A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. What is the probability of rolling a 6?
Answer:
the probability of rolling a 6 is 1/6
Step-by-step explanation:
because there are six possible outcomes and it is a fair die, each outcome must be equally as likely, therefore there is a 1/6 chance of rolling any number.
Write an inequality for the statement: negative one half is a minimum of the product of a number and negative five sixths.
N × (-5/6) ≥ -1/2 is the inequality for the statement
How to write an inequality for the statement?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given the statement: negative one half is a minimum of the product of a number and negative five sixths.
This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half
Let N represent the number. Thus, the inequality of the statement is:
N × (-5/6) ≥ -1/2
Note: The symbol ≥ is pronounced as greater than or equal to
Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2
Learn more about inequality on:
https://brainly.com/question/25275758
#SPJ1
FIND THE SLOPE OF YHE LINE
HURRYYY
The slope of given line is 43
The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.
The formula of finding the slope of line with two given points is as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1
It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43
Hence,the slope of the give line is 43
To learn more about slope of line visit the be
brainly.com/question/3493733
#SPJ1
Solve the equation below for x
Cx — 4 = 7
The equation for the value of x will be 11/C.
According to the question,
We have the following equation:
Cx — 4 = 7
Now, we can easily find the value of x from this equation by following the given steps.
We will first add 4 on both sides of the equation:
Cx = 7+4
Adding the two numbers on the right hand side:
Cx = 11
Dividing by C on both sides of the equation:
x = 11/C
(More to know: we can now find the value of x if the value of C is given.)
Hence, the equation for the value of x will be 11/C.
To know more about equation here
https://brainly.com/question/3162971
#SPJ1
rearrange the perimeter forumula for a rectangle to find the width.
P=2w+ 2l
The width of the rectangle is given as w = p/2 - l which is derived from perimeter of rectangle
Perimeter of RectangleThe perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
In this question, we simply need to make the width (w) the subject of formula.
The equation given is
p = 2w + 2l
p = perimeter of rectanglew = width l = lengthp = 2w + 2l
p = 2(w + l)
p / 2 = w + l
w = p/2 - l
learn more on perimeter of rectangle here;
https://brainly.com/question/19819849
#SPJ1
Find all zeros of f(x) = x³ - 4x² - 5x + 14. Enter the zeros separated by commas. Enter exact values,
using radicals and/or fractions if necessary, not decimal approximations.
Question Help: Message instructor
Check Answer
Jump to Answer
Answer: x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
f(x) = x³ - 4x² - 5x + 14
-2 | 1 -4 -5 14
-2 12 -14
1 -6 7 0
x³ - 4x² - 5x + 14 = (x+2)(x²-6x+7)
x²-6x+7=0
x²-6x+9-2=0
(x²-6x+9)-2=0
x²-6x+9=2
x²-3x-3x+9=2
x(x-3)-3(x-3)=2
(x-3)²=2
x-3=[tex]\sqrt{2}[/tex], -[tex]\sqrt{2}[/tex]
x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Hence, zeroes are x=-2, x=3+[tex]\sqrt{2}[/tex], 3-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
our first "suspicion" for a factoring is an integer factor of the constant term : 14.
14 = 2 × 7 or -2 × -7
I started to try 2 or -2 and found that -2 is indeed a zero solution.
so, the first factors are
f(x) = (x + 2)(x² + ...)
let's divide (x³ - 4x² - 5x + 14) by (x + 2) to get the x² term.
x³ - 4x² - 5x + 14 ÷ x + 2 = x² - 6x + 7
- x³ + 2x²
--------------
0 -6x² - 5x
- -6x² - 12x
----------------
0 7x + 14
- 7x + 14
------------
0 0
f(x) = (x + 2)(x² - 6x + 7)
the zeros for x² - 6x + 7 we get from the general solution for a quadratic equation
ax² + bx + c = 0
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (6 ± sqrt((-6)² - 4×1×7))/(2×1) =
= (6 ± sqrt(36 - 28))/2 = (6 ± sqrt(8))/2 =
= 3 ± sqrt(8/4) = 3 ± sqrt(2)
x1 = 3 + sqrt(2)
x2 = 3 - sqrt(2)
so, the zeros are
-2, 3 - sqrt(2), 3 + sqrt(2)
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 5.8 pounds/square inch (psi). Assume the population standard deviation is 1.0. The engineer designed the valve such that it would produce a mean pressure of 6.0 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
The value of the test statistic when the engineer has designed a valve is -2.83.
