By using GCF and distributive Property, it is obtained that
3550 = 5 [tex]\times[/tex] 710 as a product
What is Greatest Common Factor and distributive property?
Greatest Common factor (GCF) of two numbers a and b is the greatest number that divides both a and b.
Distributive property is the property over both addition and multiplication.
If a, b and c are three numbers, then distributive property is given by
[tex]a \times (b + c) = a \times b + a \times c[/tex]
3550 = 3000 + 550
Now,
[tex]3000 = 2\times 2 \times 2\times 3\times 5 \times 5 \times 5\\550 = 2 \times 5 \times 5 \times 11[/tex]
GCF of 3000 and 550 = 5
3550 = 5 [tex]\times[/tex] 600 + 5 [tex]\times[/tex] 110
3550 = 5 [tex]\times[/tex] (600 + 110) [Distributive Property]
3550 = 5 [tex]\times[/tex] 710
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there are 6 circles and 9 triangles what is the simplest ratio of circles to triangles?
Which graph represents a function with direct variation?
Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The graph is shown in the pictures
As we know,
The proportional relationship can be defined as:
y ∝ x
y = kx
k is the constant of proportionality:
y = kx is the equation of the line which passes through the origin.
Graph four passes through origin.
Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
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a college believes that 28% of applicants to that school have parents who have remarried. how large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 95% confidence?
The sample size required for the true proportion of students who have parents who have remarried is 607.
What is termed the Confidence Interval?
The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.
The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.
The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.
We may also need to consult the table to determine the Z value.
For the given question,
α = 0.5
Consider the Z-table,
Zα/2 = Z (0.1/2)
Z (0.025) = 1.96
Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.
For calculating the margin error 'E' is given 3%.
n = Z² (α/2) / E² × (P°(1 - P°))
Put the given values.
n = (1.96)² / (0.03)² × (0.28(1 - 0.28))
On solving,
n = 4268.444(0.2016)
n = 860.51
n ≈ 860.51
Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.
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Farmer joe separates his farm into 10 regions. He then randomly selected 5 trees from each region to estimate the number of apples produced on his apple tree farm. What type of sampling is this?.
it's a Stratified sampling
6. Your parent promises to make you a smoothie using
the blender while you're mowing the lawn. The blender
makes a sound that is 88 decibels. What is the intensity
of the sound of the blender?
The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².
Decibels:
Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.
Given,
Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels
Here we need to find the intensity of the sound of the blender
In order to find the intensity, we have to do the following steps,
First, we have to divide the decibel level by 10.
=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)
Now, we have to use that value as the exponent of the ratio.
=> 8.8 = log (x / 1 x 10⁻¹²)
Finally, we have to use that power of ten to find the intensity in Watts per square meter.
=> 6.3×10⁻⁴ .
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Given the exponential growth function †(x) = 75(1.0025)*
What is the initial value of the function?
What is the growth factor, or growth rate of the function (as a percent)?
The initial value of the function is 75.
The growth factor or growth rate of the function as a percent is 0.25%
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=75(1.0025)ˣ
A = 75 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.0025
1 + r = 1.0025
r = 1.0025 - 1
r = 0.0025
Expressing r as a percentage:
r = 0.0025×100
= 0.25%
Hence we get the required answers.
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Find the value of 49^-1/2
Find the value of (27/125)^2/3
The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
According to the question,
We have the following expressions:
[tex]49^{-1/2}[/tex]
Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:
[tex]7^{2*(-1/2)}[/tex]
[tex]7^{-1}[/tex]
Or it can be 1/7 because we have positive exponents.
Now, we have another expression:
[tex](\frac{27}{125}) ^{2/3}[/tex]
We will follow the same steps to solve this expression:
[tex](\frac{3}{5}) ^{3*2/3}[/tex]
[tex]\frac{3}{5} ^{2}[/tex]
Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:
9/25
Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
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One Step Trinomial, Two Step Factoring
Factor:
x^2 - 12x + 35
Answer:
You can FACTOR x^2-12x+35 by using the AC method
This means the answer will be:
(x-7)(x-5)
I hope this helps!
(Brainliest is optional)
Deon is going to rent a truck for one day. There are two companies he can choose from, and they have the following
prices.
Company A charges an initial fee of $41.50 and additional 70 cents for every mile driven.
Company B charges an initial fee of $35 and an additional 80 cents for every mile driven.
For what mileages will Company A charge less than Company B?
Write your answer as an inequality, using m for the number of miles driven.
Answer:
Step-by-step explanation:
answer = company b
What’s the answer to this ?? Does anyone know it ??
Please explain the steps and how you got the answer ): i have a ton more of these to answer and i need to know how to do it.
ONLY ANSWER IF YOU KNOW IT ! WILL REPORT UR ANSWER IF U PUT ANYTHING ELSE.
