If an angle measure 125° then the angle measures a fraction of 25/72 of a full circle.
What is a circle?A circle is a two-dimensional geometric shape that is defined as the set of all points that are equidistant from a single point, called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle, passing through the center, is called the diameter. The circumference of a circle is the distance around the edge or perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant that represents the ratio of the circumference to the diameter of a circle, approximately equal to 3.14159.
According to the given informationA circle has 360 degrees. To find what fraction of a circle an angle measures, we can divide the angle by 360. In this case, the angle measures 125 degrees, so the fraction of a circle it turns can be calculated as:
125/360 = 0.347222222...
To simplify this fraction, we can multiply both the numerator and denominator by 2:
125/360 = (1252)/(3602) = 250/720
We can further simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 10:
250/720 = (2510)/(7210) = 25/72
Therefore, the angle measures a fraction of 25/72 of a full circle.
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Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200
Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50
Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50
What is the slope of the line that connects the 3rd and 4th point?
50
What is the slope of the line that connects the 1st and the 4th point?
150
Is the common difference (aka slope aka rate of change) constant?
Yes
Why is it or is it not constant?
It is constant because it is a linear function.
Answer:
Step-by-step explanation:
The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.
The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.
The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.
The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.
What is 1 and 1/4
And 1 and 1/2
The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.
Given first number = 1 and 1/4.
1 and 1/4 is a mixed fraction so, we can write it in the form as [tex]1\frac{1}{4}[/tex] .
To find the value of [tex]1\frac{1}{4}[/tex] we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,
[tex]1\frac{1}{4}[/tex] = ((4x1) + 1 )/4 = 5/4.
Similary, for 1 and 1/2,
[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.
From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.
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1. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
A 0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
B (0,1) is a zero of the quadratic because it is where the parabola crosses the y-axis.
C (-0,3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
D (0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.
The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.
plot the y-get at (0,1),
x = - b/2a
To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is
f(3/4) = 1/8.
Plot the vertex at (3/4, 1/8).
Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.
To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.
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 how many kilograms are in 14500 grams
Answer: 14.5 kg
Step-by-step explanation:
Rebecca used 4.25pt of milk in her baking recipe. How many cups of milk did she use?
Answer: 8.25
Step-by-step explanation:
The following table shows students’ test scores on the first two tests in an introductory calculus class.
Calculus Test Scores
First test, x 64
59
45
73
73
76
40
56
68
55
78
83
Second test, y 68
63
55
74
68
75
43
64
61
64
77
84
Step 2 of 2 : If a student scored a 69
on his first test, make a prediction for his score on the second test. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.
if a student scored a 69 on his first test, predict that his score on the second test will be approximately 64.57.
Students’ test scores on the first two tests in an introductory calculus class.
To make a prediction for the student's score on the second test based on their score of 69 on the first test, we need to find the regression equation for the data set.
The regression equation for these data is
y = 0.6443x + 19.943
Where y is the predicted score on the second test and x is the actual score on the first test.
Substituting x = 69 into this equation, we get
y = 0.6443(69) + 19.943 ≈ 64.57
Therefore, if a student scored a 69 on his first test, we predict that his score on the second test will be approximately 64.57.
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A company knows that 32% of their customers order their product in Black and 26% in White and 22% in Grey.
2 orders are made, Find the probability that both are the same color.
(both black, white or grey)
round to 4 d.p.
After considering all the given data and running a series of calculation we reach the conclusion that the probability of receiving both orders as the same colors is 0.2184, under the condition that a company has the information that 32% of their customers order their product in Black and 26% in White and 22% in Grey.
Then the evaluated probability of both orders being the same color can be found by applying summation of the probability of both orders being black, both orders being white, and both orders being grey.
Now, the probability of both orders being black is 0.32 × 0.32
= 0.1024.
Similarly the probability of both orders being white is 0.26 × 0.26
= 0.0676.
Lastly, the probability of both orders being grey is 0.22 × 0.22
= 0.0484.
Hence, the evaluated probability of both orders being the same color is 0.1024 + 0.0676 + 0.0484 = 0.2184 (rounded to four decimal places).
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Find z
x+y=z
y-z=x
I will award brainlest
Answer:
To solve for z in terms of x and y using the given equations:
x + y = z ........(1)
y - z = x ........(2)
From equation (2), we get:
y - x = z (by adding z on both sides)
Substituting this value of z in equation (1), we get:
x + y = y - x
2x = 0
x = 0
Substituting x = 0 in equation (2), we get:
y - z = 0
y = z
Therefore, the solution is:
z = y
We cannot determine a specific value of z without knowing the values of x and y.
