Given:
\(\begin{gathered} mean(\mu)=28mpg \\ Standard\text{ }deviation(\sigma)=2mpg \end{gathered}\)To Determine: The percentage with greater than 24mpg
Solution
\(Z=\frac{x-\mu}{\sigma}\)\(\begin{gathered} P(x>Z)=P(x>\frac{24-28}{2}) \\ P(x>Z)=P(x>-2) \end{gathered}\)Use the quadratic formula to solve the equation. Use a calculator to give solutions correct to the nearest tenth
4x²= 4 + 4x Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed. Use a comma to separate answers as needed.) B. There is no real solution. .
The solution set is A. {1.3, -0.5}.for the quadratic given equation
The quadratic equation is 4x² = 4 + 4x. We can rewrite this equation as 4x² - 4x - 4 = 0.
Using the quadratic formula, we have:
x = (4 ± √(4² - 4 * 4 * -4)) / (2 * 4) = (4 ± √(4² + 64)) / 8 = (4 ± √68) / 8
The solutions are:
x = (4 + √68) / 8 ≈ 1.3 and x = (4 - √68) / 8 ≈ -0.5
Therefore, the solution set is A. {1.3, -0.5}.
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BEGINNING COORDINATES:
A- 2,2
B- 0,2
C- 4,4
Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A′B′C′. What are the coordinates of triangle A′B′C′?
Question 1 options:
A)
A′ (0, 4), B′ (4, 0), C′ (16, 16)
B)
A′ (0, –4), B′ (–4, 0), C′ (–8, –8)
C)
A′ (0, 4), B′ (4, 0), C′ (8, 8)
D)
A′ (4, 0), B′ (0, 4), C′ (8, 8)
Answer:
The correct option is;
A'(4, 4), B'(0, 4), C'(8, 8).
Step-by-step explanation:
The beginning coordinates are;
A -2, 2
B - 0, 2
C - 4, 4
Given that triangle ABC is dilated by 2, the center of dilation being the origin, (0, 0), we have;
Given that the center of dilation is the origin, we multiply the x, and y values by the scale factor as follows;
(x, y) → (2·x, 2·y)
Which gives;
A - (2, 2) → A'(2×2, 2×2) = A'(4, 4)
B - (0, 2) → B'(2×0, 2×2) = B'(0, 4)
C - (4, 4) → C'(2×4, 2×4) = C'(8, 8)
The correct option is A'(4, 4), B'(0, 4), C'(8, 8).
(1/12)^-2b•12^-2b+2=12?
Step-by-step explanation:
(1/12)^-2b x 12^-2b+2=12
12^-(-2b) x 12^-2b+2=12
12^2b+(-2b+12)=12
2b-2b+12=12
=1
The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
Pks answer this attachment
Answer:
Anita's shape
Step-by-step explanation:
A shape with less number of sides will have longer sides.
Since, Anita's shape has less number of sides as compared to others.
Therefore, Anita's shape will have longest sides.
Ethan is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and rolls a fair die in the shape of
a cube that has six sides labeled 1 to 6?
Answer:
18
Step-by-step explanation:
3x6
Given lines l, m and n are all parallel and cut by two transversal lines, find the value
of x.
11
m
X
35
The value of x is 134.
Based on the diagram, we know that lines l, m, and n are parallel. Therefore, the alternate interior angles formed by transversal line m are congruent to the corresponding alternate interior angles formed by transversal line 11:
m and 11 are alternate interior angles, so they are congruent.
Also, the corresponding angles formed by transversals line n and 11 are congruent to the corresponding corresponding angles formed by transversals line m and 35:
11 and 35 are corresponding angles, so they are congruent.
Therefore, we can set up an equation based on the fact that the sum of the measures of the angles around any point is 360 degrees:
m + x + 35 = 180
Simplifying this equation, we get:
x + m = 145
Since m and 11 are congruent, we can substitute m with 11:
x + 11 = 145
Subtracting 11 from both sides, we get:
x = 134
Therefore, the value of x is 134.
