As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.
what is probability ?Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of the occurrence and 1 denotes its certainty. For instance, since there is a one in six possibility of rolling a six, the probability of rolling a six on a fair six-sided die is 1/6 or roughly 0.167. Another way to describe probability is as a percentage or as odds. A probability of 0.5, for example, corresponds to 50% or chances of 1:1. (meaning there is an equal chance of the event occurring or not occurring). Science, engineering, economics, and banking all use probability theory, a significant area of mathematics.
given
Assume Manuel has information on 100 aircraft with delays of no more than 25 minutes, of which 40 had delays of no more than 5 minutes.
The estimated likelihood that an arbitrarily chosen flight would arrive late by 5 minutes or less would then be:
P(late by 5 minutes or less) is equal to the number of planes that are 5 minutes or less late divided by the total number of flights that are 25 minutes or less late.
P(late by no more than 5 minutes) = 40/100
P(late by no more than 5 minutes) = 0.4
As a result, it is predicted that 0.4 or 40% of flights will arrive late by 5 minutes or less.
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Subtract: (-4y^(2)+5d)-(-2y^(2)) Your answer should be in simplest terms. Enter the correct answer.
Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.
To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.
So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².
Now, combine the like terms, which are the terms that contain y²:
-4y² + 5d + 2y² = (-4 + 2)y² + 5d
So, our final answer is:
-2y² + 5d.
Since our answer is in simplest terms, the final answer is -2y² + 5d.
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8. The height of a trapezoid can be expressed as (4x + 7) while the bases can be expressed as (5x + 6) and (2x-6) and (x + 8). Write and solve an expression to represent the area of the trapezoid. (Hint: A = 0.5h(b₁+b₂)
Answer:
Step-by-step explanation:
I just knew now I forgot sorry lol
Julio pays a $300 initial fee.plus $7 a month for a membership at a baseball club.If he only has $500 set aside for this hobby.how long can he afford to pay the monthly fee?
A. Create an equation to represent this word problem.
B. Solve the equation
Solving a linear equation we can see that he can afford to pay the monthly fee for 28 months
How long can he afford to pay the monthly fee?We know that there is an initial fee of $300 plus $7 per month, so the total cost after x months is:
C = 300 + 7*x
And we know that Julio has $500 set aside, then the equation that we need to solve is:
500 = 300 + 7x
500 - 300 = 7x
200 = 7x
200/7 = x = 28.5
Rounding down we get 28.
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A package of 8 hot dogs is on sale for $4. 0. What is the price per hot dog? $0. 32 $0. 50 $2. 00 $5. 0
Answer:
$0.50
Step-by-step explanation:
We know
A package of 8 hot dogs is on sale for $4
What is the price per hot dog?
4 / 8 = $0.50
So, the price per hot dog is $0.50
Find the product of 4/6-2a x 3-a/2
a. 1
b. 2
c. 3
d. 4
The product of 4/6-2a x 3-a/2 is equal to 2a-1. To calculate this, the fractions must first be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Next, the two terms should be multiplied together, resulting in 2a-1.
The product of 4/6-2a x 3-a/2 can be found by expanding the terms and then solving the equation. First, the fractions must be simplified. 4/6 can be simplified to 2/3, and a/2 can be simplified to a/2. Once the fractions are simplified, the two terms should be multiplied together, resulting in 2a-1. Now that the two terms have been multiplied, the equation can be expanded by using the Distributive Property. The equation should be written as (2/3-2a) x (3-a/2). This can be simplified by distributing the 2/3 and 3 across the parentheses. This results in (2-6a+2a^2) x (3-1/2a). Finally, the equation should be simplified by combining like terms. This results in 2-6a+2a^2+3-1/2a, which simplifies to 2a-1. Therefore, the product of 4/6-2a x 3-a/2 is equal to 2a-1.
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What is the total surface area of the square
pyramid in square inches?
11 in
7 in
11.5 in
Answer:
To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.