How to calculate the test statistic?From the information, the following can be deduced:
Sample mean = 5.8
Population mean = 6.0
Population standard deviation = 1
Significance level = 0.02
(Sample mean - Population mean) /(Standard Deviation / ✓200)
= (5.8 - 6.0) / (1 / ✓200)
= -0.2 ✓200
= -2.83
The value is -2.83.
It's important to note that the test statistic is the z value. This will be:
=
Learn more about test statistic on:
brainly.com/question/15110538
#SPJ1
which is the correct answer ?????
Explanation:
Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.
The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.
If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.
You want to be able to withdraw $20,000 each year for 20 years. Your account earns 9% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?
a) The amount of money in the account at the beginning is $222,222.222.
b) The total amount of money withdrawn from the account is $400,000.
c) The amount of interest earned is $177,777.778.
It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".
A = $20,000*20 = $400,000
Let the amount of money in the account at the beginning be represented by the variable "P".
A = P*R*T
400,000 = P*0.09*20
400,000 = P*1.8
P = 222,222.222
The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".
I = A - P = $400,000 - $222,222.222 = $177,777.778
To learn more about interest, visit :
https://brainly.com/question/22621039
#SPJ1
Pahelpppp po pang grade 6 po yan na math
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ. Match each angle of rotation to the
point that A' (the image of A) coincides with after that rotation.
252°
108°
135°
180°
288°
324°
A0DO
D after three rotations: 3 × 36° = 108°
F after five rotations: 5 × 36° = 180°
H after seven rotations: 7 × 36° = 252°
I after eight rotations: 8 × 36° = 288°
Given,
In the question:
ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A'B'C'D'E'F G'HIJ.
To find the each angle of rotation to the point A' coincides with after that rotation.
Now, According to the question:
let's know about Decagon:
A decagon is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. A self-intersecting regular decagon is known as a decagram.
Every regular polygon with n sides can be divided into n congruent triangles. The angle with vertex the center of the polygon will measure
360 : n degrees. We are given a regular decagon, therefore:
n = 10
α = 360 : n = 36°
We consider that, if the decagon is not rotated, A' coincides with A and the rotation is towards the next letter of the alphabet. This means that after one rotation of 36° A' will coincide with B, after two rotations A' will coincide with C and so on.
A' will coincide with D after three rotations: 3 × 36° = 108°
A' will coincide with F after five rotations: 5 × 36° = 180°
A' will coincide with H after seven rotations: 7 × 36° = 252°
A' will coincide with I after eight rotations: 8 × 36° = 288°
Learn more about Angle Rotation at:
https://brainly.com/question/14380185
#SPJ1
find the missing angle measures
a=b
b=(b+16)
c=(2b)
Answer:
a = 41°
b = 57°
c = 82°
Step-by-step explanation:
all angles in a triangle must add up to equal 180°
so 4b + 16 = 180180 - 16 = 4b164 = 4b164 / 4 = 41b = 41°therefore a = 41°, b = (41 + 16) --> 57°, and c = 2(41) = 82°(MARKING BRAINLIEST) Sam works as a salesman and earns 5.5% commission on everything he sells if Sam sells a television for $1200 how much commission will he earn ?
Answer:
$66
Explanation:
Sam earns a 5.5% commission on everything he sells. He sells a television for $1200. What is 5.5% of $1200?
