using the normal distribution, the warranty period of motor last at 6.24 years.
According to given question , the average life of motor = 10 years and standard deviations = 2 years .
let X be the time period in which the warranty period of motor last . X ~ N( μ, σ²) where u is mean and s is standard deviations. X ~ N( 10, 2²) ⁼ N(μ, σ²)
it is given that only 3% number of motors are replaced and 3% = 0.03
Using normal distribution , P( X≤ x)= P(( X - μ )/ σ ≤ (x- μ)/σ ) = P ( Z ≤ (x- μ ) / σ ) =0.03
Z = (X- μ) / σ => X = Z (σ) + μ
p (Z ≤ -1.88) = 0.03 so, Z-value is - 1.88..
put all the value of variables in above formula we get , -1.88 ( 2) + 10 = X => X = - 3.76 + 10
=> X = 6.24
Thus , the motor's warranty period lasted about 6.24 years.
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You have saved some money to purchase five different songs to download to your portable music device. Solve an inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars.
If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.
InequalityGiven:
Numbers of different songs to download = 5
Cost = $20
Hence,
The inequality is ; 5 x ≤ 20
Now let solve the inequality
5 x ≤ 20
x = 20 /5
x = 4
So,
= x ≤ 4
Therefore the inequality is 5 x ≤ 20.
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3. At a carnival, of the games cost $1. Another 2.5% of the games cost $2. What
percent of the games do not cost $1 or $2?
Percent of the games do not cost $1 or $2 is 35%.
What is percentage?
A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
Given,
games = 58
5/8 is 62.5%
2.5% + 62.5% = 65%
100%-65% = 35%
A third of the games (35%) are free.
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Complete question -
At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?
standard to intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y - 6x = 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 5y = 6x + 5[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + \frac{5}{5} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Jaime, ralph, marvin and victor decided to put up a small business. their initial investment is in the ratio of 8:3:12:2 respectively and marvin's had ivested php 240,000. interms of profit they have decided to split them base on the ratio of their investment. in the first three months of their company made a total of php 150,000 profit. based on marvin's initial deposit. how much did victor invested?
Answer:
php 40,000
Step-by-step explanation:
In the ratio, Marvin corresponds to 12 and Victor to 2.
Marvin invested php 240,000.
His part of the ratio is 12.
240,000/12 = 20,000
Victor's part in the ratio is 2.
Victor's investment amount is 2 × php 20,000 = php 40,000
Four pencils held together with a band
Step-by-step explanation:
The length of the band is the number of units it covers
The actual length of the band is: \mathbf{40 + 10\pi}40+10π
The diameter of 1 pencil is given as:
\mathbf{d = 10}d=10
The circumference of 1 pencil is:
\mathbf{C = \pi d}C=πd
So, we have:
\mathbf{C = 10\pi }C=10π
Multiply by 4, to calculate the circumference of all pencils
\mathbf{4C =4 \times 10\pi }4C=4×10π
\mathbf{4C =40\pi }4C=40π
The rubber band covers a quarter of the 4 pencils.
So, we divide by 4
\mathbf{C = 10\pi }C=10π
The length of the band on one pencil is:
\mathbf{L = 10}L=10
Multiply by 4, for the 4 pencils
\mathbf{L = 40}L=40
So, the actual length of the band is:
\mathbf{Length = 40 + 10\pi}Length=40+10π
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3-3k+7k=5b solve for x
Hey there!
[tex]3-3k+7k=5b[/tex]
Assuming you're trying to solve for b or k, I'll solve both.
Solve for b:
[tex]3-3k+7k=5b[/tex]
We will need to flip the equation:
[tex]5b=4k+3[/tex]
Now, let's divide both sides by 5:
[tex]\frac{5b}{5} =\frac{4k+3}{5}[/tex]
[tex]b=\frac{4}{5} k+\frac{3}{5}[/tex]
Solve for k:
[tex]3-3k+7k=5b[/tex]
Let's add -3 to both sides:
[tex]4k+3+-3=5b+-3\\4k=5b-3[/tex]
Now, let's divide both sides by 4:
[tex]\frac{4k}{4} =\frac{5b-3}{4}[/tex]
[tex]k=\frac{5}{4} b+\frac{-3}{4}[/tex]
Now, we've solved for b and k.
Hope this helps!
Type the missing number to complete the proportion. 80 minutes for 22 songs minutes for 11 songs Submit
80 : 22 :: x : 11
x = (11 x 80) / 22
x = 880/22
x = 40
The missing number is 40
Match each problem to its solution.32672.72671.7216Jeff wants to buy a new guitar that costs$1,701.04. Currently, he has 51,029.32How many more dollars does he need tobuy the guitar?Rose walks 3.2 miles every day. How manymiles will she have walked in 5 days?Christie was on a road trip. She traveled320.95 miles on day one, 231.45 miles onday two, and 120.32 miles on day three.How many miles did she travel duringher three-day trip?Hugh drove 774.4 miles. His car averaged24.2 miles per gallon of gas. How manygallons of gas did the car use?No
Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?
3.2*5 = 16 miles
Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?
320.95 + 231.45 + 120.32 = 672.72 miles
Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?
774.4/24.2 = 32 gallons
1. You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long
will it be before you and your sister have the same amount of money? Write an equation and solve.
It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.
How to write equation?A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.
What is equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
The given condition,
You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.
Let x be the time period in weeks. So we need same amount of money.
60+7x=120+5x
This is the equation needed.
2x=60
x=30 weeks
If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.
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Find the multiplicative inverse of −1 x -3/10.
Step-by-step explanation:
-1 × -3/10
=> 3/10
Multiplicative Inverse/Reciprocal of 3/10 = 10/3
Which point would describe the rate of change for the line modeled by y = 4/3x+2?
A. Vertical change of 2 units for each horizontal change of 1 unit
B. Vertical change of 1 unit for each horizontal change of 2 units
C. Vertical change of 4 units for each horizontal change of 3 units
D. Horizontal change of 4 units for each horizontal change of 3 units
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be; C. Vertical change of 4 units for each horizontal change of 3 units
How to find the rate of change of a linear equation?Suppose that the considered linear equation is of the form y=mx+c
Then, when we change x by 1 unit, then:
[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]
where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.
It is found that this change is the value of 'm' called slope of the line this equation represents (each linear equation represents a line).
We have been given that the line modeled by y = 4/3x+2
The slope is given as m = 4/3
The point which describe the rate of change for the line modeled by y = 4/3x+2 would be;
C. Vertical change of 4 units for each horizontal change of 3 units
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1. Between which two whole numbers is
√12?
Convince Me!
2. Which of the two numbers is a better
estimate for √12? Explain.
The two whole numbers between which is √12 are 3 and 4.
What is an example of a whole number?
Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.
The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.
i.e 3 < √12 < 4
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Help!! i’ll give brainlest
The equivalent expression is 54 divided by 18, and the quotient is 3.
between 9 am and 6:36 am, the water in a swimming pool decreased by 8/25 in. assuming that the water level decreased at a constant rate, how much did the water level drop each hour
Answer: 2/15 in/hour
Step-by-step explanation:
[tex]\displaystyle\\1)\ 6:36=\\\\6\frac{36}{60}=\\\\6\frac{3(12)}{5(12)}=\\\\6\frac{3}{5}=\\\\\frac{6*5+3}{5}=\\\\\frac{30+3}{5}=\\\\\frac{33}{5} \ hours[/tex]
[tex]\displaystyle\\2)\ 9-\frac{33}{5} =\\\\\frac{9(5)-33}{5}=\\\\\frac{45-33}{5} =\\\\\frac{12}{5}\ hours[/tex]
[tex]\displaystyle\\3)\ \frac{8}{25}:\frac{12}{5} =\\\\\frac{8}{25}*\frac{5}{12} =\\\\\frac{8(5)}{25(12)} =\\\\\frac{2*4*5}{5*5*4*3} =\\\\\frac{2}{5*3} =\\\\\frac{2}{15}\ in/hour[/tex]
4.7.4 pt. 2 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you, all the info you need is on part 1 on my account
Considering that the pumpkin is on the ground at x = 0 and x = 50, it is found that:
5. The roots of the quadratic function are: r1 = 0, r2 = 50.
6. The function is written as follows: y = a(x - 0)(x - 50).
7. The leading coefficient is a = -0.0992.
8. The function is: y = -0.0992(x - 0)(x - 50).
9. Applying the distributive property, the function is: y = -0.0992(x² - 50x).
10. The graph is given at the end of the answer.
Building a quadratic function from it's rootsA quadratic function of roots x' and x'' is defined as follows:
y = a(x - x')(x - x'').
In the context of this problem, the roots are the values of x when the pumpkin is on the ground, hence:
x' = 0, x'' = 50.
Hence, considering the roots, the function is written as:
y = a(x - 0)(x - 50).
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet(mean of the roots), hence the vertex is given by these following coordinates:
(25, 62)
The coordinates are used to find the value of a, which is the leading coefficient of the function, as follows:
62 = a(25² - 50 x 25)
62 = -625a
a = -62/625
a = -0.0992.
Then the equation is written as:
y = -0.0992(x - 0)(x - 50).
The distributive property means that the outer term multiplies each the inside terms, and then the common terms are added, hence the function is:
y = -0.0992(x² - 50x).
Which is sketched at the end of the answer.
Missing informationThe pumpkin is on the ground when x = 0 and x = 50.
The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet.
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What is the probability that the sample proportion is greater than .43?
Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.
Calculate probability ?
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.Probability and odds are two distinct ideas.Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. Theoretical Probability is one of three main categories of probability.Scientific Probability.Probability axiomatically. Sampling is frequently used to calculate the percentage of a population that possesses a particular attribute, such as the percentage of all defective goods that come off an assembly line or the percentage of all customers who enter a store and make a purchase before leaving.The proportions of the population and sample are represented by the letters p and p, respectively.
Therefore,
p = 0.43
if, in fact, 43% of shoppers make a purchase before leaving a store;
p = 78/200
= 0.39
if, in a sample of 200 shoppers, 78 make a purchase.
The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.
It will be represented as a random variable by the letter P.
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If the two triangles shown below are similar
based on the given information, complete
the similarity statement, otherwise choose
the "Not Similar" button.
C
2 in
4 in
ABCA ~ A
A
8 in
B
G
H
16 in
Answer: Similar by SAS
Step-by-step explanation:
Note that [tex]\frac{AC}{AB}=\frac{JG}{HG}=\frac{1}{4}[/tex].
So, the triangles are similar by SAS (since the congruent angle is included between the proportional sides).
Answer for both A, B, and C. Need help asap!!! Giving brainliest.
Answer:
Step-by-step explanation:
Question a: Solve for c
0.9c = 17.01 - 18.9r
c = 17.01-18.9r/0.9
c = 18.9 - 2.1r
Question b: Solve for r
18.9r = 17.01-0.9c
r = 9 - [tex]\frac{0.9}{18.9}[/tex]c
r = -10/21c + 9
(0.9/18.9 = 10/21)
Question c:
It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.
c = 18.9 - 2.1r
Substitute r with 3.25
c = 18.9 - 2.1(3.25)
c= 18.9 - 6.825
c = 12.075
The melting point of nitrogen is -210 °C. The melting point of magnesium is 650 °C.
What is the difference in melting points of the two elements?
Answer:
860 degrees
Step-by-step explanation:
-210+210=0
0+650=650
650+210=860
What’s the term for 5 _ 13
The nth term for the given series is given by 4n-3.
What is meant by series?
The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered collection of elements for which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression. A series can be finite or infinite in length and has a length that corresponds to the number of terms.The number series is 1, 5, 9, 13, 17,...
Common deviation (d)=5-1=4
A=1 is the first phrase.
A+(n1)d=1+(n1) is the formula for the nth term.
4=4n−3
∴tn =4n−3
The nth term for the given series is given by 4n-3.
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Express in decimal notation 4.93 x 10^(3)
The decimal notation of 4.93 x 10³ will be 4930.00.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is;
4.93 x 10³
Now, Solve for decimal notation as;
4.93 x 10³ = 4.93 x 10 x 10 x 10
= 49.3 x 10 x 10
= 493 x 10
= 4930.00
Thus, The decimal notation of 4.93 x 10³ will be 4930.00.
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One endpoint of a line segment is (10,-1). The point (7,-2) i s one-third of the way from that endpoint to the other endpoint. Find the other endpoint
The coordinates of the other endpoint of the Line segment is (-2,-5).
If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,
x = (mc + na)/(m+n)
y = (md + nb)/(m+n)
This above mentioned formula is known as The section Formula.
The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.
Let us assume the other end point to be (a,b).
Now, applying Section Formula,
7 = [(1)(a)+(3)(10)]/4 and
-2 = [(1)(b)+(3)(-1)]/4
Further solving,
a = -2 and
b = -5
So, the coordinates of the endpoint is (-2,-5).
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What is the value of this expression when m = 3 and n=−1?
−4(m−n)2
Answer:
-32
Step-by-step explanation:
m=3 , n=-1 ( given )
then, -4(m-n)2 = -4(3-(-1))2 = -32
are lines AC and DF parallel explain
Answer:
yes
Step-by-step explanation:
ac goes straight forever and df does straight forever and they are parallel
What is the probability that A occurs given that B occurs ?
This is an instance of conditional probability and the formula to use is;
[tex]P(\text{AIB)}=\frac{P(A\cap B)}{P(B)}[/tex]Where:
P(A|B) = the probability of event A occurring given that event B occurred
P(A ∩ B) = the probability that both events A and B occur
P(B) = the probability of event B
[tex]\begin{gathered} P(\text{AnB)}=\frac{1}{3} \\ P(B)=\frac{2}{5} \end{gathered}[/tex][tex]P(\text{AIB)}=\frac{\frac{1}{3}}{\frac{2}{5}}=\frac{1}{3}\times\frac{5}{2}=\frac{5}{6}[/tex]Therefore, the probability that A occurs given that B occurs is 5/6
9+x=11 what is the value of x?
Answer: the answer to that problem is
X=2
Which equation represents a proportional relationship? responses 14x y=10 fraction 1 over 4 end fraction x plus y equals 10 y=14x y equals fraction 1 over 4 end fraction x y=13x 1 y equals fraction 1 over 3 end fraction plus 1 i don't know.
We identify the proportional relationship because it does not have a constant term, the correct option is:
y = (1/4)x
Which equation represents a proportional relationship?
A proportional relationship between two variables x and y is written as:
y = k*x
Where k is called the constant of proportionality.
Here the options are:
(1/4)x + y = 10 (this is a linear equation)y = (1/4)*x (this is a proportional relation)y = (1/3)*x + 1 (this is a linear equation)The only option that has not a constant term is the second one:
y = (1/4)*x
And that is the proportional relationship.
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Answer:
y=(1/4)x
Step-by-step explanation:
I took the test :)
Justin has nine fudge popsicles.
He sells two popsicles to Sidney and three to Doryin.
What fraction of popsicles does Justin have left to eat?
Justin has sold 5 popsicles so from the original 9 if we take away 5, he has 4 popsicles left to eat.
A student claimed that reflect a triangle in a line, translating a triangle , rotating a triangle, and reflecting it in a point result in an image that is congruent to the original( pre-image) triangle. explain why they are correct.
If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.
This is a problem from triangular geometry. We can solve this problem by following a few steps.
Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.
After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.
After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.
∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''
( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )
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URGENT PLEASE HELP
A triangle is translated 6 units left and then dilated by a factor of 0.5.
Which statement about the triangle's image and pre-image is correct?
A) The image and pre-image are congruent figures because one of the transformations is a rigid transformation, and the other
is not.
B) The image and pre-image are congruent figures because both transformations are rigid transformations.
C) The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the
other is not.
D) The image and pre-image are not congruent figures because both transformations are rigid transformations.
A triangle is translated 6 units left and then dilated by a factor of 0.5. the statement about the triangle's image and pre-image that is correct is: The image and pre-image are not congruent figures because one of the transformations is a rigid transformation, and the other is not.
What is a rigid transformation?Transformation is a term that refers to movement of an image from one position to the other.
When the intervals or distances between the points of the image being moved is not altered then the transformation is rigid transformation. However when the interval is altered it is a rigid transformation.
Translation is a rigid transformation while dilation is a non rigid transformation.
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