As a result, the cylinder's lateral surface area is about 59.69 cm²to the nearest tenth.
Define cylinder?The three-dimensional shape of a cylinder consists of two parallel circular bases joined by a curving surface. It is comparable to a prism with an endless number of sides.
Side Surface Area = 2 ×πrh
where h is the cylinder's height and r is its radius.
The result of entering the specified values into this formula is:
Surface Area Lateral = 2π(2) (9.5)
π = 3.141 , 6.282 ×19
= 119.32 cm
So , 59.69 cm² is the lateral surface area.
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The complete question is : Find the lateral surface area of the cylinder to the nearest hundredth. where radius is 2cm and height is 9.5 cm
Jennifer, Grace, and Janet played Computer games. Jennifer won 30% of the total games, Grace 25%, and Janet 45%. There were no ties. What is the least possible number of the games that Jennifer won?
The least possible number of games that Jennifer won is three. This is because when the total number of games won is 300.
What is game?A situation where two or more decisions makers (players) have to make decisions based on the probabilities of each outcome.
To find this number, we must first calculate the total number of games played. Since Jennifer won 30%, Grace won 25%, and Janet won 45%, the total number of games played can be determined by multiplying the total percentage by the number of players.
30% + 25% + 45% = 100%
100% x 3 players = 300 games played
To find out how many games Jennifer won, we must multiply 30% by the total number of games played.
30% x 300 games = 90 games
Since Jennifer won 90 games, Grace won 25% of 300 games, which is 75 games, and Janet won 45% of 300 games, which is 135 games, the total number of games won is 300.
Therefore, the least possible number of games that Jennifer won is three. This is because when the total number of games won is 300, the least possible number of games that one player can win is three.
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When a number is decreased by 40% of itself, the result is 54 . What is the number?
Answer:
90
Step-by-step explanation:
We can translate this into the following equation:
x - 0.4x = 54
Simplifying the left side of the equation, we get:
0.6x = 54
Dividing both sides by 0.6, we get the following:
x = 90
Therefore, 90 is the number decreased by 40% leaving 54.
A grain silo has a cylinder shape it’s radius is 7ft and it’s height is 31ft what is the volume of the silo
Answer:
The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
V = π(7ft)^2(31ft)
V = π(49ft^2)(31ft)
V = 49π(31ft^3)
V ≈ 15,067.05 cubic feet (rounded to two decimal places)
Therefore, the volume of the silo is approximately 15,067.05 cubic feet.
Can someone help me put these values in order?
The steps to verify the identity cos(-Θ)/(1 + sin(-Θ)) = sec(Θ) + tan(Θ) are:
cos(-Θ)/(1 + sin(-Θ))cos(Θ)/(1 - sin(Θ))cos(Θ)(1 + sin(Θ))/((1 - sin²(Θ)))cos(Θ)(1 + sin(Θ))/(cos²(Θ))1/cos(Θ) + sin(Θ)/cos(Θ) sec(Θ) + tan(Θ)How to verify an identity's order?Start with the left-hand side of the identity: cos(-Θ)/(1 + sin(-Θ))
Use the fact that cos(-Θ) = cos(Θ) and sin(-Θ) = -sin(Θ) to rewrite the expression as: cos(Θ)/(1 - sin(Θ))
Multiply the numerator and denominator by (1 + sin(Θ)) to get: cos(Θ)(1 + sin(Θ))/((1 - sin²(Θ)))
Use the Pythagorean identity sin²(Θ) + cos²(Θ) = 1 to simplify the denominator to cos²(Θ): cos(Θ)(1 + sin(Θ))/(cos²(Θ))
Rewrite the expression using the definitions of secant and tangent: cos(Θ)/cos(Θ) + sin(Θ)/cos(Θ) = sec(Θ) + tan(Θ)
Simplify the expression to arrive at the right-hand side of the identity: sec(Θ) + tan(Θ)
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Image transcribed:
1. Put the steps in order to verify the identity.
cos(-Θ)/1 + sin(-Θ) = sec Θ + tan Θ
↑↓ (cos Θ/1 - sin Θ) (1+ sin Θ/1 + sin Θ)
↑↓ (cos Θ + sin Θ cos Θ) / (1-sin² Ө)
↑↓ cos Θ + sin Θ cos Θ)/ cos² Θ
↑↓ cos Θ/(1- sin Θ)
↑↓ 1/cos Θ + sin Θ/ cos Θ
↑↓ sec Θ +tan Θ
Please help - will mark branliest
Answer:
[tex]sin( \alpha ) = \frac{12}{13} [/tex]
[tex] \cos( \alpha ) = \frac{5}{13} [/tex]
[tex] \tan( \alpha ) = \frac{12}{5} [/tex]
It follows that:
[tex] \cot( \alpha ) = \frac{5}{12} [/tex]
[tex] \sec( \alpha ) = \frac{13}{5} [/tex]
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You select a family with three children. If M represents a male child and F a female child, the set of equally likely outcomes for the children's genders is shown below. Find the probability of selecting
a family with at least two male children.
(MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF)
The probability of having at least two male children is
(Type an integer or a simplified fraction.)
There are 8 possible outcomes and we need to find the probability of having at least two male children.
Out of the 8 outcomes, there are 3 outcomes where all children are female (FFF, probability = 1/8) and 3 outcomes where there is exactly one male child (FMF, FFM, MFF, probability = 3/8).
Therefore, the probability of having at least two male children is the complement of these outcomes, which is 1 - (1/8 + 3/8) = 4/8 or 1/2.
So the probability of selecting a family with at least two male children is 1/2 or 0.5.
The probability of selecting a family with at least two male children is 3/8.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
There are 8 equally likely outcomes, and we want to find the probability of selecting a family with at least two male children.
There are three outcomes that satisfy this condition:
MMM, MMF, and MFM.
The probability of each of these outcomes is:
MMM: (1/2) x (1/2) x (1/2) = 1/8
MMF: (1/2) x (1/2) x (1/2) = 1/8
MFM: (1/2) x (1/2) x (1/2) = 1/8
So the total probability of selecting a family with at least two male children is:
1/8 + 1/8 + 1/8 = 3/8
Therefore,
The probability of selecting a family with at least two male children is 3/8.
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Which of the following expressions is equal to 4?
A) 4 x (one-half x 6) ÷ 3
B)6 ÷ (one-fourth x 3 x one and one-fourth)
C)8 + (one-third x 6) ÷ 5
D)10 − (one-fifth x 10) + 1
Answer:
A) 4 x (one-half x 6) ÷ 3
Step-by-step explanation:
Hope it helps:)
Pls help me on this
The proof for the above question are given above accordingly.
What is the proof for the above prompts?10) Since OA ⊥ OC; and
OB ⊥ OD (Given)
Thus,
∠AOC = 90°; perpendicular bisector theorem
∠BOD = 90°; perpendicular bisector theorem
Therefore,
90° Less ∠1 = ∠BOC; and
90° less ∠3 = ∠BOC,
Thus,
∠1≅∠3 - subtraction theorem of congruence
11)
Since ∠A is complimentary to ∠ ADB; Given.....1
and ∠C is complimentary to ∠CDB - Given. .....2
Where DB bisects ∠ADC, thus,
∠DBC = 90° ----Line bisector theorem .......3
∠BDC = 90° -----Line bisector theorem........4
From 1 and 2 above, we know that:
∠A + ∠ADB = 90°
∠C + ∠CDB = 90°, thus,
Since
∠A + ∠ADB + ∠DBA = 180° - Sum of Angles in a triangle; and
∠C + CDB + ∠BDC = 180° - Sum of angles in a triangle, we can state that
∠A ≅∠C.
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Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. If the first 6 children born are girls, what is the probability the next born child is a boy?
For given Sample Space, the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5 i.e. A.
What exactly is a sample space?
A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.
Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.
Now,
The probability of a baby being a boy or a girl is 0.5 each, and each birth is an independent event, meaning that the outcome of one birth does not affect the outcome of the others. Therefore, the probability of having 6 girls in a row is (0.5)⁶ = 0.015625, or approximately 1.5625%.
Now, we want to find the probability that the next born child is a boy, given that the first 6 children born were girls.
Using the conditional probability formula:
P(boy | 6 girls) = P(boy and 6 girls) / P(6 girls)
The probability of having 6 girls and a boy is the same as the probability of having 7 children in a row, with the last one being a boy. The probability of having 7 children in a row, with any gender, is (0.5)⁷ = 0.0078125, or approximately 0.78125%.
Therefore,
P(boy | 6 girls) = (0.5)⁷ / (0.5)⁶ = 0.5
So the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5.
