The equation representing 'twenty less than the product of 3 and a number is -29' is 3n - 20 = -29. Solving for n, we find that n equals -3.
When solving the equation twenty less than the product of 3 and a number is -29, we can translate this into a mathematical expression as 3n - 20 = -29, where n represents the unknown number. To find the value of n, add 20 to both sides of the equation, which gives us 3n = -9. Dividing both sides by 3, we find that n = -3. Thus, the number we are looking for is -3.
A train station employee collects data on 160 incoming trains to the station. He notices that 18 of the 90 incoming trains on line A arrive late, and 14 of the 70 incoming trains on line B arrive late.
What is the probability that a train on line A arrives on time? What is the probability that any train arrives on time?
Answer:
Probability of a train on line A arriving on time: 80%
Probability of any train arriving on time: 96%
Step-by-step explanation:
If 18 of the 90 incoming trains on line A arrive late, we have that 90 - 18 = 72 trains of the 90 arrive on time, so the probability of a train on line A arriving on time is:
P(A) = 72/90 = 0.8 = 80%
on line B, we have that 70 - 14 = 56 trains of the 70 arrived in time, so the probability of a train from line B arriving on time is:
P(B) = 56/70 = 0.8 = 80%
To find the probability of any train arriving on time, we can use this formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.8 + 0.8 - 0.8*0.8
P(A or B) = 1.6 - 0.64 = 0.96 = 96%
The probability that a train on line A arrives on time is 0.8 or 80%. The probability that any train arrives on time, considering both line A and line B, is also 0.8 or 80%.
Explanation:To calculate the probability that a train on line A arrives on time, we subtract the number of trains that arrive late from the total number of trains on line A:
Probability = (Total trains on line A - Trains on line A that are late) / Total trains on line A
Probability = (90 - 18) / 90
Probability = 72 / 90
Probability = 0.8 or 80%
To calculate the probability that any train arrives on time at the station, we need to consider the total number of trains arriving on time for both lines:
Total trains on time = (Total trains on line A - Trains late on line A) + (Total trains on line B - Trains late on line B)
Total trains on time = (90 - 18) + (70 - 14) = 72 + 56 = 128
Then, we divide the number of trains on time by the total number of trains:
Probability = Total trains on time / Total trains
Probability = 128 / (90 + 70)
Probability = 128 / 160
Probability = 0.8 or 80%
Given this data, what is the range of the average word
lengths?
Student
1
2
3
4
5
6
7
8
Mean Word Length
7.1
4.5
6.9
5.2
5.0
4.7
6.1
4.5
Is the variation between sample means large or small?
Answer:2.6
Small
Step-by-step explanation:
Answer:
2.6 and the variation is small
Step-by-step explanation:
u welcome
The product of 1.3 times 10 Superscript negative 4 and a number n results in 2.6 times 10 Superscript 12. What is the value of n?
2 times 10 Superscript negative 8
2 times 10 Superscript negative 3
2 times 10 Superscript 16
2 times 10 Superscript 48
Answer:
2 x 10^16
Step-by-step explanation:
[tex](1.3\times 10^{12})n=(2.6\times 10^{-4})[/tex]
Divide both sides by the coefficient of n.
[tex]n=\frac{2.6\times 10^{12}}{1.3\times 10^{-4}}[/tex]
The answer can be found by doing two calculations:
Divide 2.6 by 1.3 to get 2.
For the powers of 10, divide [tex]10^{12}[/tex] by [tex]10^{-4}[/tex] by subtracting exponents.
12 - (-4) = 12 + 4 = 16.
The answer is
[tex]n=2\times 10^{16}[/tex]
Answer:
2 x 10^16
Step-by-step explanation:
i think
how many dollars will you earn if you mow the lawn 10 times
PLEASE HURRYYYY!!!!!!!!!!
What is the total area of the following composite figure?
54.28 ft2
60.56 ft2
73.12 ft2
98.24 ft2
Answer:
A. 54.28 ft^2
Step-by-step explanation:
Area of the parallelogram = 48 ft^2
Area of the semicircles = 6.28 ft^2
A = π r^2
A = 3.14 (2)
A = 3.14 (4)
A = 12.56
12.56 ÷ 2 = 6.28 ft^2
48 + 6.28 = 54.28 ft^2
Answer:
54.28 ft^2
Step-by-step explanation:
Riley is going snowboarding over the holiday break. To go snowboarding you have a one time fee of $75 to rent the snowboard equipment, plus a fee of $5 per ride on the ski lift to get up and down the mountain. Write an equation that could be used to find the total amount it would cost to go snowboarding.