Convert 5.5% to decimal form: 0.055. Now, multiply 1200 by 0.055.
Sam will earn $66 because 5.5% of 1200 is 66.
Find the rectangular equation for the plane curve defined by the parametric equation
x=t+4, y=t^2
-infinity < t < infinity
The rectangular equation for the plane curve defined by the parametric equation x = t + 4, y = t² is; y = x² - 8x + 16
What is the Rectangular Equation?We are given the parametric equations as;
x = t + 4
y = t²
Now, for us to convert parametric equations to a rectangular equation (cartesian equation) means that we are solving for t in terms of x and then plugging it back into the y equation. Therefore, we have;
x = t + 4
t = x - 4
Thus;
y = (x - 4)²
Expanding this gives;
y = x² -4x - 4x + 16
y = x² - 8x + 16
Read more about Rectangular Equation at; https://brainly.com/question/27115097
#SPJ1
Which function represents the graph of f (x) = -3 |x| after it is translated 5 units down?
The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5
How to find the function of the graph ?
To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.
As it is already given in the question that the function
f(x) = -3|x|
We will use transformation rules to solve the given question
f(x)→f(x-a) ⇒ Graph shifted to right by a units
f(x)→f(x+a) ⇒ Graph shifted to left by a units
f(x)→f(x) - a ⇒ Graph shifted downwards by a units
f(x)→f(x) + a ⇒ Graph shifted upwards by a units
When it is translated 5 units down
Then we subtract 5 outside of the given function
∴ f(x) = -3 |x| - 5
To learn more about finding the function of the graph from the given link
https://brainly.com/question/7224793
#SPJ1
One card is drawn from a well-shuffled deck of fifty-two cards (no jokers).
(a) Find the probability of drawing a card below a 6 (count an ace as high). (Enter your answer as a fraction.)
(b) Find the odds of drawing a card below a 6 (count an ace as high).
(c) Use the Law of Large Numbers to interpret both the probability and the odds of drawing a card below a 6 (count an ace as high).
(Refer to the picture attached for answer choices)
Probability of drawing a card below a 6 (count an ace as high) is 4/13
Total number of outcome : n(S) = 52
(a) In a deck number of card below a 6 (counting ace as high) is {5 , 4 , 3, 2}
so , n(E) = 4 × 4 = 16
The probability of drawing a card below a 6 (count an ace as high) = P(E)
[tex]P(E) =\frac{n(E)}{n(s)}[/tex] =16/52
P(E) = 4/13
(b) Probability of drawing a card below a 6 (count an ace as high) is 4/13
Hence , the odds of drawing a card below a 6 (count an ace as high). is 0.308
(c) we should expect to draw a card below a 6 about four times out of every 13 attempts .Also, we should expect to draw a card below or 6 four times for every nine times we draw a 6 or above is the law of large number to interpret both the probability and odds of drawing a card below 6
To know more about Deck of card here ,
https://brainly.com/question/9627169
#SPJ1
Fin the measurement of the angle
A=
B=
C=
D=
E=
F=
G=
45°
Answer:
Step-by-step explanation:
A=60
B=75
C=45
D=60
E=75
F=45
G=90
The table shows the outputs, y, for different inputs, x:
Input
(x) 5 6 7 8
Output
(y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer.
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7?
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?
A. Yes, the data justifies a function because there is no repeating x values.
B. The relation f(x) = 2x + 13 has a greater value at x = 7
C. The value of x when f(x) = 75 is; 31
How to Interpret Function Tables?A) The general formula for equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Slope is;
m = (y₂ - y₁)/(x₂ - x₁)
m = (5 - 2)/(6 - 5)
m = 3
Let us test the first coordinate;
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
B) When x = 7, we have;
y = 3(7) - 13
y = 21 - 13
y = 8
Let us now test for when f(x) = 2x + 13 to get;
f(x) = 2x + 13, when x = 7
f(7) = 2(7) + 13
f(7) = 14 + 13
f(7) = 27
the function has a greater value for f(x) = 2x + 13
C. f(x) = 2x + 13
when f(x) = 75
Thus;
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x
Read more about Function Table at; https://brainly.com/question/3632175
#SPJ1
I need help with solving problem.
