The properties in each step is:
Step 1 and 2: distributive property
Step 3: addition property of equality
Step 4: division property of equality
How to Apply the Property of Equality?Given the equation, x + 0.06x - 1.50 = 3.80, we can solve for x using the steps with the following appropriate properties shown below:
Step 1:
(1 + 0.06)x - 1.50 = 3.80 (distributive property)
Step 2:
1.06x - 1.50 = 3.80 (distributive property)
Step 3: Add 1.50 to both sides of the equation
1.06x = 5.30 (addition property of equality)
Step 4: Divide both sides by 1.06
x = 5.00 (division property of equality)
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9,369 divided 53 help
Answer - 9,369 divided 53 = 176.773584906
4 A number generator produces two digits in boxes like this. Each digit is generated randomly. It can be any digit from 0 to 9. Find the probability that: a the first number is 4 b the second number is less than 8 numbered 1 to 4 4 6 c there are no Os.
a. The probability that a first number is 4 is 1/10
b. The probability that the second number is less than 8/10.
c. The probability that there will not be any zero's is 81/100
Given, a number generator produces two digits in a box, each of it is generated randomly from 0 to 9.
a. The probability that the first number is 4 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 1/10
b. The probability that the second number is less than 8 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 8/10
c. The probability that there are no zero's = ?
since there are two boxes, there is possibility of getting two zero's.
probability of an event = favourable number of outcomes/ Total number of outcomes.
9/10 × 9/10
= 81/100
Hence we get the required results.
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The Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky. Describe the type of lines formed by the bridge and the river.
The Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky, the lines formed buy the bridge and the river is skew lines
Given,
The situation, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky.
The line formed by the bride and the river that do not intersect and are not coplanar
So, those are skew lines
Hence, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky, the lines formed buy the bridge and the river is skew lines
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Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
two thirds
18 over 54
negative two ninths
negative two and 42 over 54
Negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity will be C. negative two ninths
How to compute the expression?Based on the information given, the expression will be:
= 1/6 ×( 3 - 15 ) × (1/3)²
= -1/6 × -12 × 1/9
= -2 × 1/9
= -2/9
In conclusion, the correct option is D.
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As seen in the diagram below, Sydney is building a walkway with a width of x feet to
go around a swimming pool that measures 8 feet by 7 feet. If the total area of the pool
and the walkway will be 240 square feet, how wide should the walkway be?
Answer: 4 feet
Step-by-step explanation:
[tex]Let\ width=x > 0\\Hence,\\(8+2x)(7+2x)=240\\(8)(7)+(2x)(7)+(8)(2x)+(2x)(2x)=240\\56+14x+16x+4x^2=240\\4x^2+30x+56=240\\4x^2+30x+56-240=240-240\\4x^2+30x-184=0\\[/tex]
Divide both parts of the equation by 4 :
[tex]x^2+7.5x-46=0\\x^2+11.5x-(4)(x)-(4)(11.5)=0\\(x)(x+11.5)-(4)(x+11.5)=0\\(x+11.5)(x-4)=0\\x+11.5=0\\x=-11.5\ feet\notin, \ hence\ x > 0\\x-4=0\\x=4\ feet\in,\ hence\ x > 0[/tex]
A fair coin is tossed 16 times. (10 points) what is the mean number of heads? (5 points) what is the standard deviation for the number of heads? (5 points)
The mean number of heads is 8.
What is meant by Binomial distribution?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. The probability of observing x successes in N trials is calculated using the binomial distribution, with p standing for the probability of success on a single trial. According to the binomial distribution, p is fixed throughout all trials.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution. In mathematics and statistics, the binomial distribution is the likelihood that a specific outcome in a series will occur when there are only two possible outcomes: success or failure. Bi is the prefix for two.
Use the formula for the mean for the Binomial Distribution: μ = np
• n = 16
• p = ½
Therefore μ = 16 × ½ = 8
The mean number of heads is 8.
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The maximum upload size allowed for a file is 1.024x108 bytes. Write this number in standard
form.
It would be 0.00000001024 in standard form
Describe in words where the square root of 45 minus 9 would be plotted on a number line.
