Answer:
$138.46
Step-by-step explanation:
30×12=360
360÷2.60=138.46
Suppose your PRNG uses the following formula: X = X * 3 - 2. And suppose that X is 5. What are the next three numbers that would be generated?
The next three numbers that would be generated are 13, 37, and 109.
What is formula?Formula is a mathematical expression that is used to calculate the value of a particular quantity, such as a number, a quantity of a certain type of material, or a number of elements. The most common form of a formula is an equation, which contains two or more variables and is written in the form of a mathematical expression. Formulas are used in many disciplines, including physics, chemistry, engineering, and economics, to solve problems and determine relationships between quantities.
This is because the formula applies the operation of multiplying the current number by 3 and then subtracting 2. Applying this formula to 5 gives 13, and then applying the formula to 13 gives 37, and so on. The resulting sequence is 5, 13, 37, 109, and so on. This is a simple PRNG that can be used to generate sequences of random numbers.
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Practice 21: Combine the like terms to make a simpler expression
A. -3n-7+6n + 1
B 7x+5-3x
D. 12x² -5+7x² - 11x
a)
C. 6x + 4 + 15-7x
E 6g + 11 + 8g² - 15w
1 point
The like terms to make a simpler expression is 19 x^2-6 x+9 n-6
Group like terms
What is simpler expression?
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.
[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]
[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]
[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$3 n+6 n=9 n$[/tex]
[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]
Add the numbers: [tex]$-7+1+5-5=-6$[/tex]
[tex]=19 x^2-7 x+9 n-6[/tex]
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Multiply. State the product in simplest form..
p²-4p-12
18p
6p+12 p²-9p+18
, p‡ - 2,3,6
The simplest form of [(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)] is 3p/ (p - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given expression is
[(p²- 4p -12)/(6p + 12)] × [18p/(p²-9p+18)]
Now factories p²- 4p -12, p²-9p+18, and 6p + 12:
p²- 4p -12
= p²- (6 - 2)p -12
= p²- 6p + 2p -12
= p(p - 6) + 2(p - 6)
=(p - 6)(p + 2)
p²- 9p + 18
= p²- (6 + 3)p + 18
= p²- 6p -3p + 18
= p(p - 6) -3(p -6)
=(p - 6)(p - 3)
6p + 12
=6(p+2)
Now putting p²- 4p -12 = (p - 6)(p + 2); p²- 9p + 18 = (p - 6)(p - 3); 6p + 12 = 6(p+2) in the given expression:
[ (p - 6)(p + 2)/6(p+2)] × [18p/(p - 6)(p - 3)]
Multiply the denominator with denominator and numerator with numerator:
= 18p (p - 6)(p + 2)/ 6(p+2)(p - 6)(p - 3)
Now cancel out (p+2)(p - 6) from denominator and numerator:
= 18p/ 6(p - 3)
Divide denominator and numerator by 6:
= 3p/ (p - 3)
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PLEASE HELP WILL GET BRAINLIEST!!
Answer:
235.5
Step-by-step explanation:
cylinder volume formula
V = pi * r^2 * h
V = 3.14 * 5^2 * 3
V = 3.14 * 25 * 3
V = 3.14 * 75
V = 235.5
What is the measure of ZE, in degrees? D 48 5 O A. Cannot be determined OB. 48° O C. 96° D. 84°. :)
Answer:
84
Step-by-step explanation:
EFD is an iscosilies triangle therefore angle F = angle D = 48
and therefore angle E= 180-48-48=84
a random sample of 100100 observations from a population with standard deviation 17.037078307720517. yielded a sample mean of 93.1). Given that the null hypothesis is μ≤90 and the alternative hypothesis is μ>90 using α=.05, find the following:(a) Test statistic(b) P-value:(c) The decision for this test is:i. Reject the null hypothesis.ii. Fail to reject the null hypothesis.
1)Test Static: 1.82
2)P-Value: < 0.05
3)Decision: i. Reject the null hypothesis.
To test the claim that the population mean is greater than 90, we can use a one-sample t-test.
(a) The test statistic for the one-sample t-test is calculated as:
t = (sample mean - population mean) / (standard deviation / sqrt(sample size))Plugging in the values, we get:
t = (93.1 - 90) / (17.037078307720517 / sqrt(100)) = 3.1 / (17.037078307720517 / 10) = 3.1 / 1.7037078307720517 = 1.82(b) To find the p-value for the test, we can use a t-table or a statistical software package to find the probability of observing a t-value as extreme or more extreme than the one we obtained, given that the null hypothesis is true. For a one-tailed test with α = 0.05 and df = 99 (the sample size - 1), the critical value for t is approximately 1.65. Since our test statistic (1.82) is greater than the critical value, the p-value is less than 0.05.