Answer:
i can help but first what the questions and where are the options?
Step-by-step explanation:
In 2016 the cdc estimated the mean weight of us women over the age of 20 years was 168.5 pounds with a standard deviation of 68 pounds. What is the expected mean for a sample of 150 women
The expected mean for a sample of 150 women is 168.5 pounds.
What is expected mean?Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.
The formula for expected mean is :
E ( X ) = μ = ∑ x P ( x )
Where:
x = values of the random variable X
P(x) = Corresponding probability
∑ =Sum of all products xP(x)
μ = mean
Therefore the expected mean is 168.5 pounds.
Learn more about expected mean here: https://brainly.com/question/10675141
#SPJ1
Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 11 Answer
row 2 Answer
−3
Answer:
(1,3)
(4,-3)
Step-by-step explanation:
To find y, replace x with 1 in the equation and solve for y
6x + 3y = 15
6(1) + 3y = 15
6 + 3y = 15 Subtract 6 from both sides
3y = 9 Divide both sides by 3
y = 3
(1,3)
To find x, replace y with -3 in the equation and solve for x
6x + 3y = 15
6x + 3(-3) = 15
6x - 9 = 15 Add 9 to both sides
6x = 24 Divide both sides by 6
x = 4
(4, -3)
I need help answer please
I need help quick this assignment has to be turn in soon please and thanks
Answer:
Step-by-step explanation:
Solve the following facts. (Round to the nearest hundredth.) A. Current ratio _______________ B. Acid test __________________ C. Average day's collection ___________ D. Asset turnover _____________ E. Profit margin on sales _____________ Current Assets $ 18,000 Accounts Receivable 3,000 Current Liabilities 16,000 Inventory 2,000 Net Sales 41,000 Total Assets 29,000 Net Income 6,000
The solutions to the financial ratio requirements based on the supplied facts are:
A. Current ratio is 1.125.
B. Acid test is 1.
C. Average days' collection is 26.7 days.
D. Asset turnover is 1.4x.
E. Profit margin on sales is 14.63%.
What are financial ratios?Financial ratios are ratios that show the relative magnitude of one financial account to another.
Financial ratios are used to compare or represent an entity's financial performance or position in relative terms.
Current Ratio = Current Assets ÷ Current Liabilities
= $18,000 ÷ $16,000
= 1.125
Acid Test Ratio = (Current Assets - Inventory) ÷ Current Liabilities
= ($18,000 - 2,000) ÷ $16,000
= $16,000 ÷ $16,000
= 1
Average Days' Collection = Accounts Receivable ÷ Net Sales x 365 days
= $3,000 ÷ $41,000 x 365
= 26.7 days
Asset Turnover = Net Sales ÷ Total Assets
= $41,000 ÷ $29,000
= 1.4x
Profit Margin on Sales = Net Income ÷ Net Sales x 100
= $6,000 ÷ $41,000 x 100
= 14.63%
Current Assets = $18,000
Accounts Receivable = $3,000
Current Liabilities = $16,000
Inventory = $2,000
Net Sales = $41,000
Total Assets = $29,000
Net Income = $6,000
Learn more about financial ratios at https://brainly.com/question/9091091
#SPJ1
write -(1/4x1/4x1/4x1/4) using exponents
The solution to the mathematical expression -(1/4x1/4x1/4x1/4) in exponent form is [tex]\mathbf{-4^{-4}}[/tex]
Writing mathematical expressions in exponents formNumber multiplication is a basic and common operation. However, the product of multiplication can be stated differently at times, whether to reduce the equation or to explain the mathematics required. Many numbers can be expressed exponentially.