In this case, the base is a square with side length 11.5 inches. Therefore, its area is:
Area of base = 11.5^2 = 132.25 square inches
Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
a^2 + b^2 = c^2
where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:
c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)
The area of each triangular face can be found using the formula:
Area of triangle = (1/2) * base * height
where the base is 11.5 inches and the height is 8.121 inches.
Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)
So, the total surface area of the square pyramid is:
Total surface area = Area of base + 4 * Area of each triangular face
Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)
Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.
Please! I really need help with this!
8×4=32
11-8=3
4×3=12
12÷2=6
32+6=38
=38inch^2
it might b wrong tho?
How do find volume of a solid that is a cylinder with a hemispherical hole cut from the top of it with the shaded rim 3 inches thick height is 12 in and part of hemisphere is a triangle with hypotenuse side 10 in
The volume of the solid is 284π/3 cubic inches.
To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.
The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.
The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:
Vcylinder = π(5^2)(12) = 300π cubic inches
Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.
Substituting the values, we get:
Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches
Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:
Vsolid = Vcylinder - Vhemisphere
Vsolid = 300π - 16π/3
Vsolid = 284π/3 cubic inches
Therefore, the volume of the solid is 284π/3 cubic inches.
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Find the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) to the nearest tenth of a degree The angle between \( \mathbf{u} \) and \( \mathbf{v} \) is (Round
The angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.
To find the angle between two vectors \( \mathbf{u} \) and \( \mathbf{v} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\| \mathbf{u} \| \| \mathbf{v} \|} \]
where \( \theta \) is the angle between the vectors, \( \mathbf{u} \cdot \mathbf{v} \) is the dot product of the vectors, and \( \| \mathbf{u} \| \) and \( \| \mathbf{v} \| \) are the magnitudes of the vectors.
First, we need to find the dot product of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \mathbf{u} \cdot \mathbf{v} = (-4)(-5) + (-1)(-2) = 20 + 2 = 22 \]
Next, we need to find the magnitudes of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \| \mathbf{u} \| = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \]
\[ \| \mathbf{v} \| = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]
Now we can plug these values into the formula and solve for \( \theta \):
\[ \cos \theta = \frac{22}{\sqrt{17} \sqrt{29}} \]
\[ \theta = \cos^{-1} \left( \frac{22}{\sqrt{17} \sqrt{29}} \right) \]
Using a calculator, we find that \( \theta \approx 12.5 \) degrees.
Therefore, the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.
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How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line
A double number line means the values of two different quantities are expressed in two separate lines such as corresponding values align. Here 1ml of blue water will need 3 ml of yellow water.
Here double line represents the relation between yellow water and blue water required to produce green water. 5ml of blue water needs 15ml of yellow water.
So the ratio is 5 : 15
3. One division in the line for blue water represents 1ml and 1 division in yellow water line is 3 ml.
We can also solve it using proportions
5 : 15 :: 1: x
5/15 = 1/x
x = (1×15)/5 = 3 ml
4. For 11 ml of blue water, it will require 33 ml of yellow water.
5. For 8 ml of blue water, 24 ml of yellow water is needed.
6. If we know the volume needed with 1ml of blue water, we can multiply that volume with any quantities of blue water to calculate the volume needed. For example 4 ml of blue water needs 4×3 = 12 ml of yellow water.
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The complete question is as below.
The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water. We want to make a very small batch of the same shade of green water. We need to know how much yellow water to mix with only 1 ml of blue water.
1. On the number line for blue water, label the four tick marks shown.
2. On the number line for yellow water, draw and label tick marks to show the amount of yellow water needed for each amount of blue water.
3. How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line.
4. How much yellow water should be used for 11 ml of blue water?
5. How much yellow water should be used for 8 ml of blue water?
6. Why is it useful to know how much yellow water should be used with 1 ml of blue water?
elizabeth buys a package of 360 marbles. she gives away 216 of the marbles. what percent of the marbles did elizabeth give away?