Answer:
y = 5x + 75
Step-by-step explanation:
"One time" = no change = constant
"per" = varies per person = variable
It is 5 dollars per ride, 5 dollars per x, 5x.
y = 5x + 75
A chain lying on the ground is 19 meters long and its mass is 84 kilograms. The chain is threaded through a pulley, which is fixed to the ground, and pulled directly up so that it forms the shape of an L. How much work is required to raise one end of the chain to a height of 7 meters? Use that the acceleration due to gravity is 9.8 m/s^2. You may assume that the chain slides effortlessly and without friction along the ground as its end is lifted.
Answer:
Step-by-step explanation:
Given that, the length of the chain is
L= 19m
And the mass of the chain is
M= 84kg
Work to raise the chains to a height of
H = 7m
Acceleration due to gravity
g = 9.8m/s²
Since the chain is 19m long and it has a mass of 84kg
Then, it mass/ length is 84/19
M/L = 4.42kg/m
So, it weight / length is mass / length × gravity
W/L = M/L × g
W/L = 4.42 × 9.8
W/L = 43.33 N/m
So, workdone can be calculated using
Work = ∫F∆x
Work = ∫(W/L)•xdx.
Work = ∫43.33x dx. From x = 0 to 7
Work = 43.33 ∫x dx.
Work = 43.33 x²/2. From x = 0 to 7
Work = 21.66 [x²] from x = 0 to 7
Work = 21.66 ( 7²-0²)
Work = 21.66 × 49
Work = 1061.5 Joule
The workdone to lift the chain to 7m is 1061.5 J
"When work is done to lift the chain to 7m is 1061.5 J. To understand the calculations, check below".
Calculation of Acceleration due to GravityGiven that, the length of the chain as per the question is:
L= 19m
And also the mass of the chain is
Then M= 84kg
Now Work to raise the chains to a height of
After that H = 7m
Acceleration due to gravity
Then g = 9.8m/s²
Since When the chain is 19m long and it has a mass of 84kg
Then, it mass/ length is 84/19
M/L = [tex]4.42kg/m[/tex]
After that, it weight / length is mass / length × gravity
W/L = M/L × g
W/L = 4.42 × 9.8
W/L = 43.33 N/m
Then, work done can be calculated using
Work is = ∫F∆x
Work is = ∫(W/L)•xdx.
Then Work = ∫43.33x dx. From x = 0 to 7
After that Work = 43.33 ∫x dx.
Now Work = 43.33 x²/2. From x = 0 to 7
Work is = 21.66 [x²] from x = 0 to 7
Work is = 21.66 ( 7²-0²)
Then Work = 21.66 × 49
Hence Work = 1061.5 Joule
Therefore, The work done to lift the chain to 7m is 1061.5 J
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Which of these myths do you think is probably believed by more people?
SELECT AN ANSWER
Europeans "discovered" new parts of the world during the Age of Discovery.
European explorers, like Christopher Columbus, were the first to cross the great oceans of the world.
Answer:
European explorers, like Christopher Columbus, were the first to cross the great oceans of the world.
What is the mean of these numbers? 2,2,8
Answer:
4
Step-by-step explanation:
(2+2+8)/3
brainliest please
The wind speed s (in miles per hour) is related to the distance (in miles) the tornado travels by the equation s = 93log d + 65. On March 18, 1925, a tornado whose wind speed was about 280 miles per hour struck the Midwest. How far did the tornado travel?
Answer:
The distance the tornado traveled was approximately 205 miles.
Step-by-step explanation:
The equation representing the relationship between the wind speed (in miles per hour) and the distance the tornado travels (in miles) is:
[tex]s=93\log d+65[/tex]
Compute the value of d for s = 280 as follows:
[tex]s=93\log d+65[/tex]
[tex]280=93\log d+65[/tex]
[tex]93\log d=280-65\\93\log d=215[/tex]
[tex]\log d=2.312\\[/tex]
[tex]d=10^{2.312}\\d=205.035\\d\approx 205[/tex]
Thus, the distance the tornado traveled was approximately 205 miles.
Could you help me solve this problem ASAP :D
Answer:
B) 1/4x+1/2=1/3x
Hope this helps!
.
Each CD costs $5, and you have $40 to spend on CDs. Write
an inequality for the possible number of CDs you could buy,
then find the maximum number of CDs you can buy.
