt{80}} = 16.91[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 498.76 - 16.91 = $481.85
The upper end of the interval is the sample mean added to M. So it is 498.76 + 16.91 = $515.67
The 98% confidence interval for the mean monthly rent for all studio apartments in this city is between $481.85 and $515.67
Question b:
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 2.327\frac{65}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 2.327*65[/tex]
[tex]\sqrt{n} = \frac{2.327*65}{15}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*65}{15})^2[/tex]
[tex]n = 101.68[/tex]
Rounding up:
A sample size of 102 is needed.
what is the total surface area?
Answer:
231.5in squared
Step-by-step explanation:
Both faces area formula
Rectangle: l x w
triangle: b x h / 2
i need help asap please and thank you
Answer:
113
Step-by-step explanation:
First we need to find theother 2 angles of the triangle.
We are given that the top angle is 60°
We know that the angles of a triangle add up to 180°
To find the bottom left angle of the triangle...
We can see that it is alternate exterior angles so they will equal.
To find the third angle of the triangle...
180 - 60 (given angle) -53 (alternate exterior angle) = 67°
Now we know that the bottom right angle inside the triangle is 67°.
To find x...
subtract 67 from 180 because the like is a combination of x and the 67° angle we just found. (a straight line angle = 180°)
180 - 67 = 113
x=30 y=6
X x Y - 4 + 15 /2=?
Also Anyone on here got Queston cove?
Lol
Answer:
Hey mate.....
Step-by-step explanation:
This is ur answer.....
= 30 × 6 - 4 + 15 / 2= (30 × 6) - (4 + 15) / 2
= (180 - 19) / 2
= 161 / 2
= 80.5
Hope it helps!
mark me brainliest pls.....
Follow me! :)
PLEASE ANSWER ASAP: On a farm, the farmer decides to give pizza to her 18 ducks as a special treat. She orders 3 pizzas, and the total price is $26.28. What is the unit price of each pizza? (4 points)
PLEASE SHOW STEP AND ANSWER!
Answer:
8.76
Step-by-step explanation:
$26.28 ÷3=8.76
since 26.38 is the total amount of all the 3 pizzas then we would have to divide 26.28 by the amoun of pizzas that was bought, which is 3, and you will get your answer
Which angle number represents an angle vertical to ZUXR?
T
X1
R
3/2
S
Y
4
5
U
W
Answer:
angle number 1
Step-by-step explanation:
An angle that is vertical to <UXR is an angle that is directly opposite to <UXR, which share the same vertex, X, as <UXR.
From the diagram given, the angle number that shares the same vertex as <UXR and is directly opposite to <UXR is angle number 1 (<SXT).
<1 = <UXR
An airplane is flying with a constant altitude at a speed of 450 mph in a direction 10° north of west directly towards its final destination. The airplane then encounters wind blowing at a steady 34 mph in a direction 85° north of east. If the pilot does not correct his course after encountering the wind, at what speed and in what direction (counterclockwise from east) will the plane be traveling? Speed: _____mph Direction:______ ° If the airplane had encountered no wind at all, it would have reached its final destination in two hours along its original course. Assuming the pilot never corrected his course and that the wind continues to blow at the given speed and direction, how far from its final destination is the airplane after two hours of flying under the given conditions?____ miles
Answer:
21
Step-by-step explanation:
A narrow arch supporting a stone bridge is in the shape of half of an ellipse and is 24 meters long and 8 meters high. A person standing at one location throws a rubber ball against the arch. No matter what direction the ball is thrown it always bounces off the arch once and strikes the same point on the ground. What is the distance between he person throwing the ball and the point on the ground at which the ball first strikes
Answer:
[tex]X=17.9m[/tex]
Step-by-step explanation:
Length of arc [tex]L_a=24m[/tex]
Height of arc [tex]H_a=8m[/tex]
Tet the length on the ground be
[tex]2a=24\\ a=12m[/tex]
Generally the Pythagoras equation is mathematically given by
[tex]a^2=b^2+c^2[/tex]
[tex]c^2=a^2+b^2[/tex]
[tex]c^2=12^2+8^2[/tex]
[tex]c^2=144^2+64^2[/tex]
[tex]c=8.9[/tex]
Therefore the distance between he person throwing the ball and the point on the ground at which the ball first strikes X
[tex]X=2c\\X=2*8.9[/tex]
[tex]X=17.9m[/tex]
Is this correct? Can someone help me pls
Answer:
ye
Step-by-step explanation:
What is the approximate volume of a half sphere with a diameter of 8 cm?
