Answer:
x = 4
Step-by-step explanation:
5x-9 = 2x+3
3x = 12
x = 4
Answer:
4
Step-by-step explanation:
What does it mean to say that a data point has a residual of -1?
A. The point lies 1 unit above the regression line.
B. The point lies directly on the regression line.
C. The point lies 1 unit below the regression line.
O D. The predicted value for that point is -1.
I'm sorry if it's wrong but i think it's C.
Answer:
C. The point lies 1 unit below the regression line.
Step-by-step explanation:
A residual is calculated by doing the true value minus the predicted value. For instance, if a point's true value is 5, but the predicted value is 3, the residual of the point will be 5 - 3 = 2.
The regression line is the line of predicted values. So, if a data point has a residual of -1, that means that the predicted value overpredicted the point's value. So, the point will lie C. 1 unit below the regression line.
Hope this helps!
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of miles and a standard deviation of miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Complete question is;
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answer:
The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.
Step-by-step explanation:
Let X = Life expectancy of the automobile tire
For the normal distribution, we are given;
μ = 34000
σ = 2700
Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.
Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:
P(X ≤ y) = 0.1
Using the z formula, we have;
P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1
Thus;
P(Z ≤ ([y - μ]/σ) = 0.1
From z-distribution table the Z-score at 0.1 is approximately -1.2816
This is P(Z ≤ -1.2816)
Thus;
[y - μ]/σ = -1.2816
(y - 34000)/2500 = -1.2816
y - 34000 = -1.2816 × 2500
y - 34000 = -3204
y = 34000 – 3204
y = 30796
So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.
Please answer correct answer now fast
Answer:
Approximately 13.9 units.
Step-by-step explanation:
First, note that ΔTVW is a right triangle.
Since we are given that ∠UTV is 112°, this means that ∠WTV is 68° because 180-112 is 68°.
Now that we know ∠WTV is 68°, we can use the basic trigonometric ratios to solve for VW. VW is the side opposite ∠WTV. We also know the hypotenuse. So, we would use sine. Recall that:
[tex]\sin(\theta)=opp/hyp[/tex]
Plug in 68° for theta, VW for the opposite, and 15 for the hypotenuse:
[tex]\sin(68)=VW/15\\VW=15\sin(68)\\VW\approx13.9078\approx13.9[/tex]
A ball is thrown vertically upward from the top of a cliff. The height
of the ball is modelled by the function h(t) = 65 + 10t - 5t squared,
where h(t) is the height in metres and t is time in seconds. Determine
when the ball reaches its maximum height?
Answer:
Step-by-step explanation:
To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:
[tex]-5t^2+10t=-65[/tex]
The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:
[tex]-5(t^2-2t)=-65[/tex] . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:
[tex]-5(t^2-2t+1)=-65-5[/tex]
The perfect square binomial on the left side and simplifying the right:
[tex]-5(t-1)^2=-70[/tex] . Now we'll move the 70 over and set the quadratic back equal to y:
[tex]-5(t-1)^2+70=y[/tex]
That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.
You could also do it the "calculus way" which is to find the derivative of the position function, which is
-10t + 10 = 0 and solve for t:
-10t = -10 so
t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:
[tex]h(t)=-5(1)+10(1)+65[/tex] which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.
A rectangle has a perimeter of 35.8 inches and a base of 12.6 inches. What is the height?
Answer:
Height is 5.3 inches.
Step-by-step explanation:
2* base + 2*height = 35.8
2*12.6 + 2h = 35.8
h = (35.8 - 2(12.6) / 2
= (35.8 - 25.2) /2
= 10.6 / 2
= 5.3 inches.
Answer:
5.3inStep-by-step explanation:
The formula of a perimeter of a rectangle:
[tex]P=2(l+w)[/tex]
l - length
w - width
We have
[tex]P=35.8in\\l=12.6in[/tex]
Substitute:
[tex]35.8=2(12.6+w)[/tex] divide both sides by 2
[tex]\dfrac{35.8}{2}=\dfrac{2(12.6+w)}{2}[/tex]
[tex]17.9=12.6+w[/tex] subtract 12.6 from both sides
[tex]17.9-12.6=12.6-12.6+w\\\\5.3=w\to w=5.3\ (in)[/tex]
An inverse variation includes the point (4,17). Which point would also belong in this inverse variation?