The equilibrium quantity is 97 items and equilibrium price is $582
The equation of the price when quantity demanded
p = 873 - 3q
The equation of the price when quantity supplied
p = 6q
At equilibrium price and quantity
873 - 3q = 6q
Move the like terms to one side
6q + 3q = 873
Add the like terms
9q = 873
q = 873 / 9
Divide the terms
q = 97 items
Substitute the value of q in the equation 2
p = 6q
p = 6 × 97
Multiply the terms
p = $582
Hence, the equilibrium quantity is 97 items and equilibrium price is $582
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what is the answer to 5=6h+5(h-5)
Answer: the answer is 30/11
Step-by-step explanation:
hope it helps:)
an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
The first and second cars are 7724 feet apart from each other.
The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:
tan = opposite/ adjacent
⇒ tan(31°) = 3500/x
⇒ 0.60086 = 3500/x
⇒ 0.67 x = 3500 [ rounding up 0.60086 = 0.67]
⇒ x = 5223.88
That means the first car is 5223.88 feet from the point on the highway below the plane.
We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:
tan(53°) = 3500/x
⇒ 1.327 = 3500/x
⇒ 1.4x = 3500 [ rounding 1.327 = 1.4]
⇒ x = 3500/1.4
⇒ x = 2500
That means the second car is 2500 feet from the point on the highway below the plane.
Add the two distances together to get the total distance from car to car:
5223.88 + 2500.00 = 7723.88
So, rounded to the nearest foot, the cars are 7724 feet apart.
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factorise x squared +3x - 40
Answer:
(x-5)(x+8)
Step-by-step explanation:
Factors of -40:
-1, 40
-2, 20
-4, 10
-5, 8
-5 + 8 =3
x^2+3x-40
x^2 -5x +8x -40
=(x-5)(x+8)
if you place a 38- foot ladder against the top of a 32-foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.
Answer:
6 feet
Step-by-step explanation:
38-32=6
for 50 points and brainliest! (Part 2)
Lesson: Linear Inequalities in Two Variables
Directions: Answer the following problem. And graph it.
Please I want a complete answer with a clear explanation. Thank you in advance :)
Answer:
4.a) Broken line.
4.b) True.
5.a) Solid line.
5.b) True.
Step-by-step explanation:
When graphing inequalities:
< or > : broken line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Question 4Given inequality:
[tex]y < -\dfrac{1}{2}x+2[/tex]
a) As the "<" sign has been used, the line will be a broken line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & < -\dfrac{1}{2}(0)+2\\0 & < 0+2\\0 & < 2\end{aligned}[/tex]
As zero is less than 2, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-2: \quad y &=-\dfrac{1}{2}(-2)+2\\y &=1+2\\y&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=4: \quad y &=-\dfrac{1}{2}(4)+2\\y &=-2+2\\y&=0\end{aligned}[/tex]
Plot the points (-2, 3) and (4, 0).
Draw a broken straight line through the points.
Shade below the line.
Question 5Given inequality:
[tex]2x+5y \leq 10[/tex]
a) As the "≤" sign has been used, the line will be a solid line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 2(0)+5(0) &\leq 10\\0+0 &\leq 10\\0 &\leq 10\end{aligned}[/tex]
As zero is less than 10, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-5: \quad 2(-5)+5y &=10\\-10+5y &=10\\5y &=20\\y&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=5: \quad 2(5)+5y &=10\\10+5y &=10\\5y &=0\\y&=0\end{aligned}[/tex]
Plot the points (-5, 4) and (5, 0).
Draw a solid straight line through the points.
Shade below the line.
write the percent 144 as a decimal
Evaluate the expression if a = −2, b = −3, c = 2, x = 2.1, y = 3, and z = −4.2.
4a−|3b+2c|
The value of the expression when evaluated is: -18.
How to Evaluate an Expression?Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.
Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:
4(-3) - |3(-3) + 2(2)|
-13 - |-9 + 4|
-13 - |-5|
-13 - 5
= -18
The value of the expression is: -18.
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2) Ahmad had 15 coins in nickels and quarters. He knows he has a $2.95 in change. How many
quarters and nickels does he have?
Answer:
11 quarters and 4 nickels
Hope this helps! :3
Please mark brainliest! <3
6. Fill in the missing numbers so that the scaling is consistent. For part (a) what number is represented
for each letter?
12
SHOW YOUR WORK!
a.
Point A: Point B: 52 Point C:
The number represented on number line by (A) -13 (B) 26 (C) 65
According to the number line given in part a
there are for parts in between 0 to 52
To find the numbers in one part = 52/4
= 13
Therefore,
For (A)
0 - 13 = -13
For (B)
0 + 2*13 = 26
For (C)
52 + 13 = 65
Hence, A is -13, B is 26 and C is 65.
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5 km to m convert the following
Answer:
5 km = 5000 m
Hope this helps : )
8. Emily predicted her car
payment to be
$250 each month. Her actual car
$275 each month.
payment is
Enrique predicted his car
payment to be $200 each month. His actual
car payment is $225 each month.
a. By what percent was Emily's prediction off?
b. By what percent was Enrique's prediction off?
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
What is a percentage?The percentage is calculated by dividing the required value with the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Emily:
Each month payment = $250
Each month actual payment = $275
The percentage prediction is off by.