(c) Since the p-value is less than the significance level of α = 0.05, we reject the null hypothesis and conclude that the population mean is indeed greater than 90. Therefore, the decision for this test is: i. Reject the null hypothesis.
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one urn, u1, contains one blue ball (labeled b1) and three red balls (labeled r1, r2, and r3). a second urn, u2, contains two red balls (labeled r4 and r5) and two blue balls (labeled b2 and b3). an experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement.
Two urns contains different numbers of different colour balls. Two balls are randomly chosen from both of urns. The probability that two red balls are choosen is 1/3..
We have given that
First Urn, u₁ contains 3 Red( labelled r₁,r₂,r₃) ; 1 blue ball ,(labelled b₁).
Total number of balls in urn, u₁ = 4 balls
Second Urn, u₂ contains 2 red (labelled r₄,r₅) and 2 blue (labelled b₂, b₃) .
Total number of balls in urn, u₂ = 4 balls
Assume , A = first urn , u₁ is selected
Assume, B = Second urn u₂ is selected
Assume , R = selected balls are red
Case 1 : Urn u₁ is choose and two balls without replacement are withdraw.
Probability to choose the first urn, P(A) = 1/2
Probability that the two withdraw without replacement balls are red in colour, P(A/R)
= 3/4 × 2/3 = 1/2
Case 2 : Urn u₂ is choose and two balls without replacement are withdraw.
Probability to choose the second urn, P(B) = 1/2
Probability that the two without replacement withdraw balls are red in colour, P(B/R)
= 2/4 × 1/3 = 1/6
The required probability= P(A) P(A/R) + P(B)P(B/R) = 1/2(1/2) + 1/2(1/6) = 1/4 + 1/12
= 4/12 = 1/3
Hence, the required probability is 1/3..
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Complete question:
One urn u1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn u2 contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. Probability that two red balls are choosen.
Find the perimeter of the figure shown above with aside length 5 unit
The perimeter of the figure with side length of 5 units is 50 units
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = rectangle
Smaller shapes = squares
Side lengths = 5 units
The perimeter of the figure is calculated as
Perimeter = Number of visible sides * Side length of the square shape
In this case, we have
Number of visible sides = 10
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 10 * 5
Evaluate the products
Perimeter = 50 units
Hence, the perimeter is 50 units
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PLEASE HELP ASAP
A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?
Answer:
D
Step-by-step explanation:
slope of the given line :
(-4-2)/(-1-4)
-6/-5
6/5
slope of a perpendicular line : -5/6
y-7 = -5/6 (x-(-3)
y -7 = -5/6 (x+3)
y -7 = -5/6 x - 5/2
5/6 x + y - 7 + 5/2 = 0
5/6 x + y + (-14 + 5)/2 = 0
5/6 x + y - 9/2 = 0
5x + 6y - 27= 0
5x + 6y = 27
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, - 4 ) and (x₂, y₂ ) = (4, 2 )
m = [tex]\frac{2-(-4)}{4-(-1)}[/tex] = [tex]\frac{2+4}{4+1}[/tex] = [tex]\frac{6}{5}[/tex] ← slope of graphed line
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{6}{5} }[/tex] = - [tex]\frac{5}{6}[/tex] , then
y = - [tex]\frac{5}{6}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 3, 7 ) into the partial equation
7 = [tex]\frac{5}{2}[/tex] + c ⇒ c = 7 - [tex]\frac{5}{2}[/tex] = [tex]\frac{14}{2}[/tex] - [tex]\frac{5}{2}[/tex] = [tex]\frac{9}{2}[/tex]
y = - [tex]\frac{5}{6}[/tex] x + [tex]\frac{9}{2}[/tex] ← equation in slope- intercept form
multiply through by 6 ( the LCM of 6 and 2 ) to clear the fractions
6y = - 5x + 27 ( add 5x to both sides )
5x + 6y = 27 ← equation of perpendicular line in standard form
As a hardworking student, plagued by too much homework, you spend all night doing math homework. By 6am, you imagine yourself to be a region bounded by
y = 8 x^2
x=0
x=4
y=0
As you grow more and more tired, the world begins to spin around you. However, according to Newton, there is no difference between the world spinning around you, and you spinning around the world. Unfortunately, you are so tired that you think the world is the x-axis. What is the volume of the solid you (the region) create by spinning about the x-axis?
The volume of the solid you (the region) create by spinning about the x-axis is V = 225units³
How is the volume of a solid object calculated?Depends whether it is a solid with sides, height, and depth. In this case it is the multiplicarion of the three to get the volume.