Answer:
(2, 34 )
Step-by-step explanation:
Since the points vary inversely then half the x, means double the y, thus
(2, 34) or (1, 68 ) would also belong in this inverse variation
These tables of values represent continuous functions. In which table do the
values represent an exponential function?
Answer:
did you have more
Step-by-step explanation:
Answer: i’ll attach the tables that my quiz had and if they’re the same tables that your quiz has then you can use this answer! but the answer is C. x | y
1 | 2
2 | 6
3 | 18
4 | 54
5 | 162
Step-by-step explanation:
every y-value can be multiplied by 3 to get the next y-value. also this answer is reliable because i got a 100 on my quiz on this! but here are the tables that were on my quiz:
3. The ratio of the number of male and female teachers in a school is 2 : 11. If the
number of male teachers is 112, find the number of female teachers.
Answer:
the number of female teachers is 616
Step-by-step explanation:
male 2: 112
Female 11 : x
now you want to find x which is the number of female teachers
multiply 11 with 112 and 2 with x
11 x 112= 2x
divide 2
1 232 = 2x/2
616 = x
Hope that help :)
Solve the following proportion. x−2=57 x=?
Answer:
x = 59
Step-by-step explanation:
x−2=57
Add 2 to each side
x−2+2=57+2
x = 59
Answer:
X=59
Step-by-step explanation:
x−2=57
to isolate X you would have to add 2 to each side. x-2(+2)=x and 57(+2)=59
I really need this ASAP. There are 25 students in a class. How many ways can the teacher (randomly) pick two students for the lead roles in the class play?
Answer: 300 ways
Step-by-step explanation:
We have to calculate each pair of students. You do this by multiplying 25*24 and then dividing it by 2 because then you would count them 2 times. After solving, you get 300 ways. ( It is correct because I entered it. ).
5. Lisa sold costume jewelry at a bazaar. The
first hour she sold 2 bracelets and 3 rings
for a total of $26. Later a customer bought
2 rings and paid $12. All bracelets were
priced the same. All rings were priced the
same. How much did a bracelet cost?
Answer:
$4
Step-by-step explanation:
2 Bracelets + 3 rings = $26
2 rings = $12
3 rings = x
To get the cost of 1 ring you divide 12 by 2 and the answer you get is 6.
The total cost of the 3 rings is $18( $6*3)
Then you subtract the cost of both 2 bracelets and 3 rings($26) from the cost of 3 rings($18). The answer is $8. ( THIS IS THE COST OF 2 BRACELETS)
1 BRACELET= $4( $8/2)
Select the correct answer from each drop-down menu.
Tom used the following steps to find the inverse of fx), but he thinks he made an error.
Step 1
$(x) = 4x - 2
given
Step 2
y = 4x - 2
change f(x) to y
Step 3
= 4y - 2
switch r and y
Step 4
- 2 = 4y
subtract 2 from each side
Step 5
=y
divide each side by 4
Step 6
change y to y-1(x)
Answer:
Step 3.not switch the variables.Step-by-step explanation:
Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.
Tom's first mistake was in Step 3.
To correct the mistake, he should not switch the variables.
The correct procedure is:
Step 1 : Given
f(x) = 4x - 2
Step 2 : Change f(x) to y
y = 4x - 2
Step 3 : Add 2 to both sides
[tex]4x=y+ 2[/tex]
Step 4: Divide each side by 4
[tex]x=\dfrac{y+2}{4}[/tex]
Step 5: Change x to [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\dfrac{y+2}{4}[/tex]
Solve the following equation for x . 9=x2+2
Answer:
X=3.5
Step-by-step explanation:
9=x2+2
9-2=x2
(9-2)÷2=x
PLEASE help me with this question! No nonsense answers please, and full solutions!
Answer:
third option
Step-by-step explanation:
Given
[tex]\frac{x+5}{x-2}[/tex] + [tex]\frac{x+6}{x-4}[/tex]
Multiply the numerator/denominator of the first fraction by (x - 4)
Multiply the numerator/denominator of the second fraction by (x - 2)
=[tex]\frac{(x+5)(x-4)}{(x-2)(x-4)}[/tex] + [tex]\frac{(x+6)(x-2)}{(x-2)(x-4)}[/tex]
Express the 2 fractions over the common denominator
= [tex]\frac{(x+5)(x-4)+(x+6)(x-2)}{(x-2)(x-4)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{x^2+x-20+x^2+4x-12}{x^2-6x+8}[/tex]
= [tex]\frac{2x^2+5x-32}{x^2-6x+8}[/tex]
How does the graph of f(x) = 5cos(1/2 x) - 2 differ from the graph of g(x) = 5 cos(x) - 2?