Answer:
Elizabeth gave away 216 marbles out of a total of 360 marbles.
To find the percentage of marbles that Elizabeth gave away, we can use the formula:
percentage = (part/whole) x 100%
where "part" is the number of marbles Elizabeth gave away, and "whole" is the total number of marbles.
So, plugging in the values we have:
percentage = (216/360) x 100%
percentage = 0.6 x 100%
percentage = 60%
Therefore, Elizabeth gave away 60% of the marbles.
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The total surface area of the given figures is:
1) 376 sq. feet
2)92sq. feet
What is meant by surface area?
The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. A solid object's surface area is a measurement of the overall space that the object's surface takes up. Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces.
1) This figure is a cuboid.
It has six faces and the opposite faces are of equal dimensions.
The surface area of a cuboid is the sum of the areas of each face.
Length l = 10 ft
Width w = 6 ft
Height h = 8 ft
Surface area = 2lw+2lh+2hw = 2 ( lw+ lh+ hw)
= 2 ( 10*6 + 10*8 + 8*6) = 376 sq. feet
2) This figure has 2 similar right triangle faces.
Sum of area of both triangles = 2 * 1/2 * base * height = 3 * 4 = 12 sq. feet
There are two rectangular faces.
Area of front rectangular face = 10 * 5 = 50 sq. feet
Area of base rectangular face = 10*3 = 30 sq. feet
Total surface area = 12 + 50 + 30 = 92sq. feet
Therefore the total surface area of the given figures is:
1) 376 sq. feet
2)92sq. feet
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Please help
Solve the equation.
- 6x-24 = 3x + 12
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. X =
OB. The solution is all real numbers.
OC. There is no solution.
Answer:
A. X = -4
Step-by-step explanation:
[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]
FRACTIONS Multiplicative property of equality with fractiol Solve for u. 30=(5)/(6)u Simplify your answer as much as possible. u
The solution for u is 36.
To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:
(6/5) * 30 = (6/5) * (5/6) * u
Simplifying the right side of the equation gives us:
(6/5) * 30 = u
Multiplying the fraction and the whole number gives us:
(180/5) = u
Simplifying the fraction gives us:
36 = u
Therefore, the solution for u is 36.
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There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3:5. There
are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
Answer:
Step-by-step explanation:
18
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1) Identify the slope of the line y - 3 = 4(x + 1). Then use the equation to identify a point the line passes
through
Answer:
slope = 4 , point on line (- 1, 3 )
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y - 3 = 4(x + 1) ← is in point- slope form
with slope m = 4 and (a, b ) = (- 1, 3 )
Use either method to simplify the complex fraction. ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2)))
To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.
Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).
Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.
Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))
Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))
Step 3: Simplify the numerator and denominator by combining like terms.
Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))
Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))
Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).
Simplified fraction: (a-f)/(f^(1))(a^(1))
Step 5: Simplify the final fraction by canceling out the common factors.
Final answer: (a-f)/(fa)
Therefore, the simplified complex fraction is (a-f)/(fa).
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The sum of the digits of a certain two-digit number is 3. Reversing its digits decreases the number by 27. Find the number.
The number is 30.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum
Given that,
The sum of the digits of a certain two-digit number is 3.
Since it is a two digit number, there will be a tens place and a ones place.
Let x be the digit in tens place and y be the digit in ones place.
x + y = 3
The number can also be written as 10x + y, since x is in the tens place.
When the number is reversed, tens place changed to ones place and vice versa.
The reversed number is 10y + x.
Given that the value of the number is decreased by 27 when the digits is reversed.
Original number - 27 = Reversed number
10x + y - 27 = 10y + x
9x - 9y = 27
x - y = 3
Also, we have,
x + y = 3 [Equation 1]
x - y = 3 [Equation 2]
Adding the equations,
2x = 6
x = 6/2 = 3
Substituting in equation 1, y = 0
Hence the number is 30.