_ CDs
|
PETE
BER
EFT
|
EESTER
|
ENERAL
|
|
| Enter the answer
I
|
|
Answer:
x ≤ 8
Step-by-step explanation:
"Each" = variable
5 dollar each => 5x
You can spend 40 exactly or less, exactly => equal to
5x ≤ 40
5x/5 ≤ 40/5 (Divide both sides by 5)
x ≤ 5
Please help will give brainlist
Answer:
The answer is 236.52.
Step-by-step explanation:
First you want to figure out the radius of the semi circle so you take the length of 12 and divide it by 2. Then you want to use the formula for area of a circle 3.14 times radius squared and divide that by 2 and add 12x15 to get your answer.
If there are 30 chopsticks in a drawer with 47 pieces of silverware, what is the ratio of chopsticks to silverware?
Answer: the ratio is 30:47
Step-by-step explanation: this is the most you can simplify this number so it stays like this
hope this helps mark me brainliest if it helped
Answer:
Ratios can be written like so:
a to b
a : b
a/b
There are 30 chopsticks and 47 silverware, and we want the ratio of chopsticks to silverware, so we can write it as
30 to 47
30:47
30/47
Which answer includes the intervals that contain the solution to the inequality?
The correct option is D (-∞,-3)∪(-1,1)
Step-by-step explanation:
Given,
[tex]\frac{x^{2}-1 }{3x+9}[/tex] ≤ 0
To find the solution.
The solution could be found if
[tex]x^{2} -1[/tex] ≤ 0 and
3x+9 ≠ 0 [if the denominator is 0, it gives ∞ as solution]
Now,
[tex]x^{2} -1[/tex] ≤ 0
or, (x+1)(x-1) ≤0
or, x ≤1 and x≤-1
Both of the above condition holds is x≤1
Again,
3x+9≠0
or, x≠-3
All the conditions gold for the values (-∞,-3)∪(-1,1)
Hence the correct option is D.
Select the expression that is equivalent to: 3 root 1089
Answer:
[tex]3\sqrt{1089}=3\sqrt{3^2(11)^2}[/tex]
Step-by-step explanation:
Given : Expression [tex]3\sqrt{1089}[/tex]
To find : Select the expression that is equivalent to expression ?
Solution :
Re-write the expression as,
[tex]3\sqrt{1089}=3\sqrt{3\times 3\times 11\times 11}[/tex]
[tex]3\sqrt{1089}=3\sqrt{3^2\times 11^2}[/tex]
[tex]3\sqrt{1089}=3\sqrt{(3\times 11)^2}[/tex]
[tex]3\sqrt{1089}=3\sqrt{(33)^2}[/tex]
[tex]3\sqrt{1089}=3\times 33[/tex]
[tex]3\sqrt{1089}=99[/tex]
The above are the possible equivalent expressions.
Answer:
A
Step-by-step explanation:
If you are given the two sides that are not the hypotenuse, which trig function should
you use?
A) tangent
B) sine
C) cosine
D) cotangent
Answer:
A
Step-by-step explanation:
Tangent = opposite/adjacent
The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.
The sides of a right angle triangle are as follows:
HypotenuseAdjacent sideOpposite sideThe simplest trigonometric ratio we can use to solve for the angles of a right angle triangle are as follows:
sin∅ = opposite / hypotenusecos∅ = adjacent / hypotenusetan∅ = opposite / adjacentTherefore, the trigonometric function one can use to find the angle of a right angle triangle when given 2 sides apart from hypotenuse is tangent
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Which rigid transformation(s) can map TriangleABC onto TriangleDEC?
The triangles are congruent by the SSS congruence theorem.
Triangles A B C and D E C are connected at point C. Triangle A B C is reflected across B C and then is rotated about point C to form triangle D E C.
Answer:
A - reflection then rotation
In ΔFGH, the measure of ∠H=90° GF = 37 HG = 12 and FH = 35.
What ratio represents the sine of ∠F?
Answer:
[tex]\sin F =\dfrac{12}{37}[/tex]
Step-by-step explanation:
We are given the following in the question:
GF = 37 units
HG = 12 units
FH = 35 units
We have to find the ratio that represents sine of ∠F.
Formula:
[tex]\sin F = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\sin F = \dfrac{HG}{GF}=\dfrac{12}{37}[/tex]
is the required ratio of sine of ∠F.
The attached image shows the triangle.
In the right triangle ΔFGH, the sine of ∠F is represented by the ratio of the opposite side (HG) to the hypotenuse (FH), so the sine of ∠F is 12/35.
