Answer:
18 + 30 + 57 + 30 + 15 = 150
P(1) = 18/150 = 3/25 = .12 = 12%
The probability that a teenager has exactly 1 pair of shoes in their closet is [tex]\( \dfrac{3}{25} \)[/tex].
Given the distribution:
Pairs of Shoes | Frequency
--------------------------
1 | 18
2 | 30
3 | 57
4 | 30
5 | 15
The frequency of teenagers with exactly 1 pair of shoes is 18.
The total number of teenagers is the sum of all the frequencies:
Total number of teenagers = 18 + 30 + 57 + 30 + 15
= 150
Now, the probability:
[tex]\[ P(1) = \frac{\text{Number of teenagers with exactly 1 pair of shoes}}{\text{Total number of teenagers}} = \frac{18}{150} \][/tex]
[tex]\[ P(1) = \frac{3}{25} \][/tex]
So, the probability is [tex]\( \dfrac{3}{25} \)[/tex].
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The notation P(F E)means the probability of event ____ given event ___.
.
The notation P(F|E) means the probability of event F given event E.
In probability notation, P(F|E) represents the conditional probability of event F occurring given that event E has already occurred. It is read as "the probability of F given E." The vertical bar "|" indicates "given" or "conditional on." This notation allows us to calculate the probability of one event happening, taking into account the occurrence of another event. For example, P(F|E) would represent the probability of rain (event F) given that the weather forecast predicts a cloudy day (event E). The conditional probability allows us to analyze how events are related and make more accurate predictions or assessments based on the given information.
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The original price of a book was $48. It is now 70% off. What is the sale price of the book?
Answer:
$14.40-------------
Original price is $48 and it is now 70% off, then the sale price is:
$48 - 70% of $48 = $48 - 0.7*$48 = 0.3*$48 = $14.40Therefore, the sale price of the book is $14.40.
a range of values, that with a certain degree of probability contain the population parameter, is known as a: group of answer choices point estimate confidence interval estimate ballpark estimate none of these are correct.
Main Answer: A range of values, that with a certain degree of probability contain the population parameter, is known as a "confidence interval estimate."
Supporting Question and Answer:
What is the purpose of a confidence interval estimate in statistics?
The purpose of a confidence interval estimate in statistics is to provide a range of values that, with a certain degree of probability, contains the population parameter of interest. This range allows for a measure of uncertainty and provides a level of confidence in the estimation process.
Body of the Solution: The correct answer is "confidence interval estimate."
A confidence interval estimate is a range of values that, with a certain degree of probability (often represented by a confidence level), is believed to contain the population parameter of interest. It is used in statistics to provide an estimate of an unknown population parameter based on sample data. The confidence interval provides a range rather than a single point estimate, allowing for a measure of uncertainty in the estimation process.
Final Answer: The correct answer is "confidence interval estimate."
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A range of values, that with a certain degree of probability contain the population parameter, is known as a "confidence interval estimate."
What is the purpose of a confidence interval estimate in statistics?The purpose of a confidence interval estimate in statistics is to provide a range of values that, with a certain degree of probability, contains the population parameter of interest. This range allows for a measure of uncertainty and provides a level of confidence in the estimation process.
The correct answer is "confidence interval estimate."
A confidence interval estimate is a range of values that, with a certain degree of probability (often represented by a confidence level), is believed to contain the population parameter of interest. It is used in statistics to provide an estimate of an unknown population parameter based on sample data. The confidence interval provides a range rather than a single point estimate, allowing for a measure of uncertainty in the estimation process.
The correct answer is "confidence interval estimate."
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There are 16 airplanes at the airport. Some are big, and 11 are small how many airplanes are big
Answer:
5 Big Airplanes
Step-by-step explanation:
16 airplanes IN TOTAL
11 airplanes ARE SMALL
so we simply subtract 11 from 16 to find how many airplanes are left besides the small ones.