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Write an equation in slope-intercept form of the line that has the given slope and which passes through the given point
m=5, (-1,-12)
A. y=-x
B. y=5x-1
C. y=5x-7
D. y=5x-17
Answer:
C) y = 5x - 7
Step-by-step explanation:
Slope- intercept form: y =mx +b
Here, m is the slope and b is the y intercept.
Substitute m = 5 and (-1 , -12) in the above equation and find the value of b.
-12 = 5*(-1) + b
-12 = -5 + b
-12 + 5 = b
b = -7
Equation in slope intercept form:
[tex]\boxed{\bf y = 5x -7}[/tex]
Bianca calculated the height of the equilateral triangle with side lengths of 10.
tangent (30) = StartFraction 5 Over h EndFraction An equilateral triangle with side lengths of 10 is shown. A bisector is drawn to split the side into 2 equal parts and splits the angle into 2 30 degree segments.
Then, she used the formula for area of a triangle to approximate its area, as shown below.
A = one-half b h. = one-half (10) (8.7). = 43.5 units squared.
Calculate the area of the equilateral triangle using the formula for area of a regular polygon, and compare it to Bianca’s answer.
The apothem, rounded to the nearest tenth, is
2.9
units.
The perimeter of the equilateral triangle is
units.
Therefore, the area of the equilateral triangle is
, or approximately 43.5 units2.
The calculated areas are
.
The calculated areas are the same for regular polygon and equal to 43.5 units squared.
What is area of polygon?The area of polygon is given by the formula:
A = (1/2)ap,
where A is the area, an is the apothem (the distance from the centre of the polygon to the midpoint of any side), and p is the polygon's perimeter, is the formula for calculating the area of a regular polygon.
The apothem of the equilateral triangle can be found using the formula:
a = s / (2 tan(π/n))
Substituting the value of s = 10 we have, and n = 3 side.
a = 10/ / (2 tan(π/3))
a ≈ 2.9 units
The perimeter of the triangle is given as:
p = 3 x 10 = 30 units
Now, the area of the triangle is given as:
A = (1/2)ap
A = (1/2)(2.9)(30) = 43.5 sq. units.
Hence, the calculated areas are the same and equal to 43.5 units squared.
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Answer:
Step-by-step explanation:
Bianca’s answer.
The apothem, rounded to the nearest tenth, is
✔ 2.9 units.
The perimeter of the equilateral triangle is
✔ 30 units.
Therefore, the area of the equilateral triangle is
✔ 1/2(2.9)(30) , or approximately 43.5 units2.
The calculated areas are
✔ the same, despite using different formulas
.
A textile factory uses a 43 liter bucket of dye per 1 roll of fabric that is 1,067 feet long. If the factory has 4 buckets of dye, can it dye 5 rolls of fabric?
The textile factory does not have enough dye to dye 5 rolls of fabric using 4 buckets of dye which is certain feet long.
Calculating the amount of dye needed to color one roll of fabric and comparing it to the total amount of dye available will help us decide whether the textile mill can dye 5 rolls of cloth with 4 buckets of dye.
We are aware that a single roll of fabric is 1,067 feet long and need for a 43-liter dye bucket. We divide the dye's volume by the fabric's length to get how much dye is needed per foot of fabric:
0.0403 litres per foot or 43 litres divided by 1,067 feet
Consequently, the factory needs 0.0403 litres of dye to colour one foot of fabric.
Considering there are 4 buckets and each bucket holds 43 litres of colour, the total amount of dye accessible is:
4 buckets at a rate of 43 litres each equal 172 litres.
The factory must dye a total of: to dye 5 rolls of fabric.
5,335 feet are equal to 5 rolls at 1,067 feet each.
We calculate the required amount of dye per foot by the total length of fabric to see if the factory has enough dye to colour this length of fabric:
5,335 feet * 0.0403 litres per foot = 215.1 litres
The manufacturer cannot colour 5 rolls of fabric with 4 buckets of dye because the whole amount of dye needed (215.1 litres) is more than the total amount of dye available (172 litres).
In conclusion, there isn't enough dye in the textile plant to colour 5 rolls of fabric using 4 buckets of dye.
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Which statements about parallelograms are always true or sometimes true?
Diagonals are congruent.
Diagonals bisect each other.
Diagonals are perpendicular.
Opposite sides are congruent.
Opposite angles are congruent.
Opposite angles are supplementary.
All sides are congruent.
Consecutive angles are supplementary.
The following statements are true about parallelograms: diagonals bisect each other, opposite sides are congruent, opposite angles are congruent and opposite angles are supplementary.
