First, rewrite the equation in its slope intercept form:
(slope intercept form: y = mx + b where m = slope ; b = y-axis intercept)
15x + 12y = -108
Subtract 15x from both sides:
15x + 12y - 15x = -108 - 15x
12y = -108 - 15x
Divide both sides by 12:
12y/12 = (-108 - 15x)/12
y = -5x/4 - 9
As you can see the slope of this line is -5/4
Now, two lines are perpendicular if:
m1*m2 = -1
Where:
m1 = Slope of the line 1
m2 = Slope of the line 2
m1 in this case would be -5/4
so:
-5/4* m2 = -1
Solving for m2:
m2 = -1/(-5/4) = 4/5 = 0.8
{3x}^{2} + 4x + 1 = 0 using factorisation method
Step-by-step explanation:
Hope it helps you ..
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
Determine which expression is equivalent to the expression 3 over 4 times g minus 6 minus 7 over 8 times g minus the expression one over 2 times g plus 13. negative 5 over 8 times g plus negative 19 3 over 8 times g plus negative 19 negative 5 over 8 times g plus negative 7 5 over 8 times g plus negative 7
The equivalent expression in the form of statement will be -
"negative 5 over 8 times g plus negative 19".
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the following statement - "3 over 4 times g minus 6 minus 7 over 8 times g minus the expression one over 2 times g plus 13"
We can write the statement in the form of a equation as -
(3g/4 - 6) - (7g/8) - (g/2 + 13)
3g/4 - 6 - 7g/8 - g/2 - 13
(3g/4 - 7g/8 - g/2) - (6 + 13)
On solving, we get -
- 5g/8 - 19
Therefore, the equivalent expression in the form of statement will be -
"negative 5 over 8 times g plus negative 19".
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I don´t quite understand this Question 5% of 40
Answer:
5% of 40 = 20
Step-by-step explanation:
To find 5% of 40, you can turn the 5% to 0.5, and the "of" means multiplication.
So, in turn you would have:
0.5 x 40 = 20
i need help 9% of 71 and 126% of 80
Answer:
6.39 and 100.8
Step-by-step explanation:
To find a certain percent of a number, convert the percent to a decimal and multiply them together
0.09 * 71 = 6.39
1.26 * 80 = 100.8
please help asap! ty
Answer:
Step-by-step explanation:
The linear line interacts with the y-axis at 0. Meaning that the y-int is 0. This represents that the original amount of gasoline was 0.
mnm corporation gives each of its employees an aptitude test. the scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. a simple random sample of 25 is taken from a very large population. what is the probability that the average aptitude test score in the sample will be less than 78
a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.
b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.
d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.
e) The value of C = 81.51.
What is meant by Normal probability distribution?When the distribution is normal, we use the z-score formula.
In a set with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the z-score of a measure X is given by:
[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]
The Z-score calculates the deviation of the measure from the mean in standard deviations. We glance at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]$\mu$[/tex] and standard deviation [tex]$\sigma$[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]$\mu$[/tex] and standard deviation [tex]$s=\frac{\sigma}{\sqrt{n}}$[/tex].
The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.
This means that [tex]$\mu=75, \sigma=15$[/tex]
a. By the Central Limit Theorem, it will be approximately normal, with expected value [tex]$\mu=75$[/tex] and standard deviation [tex]$s=\frac{15}{\sqrt{25}}=3$[/tex]
b. The p-value of Z when X = 82.14 subtracted by the p-value of Z when X = 70.14.
X = 82.14
[tex]$Z=\frac{X-\mu}{\sigma}$[/tex]
By the Central Limit Theorem
[tex]$Z=\frac{X-\mu}{s}$[/tex]
[tex]$Z=\frac{82.14-75}{3}$[/tex]
Z = 2.38
Z = 2.38 has a p-value of 0.9913.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$Z=\frac{70.14-75}{3}$[/tex]
Z = -1.62 has a p-value of 0.0526
0.9913 - 0.0526 = 0.9387
0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c. This is 1 subtracted by the p-value of Z when X=82.68.
[tex]$Z=\frac{X-\mu}{s}[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{82.68-75}{3} \\[/tex]
Z = 2.56 has a p-value of 0.9948.
