What is the variable used in the equation 5x + 2 =100?
Answer:
\(5x + 2 = 100 \\ 5x = 100 - 2 \\ 5x = 98 \\ x = \frac{98}{5} \\ x = 19.6\)
Answer: the answer would be x because that's the actual variable in the question then if 19.6 was not an option
Step-by-step explanation:
Out of 120 customers asked at a restaurant, 38 rounded their bill up to the next whole dollar and donated the difference to the local Children's Hospital. How many consecutive customers must round up the bills so that the percentage of people who donated increases to 50%?
A. 44 customers
B. 40 customers
C. 36 customers
D. 32 customers
Using proportions, it is found that 44 consecutive customers must round up the bills so that the percentage of people who donated increases to 50%, so option A is correct.
A proportion is the number of desired outcomes divided by the number of total outcomes.
Considering that 38 out of 120 customers rounded their bill up, with x customers added, the proportion will be of 38 + x out of 120 + x.
The desired proportion is 0.5, hence:
\(\frac{38 + x}{120 + x} = 0.5\)
\(38 + x = 60 + 0.5x\)
\(0.5x = 22\)
\(x = \frac{22}{0.5}\)
\(x = 44\)
44 customers, so option A.
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What is the meaning of \(r_{i-j}\)?
This expression \(r_{i-j}\) describes the distance between two points i and j in a geometric object
Explaining the meaning of the expressionIn the context of symmetry and rotations, \(r_{i-j}\) typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.
It is a vector that points from point i to point j, and its magnitude is the distance between the two points.
The distance vector \(r_{i-j}\) is also used to describe the position of a point in the crystal lattice relative to the rotation axis.
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Which real-life situation involves a linear function whose graph passes through the points? Y (0, 20) and x (4, 80)
A) the entrance fee to an amusement park is $15 and each book of ride tickets costs $20.
B) Jet ski rental costs $20 initially plus $15 for each hour.
C) Shoes are on a sale at a shoe store for $20 for the first pair and $17 for each additional pair.
D) You earn and deposit into a bank account money from chores at the rate of $20 per week.
Answer:
B) Jet ski rental costs $20 initially plus $15 for each hour.
Step-by-step explanation:
The equation of a line has the following format:
\(y = mx+b\)
In which m is the slope, which having two points on the line, is given by the change in y divided by the change in x, and b is the y-intercept, which is the value of y when \(x = 0\).
Passes through point Y (0, 20):
This means that \(b = 20\). So
\(y = mx+20\)
Slope:
Through points (0,20) and (4,80). So
Change in y: 80 - 20 = 60
Change in x: 4 - 0 = 4
Slope: 60/4 = 15
So
\(y = 15x+20\)
Situation:
We want a situation in which we have a fixed fee of 20, and then for each unit of time or of the product, and increase of 15. So the correct option is B
Which of the following would you see on a circle graph?
OA. Percentages
OB. Bars
C. Points
OD. A y-axis
A, percentages
You would see percentages on a circle graph, because it's how many parts of the whole that they take up.
Happy to help, have a great day! :)
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Answer:
b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2
c)CI 95 % = ( 0.00002 ; 0.09998)
Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.
Recent Sample
Sample size n₁ = 1000
Number of events of people with financial fitness more than fair
x₁ = 410
p₁ = 410/ 1000 = 0.4 then q₁ = 1 - p₁ q₁ = 1 - 0.4 q₁ = 0.6
Sample a year ago
Sample size n₂ = 1200
Number of events of people with financial fitness more than fair
x₂ = 420
p₂ = 420/1200 p₂ = 0.35 q₂ = 1 - p₂ q₂ = 1 - 0.35 q₂ = 0.65
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
CI 95 % then significance level α = 5% α = 0.05 α/2 = 0.025
To calculate p-value:
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ 0.4*0.6/1000 + 0.65*0.35/1200
SE = √ 0.00024 + 0.000189
SE = 0.021
z(s) = ( p₁ - p₂ ) / SE
z(s) = ( 0.4 - 0.35 )/0.021
z(s) = 0.05/ 0.021
z(s) = 2.38
We find p-value from z-table to be p-value = 0.00842
Comparing
p-value with α/2 = 0.025
α/2 > p-value
Then z(s) is in the rejection region for H₀. We reject H₀
CI 95 % = ( p₁ - p₂ ) ± 2.38*SE
CI 95 % = ( 0.05 ± 2.38*0.021 )
CI 95 % = ( 0.05 ± 0.04998)
CI 95 % = ( 0.00002 ; 0.09998)
CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate
the pic the pic this is it
Answer:
yes I agree with you
Step-by-step explanation:
thanks for the free question
Answer: mmmmmm Otae?