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Rachel is a stunt driver, and she's escaping from a building that is about to explode! the variable d models rachel's distance from her exit (in meters) ttt seconds after the cameras began recording the stunt. d=-38t + 220, what is rachel's speed?
Its speed of Rachel would be 30 meters per second.
Given that,
Stunt driver Rachel is trying to get out of a building that is going to blow up.
Here, the equation is,
\(d = - 38t + 220\)
Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.
Now, Velocity is the rate at which a distance changes over time.
\(d = - 38t + 220\)
\(\dfrac{d(d)}{dt} = - 38\)
Hence, Speed is the magnitude of velocity.
\(|- 38| = 38\)
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Solve The Equation On The Interval [0, 2.phi). Sin 2x + Sin X = 0
The equation sin(2x) + sin(x) = 0 is satisfied by two solutions on the interval [0, 2π): x = 0 and x = π.
To solve the equation sin(2x) + sin(x) = 0, we can rewrite it as sin(2x) = -sin(x).
Using the double-angle formula for sine, we have 2sin(x)cos(x) = -sin(x).
Now, we can consider two cases:
Case 1: sin(x) ≠ 0
In this case, we can divide both sides of the equation by sin(x), giving 2cos(x) = -1. Solving for cos(x), we find cos(x) = -1/2. This occurs at x = π/3 and x = 5π/3. However, we need to check if these values fall within the given interval [0, 2π). Only x = π/3 satisfies this condition.
Case 2: sin(x) = 0
If sin(x) = 0, then x must be an integer multiple of π. Within the given interval [0, 2π), x = 0 and x = π are solutions.
Therefore, the equation sin(2x) + sin(x) = 0 is satisfied by two solutions on the interval [0, 2π): x = 0 and x = π.
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The value of x is:
.
9.
18.
None of these choices are correct.
Hello!
In the given figure we can see that it is a right angled triangle .
Where,
Base is 9
We have to find the value of x i.e Hypotenuse
Here we are given base and we need to find the Hypotenuse.
Also we have been given the value of theta = 45°
Using trigonometric ratio :
cos \(\theta = \dfrac{ B}{H} \)
As per the question we have hypotenuse = x
Plugging the required values,
\( \cos 45 \degree = \dfrac{9}{x} \)
\( \dfrac{1}{ \sqrt{2} } = \dfrac{9}{x} \: \: \: \: \bigg(\because \cos 45\degree = \dfrac{1}{\sqrt2} \bigg)\)
further solving by cross multiplication
\(x = 9 \sqrt{2} \)
Hence, The value of x is 9√2
Answer : Option 1
Hope it helps! :)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 5 hours.
23.0
0.70
0.23
0.16
The probability that a student studied for 5 hours is given as follows:
0.23.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of students in this problem is given as follows:
1 + 3 + 2 + 5 + 9 + 7 + 3 = 30.
Out of those 30 students, 7 studied five hours, hence the probability is given as follows:
p = 7/30 = 0.23.
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Uber has no pickup fee but charges $0.25 per mile. Lyft charges $3 for pickup and $0.15 per mile. Find the number of miles for which the cost of your Uber and Lyft is the same.
Answer:
Step-by-step explanation:
15
The number of miles for which the cost of Uber and Lyft is the same is 30.
How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.
Let the number of miles covered be = x
Given, the cost of travel = Pickup Fee + Cost per mile
Given, the pickup fee for Uber = $ 0
The cost per mile for Uber = $ 0.25
Again, the pickup fee for Lyft = $ 3
The cost per mile for Lyft = $ 0.15
Thus, the cost of travel for Uber = 0 + 0.25x -- (i)
Also, the cost of travel for Lyft = 3 + 0.15x -- (ii)
As per question, (i) and (ii) are equal.
Thus, 0 + 0.25x = 3 + 0.15 x ⇒ (0.25 - 0.15)x = 3 ⇒ 0.10x = 3
⇒ x = 3/0.10 ⇒ x = 30
Thus, for 30 miles the cost of Uber and Lyft is the same.
