Unfortunately, there is no way to answer this question without more information.
We would need to know the amount of the ATM withdrawal, as well as the starting balance before the withdrawal, in order to calculate the ending balance.
For example, if the starting balance was $1500 and the withdrawal was for $50, the ending balance would be $1450.
However, if the starting balance was $1300 and the withdrawal was for $50, the ending balance would be $1250.
Without this information, we cannot determine the correct answer.
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Ali uses 21/2 scoops of drink mix to make 10 cups of drinks how much drink mix which you need to use to make one cup of the drink
The drink mix that is needed to make one cup of drink is 21/20
How to calculate the amount of drink mix needed to make a cup of drink?Ali uses 21/2 scoops of drink mix to make 10 cups off drinks
The amount of drink mix needed to make one cup can be calculated as follows
21/2= 10
x= 1
cross multiply both sides
10x= 21/2
Divide by the coefficient of x which is 10
x= 21/2 ÷ 10
x= 21/2 × 1/10
x= 21/20
Hence the drink mix needed to make one cup is 21/20
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When finding the Quotient of 8,397 divided 12, Calida first divided 83 by 12
In a case whereby When finding the Quotient of 8,397 divided 12, Calida first divided 83 by 12, then she will be wrong, because the answer is 699.75.
What is division in maths?In maths, a division can be described as the process of splitting a specific amount which can be spread to equal parts instance of thisd is when we divide a group of 20 members into 4 groups and this can be done using the mathematical sign.
In the case of Calida above, the division can be made as
8,397 divided 12
=8,397 / 12
=699.75
Therefore we can say that the right answer to the querstion is 699.75
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Ali needed new pencils for school today. He took 6 pencils from a new box of pencils. If there are 18 pencils left in the box, how many pencils were in the brand new box?
If Ali took 6 pencils from a new box of pencils and there are 18 pencils left in the box, then there were 24 pencils in the brand new box.
To see why, you can add the number of pencils Ali took to the number of pencils left in the box:
6 + 18 = 24
Therefore, there were 24 pencils in the brand new box before Ali took 6 of them.
Find the derivative y = cos(sin(14x-13))
To find the derivative of y = cos(sin(14x-13)), we will use the chain rule.
Let's start by defining two functions:
u = sin(14x-13)
v = cos(u)
We can now apply the chain rule:
dy/dx = dv/du * du/dx
First, let's find dv/du:
dv/du = -sin(u)
Next, let's find du/dx:
du/dx = 14*cos(14x-13)
Now we can put it all together:
dy/dx = dv/du * du/dx
dy/dx = -sin(u) * 14*cos(14x-13)
But we still need to substitute u = sin(14x-13) back in:
dy/dx = -sin(sin(14x-13)) * 14*cos(14x-13)
So the derivative of y = cos(sin(14x-13)) is:
dy/dx = -14*sin(sin(14x-13)) * cos(14x-13)
To find the derivative of the function y = cos(sin(14x - 13)), we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = sin(14x - 13), so y = cos(u). Now we find the derivatives:
1. dy/du = -sin(u)
2. du/dx = 14cos(14x - 13)
Now, using the chain rule, we get:
dy/dx = dy/du × du/dx
dy/dx = -sin(u) × 14cos(14x - 13)
Since u = sin(14x - 13), we can substitute back in:
dy/dx = -sin(sin(14x - 13)) × 14cos(14x - 13)
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Carmen mixed 1/4 cup of strawberry frosting with 1/3 cup of lemon frosting Carmen needs 2 cups of her frosting mixture how many cups of strawberry frosting and how many cups of lemon frosting will Carmen need
Carmen needs (6/7) cups of strawberry frosting and (1 1/7) cups of lemon frosting to make 2 cups of the frosting mixture.
To determine the amount of strawberry frosting and lemon frosting that Carmen needs to make 2 cups of the frosting mixture, we need to use a proportion.
Let x be the amount of strawberry frosting needed in cups, and y be the amount of lemon frosting needed in cups.