Step-by-step explanation:
Caleb is saving money to buy a bike next year. So far he has saved $150. Write an inequality to show how much he needs to
save each month for the next year so he has at least $800 to spend on the bike, then solve the inequality
A bakery sold a total of 120 cupcakes in a day, and 66 of them were mocha flavored.
What percentage of cupcakes sold that day were mocha flavored?
Answer:
55%
Step-by-step explanation:
55% of the cupcakes were mocha flavored.
Exactly 10% of the students in a school are left-handed. Select 15 students at random from the school and define W = the number who are left-handed.
a. yes
b. no
c. unsure
The statement is true , that the given sample follows binomial distribution.
If a random variable has two alternative outcomes (success or failure), it has a binomial distribution.
Each draw must be separate from the ones that came before it.
There is a set number of drawn components.
We randomly select 15 students, and since the sample size of 15 is less than 10% of the total population, we can assume that each draw is independent.
Because X has a binomial distribution, success is determined by whether the student is left-handed (failure is determined by whether the student is not left-handed).
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for success or failure as the possible outcomes of an experiment.
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The graph of a quadratic function with vertex (4, 2) is
Find the range and the domain.
Write the range and domain using interval notation.
For the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
As given in the question,
For the given graph of quadratic function ,
Given graph represents the parabola.
Standard equation of the parabola with vertex ( h, k) is given by,
y = a ( x - h )² + k
Substitute the value ( h ,k ) = ( 4, 2 )
y = a ( x - 4 )² + 2
As it is a parabola in the first quadrant and faces in the upward direction,
Value of x tends to -∞ to ∞
Domain = ( -∞ , ∞ )
Minimum value of y coordinate is 2 and increases to ∞.
Range = ( 2, ∞ )
Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
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The model shown below is a perfect cube with a volume of 27 cubic units. Which statement is true about all perfect cubes?
A. A perfect cube represents 3 times the area of a face of the cube.
B. A perfect cube represents the sum of 9 edge lengths of the cube.
C. A perfect cube represents the volume of a cube with equal integer side lengths.
D. A perfect cube represents the surface area of a cube with equal integer side lengths.
The correct statement which is true about all perfect cubes is,
⇒ A perfect cube represents 3 times the area of a face of the cube.
We have to given that;
The model shown below is a perfect cube with a volume of 27 cubic units.
Now, We can formulate;
⇒ V = 27 cubic units.
⇒ V = 3 × 9 cubic units.
⇒ V = 3 × 3² cubic units.
Thus, The correct statement which is true about all perfect cubes is,
⇒ A perfect cube represents 3 times the area of a face of the cube.
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What is 20% of 50 apples
Answer:
10
Step-by-step explanation:
Answer:
10 apples
Step-by-step explanation:
20% of 50 = 10
10 apples
Write an expression that represents the perimeter of the equilateral triangle
Answer:
P = 3s where "s" is the measure of a side.
Step-by-step explanation:
Perimeter of a equilateral triangle is s + s + s or 3s because all sides are equal.
Let s = a side and there are three equal sides in an equilateral triangle.
P = 3s
How many ways can 12 DVDs be arranged on a shelf?
.
Answer:
12!
Step-by-step explanation:
А=12*11*10*9*8*7*6*5*4*3*2*1=12!=479001600
Determine the height of the can of beans(cylinder) given the volume of the
can is 314 in and a radius :of 5 inches. Round to the nearest whole inch.
a. 4 in
b. 20 in
c. 500 in
d. 5 in
Answer:
4 in(a)
Step-by-step explanation:
height-?
volume-314
radius-5
pie-22÷7 or 3.14
volume= πrsquared h
314=3.14×5×5×h
314= 78.5h
314÷78.5
= 4 in
Lara grows apples in her orchard and sells them at the weekly farmer's market. Each week, she sells the apples for a different price and records the number of apples sold. The scatter plict below
shows the price of one apple and the number of apples that were sold. A line of best fit for these data points, the equation y=-z+32, is also shown on the plot
Apples Number of Apples Sold
A computer is priced $500 but is on sale for 30% off. What is the sale price of the computer
Answer: $350.00
Step-by-step explanation:
Answer:
$350
Step-by-step explanation:
if the sale is 30% we have to find what is 30% of 500 so we can subtracted from what we pay .
line up what you know:
$500 represents 100%
$x represents 30 %
cross multiply
x*100 = 500* 30 ; divide both sides by 100
x= 500*30 /100 = 150
the sale price is 500-150= $350
For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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-60 Minutes (8.44) -40 (4,22) -20 Miles 2 6 8. what is the constant of proportionality?
