Answer:
336.
Step-by-step explanation:
8P3 = 8! / (8 - 3)!
= 8*7*6*5*4*3*2*1 / 5*4*3*2*1
= 8*7*6
= 336
Quick my grade is down from this Exam, and I'm honestly so lost on this question
Which of the following expressions represents the simplified version of the expression below?
(5x3y2−3xy+2)+(2x3y2−3x2y2+4xy−7)
(Just tell me the color and explain if you want)
The equivalent expression of the given expression is 7x³y² -3x²y² + xy -5. Second option is the correct option.
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. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).
What are like terms?
Similar variables and powers are referred to as like words in algebra. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.
Given expression is
(5x³y²−3xy+2)+(2x³y²−3x²y²+4xy−7)
Now open the brackets:
= 5x³y²−3xy+2+2x³y²−3x²y²+4xy−7
Combine like terms:
= (5x³y²+2x³y²)+ (−3xy + 4xy )+(2−7)−3x²y²
= 7x³y² + xy -5 -3x²y²
= 7x³y² -3x²y² + xy -5
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Evaluate the integral by reversing the order of integration. Double integrate e^x^2 dxdy=
the integral by reversing the order of integration. Double integrate e^x^2 dxdy= 1/3x e^x^3 + C
The integral can be written as:
∫ ∫ e^x^2 dx dy
∫ ∫ e^x^2 dy dx
Applying the formula for double integrals, the answer is:
∫ e^x^2 dy × ∫ dx
Since the inner integral is a constant, it is simply equal to x.
The answer is therefore:
∫ e^x^2 dy × x = x × ∫ e^x^2 dy
The outer integral is a standard antiderivative, and is equal to:
1/3e^x^3 + C
Therefore, the final answer is:
1/3x e^x^3 + C
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if a fair coin is tossed 100 times. the distribution of the number of heads is b(100, 0.5). what is the probability that the obtained heads, x, is between 45 and 55? p (45 less or equal than x less or equal than 55 )
The probability that obtained heads, x, is between 45 and 55 is 0.6826.
The Binomial distribution provides the precise response. Wolfram Alpha is one of the software tools that may perform the computation for you. Using this method manually is painful.
Maybe you're supposed to use the binomial's normal approximation. If there are X heads, then X has a roughly normal distribution first we have to find what is the mean and standard deviation.
Given that n = 100 is a relatively large number, we will assume a normal distribution.
mean M = n*p 100*0.5 =50
Consequently, Sd = √(npq) = √1000.5*0.5 = 5.
The standard deviation is 5.
Z = x-µ/σ
Z = (x-50)/5
we have to find the probability in this range.
P(45<X<55) = P((45-50)/5<X<(55-50)/5
P(-1<X<1) = 0.8413 - 0.1587
0.6826
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Solve the equation for the variable y.
ay +4=3ay-b
Answer:
a = [tex]\frac{b-4}{-2y}[/tex]
Step-by-step explanation:
ay + 4 = 3ay - b Subtract 4 from both sides
ay = 3ay -b - 4 Subtract 3ay from both sides
ay - 3ay = b - 4 Factor out the a
a (y -3y) = b =4 Combine like terms
a(-2y) = b - 4 Divide both sides by -2y
a = [tex]\frac{b-4}{-2y}[/tex]
What is the equation of the line that is perpendicular to the linear graph of y=−23x+5 and passes through the point (0, –2)?
The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0
When two lines cross at a straight angle or 90° then the pair of lines said to a pair of perpendicular lines. If the slopes of the two perpendicular lines are m₁, m₂, then the connection between the slopes of perpendicular lines will be represented by the following formula
m₁.m₂ = -1
Here we have
Given line y = −23x+5 ------ (1)
A line perpendicular to the line (1) passes through the point (0, –2).
Here given line is y = −23x+5 which is in the form of y = mx + c
On comparing both equations
=> Slope of line m = −23
Let (y - y₁) = m(x - x₁) be the required equation
=> (y - y₁) = m(x - x₁) ----- (2)
As we know product of slopes of line(1) and (2) is - 1
=> mm₁ = - 1
=> −23m₁ = -1
=> m₁ = 1/23
Substitute m₁ = 1/23 in line (2)
=> (y - y₁) = [1/23](x - x₁)
=> 23(y - y₁) = (x - x₁)
Given the line passes through the point (0, –2).
=> 23(y - (-2)) = (x - 0)
=> 23(y + 4) = x
=> 23y + 4 = x
=> x - 23y - 4 = 0
Therefore,
The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0
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what is the solution to the equation 3 (2 x 5) = 3 x 4 x?x = 0x = 4x = 5
The answer to the equation 3(2x-5)=3x is 5, which corresponds to value option C first from list.
What is 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. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.