= (275 - 250) / 275 x 100
= 25/275 x 100
= 9.09%
Enrique:
Each month payment = $200
Each month actual payment = $225
The percentage prediction is off by.
= (225 - 200)/225 x 100
= 25/225 x 100
= 11.11%
Thus,
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
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Tiffany’s allowance is reduced $1. 25 every time she forgets to clean her room. If she forgets to clean her room 7 times this month, by how much money is tiffany’s allowance reduced?.
The amount of money that is reduced from Tiffany's allowance is $8.75
The amount of allowance reduced every time she forget to clean her room = $1.25
Number of times that she forgets to clean her room = 7 times this month
The amount of money is reduced from Tiffany's allowance = Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room
Here we have to use the multiplication to find the amount
Substitute the values in the equation
The amount of money is reduced from Tiffany's allowance = 7 × 1.25
Multiply the terms
= $8.75
Hence, the amount of money that is reduced from Tiffany's allowance is $8.75
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find measure of each missing angle PLSSSS HELP
The interior angles of the triangle are 43°, 43° and 94°. The exterior angle of the triangle is 86°.
How to find interior and exterior angles of a triangle?A triangle is polygon with three sides. The sum of angles in a triangle is 180 degrees.
The triangle above is an isosceles triangle. The base angles of a triangle is congruent.
Therefore, the base angles are 5x - 12 and 5x -12.
The sum of the remote interior angles is equal to the opposite exterior angles.
5x - 12 + 5x - 12 = 8x - 2
10x - 24 = 8x - 2
10x - 8x = -2 + 24
2x = 22
x = 22 / 2
x = 11
Therefore,
5x - 12 = 5(11) - 12 = 43°
Third angle = 180 - 43 - 43 = 94°
Exterior angle = 8x - 2 = 8(11) - 2 = 86°
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suppose that pulse rates among healthy adults are normally distributed with a mean of 80 beats/minute and a standard deviation of 10 beats/minute. what proportion of healthy adults have pulse rates that are more than 86 beats/minute? round your answer to at least four decimal places.
The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%
Z- Score gives an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , mean = 80beats/minute
standard deviation = 10 beats/minute
x = 86 beats/minute
Applying z score formula :
z-score = (x-mean)/standard deviation
P(x>86) = P(z > 86-80/10)
=P(z>6/10)
=P(z>0.6) = 1 - P(z<0.6)
= 1 -0.7257
= 0.2742
Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742
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Jim ate 3/4 of his lunch. What fraction of it was left?
Jim ate 3/4 part of his lunch is in fraction form then the left part of his lunch is a fraction equal to 1/4 .
Fraction : A fraction represents a part of whole . It is a numerical value. It is evaluated by dividing a whole into number of parts . It has two parts one is called numinator (dividend) and other one is denominator ( divisor) . Denominator tells you how many part of lunch is divided into.
Types : Three types are
proper fractionimproper fraction mixed fractionWe have given in question that,
Jim ate 3/4 of his lunch .
let his lunch be x as a whole number .
Now , 3/4 part of x is ate by Jim i.e 3x/4
left part of x = x - 3x/4 = x/4
so, 1/4 part of x i.e lunch is left .
Hence, after eating the 3/4 of lunch by Jim the left part of lunch is 1/4 .
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Need help on algebra
The required value of the given equation when x = 5 is y = 585.5
What is an algebra ?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
Given : y = 114.50x + 13
To find ; The value of this equation when x = 5
Thus to find this value we have to simply substitute the value of x in the given equation
Hence, we will get ,
y = 114.50 × 5 + 13
this implies y = 572.5 + 13
which is equal to y = 585.5
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Select the correct answer.
Solve the following equation by completing the square.
4z²-16z +8=0
O A z = 2 + √2 orz = 2-√2
OB.
z = 2 + √2 or z = − 2 + √2
z = −2+ √2 orz = -2-√2
z = 4 or z = 0
O C.
O. D.
Reset
Next
Step-by-step explanation:
4z-16z+8=0
[4×8]=32
factors of 32
1,2,4,8,....
20 units rotated to 90 cc reflected over the x axis and translated 6 units down is ?
Answer:
.
Step-by-step explanation:
Which value of x solves the equation cos x° = sin (20° + x°), where 0 < x < 90?
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
The value of x is 35°
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cos x° = sin (20° + x°), where 0 < x < 90
We know that,
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
x + 90 - x = 90
Now,
cos x = sin (20 + x)
x + 20 + x = 90
2x + 20 = 90
2x = 70
x = 35
Thus,
The value of x is 35°
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Write the correct function in the table below
HELP ASAP
The function that represent the given table is f(x) = 2n+1.
In the given question we have to write the correct function for the table given below.
The given table is
x y
0 3
1 5
2 7
3 9
We can write it as
x y
0 3=1+2
1 5=3+2
2 7=5+2
3 9=7+2
So we can see that in each odd number we are adding 2.
So the function should be
f(x) = (2n−1)+2
f(x) = 2n−1+2
f(x) = 2n+1
Hence, the function that represent the given table is f(x) = 2n+1.
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