You have the following points for the relation between minutes and miles respectively:
(4 , 22)
(8, 44)
In order to calculate the constant of porportionality use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are the given points:
m = (44 - 22)/(8 - 4)
m = 22/4
m = 5.5
Hence, the constant of proportionality is 5.5
THe meaning of the point (4 , 22) is:
4 means 4 miles and 22 means 22 minutes. That is, it has been traveled 4 miles in 22 minutes.
A rectangular cement patio with a length of 5X and a width of 3X has been constructed in Santa rectangular field that has a length of 12 X and a width of 7X what is the area of the field that is not cement patio
The area of the rectangular field that is not cement patio is 28x² square units
How to determine the areaIt is important to note that the formula for determining the area of a rectangle is expressed as;
A = lw
Where;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Length of the cement patio = 5x
Width of the cement patio = 3x
Total length of the rectangular field = 12x
Total width of the rectangular field = 7x
Then,
Length of the non- cement patio = 12x - 5x = 7x
Width of the non- cement patio = 7x - 3x = 4x
Now, substitute the values into the formula for area
Area = 7x (4x)
multiply the values
Area = 28x² square units
Hence, the value is 28x² square units
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4.
Zuber is a rideshare company that you and your friends decide to hire to go to Navy Pier. The $20
cost is shared equally by your group of r people. If there is one less person in the group then each
of the remaining people has to pay $1 more. What is x?
a. -4
C. 5
b. 0
d. 20
Answer: 20
Step-by-step explanation:
Weekly wages at a certain factory are normally distributed with a mean of 400 dollars and a standard deviation of 50 dollars. Find the probability that a worker selected at random makes between 400 dollars and 550 dollars.
49.87% is the probability that a worker selected at random makes between 400 dollars and 550 dollars.
To find the probability that a worker selected at random makes between $400 and $550, we can use the properties of the normal distribution.
Given that the weekly wages are normally distributed with a mean (μ) of $400 and a standard deviation (σ) of $50, we can use these parameters to standardize the values and then find the corresponding probabilities.
To standardize the values, we use the z-score formula:
z = (x - μ) / σ
where x is the value we want to find the probability for.
For $400:
z1 = (400 - 400) / 50 = 0
For $550:
z2 = (550 - 400) / 50 = 3
Now, we can use the standard normal distribution table or a calculator to find the probabilities associated with these z-scores.
The probability of a worker making less than or equal to $400 is the same as the probability of z1 or less, which is P(z ≤ 0). From the standard normal distribution table, we find that P(z ≤ 0) is approximately 0.5.
The probability of a worker making less than or equal to $550 is the same as the probability of z2 or less, which is P(z ≤ 3). From the standard normal distribution table, we find that P(z ≤ 3) is approximately 0.9987.
Therefore, the probability that a worker selected at random makes between $400 and $550 is the difference between these two probabilities:
P(400 ≤ x ≤ 550) = P(z ≤ 3) - P(z ≤ 0) ≈ 0.9987 - 0.5 ≈ 0.4987
So, the probability is approximately 0.4987 or 49.87%.
Using the z-score, we transformed the values into a standard normal distribution, looked up the probabilities associated with the z-scores from a standard normal distribution table, and found the difference in probabilities to determine the probability of the worker's wage falling between $400 and $550.
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70 adults with gum disease were asked the number of
times per week they used to floss before their
diagnoses. The (incomplete) results are shown below:
# of
times
floss
per
week
0
1
2
3
4
5
6
7
4
11
15
11
6
7
(6 is blank)
6
Relative
Frequency
(4 is blank)
0.1571
0.1429
0.2143
0.1571
0.0857
0.1
0.1429
0.0857
Cumulative
Frequency
4
15
30
41
47
(5 is blank)
64
70
a. Complete the table (Use 4 decimal places when
applicable)
b. What is the cumulative relative frequency for
flossing 3 times per week?
%
The cumulative relative frequency for flossing 3 times per week is 58.57%.
How to solvea. Let's complete the table.
We can calculate the missing relative frequency for 0 times flossing per week by dividing the frequency (4) by the total number of people (70).
