The Diameter of the cube would be 3 inches
What is Variation?
A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.
Solution:
We know that,
Horse Power is directly proportional to RPM * Diameter
So, we can write
Horse Power = k * RPM * Diameter
here, k is any constant
From the first case given, we can find the value of k
16 = k * 2 * 120
k = 1/15
Putting the value of k in second case,
30 = 1/15 * 150 * Diameter
Diameter = 3 inches
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Consider the following table.
x y
5 0
-1 6
0 5
-3 8
4 1
Which graph corresponds to this table?
Answer:_______________________________
a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = -7.44.
b) The p-value is: < 0.0001.
c) The conclusion is that the null hypothesis is rejected.
d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.
What are the features of the test and how does it relates to the hypothesis?From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:
Test statistic: t = -7.44.P-value: < 0.0001.The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.
Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.
Missing InformationThe pop-ups with the information of the test are given by the image at the end of the answer.
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What is the y-intercept of a line that has a slope of and passes through point (8, 3)?
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The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).
what is the slope-intercept?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
The slope-intercept form: y = mx + b
m - a slope
b - y-intercept
Here, we have
A slope m = 1/4.
Substitute: y = 1/4 x + b
We know that
the line passes through the point (8, 3) → x = 8, y = 3.
Put the values of x and y into the slope of the line:
1/4 · 8 + b = 3
2 + b = 3 |-2
b = 1
Hence, the y-intercept is (0, 1)
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A school is arranging a field trip to the zoo. The school spends 654.84 dollars on passes for 32 students and 2 teachers. The school also spends 281.92 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The money was spent on a pass and lunch for each student is $28.07
How to calculate the amount?It was stated that the the school spends 654.84 dollars on passes for 32 students and 2 teachers while the school also spends 281.92 dollars on lunch for just the students.
Therefore the amount spent on pass will be:
= Total amount / Number of people
= 654.84 / 34
= 19.26
The amount spent on each student will be:
= 281.92 / 32
= 8.81
The amount spent in pass and lunch will be:
= 19.26 + 8.81
= $28.07
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What is the unit rate of the table y = -4x + 2
The unit rate of the equation y = -4x + 2 is -4
How to determine the unit rate?From the question, we have the following equation
y = -4x + 2
The above equation is a linear equation
Linear equations are represented as
y = mx + c
Where
Unit rate = mY-intercept = cWhen the equations y = mx + c and y = -4x + 2 are compared, we have
Unit rate, m = -4
Y-intercept, c = 2
Note that all linear equations have a constant rate of change
Hence, the unit rate in the linear equation is -4
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Help me with these 2
1) y = 3x+2, where slope is 3 and point is(3, -5).
2) y+6 = 4(x-5) is the equation for the given slope and point.
The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,y = mx + b
The slope of a line can be calculated using two points lying on the straight line. Given the coordinates of the two points, we can apply the slope of line formula.Slope = m = tan θ = (y2 - y1)/(x2 - x1)
1) y + 5 = 3(x-1)x-x
Compare this equation to y - y₁ = m(x - x₁)
y = 3x - 3 + 5
y = 3x + 2
2) Given:
Slope = 4; point (5, -6)
y - y₁ = m(x - x₁)
y + 6 = 4(x -5 )
Option A
Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.
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I can't do math so I need someone to help me. what's the answer?
The value of TV for the similar triangles is 25
What are similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
Similar triangles are not the same as congruent triangles though.
triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.
Let UV = p, it means also that WV = P. which means WU = 2p
so since the two triangles are similar, the ratio of their corresponding lengths are equal
meaning,
UV/UW = TV/XW
substituting their values, we have
p/2p = TV/50
by cross multiplying,
2p x TV = 50p
2TV = 50
TV = 50/2 = 25
In conclusion, the value of TV is half the value of WX = 25
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Graph the polygon with the given vertices and its image after a reflection in the line y = -x .
A(2, 0), B(3, 4), C(6, 4), D(5, 0)
As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.
Transformation:
Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.
Given,
Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.
Now we have to plot the graph with the given vertices and its image after a reflection in the line y = -x .
Here reflection refers flipping of a figure.
Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)
For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:
A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)
The image of the polygon is attached below.
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In the fall of 2017, there were 48 thousand more female undergraduate students enrolled at a college than male
undergraduate students. If the total undergraduate enrollment was 414 thousand that fall, find the numbers of female
undergraduate students and male undergraduate students who were enrolled.
The number of female undergraduate students was
thousand.
Answer: 231 thousand
Step-by-step explanation:
given,
total number of undergraduate students enrolled = 414000
let us take number of total number of male students as, X
then, total number of female students will be X + 48000
now we get,
total number of male students + total number of female students = total number of students enrolled.