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Division involving a whole number and a Divide. Write your answer in simplest form. 3-:(2)/(3)
The answer in simplest form is 9/2
The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.
The reciprocal of a fraction is obtained by flipping the numerator and denominator.
In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).
So, we can multiply 3 by (3/2) to simplify the division:
3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2
Therefore, the answer in simplest form is 9/2.
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A standard deck of cards contains 52 cards. One card is selected from the deck.
(a) Compute the probability of randomly selecting a diamond or heart
(b) Compute the probability of randomly selecting a diamond or heart or spade
(c) Compute the probability of randomly selecting a seven or a heart
The probabilities are:
(a) P(diamond or heart) = 0.5
(b) P(diamond or heart or spade) = 0.75
(c) P(seven or heart) ≈ 0.308.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
(a) To compute the probability of randomly selecting a diamond or heart from a standard deck of 52 cards, we need to count the number of diamond cards and heart cards in the deck. There are 13 diamond cards and 13 heart cards, so the total number of cards that are either diamonds or hearts is 13 + 13 = 26. Therefore, the probability of randomly selecting a diamond or heart is:
P(diamond or heart) = number of diamond cards + number of heart cards / total number of cards
P(diamond or heart) = 26/52
P(diamond or heart) = 1/2
P(diamond or heart) = 0.5
(b) To compute the probability of randomly selecting a diamond or heart or spade from a standard deck of 52 cards, we need to count the number of cards that belong to any of these three suits. There are 13 diamond cards, 13 heart cards, and 13 spade cards in the deck, so the total number of cards that are either diamonds, hearts, or spades is 13 + 13 + 13 = 39. Therefore, the probability of randomly selecting a diamond or heart or spade is:
P(diamond or heart or spade) = number of diamond cards + number of heart cards + number of spade cards / total number of cards
P(diamond or heart or spade) = 39/52
P(diamond or heart or spade) = 3/4
P(diamond or heart or spade) = 0.75
(c) To compute the probability of randomly selecting a seven or a heart from a standard deck of 52 cards, we need to count the number of seven cards and the number of heart cards in the deck. There are 4 seven cards and 13 heart cards, but we need to be careful not to double-count the seven of hearts. Therefore, the total number of cards that are either sevens or hearts is 4 + 12 = 16. Therefore, the probability of randomly selecting a seven or a heart is:
P(seven or heart) = number of seven cards + number of heart cards - number of seven of hearts / total number of cards
P(seven or heart) = 16/52
P(seven or heart) = 4/13
P(seven or heart) ≈ 0.308
Hence, The probabilities are:
(a) P(diamond or heart) = 0.5
(b) P(diamond or heart or spade) = 0.75
(c) P(seven or heart) ≈ 0.308.
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Gavin wants to buy a skateboard that sells for $49. 99. An advertisement says that next week the skateboard will be on sale for $42. 50 how much will Gavin save if he waits until next week to buy the skateboard
Answer:$7.49
Step-by-step explanation:
just subtract 42.50 from 49.99
49.99-42.50=7.49
a) Find the monthly payment needed to repay a $40,000 loan over 20 years, given that, as usual, the first repayment is made at the end of the first month, and the last at the end of the 240th. The interest rate is 0.5% per month.
b) Another $40,000 loan is repaid monthly, also over 20 years in a similar fashion. The monthly payment is $544.53. Find the monthly interest rate.
a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent
To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)
Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30
Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:
Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:
0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000
0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)
$200 = $544.53 * (1 - (1 + 0.005)^-240)
$200 / $544.53 = 1 - (1 + 0.005)^-240
0.367 = 1 - (1 + 0.005)^-240
(1 + 0.005)^-240 = 0.633
1 + 0.005 = 0.633^-240
0.005 = 0.633^-240 - 1
0.005 = -0.367
Monthly interest rate = -0.367 / -240
Monthly interest rate = 0.00153
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in online music retailer generated an internal report about how many songs in each genre vere sold last year. Online music sales What is the measure of the central angle in the "Punk" section?