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.
The properties of a parallelogram are shared by the shapes of a square and a rectangle.
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24
A
Step 1
Algebra 1
1A: 2198 262 2A:
3A:
Topic 6-Quadratic Functions - Assessment 2 Retake A
4A:
Here is a pattern of squares.
2. Draw a diagram to show that 5(x+2) = 5x + 10.
Step 2
Step 3
3A: Write an expression for step n of this pattern:
2A: Is this pattern linear, exponential, or quadratic?
How do you know?
5A:
revenue (dollars)
1000
800
600
400
200
Name Marc burke
2 4 6 8 10 12 14 16 18 20
price (dollars)
Use the graph to answer the following question:
5A: What is the domain of this graph?
loodsholt tohut 69
The function of the sequence is T(n) = n² + n and it is quadratic
The domain of the graph is [0, 18]
The expression for the n-th termFrom the question, we have the following parameters that can be used in our computation:
Step Cells
1 2
2 6
3 12
From the table, we have
T(n) = n * (n + 1)
This gives
T(n) = n² + n
Hence, the function is T(n) = n² + n
The sequence typeThe sequence T(n) = n² + n is a quadratic sequence
The domain of the graphThis is the set of the x values
From the graph, we have
x = 0 to 18
So, we have
Domain = [0, 18]
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a fee of 100.to complete a company taxes .the account also charges and additional 35.00 per hr to complete the taxes witch of the following equation can be used to describe this problem
According to the question, the total cost to complete the company taxes is $135.
We can use the following equation to describe the problem:
Total cost = Fixed cost + Hourly rate * Number of hours
In this case, the fixed cost is $100 to complete the company taxes, and the accountant charges an additional $35 per hour to complete the taxes. Let's say it takes the accountant "h" hours to complete the taxes. Plugging in these values, we get:
Total cost = $100 + $35/h * h
Simplifying the equation, we get:
Total cost = $100 + $35
Total cost = $135
Therefore, the total cost to complete the company taxes is $135.
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Solve each equation.
(x + 3)(x - 3) = 16 - 2x^2
Answer:
[tex]x = ± \frac{5 \sqrt{3} }{3} [/tex]
Step-by-step explanation:
[tex](x + 3)(x - 3) = 16 - 2 {x}^{2} [/tex]
Use the quick multiplication formula:
[tex] {x}^{2} - 9 = 16 - 2 {x}^{2} [/tex]
[tex] {x}^{2} + 2 {x}^{2} = 16 + 9[/tex]
[tex]3 {x}^{2} = 25[/tex]
Divide both parts by 3 to make x the subject:
[tex] {x}^{2} = ±8 \frac{1}{3} [/tex]
[tex]x = ± \frac{5 \sqrt{3} }{3} [/tex]
1. Stacey tried to remove a metal lid from a glass jar, but the lid was too tight. Her mother held the jar so that the lid was in hot water for a minute. Then Stacey was able to turn the lid easily. How did the hot water make the lid easier to remove? (F) Heating the glass jar made it expand, so the lid turned easily. (G) As the metal lid was heated, it expanded so that it was not as tight. (H) Water on the metal lid made it easier to hold, so it was easier to turn. (I)The water corroded the metal, so it did not hold as tightly to the glass.
According to the solution we have come to find that, As the metal lid was heated, it expanded so that it was not as tight. The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.
what is heat?
Heat is a form of energy that is transferred between objects or systems as a result of a temperature difference. It is the energy that flows from a body of higher temperature to a body of lower temperature until they reach a state of thermal equilibrium. Heat can be transferred through three different mechanisms: conduction, convection, and radiation.
Conduction involves the transfer of heat through direct contact between two objects that are at different temperatures. Convection involves the transfer of heat through the movement of fluids, such as air or water, due to differences in temperature. Radiation involves the transfer of heat through the emission and absorption of electromagnetic waves, such as infrared radiation.
The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.
When the metal lid was placed in hot water, the heat caused it to expand. This expansion allowed the lid to loosen from the glass jar, making it easier to turn. This is because metals generally expand when heated and contract when cooled. The expansion of the metal lid due to heat causes it to become slightly larger than before, thereby loosening its grip on the jar. As a result, the lid can be turned with less force, and it comes off easily.
