0.895 with 95 repeating on and on as a simplified fraction can be re-written as 887/990.
How to determine the fractional equivalent of this repeating decimal?By critically observing the given number, we can reasonably and logically deduce that it has three (3) repeating digits. Since this number has three (3) repeating digits, we would have to multiply n by 1000 as follows:
1000n = 0.895
1000n = 895.95 .......equation 1.
10n = 8.95 .......equation 2.
Subtracting equation 2 from equation 1, we have:
1000n - 10n = 895.95 - 8.95
990n = 887
Dividing both sides by 990, we have:
n = 887/990
Simplified fraction, n = 887/990.
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Complete Question:
Write 0.895 with 95 repeating on and on as a simplified fraction.
Someone please answer this I'm offering all my points.
Answer the following. Where necessary, round your answers to 2 decimal places
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
A) Express the number of employees that prefer coffee using a simplified fraction.
B) What percentage of employees don't like either tea or coffee?
C) Express the number of employees that preferred tea using a simplified fraction.
a) Number of employees that prefer coffee are [tex]\frac{3}{7}[/tex].
b) Percentage of employees don't like either tea or coffee is 30.4%
c) Number of employees that prefer tea are [tex]\frac{28}{105}[/tex]
Define fraction.The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively. A fraction only informs us of the number of parts that make up the whole. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. [tex]\frac{1}{2}[/tex], for instance, is a fraction.
Given Data
In a work survey, it was found that:
28 employees preferred tea
45 employees preferred coffee
32 didn't like either
a) Number of employees that prefer coffee
= 45
Fraction:
= [tex]\frac{45}{105}[/tex]
= [tex]\frac{3}{7}[/tex]
b) Percentage of employees don't like either tea or coffee
= [tex]\frac{32}{105}[/tex] × 100
= 30.4%
c) Number of employees that prefer tea.
= 28
= [tex]\frac{28}{105}[/tex]
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bradley consumes an energy drink that contains caffeine. after consuming the energy drink, the amount of caffeine in bradley's body decreases exponentially. the 10-hour decay factor for the number of mg of caffeine in bradley's body is 0.2722. what is the 5-hour growth/decay factor for the number of mg of caffeine in bradley's body?
The 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. Exponential decay differs from linear decay in that the decay factor depends on a percentage of the initial sum, meaning that the amount by which the original sum may be lowered will fluctuate over time as opposed to a linear function, which reduces the original sum by the same amount each time.
Given,
10 hour decay factor = 0.2722
Let us calculate the one-hour decay factor first,
One-hour decay factor = (10 hour decay factor)^1/10 = (0.2722)^1/10 = 0.8779
Now, Calculating the 5-hour decay factor,
5 hour decay factor = ( 1 hour decay factor )^5 = (0.8779)^5 = 0.521
Hence, the 5-hour growth/decay factor for the number of mg of caffeine in Bradley's body is 0.521
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Consider the line y = = 8 x-4. Find the equation of the line that is parallel to this line and passes through the point (7, -2). Find the equation of the line that is perpendicular to this line and passes through the point (7, -2).
Answer: y=8x-58
Step-by-step explanation:
1. find the slope
Since the new line is parallel to the first one that means the slope of 8x will remain the same.
2. plug it into the point slope formula y-y1=m(x-x1)
which would look like
y-(-2)=8(x-7)
3. solve for y
y-(-2)=8(x-7)
y+2=8x-56
y=8x-58
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(We will not directly convert ton into pounds. We will follow the following steps.)
Now, we know that 1 ton is equal to 1000 kilograms.
So, half ton makes 500 kg.
Now, to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg is equal to 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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which property is used in the problem below, the commutative property or the associative property??
(4 x 2) x 3 = (2 x 4) x 3
What is the equation of the line that passes through the point (−6,−3) and has a slope of 0?
The equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3
The line is passing through the point = (-6,-3)
The slope of the line = 0
The point slope form is
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
(y-(-3)) = 0×(x-(-6))
We have to convert this equation the slope intercept form
Slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
(y-(-3)) = 0×(x-(-6))
y+3 = 0×(x+6)
y+3 = 0
y = -3
Hence, the equation of the line that passes through the point (-6,-3) and has a slope of 0 is y = -3.
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pls help meeeee xxxxxxxxx
Triangle ABC has the following angle measures:
m∠A = (x + 6)°, m∠B = (3x − 15)°, m∠C = (5x + 36)°
What is m∠C?
The measure of ∠C is 121 degrees.
Given that:-
There is a triangle ABC.
m∠A = (x + 6)°
m∠B = (3x - 15)°
m∠C = (5x + 36)°
We have to find the measure of ∠C.
We know that,
The sum of all the angles of a triangle is 180 degrees.
Hence, we can write,
m∠A + m∠B + m∠C = 180 degrees
(x + 6)° + (3x - 15)° + (5x + 36)° = 180 degrees
(x + 3x + 5x) + (6 - 15 + 36) = 180 degrees
9x + 27 = 180 degrees
9x = 180 - 27
9x = 153 degrees
x = 153/9 degrees
x = 17 degrees
Hence,
The measure of ∠C = 5x + 36 = 5*17 + 36 = 85 + 36 = 121 degrees.
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what’s is the expression that is equivalent (x^2-3x)(4x^2+2x-9)?
4x^4-10x^3-15x^2+27x
(use foiling)
HELP ME FIND X AND Y
<EOG =90° AS INDICATED IN THE DIAGRAM
<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)
[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]
<AOB =180°( STRAIGHT LINE )
<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)
[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]
[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]
ATTACHED IS THE SOLUTION
a company that manufactures mufflers for cars offers a lifetime warranty on its products, provided that ownership of the car does not change. suppose that only 20% of its mufflers are replaced under this warranty. a button hyperlink to the salt program that reads: use salt. (a) in a random sample of 400 purchases, what is the approximate probability that between 70 and 90 (inclusive) mufflers are replaced under warranty? (round your answer to four decimal places.)
The approximate probability that between 70 and 90 is 0.728.
Using normal distribution,
Mean = xbar = np = 400 × 0.2 = 80
Standard deviation = √[np(1-p)] = √(80 × 0.8) = 8
To ensure that the distribution is normal,
np ≥ 10
80 ≥ 10
And,
np(1-p) ≥ 10
80(0.8) = 320 ≥ 10
Hence, we use the z-tables for this
a) Convert 75 and 100 into standardized scores.
A value's standardized score is equal to the value minus the mean divided by the standard deviation.
z = (x - xbar) ÷ σ
For 75
z = (75 - 80) ÷ 8 = - 0.625
For 100
z = (100 - 80) ÷ 8 = 2.5
To calculate the approximate likelihood that between 75 and 100 (inclusive) mufflers will be replaced under warranty.
P(75 ≤ x ≤ 100) = P(-0.625 ≤ z ≤ 2.5)
For these probabilities, use data from the normal probability table.
P(75 ≤ x ≤ 100)
= P(-0.625 ≤ z ≤ 2.5)
= P(z ≤ 2.5) - P(z ≤ -0.625)
= 0.994 - 0.266
= 0.728
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which of the following graphs could be the graph of g (x)= (x+1) (x-2) (x+5)
D
1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial
g (x)= (x+1) (x-2) (x+5)
g(x) =x³+4x²-7x-10
As the coefficient is positive, then we'll have
Examining the options, we have as the roots S={-5,-1,2} So the answer is D
Rewrite in exponential form: \log _3x=4
Answer:
x = 3⁴
Step-by-step explanation:
You want the exponential form of log₃(x) = 4.
LogarithmIt can be helpful to remember that a logarithm is an exponent of the base of the logarithm.
log₃(x) = 4 ⇔ x = 3⁴
The exponential form is x = 3⁴.
8. Find the value of x and y.
(7x-2)°
18y°
(11x - 34)°
The degrees of the following expression are
(7x-2)° => x = 2/7°
18y° => y = 0°
(11x - 34)° => x = 34/11°
Degrees:
Degree is the unit of measure is used to measure the magnitude of an angle.
1 degree = 1/360 of a complete revolution in magnitude.
Given,
Here we have the following expressions
(7x-2)°
18y°
(11x - 34)°
Now, we have to find the value of x and y from it.
In order to find the value x and y , we have to equate every equation with 0. then we get the value of variables x and y.
When we take the first expression, and then we have to equate it with zero, then we get,
(7x - 2)° = 0°
7x = 2°
x = 2/7°
Therefore, the value of x is 2/7°.
Now, we have to take the second one and equate it with zero, then we get,
18y° = 0
y = 0°
Therefore, the value of y is 0°.
Finally, the value of the expression in degrees,
11x - 34° = 0
11x = 34°
x = 34/11°
Therefore, the value of x is 34/11 degrees.
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find the 41st term 11, 16, 21…
Answer:
You can add up to 5 each time, so we just need to multiply 5 by 40 although we already have the first three terms.
