SOLUTION
Given the question in the question tab, the following are the solution step to get the number of books they have altogether.
Step 1: Write the notations for Joseph's and Mike's books
[tex]\begin{gathered} \text{let j represents the number of books Joseph has,} \\ \text{let m represents the number of books Mike has} \end{gathered}[/tex]Step 2: Write the statements in a mathematical form
[tex]\begin{gathered} m=28---\text{statement 1} \\ \frac{1}{3}of\text{ j was given to Mike to have }m+\frac{j}{3}=28+\frac{j}{3} \\ \text{After that, }28+\frac{j}{3}=\frac{2j}{3} \end{gathered}[/tex]Step 3: Solve to get the value of j by using substitution method
[tex]\begin{gathered} \\ m=28+\frac{j}{3} \\ 28+\frac{j}{3}=\frac{2j}{3} \\ \text{ multiply through by 3} \\ 84+j=2j \\ 84=2j-j \\ 84=j \\ j=84 \end{gathered}[/tex]Therefore, Joseph had 84 books initially.
Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially
[tex]\begin{gathered} m=28,j=84 \\ \text{Total}=28+84=112 \end{gathered}[/tex]Hence, they both had 112 books altogether.
A shipping box has a volume of 1,000 cubic inches. What is the length of one side of the box?
The length of one side of the box is 10 inches.
How to find the volume of a cube?Suppose that: The side length of the considered cube is L units.
Then, we get the Volume of that cube = L³ cubic units.
The volume of a cube is of the form V = L³, where L is the side length.
Given that the shipping box has a volume of 1,000 cubic inches.
Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:
1000 = L³
Cube root both sides:
L = [tex]\sqrt[3]{1000}[/tex]
Therefore, each side is 10 inches.
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A Ford F-150 truck is considered a half-ton truck because that is how much it can haul. How many pounds can the truck haul?
The truck can haul 1102 pounds.
According to the question,
We have the following information:
A Ford F-150 truck is considered a half-ton truck because that is how much it can haul.
(More to know: ton, pounds and kilograms are the most commonly used units for measuring weight.)
Now, we already have the knowledge that 1 ton is equal to 1000 kilograms.
So, half ton will make 500 kg.
Now, in order to convert this into pounds, we will multiply 500 kg by 2.205 because we know that 1 kg makes 2.205 pounds.
1 kg = 2.205 pounds
500 kg = (500*2.205) pounds
500 kg = 1102.5 pounds
Hence, the truck can haul 1102.5 pounds.
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Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The solution of x in the mathematical statement is 11.73
How to determine the value of x?From the question, the mathematical statement is given as
x over 5 and 7 tenths equals 2 and 3 tenths.
When represented as an algebraic equation, we have
x/5.10 = 2.30
To start with, we multiply both sides of the equation by 5.10
This is represented as
5.10 * x/5.10 = 2.30 * 5.10
Evaluate the product on the left-hand side
So, we have
x = 2.30 * 5.10
Evaluate the product on the right-hand side
So, we have
x = 11.73
Hence, the value of x is 11.73
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The required simplified value of the given numeral is given as 13.11.
As given in the question, to determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
The statment given in the word string, first transform the equation in the mathematical inscription,
So,
x / 5.7 = 2.3
Simplifying,
x = 5.7 × 2.3
x = 13.11
Thus, the required simplified value of the given numeral is given as 13.11.
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Please find the coordinates and also reflect the points on the axis’s, and please demonstrate and plot the points on the graph too reflect it.
A' = (1, 3)
B' = (0, 6)
C' = (-3, 5)
D' = (-2, 2)
I’m not english person. I cannot understand those. Can someone explain some of them please? I’m trying to pass an english math exam..