16-11 = 5What are the coordinates of the center and the length of the radius of the circle
whose equation is-y-12y-20 25-07
a) center (0.5) and radius 7.5
c) center (0-6) and radius 75
b) center (0.12) and radius 45
d) center (-12) and radius 4,5
The equation of the circle, obtained by applying the completing the square method to the specified equation indicates that the center and radius of the circle are;
Center (0, 6) and radius 7.5
What is the general form of the equation of a circle?The general form of the equation of a circle is; (x - h)² + (y - k)² = r², where;
(h, k) = The coordinates of the center of the circle
r = The measure of the length of the radius
The possible equation obtained from a similar question on the internet can be presented as follows;
x² + y² - 12·y - 20.25 = 0
The above equation can be evaluated using the completing the square method and excluding the x² term as follows;
y² - 12·y - 20.25 = 0
y² - 12·y = 20.25
y² - 12·y + (-12/2)² = 20.25 + (-12/2)²
y² - 12·y + (-6)² = 20.25 + (-6)² = 56.25
(y - 6)² = 56.25
Therefore;
y - 6 = √(56.25) = ±7.5
The possible equation of the circle obtained by plugging in the x² term therefore is; (x - 0)² + (y - 6)² = 7.5²
The center of the circle is therefore;
(h, k) = (0, 6)
The radius of the circle, r = 7.5
The possible correction is therefore, option (a), where the 5 is a typing error
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18. Find the value of x.
√3
60°
30°
X
a. x = 3
b. x = 3√3
c. x = √3
d. x = 9
Answer:
3
Step-by-step explanation:
the answer is 3, the working is in the image
Write as many mathematical expressions or equations as you can about the image. Include a fraction, a decimal number, or a percentage in each. FUNDRAISER OUR GOAL: $250,000 $250,000 $200,000 $150,000 $100,000 - $50,000 O
The mathematical expressions or equations about the image 44%, 0.44 and 11/25
Writing the mathematical expressions or equations about the imageFrom the question, we have the following parameters that can be used in our computation:
The fundraiser image (see attachment)
From the image, we have the following readings
Total amount to be raised = $250,000
Amount already raised = $110,000
When represented as a percentage, we have
percentage = 110,000/250,000 * 100%
Evaluate
percentage = 44%
As a fraction, we have
percentage = 44/100 = 11/25
As a decimal, we have
percentage = 0.44
Hence, the mathematical expressions about the image are 44%, 0.44 and 11/25
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pls help Which is a step in showing that n^3+2n is divisible by 3 is true by mathematical induction?
a.Show that the statement is true for n = 1
b.Prove that the statement is true when n = k.
c.Assume that the statement is true for the (k + 1) value.
d.Assume the statement is true for all the integers.
The step in showing that[tex]n^3+2n[/tex] is divisible by 3 by mathematical induction is: Prove that the statement is true when n = k. Option B
How to determine the step showing that n^3+2n is divisible by 3 is true by mathematical inductionThis step involves substituting k for n in the expression [tex]n^3+2n[/tex] and showing that the result is divisible by 3. In other words, we need to show that:
[tex]k^3 + 2k[/tex] is divisible by 3.
If we assume that the statement is true for n = k, then we can substitute k+1 for n in the expression [tex]n^3+2n[/tex] and simplify:
=[tex](k+1)^3 + 2(k+1) = k^3 + 3k^2 + 3k + 1 + 2k + 2[/tex]
= [tex]k^3 + 3k^2 + 5k + 3[/tex]
= [tex](k^3 + 2k) + (3k^2 + 3k)[/tex]
Since we assumed that the statement is true for n = k, we know that [tex]k^3 + 2k[/tex] is divisible by 3. Also, [tex]3k^2 + 3k[/tex] is divisible by 3 because it has a factor of 3. Therefore, the entire expression [tex](k+1)^3 + 2(k+1)[/tex]is also divisible by 3.
This completes the inductive step, and we can now conclude by mathematical induction that the statement [tex]n^3+2n[/tex] is divisible by 3 is true for all positive integers n.
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Please help me solve the question in the picture
Correct answer will get 20 points
The product QS is impossible because of the dimensions
The product SR has no orderThe product QR is [tex]QR = \left[\begin{array}{cc}-3&8\\-11&36\end{array}\right][/tex]Why the product QS is impossibleFrom the question, we have the following parameters that can be used in our computation:
Matrices Q, R and S with the dimensions
Q = 2 by 2
R = 2 by 2
S = 2 by 3
The product QS is the product of matrices 2 by 2 and 2 by 3
This is not possible because the dimensions of the matrices Q and R do not match i.e. it is not possible to multiply matrices 2 by 2 and 2 by 3
The order of product SRHere, we have
S = 2 by 3
R = 2 by 2
This is also not possible because of the reason above
So, it has no order
The value of the product QR
Here, we have
[tex]Q = \left[\begin{array}{cc}2&-1\\4&3\end{array}\right][/tex]
[tex]R = \left[\begin{array}{cc}1&6\\-5&4\end{array}\right][/tex]
So, we have
[tex]QR = \left[\begin{array}{cc}2 * 1 + -1 * 5&2 * 6 - 1 * 4\\4 * 1 + 3 *-5&4 * 6 + 3 * 4\end{array}\right][/tex]
Evaluate
[tex]QR = \left[\begin{array}{cc}-3&8\\-11&36\end{array}\right][/tex]
Hence, the product QR is [tex]QR = \left[\begin{array}{cc}-3&8\\-11&36\end{array}\right][/tex]
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now consider that the penetrance of the disease is 75%. what is the probability that individual ii-2 exhibits this disease given this penetrance?
The probability that individual ii-2 exhibits the disease given a 75% penetrance is 0.75 or 75%.
Penetrance refers to the probability of an individual expressing a particular trait or disease given their genetic makeup. In this case, the penetrance of the disease is 75%, which means that there is a 75% chance that an individual with the genetic mutation for the disease will actually exhibit the disease. Therefore, the probability that individual ii-2 exhibits the disease given this penetrance is also 0.75 or 75%.
1. Penetrance is the probability that an individual with a specific genotype will express the associated phenotype or disease.
2. In this case, the penetrance of the disease is 75%, which means there is a 75% chance that an individual with the disease-associated genotype will exhibit the disease.
3. Given this penetrance, the probability that individual ii-2 exhibits the disease is 0.75 or 75%.
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The volume of a rectangular pyramid is 765 units
3
3
. If the length of the rectangular base measures 9 units and the width of the rectangular base measures 15 units, find the height of the pyramid.
The height of the pyramid is equal to 17 units.
How to calculate the volume of a rectangular pyramid?In Mathematics and Geometry, the volume of a rectangular pyramid can be calculated by using the following formula:
Volume of a rectangular pyramid = 1/3 × L × W × H
Where:
L represents the length of a rectangular pyramid.W represents the width of a rectangular pyramid.H represents the height of a rectangular pyramid.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular pyramid, we have the following;
765 = 1/3 × 9 × 15 × H
Height, H = 765/45
Height, H = 17 units.
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Find the mean median and mode for 44, 4, 27, 5
Answer:
Mean: 20
Median: 16
Mode: No mode
Step-by-step explanation:
For the mean:
44 + 4 + 27 + 5 = 80
80/4 = 20
For the median:
5 + 27 = 32
32/2 = 16
For the mode:
None of the numbers are repeated.
please help me
The diameter of a child's bicycle wheel is 18 inches. Approximately how many revolutions of the wheel will it take to travel 1,700 meters? Use 3.14 for π and round to the nearest whole number. (1 meter ≈ 39.3701 inches)
3,925 revolutions
2,368 revolutions
1,184 revolutions
94 revolutions
The answer is 1,184 Revolutions (option C).
First, we need to convert the diameter of the wheel to meters.
18 inches = 18/39.3701 meters ≈ 0.4572 meters
The circumference of the wheel is:
π × diameter = 3.14 × 0.4572 ≈ 1.436 meters
To travel 1,700 meters, the wheel needs to make:
1700/1.436 ≈ 1184 revolutions
Therefore, the answer is 1,184 revolutions (option C).
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Find the value of x that makes lines u and v parallel.
The value of x in the parallel line is 11.
How to find angles in parallel lines?When parallel lines are cut with a transversal line, angle relationship are formed such as corresponding angles, alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles etc.
Therefore, let's use the angle relationship to find the value of x .
Hence,
6x + 14 = 80(corresponding angles and vertically opposite angles)
6x + 14 = 80
subtract 14 from both sides of the equation
6x + 14 - 14 = 80 - 14
6x = 66
divide both sides of the equation by 6
x = 66 / 6
x = 11
Therefore,
x = 11
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The function f(x)=(x-4)(x-2) is shown.
-10-8- -6 -4
Mark this and return
10
0-
6
4
2
-4
-6
-8
-10-
6 8 40-X
What is the range of the function?
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
O all real numbers greater than or equal to -1
Save and Exit
Next
Submit
The statement that defines the function's range is option a) all real numbers greater than or equal to -1.
The given function is a quadratic function, which is a parabola that opens upwards. The graph of the function has its vertex at the point (3,-1), which is the minimum point of the parabola.
The range of the function is the set of all possible output values or y-values that the function can produce.
Since the parabola opens upwards and the minimum point is at y=-1/4, the range of the function f(x)=(x-4)(x-2) is all real numbers greater than or equal to -1.
Therefore, we can say that the range is all real numbers greater than or equal to -1.
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Correct Question
The function f(x) = (x − 4)(x − 2) is shown.What is the range of the function? a) all real numbers less than or equal to 3
b) all real numbers less than or equal to −1
c) all real numbers greater than or equal to 3
d) all real numbers greater than or equal to −1
a central angle of 2 radians off an arc of length 6 inches. find the area of the sector formed
[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=6 \end{cases}\implies 6=r2\implies \cfrac{6}{2}=r\implies 3=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(3)^2}{2}\implies A=9~in^2[/tex]
IF YOU SOLVE THIS CORRECTLY WITH EXPLANATION U WILL GET BRAINILEST
(2y-3)(3y-2)
6y² - 13y + 6 is the product of 2y -3 and 3y - 2.
Expanding linear equations
Given the following linear expression
(2y-3)(3y-2)
We need to expand the expression to get a quadratic function as shown below:
(2y-3)(3y-2) = 2y(3y) - 2(2y) - 3(3y) -3(-2)
(2y-3)(3y-2) = 6y² - 4y - 9y + 6
(2y-3)(3y-2) = 6y² - 13y + 6
Hence the product of 2y - 3 and 3y - 2 is equivalent to 6y² - 13y + 6
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Find the center and vertices if the ellipse x^2/49 +y^2/4=1
The center and vertices if the ellipse is,
Center = (0, 0)
Vertex = (±7, 0)
We have to given that;
Equation of Ellipse is,
⇒ x²/49 + y² / 4 = 1
Since, We know that;
For equation of ellipse,
x²/a² + y²/b² = 1
Center = (0, 0)
Vertex = (±a, 0); for a > 0
Here, Equation of Ellipse is,
⇒ x²/49 + y² / 4 = 1
Here, a² = 49
a = ± 7
And, b² = 4
b = ±2
Hence, a > b
So, We get;
Center = (0, 0)
Vertex = (±a, 0); for a > 0
Vertex = (±7, 0)
Thus, The center and vertices if the ellipse is,
Center = (0, 0)
Vertex = (±7, 0)
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How do I find the limit of
lim xy/√x^2 + y^2
(x,y) → (0,0)
To find the limit of lim xy/√x^2 + y^2 (x,y) → (0,0), we can use polar coordinates. the limit is: lim xy/√(x^2 + y^2) as (x,y) → (0,0) = 0
Let x = rcosθ and y = rsinθ. Then, the limit becomes lim (rcosθ)(rsinθ)/√(rcosθ)^2 + (rsinθ)^2 as r approaches 0. Simplifying, we get lim rcosθsinθ/√r^2(cos^2θ + sin^2θ) as r approaches 0. Canceling out the r, we get lim cosθsinθ/√(cos^2θ + sin^2θ) as r approaches 0. Since cosθsinθ is less than or equal to 1, the limit must exist and equal 0.
Therefore, the limit of lim xy/√x^2 + y^2 (x,y) → (0,0) is 0.
To find the limit of lim xy/√(x^2 + y^2) as (x,y) → (0,0), you can use polar coordinates to transform the expression. Let x = rcosθ and y = rsinθ. Then, the given expression becomes:
(r*cosθ * r*sinθ) / √(r^2*cos^2θ + r^2*sin^2θ) = r^2*sinθ*cosθ / (r*√(cos^2θ + sin^2θ))
Simplifying the expression, we get:
r*sinθ*cosθ
Now, as (x,y) → (0,0), r → 0. The limit we are looking for is:
lim r*sinθ*cosθ as r → 0
Since sinθ and cosθ are bounded between -1 and 1, the product r*sinθ*cosθ will also approach 0 as r approaches 0.
Therefore, the limit is:
lim xy/√(x^2 + y^2) as (x,y) → (0,0) = 0
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a meteorologist wishes to estimate the nitrogen dioxide content of air per unit volume in a certain area. it is known from studies that the standard deviation is 2 parts per million (ppm). how many air samples must the meteorologist analyze to be 80% certain that the error of estimate does not exceed 0.2 ppm?
The meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.
A meteorologist aiming to estimate the nitrogen dioxide content in the air needs to consider the standard deviation and desired level of certainty. In this case, the known standard deviation is 2 ppm, and the desired certainty is 80%, with an error of estimate not exceeding 0.2 ppm.
To calculate the number of air samples needed, the meteorologist can use the formula:
n = (Z * σ / E)^2
Here, n represents the required sample size, Z is the z-score corresponding to the desired certainty level (80%), σ is the standard deviation (2 ppm), and E is the margin of error (0.2 ppm).
For 80% certainty, the z-score is approximately 1.28. Plugging the values into the formula, we get:
n = (1.28 * 2 / 0.2)^2 = (12.8)^2 ≈ 164
Thus, the meteorologist needs to analyze approximately 164 air samples to be 80% certain that the error of estimate does not exceed 0.2 ppm.
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There are 36 students in Mr. Chips first block math class. 1/9 of them made a level 5 on their EOG last year. 5/6 of them made a level 4 last year. The rest made a level 3. How many of Mr. Chips first black students made a level 3?
Answer:
2 students
Step-by-step explanation:
First, you have to find how many made a level 5, so we do 36•1/9=4. So, 4 students made a level five. That leaves us with 36-4=32 students left. Next, you find the students that made a level 4. 36•5/6=30 students made a level 4, so that leaves us with 32-30=2 students that got a level 3.
In the figure below, III h. Find the values of z and x.
(3x-31)-=-
HE
M
HE
#1
A
0
The measure of angle x and z are 45.7° and 74° respectively.
Given that, straight line l and h are parallel.
Here, in the given figure,
(3x-31)°+z°=180° (Adjacent angles)
z°=180°-(3x-31)°
From the given figure,
z°=74° (Corresponding angles are equal)
180°-(3x-31)°=74°
180°-74°=(3x-31)°
(3x-31)°=106°
3x=106+31
3x=137
x=137/3
x=45.7°
Therefore, the measure of angle x and z are 45.7° and 74° respectively.
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Area of a regular polygon, I need the work
Answer:
The formula for calculating the area of a regular polygon is A = (n/2) * L * R, where n is the number of sides in the polygon, L is the length of one side of the polygon, and R is the radius of an inscribed circle.
Step-by-step explanation:
The formula for calculating the area of a regular polygon is A = (n/2) * L * R, where n is the number of sides in the polygon, L is the length of one side of the polygon, and R is the radius of an inscribed circle.
4a^3 - a^2b - 36a + 9b
Answer:
[tex]4 {a}^{3} - {a}^{2} b - 36a + 9b[/tex]
[tex] = {a}^{2} (4a - b) - 9(4a - b)[/tex]
[tex] = ( {a}^{2} - 9)(4a - b)[/tex]
[tex] = (a + 3)(a - 3)(4a - b)[/tex]
The angle of elevation from the bottom of the ski lift to the top of the mountain is 62°. If the vertical height of the mountain is 1,760 feet, what is the total distance traveled on the ski lift from the bottom to the top of the mountain?The angle of elevation from the bottom of the ski lift to the top of the mountain is 62°. If the vertical height of the mountain is 1,760 feet, what is the total distance traveled on the ski lift from the bottom to the top of the mountain?