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i need help please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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Put 1 5/8, -2.35, -4.3, and - 3/5 in order from least to greatest
Step-by-step explanation:
Numbers:
[tex]1 \frac{5}{8} [/tex]
[tex] - 2.35[/tex]
[tex] - 4.3[/tex]
[tex] - \frac{3}{5} = - 0.6[/tex]
.
From the least to the greatest:
[tex] - 4.3[/tex]
[tex] - 2.35[/tex]
[tex] - 0.6[/tex]
[tex]1 \frac{5}{8} [/tex]
Madelyn runs an animal rescue. She mentioned to her fiancé, Roger, that the dogs consumed a record 39 cups of food the previous day. She also explained that the smaller dogs get 1.5 cups of food a day, while the larger dogs get 3 cups of food a day.
Roger wondered how many smaller and larger dogs there could have been. To represent the situation, Roger defined x as the number of smaller dogs and y as the number of larger dogs. Then he wrote this equation:
1.5x+3y=39
Finally, he graphed the equation.
Answer:
based on the information provided, Madelyn has a total of 26 dogs in her animal rescue. Of these, there are 13 smaller dogs who consume a total of 19.5 cups of food per day (1.5 cups per dog), and there are 13 larger dogs who consume a total of 39 cups of food per day (3 cups per dog).
Step-by-step explanation:
We know that the total number of cups of food consumed by the dogs is 39. We can use this information to create an equation:
1.5s + 3l = 39
We also know that Madelyn has a total number of dogs, which we can represent as:
s + l = total number of dogs
However, we cannot solve for s and l with only one equation. We need another equation to help us solve for both variables.
From the information provided, we know that each smaller dog gets 1.5 cups of food per day and each larger dog gets 3 cups of food per day. Therefore, the total amount of food consumed in one day can also be represented as:
1.5s + 3l = total cups of food consumed in one day
Since we know that the total cups of food consumed in one day is equal to 39, we can substitute this value into the equation:
1.5s + 3l = 39
1.5s + 3l = 39
2s + 4l = 52
Now we have two equations with two variables:
s + l = total number of dogs
2s + 4l = 52
We can use substitution or elimination to solve for s and l. Using substitution:
s + l = total number of dogs
s = total number of dogs - l
2(total number of dogs - l) + 4l = 52
2total number of dogs - 2l + 4l = 52
2total number of dogs + 2l = 52
total number of dogs + l = 26
Now we have two equations:
s + l = total number of dogs
total number of dogs + l = 26
We can use substitution again:
s + l = total number of dogs
s = total number of dogs - l
(total number of dogs - l) + l = 26
total number of dogs = 26
Therefore, Madelyn has a total of 26 dogs. We can now solve for the number of smaller and larger dogs using one of the previous equations:
s + l = total number of dogs
s + (26 - s) = 26
s = 13
Therefore, Madelyn has 13 smaller dogs and 13 larger dogs.
The life of a Radio Shack record player is normally distributed with a mean of 3.3 years and a standard deviation of 0.8 years. Radio Shack guarantees its record players for 2 years.
Find the probability that a record player will break down during the guarantee period.
The probability that a record player will break down during the guarantee period is 26.4%.
What is cumulative distribution?Cumulative distribution shows the probability of a randomly-selected value falling below or equal to a certain value.
To find the probability that a record player will break down during the guarantee period, we need to calculate the probability of the record player breaking down within two years, which is given by the cumulative distribution function of the normal distribution.
This function uses the mean and standard deviation of the distribution, so for the Radio Shack record player, the probability of breaking down within two years is given by the cumulative distribution function
P(X ≤ 2) = CDF(X; 3.3, 0.8)
To find this probability, we can use a normal distribution calculator to find the cumulative probability of X ≤ 2.
The cumulative probability of X ≤ 2 for a normal distribution with a mean of 3.3 and standard deviation of 0.8 is 2.64.
Therefore, the probability that a Radio Shack record player will break down during the guarantee period is 2.64.
This indicates that there is a 26.4% chance that a Radio Shack record player will break down before the end of the two-year guarantee period.
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bring 7/9 of 3/7 to lowest terms
Answer:
1/3
Step-by-step explanation:
We can first find 7/9 of 3/7 by multiplying 7/9 and 3/7:
[tex]\frac{7}{9}*\frac{3}{7}=\frac{21}{63}[/tex]
Now, we can simplify the fraction by finding the GCF of the numerator and 63.