From the given information, we know that Carmen mixed 1/4 cup of strawberry frosting with 1/3 cup of lemon frosting. Thus, the ratio of the amounts of strawberry frosting to lemon frosting is:
x/y = (1/4)/(1/3)
Simplifying this ratio, we get:
x/y = 3/4
We also know that the total amount of frosting needed is 2 cups, so:
x + y = 2
Using substitution, we can solve for x:
x + (4/3)x = 2
(7/3)x = 2
x = (6/7) cups
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A theater ticket costs £63 plus a booking fee of 3% what is the total price for the ticket
Answer:
The cost of Ticket = £63Booking Fee = 3% = 63*(3/100) = 1.89 = £ 1.89The total price of the ticket = £63 + £1.89 = £64.89. Therefore, the total price of the ticket is £64.89.
If Tan=3 /5 fine the remaining trigonometric functions
The remaining trigonometric functions are:
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3
sec (θ) = (√34)/5
cot(θ) = 5/3
How to find the remaining trigonometric functions?Trigonometry is a branch of mathematics that deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Since tan θ = 3 /5
Recall: tan = opposite/adjacent. Thus, opposite = 3, adjacent = 5
hypotenuse = √(3²+5²) = √34
Therefore, the remaining trigonometric functions are
sin (θ) = 3/√34
cos (θ) = 5/√34
csc(θ) = (√34)/3 (csc (θ) = 1/sin (θ))
sec (θ) = (√34)/5 (sec(θ) = 1/cos (θ))
cot(θ) = 5/3 (cot(θ) = 1/tan (θ))
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francisco had a rectangular piece of wrapping paper that was inches on two sides and 17 inches on the longer sides. monica has a similar piece of paper with two longer sides that each measure 34 inches. what is the measurement of the two shorter sides in monica's wrapping paper? a. inches b. inches c. inches d. inches
The measurement of the two shorter sides in Monica's wrapping paper is 17 inches.
How we can use proportions to solve this problem?We can use proportions to solve this problem. Since Francisco's piece of paper is similar to Monica's piece of paper, the ratios of the corresponding sides will be equal. Specifically, we have:
17 / x = 34 / y
where x is the length of one of Francisco's shorter sides, and y is the length of one of Monica's shorter sides.
To solve for y, we can cross-multiply and simplify:
17y = 34x
y = 2x
So the length of one of Monica's shorter sides is half the length of one of her longer sides, or:
y = 1/2 * 34 = 17
Therefore, the measurement of the two shorter sides in Monica's wrapping paper is 17 inches. Answer: a. inches.
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-12+3(4-15)-40+10 plizz
Answer:
-12+3(-11)-40-10
Step-by-step explanation:
Answer:
Step-by-step explanation:
-12+12-45-40+1
0-85+1
-84
Water flows into an empty reservoir at a rate of 3200+ 5t gal/hour. What is the quantity of water in the reservoir after 11 hours? Answer:_____ gallons.
To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.
∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.
To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.
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(1 point) Use Lagrange multipliers to find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 Minimum:
function f(x,y) = 2 + y
The minimum value are f(√5, √5) = 2 + √5.
Lagrange multipliers:To find the minimum value of the function f(x,y) = 2 + y subject to the constraint xy=5 using Lagrange multipliers,
we first set up the Lagrangian function:
L(x,y,λ) = f(x,y) - λ(xy - 5)
Taking partial derivatives with respect to x, y, and λ, we get:
∂L/∂x = 0 = -λy
∂L/∂y = 1 - λx
∂L/∂λ = xy - 5
Solving for λ from the first equation and substituting into the second equation, we get:
x/y = 0/λ
1 - λx = 0
xy - 5 = 0
From the first equation, we see that either x = 0 or y = 0. But since xy = 5, neither x nor y can be zero.
Therefore, we have:
λ = 0
1 - λx = 0
xy - 5 = 0
Solving for x and y from the last two equations, we get:
x = 5/y
y = ±√5
We take the positive root for y since we are looking for a minimum value of the function.