Step-by-step explanation:
lo siento, no tengo idea de cómo explicarte esto. Ummm, hay una aplicación que puedes descargar en tu teléfono para tomar una foto de la hoja de trabajo o el papel y luego la traducirá para ti. Se llama buena traducción o algo en. buena suer
Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
Answer:
x = -55
Step-by-step explanation:
Given equation,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
Now the value of x will be,
→ 5(2 - x) - 10 = 25 - 2(3x + 40)
→ 10 - 5x - 10 = 25 - 6x - 80
→ -5x + 6x = 25 - 80
→ [ x = -55 ]
Hence, the value of x is -55.
How far does a rider travel in one complete rotation around the Ferris wheel?
Use 3.14 as an approximation for Pi and round the second answer below to the nearest whole number.
If the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel.
The diameter of the Ferris wheel = 80 meters
The radius of the Ferris wheel = Diameter / 2
= 80/2
= 40 meters
The Total distance travelled by the rider in one revolution = The circumference of the wheel
The circumference of the wheel = 2πr
Where r is the radius of the wheel
Substitute the values in the equation
The circumference of the wheel = 2×3.14×40
= 251.2 meters
Hence, if the diameter of the Ferris wheel is 80 meters, then a rider will travel 251.2 meters in one complete rotation around the Ferris wheel
The complete question is :
If the diameter of the Ferris wheel is 80 meters, how far does a rider travel in one complete rotation around the Ferris wheel?
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Learning target: I can calculate the surface area of 4 ( width) cm and 20 (height) cm
Answer:
20 times 4
Step-by-step explanation:
suricce area
Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.
The number of pieces of fish that would be there if Jorge divided each fish into tenths is 1730.
It is given that Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces.
We need to calculate the number of pieces of fish that would be there if Jorge divided each fish into tenths.
We know that each of the fish is divided into 10 parts.
The total number of fish available for the dog is 173.
The total number of pieces of fish is equal to the product of the number of available fish and the number of parts each fish is divided into.
The total number of pieces of fish is equal to 173*10.
The total number of pieces of fish is equal to 1730.
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what is the standard form of the equation for part a
Answer:
yea, correct, perfect yes sir
What is the effect on the graph of f (x) = |x| when the function is changed to g(x) =-2|x|
Here the graph shows reflection across x - axis by 2 units.
f(x) = |x| => g(x) = -2|x|.
Solution:Graph transformation is the process of modifying an existing graph or graphed equation to produce a variation of the following graph.The modification of algebraic equations is a common type of problem in algebra.Here given the parent function, f(x)=|x|
The translation is , g(x)= -2|x|
Which is an absolute function.
Here the transformation is .
f(x)=|x| => g(x)= -2|x|
The value of f(x) is reflecting over x- axis and value of y changes by 2 units.
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Rewrite one eighth times x cubed times y plus seven eighths times x times y squared using a common factor.
Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.
Given that,
Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.
This is how the equation can be rewritten:
The first equation is written as 1/8 x3y + 7/8 xy2.
It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.
Equation two:
1/4x.y.4x2 + 28y
1/4 .4 x³ .y + 28y
x3.y + 28y equation to be solved
Using the formula
y = (x3 + 28).
Third claim:
1/4. x. y. x2 + 7y
Fix the problem.
1/4 . x³ .y + 7y
Write y = (1/4x3 + 7) in a new way.
Fourth assertion:
1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x
After removing the common element x(1/8 x2y3+ 7), rewrite the equation.
Fifth Declaration
1/8 x. y. x² + 7y
1/8 x³. y + 7y
Equation y (1/8 x3 + 7) is rewritten.
Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.
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Last night, Luis read 75% more pages than Dayja, and Dayja read 75% more pages than Michael. If Dayja read 84 pages, how many pages did Luis, Dayja, and Michael read all together?
Answer:
Total pages read = 279 pages
Step-by-step explanation:
Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.
We learn that:
L = 1.75D, [Luis read 75% more pages than Dayja]
D = 1.75M, and [Dayja read 75% more pages than Michael]
D = 84 [Dayja read 84 pages]
We want the sum of L, D, and M
Total pages = L + D + M
We have three equations and 3 unknowns. We should be able to find a solution by rearranging and substituting.