Explanation:In the right triangle ΔFGH, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Considering ∠F, the side opposite to it would be HG and the hypotenuse in this scenario would be FH.
Given that HG = 12 and the length of the hypotenuse FH = 35, then the sine of ∠F (sin F) would be represented by the ratio 12/35.
Therefore, the sine of ∠F in the triangle ΔFGH is 12/35.
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Q2: The student council at Hillsdale High School is making T-shirts to sell for a fundraiser, at a price of $ 10 10 each. The costs, meanwhile, are $ 9 9 per shirt, plus a one-time setup fee of $ 79 79 . Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?
Answer:
a.The cost of making those shirts will be $790
b. The number of shirts that must be sold to recover this cost = 79 shirts.
Step-by-step explanation:
Please kindly check the attached files for explanation.
Lilly deposited $3000 into a Roth IRA that grew to $6000 at her retirement. If
Lindsay is currently in the 10% tax bracket and is retired, how much tax will
she have to pay when she withdraws the entire $6000?
O
A. $300
O
O
O
B. $0
c. $600
D. $900
The answer is $0
She can withdraw all $6000 and not have to pay anything.
Lilly will not have to pay any taxes when she withdraws the entire $6000.
Option B is the correct answer.
What is a percentage?The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying it by 100.
The percentage change is also calculated using the same method.
In percentage change, we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Since Lilly deposited $3000 into a Roth IRA, that means she had already paid taxes on that money before depositing it.
Therefore, when she withdraws the entire $6000, she will not have to pay any taxes on the original contribution of $3000.
Now,
For the remaining $3000 (the growth), she will also not have to pay any taxes since Roth IRA withdrawals of earnings are tax-free if the account holder is over 59½ and the account has been open for at least five years.
Therefore,
Lilly will not have to pay any taxes when she withdraws the entire $6000.
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Complete the steps to find the area of the trapezoid.
Area of rectangle = _ square units
Area of triangle 1 = square units
Area of triangle 2 = _ square units
Area of triangle 3 = _ square units
Area of trapezoid = _ square units
Given:
In the given diagram
Each small box along X axis = 2 unit
Each small Box along Y axis = 2 unit
For rectangle:
Length = 16 unit
Width = 16 unit
For triangle 1
Base = 8 unit
Height = 6 unit
For triangle 2
Base = 8 unit
Height = 4 unit
For triangle 3
Base = 16 unit
Height = 12 unit
Formula
Area of the trapezoid is
[tex]A = R -T_{1} -T_{2} -T_{3}[/tex]
Where, [tex]A[/tex] be the area of the trapezoid
[tex]R[/tex] be the area of the rectangle
[tex]T_{1} ,T_{2} ,T_{3}[/tex] be the area of the triangle 1, 2 and 3 respectively.
[tex]R = lb[/tex] where, l be length and b the width
[tex]T_{1} = \frac{1}{2} bh[/tex], where, b be the base and h be the height
Now,
Taking, l = 16 and b = 16 we get,
[tex]R = (16)(16)[/tex] = 256 sq unit
For Triangle 1
Taking, b = 8 and h = 6 we get,
[tex]T_{1} = \frac{1}{2}(8)(6)[/tex] sq unit
[tex]T_{1} = 24[/tex] sq unit
For Triangle 2
Taking, b = 8 and h = 4 we get,
[tex]T_{2} = \frac{1}{2}(8)(4)[/tex] sq unit
[tex]T_{2} = 16[/tex] sq unit
For Triangle 3
Taking, b = 16 and h = 12 we get,
[tex]T_{3} = \frac{1}{2}(16)(12)[/tex] sq unit
[tex]T_{3} = 96[/tex] sq unit
Therefore,
The area of the trapezoid is = 256-24-16-96 sq unit = 120 sq unit
Hence,
Area of rectangle =256 square units
Area of triangle 1 = 24 square units
Area of triangle 2 = 16 square units
Area of triangle 3 = 96 square units
Area of trapezoid = 120 square units
Answer:
Area of rectangle =256 square units
Area of triangle 1 = 24 square units
Area of triangle 2 = 16 square units
Area of triangle 3 = 96 square units
Area of trapezoid = 120 square units
Step-by-step explanation:
Do either of these display exponential behavior? Please help!
Answer:
no. 7 does
Step-by-step explanation:
brainlest please
x increases by three each time but y decreases less each time
Micah’s bicycle wheel has a radius of 14 inches. About how far will micah’s bicycle travel each time his wheel turns one full rotation?