Relative Frequency for 0 times flossing = 4/70 = 0.0571 (rounded to 4 decimal places)
For 6 times flossing per week, the frequency is missing.
We can calculate it by summing up the frequencies for all other days and subtracting that from the total number of people.
Missing frequency for 6 times flossing = 70 - (4 + 11 + 15 + 11 + 6 + 7 + 6) = 70 - 60 = 10
Now, let's calculate the cumulative frequency for 5 times flossing per week.
Cumulative Frequency for 5 times flossing = Cumulative Frequency for 4 times flossing + Frequency for 5 times flossing = 47 + 7 = 54
The completed table looks like this:
of times floss per week | Frequency | Relative Frequency | Cumulative Frequency
0 | 4 | 0.0571 | 4
1 | 11 | 0.1571 | 15
2 | 15 | 0.2143 | 30
3 | 11 | 0.1571 | 41
4 | 6 | 0.0857 | 47
5 | 7 | 0.1 | 54
6 | 10 | 0.1429 | 64
7 | 6 | 0.0857 | 70
b. The cumulative relative frequency for flossing 3 times per week is the cumulative frequency for 3 times flossing divided by the total number of people (70).
Cumulative Relative Frequency for 3 times flossing = Cumulative Frequency for 3 times flossing / Total number of people = 41 / 70 = 0.5857 (rounded to 4 decimal places)
The cumulative relative frequency for flossing 3 times per week is 58.57%.
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I need help Chad hired you to help him mow someone’s lawn. Draw a picture of
the lawn that you mowed. Make sure to label the lengths of all sides of the lawn. In
the space below, write equations to show how you found the area and perimeter of
the lawn.
The lawn must meet the following specifications:
The area is greater than 100 square feet but less than 250 square feet.
The shape is irregular (not a square or rectangle.)
Scale: 1 box = 1 square foot
Show your work in the chart below.
Answer: I don't have the ability to create and insert images or charts. However, I can provide instructions on how to draw a diagram and write the equations for the area and perimeter of the lawn based on the given specifications.
To draw the diagram, start by sketching an irregular shape that meets the given specifications. Label the lengths of all sides of the lawn using the scale of 1 box = 1 square foot. For example, if one side of the lawn is 8 feet long, label it as 8 boxes.
Once you have drawn the diagram and labeled the lengths of all sides of the lawn, you can use the following equations to find the area and perimeter of the lawn:
To find the area of the lawn, use the formula for the area of an irregular shape, which involves dividing the shape into smaller, simpler shapes and adding their areas together. For example, you could divide the lawn into a rectangle and a triangle and then use the following formula:
Area = Area of rectangle + Area of triangle
Area of rectangle = length x width
Area of triangle = 1/2 x base x height
To find the perimeter of the lawn, add up the lengths of all the sides of the lawn. For example:
Perimeter = length of side 1 + length of side 2 + length of side 3 + ... + length of last side
Make sure to substitute the appropriate values into the equations and simplify your answers.
Step-by-step explanation:
Find the length of the missing side of these right triangles?
Answer: they are uneven
Step-by-step explanation: the 30 has to be 15 on each side and the 16 stays the same
find the equation of the line. Use exact numbers
y= ( )x + ( )
Answer:
y = 3/4x - 2
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlgebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSlope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)
Step-by-step explanation:
Step 1: Define points
Find some points from the graph.
y-intercept (0, -2)
Point (-4, -5)
Step 2: Find slope m
Substitute: \(m=\frac{-5+2}{-4-0}\)Add/Subtract: \(m=\frac{-3}{-4}\)Simplify: \(m=\frac{3}{4}\)Step 3: Write linear equation
y = 3/4x - 2
please answer? options for the second box: (there is no solution) (there is one solution) (there is two solution)
Solution
We are given
\(y=4x^2+15x-4\)Here
\(\begin{gathered} a=4 \\ b=15 \\ c=-4 \end{gathered}\)The discriminant D is
\(\begin{gathered} D=b^2-4ac \\ D=15^2-4(4)(-4) \\ D=225+64 \\ D=289 \end{gathered}\)Since, the discriminant is positive, we have two x- intercept
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4 is the clope of the line
Step-by-step explanation:
a slope is just a rise ofver run from one dot to anothor so you go up 1 and over 4 and if you dont do the 2 dots that are closest to each other you have to simplify you r exspresion you will always get 1/4 on this graph
I NEED HELP STAT
=12×0.75
Answer:
9
Step-by-step explanation:
use a calculator of just think about it
Answer:
9.00
Step-by-step explanation: