The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
Let p represents the paycheck.
William paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.
He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund
If we put the parts together, the equation we get is;
p = $50 +$100 +$100 +$100
The equation can be summarized as;
p = $50 + 3($100 )
Now we can easily find how much was William paid;
p = $50 + 3($100)
p = $50 +$300
p = $350
Hence William was paid $350.
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Of the students at Milton Middle School, 192 are girls. If 60% of the students are girls, how many total students are there at Milton Middle school?
Answer:
320 Students
Step-by-step explanation:
Hope this helps :)
Упростить выражение log54+log53 и итог умножить на два
Answer:
6.913339
Step-by-step explanation:
How much water should be added to 30 mL of 18% alcohol solution to reduce the concentration to 15%
The amount of water that should be added to 30 mL of 18% alcohol solution to reduce the concentration to 15% is: 6ml.
Amount of water added to alcohol solutionLet x represent the amount of water
Hence,
15% = .18(30)/(30+x)× 100
Solve for x
.15 = 5.4/(30+x)
.15(30+x) = 5.4
30 + x = 5.4/.15= 36
x = 36 - 30
x = 6 ml
Therefore the amount of water that should be added to 30 mL of 18% alcohol solution to reduce the concentration to 15% is: 6ml.
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5) Margot buys a 5 litre bottle of lemonade for £2.30. She divides it into glasses. She
pours 250ml into each glass. She sells all the glasses at 25p each.
Work out her percentage profit.
Answer: 117.39%
Step-by-step explanation:
5 Litre x 1000 ml (1 litre=1000ml)
=5000 ml
5000÷250
=20 glasses
20 x 25p = 500p (£1 = 100p)
£(500÷100)=£5.00
5.00-2.30/2.30 x 100%
=2.7/2.3 x 100%
≈117.39%
Does this help?
You are graphing rectangle ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the rectangle: A(-7, -2), B(3, -2),A(−7,−2),B(3,−2),A, left parenthesis, minus, 7, comma, minus, 2, right parenthesis, comma, B, left parenthesis, 3, comma, minus, 2, right parenthesis, comma and C(3,-5)C(3,−5)C, left parenthesis, 3, comma, minus, 5, right parenthesis.
What are the coordinates of point DDD?
Answer:
5 units
Step-by-step explanation:
The graph, the coordinates of point D is (-7, -5).
The given coordinates of the rectangle ABCD are A(−7, -2), B(3, -2) and C(3, −5).
We need to find the coordinates of point D.
How to plot the coordinates on the cartesian plane?A cartesian plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.
Now, plot A(−7, -2), B(3, -2) and C(3, −5) on cartesian plane.
The coordinates are plotted on the graph, shown below.
From the graph, the coordinates of point D is (-7, -5).
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Find the sum horizontally.
(ab²+26²)+(-6cab² +26²)=
we get the sum of (a b² + 26² ) + ( - 6 c a b² + 26² ) as a b² ( 1 - 6 c) + 1352.
We are given the expression:
(a b² + 26² ) + ( - 6 c a b² + 26² )
We need to find its sum.
a b² + 26² - 6 c a b² + 26²
a b² - 6 c a b² + 26² + 26²
a b² - 6 c a b² + 676 + 676
a b² - 6 c a b² + 1352
a b² ( 1 - 6 c) + 1352.
Therefore, we get the sum of (a b² + 26² ) + ( - 6 c a b² + 26² ) as a b² ( 1 - 6 c) + 1352.
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17. the amount a of money in an account after simple interest has been earned is given
by the formula a = p + prt where p is the principal, r is the annual interest rate
in decimal form, and t is the time in years.
a. solve the formula for r
b. the amount of money in an account after interest has been earned is $1080, the
principal is $1000, and the time is 2 years. what is the annual interest rate?
c. solve the formula for p.
pl
a) the formula for r is r = (a/p - 1)/r
b) The interest rate for the principal is $1000, the time is 2 years and simple inters $1080 is 0.04
c) The formula for p is p = a/1+rt
Simple Interest:
Simple interest is the process of multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given,
the amount a of money in an account after simple interest has been earned is given by the formula
=> a = p + prt
where
p is the principal,
r is the annual interest rate in decimal form, and
t is the time in years.
Here we need to find the following:
a. solve the formula for r
b. the amount of money in an account after interest has been earned is $1080, the principal is $1000, and the time is 2 years. what is the annual interest rate?
c. solve the formula for p.
a) The formula for r is calculated by moving the other elements and hold on r.