Between −3 and −2, but closer to −3
Between −3 and −2, but closer to −2
Between 6 and 7, but closer to 6
Between 6 and 7, but closer to 7
Answer:
Between -3 and -2, but closer to -2
Step-by-step explanation:
The square root of 45 is approximately 6.708.
Subtract 9 from that and you get -2.292.
-2.292 is between -3 and -2, but is closer to -2.
simplify -6(2+x) i need help
How do i solve this?
Answer:
400,000,000 or [tex]4*10^{8}m[/tex]
Step-by-step explanation:
Put them both into standard form.
[tex]0.0001=1*10^{-4} and 4 trillion is 4*10^{2}[/tex]
Multiply them together.
[tex](1*10^{-4})*(4*10^{12}=4*10^{8}[/tex]
Find the center and the radius of each circle. (x+2)²+(y+4)²=50
The equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 2)^2 + (y + 4)^2 = 50, is in standard form, then
h = -2
k = -4
r = 5√2
Hence, the equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
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Determine the truth value of the following statement for each set of conditions.
If you have a fever, then you are sick. (Lesson 2-3)
You have a fever, and you are not sick.
The truth value of the statement "If you have a f e v e r, then you are s i c k." can be classified as T because it is true.
The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as Fa l s e.
What is the Truth Value?The definition of a truth value is the a t t r i b u t e of a p r o p o s i t i o n as to whether the p r o position is true or false.
For example, the truth value for "3 is odd" is true, which can be denoted as T. The truth value of "2 + 2 = 5" is false.
Now, it is well known that fever is a symptom of a s i c k n e s s. Thus, if you have f e v e r, then you are classified as being s i c k. Thus;
The truth value of the statement "If you have a fever, then you are s i c k." can be classified as T because it is true.
The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as False
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During one week, Sheila made
several changes to her bank account.
She made three withdrawals of $30
each from an ATM. She also used
her check card for a $156 purchase.
Then she deposited her paycheck of
$325.
By how much did the amount in her
bank account change during that
week?
$59 increase in her bank account during that week.
What is algebraic operation ?Any of the basic arithmetic operations—addition, subtraction, multiplication, division, raising to the power of a whole number, and taking roots (fractional power)—is considered an algebraic operation. These procedures could be applied to numerical data, in which case they are frequently referred to as arithmetic operations. Similar operations can be carried out on variables, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of a set to the same set.
Given that : Sheila made four withdrawals of each from an ATM. . She also made a $156 purchase with her check card. She then deposited her $375 salary.
It's difficult to determine the solution because we don't know how much money she had in her bank account before making 4 withdrawals, thus a like and rating would be really appreciated. We know she took out $40 four times, which is $160. She also used her card to make a $156 purchase, so when we sum the two amounts, we get $316. She then placed a check for $375 into the bank account, therefore we must deduct $316 from that sum to get at $59; but, since we deducted, Given that we end up with $59 rather than the money we wasted at the beginning, the fact that the price is higher than $316 indicates that there has been an increase.
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6 5/15 in its simiplist form
Answer:
6 1/3
Step-by-step explanation:
Well 5 goes into 15 3 times because 5 * 3 = 15.
So the answer would be 1/3 for the fraction and 6 1/3 for the answer.
Answer:
6 1/3
Step-by-step explanation:
6 is already in its simplest form.
5/15 = 1/3
^ 5/15 is equivalent to 1/3
Evaluate each expression for x=-2,0,1 , and 4.
(1/2)x-8
The value for x = -2,0,1 , and 4 will be -9, -8, -15/2 and -6 respectively.
For x = -2
The value will be -
(1/2)x-8
(1/2)(-2) - 8
= -9
For x = 0
The value will be -
(1/2)x - 8
(1/2)(0) - 8
= -8
For x = 1
The value will be -
1/2(1) - 8
= -15/2
For x = 4
The value will be -
1/2(4) - 8
= -6
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A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after m months is given by the
following function.
H(m)=51+m
What is the plant's height after 18 months?