If it is an irregular shaped object it is done by water displacement. Fill a container with a known amount of water, immerse the object, and the difference in volume in the water is the volume of the object.
How do I find the volume of an irregular shape?Break the volume down into prisms and pyramids that you can calculate the volume of and sum the pieces up to get the total volume. If the shape has curved surfaces, it gets much more complicated.
This gives a y = 15
x = 3
The straight line equation will be y = 5x
The volume of a pyramid is given by the following equation:
where r = radius of the base
h= height of the cone
from the graph, roating about the x - axis gives h = 3, r = 15
Volume =
= 225 units³
Volume of cone formed is 225 units³.
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Express 2678 as a product of prime numbers
Answer:
2, 13, 103
Step-by-step explanation:
These prime numbers are the ones.
2678 = 2 * 13 * 103
A prime number is a natural number that is greater than one and is not a product of smaller natural numbers. For example, 3 is a prime number and we can write it as a product, 1 * 3 or 3 * 1, which involves 3 itself.
So, prime numbers are those numbers that have only two factors, which are 1 and the number itself.
A natural number that is greater than 1 and is not a prime number, is called a composite number. Every natural number which is greater than 1, is either a prime itself or can be factorized as a product of primes that is unique up to their order.
The answer is -
2678 = 2 * 13 * 103
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If you wanted to make $798 by investing $6139 for 3 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
Answer:
Below
Step-by-step explanation:
6139 * x * 3 = 798
x = 798/(3*6139) = .0433= 4.33%
DIG DEEPER You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and ( 45w + 25) dollars in checking account. how much money do you save each week?
The sum of both accounts' expression in its most basic form is 55w + 145.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the instructions given in the question,
Amount in savings account = 10w + 120
Amount in checking account = 45w + 25
Then, total money shaved each week will be,
(10w + 120) + (45w + 25)
10w + 45w + 120 + 25
= 55w + 145
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Abdul was scuba diving 76 feet below the surface of the ocean. To get a closer look at a school of fish, he swam up 28 feet.
What is Abdul's position now relative to the surface of the ocean?
Answer:
-48 ft.
Step-by-step explanation:
-76+28= -48
Hope this helps! Had this on one of my quizzes
Answer:
-48 espero te sirva perdon por llegar tarde
what is answer to 3/7 x 5/2?
Answer:
15/14 or 1 1/14
Step-by-step explanation:
multiple the numerators and deno
3x5=15
7x2=14
15/14 or 1 1/14
Answer:
Step-by-step explanation:
Exact form
15/14
Decimal Form:
1.07142857........
mixed number is
1, 1/14
Find the value of x
Area of rectangle = 50
Answer:
x = 3.66
Step-by-step explanation:
Area of a rectangle = length * width
In this case:
(x+10)x = 50
x*x + x*10 = 50
x² + 10x - 50 = 0
x = {-10±√((10²) -(4*1*-50))} / (2*1)
x = {-10±√(10² + 200)} / 2
x = {-10±√(100+200)} / 2
x = {-10±√300} / 2
x = {-10±17.321} /2 aprox,
It is a geometric figure so only the positive value is taken.
x = {-10+17.321} / 2
x = 7.321/2
x = 3.66
Check:
3.66(3.66+10) = 50
3.66*13.66 = 50
c) If the gradient of a line, C, is a 2/3 , what is the gradient of the line which is perpendicular to C?
Any line perpendicular to line C must have a slope equal to -3/2.
Which is the slope of a line perpendicular to line C?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two linear equations are perpendicular if the product between the slopes is -1, then if the slope of the line perpendicular to line C is x, then we can write:
x*(2/3) = -1
Solving for x we get:
x = -3/2
That is the slope of the perpendicular line.
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If you are given an equation of a line
and a set of points, and are asked to find
an equation of a line parallel to Line #1,
what do you need to do?
5. (8.51) What is the equation of the line shown?
HELP PLEASE!!
Answer:
D
Step-by-step explanation:
D. If it's not D, C. It's a negative slope with a negative y-intercept of -1
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
point
vertex
one
face
face
circular
length
area
volume
This bar chart shows the numbers of pets owned by people
questioned in a survey. Note that the scale on the vertical
axis is missing.
The total number of pets
owned by the respondents
is 92.
How many people owned
exactly 2 pets?
Answer: C. The width of the bar representing dogs is more than the widths of the other bars.
Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.
If you are given an equation of a line
and a set of points, and are asked to find
an equation that is perpendicular to Line
#1, what do you need to do?
If you are given an equation of a line and a set of points, you should determine the slope of the equation that is perpendicular to the given equation of line. Lastly, you should use the set of points to write an equation for the perpendicular line.