A: 40*5 = 200
Step-by-step explanation:
21 + 200 = 221
The cost (in dollars) of a basic music streaming service for m months
is represented by B(m) = 5m. The cost of the premium service is represented by
P(m) 10m. Describe the transformation from the graph of B to the graph of P.
The transformation from the graph of B to the graph of P is a vertical stretch by a scale factor of 2
How to determine the transformation?From the question, the function definitions are given as
B(m) = 5m
P(m) = 10m
Rewrite the function P(m) as follows
P(m) = 2 x 5m
Substitute B(m) = 5m in the equation P(m) = 2 x 5m
P(m) = 2 x B(m)
When a function is represented as
f(x) = kg(x), then the transformation is a vertical stretch by k
Hence. the transformation a vertical stretch by 2
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PLEASE HELP 20−(2)(−7)+(−9)÷(−3)
Answer:
37
Step-by-step explanation:
Use PEMDAS, in this case, start with multiplication: (2)(-7), don't forget there is a minus sign in front of the two which is important later, then move on to dividing (-9) by (-3). Then you are left with 20-(-14)+3, which is the same as 20+14+3, which equals 37.
Please help me I have 5 minutes left!!!
A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion
What is Ratio and Proportion?Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
A proportion is an equation in which two ratios are set equal to each other.
In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.
we can write this
320miles/5 = 768 miles/12
320miles/768 miles=5/12
In option d the values are not given in a correct way. It doesnot hold for the proportion.
Hence no option is correct.
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Hi thank you so for all your time and help
Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.
We want to find x such that:
[tex]\tan (x)=\sqrt[]{3}[/tex]We'll use the second right triangle to show what we want.
First, given a triangle:
We know that the hypotenuse will be:
[tex]\sqrt[]{x^2+y^2}[/tex]But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.
[tex]\tan (\alpha)=\frac{y}{x}[/tex]and
[tex]\tan (\beta)=\frac{x}{y}[/tex]Now look at the triangle we have:
We can easily check that:
[tex]\sqrt[]{3}=\frac{\sqrt[]{3}}{1}[/tex]So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!
Therefore, we have:
[tex]\tan (60^{\circ})=\frac{\sqrt[]{3}}{1}=\sqrt[]{3}[/tex]And the solution to x is:
[tex]x=60^{\circ}[/tex]Find the volume of a cone with a base diameter of 6 m and a height of 10 m.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit in your answer.
ANSWER:
94.2m^3
STEP BY STEP:
V = 1/3 x PI x R^2 x h = 1/3 x 3.14 x 3^2 x 10 =94.2^3
Answer:
V = 94.25m³
I don't have enough time to show work because I have to go, but I hope this helped.
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
2nd one
Simplify nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight. eleven square root of two minus five square root of seven eleven square root of four minus five square root of fourteen six square root of five six square root of nine
Squares are the numbers that are produced when a value is multiplied by itself.
If expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex] then the value exists [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex].
What is meant by square root?The radical symbol for the number's root is "√" in this instance. The square of the positive number is represented by multiplying it by itself.
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root exists a value that, when multiplied by itself, returns the original value.
The original number can be attained by multiplying the square root of an integer by itself.
Only a perfect square number can have a perfect square root. Even perfect squares have an even square root. An odd perfect square will contain an odd square root. A perfect square cannot be negative and hence the square root of a negative number exists not defined.
Let the expression be [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
Now, [tex]$\sqrt{8}=\sqrt{2 \times 2 \times 2}=2 \sqrt{2}$[/tex]
[tex]$\sqrt{28}=\sqrt{2 \times 2 \times 7}=2 \sqrt{7}$[/tex]
therefore [tex]9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
simplifying the given expression, we get
[tex]$=9 \sqrt{2}-3 \sqrt{7}+2 \sqrt{2}-2 \sqrt{7}$[/tex]
[tex]$=9 \sqrt{2}+2 \sqrt{2}-3 \sqrt{7}-2 \sqrt{7}$[/tex]
[tex]$=11 \sqrt{2}-5 \sqrt{7}$[/tex]
Therefore, the correct answer is option a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
The complete question is:
Simplify [tex]$9 \sqrt{2}-3 \sqrt{7}+\sqrt{8}-\sqrt{28}$[/tex]
a) [tex]$11 \sqrt{2}-5 \sqrt{7}$[/tex]
b) [tex]$11 \sqrt{4}-5 \sqrt{14}$[/tex]
c) [tex]$6 \sqrt{5}$[/tex]
d) [tex]$6 \sqrt{9}$[/tex]
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A pole 5 feet tall is used to support guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Zoe measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire to the nearest foot
The length of the guy wire to the nearest foot is 42 feet.
