[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (1500)(0.07)(8) \implies I = 840[/tex]
Choose the best initial step in solving the following system by substitution.
2x + 3y = –12
6x + y = 18
Answers:
1.Solve the first equation for x.
2.Solve the first equation for y.
3.Solve the second equation for x.
4.Solve the second equation for y.
Using substitution method, the best initial step in solving the equation is solve the first equation for x.
How to solve equation by substitution method?The equation can be solved by substitution method as follows:
2x + 3y = -12
6x + y = 18
Hence, let's make y the subject of the formula in equation(ii)
6x + y = 18
y = -6x + 18
We have to substitute the value of y in equation(i)
2x + 3y = -12
2x + 3(-6x + 18) = -12
2x - 18x + 54 = -12
- 16x + 54 = -12
-16x = - 12 - 54
- 16x = -66
x = 66 / 16
x = 33 / 8
Therefore,
6(33 / 8) + y = 18
99 / 4 + y = 18
y = 18 - 99 / 4
y = - 27 / 4
From the solving above the best step to solve the equation is solving the first equation for x.
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A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbound train. After 2 hours, they are 240 miles apart. At what speeds are the two trains traveling?
please help me, I'm gonna fail my test tomorrow
Answer:
Speed of northbound train = 66
Speed of southbound train = 54
Step-by-step explanation:
First, let's make the variables simpler:
Speed of southbound train = x
Thus:
Speed of northbound train = y = x + 12
Distance = speed · time
240 = 2 ( x + x + 12 ) = 2 ( 2x + 12 ) = 4x + 24
216 = 4x
x = 54
Now, plug in x to find the speed of the northbound train (y):
y = 54 + 12 = 66
The heartbeat of a horse is about 42 beats per minute. About how many times would it beat in ten minutes?
A. 400 beats
B. 450 beats
C. 475 beats
D. 500 beats
The number of heartbeat in ten minutes is 420 beats
What are unit rates?Unit rates are the rates of a quantity to one of another quantity
How to determine the number of heartbeats?From the question, the given parameters are:
Number of heartbeats per minute = 42 beats per minute -- this represents the unit rateNumber of minutes = 10 minutesThe number of heartbeats in these ten minutes is then calculated as
Total heartbeats = Number of heartbeats per minute x Number of minutes
Substitute the known values in the above equation
So, we have
Total heartbeats = 42 x 10
Evaluate
Total heartbeats = 420
Hence, the total heartbeat is 420 beats
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Which expressions can be factored using the difference of squares identity?
The expression, for example, x²- 49 may be factored as (x+7)(x-7). can be factored in using the difference of squares identity.
What is the "Difference of Squares" identity?The difference of the square's identity is shown below:
(a+b)(a-b) = a² -b²
When an expression can be seen as the difference of two perfect squares, i.e. a² -b², we can factor it as (a+b) (a-b).
For example, x²- 49 may be factored as (x+7)(x-7).
This approach is based on the pattern (a+b)(a-b) = a² -b², which may be validated by extending the parenthesis in (a+b)(a-b).
Thus, the expression, for example, x²- 49 may be factored as (x+7)(x-7). can be factored in using the difference of squares identity.
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giving ten points since thats all i have
example of an event which has a probability of 0. Explain why the probability equals 0.
The example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.
The probability is the branch of mathematics that shows the occurrence of the random event. The value of the probability varies from 0 to 1.
The equation of the probability is
Probability = Number of favorable outcomes / Total number of outcomes
The probability of getting number number 7 when you throw a die once is zero. Because when you throw a die the possible outcomes are 1, 2, 3, 4, 5 and 6. We wont get number 7. Therefore the probability is zero
Hence, the example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.
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Simplify the expression. Show your work.
[tex]\sqrt[3]{27x^6y^4}[/tex]
[tex]\sqrt[3]{27x^6y^4}\implies \sqrt[3]{3^3 (x^2)^3 y^3 y^1}\implies 3x^2 y\sqrt[3]{y}[/tex]
Identify the location of the values √10. √13. and 22
on the number line.