Which of the following statements is true and would show that the 4 points are the vertices of a parallelogram? A. DA = AB = BC = CD = v17 B. AB = CD = v13; DA = BC = v17C. DB = v18; AC = v38
Answer:
B. AB = CD = sqrt(13); DA = BC = sqrt(17)
This is because in a parallelogram, opposite sides are equal in length. In this statement, AB is equal to CD and DA is equal to BC, so opposite sides are equal. The values of AB, CD, DA, and BC are given as the square root of 13 and the square root of 17, which matches the condition of the statement.
In statement A, all sides are equal in length, which means the shape is a rhombus, not necessarily a parallelogram.
Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
-3, √3, 13/3
The other zeros are
(Use a comma to separate answers.)
Answer:
{-3, √3, -√3, 13/3}
Step-by-step explanation:
Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.
We can write the polynomial with these zeros as:
p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)
where a is some constant coefficient. Multiplying out the factors, we get:
p(x) = a(x + 3)(x^2 - 3)(x - 13/3)
To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:
a(x + 3)(x^2 - 3)(x - 13/3) = 0
This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:
(x + 3)(x^2 - 3)(x - 13/3) = 0
Expanding the quadratic factor, we get:
(x + 3)(x - √3)(x + √3)(x - 13/3) = 0
Canceling out the (x - √3) and (x + √3) factors, we get:
(x + 3)(x - 13/3) = 0
Solving for x, we get:
x = -3 or x = 13/3
Therefore, the other zeros are -3 and 13/3.
The complete set of zeros is {-3, √3, -√3, 13/3}.
Hope it helps^^
A box contains 16 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
a. The probability is.
(Type a fraction. Simplify your answer.)
***
The probability of selecting all defective transistors is 1/560.
To find the probability of the statementsThe probability of selecting all defective transistors can be calculated as:
P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)
The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:
total number of ways = number of combinations of 3 transistors out of 16
= (16 choose 3)
= 560
Therefore, the probability of selecting all defective transistors is:
P(all defective) = 1 / 560
To simplify the answer, we can write it as a fraction in lowest terms:
P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560
Therefore, the probability of selecting all defective transistors is 1/560.
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Find the y value if the line through (-4, -10) and (2, y) has a slope of 4.
Answer:
y=14
Concept Used:
Slope of a line: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where (x1,y1) and (x2,y2) are passing points
Step-by-step explanation:
On substitution:
[tex]4 = \frac{y-(-10)}{2-(-4)}[/tex]
Solving for y:
y = 14
lim h -> 0 [f(x_{0} + h) - f(x_{0})] / h
the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.
what is derivative ?
The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.
In the given question,
The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.
To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:
[tex]lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})[/tex]
where f'(x_0) denotes the derivative of f(x) at x = x_0.
Therefore, the limit expression gives the value of the derivative of a function at a specific point.
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Find the missing side lengths. Leave your answers as radicals in simplest form. I need help quickly!
Answer:
[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]
[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]
Not sure which form your teacher wants the answers, would suggest putting in both
Step-by-step explanation:
The missing angle of the triangle = 180 - (60 + 90) = 30°
We will use the law of sines to find m and n
The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles
Therefore since m is the side opposite 90° and 2 is the side opposite 60°,
[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]
sin 90 = 1
sin 60 = √3/2
So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]
We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)
To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]
sin 30 = 1/2 giving
[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]
In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]
Car A travels 221.5 km at a given time, while car B travels 1.2 times the distance car A travels at the same time. What is the distance car B travels during that time?
Answer:
Distance that car B travels =1.2× distance that car A travels
=1.2×221.5=265.8 km
Answer:
car B travels a distance of 265.8 km during the same time.
Step-by-step explanation:
Car A travels 221.5 km at a given time.
To find the distance traveled by car B, which is 1.2 times the distance traveled by car A, we can multiply the distance of car A by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, car B travels a distance of 265.8 km during the same time.
PLEASE HELP WITH THE IMAGE!! DUE TOMORROW!!!
The calculations of the down payments, monthly income or payments are as follows:
Part 1:
Annual income = $226,000
Federal Tax = $62,582
State Tax = $16,385
Local Tax = $5,537
Healthcare = $4,520
Yearly income = $136,976
Monthly income = $11,414.67.
Part 2:
Down payment = $150,000
The amount to borrow (Mortgage loan) = $600,000
Estimated interest = $810,000
Total installment payments = $1,410,000
Monthly payment = $3,916.67.
Part 3:
Down payment = $2,902.50
Mortgage loan = $16,447.50
Estimated interest = $3,700.69
Interest + Mortgage loan = $20,148.19
Monthly payment = $335.80.
Part 1:
Annual income = $226,000
Federal Tax:
25% of $89,350 = $22,337.50
28% of $97,000 = $27,160.00
33% of $39,650 = $13,084.50
Total federal tax = $62,582
State Tax = 7.25% of $226,000 = $16,385
Local Tax = 2.45% of $226,000 = $5,537
Healthcare = 2% of $226,000 = $4,520
f) Total of Federal, State, Local, and Healthcare = $89,024
Yearly income = $136,976 ($226,000 - $89,024)
Monthly income = $11,414.67 ($136,976 ÷ 12)
Part 2:
a) House price = $750,000
b) Down payment = 20%
= $150,000 ($750,000 x 20%)
c) Mortgage loan = $600,000 ($750,000 - $150,000)
d) Interest rate = 4.5%
Number of mortgage years = 30 years
Mortgage period in months = 360 months (30 x 12)
Estimated interest = $810,000 ($600,000 x 4.5% x 30)
Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)
Monthly payment = $3,916.67 ($1,410,000 ÷ 360)
Part 3:
Price of car = $19,350
Down payment = 15%
= $2,902.50 ($19,350 x 15%)
Mortgage loan = $16,447.50 ($19,350 - $2,902.50)
Number of years = 5 years
Mortgage period in months = 60 months (5 x 12)
Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)
Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)
Monthly payment = $335.80 ($20,148.19 ÷ 60)
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a) What information is provided by each of the graphs below? b) Explain below which of the two graphs is the best representation of the data. Support your thinking by using numbers from each graph.
The information provided by each of the graphs is Sales from July to December and graph A best represents the data
What information is provided by each of the graphs?From the question, we have the following parameters that can be used in our computation:
The graphs
On the graphs, we have the information to be
Sales from July to December
Which of the two graphs is the best representation of the data.The graph that is the best representation of the data is the A
This is because the scale and origin of the graph are defined
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A store sells rectangular picture frames in two sizes. The shorter side of the larger picture frame is 8 inches long and its longer side is 10 inches long. The longer side of the smaller picture frame is 6 inches long. The picture frames are similar shapes. What is the length of the shorter side of the smaller picture frame? Enter your answer as a decimal in the box.
inches
Answer: 4.8 Inches
Step-by-step explanation:
6 is 60% of 10
Therefore (60%*8 = 4.8)
*since they are similar, and therefore proportional
Select the two values of x that are roots of this equation x^2-5x+3=0
The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.
To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
Substituting the values of a, b, and c from the given equation, we have:
x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)
x = (5 ± √(25 - 12)) / 2
x = (5 ± √13) / 2
Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.
To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:
(5 + √13)² - 5(5 + √13) + 3 = 0
Simplifying this equation, we get:
13 - 5√13 + 8 + 13 - 5√13 + 3 = 0
This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.
These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.
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B as a % of A is equal to A as a % of (A+B). Find B as a % of A.
Option (b), 62% is correct.
How to solveBy the given condition,
B/A = A/(A + B) ..... (1)
Now to find the percentage of A = B, we consider B = Ax. From (1), we get
Ax/A = A/(A + Ax)
or, x = 1/(1 + x)
or, x² + x - 1 = 0
Using the quadratic formula, we get
x = {- 1 ± √(1 + 4)}/2
= (- 1 ± √5)/2
Since x cannot be negative, we take
x = (- 1 + √5)/2
≈ 0.62
Therefore the required percentage is
= 0.62 × 100%
= 62%
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B as a percentage ofAis equal to Aas a
percentage of(A+B). How much percent
of A is B?
(a) 60%
(b) 62%
(C) 64%
(d) 66%
2. Four friends have stamps, as described below.
• Samir has 60 stamps.
•Lisa has 24 times as many stamps as Samir.
Kwame has 443 stamps.
To the nearest whole number, what is the mean of the
Jake has 159 fewer stamps than Kwame.
number of stamps for these four friends?
Answer:
All of them have a combined of 2,227 Stamps
Mean: 2014
A publisher reports that 72% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 380 found that 67% of the readers owned a personal computer. Find the value of the test statistic. Round your answer to two decimal places.
Answer: The value of the test statistic to 2 d.p is z= 1.65
Step-by-step explanation:
P cap= 0.72
n= 170
P= 0.66
q= 1- p
q= 1- 0.66
q= 0.34
Z=( p cap - p)/√(p*q)/n
Z= (0.72- 0.66)/√(0.66*0.34)/170
Z= 0.06/0.036332
Z= 1.65
Given u=12i-3j and v=-5i+11j, what is u x v?
Answer:
117
Step-by-step explanation:
You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).
Cross productThe cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.
u×v = (12)(11) -(-3)(-5) = 132 -15
u×v = 117
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Please help !!!!!
!!!!!
Answer: 10w + 3 + 4.5w = 90
Step-by-step explanation:
a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees
Use the figure below to answer the following questions. Each square on the grid measures 1 unit by 1 unit. a. What is the radius of the circle? b. What is the diameter of the circle? c. Estimate the area of the circle using the grid.
a. The radius of circle is 4 units.
b. The diameter of the circle is 2 x 4 = 8 units.
c. The area of the circle to be around 31 to 32 square units.
What is a circle?A circle is a geometrical shape consisting of all points that are at an equal distance from a central point.
The distance from the center to any point on the circle is called the radius of the circle.
a. To find the radius of the circle, we need to measure the distance from the center point N to any point on the circumference of the circle.
Using the grid, we can count the number of squares from N to the edge of the circle.
In this case, we can count 4 squares horizontally and 4 squares vertically.
b. The diameter of the circle is twice the radius. Therefore, the diameter of the circle is 2 x 4 = 8 units.
c. To estimate the area of circle using the grid, we can count the number of complete squares that are either fully inside the circle or partially covered by the circle.
In this case, we can count 31 complete squares. We can also see that there are some squares that are partially covered by the circle, so we can estimate that the total area of the circle is slightly more than 31 square units. Therefore, we can estimate the area of the circle to be around 31 to 32 square units.
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PLS HELP ME OUT! A sporting event has a promotion in which the first 1,000 fans to enter the arena receive either a blue cap or a red cap. A random number generator is used to simulate the color of a cap given to a person where indicates a blue cap and indicates a red cap. Ten simulations, each consisting of ten random numbers, are conducted, and the results
are shown in the following table:
Based on the simulations, what is the probability that ten hats given to ten people will consist of more blue caps than red caps? a. 0.20
b. 0.40 c. 0.60 d. 0.80
The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:
a. 0.2.
Here, we have 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 outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:
2. (simulation number 7 and simulation number 10).
Hence the probability is of:
p = 2/10
p = 0.2.
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The mean daily demand for water, in millions of gallons, in a local city is 300, with a standard deviation of 30. Every morning the water treatment plant produces 380 million gallons of water. What is the probability that the water will run out on a given day, if the mean daily demand of water is normally distributed?
The probability that the water will run out on a given day is 0.0038.
What is the probability that water will run out?To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:
z = (x - µ) / σwhere;
x = of 380 million gallons,
µ is the mean daily demand of water = 300 million gallons,
σ is the standard deviation = 30 million gallons.
Substituting the given values:
z = (380 - 300) / 30
z = 2.67
Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.
Therefore, the probability that the water will run out on a given day is 0.0038.
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Use the FOIL method to find the product. Express the product in descending powers of the variable.
(7+6x)(1-5x)
Three fourths of the girls in the eighth grade have long hair. One half of the girls are wearing dresses today. What is the probability that an eighth grade girl will have long hair and be wearing a dress?
The probability that an eighth-grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To solve the problem, we need to find the intersection of the events "having long hair" and "wearing a dress" and calculate the probability of that intersection.
Let L be the event "having long hair" and D be the event "wearing a dress". Then we know:
P(L) = 3/4, since three-fourths of the girls have long hair.
P(D) = 1/2, since half of the girls are wearing dresses.
To find P(L ∩ D), we need to multiply the probabilities of the two events:
P(L ∩ D) = P(L) × P(D) = (3/4) × (1/2) = 3/8
Therefore, the probability that an eighth grade girl will have long hair and be wearing a dress is 3/8 or 0.375, which is the same thing expressed as a decimal.
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Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) - 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x - 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.
The simplification of the function is r(x)=10x - 95.
We are given that;
s(x) = -85 and a(x) = 10(x - 1)
Now,
To create a function that combines them, you can substitute these expressions into the formula above:
r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)
You can simplify this function by distributing the 10 and combining the constants:
r(x) = -85 + 10x - 10 r(x) = 10x - 95
Therefore, the function will be r(x)=10x - 95.
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