Total pages = L + D + M
We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75
Total pages = L + D + M
Total pages = 1.7D + D + D/1.75
Total pages = D(1.7 + 1 + 1/1.75) [Isolate the D, for optional simplification]
Total pages = D(3.271)
We know D = 84, so:
Total pages = 84(3.271)
Total pages = 274.8
We'll round that to 275 pages.
Check:
L = 1.75D: L read 1.75*275 or 147 pages
D read 84 pages
D = 1.75M, or M = D/1.75; M read 84/1.75) or 48 pages
Total pages read = 147 + 84 + 48
Total pages read = 279 pages
Which statement about the data in the table is true?
O The data represent a proportional relationship, and the constant of proportionality is $10.
The data do not represent a proportional relationship, but the rate of change of the data is $5 per shirt.
There is not a constant rate of change for these data.
The data represent a proportional relationship, and the constant of proportionality is $5.
B) The data does not represent a proportional relation, but it has constant rate of change of $5 per shirt.
A)
Take number of T-shirts up to 3 and calculate their proportions.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
Clearly the rate of T- shirts is not proportional.
B)
From option (A) we found the given data is not proportional but from the table given in question the rate of change of T- shirts is indeed $5.
C)
No, there is a constant rate of change of $5 as shown in the table below.
D)
No, the data does not represent a constant proportionality. The rate varies.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
What is rate of change ?Rate of change is the rate that describes how one quantity changes relative to another quantity. If x is the independent variable and y is the dependent variable, then
rate of change change=change in y / change x
Rate of change can be positive or negative. This corresponds to an increase or decrease in the y-value between two data points. If a quantity does not change over time, it is called zero rate of change.
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Olivia purchased two blouses for $12.50 each and a shirt for $11.25.The sales tax rate is *8.5 %. How much will Olivia pay including tax?
Answer:
$39.33
Step-by-step explanation:
11.25 + 12.50 +12.50 = 36.25
36.25 + 8.5% = 39.33
HELP PSLSPSLAPSLSPSLSPSLSPSLSPSL
Answer: D) 40
Step-by-step explanation:
mph (miles per hour)
60 minutes is an hour, so the number of miles above 60 minutes (which is 40) is the answer.
Hope this helps!
What is the smallest and greatest number that rounds to 380 when
rounding to the nearest ten?
The smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
What is rounding a number?Adjusting a number's digits so that it produces an approximation of a result is known as rounding.
The given number is 380.
When rounding a number to the nearest ten, pay attention to the last digit; if it is less than five, round down; if it is five or more, round up.
Therefore, the smallest number that rounds to 380 when rounding to the nearest ten is 375.
Similarly, the greatest number that rounds to 380 when rounding to the nearest ten is 384.
Hence, the smallest and greatest number that rounds to 380 when rounding to the nearest ten are 375 and 384 respectively.
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There are two bags containing only black and green marbles.
Event 4, Event 1, Event 3, Event 2
Explanations:Number of black marbles in bag A = 11
Number of green marbles in bag A = 9
Total number of marbles in bag A = 11 + 9 = 20
Number of black marbles in bag B = 8
Number of green marbles in bag B = 2
Total number of marbles in bag B = 8 + 2 = 10
Event 1:
Likelihood of choosing a black marble from bag A = 11/20 = 0.55
Event 2:
Likelihood of choosing a black or green marble from bag A = 11/20 + 9/20
Likelihood of choosing a black or green marble from bag A = 0.55 + 0.45
Likelihood of choosing a black or green marble from bag A = 1
Event 3:
Likelihood of choosing a balck marble from bag B = 8/10 = 0.8
Event 4:
Likelihood of choosing a purple marble from bag B = 0
Since there is no purple marble in bag B
Arrangement of the events from the least likely to the most likely will be:
Event 4, Event 1, Event 3, Event 2
solve and show working:- log(x^2 + 7) base 4 = 2
The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
It is known that [tex]log_{a}b[/tex] = c can be written as [tex]a^{c}[/tex] = b.