Then, the given formula,
=> a = p + prt
=> a = p (1 + rt)
=> a/p = 1 + rt
=> a/p - 1 = rt
=> r = (a/p - 1)/r
b) The given values are
p = $1000
t = 2
a = $1080
Now apply the values on the formula r to find the value of it,
=> r = ([1080/1000] - 1)/2
=> r = (1.08 - 1) /2
=> r = 0.08/2
=> r = 0.04
c) The formula for p can be derived as follows:
=> a = p + prt
=> a = p(1+rt)
=> p = a/1+rt
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2. The daily changes in four stock prices are shown in the table. Write
the changes from least to greatest in fraction form with a common
denominator.
Stock
-2 35/100
-1.64
2.05
1 9/40
We get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.
We are given the daily changes in four stock prices as shown in the table.:
-2 35/100
-1.64
2.05
1 9/40
We have to arrange them from least to greatest in fraction form with a common denominator.
We can write -2 35/100 as:
-235 / 100 ( mixed fraction converted into the improper fraction)
= -2350 / 1000
We can write -1.64 as:
- 1.64 = -164 / 100 ( decimal into fraction)
= -1640 / 1000
We can write 2.05 as:
2.05 = 205 / 100 (decimal into fraction)
= 2050 / 1000
We can write 1 9/40 as:
1 9/40 = 49 / 40 ( mixed fraction converted into the improper fraction)
49 / 40 × 25 / 25
= 1225 / 1000
Arranging it from least to greatest, we get that:
-2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000
Therefore, we get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.
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(7x-11) (6x-1) find the value of x
Answer:
Hey!
Since we know that both expressions lay on a straight line, we know that when both lines add up it should be 180°
We can write the expression as (7x - 1) + (6x - 1) = 180
Simplify
→ (7x + −1) + (6x + −1) = 180
Combine Like Terms
→ (7x + 6x) + (-1 + -1) = 180 → 13 + -2 = 180
Add 2 To Both Sides
→ 13x - 2 + 2 = 180 + 2 → 13x = 182
Divide 13 To Both Sides
13x/13 = 182/13 → x = 14
Hence, the value of x is 14!
-------------------------------------------------
Hope This Helped! Good Luck!
The vertical asymptote of the function = ln(x-6) + 5 is:
O A. x = -6
B. x = -5
O C. x = 6
D. x = 5
The vertical asymptote of the function = ln(x-6) + 5 is option C: x = 6.
The given function is f(x) = ln(x - 6) + 5.
A vertical asymptote is a vertical line that a function approaches but never crosses as it approaches infinity or negative infinity. For a logarithmic function like ln(x), the domain of the function is restricted to positive values only since the natural logarithm is undefined for non-positive arguments.
In the given function, we have f(x) = ln(x - 6) + 5. To find the vertical asymptote, we need to identify the value of x that would make the argument of the natural logarithm equal to zero.
Let's set the argument of the natural logarithm to zero:
x - 6 = 0
Now, solve for x:
x = 6
Thus, the value of x that would make the argument of the natural logarithm zero is x = 6.
So, the correct answer is option C: x = 6.
This means that the vertical asymptote of the function f(x) = ln(x - 6) + 5 is the vertical line x = 6. As x approaches 6 from either side (but never equaling 6), the function's values approach infinity. Similarly, as x approaches negative infinity, the function's values also approach infinity. The function never crosses the vertical line x = 6.
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help me solve this! (with explanation)
Answer:
a) 512cm³ b) 2 × 2 ×2
Step-by-step explanation:
A CUBE'S LENGTH WIDTH AND HEIGHT ARE EQUAL
a) Volume of a cube = length × width × height
as the length width and height are equal so it will be
8 × 8 × 8 = 512
b) Volume of a cube = length × width × height
as length, width and height are equal lets suppose the value of each of them will be = x
volume = x × x × x
vol = x³
8 = x³
∛8 = x
x = 2
show that 2 1/4 - 6/7 = 11/28
blehh
Hence the required expression is Proved.
Given the expression is 2 1/4 ₋ 6/7 = 39/28
Consider L.H.S 2 1/4 ₋ 6/7
Convert improper fraction to proper fraction.
2 1/4 = 9/4
take LCM of the denominators.
The LCM is 28.
9×7/28 ₋ 6×4/28
63/28 ₋ 24/28
Now subtract.