M
the plants height would be 69cm
what is the absoulte value of 0.75
Answer: 0.75
Step-by-step explanation:
Point D(2,4) is rotated 180 degrees about the origin. What are the coordinates of D'?
The coordinates of D' are D' = (-2, -4)
What are the coordinates of D'?The given paramaters are
D = (2, 4)
The rule is given as
180 degrees about the origin.
This is represented as
(x, y) = (-x, -y)
So, we have
D' = (-2, -4)
Hence, the coordinates of D' are D' = (-2, -4)
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5years ago a woman was 4 times as old as her daughter.in four years time the woman will be two and a half times as old as her daughter.find their present age
At present, the age of the woman is 29 years, while the age of her daughter is 6 years.
In the question, we are given two characters, a woman and her daughter, and told to find their present age. We are also given some clues as to how we will arrive at the answer. Let's consider the first one.
In the first sentence, we are told that 5 years ago, the woman was 4 times as old as her daughter. We don't know the woman's age or her daughter's, so let's call the woman's present age x and her daughter's present age y for now. To know the age of the woman 5 years ago, we will subtract 5 from her current age, which will give us x - 5. Also, the woman was 4 times as old as her daughter 5 years ago, hence:
x - 5 = 4y
If we rearrange that; x = 4y + 5 (let's call this equation 1)
Now, on to the second clue.
In the second sentence, we are told that in four years time, the woman will be two and a half times as old as her daughter. The woman's age in 4 years time is x + 4, hence:
x + 4 = 2[tex]\frac{1}{2}[/tex]y
x + 4 = 5y/2
2x + 8 = 5y (let's call this equation 2)
Next, we will find the value of y (the daughter's present age) by substituting equation 1 into equation 2, that is, putting '4y + 5' in place of x in equation 2, thus:
2(4y + 5) + 8 = 5y
8y + 10 + 8 = 5y
8y - 5y = 18
3y = 18
y = 6
Therefore, at present, the daughter is 6 years old. To find the mother's age, we will substitute the daughter's age in place of y in equation 1:
x = 4y + 5
x = 4(6) + 5 = 29
Hence, the woman is 29 years old, and her daughter is 6 years old.
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(7.2 x 107) + (5.5 x 106) Express the result
in scientific notation
Answer:
1353.4 x 10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) = 770.4 + 583 = 1353.4
Scientific Notation: 1353.4 = 1353.4 x 10^3
Answer: 1.3534x10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) =6767/5 = 1353.4 = 1.3534x10^3
a²b-b² if a = 3 and b = -4
this was to my last promt sorry
Answer:
21
Step-by-step explanation:
Answer:
The answer is -20
Step-by-step explanation:
This prblem calls for substitution. In this case, if a = 3 and b = -4, then
(3)²(-4) - (-4)²
Now we can solve using order of operations.
(9)(-4) + 16 << (two negatives make a positive)
-36 + 16
= -20
Hope this helps!
Ben joins a book club. He pays $12 for each book and $5 for shipping and handling charges for each order. A. Name the quantities that change in this problem situation and the quantities that remain constant. Determine which quality is independent and which quantity is dependent. B. Create a table of values to represent the total cost if Ben orders 1 or 2 books or spends $41, $65, or $125
ignore question A
Ben joins a reading group. Each order costs him $12 for the book and $5 for postage and handling. A. Identify the variables that change and the variables that don't change in this issue. Identify the dependent and independent components of each quantity.
I can say that the price of the books is independent and the shipping and handling charges is dependent.
Given that Ben joins a book club.
Ben pays $12 for each book and $5 for shipping and handling charges for each order.
Shipping and handling quantities remain the same.
The amount he pays for each book quantities change every time so it is not constant.
Therefore, We can say that the price of the books is independent and the shipping and handling charges is dependent.
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At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Type the answer in the box to represent the Cookie Shop's profit at the end of January.
Please dont put random answers
Ill give brainlyist to the correct answer
The Cookie Shop's profit at the end of January due to the decrease was $12000
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Hence:
Decrease in profit = 20% of $15000 = 0.2 * 15000 = $3000
Profit at end of January = $15000 - $3000 = $12000
The Cookie Shop's profit at the end of January due to the decrease was $12000
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For a fundraising project, your math club is publishing a calendar. The cost of the digital images and the permission to use them is $125. In addition to these “one time” charges, the unit cost of printing each calendar is $3.25.