Substituting y = √5 into x = 5/y, we get x = √5.
Therefore, the minimum value of f(x,y) = 2 + y subject to the constraint xy=5 is:
f(√5, √5) = 2 + √5.
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Help I don't know what I did wrong.
[tex]4\sqrt{125} -2\sqrt{243} -3\sqrt{20}+5\sqrt{27}[/tex]
A triangle with area 28 square inches has a height that is six less than twice the width. Find the height and width of the triangle. [Hint: For a triangle with base b and height h , the area, A , is given by the formula
The height of the triangle is 8 inches and the width is 7 inches.
Find the height and width of a triangle with area 28 square inches, where the height is six less than twice the width.Let's start by using the formula for the area of a triangle:
A = (1/2)bh
where A is the area of the triangle, b is the base, and h is the height.
We are given that the area of the triangle is 28 square inches, so we can write:
28 = (1/2)bh
Next, we are given that the height h is six less than twice the width w. In other words:
h = 2w - 6
Now we can substitute this expression for h into the formula for the area:
28 = (1/2)bw(2w - 6)
Simplifying this equation, we get:
56 = bw(2w - 6)
28 = w(w - 3)
w^2 - 3w - 28 = 0
We can solve this quadratic equation using the quadratic formula:
w = [3 ± √ ([tex]3^2[/tex] - 4(1)(-28))] / 2
w = [3 ± √ (121)] / 2
w = (3 + 11) / 2 or w = (3 - 11) / 2
w = 7 or w = -4
Since a negative width doesn't make sense in this context, we can ignore the second solution and conclude that the width of the triangle is 7 inches.
Now we can use the expression for h in terms of w to find the height:
h = 2w - 6
h = 2(7) - 6
h = 8
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Define place value and explain how you could use place value to solve the equation 19 + 50 =
Place value is the value of a digit based on its position within a number system. To solve the equation 19 + 50, we use place value to add the digits in the ones and tens place.
Place value is a fundamental concept in mathematics that helps in understanding the value of digits in a number system. In the decimal system, each digit's value depends on its position relative to the decimal point, with the position to the left representing higher values than those to the right.
To solve 19 + 50, we add the digits in the ones place (9 + 0 = 9) and the digits in the tens place (1 + 5 = 6) separately, then combine the results to get the final answer of 69. This is possible due to the place value concept. The digit 9 in the ones place of 19 represents a value of 9 units, while the digit 1 in the tens place represents 10 units.
Similarly, the digit 5 in the tens place of 50 represents 50 units, and the digit 0 in the ones place represents 0 units. By adding the digits based on their place value, we get the answer 69, where 9 is in the ones place and 6 is in the tens place.
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The table shows the daily amount that Trevor spent on snacks. During
which week did Trevor spend a mean amount of $0. 85 per day on snacks? *
1 point
Week
Friday
$0. 50
1
Monday Tuesday Wednesday Thursday
$0. 75 $0. 50
$1. 00 $1. 25
$1. 25 $0. 75 $0. 25 $1. 00
$0. 50 $0. 75
$0. 25 $0. 25
$1. 25 $0. 25 $0. 75 $1. 00
$1. 00
AWN
$1. 25
$0. 50
Week 1
Week 2
Week 3
Week 4
Trevor spent a mean amount of $0.85 per day on snacks during
Week 1.
We have,
To determine during which week Trevor spent a mean amount of $0.85 per day on snacks, we need to calculate the mean (average) amount spent per day for each week and find the week that matches $0.85.
Let's calculate the mean amount spent per day for each week:
Week 1:
= (0.50 + 0.75 + 0.50 + 1.00 + 1.25 + 1.25 + 0.75 + 0.25 + 1.00) / 9
= $0.86 (approximately)
Week 2:
= (1.00 + 0.50 + 0.75 + 0.25 + 0.25 + 1.25 + 0.25) / 7
= $0.61 (approximately)
Week 3:
= (0.75 + 1.00) / 2
= $0.88
Week 4:
= (1.25 + 1.00 + 1.00 + 1.25 + 0.50) / 5
= $1.00
From the calculations, we can see that the mean amount spent per day for Week 1 is closest to $0.85.