Here,
3(2x-5)=3x
6x-15=3x
3x=15
x=5
The solution to the expression 3(2x-5)=3x is 5 that is option C from the given choices of value.
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(1,4) and (6,-1) in linear equation
y = 5 - x. is the linear equation in point-slope form.
How To find the Slope from two points ?Using the slope formula, determine the slope.To find the y-intercept (b), use the slope and one of the points.You may obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).Points (1,4) and (6,-1).
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).
where , m = slope of the line. x₁ = the x-coordinate of the first point.
m = (-1 - 4) / (6 - 1 ).
m= -1
Substitute the values into the point-slope form,
y − y 1 = m ( x − x 1 ) .
y − 4 = -1 ( x − 1) .
y − 4 = 1 - x.
y = 5 - x.
complete question : Write the linear equation in point-slope form that passes through the given points. (1, 4) and (6, -1).
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A toy is being constructed in the shape of a pyramid. The maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. The height of the toy is double the side length. What are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base?.
The maximum dimensions (side length and height) of the pyramid for a given square base is equal to 6.99cm and 13.98cm respectively.
As given in the question,
Maximum amount of material used to cover sides of pyramid and its bottom = 250cm²
Surface area of the ( sides + bottom ) = 250cm²
Base is square :
Let 's' represent the the side length
Then height 'h' of the toy = 2 ( side length)
= 2s
Surface area of Pyramid = s² + 2s√(s²/4) + h²
⇒ 250 = s² + 2s√(s²/4) + (2s)²
⇒250 = s² + 2s√(s² + 16s²)/4
⇒250 = s² + 2s√17s²/4
⇒250 = s² + 2s(s/2)√17
⇒250 = s²+ s²√17
⇒250 = s² ( 1+ √17)
⇒250 = s²( 1 + 4.123 )
⇒ 250 = 5.123s²
⇒s² = 250/5.123
⇒ s= 6.99cm
Height 'h' = 2(6.99)
= 13.98cm
Therefore, the side-length and height of the pyramid with square base is equal to 6.99cm and 13.98cm respectively.
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Use I=PRTI=PRT to find the total amount in the savings account. Type in "money form".
$4500.00 at 8% for 3 years
The total amount earned after 3 years at 8% rate is $5580
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Given that, $4500 is invested at 8% for 3 year,
SI = PxRxT/100
= 4500x8x3/100
= 1080
Amount = interest + principal
Amount = 1080 + 4500 = 5580
Hence, The total amount earned after 3 years at 8% rate is $5580
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jamal can run 0.5 miles in 5 minutes if he keeps the same pace and runs for 14.4minutes how many miles will he have run
Answer:
I pretty sure it's 2.4 miles
YOO need help with a short word problem :)
Using a system of linear equations the number of quarter and dime present are 1 and 8 respectively
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.
Let:
q = quarterd = dime1 quarter = $0.25
1 dime = $0.1
A) An equation for the number of coins
q + d = 9 ...eq(i)
B) The amount of money can be represented as;
0.25q + 0.1d = 1.05 ..eq(ii)
C) The number of dimes; solving equation (i) and (ii)
q + d = 9 ..eq(i)
0.25q + 0.1d = 1.05 ...eq(ii)
q = 1, d = 8
There are 8 dimes
D) There is 1 quarter in the money
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Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to use all her savings on the book. Giselle's grandma offers to pay some of the cost of the book for every weed she pulls in her grandma's garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma's garden.
1. The book is $18.
2. Giselle can earn up to $18 pulling weeds for her grandma.
3. Giselle's grandma pays her $1 for every 5 weeds she pulls.
4. Giselle does not have to use any of her own money toward the purchase of the book when she pulls 90 weeds.
5. Giselle only needs to pull 18 weeds to not use any of her own money.
The correct statements regarding the linear function graphed are given as follows:
The book is $18.Giselle's grandma pays her $1 for every 5 weeds.Giselle does not have to use any of her money when she pulls 90 weeds.What are the correct statements?The correct statements are identified from the graph of the function.
The y-intercept of the function is of 18, which represents how much she has to pay when she does not pull any week, that is, the price of the book.
The x-intercept of the function is of 90, meaning that if she pulls 90 weeks, she earns $18 from her grandmother, which is the entire price of the book.
From the intercept, we get that when the input increases from 90, from 0 to 90, the output decays by 18, from 18 to 0, hence the slope of the function is given as follows:
m = -18/90 = -0.2.
Meaning that for each weed pulled, the amount her grandma pays is of $0.2, and thus for five weeds she is paid one dollar.