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PLZ HELP!!!!!!! (20 points)
Which of the sets of ordered pairs represents a function? (4 points)
A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}
Group of answer choices
Only A
Only B
Both A and B
Neither A nor B
Answer:
Neither A nor B
Step-by-step explanation:
The set of pairs, where the front member of every sequence pair must be unique.
Determine if the two figures are similar by using transformations
Step-by-step explanation:
they are the same because FIGH just the ENLARGEMENT of ABCD
do you think i should do airsoft i always wanted to
Answer:
Sounds like a good idea
Step-by-step explanation:
(mark this branliest if you do)
Answer:
YES
Step-by-step explanation:
Its so fun
consider the matrix : what is the minimal approximation error achievable by a rank-1 approximation to ?
The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is
||A - A1||₂=0 where A is 2×2 matrix.
We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]
note here that C₂= 3C₁
where Cᵢ --> iᵗʰ column
v = [ 5 ; 6 ; -1 ; -4 ; 2]
||v||² = 82 => ||v|| = √82
and A At v = 820 v
and A At = [ 82 246 ; 246 738]
AAt [1;3] = 820[1;3]
=> v1 = 1/√10(1,3)^t
Then the best rank of 1 approx
= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]
= A
Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0
Hence, the minimal Approx. ||A - A1||2 = 0 .
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Complete question:
Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?
calculate the probability when x=4 of a binomial probability distribution where n=8 and p=0.20 submit final answer only & be sure answer is 4 decimal places.
The probability, when x = 4, in a binomial probability distribution with n = 8 and p = 0.20, is 0.1653.
In a binomial probability distribution, the formula to calculate the probability of a specific value is P(x) = C(n, x) * p^x * (1 - p)^(n - x), where P(x) is the probability, n is the number of trials, x is the desired value, p is the probability of success in a single trial, and C(n, x) represents the binomial coefficient.
In this case, we are given n = 8 (the number of trials) and p = 0.20 (the probability of success in a single trial). We want to calculate the probability when x = 4.
Plugging these values into the formula, we have P(4) = C(8, 4) * (0.20)^4 * (1 - 0.20)^(8 - 4). Using the binomial coefficient, C(8, 4) = 70, we can simplify the equation further: P(4) = 70 * (0.20)^4 * (0.80)^4.
Evaluating the equation, we find that P(4) = 0.1653.
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(1+tanx/1-tanx)+(1+cotx/1-cotx)=0
The expression (1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) = 0 is true
How do i prove that (1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) = 0?We can prove that the expression (1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) = 0 as illustrated below:
Consider the left hand side, LHS
Multiply (1 + cotx / 1 - cotx) by (tanx / tanx), we have:
(1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) × (tan x / tan x)
(1 + tanx / 1 - tanx) + (tanx + cotxtanx / tanx - cotxtanx)
Recall,
cotx = 1/tanx
Thus, we have
(1 + tanx / 1 - tanx) + (tanx + 1 / tanx - 1)
Rearrange
(1 + tanx / 1 - tanx) + (1 + tanx / -1 + tanx)
(1 + tanx / 1 - tanx) + (1 + tanx / -(1 - tanx)
(1 + tanx / 1 - tanx) - (1 + tanx / 1 - tanx) = 0
Thus,
LHS = 0
But,
Right hand side, RHS = 0
Thus,
LHS = RHS = 0
Therefore, we can say that the expression (1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) = 0, is true
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Complete question:
Prove that (1 + tanx / 1 - tanx) + (1 + cotx / 1 - cotx) = 0
Use two variables and two equations:
a. Five albums and 2 tapes cost $57
Four albums and 1 tape cost $42.
How much does each item cost?