Therefore,
Trevor spent a mean amount of $0.85 per day on snacks during
Week 1.
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Suppose that you invest $7000 in a risky investment. at the end of the first year, the
investment has decreased by 70% of its original value. at the end of the second year,
the investment increases by 80% of the value it had at the end of the first year. your
investment consultant tells you that there must have been a 10% overall increase of
the original $7000 investment. is this an accurate statement? if not, what is your
actual percent gain or loss on the original $7000 investment. round to the nearest
percent.
The actual percent loss on the original $7000 investment is 46%. This means that the investment consultant's statement of a 10% overall increase is not accurate.
To calculate the actual percent gain or loss on the original $7000 investment, we can use the following formula:
Actual percent gain or loss = (Ending value - Beginning value) / Beginning value * 100%
At the end of the first year, the investment decreased by 70% of its original value, which means its value was only 30% of $7000, or $2100.
At the end of the second year, the investment increased by 80% of the value it had at the end of the first year. So, its value at the end of the second year was:
Value at end of second year = $2100 + 80% of $2100
Value at end of second year = $2100 + $1680
Value at end of second year = $3780
Therefore, the actual percent gain or loss on the original $7000 investment is:
Actual percent gain or loss = ($3780 - $7000) / $7000 * 100%
Actual percent gain or loss = -46%
So, the actual percent loss on the original $7000 investment is 46%.
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A circumscribed angle is an angle whose sides are to a circle
A circumscribed angle is an angle whose sides are tangent to a circle. In other words, the angle is formed by two intersecting chords of the circle. The vertex of the angle is located outside of the circle, while the two endpoints of the angle lie on the circle.
Circumscribed angles have some important properties in geometry. For example, the measure of a circumscribed angle is half the measure of its intercepted arc (the arc of the circle that lies inside the angle). Additionally, if two angles intercept the same arc of a circle, they are congruent.
Circumscribed angles also appear frequently in trigonometry, where they are used to define the sine, cosine, and tangent functions. The sine of a circumscribed angle is defined as the ratio of the length of the opposite side of the angle to the length of the circle's radius. The cosine of a circumscribed angle is defined as the ratio of the length of the adjacent side of the angle to the length of the radius.
Finally, the tangent of a circumscribed angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
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The Rialto Theater sells balcony seats for $10 and main floor seats for
$25. One afternoon performance made $6250. The number of balcony
seats sold was 20 more than 3 times the number of main floor seats. Write
the system of equations to determine the number of main floor and
balcony seats.
The system of equations is:
Revenue from balcony seats = $10 × B
Revenue from main floor seats = $25 × M
Total revenue = $6250
B = 3M + 20
Let's define the following variables:
B = number of balcony seats sold
M = number of main floor seats sold
We know that the price of a balcony seat is $10 and the price of a main floor seat is $25.
From the given information, we can create the following equations:
The total revenue from balcony seats sold (B) is given by: Revenue from balcony seats = $10 × B
The total revenue from main floor seats sold (M) is given by: Revenue from main floor seats = $25 × M
The total revenue from the afternoon performance is $6250: Total revenue = Revenue from balcony seats + Revenue from main floor seats
The number of balcony seats sold (B) is 20 more than 3 times the number of main floor seats (M): B = 3M + 20
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To solve 6÷1/4, james thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. what is the quotient of 6 and 1/4? enter your answer in the box.
The quotient of 6 and 1/4 is 24.
We have applied division operation to this question. Firstly, we will understand the meaning of a proper fraction. A fraction in which the numerator is less than the denominator is called a proper fraction. This means that the denominators will always be bigger than the numerators for appropriate fractions.
We can represent this condition in either of the two ways.
Denominator < Numerator
(Or)
Numerator > Denominator
We are given a numerical expression which is 6÷ 1/4 and we have to solve this.