Given that, log(x^2 + 7) base 4 = 2
Therefore, x² + 7 = 4²
x² + 7 = 16
x² = 16 - 7 = 9
x² = 9
x = ±3
Hence "The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3".
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f (x)=(x-3)^2 + 4 when is f increasing
Answer:
(3,∞)
Explanation:
Given the function:
[tex]f(x)=\mleft(x-3\mright)^2+4[/tex]The graph of f(x) is attached below:
The interval when f(x) is increasing is therefore: (3,∞)
I need help with this geometry question !! Pls help
The values of variable x are x₁ = 16, x₂ = - 4.
The measure of angle R is 60°.
The lengths of side RS are RS₁ = 256 and RS₂ = 16.
The lengths of side RT are RT₁ = 256 and RT₂ = 16.
How to find the variables associated to a given triangle
In this problem we need to find the values of four variables related to a triangle, which is seen in the picture, indicating an equilateral triangle. The solution of this question must be done by using definitions and theorems from Euclidean geometry:
Value of variable x
According to Euclidean geometry, the measures of the three sides in an equilateral triangle are the same. Then, the variable x can be found by solving the following equation:
RT = RS
x² = 12 · x + 64
x² - 12 · x - 64 = 0
(x - 16) · (x + 4) = 0
There are two possible solutions:
x₁ = 16, x₂ = - 4
Measure of the angle R
Equilateral triangles have three internal angles of 60°. Therefore, m ∠ R = 60°.
Length of side RS
There are two options:
RS₁ = 16²
RS₁ = 256
RS₂ = (- 4)²
RS₂ = 16
Length of side RT
There are two options:
RT₁ = 12 · 16 + 64
RT₁ = 256
RT₂ = 12 · (- 4) + 64
RT₂ = 16
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math pease help me i need it now asap
1. The mathematical expression for the length is C. 2x + 5.
2. The quadratic equation is A. 2x² + 5x - 18 = 0.
3. The width of the tarpaulin is A. 2 ft.
4. The length of the tarpaulin is D. 9 ft.
5. The perimeter of the tarpaulin is C. 22 feet.
How to calculate the value?From the information, the following can be deduced:
Width = x
Length = (2 × x) + 5 = 2x + 5
Area = 18 ft²
The equation will be:
Length × Width =Area
(2x + 5)x = 18
2x² + 5x = 18
2x² + 5x - 18 = 0
2x² - 4x + 9x - 18 = 0
2x(x - 2) + 9(x - 2)
Therefore, x - 2 = 0
x = 0 + 2 = 2
Width = 2
Length = 2x + 5 = 2(2) + 5 = 9ft
Perimeter = 2( Length + Width)
= 2(2 + 9)
= 22 feet.
This illustrates the concept of addition to calculate the perimeter.
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Find the two square roots of 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 1/16 = 1/4
they probably
Jessica wants to make a spinner that has all of the following characteristicsSketch a possible spinner for Jessica. Be sure to label each section of thespinner with a name and with its theoretical probability.• Blue, red, purple, and green are the only colors on the spinner.• It is half as likely to land on blue as to land on red.• It is three times as likely to land on purple as green.• There is a 50% probability of landing on either blue or red and a 50%probability of landing on either purple or green.
First we have to split the spinner into two equal parts. One half belongs to the blue and red sections, and the other half belongs to the green and purple sections.
Formulating an equation for the first part, we have:
P(b) + P(r) = 0.5 ( P(b): probability of landing on blue section, P (r): probability of landing on red section)
P(r) + 1/2*P(r) = 0.5 ( Since it is half as likely to land on blue as to land on red)
3/2*P(r) = 0.5 (Adding like terms)
P(r)= 0.5 / (3/2) (Dividing on both sides by 3/2)
P(r)= 1/3 (Dividing)
P(b)=1/2*P(r) (Finding the probability of landing on blue section)
P(b)= 1/6
Formulating an equation for the second part, we have:
P(g) + P(p) = 0.5 ( P(g): probability of landing on green section, P (r): probability of landing on purple
section)
P(g) + 3*P(g) = 0.5 ( Since it is three times as likely to land on purple as green)
4*P(g) = 0.5 ( Adding like terms)
P(g) = 0.5/4 (Dividing by 4 on both sides of the equation)
P(g) = 1/8 (Dividing)
P(p) = 3*P(g) (Finding the probability of landing on purple section)
P(p)= 3/8
a force of 4 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length?
