The simplified fraction and the original fraction have the same value. Option D is correct.
Given that,
To justify, how is a fraction related to its simplified form.
Fraction is defined as the number of compositions that constitute the Whole.
Here,
The value of the fraction does not change when it is brought into a simplified form.
Thus, the simplified fraction and the original fraction have the same value. Option D is correct.
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The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 7 months. Find the probability that a random sample of 28 smoke detectors will have a mean lifetime between 57 and 62 months. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.
The probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.
Let x represent the lifespan of smoke detectors manufactured by a business.
We assume that the lifetime of smoke detectors manufactured by a business is normally distributed.
Given: The average lifetime of a company's smoke detectors is 5 years, or 60 months, with an 8-month standard deviation.
μ = 60, σ = 8 and samle size n = 30
The probability that a random sample of 30 smoke detectors will have a mean lifetime of 57 to 62 months is :
P(57 < P < 62) = P{(57-60)/(8/√30) < ((x-μ)/σ)/(σ/√n) < (62-60)/(8/√30)}
P(57 < P < 62) = P(-1.37 < z < 2.05)
= P(z<2.05) - P(z< -1.37)
= P(<2.05)-(1-P(<1.37)) P(Z) = 1 − P(Z < 2)]
= 0.9798178-(1-0.9146565) [By using p-value table for z]
= 0.8944743≈ 0.8945
Hence, the probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.
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Please help Image below
Function g can be thought of as a translated (shifted) version of f(x)=x².
Write the equarion for g(x).
Answer:
[tex]g(x)=(x+4)^2-5[/tex]
Step-by-step explanation:
The graph of [tex]f[/tex] was shifted 4 units left and 5 units down,
Equations/Rules 2
What is the zero of the function f(x)=3 x-9 ? Explain how you know.
?
What is the zero of the function f(x)=-x+4 ? Explain how you know.
?
The zero of the function f(x) = 3x - 9 is x = 3.
The zero of the function f(x) = -x + 4 is x = 4.
How to find zero of a function?The zero of a function is any replacement for the variable that will produce an answer of zero.
Therefore, let's find the zero of the function f(x) = 3x - 9.
0 = 3x - 9
add 9 to both sides of the equation
0 + 9 = 3x - 9 + 9
9 = 3x
divide both sides by 3
x = 9 / 3
x = 3
The zero of the function is x = 3.
Therefore, let's find the zero of the function f(x) = -x + 4.
0 = - x + 4
subtract 4 from both sides of the equation
0 - 4 = -x + 4 - 4
-4 = - x
x = 4
The zero of the function is x = 4.
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A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.
The cost of each friend's meal in terms of a is 35/a.
The cost of each friend's meal when the number of friends is 5 is $7.
How to solve linear equation problems?We are given that;
Total amount that they can spend on food bill = $41 including delivery charge of $6
The equation is given as;
6 + ax = 41
Where;
a is the number of people
x is the cost of each friend's meal.
Thus;
ax = 41 - 6
ax = 35\
x = 35/a
So it will be the cost of each friend's meal in terms of a.
Now,
If the number of friends = 5
Then,
a = 5
Thus;
x = 35/5 = $7
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Complete question is;
A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.
The cost of each friend's meal in terms of a is
.
The cost of each friend's meal when the number of friends is 5 is $
Evaluate the function f(x) = 2x² – 3x
According to the solving the value of the Quadratic equation are as follows:
x = 0
x = 2
Describe the quadratic formula:We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, but instead c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. View instances of the formula being used to solve various equations.
How should a quadratic equation be presented to students?Make a video of the pupils utilizing one technique to solve a quadratic equation. Allowing pupils to pick is an option, but you can also direct them to utilize the quadratic equation, factoring, or square-rooting.
According to the given information:f(x) = 2x² – 3x
x- (2x² – 3x) = 0
x - 2x² + 3x = 0
4x - 2x²= 0
x = 0
x = 2
According to the solving the value of the Quadratic equation are as follows:
x = 0
x = 2
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There are 40 kg of sugar in the bag. Strawberry jam was used
4 kg, but 1/4 of the remaining sugar was used for the cherry jam. How many kilograms of sugar were used for cherry jam?
The kilograms of sugar that were used for cherry jam is 9kg.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Since there are 40 kg of sugar in the bag. Strawberry jam was used which was 4 kg. The remaining kilograms will be:
= 40kg - 4kg
= 36 kg
Since 1/4 of the remaining sugar was used, the amount used will be:
= Fraction × Total amount
= 1/4 × 36
= 9kg.