Help, I need to answer this question
Answer:
Step-by-step explanation:
factors of 8
Answer:
F- of a 8* i think
Step-by-step explanation:
True/False. a. _____ If F is a vector field, then div F is a vector field. b. _____ If F is a vector field, then curl F is a vector field. c. _____ lf F has continuous partial derivatives of all orders on R^3, then div (curl Nabla f) = 0. d. _____ Stokes' Theorem states that under the proper conditions. integral_C F middot dr = double integral_S curl F middot dS. e. _____ This has been your favorite math class of all time.
pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. a small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively
The mean is a measure of location which tells us the average of observation.
Standard deviation tells us how dispersed a data is or how much variation our data contains.
According to question,
The population size : N = 1500
Number of fraudulent in a month : 28
Population proportion : P = 28/1500
=> P = 0.0187
Sample size: n = 180
Sample proportion : p = 28 / 180
=> p = 0.156
Therefore The mean of sampling distribution for the sample size 28,
μ = P
=> μ = 0.0187
The standard deviation will be
=> σ = \(\sqrt{\frac{p(1-p)}{n}}\)
Substituting the value,
=> σ = \(\sqrt{\frac{0.0187(1-0.0187)}{180}}\)
=> σ = 0.010
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1. A parabola has an axis of symmetry y =3 and passes through the point (2, 1). Find
another point that lies on the graph of the parabola. Explain your reasoning.
A parabola has an axis of symmetry y =3 and passes through the point (2, 1), another point that lies on the graph of the parabola is (2,5).
Axis of symmetry:
Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.
Given,
Axis of Symmetry y = 3.
One point = (2,1)
Here we need to find the another point that lies on the graph of the parabola.
Use the axis of symmetry.
Point given (2,1) is 2 units away from that axis, lower.
=> 1 + 2 = 3
Take two units higher,
=> 3 + 2 = 5
and is the another point (2,5), on the same parabola.
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What is the slope y =- 5x 3?
Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.
In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.
The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.
Slope-Intercept Form:
When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.
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If a recipe requires 1/4 pounds of ground beef
to make 6 servings of chili, how many servings
can be made with 1 1/2 pounds of ground beef?
Answer:
36 servings
Step-by-step explanation:
1/4p = 6s
6(1/4p) = 6(6s)
1 1/2p = 36s
What are the domain and range of this exponential function?y=2x–9
The value of both domain and range of this exponential function is (−∞,∞).
y = 2x-9
The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).
The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).
Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).
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help please.., asap thanks
Answer:
4.5
Step-by-step explanation:
1. The slope/unit rate in this equation is 4.5. The constant of proportionality, k, is the same thing as the slope, meaning that's the k = 4.5.
.....................
Answer:
..................................
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
The correct answer is 8.5 in.
What is Heron's formula in math?Heron's formula, formula credited to Heron of Alexandria for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.we know that
The formula of area of triangle is equal to
\(A = \frac{1}{2} (b) (h)\)
We have
b = BC = 6 in
h = AD = x in
substitute
\(A = \frac{1}{2} (6) (x)\)
\(A = 3x^{2} in^{2} ..................(1)\)
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let a,b,c be the lengths of the sides of a triangle.
The area is given by:-
\(A = \sqrt{p(p-a) (p-b) (p-c)}\) where p is half the perimeter
\(p = \frac{a +b+ c}{2}\)
a = 9 in , b= 9 in, c = 6 in
\(p = \frac{9 + 9 + 6}{2} = 12 in\)
Find the area
\(A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}\)
\(A = \sqrt{12 (3)(3)(6)}\)
\(A = \sqrt{648}\)
\(A = 25.46 in^{2}\)
Substitute the value of the area in the equation 1 and solve for x
\(A = 3x in^{2}\)
25.46 = 3x
x = 25.46/3
x = 8.5 in
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The complete question is -
HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
A. 8 in.
B. 11.3 in.
C. 8.5 in.
D. 6.2 in.
Find the perimeter and the area of the composite shape..
Answer:
I think that it is 39.2 but i'm not 100% sure
Step-by-step explanation:
Hope this helps!