Using the spring's force we know that 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
What does a spring's force mean?When a spring is in its equilibrium position, it applies a force F = -kx in that direction. A spring's force works as a restoring force, bringing the spring back to its equilibrium length.So, F is the 4 lb force required to maintain the spring's stretched position.
The spring has a 0.2-foot stretch, and its spring constant is k.Applying the equation F = k x 4 = k (0.2) k = 80 lb/ft.U is the effort put in to expand the spring, where x' is equal to 1.1 feet.The labor of extending a spring is denoted by the formula:
U = (0.5) k x'2So, calculate:
U = (0.5). (80). (1.1)² U = 48.4 lb-ftTherefore, 48.4 lb-ft work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
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A one way train ticket in the city cost 1.85 a monthly pass cost 65$. For what number of rides should you buy the monthly pass?
Answer: 36 rides
Step-by-step explanation: Because is you divide 65 by 1.85 you get 35.13513513513514 so just round it to the next integer of 36.
Estimate √172 to the nearest tenth. Locate the irrational number on a number line.
The irrational number on a number line is 13.1. All real numbers that are not rational are considered irrational numbers. In other words, it is impossible to describe an irrational number as the ratio of two integers.
What is irrational number ?All real numbers that are not rational numbers are referred to be irrational numbers in mathematics. In other words, it is impossible to describe an irrational number as the ratio of two integers.There is no length, no matter how short, that could be used to express the lengths of both of the two supplied segments as integer multiples of itself.
Square Root of 172 to the nearest tenth, means to calculate the square root of 172 where the answer should only have one number after the decimal point.
CalculateWe calculate the square root of 172 to be:
√172 = 13.11487704860400
ReduceReduce the tail of the answer above to two numbers after the decimal point: 13.11
RoundRound 13.11 so you only have one digit after the decimal point to get the answer: 13.1
To check that the answer is correct, use your calculator to confirm that 13.1² is about 172.
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In a sale, the normal price of a TV is reduced by 20%.
The sale price of the TV is £660
Work out the normal price of the TV.
Find the first five terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 4n − 5
Okay, here we have this:
Considering the provided sequence, we are going to find the requested first five terms of the sequence, so we obtain the following:
So what we will do is replace n from 1 to 5, we have:
n=1:
an=4n-5
a1=4(1)-5
a1=4-5
a1=-1
n=2:
an=4n-5
a2=4(2)-5
a2=8-5
a2=3
n=3:
an=4n-5
a3=4(3)-5
a3=12-5
a3=7
n=4:
an=4n-5
a4=4(4)-5
a4=16-5
a4=11
n=5:
an=4n-5
a5=4(5)-5
a5=20-5
a5=15
Finally we obtain that the first five terms are: -1, 3, 7, 11, 15
Please help ASAP! Compare and contrast the formulas for P(A and B) for dependent and independent events. What is the relationship between P(B) and P(B|A) and can one equation be used for both independent and dependent events?
Dependent events;
The probability of one event DOES effect the probability of a 2nd event.
Independent events;
The probability of one event DOES NOT effect the probability of a 2nd event
Give the equation for calculating the likelihood that events A and B will occur when A and B are dependent events. The equation P(A and B) = P(A) P(B|A) yields the likelihood that A and B will occur.If the events A and B are not mutually exclusive, the probability is: (A or B) = p(A) + p(B) – p(A and B).We cannot use one equation for both independent and dependent events.Learn more about dependent and independent events here;
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