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Which of the following equations has no real roots
a. x² - 4x + 3√2 = 0
b. x² + 4x - 3√2 = 0
c. x² - 4x - 3√2 = 0
d. 3x² + 4√3x + 4 = 0
The equation (A) x² - 4x + 3√2 = 0 has no real roots.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
(A) x² - 4x + 3√2 = 0
b² - 4ac = (-4)² - 4(1)(3√2)
= 16 - 12√2
= 16 - 12(1.414)
= 16 - 16.968
= -0.968 < 0
There are no true roots to the equation.
(B) x² + 4x - 3√2 = 0
b² - 4ac = (4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
There are 2 different real roots in the equation.
(C) x² - 4x - 3√2 = 0
b² - 4ac = (-4)² - 4(1)(-3√2)
= 16 + 12√2 > 0
There are 2 different real roots in the equation.
(D) 3x² + 4√3x + 4 = 0
b² - 4ac = (4√3)² - 4(3)(4)
= 48 - 48
= 0
The equation contains two equal roots.
Therefore, the equation (A) x² - 4x + 3√2 = 0 has no real roots.
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Sam and ben are grading english tests. Sam grades 6 6 tests in 24 24 minutes and ben grades 5 5 tests in 20 20 minutes. At these rates, what is the total number of tests they can grade in 3 3 hours? enter the answer in the box.
The total number of tests graded by them in 180 minutes (3 hours) will be 90 tests.
Sam ,
6 tests in 24 mins
Therefore ,
1 test in 24/6 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Ben,
5 tests in 20 mins
Therefore ,
1 test in 20/5 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Therefore at the end of 180 mins
they would have graded 45 + 45 = 90 tests.
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.
In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers.
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A middle school is having a fundraiser. Edwin wants to buy two candles for $5.95 each, three cans of candy for $2.50 each, and an ornament for $7.95.
Answer:
$27.35
Step-by-step explanation:
To solve this, we just set up an equation based on the situation given:
2 candles for 5.95 each would be (2 x 5.95)
3 cans of candy for 2.50 each would be (3 x 2.50)
1 ornament for 7.95 would just be 7.95
(2 x 5.95) + (3 x 2.50) + 7.95 = total cost
11.90 + 7.50 + 7.95 = total cost
$27.35 = total cost
Which of the following is NOT a descriptor of a normal distribution of a random variable? Choose the correct answer below. The graph is centered around 0. The graph of the distribution is symmetric. The graph is centered around the mean. The graph of the distribution is bell-shaped.
The incorrect descriptor is :
The graph is centered around 0 , using the properties of graph of normal distribution of random variable.
What is normal distribution?
Normal distribution is continuous probability distribution of a real valued random variable.
Properties:
1.The curve is symmetric at center around the mean .
2. The curve shape is bell-shaped.
So, from above properties, we can say that the statement - "The graph is centered around 0" is incorrect.
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80 of the students walk to school.
60 of the students cycle to school.
(c) Write the ratio of the number of students who walk to school to the number of
students who cycle to school.
Give your ratio in its simplest form.
Answer:
4/3 also can be written 4:3
Step-by-step explanation:
Compare numbers in the order that the question asks for them. Order matters.
walkers/cyclers
= 80/60
Simplify.
= 8/6
= 4/3
The ratio of walkers to cyclers is 4/3 (also can be written 4:3)
Jack sketches ΔABC. The measure of angle B is 6 degrees less than twice the measure of angle A. The measure of angle C is 111°.
Which equation can be used to find the measure of Angle A? What is the measure of Angle A?
The equation that can be used to find the measure of Angle A is (b) a + 2a - 6 + 111 = 180, a = 25
Which equation can be used to find the measure of Angle A?From the question, we have the following parameters that can be used in our computation:
Angle B = 6 degrees less than twice the measure of angle A
Angle C = 111 degrees
These mean that
b = 2a - 6
c = 111
The sum of angles in a triangle is 180
So, we have
a + 2a - 6 + 111 = 180
What is the measure of Angle A?In (a), we have
a + 2a - 6 + 111 = 180
Evalate the like terms
3a = 75
So, we have
a = 25
Hence, the equation is a + 2a - 6 + 111 = 180
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A company that makes hair-care products had 2,000 people try a new shampoo. 2,000
Of the people, 16 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
The percentage of people having a mild allergic reaction is 0.8%.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
16 out of 2000 have a mild allergic reaction.
Percentage of 16 out of 2000 = (16/2000)100 = 0.8%
Hence "The percentage of people having a mild allergic reaction is 0.8%".
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Mark did a survey.
He asked pupils in his school:
‘Do you like the colour of the school uniform?’
Mark asked this question to 40 pupils in year 11
25% said ‘Yes’. 50% said ‘No’. The rest said ‘Don’t know’.
Complete the table to show how many pupils from year 11 gave each answer.
The following numbers will be illustrated in the table:
Those that said yes = 10
Those that said no = 20
Those that said don't know = 10
How to illustrate the percentage?It should simony be noted that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Number of pupil = 40
25% said ‘Yes’. This will be:
= 25% × 40.