X + (X + 48000) = 414000
X + X + 48000 = 414000
2X = 414000 - 48000
X = 366000/2
X = 183000
total number of male students is 183000
total number of female students is
X + 48000
183000 + 48000 = 231000
v+8w=4v,for v
-m+5n=-2, for n
Answer:
v = 8w/3,n = (m - 2)/5.---------------------------
Given equationsv + 8w = 4v and - m + 5n = - 2Solve the first equation for vv + 8w = 4v4v - v = 8w3v = 8wv = 8w/3Solve the second equation for n- m + 5n = - 25n = m - 2n = (m - 2)/5Answer:
Value of v = (8w)/3Value of n = (m - 2)/5Step-by-step explanation:
1) v + 8w = 4v, for v?
→ v + 8w = 4v
→ 8w = 4v - v
→ 8w = 3v
→ [ v = (8w)/3 ]
Thus, value is (8w)/3.
2) -m + 5n = -2, for n?
→ -m + 5n = -2
→ 5n = -2 + m
→ 5n = m - 2
→ [ n = (m - 2)/5 ]
Thus, value is (m - 2)/5.
NEED HELP ASAPPPPPPPP
1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4. The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.
2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.
Complete sentence:
1) The formula for the number of shaded squares in the Nth figure is n+n-1.
2) There would be 99 shaded squares in the 50th figure.
explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.
What is an equation of the line that passes through the points (4, -2)(4,−2) and (8, 3)(8,3)
The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given pair of points are (4,−2) and (8, 3).
The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,
y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁
Substitute the respective values to get the equation of line as,
y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)
y = ((x - 4 ) / 4) × 5 - 2
4(y + 2) = 5(x - 4)
4y - 5x + 28 = 0
Hence, the equation of line for the given points is 4y - 5x + 28 = 0.
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I NEED HELP ASAP PLS!!
Answer:
7.8
Step-by-step explanation:
Switch 8 and 7, it round to 8 and end in tenths.
Answer:
7.8
Step-by-step explanation:
7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.
|y + 4| < 1
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.
What is an inequality?An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:
Greater than or equal to (≥).Less than or equal to (≤).Greater than (>).Less than (<).Adding -1 to both sides of the inequality, we have:
|y + 4| + (-1) < 1 + (-1)
|y + 4| - 1 < 0
Evaluating the absolute value function, we have the following:
y + 4 < ±1
For the positive interval, we have:
y < -4 + 1
y < -3
For the negative interval, we have:
y < -4 - 1
y < -5
Finally, we would express the solution to this inequality as an interval as follows:
-5 < y < -3.
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Complete Question:
What is a solution to this inequality |y + 4| < 1?
A. −5 < y < –3
B. –3 < y < 5
C. –4 < y < 1
D. 1 < y < 4
The graph below shows the relationship between the number of ounces and the number of calories in steak.
Which equation best represents this relationship?
Responses
Answer:
??
Step-by-step explanation:
where are the equations ?
Answer:
Step-by-step explanation:
In the first hour Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, the sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes. How many did they sell?
The number of cupcakes sold will be 4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.
The number of cupcakes sold will be,
N = (1/3) + (3/8) +[(2-1/3-3/8)]+3
N = (1/3)+(3/8) + (7/24)
N = 96 / 24
N = 4
Therefore, the number of cupcakes sold will be 4.
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In 2012, 1,664,479 students took the SAT exam. The distribution
of scores in the verbal section of the SAT had a mean μ = 496 and a
standard deviation of o= 114.
Let X = a SAT exam verbal score section for 2012.
Then X-N (496, 114)
Find the z-scores for x1 = 325 and x2= 366.21.
Interpret each z-score.
What can you say about the x1= 325 and the x2= 366.21?
By using normal distribution of probability, it can be inferred that
For [tex]x_1 = 325[/tex], z = -1.5
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex], z = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-
[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]
where [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
For [tex]x_1 = 325[/tex]
[tex]z = \frac{325 - 496}{114} = -1.5[/tex]
This means 325 is 1.5 standard deviation below the mean.
For [tex]x_2 = 366.21[/tex]
[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385
This means 366.21 is 1.1385 standard deviation below the mean.
[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.
[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.
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What is the function rule for the line?
f (x) = 2x - 4
f(x)=-4x - 2
f(x) = 4x - 2
f (x)= -2x + 4
Answer: f (x)= -2x + 4
15. Mohammed has $8376 in his bank account. In the next month he takes out $4595 to buy a car. He then buys some new tires for his car for $1200. The next day, he receives his salary of $2709 in his bank account. How much is in his account at the end of the month?
By doing addition and subtraction of integers, the result obtained is
Mohammed had $5290 at the end of the month
What is addition and subtraction of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.