The concept of exponential form is a method of expressing a number that has been multiplied by itself several times. The fundamental formula is [tex]\mathbf{y=b^x}[/tex]
Exponential expressions are simply a shorthand way of writing powers. The exponent specifies how many times the base has been utilized as a factor.
From the information given
:= -(1/4*1/4*1/4*1/4)[tex]
=-(4^{-1}\times4^{-1}\times4^{-1}\times4^{-1})[/tex][tex]=-(4^{(-1+(-1)+(-1)+(-1))})[/tex][tex]=-(4^{(-1-1-1-1)})[/tex][tex]=-(4^{(-4)})[/tex][tex]\mathbf{=-4^{-4}}[/tex]
Learn more about exponent on:
https://brainly.com/question/13669161
#SPJ1
A metallurgist has one alloy containing 29% aluminum and another containing 51% aluminum. How many pounds of each alloy must he use to make 48 pounds of a third alloy containing 50% aluminum? (Round to two decimal places if necessary.)
The number of pounds of 29% alloy and 51% alloy required to make the third alloy containing 50% aluminum is 45.82 pounds and 2.18 pounds respectively.
The number of pounds of alloy that must be used.Let
x = pounds of 29% alloyy = pounds of 51% alloyx + y = 48
29x + 51y = 50*48
x + y = 48
29x + 51y = 2400
Solve simultaneously
From (1)
x = 48 - y
Substitute into (2)
29x + 51y = 2400
29(48 - y) + 51y = 2400
1392 - 29y + 51y = 2400
- 29y + 51y = 2400 - 1392
22y = 1008
divide both sides by 22y = 1008/22
y = 45.82 pounds
Substitute y = 45.82 pounds into (1)
x + y = 48
x + 45.82 = 48
x = 48 - 45.82
x = 2.18 pounds
So therefore, the number of pounds of 29% alloy and 51% alloy is 45.82 pounds and 2.18 pounds respectively.
Read more on simultaneous equation:
https://brainly.com/question/16863577
#SPJ1
16. Doug's family buys 7 postcards while on vacation. Each
postcard costs $0.25 including tax.
Part A
How can Doug use place-value blocks to
find the total cost of the postcards? What is
the total cost?
The total cost is $1.75
What is Place value?The foundation of our entire number system is place value. In this approach, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are distinct from one another.Given that we've done it:
7 postcards were purchased by Doug's family.Each postcard costs $0.25 after tax.The total price is shown by:
7 x 0.25 = $1.75Now, let's display the following in a number line:
Put all the numbers with a difference of 0.25 on the number line, run it seven times, and the result will appear.There are 7 hops between each step of 0.25 duration to get to the needed answer.So, after seven hops, we arrive at 1.75, which is the correct response.
Hence, the total cost is $1.75
To learn more about Place value click on the link
brainly.com/question/25137147
#SPJ1
Determine which integer will make the inequality 12 > 2x + 4 true.
Answer: Integers less than 4 will make the inequality true.
Step-by-step explanation:
1) subtract both sides by 4 to isolate 2x so we are now left with 8 > 2x.
2) divide both sides by 2 so we are left with just x, leaving us now with 4 > x.
Integers must be less than 4 because if you substitute x as 4, we have 12 > 12, which is not true. But, if we substitute x as 3, we are left with 12 > 10, which makes the inequality true.
The school play ran for 3 nights. 185 tickets were sold for the first night. 160 tickets were sold for the second night. 192 tickets were sold for the third night. The tickets cost $4 each. What information is NOT necessary to calculate the total amount of money raised from ticket sales?
A) 192 tickets were sold the for the third night.
B) The school play ran for 3 nights.
D) 185 tickets were sold for the first night.
C) The tickets cost $4 each.
Answer:B
Step-by-step explanation:
Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.
Find the ordered pairs corresponding to the x- and y-intercepts of the graph of the equation.
6x + 12y = 24
Answer:
6x=24-12y
x=24-12y/6
x=4-12y