To convert this division sign into a multiplication sign, we will take the reciprocal of 1/4.
The reciprocal of 1/4 is 4.
Therefore,
6÷ 1/4
= 6 × 4
= 24
Therefore, the quotient of 6 and 1/4 is 24.
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Consider the diagram shown. The sphere and cylinder have the same diameter. The height of the
cylinder is equal to the diameter of the sphere.
Find the approximate volume of the sphere by using 3.14 for 7. Round to the nearest tenth
of a cubic unit.
8.4
8.4
Answer:
310.2 cubic units
Step-by-step explanation:
since we know the diameter of the sphere (8.4), the radius is [tex]8.4/2 = 4.2[/tex]
The volume of a sphere is [tex]\frac{4}{3}\pi r^3[/tex]
Plugging in 3.14 as [tex]\pi[/tex] and 4.2 as r, we get 310.2
Find dx/dy, if x=sin^3t,y=cos^3t.
dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
To find dx/dy, we first need to find dx/dt and dy/dt, and then we can use the chain rule.
Given x = sin^3(t) and y = cos^3(t),
dx/dt = d(sin^3(t))/dt = 3sin^2(t) * cos(t) (using the chain rule)
dy/dt = d(cos^3(t))/dt = -3cos^2(t) * sin(t) (using the chain rule)
Now, we can find dx/dy by dividing dx/dt by dy/dt:
dx/dy = (dx/dt) / (dy/dt) = (3sin^2(t) * cos(t)) / (-3cos^2(t) * sin(t))
Simplify the expression:
dx/dy = -sin(t)/cos(t)
So, dx/dy = -sin(t)/cos(t) when x = sin^3(t) and y = cos^3(t).
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A researcher surveyed 220 residents of a city about the number of hours they
spend watching news on television each day. The mean of the sample was
1. 8 with a standard deviation of 0. 35.
The researcher can be 95% confident that the mean number of hours all the
residents of the city are watching news on television is 1. 8 with what margin
of error?
The researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.
Based on the information provided, the researcher surveyed 220 residents of the city and found that the mean number of hours they spend watching news on television each day is 1.8, with a standard deviation of 0.35.
The researcher wants to know the margin of error at a 95% confidence level for the mean number of hours all residents of the city are watching news on television.
To calculate the margin of error, we need to use the formula:
Margin of error = Critical value x Standard error
The critical value for a 95% confidence level is 1.96, and the standard error can be calculated as:
Standard error = Standard deviation /square root of sample space
Substituting the values given:
Standard error = 0.35 / sqrt(220) = 0.0236
Therefore, the margin of error can be calculated as:
Margin of error = 1.96 x 0.0236 = 0.0462
So, the researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.
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what is an equation of the line perpendicular to y= -3x + 4 that contains (-6,2)
The equation of the perpendicular line to y = -3x + 4 and passing through (-6, 2) is y = (1/3)x + 4.
What does a perpendicular line look like?
There are a lot of perpendicular lines that we may see in reality. The corners of a chalkboard, a window, the sides of a set square, and the Red Cross symbol are a few examples.
Knowing that the slopes of perpendicular lines are the negative reciprocals of one another is necessary to determine the equation of a line perpendicular to a given line.
The given line has a slope of -3, so the slope of a line perpendicular to it would be the negative reciprocal of -3, which is 1/3.
We also know that the line passes through the point (-6, 2).
The equation of the line passing through (-6, 2) and perpendicular to y = -3x + 4 can be found using the point-slope form of a line:
y - 2 = (1/3)(x + 6)
Simplifying this equation, we get:
y = (1/3)x + 4
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This table shows dogs’ weights at a competition.
Dogs' Weights (pounds)
35, 22, 31, 23, 35, 22, 30, 35, 40
One 42-pound dog could not make it to the competition. ++++Select all++++ the ways the measures of center of the data set change if she had entered the competition.
A. The median increases
B. The mode increases
C. The mean increases
D. The median decreases
E. The mode decreases
F. The mean decreases
The measures of central tendencies changed as mode remained the same, the median increased and the mean increased.