O A. The graph of f(x) is stretched vertically.
O B. The graph of f(x) is compressed vertically.
O C. The graph of f(x) is stretched horizontally.
O D. The graph of f(x) is compressed horizontally
The difference between the graph of the function is
The graph of f(x) is stretched horizontally.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
We have two function,
f(x) = 5 cos ( 1/2 x ) - 2
g(x) = 5 cos (x) -2
The graph represented by red line is function f(x) and the graph represented by blue line is g(x).
As, seen from the f(x) is stretched by 2 units then g(x).
Learn more about Function here:
https://brainly.com/question/12431044
#SPJ7
the diagram above shows a rectangle inscribed in a circle AB=10 and AC =12 caculate the total surface area of the shaded part
Answer:
[tex]71.63 \: \: \mathrm{cm^2 }[/tex]
Step-by-step explanation:
Once we know the diameter of the circle, we can figure out the problem.
The diameter of the circle = The diagonal of the rectangle inscribed in the circle
To find the diagonal of the rectangle, we can use a formula.
[tex]d=\sqrt{w^2 + l^2}[/tex]
The width is 10 cm and the length is 12 cm.
[tex]d=\sqrt{10^2 + 12^2}[/tex]
[tex]d \approx 15.62[/tex]
The diagonal of the rectangle inscribed in the circle is 15.62 cm.
The diameter of the circle is 15.62 cm.
Find the area of the whole circle.
[tex]A=\pi r^2[/tex]
The [tex]r[/tex] is the radius of the circle, to find radius from diameter we can divide the value by 2.
[tex]r = \frac{d}{2}[/tex]
[tex]r=\frac{15.62}{2}[/tex]
[tex]r=7.81[/tex]
Let’s find the area now.
[tex]A=\pi (7.81)^2[/tex]
[tex]A \approx 191.625[/tex]
Find the area of rectangle.
[tex]A=lw[/tex]
Length × Width.
[tex]A = 12 \times 10[/tex]
[tex]A=120[/tex]
Subtract the area of the whole circle with the area of rectangle to find area of shaded part.
[tex]191.625-120[/tex]
[tex]71.625 \approx 71.63[/tex]
a circular garden has a diameter of 6 yards.What is the area of the garden. Use 3.14
Answer:
28.26 yd^2
Step-by-step explanation:
A = 3.14 • r^2
Radius is half of the diameter, so 3.
A = 3.14 • 3^2
A = 3.15 • 9
A = 28.26 yd^2
Answer: The area of the garden is 28.26
Step-by-step explanation:
1. Divide the diameter in half, that gives you the radius, in this case: 3
2. Use the formula for finding the area with the radius: A= π r², and use 3.14 instead of pi. Multiply 3.14 by 3²
3. You should get 28.26 as your answer.
TRUE OF FALSE : -2 > 6
Answer: False for sure
Answer:
[tex]\boxed{\mathrm{False}}[/tex]
Step-by-step explanation:
[tex]-2<6[/tex]
-2 is less than 6.
6 is a greater value than -2.
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is
worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each
noint value are on the test
Let X be the number of questions worth 5 points, and let Y be the number of questions worth 2 points
(Answers are in the picture)
Answer:
x + y = 29
5x + 2y = 100
Step-by-step explanation:
Has 29 problems
then
x + y = 29
x be the number of worth 5 points questions:
5x
y be the number of worth 2 points questions
2y
the total both worth is 100 points
then:
5x + 2y = 100
Answer:
x + y = 29 5x + 2y = 100
Answer:
answer in picture
Step-by-step explanation:
I SHALL NAME THEE BRAINLIEST! (: Use Associative and Commutative Properties to combine like terms. Simplify the expression. Plz help me. -5X + 8X - 4 -5Y + 3 - 6Y + 2Y + 4 6 + X - 5 + 3X + 8 3B - B + 7 + 4B
Answer
6B+7X-9Y+19
Step-by-step explanation:
What is the surface area of the box if it is scaled up by a factor of 10? Boxes Dimensions 7in Height 6in Length 2in Width
Answer:
13,600 [tex]in^{2}[/tex]
Step-by-step explanation:
(h = 7, l = 6, w = 2) 10
70, 60, 20
2(h × w) + 2(h × l) + 2(w × l)
= 2(70 × 20) + 2(70 × 60) + 2(20 × 60)
= 2(1400) + 2(4200) + 2(1200)
= 2800 + 8400 + 2400
= 13,600
WILL MARK BRAINLIEST!!! PLZ HELP!!!