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ents
K-12
X Y
7 21
8 24
9 27
Function B
10
1
6
4
2
0
Function B
10
Which statement best compares the rate of change of the two functions? (1 point)
The rate of change of both functions is 2.
The rate of change of both functions is 3.
O The rate of change of function A is greater than the rate of change of function B.
O The rate of change of function B is greater than the rate of change of function A
Answer:
C
Step-by-step explanation:
FUNCTION A
21 : 7 = 3
FUNCTION B
8: 4 = 2
3 is greater than 2
helpppppppppppppppppp
when y equals zero, x equals -2
or, at y = 0, the function touches the x-axis at -2
Can someone help me I don’t understand this question it’s geometry
All the missing lengths and missing angles of the given right angle triangle are as calculated below
How to use trigonometric ratios?We are given a right angle triangle and as such we can use the trigonometric ratios as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
a) A = 30°, Thus;
B = 180 - (90 + 30)
B = 60°
Using sine rule;
a/sin A = b/sin B
a/sin 30 = 6/sin 60
a = 3.464
c/sin 90 = 6/sin 60
c = 6.928
b) a = 13 and b = 13
Using Pythagoras theorem;
c = √(13² + 13²)
c = 18.385
Since a = b, it means it is an isosceles triangle and so;
A = B = 45°
c) B = 30°, c = 10
A = 180 - (30 + 90)
A = 60°
10/sin 90 = b/sin 30
b = 5
10/sin 90 = a/sin 60
a = 8.66
d) A = 45°, c = 12
B = 45°
c/sin 90 = b/sin 45 = a/sin 45
b = a = 12 * sin 45 = 8.485
e) c = 1, b = 1/√2
c/sin 90 = b/sin B
1/sin 90 = (1/√2)/ sin B
B = 45° = A
a = √(1² - (1/√2)²)
a = 0.7071
f) c = 4 and b = 4;
a = √(4² - (4)²)
a = 0
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Find all values of m for which the equation has two real solutions.
3x² + 7x- (m + 1) = 0
0.25 as a percentages
Answer:
25%
Step-by-step explanation:
got it right on my quiz .
Differentiate the function with respect to x. Shot steps
The value after differentiate will be;
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ [tex]y = 3^{x^{3} }[/tex]
Now,
Differentiate the function with respect to x as;
The function is,
⇒ [tex]y = 3^{x^{3} }[/tex]
⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 \frac{d}{dx} (x^3)[/tex]
⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 * 3x^2[/tex]
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
Thus, The value after differentiate will be;
⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]
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Suppose f(x)=√x+1 and g(x)=x² + n. If f(g(7)) = 9, what is the value of g(n)?
..
Step-by-step explanation:
g(7)=
[tex] {7}^{2} + n[/tex]
[tex]49 + n[/tex]
f(g(7))=n
[tex]f(g(7)) = \sqrt{49 + n + 1} [/tex]
[tex]f(g(7)) = \sqrt{n + 50} [/tex]
[tex]9 = \sqrt{n + 50} [/tex]
[tex]81 = n + 50[/tex]
[tex]n = 31[/tex]
So
[tex]g(31) = 31 {}^{2} + 31[/tex]
[tex] = 992[/tex]
Find the number of ways five out of seven patients are called to remind them of their appointment.
The number of ways that five out of seven patients are called to remind them of their appointment is 21 ways
Total number of patients = 7
Number of patients that called to remind them of their appointments = 5
To find the total number of ways we have to use the combination methods
The combination is the method of selection of elements from the collection. In the combination order of the selection does not matters
Total number of ways = [tex]7C_5[/tex]
= 7! / (5!(7 - 5)!)
Subtract the terms
= 7! / 5! × 2!
= (7×6×5!) / (5!×2!)
= 7 × 6 / 2 × 1
= 42 / 2
= 21 ways
Hence, the number of ways that five out of seven patients are called to remind them of their appointment is 21 ways
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The ratio of students to adults on a field trip is 5 to 3. Which table correctly represents this ratio?
Answer: Though there is not enough information to be sure, a table to complete this ratio could be one include the sets of numbers (5,3) (10,6) and (15, 9)
Step-by-step explanation:
5. Calculate the distance around a triangle whose sides are x / 2 , x /3 , and x/4
The distance around the given triangle is [tex]\cfrac{13x}{12}[/tex].
How do I calculate the perimeter of a triangle?We are asked to calculate the distance around the triangle, commonly known as the perimeter.
