The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)
a) the independent variable is the: Number of month after the first year
b) the dependent variable is the: Amount remaining on the card
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Starting value= $25Decrease= $2.50 per monthWriting the equation according to the information gave, we have:
y = 25 - (2.50x)
Where:
Amount remaining on the card = yNumber of month after the first year = xThe relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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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!
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
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=$57.33
- What is the perimeter of a right triangle witha hypotenuse that measures 6 square root 5 cm and onealeg that measures 4 square root 5 cm
This is to hard for me help me out please
4x - 7<-27 or 29 4x - 7
Answer:x= 1/4=0.250
Step-by-step explanation:
Each square on a grid represents 1 unit on each side. Match the numbers with the slopes of the lines.
50 POINTS + BRAINLY FOR CORRECT ANSWER!!!
Answer
Graph 1 = 1/3 slope
Graph 2 = -1/3 slope
Graph 3 = 3 slope
Graph 4 = -3 slope
I found these by counting rise over run,
or y/x to points on the line that cross the x or y axis.
The graphs that have a line that go up from left to right are positive slopes
The graphs that have a line that go down from left to right are negative slopes
Problems solved!
mnm corporation gives each of its employees an aptitude test. the scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. a simple random sample of 25 is taken from a very large population. what is the probability that the average aptitude test score in the sample will be less than 78
a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.
b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.
c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.
d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.
e) The value of C = 81.51.
What is meant by Normal probability distribution?When the distribution is normal, we use the z-score formula.
In a set with mean [tex]$\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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parents have raised major concerns over a school district's proposed experiment to examine the effectiveness of removing math tracks and instead placing all students into one open math class. in response, the school district has decided not to randomly assign students to be placed in tracked or non-tracked math classes. instead, the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group. which methodological problem is very likely under this scenario? g
Since the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group, the type of design that the school district has implemented is a. matched design.
What is a matched design?
A matched group design is an experimental layout where the study subjects are selected because their variables match.
Therefore, In a matched pairs design, study participants are matched according to important variables or shared traits that are pertinent to the study's subject. The second step involves assigning one member of each pair to the control group and the other to the experimental group.
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See full question below
Parents have raised major concerns over a school district's proposed experiment to examine the effectiveness of removing math tracks and instead placing all students into one open math class. In response, the school district has decided not to randomly assign students to be placed in tracked or non-tracked math classes. Instead, the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group.
which methodological problem is very likely under this scenario
Select one:
a. matched design
b. pre-post design
c. nonequivalent comparison design
d. multiple time-series design
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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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.
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
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
The equation 9(u + 2) = -45 is solved in several steps below. For each step, choose the reason that best justifies it.
Step 1: Distributive property:
Step 2: Subtraction Property of Equality
Step 3: Simplifying
Step 4: Division property of equality
Step 5: Simplifying
Explanation:Given the expression
9(u + 2) = -45
Step 1: Expand using the Distributive property:
9u + 9(2) = -45
9u + 18 = -45
Step 2: Subtract 18 from both sides (Subtraction property of equality)
9u + 18 - 18 = -45 - 18
Step 3: Simplifying
9u = -63
Step 4: Divide both sides by 9 (Division property of equality)
9u/9 = -63/9
Step 5: Simplifying
u = -7
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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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
Hi please help explain. Image attached. Thanks!
102 plus what equals 180
Answer:
78
Step-by-step explanation:
80-2+78 soo,
78+2 +80 with means 102+78 =180
Answer:
102 + 78 = 180
Step-by-step explanation:
{3x}^{2} + 4x + 1 = 0 using factorisation method
Step-by-step explanation:
Hope it helps you ..
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
What is the answer to this equation: -13<2x+5<15
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
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
a linear function has the rule shown
input: a number
output: 8 less than 3 times x
which equation represents this rule
(100 POINTS!!!)
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]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
I have the problem as a picture, can I show u?
corresponding (option D)
Explanation:Since the lines are parallel and a tranversal line cuts the two lines:
The angle 2 at the top of the first line correspods to angle 6 at the top of the second line.
Angle 2 and angle 6 are equal.
Hence. we say angle 2 and angle 6 are corresponding angles (option D)
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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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.