The GCF shared by 21 and 63 is 21, as 21 is the highest number that both the numerator (21) and the denominator (63) are evenly divisible by. Thus, we divide both the numerator and denominator by 21 to simplify the fraction fully and bring it to lowest terms:
[tex]\frac{21/21}{63/21}=\frac{1}{3}[/tex]
PLEASEEEEEEEEE HELPPPP!!! PLEASEEEE OMG I NEED THIS DONE!!! MAKE SURE U SHOW WORK!
The calculated values of the angles 1 and 2 are <1 = 95.9 and <2 = 56.8
Calculating the values of angles 1 and 2from the question, we have the following parameters that can be used in our computation:
The triangle
The adjacent angle of 117.5 is
Angle = 180 - 117.5
Angle = 62.5
The third angle in the big triangle is
Angle = 180 - 62.5 - 39.1
Angle = 78.4
So, the measure of angle 2 is calculated as
<2 = 180 - 21.6 - (180 - 78.4)
<2 = 56.8
Also, the measure of angle 1 is calculated as
<1 = 39.1 + <2
<1 = 39.1 + 56.8
<1 = 95.9
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the 2020 Federal Tax Rates for Individuals to calculate the estimated taxes for a taxable income of $63,700
Answer:32
Step-by-step explanation:
Jackson started a savings account with $25. He plans to deposit $25 each month for the next 12 months, then continue those monthly deposits in the following years. The account earns interest at an annual rate of 4% compounded annually, based on his final yearly balance. What is the total amouny that Jackson will save at the end of 3 years? How much intresr will jackson have earned at the end of the 3 years?
Jackson will have earned $72 in interest at the end of 3 years.
How to solve for the interest earnedJackson saves $25 per month for 12 months:
$25 * 12 months = $300 per year
Now, let's calculate the total amount saved at the end of each year:
Year 1: $300
Year 2: $300 + $300 = $600
Year 3: $300 + $600 = $900
Next, we'll apply the 4% interest rate compounded annually to the final yearly balance:
Year 1: $300 * (1 + 0.04) = $300 * 1.04 = $312
Year 2: $600 * (1 + 0.04) = $600 * 1.04 = $624
Year 3: $900 * (1 + 0.04) = $900 * 1.04 = $936
So, the total amount Jackson will save at the end of 3 years is:
$312 (Year 1) + $624 (Year 2) + $936 (Year 3) = $1,872
Total deposited:
$300 + $600 + $900
= $1,800
Total interest earned:
$1,872 - $1,800
= $72
So, Jackson will have earned $72 in interest at the end of 3 years.
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The map of a rectangular park drawn to scale has a scale of 1 cm = 50 m. What is the actual area of the park if the park is 10 cm by 15 cm on the map?
Answer: The dimensions on the map are 10 cm by 15 cm, so the area on the map is 10 cm × 15 cm = 150 cm^2.
Since the scale is 1 cm = 50 m, every 1 cm on the map corresponds to an actual distance of 50 m. Therefore, the actual dimensions of the park are 10 cm × 50 m/cm = 500 m by 15 cm × 50 m/cm = 750 m.
The actual area of the park is the product of the actual dimensions, so the actual area is 500 m × 750 m = 375000 square meters.
Step-by-step explanation:
Find an expression which represents the difference when (-2x - 6) is subtracted
from (-10x - 2) in simplest terms.
subtract each seperately
first the numbers with x
-2 - -10 becomes -2 + 10 which is 8x
now the constants
then -6 - -2 becomes -6 + 2 which is -4
so its 8x - 4
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I’ll give 80 points if you can answer all these problems
solve the equation 3(3-2x)=2x-11
Answer:
x = 2,5
Step-by-step explanation:
3(3 - 2x) = 2x - 11
Multiply every term inside the bracket by the term on the outside:
9 - 6x = 2x - 11
Collect like terms and add them together (also, when moving the terms to the other side, the sign changes to the opposite)
-6x - 2x = -11 - 9
-8x = -20 / : (-8)
x = 2,5
scenario A: jake has an investment account that earns 2.5% interest compound semi-annually.
Scenario B: maria has a savings account that earns 1.25% simple.interest.
Scenario C: a companies production increases from january until june when it reached a maximum, and then decreases until the end of December
Is scenario A: linear, quadratic, or cannot be determined?
Scenario B: linear, quadratic, or cannot be determined?
Scenario C: linear, quadratic, or cannot be determined.
Pick an answer for each scenario
Scenario A: Cannot be determined
Scenario B: Linear
Scenario C: Cannot be determined