The perimeter is the sum of all side lengths in any shape. For a triangle, you add up all the side lengths and that is your perimeter.
What we know:Side 1 = [tex]\cfrac{x}{2}[/tex]Side 2 = [tex]\cfrac{x}{3}[/tex]Side 3 = [tex]\cfrac{x}{4}[/tex]CalculateNow we need to add up all these side lengths.
[tex]\cfrac{x}{2} +\cfrac{x}{3} +\cfrac{x}{4}[/tex]
We have fractions with unlike denominators. We need to get common denominators in order to solve. To do this, we need to obtain the GCF (Greatest Common Factor) of the numbers 2, 3, and 4.
This number is 12.
By changing the fractions so they all have denominators of 12, we retrieve our new equation:
[tex]\cfrac{6x}{12} +\cfrac{4x}{12} +\cfrac{3x}{12}[/tex]
Now we add them:
[tex]\cfrac{6x+4x+3x}{12}=\cfrac{13x}{12}[/tex]
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-2≤x<7 what is the equivalent interval notation
Answer:
576482670576482670576482670576482670576482670576482670576482670576482670576482670576482670
Step-by-step explanation:
A jar has marble ms in these three colors only: 7 green, 10 blue, 3 red.
What is the probability of randomly choosing a green marble, after choosing (and keeping) a red marble?
Answer with a percentage rounded to the nearest tenth.
The probability of randomly choosing a green marble after you have chosen red is 4.4%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given
A jar has 20 marbles: 3 green, 12 blue, 5 red.
Probability;
In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.
The total number of marbles = 20
The number of green marbles= 3
The number of blue marbles = 12
The number of red marbles = 5
The probability of choosing a red marble = Number of red marbles / Total number of marbles
= 5/20
The probability of choosing a green marble is = Number of green marbles / New total number of marbles
= 3/19
Therefore,
The probability of randomly choosing a green marble after you have chosen red is;
= 5/20 * 3/19
= 3/68
percentage = 3/68 * 100 = 4.4%
Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%
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The binary operation * on the set of real numbers is defined as a * b = 2a + 3b - 5. Find the inverse element in *.
The inverse element of the binary operation is given by (20-7a)/9 .
The binary operation is defined by a * b = 2a + 3b - 5
Now let us first find the identity element of the operation.
let e be the identity element.
Hence we know that a * e = a
Therefore a * e = 2a + 3e - 5
or, a = 2a + 3e - 5
or, a - 2a = 3e - 5
or, -a = 3e - 5
or, e = (5-a) / 3
Now we know that the inverse of the operation will be such that
a * a⁻¹ = e
or, a⁻¹ = (20-7a) / 9
Therefore the inverse of the operation is given by (20-7a) / 9 .
A binary operation or dyadic operation is a rule that combines two elements (referred to as operands) to produce a third element. Formally, a binary operation is a two-arity operation.
An internally binary operation on a set is a binary action with the same set as its two domains or codomain. Examples include addition, multiplication, and other basic mathematical operations.
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what is the correct procedure when you want to do a test of the population mean but the population standard deviation is unknown? select all that apply.
When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).
help me fast rapidly is of khan academy:
Answer:
0 hundreds
0 tens
7 ones
.
4 tenths
0 hundredths
8 thousandths
Standard form=7.408
Step-by-step explanation:
Lets first solve (7x1)+(4x1/10)+(8x1/1000)
7+0.4+0.008
Simplify:
7.408
PLEASE MARK AS BRAINLIESTThe sum of three smallest factors (including 1) of the number N equals 6, and the sum of the three greatest factors of N (including N itself) equals 462. What is the value of N?
You will get brainiest if you include a detailed explanation. Thank You!
Answer:
252
Step-by-step explanation:
The second and third smallest factors must add to 5. The only possibility is that these factors are 2 and 3.
The second and third largest factors must add to [tex]462-N[/tex]. These factors are [tex]N/2[/tex] and [tex]N/3[/tex].
[tex]462-N=\frac{N}{2}+\frac{N}{3} \\ \\ 462-N=\frac{5N}{6} \\ \\ 462=\frac{11N}{6} \\ \\ N=252[/tex]
Write 33×√3 as a single power of 3.
Answer:
[tex]3^{7/2}[/tex]
Step-by-step explanation:
[tex]3^3 \sqrt{3} \\ \\ =3^3 \cdot 3^{1/2} \\ \\ =3^{3+\frac{1}{2}} \\ \\ =3^{7/2}[/tex]
If the data in the stem-and-leaf graph below were shown in a line plot, which statement(s) would be true of the line plot? ( Can pick more than one answer)
The statement that would be true if the data in the data in the stem-and-leaf plot is shown in a line plot is: D. We could calculate the range and median.