= 10
50% said ‘No’. This will be:
= 50% × 40
= 20
The rest said ‘Don’t know’. This will be:
= 25% × 40
= 10
In conclusion, those who said yes are 10 while those who said no are 20.
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Determine the measure of the indicated angle 53 106 127 307
Answer: 127
Step-by-step explanation: It must add up to 180 degrees
Interior consecutive = congruent
Corresponding = 180
16 donuts in 4 boxes =
donuts in 2 boxes
Answer:
8
Step-by-step explanation:
First, divide 16 by 4 to see how many donuts are in each box. This equation gives us 4. Then, multiply 4 by 2 to see get the answer of 8.
Answer: well if there are 16 donuts in 4 boxes that means there are 4 donuts in each box
Step-by-step explanation:
4=4
4+4=8
4+4+4=12
4+4+4+4=16
so your answer is 8
A direct variation includes the points (3, -18) and (-2, n). Find n. Write and solve a direct variation equation to find the answer.
n =
Using Direct Variation, the value of n = 26
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We need to Write y = kx based on the conditions stated.
Replace with: -18 = k x 3
Turn the sides around: k × 3 = -18
Now Subtract the coefficient of the variable from both sides of the equation:
k = 26 compute the product or quotient.
Write the function's equation as;
y = 26x
Replace with:
n = 26 × 4
n = 104; compute the product or quotient.
Response: n = 26
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A farmer uses 920 grams of grain to feed his 8 chickens. At this rate how many grams of grains does he use to feed 100 chickens
Answer: 11,500 grams
Step-by-step explanation: 920/8=115 115*100= 11,500
Find x. Please give a correct answer
Answer: x = 110
Step-by-step explanation:
A 7-sided shape, also known as a septagon, has a total of 900° among its angles. We will set up an equation and solve by combining like terms and using inverse operations.
105° + 150° + 140° + x° + 135° + 125° + 135° = 900°
790° + x° = 900°
x = 110
An equation that pass through -4,-1 and perpendicular to the line y = 4/3x + 6
The equation of the perpendicular line is y = 3/4(x + 4) - 1
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 4/3x + 6
Also, from the question;
We have the following points
The point is given as
Point = (-4, -1) i.e. (x, y) = (-4, -1)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is 3/4
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = 3/4
(x₁, y₁) = (-4, -1)
So, we have
y = 3/4(x + 4) - 1
Hence, the line has an equation of y = 3/4(x + 4) - 1
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a drawer contains 7 black socks, 3 brown socks, and 1 gray sock. a sock is chosen at random. what is the probability that the sock is black or gray? use the formula below to solve this problem. question 2 options: 7/11 1/11 6/11 8/11
The Probability that the sock is black or gray is
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Total number of socks in a bag = 7+3+1 =11
so total number of outcomes possible = 11
The chance that black or gray will occur, resulting in a greater number of favorable outcomes
Number of favourable outcome will be -
Number of Black sock + Number of gray sock
=7+1
=8
Therefore probability (P) will be 8/11
=0.7272
and individual probability of coming black and gray sock will be
Probability for black socks is 7/11
Probability for gray socks is 1/11
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How do you solve 3(x−4)=15?
Answer:
9
Step-by-step explanation:
3(x-4)=15
Use distributive property with the 3 (multiply 3 times x and 3 times -4)
3x-12=15
Add the 12 to both sides.
3x=27
divide 27 by 3.
x=9
Answer:
x = 9
Step-by-step explanation:
How do you solve 3(x−4)=15?
3(x − 4) = 15
divide both side by 3
x - 4 = 5
x = 5 + 4
x = 9
----------------
check
3(9 - 4) = 15
9 - 4 = 5
5 = 5
the answer is good
this take over causes the cell to _____________ instead of makeing new cells
Meiosis causes the cell to divide instead of makeing new cells.
What are cells?Cells are the fundamental building blocks of all life. Trillions of cells make up the human body. They support the body's structure, absorb nutrients from food, convert those nutrients into energy, and perform specialized functions.
Meiosis is a type of cell division that occurs in sexually reproducing organisms and results in a reduction in the number of chromosomes in gametes; he sex cells, or egg and sperm. Body or somatic cells in humans are diploid, with two sets of chromosomes one from each parent.
It should be noted that meiosis is a type of cell division of germ cells that produces gametes such as sperm or egg cells in sexually reproducing organisms. It consists of two rounds of division that result in four cells with only one copy of each chromosome.
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Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.
Enter an expression in the box to represent the number of songs Marcus now has on his phone.
Answer:
x + 20 = y
Step-by-step explanation:
x + 20 = y
where x= number of songs
y = total songs marcus has