How to determine an equation of this line?Mathematically, the slope-intercept or standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.In Mathematics, a condition that must be met for two lines to be perpendicular is given by this mathematical expression:
m₁ × m₂ = -1
Assuming the given equation of a line is y = 2x, the slope of the equation that is perpendicular to this line would be calculated as follows;
m₁ × m₂ = -1
2 × m₂ = -1
Slope, m₂ = -1/2.
In conclusion, you will use the newly calculated slope alongside the set of points to determine the equation for the perpendicular line either by using the slope-intercept form or point-slope form.
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Last year at a certain high school, there were 56 boys on the honor roll and 135 girls on the honor roll. This year, the number of boys on the honor roll increased by 25% and the number of girls on the honor roll increased by 20%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
There is an effective change of 50% in the school.
What is Percentage?
A percentage is a relative figure that represents the hundredth part of any amount. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.
Solution:
To find the net/effective change we can the use the formula:
(a + b + ab/100)
here a and b are the rate of change
a = 25% and b = 20%
Net change = (25 +20 + 500/100) = 45 + 5 = 50%
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Which graph represents the inequality y ≥ 2−2x?
I took a guess on this question. I just want to be sure my guess was right!
Answer:
Yes, your answer would be correct.
Step-by-step explanation:
That graph intersects at (0, 2), is a solid line, and the slope is -2.
Evaluate the expression when c=4 and d=5.
d+6 c
Answer:
29 is the correct answer
I need help with these problems
Step-by-step explanation:
whenever you see a variable ( a letter ) without a number in front of it, add a 1 ! It means the same thing...
y is the same as 1y
1). 3y + y = ?
Add that 1!
3y + 1y = ?
This problem is the same as 3 + 1
3y + 1y = 4y
2). b + b = ?
Add those 1's !
1b + 1b = ?
this is the same as 1 + 1
1b + 1b = 2b
Remember to keep the variable !
Part B is like a puzzle and the instructions give us hints.
It is telling us, when we see an r, we replace it with the number 3
and when we see t , we replace it with the number 9
Let's solve these puzzles!
8). [tex]\frac{r}{t} = ?[/tex]
We see and r and a t, let's plug in 3 and 9
Now we have ...
[tex]\frac{3}{9} = ?[/tex]
Divide using a calculator!
We get ....
[tex]\frac{3}{9} = \frac{1}{3}[/tex] or 0.33
9). [tex]rt = ?[/tex]
When variables are right next to each other, this means they are being MULTIPLIED!
Let's replace r and t with 3 and 9 and multiply them together!
[tex]rt =[/tex] 3 × 9
3 × 9 = 27
We do similar things for Part C
12). [tex]ab = ?[/tex]
It tells us a = 5 and b = -4
Let's plug it in
[tex]ab =[/tex] 5 × -4
5 × - 4 = -20
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COMMENT THEM BELOW
Find the value of x in the following equation:
1.2(3x + 5) = 3.6x + 6
A:Infinite solutions
b: No solution
c: x = 1.8
d: x = 0
Answer:
A:Infinite solutions
Step-by-step explanation:
1.2 ( 3x + 5 ) = 3.6x + 6
1.2 ( 3x ) + 1.2 ( 5 ) = 3.6x + 6
3.6x + 6 = 3.6x + 6
Answer: A
Step-by-step explanation:
what number do you get by adding 59 hundred to 31 thousandths?
im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.
In the figure below, R is between Q and S, and S is between R and T. If QS = 12, RT=9, and QT=17, find RS.
In the given figure QT is of 16 units.
What is a line segment ?A line segment has two end points unlike a line which can extend indefinitely in both the directions.
According to the given question S is between Q and T and R is the midpoint of QS. RS=4 And RT= 12 we have to find QT.
As R is the midpoint of QS It will be twice of RS which
= 8 units.
And if RS is 4 units then QR is also 4 unit as R is the midpoint.
QT = QR + RT.
QT = 4 + 12
QT = 16 units.
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Which ordered pairs are solutions to this system of inequalities?
x+5 y>8
4 x-y<6
Select each correct answer.
(2,-3)
(-1,5)
(10,2)
(-4,1)
(0,4)
(-6,7)
The ordered pairs to the system of linear inequality are (-1, 5), (0, 4), (-6, 7)
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
In the problem given;
x + 5y > 8 ...eq(i)
4x - y < 6 ...eq(ii)
From eq(i)
x + 5y > 8
x > 8 - 5y ...eq(iii)
however, this can easily be solved using a graph.
Plotting the inequality in a graph line;
The ordered pairs are (-1, 5), (0, 4), (-6, 7)
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