What is a Line Plot?A line plot is a graph that shows individual data in a data set with the use of dots. Each dot represents a data plot.
In a line plot, we can easily find the middle of the data distribution which is the median of the data and also we can determine the highest and lowest value which enables us to find the range of the data.
Thus, using the stem-and-leaf plot in the diagram, below, write out each data points given, which are:
68, 70, 80, 86, 88, 88, 96, 96, 97, 97, 98, 98, 99, 100, 100, 100, 100, 100
The line plot for these data would have the following frequency for each data point:
68 - 1 dot
70 - 1 dot
80 - 1 dot
86 1 dot
88 - 2 dots
96 - 2 dots
97 - 2 dots
98 - 2 dots
99 - 1 dot
100 - 5 dots
The line plot is shown in the diagram below.
Range = 100 - 68 = 32
Median = 97
Therefore, the answer is: D. We could calculate the range and median.
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write the equation of the circle whose center and radius are given 1 . center (2,-2) radius =6
Help to please and thank you
As per the given population function, the growth function is written as, P = 13000(1.05)ˣ
Population function:
Population function refers the positive change in a particular population as a function of time. And this growth is not linear, but exponential, and so the formula for population growth can be found by starting with the premise that P (population) multiplies by a rate r over time.
Given,
A population numbers 13,000 organisms initially and grows by 5% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = abˣ
Now, we have to find the population growth function for this situation.
From the given question, 'we have the following details,
Population numbers = 13,000
So, the value of a in the population function is 13,000
And it grows every year as 5%.
So, in decimal form in can be 0.05.
So, the value of b is calculated as,
=> b = 1 + 0.05
=> b = 1.05
Now, we have to apply these values on the function,
Then we get,
=> P = 13000(1.05)ˣ
Therefore, the population growth function is been identified
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Find two numbers that multiply to give 100 and have a difference of 21
The values can be 4, 25 and -4, -25.
What is a Linear Equation in Two Variable?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Let,
The first number be x and second number be y
Equation 1: x*y = 100
Equation 2: x - y = 21
From equation 2 we can write x = 21 + y
Substituting the value of x in equation 1
(21 + y)*y = 100
21y + y^2 - 100 = 0
y = 4, -25
this implies that x = 25, -4
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Can someone please help me.
Answer:
We have to prove the triangles ΔXYW and ΔZYW are similar. We can do this by showing that they have two equal/in-ratio corresponding sides with the same angle between them (SAS/side-angle-side), or by showing they have two equal corresponding angles (AA/angel-angle), or by showing their sides are in ratio (SSS).
We are told XY=ZY, so we already know the triangles share an equal side.
Both triangles also share YW as a side.
Because YW bisects <XYZ, we know <XYW = <ZYW, so we know the angle between the triangle's corresponding sides are the same.
Therefore, since the triangles have two equal corresponding sides with the same angle between them (SAS), we can say they are similar.
Hope this helps :)
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary).
(-8,-7) and (-6,2)
*Click twice to draw a line. Click a segment to erase it.
The triangle has a hypothenuse 9.21 units and the graph it's attached below
Distance Between Two PointsThe distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.
The formula of distance between two points is given as
d = √(y₂ - y₁)² + (x₂ - x₁)²
The two points are
(-8, -7)(-6, 2)Substituting the values into the formula above;
d = √(2 -(-7))² + (-6-(-8))²
d = √85
d = 9.21 units
The hypothenuse of the triangle is 9.21 units
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Compute the standard error for sample means from a population with mean
μ = 90 and standard deviation o = 25 for sample sizes of n = 440, n = = 230,
and n =1200
The standard errors for the sample sizes of 440, 230, and 1200 are 1.2, 1.65, and 0.72, respectively.
The mean of the population is μ = 90. The standard deviation of the population is σ = 25. We are given three sample sizes. We need to compute the standard error for each sample size.
The standard error is computed by dividing the standard deviation by the square root of the sample size. It calculates the accuracy of a sample mean by factoring in sample-to-sample variability.
Let S1, S2, and S3 represent the standard errors for the sample sizes of 440, 230, and 1200, respectively.
S1 = σ/√n
S1 = 25/√440
S1 = 1.2
S2 = σ/√n
S2 = 25/√230
S2 = 1.65
S3 = σ/√n
S3 = 25/√1200
S3 = 0.72
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