How will the data set change if she had entered the competition?To determine how the data set would've changed if she entered the competition, we simply need to work on the mean, median and mode of the data.
Given data;
35, 22, 31, 23, 35, 22, 30, 35, 40
Rearranging this data;
22, 22, 23, 30, 31, 35, 35, 35, 40
The mean of this data will be
mean = 30.3
The mode = 35
The median = 31
When her weight is added, the measures of central tendencies change to;
mean = 31.5
median = 33
mode = 35
The median decreases, the mode remains the same and the mean increases
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the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 37,014 miles, with a standard deviation of 4617 miles. what is the probability that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires if the manager is correct? round your answer to four decimal places.
Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.
We have data of an operation manager at a tire manufacturing company.
Mean mileage of a tire, [tex] \mu[/tex]
= 37,014 miles
standard deviation, [tex] \sigma[/tex]
= 4617 miles.
Sample size, n = 56
We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, [tex]\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},[/tex]
Plugging all known values in above formula, [tex]z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}[/tex]
= 59.634
[tex]P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ [/tex]
=> P ( z < 59.63) = P( \bar x < 221)
Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.
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Use linear approximation, i.e. the tangent line, to approximate (1/0.504) as follows: Find the equation of the tangent line to f(x)=1x at a "nice" point near 0.504. Then use this to approximate (1/0.504).
The equation of the tangent line to f(x) is y = -4x + 4
How to find the equation of the tangent line to f(x)?The equation of the tangent line to f(x) = 1/x at a point x = a is given by:
y - f(a) = f'(a) * (x - a)
where f'(x) is the derivative of f(x) with respect to x.
We can find a "nice" point near 0.504 by choosing a = 0.5, which is close to 0.504 and makes the calculation easy.
The derivative of f(x) = 1/x is given by:
[tex]f'(x) = -1/x^2[/tex]
At x = 0.5, we have:
f(0.5) = 1/0.5 = 2
[tex]f'(0.5) = -1/(0.5)^2 = -4[/tex]
Plugging these values into the equation of the tangent line, we get:
y - 2 = -4 * (x - 0.5)
Simplifying, we get:
y = -4x + 4
Now we can use this tangent line to approximate (1/0.504) as follows:
(1/0.504) ≈ y(0.504)
Plugging x = 0.504 into the equation of the tangent line, we get:
y(0.504) = -4(0.504) + 4 = 1.784
Therefore, (1/0.504) ≈ 1.784
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A family camping in a national forest builds a temporary shelter with a
tarp and a 4-foot pole. the bottom of the pole is even with the ground, and one corner
is staked 5 feet from the bottom of the pole. what is the slope of the tarp from that
corner to the top of the pole?
A family camping in a national forest used a 4-foot pole and a tarp to build a temporary shelter. One corner of the tarp was staked 5 feet from the bottom of the pole. The slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
We can draw a right triangle with the pole being the height, the distance from the pole to the stake being the base, and the slope of the tarp being the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite to the right angle.
Using the Pythagorean theorem, we can find the length of the hypotenuse
hypotenuse² = height² + base²
hypotenuse² = 4² + 5²
hypotenuse² = 41
hypotenuse = √(41)
Therefore, the slope of the tarp is the ratio of the height to the base, which is
slope = height / base = 4 / 5 = 0.8
So the slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
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How to show (sin 7x)/sin x = 64(cos x)^6 - 80(cos x)^4 +24(cos x)^2 - 1 ?
Following shows (sin 7x)/sin x = 64(cos x)^6 - 80(cos x)^4 +24(cos x)^2 - 1:
12sin^3 x - 8sin^
To show that (sin 7x)/sin x is equal to 64(cos x)^6 - 80(cos x)^4 + 24(cos x)^2 - 1, we can use trigonometric identities and algebraic manipulation.
Let's start with the left-hand side of the equation:
(sin 7x)/sin x
Using the trigonometric identity for sin(A + B):
sin(A + B) = sin A cos B + cos A sin B
We can rewrite sin 7x as sin (6x + x):
sin (6x + x) = sin 6x cos x + cos 6x sin x
Now we can substitute sin 7x with sin 6x cos x + cos 6x sin x:
(sin 6x cos x + cos 6x sin x)/sin x
Next, we can simplify this expression by dividing both terms by sin x:
(sin 6x cos x)/sin x + (cos 6x sin x)/sin x
The sin x term cancels out, leaving us with:
sin 6x cos x + cos 6x
Now, we can use the double-angle identity for sin 2A:
sin 2A = 2sin A cos A
To rewrite sin 6x cos x, we can treat it as sin 2A with A = 3x:
sin 6x cos x = 2sin 3x cos 3x
Next, we can use the triple-angle identity for sin 3A:
sin 3A = 3sin A - 4sin^3 A
To rewrite sin 3x, we can treat it as sin A with A = x:
sin 3x = 3sin x - 4sin^3 x
Substituting this into our expression:
2sin 3x cos 3x = 2(3sin x - 4sin^3 x) cos 3x
Expanding further:
= 6sin x cos 3x - 8sin^3 x cos 3x
Now, we can use the double-angle identity for cos 2A:
cos 2A = cos^2 A - sin^2 A
To rewrite cos 3x, we can treat it as cos A with A = x:
cos 3x = cos^2 x - sin^2 x
Substituting this into our expression:
6sin x cos 3x - 8sin^3 x cos 3x = 6sin x (cos^2 x - sin^2 x) - 8sin^3 x (cos^2 x - sin^2 x)
Expanding further:
= 6sin x cos^2 x - 6sin x sin^2 x - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
Now, we can use the Pythagorean identity for sin^2 x + cos^2 x:
sin^2 x + cos^2 x = 1
To rewrite sin^2 x, we can subtract cos^2 x from both sides:
sin^2 x = 1 - cos^2 x
Substituting this back into our expression:
= 6sin x (cos^2 x - (1 - sin^2 x)) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 6sin x (2sin^2 x) - 8sin^3 x cos^2 x + 8sin^3 x sin^2 x
= 12sin^3 x - 8sin^
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Admission Charge for Movies The average admission charge for a movie is $5. 81. If the distribution of movie admission charges is approximately normal with a standard deviation of $0. 81, what is the probability that a randomly selected admission charge is less than $3. 50
The probability that a randomly selected admission charge is less than $3. 50 is 0.23% or 0.0023.
To find the probability that a randomly selected admission charge is less than $3.50, we will use the z-score formula and a standard normal table. The z-score formula is:
Z = (X - μ) / σ
Where X is the value we are interested in ($3.50), μ is the average admission charge ($5.81), and σ is the standard deviation ($0.81).
Z = (3.50 - 5.81) / 0.81 ≈ -2.84
Now, look up the z-score (-2.84) in a standard normal table, which gives us the probability of 0.0023. Therefore, the probability that a randomly selected admission charge is less than $3.50 is approximately 0.23% or 0.0023.
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Unit 6: similar triangles
homework 5: parallel lines & proportional parts
what are the answers to these equations? # 1-16
To understand how to approach problems involving similar triangles, parallel lines, and proportional parts.
When you have two similar triangles, their corresponding sides are proportional. This means that the ratio between the sides of one triangle is the same as the ratio between the sides of the other triangle.
If you have parallel lines cut by a transversal, corresponding angles will be congruent, which can help establish similarity between triangles.
For example, if you have two similar triangles ABC and DEF, where AB/DE = BC/EF = AC/DF, then you can use these ratios to solve for unknown side lengths or other values.
To answer questions 1-16, identify the given information and determine whether the triangles are similar. If they are, use the proportional relationships to solve for the unknowns.
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How do you solve these problems on Unit 6: similar triangles homework 5: parallel lines and proportional parts?
7. X-5/6 = 14/2x+3
16. X-7/35 = 4/x-3