How to find the length of the guy wire?The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.
The situations forms a right angle triangle.
Therefore, the length of the guy wire can be found as follows:
Using trigonometric ratios, we can find the angle the guy wire made with the ground.
tan ∅ = opposite / adjacent
tan ∅ = 5 / 15
∅ = tan ⁻¹ 1 / 3
∅ = 18.4349488057
∅ = 18.43°
Therefore, let's find the length of the guy wire using the angle.
cos 18.43° = adjacent / hypotenuse
0.94871060813 = 40 / h
h = 40 / 0.94871060813
h = 42.162488395
Therefore,
length of the guy wire = 42 feet
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sarah has 85 and 89 on her first two math 23 tests. what must she get on the third test to have at least 90% test average?Assume three tests and represent the problem with an inequality
The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.
In this case, Sarah has 85 and 89 on her first two math 23 tests.
Let the third test be represented as x. This will be illustrated as:
(85 + 89 + x) / 3 ≥ 90
Cross multiply
85 + 89 + x ≥ 90 × 3
174 + x ≥ 270
Collect like terms
x ≥ 270 - 174
x ≥ 96
The value is x ≥ 96.
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For the following equation, complete the given ordered pairs, and use the results to graph the solution set for the equation.
Given:
[tex]y=-\frac{3}{4}x+1[/tex]Aim:
We need to graph the given function.
Explanation:
Replace x =-4 in the given equation.
[tex]y=-\frac{3}{4}(-4)+1[/tex][tex]y=-3(-1)+1[/tex][tex]y=3+1[/tex][tex]y=4[/tex]We get the point (-4, 4).
Replace x = 0 in the given equation.
[tex]y=-\frac{3}{4}(0)+1[/tex][tex]y=1[/tex]We get the point (0,1).
Replace x =4 in the equation.
[tex]y=-\frac{3}{4}(4)+1[/tex][tex]y=-3+1[/tex][tex]y=-2[/tex]We get the point ( 4, -2).
Mark the points (-4, 4), (0,1), and ( 4, -2) on the graph and join them by ray.
Final answer:
[tex](-4,4),\text{ }(0,1),\text{ }(4,\text{ -2}).[/tex]The graph of the given eqaution:
hi how are you today can you please help me with this question
If:
[tex]\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{a+c+e}{b+d+f}[/tex]so:
[tex]\begin{gathered} 15\colon9\colon4 \\ \frac{15}{1}=\frac{9}{1}=\frac{4}{1}=\frac{15+9+4}{3}=\frac{28}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{3}{x}=\frac{28}{3} \\ x=\frac{9}{28} \end{gathered}[/tex]Or:
0.32 liters
(b)
We need to find the volume of the rectangular prism, therefore:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ V=40\cdot20\cdot35 \\ V=28000cm^3 \end{gathered}[/tex]However, we need to express the volume in liters, so:
[tex]28000cm^3\times\frac{1L}{1000cm^3}=28L[/tex]Since we need to know the amount of mango juice:
[tex]28\cdot\frac{2}{5}=11.2L[/tex]t + 4 < 13 solve the inequality of t and simplify your answer as much as possible
Answer:
9
Step-by-step explanation:
t < 13 - 4
t < 9
again as far as it goes
In an examination, Sarah obtained 87.5% by gaining 105 marks. How
many marks did she lose?
Answer: 14
Step-by-step explanation:
87.5% of 105 is 91.875 (91)
105-91=14
find x and y intercepts of x+4y=8
Answer: You could assume that X=8 and y=0
Step-by-step explanation:
Answer:
Solutions below.
Step-by-step explanation:
This Question involves the concept of intercepts of a graph.
InterceptsIntercepts of a graph are namely the x-intercept and y-intercept.
x-intercept is when y = 0. Example: (3,0)
y-intercept is when x = 0. Example: (0,9)
ApplicationWe are given the equation: x + 4y = 8
To find x-intercept, we can substitute y = 0 into the equation to obtain the value of x.
x + 4(0) = 8
x + 0 = 8
x = 8
Coordinates: (8, 0)
To fins y-intercept, we can substitute x = 0 into the equation to obtain the value of y.
0 + 4y = 8
4y = 8
y = 8 ÷ 4
y = 2
Coordinates: (0, 2)