Answer:
134.04
Step-by-step explanation:
What is the axis of symmetry for this function?
y=x2 - 2x - 3
.
Answer:
x=1
Step-by-step explanation:
You can find the axis of symmetry from the equation of a function by using the formula x= -b / 2a ( ax^2 + bx + c).
In this particular function, you can see that b is 1 and c is -3.
x= -b / 2a
x= - (-2) / 2(1)
x= 2 / 1
x= 1
john takes a small business loan
for $18,000. the term for
repayment is 60 months and
the annual interest rate is 5.25%.
using the monthly payment
formula, what is the estimated
monthly payment?
9514 1404 393
Answer:
$341.75
Step-by-step explanation:
You have not provided the formula, so we'll use one we like:
A = P(r/12)/(1 -(1 +r/12)^(-n)) . . . . principal P, annual rate r, n months
A = $18,000(0.0525/12)/(1 -(1 +0.0525/12)^-60) ≈ $341.75
The monthly payment is about $341.75.
Pls help !!!! Due today
Answer:
Im not so sure but i think its the 3rd option 168cm^2
Step-by-step explanation:
Please help me :) I will give BRAINLIEST !! Please help it’s so confusing for me!
Answer:
Step-by-step explanation:
4. LA and B form a linear pair. If
MZA = (6x – 19) and mZB = (11x-22),
find mZB.
I
A. 59
B. 65
C. 115
D. 121
Help!
Answer:
Supplementary angles - d ... 4. The complement of an angle of t° is an angle of_70-7_º mais. 5. If 4 1 and 22 are ... Linear Pair Postulate - If two angles form a linear pair, then they are supplementary. 1. 2 ... LA and Z B are complementary.
Step-by-step explanation:
The value of x is 13, then the measure of angle ∠B will be 121 degrees. Then the correct option is D.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
The angle ∠A and ∠B form a linear pair.
If ∠A = (6x – 19) and ∠B = (11x – 22).
Then we have
∠A + ∠B = 180°
(6x – 19) + (11x – 22) = 180
17x – 41 = 180
17x = 221
x = 13
The value of x is 13, then the measure of angle ∠B will be
∠B = (11 × 13 – 22)
∠B = 143 – 22
∠B = 121
More about the angled link is given below.
https://brainly.com/question/15767203
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x²/2x + 6/
3х - 5/X +3
Option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
What is a rational expression?A rational expression is the ratio of two polynomials. It looks like fractions that have variables in their denominators. A rational expression is considered simplified if there are no common factors in its numerator and denominator.
For the given situation,
The rational expression is
7x²/(2x + 6) ÷ (3х - 5)/(x +3)
⇒ [tex]\frac{\frac{7x^{2} }{2x+6} }{\frac{3x-5}{x+3} }[/tex]
In conversion of division to multiplication, we need to change the division sign to multiplication sign and reciprocal the rational expression for simplification.
⇒ [tex](\frac{7x^{2} }{2x+6} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(x+3)} )(\frac{x+3}{3x-5} )[/tex]
⇒ [tex](\frac{7x^{2} }{2(1)} )(\frac{1}{3x-5} )[/tex]
⇒ [tex]\frac{7x^{2} }{6x-10}[/tex]
Hence we can conclude that option (E) 7x^2/(6x-10) is the reduced form of the rational expression is the correct answer.
Learn more about rational expression here
https://brainly.com/question/17134322
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