Answer:
x= -5
Step-by-step explanation:
The solution of f(x) = g(x) is where both functions intercept
they intercept in x = -5
Solve the following quadratic equation by completing the square ✓3x^2 + 10x + 7✓3 = 0
[tex]\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 = \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 = -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}[/tex]
What is the difference of the rational expression below?
3x/x+1 - 5/x
Answer:
3x%x+1-5/5
3× 5x
Step-by-step explanation:
3x-5x
35yx 53yx
commander wished to arrange his 8,000 soldiers in the form of a square how many more will be required to complete the square
Answer:
100
Step-by-step explanation:
Hello,
We are looking for the surrounding perfect squares.
[tex]\sqrt{8000}=89.44272...[/tex]
so
[tex]7921=89^2< 8000<90^2=8100[/tex]
So we need 100 more soldiers to form a perfect square.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the probability of rolling a three first and then a ten when a pair of dice is rolled twice
Answer:
1/216
Step-by-step explanation:
When a pair of dice is rolled, there are 36 possible different outcomes.
Of those 36 different outcomes, a sum of 3 is obtained in 2 different ways: 1, 2 and 2, 1.
Of those 36 different outcomes, a sum of 10 is possible in 3 different ways: 6, 4; 5, 5; 4, 6.
p(3 followed by 10) = p(3) * p(10) = 2/36 * 3/36 = 1/18 * 1/12 = 1/216
Which of the following steps would you perform to the system of equations
below so that the equations have equal x-coefficients?
4x+2y = 4
12x+y = 22
A. Divide both sides of the bottom equation by 2
B. Multiply both sides of the top equation by 3
C. Multiply both sides of the bottom equation by 3
D. Divide both sides of the top equation by 3
Answer:
B. Multiply both sides of the top equation by 3
Step-by-step explanation:
Given:
4x+2y = 4
12x+y = 22
For the equations to have equal x-coefficients, you'll multiply both sides of (1) by 3
4x+2y = 4 (1)
12x+y = 22 (2)
B. Multiply both sides of the top equation by 3
3(4x+2y=4)
We have,
12x+6y=12 (3)
12x+y=22 (2)
Subtract (2) from (3)
5y=12-22
5y=-10
y= -10/5
y=-2
Substitute y=-2 into (1)
4x+2y = 4
4x+2(-2)=4
4x-4=4
4x=4+4
4x=8
x=8/4
x=2
Therefore, y= -2 and x=2
Answer:
its B
Step-by-step explanation:
A pex:)
Tristan wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3% and the other bank is offering a rate of 2.5% compounded annually. If Tristan decides to deposit $7,000 for 4 years, which bank would be the better deal? 1. a simple interest rate of 3% 2. a compound interest rate of 2.5%
Answer:
The bank offering simple interest at rate of 3% for four years
Step-by-step explanation:
Hello,
To find out which deal would be better, we have to find how much accrued on the simple and compound interest.
Data;
Principal (P) = $7,000
Time = 4 years
Simple interest rate = 3%
S.I = PRT / 100
S.I = (7000 × 3 × 4) / 100
S.I = $840
In four years, he would have $7000 + $840 = $7840.
For compound interest,
C.I = P(1 + r/n)^nt
Where n = number of time compounded = 1 (since it's annually)
rate = 2.5% = 2.5/ 100 = 0.025
C.I = 7000(1 + 0.025/1)⁽¹*⁴⁾
C.I = 7000 (1 + 0.025)⁴
C.I = 7000×(1.025)⁴
C.I = 7000 × 1.1038
C.I = $7726.6
In four years he would have $7,726.6
After calculating and evaluating both option, it's advisable for him to select the bank offering a simple interest of 3% for four years
Colin, Sara and Gordon share some sweets in the ratio 7:3:1. Colin gets 54 more sweets than Gordon. How many sweets does Sara get?
let the no of sweets be 7x, 3x, and 1x
Colin gets 7x
Sara gets 3x
gordon gets 1x
7x = 1x+54 (given)
7x - 1x= 54
6x= 54
x=9
hece sara gets 3x= 3*9
=27
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
-2
Step-by-step explanation:
when setting up the synthetic division
it starts with -1(2) = -2