Part a: Write an equation for the total cost of the calendars.
Part b: Write a model that gives the average cost A per calendar as a function of the number of calendars printed.
Part c: Use the graph of the model shown below to estimate the number of calendars that must be sold before the average cost drops to $5 per calendar.
The require answers are,
Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Cost of the digital images and the permission = $125
“one time” charges = $3.25
Part a: The equation for the total cost of the calendars
THere are 100 calendars printed.
So, “one time” charge = 3.25*100
So, the total cost of the calendars C is given as,
C = 125 + 3.25*100
C = 125 + 325 = 450
Thus, the equation for the total cost of the calendars is given as,
C = 125 + 3.25*100 = 450
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed
Let there are x calendars printed
Total “one time” charges = 3.25x
So, Average cost is given as,
A = 125 + 3.25x
this is the model that gives the average cost A per calendar
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar
Now from the graph it must be seen that the average cost drops to $ 5 per calender at 70.
Thus, number of calendars that must be sold before the average cost drops to $5 per calendar = 70
Thus, the require answers are,
Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350
Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x
Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.
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Find the inverse function for: f(x)=5x-15
Reduce your answer
F-1(x)=x/?+?
Answer:
[tex]f^{-1}(x)=\dfrac{x}{\boxed{5}}+\boxed{3}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=5x-15[/tex]
An inverse function is a reflection of the function in the line y = x.
To find the inverse of the given function, replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=5x-15[/tex]
Rearrange the equation to make x the subject:
[tex]\implies y+15=5x-15+15[/tex]
[tex]\implies y+15=5x[/tex]
[tex]\implies 5x=y+15[/tex]
[tex]\implies \dfrac{5x}{5}=\dfrac{y}{5}+\dfrac{15}{5}[/tex]
[tex]\implies x=\dfrac{y}{5}+3[/tex]
Replace x with f⁻¹(x) and y with x. This is the inverse function:
[tex]\implies f^{-1}(x)=\dfrac{x}{5}+3[/tex]
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Find the coordinates of Z if Y is the midpoint of XZ, X(-10, 9), and Y(-4, 8).
The coordinates of Z are (2,7).
What is coordinates in math?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The formula to calculate the midpoint between two points is equal to
[tex]Y = ( \frac{(x_{1} + x_{2}) }{2} , (\frac{y_{1} + y{2} }{2} )[/tex]
we have
X(-10,9),Y(-4,8)
Let
(x2,y2) ----> the coordinates of Z
substitute the values
( -4.8) = ( -10 + x₂ /2 , 9 + y₂/2)
Solve for x2
-4 = ( -10 + x₂/2
-8 = -10 + x₂
x₂ = -8 + 10
x₂ = 2
Solve for y2
8 = (9 + y₂)/2
16 = 9 + y₂
y₂ = 16 - 9
y₂ = 7
therefore, The coordinates of Z are (2,7)
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Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above
Answer:
A. $93.28
Step-by-step explanation:
The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get $93.28
5 ( C - 3 ) = 10 find C
Answer: c=5
Step-by-step explanation:
5(c-3)=10
5c-15=10
5c=10+15
5c=25
c=5
Answer:
5(c-3)=10
(c-3) =10-5
(c-3)=5
c=5+3
c=8
Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(4,0) and (-3,-7)
y = x - 4 is an equation of the line in slope-intercept form passing through points (4 , 0) and (-3 , -7)
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(4 , 0) and Point 2(-3 , -7)
slope = m = (y2 - y1) / (x2 -x1)
m = (-7 - 0) / (-3 - 4)
m = -7/-7
m = 1
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = 1x + b
Using Point 1,
0 = 1(4) + b
b = -4
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = 1 and b = -4
y = x - 4
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Please help asap (Show work)
Answer:
See attached image.
Step-by-step explanation:
Substitute 1,2,3, or 4 for [tex]x[/tex]. Then calculate using the order described by PEMDAS.