A
B
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
A: Point A is 22 point B is √10. and point C is √13
B:Point A is √10. point B is √13, and point C is 22
C:Point A is 22, point B is 13. and point C is √10
D:Point A is √10. point B is
and point C is √13
Answer:
1
Step-by-step explanation:
Write an equation of each parabola in vertex form vertex : (1/2,1) point: (2,-8)
Answer: [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]
Step-by-step explanation:
Using the vertex form, the equation is
[tex]y=a \left(x-\frac{1}{2} \right)^2 +1[/tex]
Substituting in the coordinates (2, -8) to solve for a,
[tex]-8=a \left(2-\frac{1}{2} \right)^2 +1\\\\-8=\frac{9}{4}a+1\\\\-9=\frac{9}{4}a\\\\a=-4[/tex]
So, the equation is [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]
Larry can carry a maximum of 60 pounds.
He is already carrying a chair that weighs 20 pounds. He has boxes as well to carry that weigh 5 pounds each.
Which inequality represents all possible values of x, the number of boxes that he can carry?
A. 20x +5 ≤ 60
B. 5x + 20 ≥ 60
C. 20x + 5 ≥ 60
D. 5x + 20 ≤ 60
Answer: Your answer would be D
Step-by-step explanation: The reason why is because in the question it said he is already carrying a 20 pound chair. It then say he can carry some boxes that weigh 5 pounds each. The word each is your keyword. With that you can replace the x variable with some single digit numbers. But you also need to make sure your total is less than or equal to 60 pounds. You would pick the less than or equal to sign since he can only carry 60 pounds or less.
The histogram shows information about the weights of some of the parcels handled by a delivery company in one month.
Zoe says:
"There are fewer parcels weighing between g and g than parcels weighing between g and g."
Is Zoe correct?
Show how you decide.
(4 marks)
From the histogram of the distribution, it is found that Zoe is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed in the distribution. When the input is an interval of values, as is the case in this problem, it shows the number of observations that is in each interval.
Hence, from the histogram in this distribution, it is found that:
There are approximately 75 people weighing between 300 g and 450 g.There are 50 people weighing between 450 g and 700 g.75 is a greater amount than 50, hence Zoe's statement is not correct, as there are more people weighing between 300 g and 450 g than people weighing between 450 g and 700 g.
What is the missing information?The complete problem is given by the image at the end of the answer.
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Use the parent function f(x) and the description of the transformation to write the new function g (x) Rotate the graph f(x) = - 4x + 5 until it has the same steepness in the opposite direction. This represents reflecting the graph across the y-axis. Therefore the new function is g(x) = What is the answer
Given:
The given function is, f (x) = -4x + 5.
The objective is to reflect the graph across the y - axis and find the new function.
Explanation:
The general transformation formula for reflection over y-axis is,
[tex]g(x)=f(-x)[/tex]To find f(-x):
The required transformation can be calculated as,
[tex]\begin{gathered} g(x)=f(-x) \\ g(x)=-4\mleft(-x\mright)+5 \\ g(x)=4x+5 \end{gathered}[/tex]Hence, the new function is g(x) = 4x + 5.
each side of a square is increasing at a rate of 8 cm/s. at what rate is the area of the square increasing when the area of the square is 81 cm2?
The area of square is increasing with the rate of 144 cm/s2.
What is rate of expansion of solid ?For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for thermal expansion of solids in daily life.
A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.
CalculationL = length of a side
A = L2
dA/dt = 2L dL/dt
dL/dt = 8 cm/s
A = 81 cm2 ⇒ L = √A = √81 cm = 9 cm
dA/dt = 2(9cm)(8 cm/s) = 144 cm/s2
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NEED DONE ASAP WILL MARK BARINLIEST
Including both end zones, a football field is 4,320 inches long. What is this value expressed in scientific notation?
A
4.32×10−4
B
4.32×10−3
C
4.32×103
D
4.32×104
Answer:39.2 40.2 444.96
Step-by-step explanation:
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) It takes 51 pounds of seed to completely plant a 9-acre field.
How many acres can be planted per pound of seed?
acres per pound
(b) Christine runs 4 miles in 22 minutes.
How many minutes does she take per mile?
minutes per mile
Answer:4
Step-by-step explanation:
Answer:a) Given :
51 pounds of seed can be planted in = 9 acre field.
Per pound of seed =
We can convert 9/51 in simplest fraction by dividing top and bottom by 3.
We get
Therefore, 3/17 of an acrs can be planted per pound of seed.
b) $10 amount = 16 pounds of sugar.
$1 amount = 16/10 = 1.6 pounds of sugar.
Therefore, 1.6 pounds of sugar she got per dollar.
Step-by-step explanation:
what does 6/3 = and what does 30/10 =
Answer:
6/3=2
30/10=3
Step-by-step explanation:
For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.
The White family purchases a new pool table on a no-interest-for-one-year plan. The cost is $2,665. There is a d dollars down payment. If they make a minimum monthly payment of m dollars until the last month, express their last month's payment algebraically.
The last month's payment for White family can be algebraically expressed as;
⇒ 2665 - d - 11m.
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Cost of a new pool table = $2,665
Down payment = d dollars
And, The monthly payment = m dollars.
Since, we have to given a duration of twelve months, we will have to subtract one month from 12 to give, 11 months.
Hence, We can formulate an algebraic equation as;
2665 - d - 11m.
Thus, The last month's payment for White family can be algebraically expressed as;
⇒ 2665 - d - 11m.
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Question 3 options:
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of ___________________________makes this argument true.
The law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
It is given that:
The statement is:
If you have a cat, then it will chase mice.
As we know, from the definition of the Law of Syllogism, the legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
Your cat will chase mice.
The Law of syllogism makes this argument true.
Thus, the law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
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if test scores for an exam were normally distributed with a mean of 75 and a standard deviation of 5, find the probability that a randomly selected student scored less than 82.
the probability that a randomly selected student scored less than 82.
Then the value is P( X< 82)=0.9192
From the question we are told that
The sample size is n = 24
The mean is =75
The standard deviation is =5
Generally the probability that a randomly chosen student scored is less than 82 is mathematically represented as
P( X < 82) = P ( Z< 82-75/5)
=P(Z <1.4)
=0.9192
From the z table the area under the normal curve corresponding to 1.4 is 0.9192
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sally has a cube of side length units such that the number of square units in the surface area of the cube equals of the number of cubic units in the volume. she also wants to make a square for which the number of square units in the area of the square is equal to the number of cubic units in the volume of the cube. what should the side length of the square be?
The side of square is 216 units and side of cube is 36 units.
According to question we have given that Sally has a cube of some length in units. Let the length of side of cube is S units .
As we know , Area of cube = 6 (side)²= 6S² square units.
Volume of cube = (side)³ = S³ cubic units
Then, as given area in square units of cube = 1/6 of volume of cube in cubic units . That is 6S²= 1/6 S³ => S = 36 units
Area of cube with side 36 units = 6×36²=46656 square units
Volume of cube with side 36 units = 36 ³ cubic units
So, the side of cube is 36 units.
Also, the number of square units in area of Square = number of cubic units in volume of cube
Area of square (S²) = 46656
Side of square = sqrt (46656 ) = 216 units
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PLEASE HELP I AM GROUNDED AND MY MOTHER IS SO MAD AT ME FOR MY GRADE
Answer:
64°
Step-by-step explanation:
it's a right angle (90°) so u take away the other angle (26°) which gets you 64°
27/50 as a percentage
Answer: 54%
Step-by-step explanation:
1. The Mariaskis' home is located in a community where the rate of
assessment is 45% of the market value. The tax is $65 per $1,000 of
assessed value. The Mariaskis' home has a market value of $97,400.
a. What is the assessed value?
b. What is the yearly real estate tax?
a.) The Assessed value is $43,830
b.) Annual Tax is $2,848.95
Define marked price
'Marked price' is the general price of the thing without any discount. 'discount' is a percentage of the marked price.
Given,
Assessment rate = 45%
Tax rate is $65 per $ 1000 of assessed value
Marked value = $97,400
a.)
To obtain assessed value,
calculate the 45% of $97,400 like that
45/100 = x/97,400
cross multiply the ratios
100x = 45 * 97,400
x = (45 * 97,400) / 100
x = 45 * 974
x = 43,830
Hence,the Assessed value is $43,830
b.)
Find yearly real estate tax,
Assessed value = $43,830
Tax rate is = 65 / 1000 of assessed value
= 0.065 * 43830
= 2,848.95
Hence, the annual tax is $2,848.95
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A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5? OA) yes: The packs of socks are marked up to $7 and then discounted to $5. OB) yes; The packs of socks are marked up to $9 and then discounted to $5. OC) no: The packs of socks are marked up to $7 and then discounted to $4.20. OD) no, The packs of socks are marked up to $5.20 and then discounted to $4.99.
Answer:
C) no: The packs of socks are marked up to $7 and then discounted to $4.20
Step-by-step explanation:
You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.
Marked-up priceWhen the $5 cost is marked up by 40%, the resulting price is ...
$5 + 0.40×5 = $5 +2 = $7.
The socks are marked up to $7.
Marked-down priceWhen the $7 price is marked down by 40%, the resulting price is ...
$7 - 0.40×7 = $7.00 -2.80 = $4.20
The socks are discounted to $4.20.
Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
s:[-2,-3] is the answer
The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
The set S : { - 2 , - 3 , - 4 , - 5 }
The inequality relation is 2p - 8 < 5p + 4
Now , substituting the value from set S in the inequality , we get
When p = - 2 :
2p − 8 < 5p + 4
2(-2) − 8 < 5(-2) + 4
-4 − 8 < -10 + 4
-12 < -6 TRUE
When p = - 3
2p − 8 < 5p + 4
2(-3) − 8 < 5(-3) + 4
-6 − 8 < -15 + 4
-14 < -11 TRUE
When p = - 4
2p − 8 < 5p + 4
2(-4) − 8 < 5(-4) + 4
-8 − 8 < -20 + 4
-16 < -16 FALSE
When p = - 5
2p − 8 < 5p + 4
2(-5) − 8 < 5(-5) + 4
-10 − 8 < -25 + 4
-18 < -21 FALSE
Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation
Hence , the set S:{ -2,-3 } is the solution
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NEED HELPPP ASAPPPPPPP
For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.
What is an inverse in a function?In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.
How do you find the inverse of a function?To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.
What is inverse example?Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.
What are the properties of inverse function?Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.
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48x35 in smtandard algorithm
48×35. By using standard algorithm we got 1680.
Given that,
48×35
We have to find the multiplication of the numbers by standard algorithm.
Standard algorithm is nothing but the words "Standard" and "Algorithm" make up the standard algorithm. Standard refers to the standard or standard way of doing anything, such as eating, bathing, or brushing one's teeth. Algorithms are nothing more than a task's sequential execution. As a result, solving a problem step by step is a common algorithm in mathematics. You will discover what a standard algorithm is in this article, along with the addition, subtraction, multiplication, and division standard algorithms.
If you don't use the standard algorithm , your answers will be incorrect.
48×35=1680
Therefore, By using standard algorithm we got 1680.
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Rory is adding a sidewalk to his front yard. The picture shows the dimensions of the
sidewalk.
How much cement, in cubic feet, does Rory need to build the sidewalk?
A. 156
B. 96
C. 60
D. 4608
Answer:
348 ft
Step-by-step explanation:
First split the sidewalk into two rectangles. then multiply the LxWxH (length times width times height) of both rectangles. 8 times 6 times 6 = 288 ft. then 10 times 2 times 2 = 60. then add the two volumes of the rectangles to result in 348 cubic ft
Nicole has a machine that will produce a number from 1 through 50 when she pushes a button. a. p (multiple of 10)? b. p (not 100)? c. p (not a multiple of 4)? d. p (one-digit number)?
Total outcome is 50 [because the number produced by the machine is from 1 to 50]
Question a:
Multiple of 10 are 10, 20, 30, 40, 50
There are five possible outcomes for multiple of 10
P(Multiple of 10) = 5/50 = 1/10
Question b:
Number 1 to 50 will be all the outcomes that are not 100
There are 50 possible outcomes
P(not 100) = 50/50 = 1
Question c:
Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
There are 12 possible outcomes for multiple of 4
We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes
P(not a multiple of 4) = 38/50 = 19/25
Question d:
One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9
There are 9 possible outcomes
P(one-digit number) = 9/50
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if you want to change m² to cm² what will you do
Answer:
Use this relation
Im^2 = 10000cm^2
Answer:
multiply m² by 10000
Step-by-step explanation:
1 m = 100 cm
1 m² = 100² = 10000 cm²
then to change m² to cm² , multiply m² by 10000