Answer:
D. 88 inches
Step-by-step explanation:
to get the circumference of a circle the equation is C=2πr
C=87.96
Final answer:
Every time Micah's wheel turns one full rotation, the bicycle would travel approximately 88 inches.
Explanation:
The student's question relates to the travel distance of a bicycle wheel in one full rotation.
The distance traveled by a wheel in one rotation is equal to the circumference of the wheel, which is calculated by the formula:
Circumference = 2π × radius.
Given Micah's bicycle wheel has a radius of 14 inches, the calculation would be:
Circumference = 2 × π × 14 inches
Circumference = 2 × 3.1416 × 14 inches
Circumference ≈ 88 inches
Therefore, every full rotation of Micah’s 14-inch-radius bicycle wheel will result in the bicycle traveling approximately 88 inches, which is the circumference of the wheel.
Phil collected 60 eggs and sold 44 of them to the local grocer. Phil wrote down that he sold 0.44 of the eggs he
collected. Did Phil write the decimal correctly? Explain.
Answer:
Yes
Step-by-step explanation:
Answer:
No, Phil did not write the decimal correctly. If Phil started out with 100 eggs and sold 44 then the decimal would be 0.44, but he only had 60, so the decimal would be 0.73
Step-by-step explanation:
enable to find the decimal of 2 numbers, you must divide usually the smaller number by the larger number anable to get the percentage. so, in this question, you divide 44 by 60 and therefore getting your answer, Phil sold 0.73 of his eggs.
Neil saves money at the end of each week. The function m(x) = 25x + 50 models the amount of money he has saved after x weeks. What
is the most appropriate domain for the function?
A. all non-negative integers
B. all positive real numbers
C. all real numbers
D. all integers
Answer:
b
Step-by-step explanation:
Use Vieta's Theorem to solve the problems.
The difference of the two solutions of x^2+19x+c=0 is 15. Find the solutions.
Answer:
The answer is -2, -17
Step-by-step explanation:
You write a system of equations
[tex]x_{1} +x_{2}=-19\\x_{1}-x_{2}=15[/tex]
Then you solve:
-2, -17
The answer is -2, -17.the solutions.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
The difference of the two solutions of x^2+19x+c=0 is 15.
now,
You write a system of equations
x_1+x_2= -19
x_1-x_2=15
Then you solve:
-2, -17
hence, The answer is -2, -17.the solutions.
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How is the process of finding the surface area of a rectangular prism the same as finding the surface area of a triangular prism? How is it different?
ANSWER:
For both prisms, you can draw a net to help you find the areas of the faces. Add the areas together to find the surface area. A rectangular prism has only rectangular faces, and you use the formula bh to find area. A triangular prism has triangular and rectangular faces, and you use the area formula bh for rectangular faces and the area formula 1/2bh for triangular faces.
Final answer:
The process of finding the surface area of a rectangular prism is similar to finding the surface area of a triangular prism. Both involve drawing a net and adding the areas of the faces. However, the formulas used are different because the shapes have different types of faces.
Explanation:
For both prisms, you can draw a net to help you find the areas of the faces. Add the areas together to find the surface area. A rectangular prism has only rectangular faces, and you use the formula bh to find area. A triangular prism has triangular and rectangular faces, and you use the area formula bh for rectangular faces and the area formula 1/2bh for triangular faces.
Katie has to drive 15 miles east and 36 miles north to get to her aunt's house. What is the direct distance to her aunt's house?
Answer: 39 miles
Step-by-step explanation:
Hi, since the travelling forms a right triangle, (see attachment) we have to apply the Pythagorean Theorem formula.
a^2 +b ^2 =c ^2
Assuming a and b are the distances driven, and c the direct direction formed (hypotenuse)
15^2 +36 ^2 =c ^2
225+1,296 =c ^2
1,521 =c ^2
√1,521= c
c= 39 miles
Feel free to ask for more if needed or if you did not understand something.
Answer:
39 miles
Step-by-step explanation:
The sum of 3 times a number and 4 is no more than 10 and no less than -8.
Answer:
Equation -8 ≤ 3n+4 ≤ 10
Solution -4 ≤ n ≤ 2
Step-by-step explanation:
sum of 3 times a number and 4
3n+4
is no more than 10
3n+4 ≤ 10
and no less than -8
-8 ≤ 3n+4 ≤ 10
To solve
Subtract 4 from all sides
-8-4 ≤ 3n+4-4 ≤ 10-4
-12 ≤ 3n ≤ 6
Divide all sides by 3
-12/3 ≤ 3n/3 ≤ 6/3
-4 ≤ n ≤ 2