To find how big or small one integer is from the other, then the operation used is called subtraction of integers.
Here we will use addition and subtraction of integers
Bank balance of Mohammed = $8376
Amount of money taken out by Mohammed next month to buy a car = $4595
Amount of money needed to buy new tires for his car = $1200
Amount of salary received by Mohammed next day = $2709
Amount of money Mohammed had at the end of the month =
$(8376 - 4595 - 1200 + 2709)
= $5290
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what is the answer for -1/5x + 4 < 39
solution: [tex]x > -175[/tex]
interval notation: (-175, ∞)
explanation:
[tex]-\frac{1}{5}x + 4 < 39\\[/tex]
Subtract 4 from both sides
[tex]-\frac{1}{5}x +4-4 < 39-4\\[/tex]
Simplify
[tex]-\frac{1}{5}x < 35[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex](-\frac{1}{5}x )(-1) > 35(-1)[/tex]
Simplify
[tex]\frac{1}{5}x > -35\\[/tex]
Multiply both sides by 5
[tex]5[/tex] ·[tex]\frac{1}{5}x > 5(-35)[/tex]
Simplify
[tex]x > -175[/tex]
Classify the following number: 5√2. Choose all that apply.
Answer:
Real, Irrational
Step-by-step explanation:
5sqrt2 is NOT:
Natural (1,2,3...)
Whole (0,1,2,3...)
Integer (...-3,-2,-1,0,1,2,3...)
Rational (can be written like a ratio)
Imaginary (have the number i in it.)
It IS Irrational, will have neverending decimal with no repeating pattern.
5sqrt2 = 7.0710678119...
It IS REAL and IRRATIONAL.
Aim: How can you earn money with a Savings Account?
Exit Ticket #5 Simple Interest
Find the simple interest on a $2,350 principal
deposited for 6 years at a rate of 2.77%
I =
P =
t =
I = prt
I=( )( )( )
Answer:
I = (2350)(0.0277)(6)
Step-by-step explanation:
We're told the principal, rate, and time so we just plug in.
We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277
Given: Gross sales, $170,000; sales returns and allowances, $9,000; beginning inventory, $8,000; net purchases, $18,000; ending inventory, $5,000; and operating expenses, $56,000. a. Calculate net sales. b. Calculate cost of merchandise (goods) sold. c. Calculate gross profit from sales. d. Calculate net income.
The calculation of the following income statement figures are as follows:
a) Net Sales are $161,000.b) Cost of goods sold is $21,000.c) The gross profit from sales is $140,000.d) The net income is $84,000.What is the income statement?The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.
One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.
The other profit points include the operating income, income before tax, and net income.
Income StatementGross sales $170,000
Sales returns and allowances 9,000
Net Sales $161,000
Cost of goods sold:
Beginning inventory $8,000
Net purchases 18,000
Ending inventory (5,000) $21,000
Gross profit $140,000
Operating expenses (56,000)
Net Income $84,000
Thus, the calculation of the income statement figures shows a net income of $84,000.
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Please help :(
Solve each equation for x. Show all steps.
1) log base4 (x^2 -12x+48) =2
2) 27^(4x-6) = (1/9)^(2x-7)
The values of x in the equations are as follows:
1. x = 8 or 4
2. x = 2
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, let's solve the equation as follows:
log₄ x² - 12x + 48 = 2
using law of logarithm
4² = x² - 12x + 48
16 = x² - 12x + 48
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
x² - 4x - 8x + 32 = 0
x(x - 4) - 8(x - 4) = 0
(x - 8)(x - 4) = 0
Therefore,
x = 8 or x = 4
[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]
[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]
[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]
[tex]3^{12x-18} =3^{-4x+14}[/tex]
Cancel the base
Therefore,
12x - 18 = - 4x + 14
12x + 4x = 14 + 18
16x = 32
x = 32 / 16
x = 2
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I dont understand, please help
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
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Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 20 years?
The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20
How to find the value of money?When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.
If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.
In 20 years therefore, the value of $100 would be:
Value in 20 years = Value today x (1 - inflation rate) ^ number of years
= 100 x (1 - 4%) ²⁰
= $44.20
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2x=9 what is the value of x
Answer:
The answer is x=4.5
Step-by-step explanation:
I hope this helps
Tell which number is greater 3/8,30
Answer:
30
Step-by-step explanation:
3/8 is less than 1.
30 is much greater than 1.
Answer: 30
Answer:30 is greater
Step-by-step explanation:
What is the sum?
3
+
x+3x+3x+3
X
2
Put these numbers in order from smallest to largest.
Smallest
-75
-28
-3
13
103
341
619
Largest
Answer:
Step-by-step explanation:
Here by using the ascending property:
-75, -28, -3, 13, 103, 341, 619