1 - 0.9948 = 0.0052
0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68
d. This is the p-value of Z when X=78.69. So
[tex]$&Z=\frac{X-\mu}{s} \\[/tex]
substitute the values in the above equation, we get
[tex]$&Z=\frac{78.69-75}{3} \\[/tex]
Z = 1.23 has a p-value of 0.8907
0.8907 = 89.07 % probability that the average aptitude test in the sample will be less than 78.69.
e. Find a value, C, such that P((x>C) = 0.015.
This is X when Z has a p-value of 1 - 0.015 = 0.985.
So X when Z = 2.17.
[tex]$Z=\frac{X-\mu}{s}$[/tex]
substitute the values in the above equation, we get
[tex]$2.17=\frac{X-75}{3}$[/tex]
X - 75 = 3 × 2.17
X = 81.51
Therefore, the value of C = 81.51
The complete question is:
MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population of 500.
a. What are the expected value, the standard deviation, and the shape of the sampling distribution of?
b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?
c. What is the probability that the average aptitude test in the sample will be greater than 82.68?
d. What is the probability that the average aptitude test in the sample will be less than 78.69?
e. Find a value, C, such that P(( x>C) = .015.
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10-9x24/8x6 (pemdas)
Answer:
-152
Step-by-step explanation:
1. Parenthesis
2. Exponents
3. Multiplication/Division (left to right)
4. Addition/Subtraction (left to right)
Always look left to right.
The first thing is 9x24=216 (3. multiply)
10-216/8x6
Then 216/8=27 (3. divide)
10-27*6
Then 27*6=162 (3. multiply)
10-162
Then finally 10-162=-152 (4. subtract)
The expression 10 - 9 x 24/8 x 6 following (PEMDAS/BODMAS) is 5.5.
We have,
To solve the expression using the order of operations (PEMDAS/BODMAS), follow these steps:
Perform multiplication and division from left to right:
10 - 9 x 24/8 x 6 can be rewritten as 10 - (9 x 24) / (8 x 6).
Perform the multiplication inside the parentheses:
10 - (9 x 24) / (8 x 6)
10 - 216 / (8 x 6).
Perform the multiplication in the denominators:
10 - 216 / (8 x 6)
10 - 216 / 48
Perform the division:
10 - 216 / 48
10 - 4.5
Perform the subtraction:
10 - 4.5
5.5
Therefore,
The expression 10 - 9 x 24/8 x 6 following (PEMDAS/BODMAS) is 5.5.
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4x - 7<-27 or 29 4x - 7
Answer:x= 1/4=0.250
Step-by-step explanation:
help me pleaze its hard !!
Answer:
Angle YVX = 59°
Angle Y = 85°
x = 3
Step-by-step explanation:
You got the first two correct.
The last bit, use the fact that the shape is a parallelogram, the opposite sides are equal.
2x = 6
x = 3
Question 10 !!
Help me please
letter A = C
letter B = B
Letter C= B
Answer:
(a) Figure C
(b) Figures B and C
(c) Figures B and C
Step-by-step explanation:
Figure A does not apply to any of the 3 questions
Hope this helps
Help Me Please
A B, C, or D.
Answer correctly
Answer: D
Step-by-step explanation:
as when 3746 is rounded to the nearest hundred t is 4000
whereas when 3746 is rounded to the nearest ten it is 3800.
4000 is larger than 3800 so the answer is D.
Which of the following values make the inequality x≤16.3 truea 18.5b 8c 1/4d 32e -3f 16.3
SOLUTION
We want to find which of the following values make the inequality
x ≤ 16.3 to be true.
This inequality means that x is equal to 16.3 or less than 16.3. So the numbers that fall under this are numbers smaller than 16.3 and also 16.3.
The numbers that fall under here are 8, 1/4, -3 and 16.3
Hence the answer b, c, e and f
6th grade math, Please Help) 2 people pls answer so i can make brainliest! and you will get 20 points :)
Evaluate the Algebraic expression; j+2h= when f=6, g=8, h=12, j=2
OA) 14
OB)18
OC)26
OD)30
Answer:
the answer is 26
Step-by-step explanation:
j+2h
(2) + 2(12)
2 + 24
26
This is to hard for me help me out please
The table shows the distances between major cities.
New York to Paris 3,636 miles
Los Angeles to Toronto 2,171 miles
Mr. Santiago has a flight from Los Angeles to Toronto. If the plane travels at 520 miles per hour, how many hours long is the flight?
__ hours
Answer:
The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.
Which is 2171 (Total distance) / 520 (Distance travelled in a hour)
[tex]2171/520 = 4.175[/tex]
Which can be rounded of to 4.2
It takes 4.2 hours for the flight between Los Angeles and Toronto
the expected number of typographical errors on a page of a certain magazine is .2. what is the probability that the next page you read contains (a) 0 and (b) 2 or more typographical errors? explain your reasoning!
(a) The probability that the next page you read contain zero is 0.8187.
(b) The probability that the next page you read contains or more typographical errors is 0.0175.
What is probability?
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
The probability that the next page you read contains zero. The expected number of typographical errors on a page of a certain magazine is
That is, y = 0.2
Let is a random variable representing the number of typos per page.
Since, we have a large number of letters per page, and the number of errors in one page will be small, we use Poisson distribution. The probability function of the Poisson distribution is defined as,
[tex]P(x = i) = e^-^y\frac{y^i}{i!},..... i = 0, 1, 2, ...[/tex] ...(1)
Here, y is a parameter.
Find the probability that the next page you read contains zero.
That is, find P(y = 0)
plug y = 0 in equation (1), we get
P(x = 0) = 0.8187
The probability that the next page you read contain zero is 0.8187
Given the question that the probability that the next page you read contains more typographical errors. The expected number of typographical errors on a page of a certain magazine is 0.2
That is y = 0.2
Let is a random variable representing the number of typos per page.
Find the probability that the next page you read contains more typographical errors.
That is find P(x ≥ 2)
P(x ≥ 2) = 1 - P(x ≤ 1)
= 1 - (P(x = 0) + P(x = 1))
= 1 - 0.982477
= 0.0175
The probability that the next page you read contains or more typographical errors is 0.0175.
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hi do you think you can help me on this question
SOLUTION
From the question
[tex]\begin{gathered} 1\text{cup = 8 fluid ounces, then } \\ x\text{ cup = 560 fluid ounces } \end{gathered}[/tex]Cross multiplying you have that
[tex]\begin{gathered} x\times8\text{ fluid ounces = 560 fluid ounces }\times1\text{ cup } \\ \text{Hence } \\ x=\frac{560\times1}{8} \\ x=70\text{ cups } \end{gathered}[/tex]Hence, the answer is 70
For a science fair project, Cora tracked the temperature each day. Temperature reading (°C) Number of temperature readings 6 2 22 3 25 1 35 1 2 42 1 X is the temperature that a randomly chosen temperature reading was. What is the expected value of X? Write your answer as a decimal.
We get that the expected temperature is
[tex]\begin{gathered} E(T)=6\cdot\frac{2}{10}+22\cdot\frac{3}{10}+25\cdot\frac{1}{10}+35\cdot\frac{1}{10}+41\cdot\frac{2}{10}+42\cdot\frac{1}{10} \\ E(T)=26.2 \end{gathered}[/tex]The cost of printing digital photos is given by c(p) = 0.15p, where p is the number of photos that you print and c(p) is the cost in dollars. Find c(75). c(75) = $
The value of the function c(75) for c(p) = 0.15p is c(75) = $11.25
How to determine the function value?From the question, the function definition is given as
c(p) = 0.15p
The above function is a linear function
This is so because it is represented as y = mx where m is the slope
The function value to calculate is given as
c(75)
This means that we calculate c(p) when p = 75
So, we have
c(75) = 0.15(75)
This gives
c(75) = 0.15 x (75)
Evaluate the product
c(75) = 11.25
Hence, the function value is c(75) = 11.25
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4. Mark's age, when doubled, is Peggy's age. Peggy is 6 years older than Chris. Chris is 6 years older than
Mark. How much older is Peggy than Mark?
If <1 and <2 are
supplementary angles with
m <1 = 10x +5 and m <2= 6x-1, what are the measure-
ments of both angles?