The measure of the central angle in the "Punk" section is 72 degrees.
Determine the central angleThe measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.
To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.
For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:
200/1000 * 100 = 20%
To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).
20% * 360 = 72 degrees
Therefore, the measure of the central angle in the "Punk" section is 72 degrees.
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25pens out of 51 in ratio
Answer:
We can express 25 pens out of 51 in ratio form as:
25:51
similar triangles help
The value of x for the similar triangles is 8 units.
What is the value of x?The value of x is determined by applying the principle of similar triangles as shown below.
In the given diagram, we can assume the following for the similar triangles;
length 10 is congruent to length 10 + (3x + 1 )
length 22 is congruent to length 7x -1 + 22
So we will have the following equation;
(3x + 1 + 10 )/ 10 = (7x - 1 + 22 ) / 22
(3x + 11 ) / 10 = ( 7x + 21 ) / 22
22(3x + 11 ) = 10 (7x + 21 )
66x + 242 = 70x + 210
32 = 4x
x = 32 / 4
x = 8
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quadrilateral ABCD below is a rhombus. If AB = 10 units and BD = 12 units
a) What is the perimeter of ABCD? Show all work.
b) What is the area of ABCD? Show all work.
Katherine is working two summer jobs, lifeguarding and walking dogs. She can work no more than 14 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours lifeguarding,
�
l, and the number of hours walking dogs,
�
d, that Katherine can work in a given week
Answer:
The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:
l + d ≤ 14
This is because the sum of the hours worked in both jobs should not exceed 14 hours.
Add. Express your answer in standard form. (Highest exponent first and then descending order) ADD AN EXPLINATION!!!
(2^4 – 5^3 – 7) + (−5^5 − 5^2 + 9 + 17)
Answer:
We can start by simplifying each parentheses separately and then adding the resulting expressions:
(2^4 – 5^3 – 7) + (−5^5 − 5^2 + 9 + 17)
= (16 - 125 - 7) + (-3125 - 25 + 9 + 17) (using the fact that 2^4 = 16 and 5^3 = 125)
= (-116) + (-3124) (combining like terms)
= -3240
Therefore, the answer is -3240. To express this number in standard form, we write it as:
-3.24 x 10^3
The negative sign indicates that the number is less than zero, and the 3.24 tells us the value of the number. The "x 10^3" part means that we need to multiply 3.24 by 10^3 (which is 1000) to get the actual value of the number:
-3.24 x 10^3 = -3.24 * 1000 = -3240
So, the answer in standard form is -3.24 x 10^3.
Course... Penn State World... Dashboard (5) APA References P... FACTORING POLYNOMIALS Greatest common factor of three univariate monomials Find the greatest common factor of these three expressions. 28w,8w^(5), and 20w^(4)
The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.
The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.
First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.
Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.
Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.
Learn more about greatest common factor here: https://brainly.com/question/219464.
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an estate valued at 45,000 is divided among three daughters, Ana, Betty and Chandra in the ratio 7:10:13 respectively calculate the amount each received
so since 45000 split on a 7:10:13 ratio, so let's simply divide 45000 by (7+10+13) and distribute accordingly to each daughter.
[tex]\stackrel{Ana}{7}~~ : ~~\stackrel{Betty}{10}~~ : ~~\stackrel{Chandra}{13} \\\\\\ \stackrel{Ana}{7\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Betty}{10\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Chandra}{13\cdot \frac{45000}{7+10+13}} \\\\\\ \stackrel{Ana}{7\cdot 1500}~~ : ~~\stackrel{Betty}{10\cdot 1500}~~ : ~~\stackrel{Chandra}{13\cdot 1500} ~~ \implies~\hfill \stackrel{Ana}{10500}~~ : ~~\stackrel{Betty}{15000}~~ : ~~\stackrel{Chandra}{19500}[/tex]