Answer:
We can use trigonometry to solve this problem. Let's call the total distance traveled on the ski lift "d". We know that the angle of elevation from the bottom of the ski lift to the top of the mountain is 62°, which means the angle of depression from the top of the mountain to the bottom of the ski lift is also 62°.
Using trigonometry, we can write:
sin(62°) = 1,760 / d
To solve for "d", we can isolate it by multiplying both sides by "d" and then dividing both sides by sin(62°):
d = 1,760 / sin(62°)
Using a calculator, we get:
d ≈ 1,966.6 feet
Therefore, the total distance traveled on the ski lift from the bottom to the top of the mountain is approximately 1,966.6 feet.
what is the probability of flipping a coin three times and having them all land "heads" up?
Answer:
1/8 or 0.125 or 12.5%---------------------------
The probability of flipping a coin and having it land "heads" up is 1/2.
Since each coin flip is independent, the probability of getting three heads in a row is the product of the individual probabilities.
Therefore, the probability of flipping a coin three times and having them all land "heads" up is:
(1/2) x (1/2) x (1/2) = 1/8 or 0.125 or 12.5%Part D
At least how many mosaic squares does the artist need to cover the sculpture?
Select the correct answer from the drop-down menu.
She will need at least
tiles.
15,862
22,743
1,586,200
2,274,300
The sculpture's dimensions or the size of the mosaic tiles, it's not possible to determine the exact number of tiles needed to cover the sculpture.
The number of tiles required depends on factors such as the size of the sculpture, the desired level of detail, and the size of the individual mosaic tiles.
To calculate the minimum number of tiles needed, we would need to know the surface area of the sculpture and the surface area covered by each tile.
The surface area of the sculpture could be approximated by breaking it down into smaller geometric shapes and summing up their individual areas. Then, by dividing the sculpture's surface area by the area covered by each tile, we could estimate the minimum number of tiles required.
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Solve x^2-2=2x using the graph of the function f(x)=x^2
There are no points where the graph of f(x) = x² intersects the line y = x - 2, and the equation has no real solutions.
To solve x² - 2 = 2x using the graph of the function f(x) = x² we can start by rewriting the equation as x^2 - 2x - 2 = 0.
Then, we can graph the function f(x) = x² and find the points where the graph intersects the line y = x - 2.
These points correspond to the solutions of the equation x² - 2x - 2 = 0.
We can then use the quadratic formula to solve for x:
x = (-(-1) ± √((-1)² - 4(1)(2))) / (2(1))
x = (1 ± √(-7)) / 2
Since the discriminant is negative, there are no real solutions to the equation x² - 2 = 2x.
Therefore, there are no points where the graph of f(x) = x² intersects the line y = x - 2, and the equation has no real solutions.
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Jacob works a job where the money he earns varies directly to the hours he works. In one week, Jacob worked for 15 hours and made $146.26. how many hours did Jacob work in his second week if he earned $117?
Answer: How many hours did Jacob work in his second week if he earned $117?
Step-by-step explanation:
We can start by setting up a proportion to relate the number of hours worked to the amount earned:
hours worked / amount earned = constant of proportionality
Let's call the constant of proportionality "k". Then we have:
15 / 146.26 = k
Solving for k, we get:
k = 9.75
Now we can use this value of k to find the number of hours Jacob worked in his second week:
117 / 9.75 = 12
Therefore, Jacob worked 12 hours in his second week if he earned $117.
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Find the are of the polygon
Answer:
264 cm²
Step-by-step explanation:
You want the area of a polygon composed of a 12 cm square with triangles of height 5 cm attached to each side.
Square areaThe area of the square is the square of its side lenght:
A = s²
A = (12 cm)² = 144 cm²
Triangle areaThe area of the four triangles is ...
A = 4 × (1/2bh)
A = 4 × 1/2(12 cm)(5 cm) = 120 cm²
Total areaThe total area of the composite figure is ...
A = square area + triangle area
A = 144 cm² +120 cm² = 264 cm²
The area of the polygon is 264 cm².
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