Step-by-step explanation:
The sum of measure of supplementary angles = 180°
The measure of angle 1 is given as 10x + 5 and the measure of angle 2 is given as 6x - 1
10x + 5 + 6x - 1 = 180 add like terms
16x + 4 = 180 subtract 4 from both sides
16x = 176 divide both sides by 16
x = 11
To find the measure of each angle, relace x with 11
angle 1,
10*11 + 5 = 115
angle 2,
6*11 - 1 = 65
(x + 4)(x + 3)How do I find the answer of this with work to break it down?
In order to break down this product, we need to apply the distributive property of the multiplication.
So we need to find the product of each term inside a binomial by each term in the other binomial.
That is, first we find x times x and x times 3, then we find 4 times x and 4 times 3, finally we add them all:
[tex]\begin{gathered} (x+4)(x+3)=x\cdot x+x\cdot3+4\cdot x+4\cdot3 \\ =x^2+3x+4x+12=x^2+7x+12 \end{gathered}[/tex]So the final expression is x2 + 7x + 12.
I need help with what's on the screen, thank you.
a) We know that in the northern Hemisphere we have 4 seasons: Summer where is more sun, Spring, and autumn that the sun is like 50/50 and winter that is the season with less sun. So we can made a graph with this so:
b) In this case if we have a simple interest is going to be a streight light that is going to increase. So the graph will be:
c) An item that increase it's price by 50% is going to be increasing each time more, so this case will be an exponential so the graph will be:
d) The high of a triangle and the base of the triangle are going to to have a constant rate. so the graph will be a horizontal line so:
Hi please help explain. Image attached. Thanks!
three friends earned more than $200 washing cars. They pay their parents $28 for supplies and divided the rest of the money equally. right an equality to find possible amount each friend earned. Identify what your variable represents.
x is each friend
3x + 28 > 200
3x > 172
x > $57.33
if right can a i get brainliest pls
Answer:
Step-by-step explanation: $200-$28= $172
$172÷3=$57.33
Determine which angles are right triangles. Select all that apply
Answer:
[tex]A,B[/tex]Explanation:
Here, we want to get the right triangles
Mathematically, for us to have a right triangle, the square of the hypotenuse (which is the longest side) equals the sum of the squares of the two other sides. This is Pythagoras' theorem
We shall be testing this principle out on the given options
We proceed as follows:
[tex]\begin{gathered} a)\text{ 24}^2\text{ + 143}^2\text{ = 145}^2 \\ b)\text{ 28}^2\text{ + 195}^2\text{ = 197}^2 \\ c)\text{ 135}^2\text{ + 140}^2\text{ }\ne\text{ 175}^2 \\ d)\text{ 56}^2+\text{ 16}^2\ne\text{ 65}^2 \end{gathered}[/tex]What this means is that only options A and B is correct
v/8 - 3.1 = -15.9 solve for v
Hello!
So, we are given the following to solve.
Solve for v.
[tex]\frac{v}{8}-3.1=-15.9[/tex]
To solve for v, we to do as follows:
1. Add 3.1 to both sides.
[tex]\frac{v}{8}-3.1+3.1=-15.9+3.1[/tex]2. Simplify.
[tex]\frac{v}{8} =-12.8[/tex]3. Multiply both sides by 8.
[tex]\frac{8v}{8}=8(-12.8)[/tex]4. Simplify.
[tex]v=-102.4[/tex] ← Hence, our solution.Hope this helps!
Please help me in math the question is in the picture please
If car has 1/x part in cleaning the house in 1 hour 1/x-5 must be part of Jose if he also clean the house for 1 hr.
What is work?The scientific definition of work is different in many ways from its everyday meaning. The definition of work in physics reveals its relationship to energy – whenever work is done, energy is transferred.
For a work to be done, in a scientific sense, a force must be exerted, and there must be displacement in the direction of the force. With this said, we can say that Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
Mathematically, the above statement is expressed as follows:
W = (F cos θ) d = F. d
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- What is the perimeter of a right triangle witha hypotenuse that measures 6 square root 5 cm and onealeg that measures 4 square root 5 cm
3x
2
-6y^{2}−6y
2
+7+7-2−2-2y^{3}−2y
3
-6y^{3}−6y
3
-5−5
Answer:
Step-by-step explanation:
2
3x + y =-12x
Answer:
Step-by-step explanation:
y= 2
45−6x
2−3 y=
2− 45−6x
2 −3 , ∣x∣≤ 2
30