63 ₋ 24/28
39/28
Hence proved.
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Your question is incomplete. Please find the missing content here.
Show that 2 1/4 ₋ 6/7 = 39/28
Given n bits, how many unsigned integers can be represented with the n bits? what is the range of these integers?
2ⁿ integers can be represented and the range would be 0 to (2ⁿ) -1.
What are integers?An integer is a whole number (rather than a fraction) that can be positive, negative, or zero. Integer examples include -5, 1, 5, 8, 97, and 3,043. Numbers that are not integers include: -1.43, 1 3/4, 3.14,.09, and 5,643.1. There are three kinds of integers: Zero (0) Integers that are positive (Natural numbers) Integers that are negative (Additive inverse of Natural Numbers).So, if n bits are given then 2ⁿ integers can be represented.
And the range is the difference between the largest number by the smallest number. So, the range of 2ⁿ integers will be from 0 to (2ⁿ) -1.
Therefore, 2ⁿ integers can be represented and the range would be 0 to (2ⁿ) -1.
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The test statistic value calculated by the statistical procedure selected is known as the ______.
The test statistic value calculated by the statistical procedure selected is known as the obtained value.
What is the obtained value in statistics?The obtained value is the test statistic value derived using the specified statistical procedure.
An outcome of a statistical test of a hypothesis is a test statistic. It displays how closely your actual data match the distribution predicted by the statistical test's null hypothesis.
The p-value of these results, which is needed to decide whether to reject your null hypothesis, is calculated using the test statistic.
Therefore, the test statistic value calculated by the statistical procedure selected is known as the obtained value.
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Find the volume of the swimming pool?
depth = 9
2x+10 3x-5
Answer:
50
Step-by-step explanation:
2(9)+10
3(9)-5
18+10=28
27-5 =22
28+22=50
BD bisects ZABC. Solve for x and find mABC.
m/ABD = 11x - 10, m/CBD = 8x + 2
The value of x is 4 and the value of ∠ABC is 68°.
To solve this problem we first have to understand the concept of an angle bisector. Angle bisector is a straight line passes through the vertex of an angle dividing the angle in two equal angles.
According to the condition BD bisects ∠ABC
Therefore the two angles formed by the angle bisector are ∠ABD and ∠CBD.
The angle value of these two angles are equal.
Given:
m∠ABD=11x-10
m∠CBD=8x+2
Therefore from the above condition:
m∠ABD=m∠CBD
Substituting the values we get:
11x-10=8x+2
Solving the linear equation to find the value of x.
[tex]or,11x-10=8x+2\\or,11x-8x=2+10\\or,3x=12\\or,x=4[/tex]
Now let us find the value of ∠ABC
m∠ABC=m∠ABD+m∠CBD
or,∠ABC=11x-10+8x+2
or,∠ABC=19x-8
Substituting the value x=4 in the equation we get:
m∠ABC=19×4-8
or,m∠ABC=68°
Therefore we can conclude that the value of xis 4 and the value of ∠ABC is 68°.
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2. A container in the shape of a cube can hold 1,000 cm³ of water. What is the edge length of the container?
Answer:200
Step-by-step explanation:1,090
PLEASE HELP ME ILL RATE U 5 STARS PLEASEE
Ali and Leila are analyzing the following points. Ali thinks that most of the points are in
quadrant 2 because there are many x-values that are negative. Leila disagrees. Who is
correct?
(−3, 6), (−2, 4), (−3, −1), (−1, −6), (−4, −5), (−2, −7), (−5, −9), (−8, −9), (−12, −3), (2, 4),
(3, 2) and (4, 1).
Answer: Ali is correct because all of the negatives are mostly in quadrant 2.
Step-by-step explanation:
Find the 9th term of the arithmetic sequence 4x+44x+4, 9x+119x+11, 14x+18, 14x+18,...
Answer:
T9=60
Step-by-step explanation:
step 1: solve for x
it is an arithmetic pattern,so the 1st difference is the common difference (d)
therefore...9x+199x+11-(4x+44x+4)=14x+18-(9x+199x+11)
128x+11-48x-4=14x+18-128x-11
80x+7=-144x+7
80x+144x=7-7
224x=0
224x/224=0/224
X=0
step 2: substitute for x
4(0)+44(0)+4=4[1st term]
9(0)+119(0)+11=11(2nd term)
14(0)+18=18(3rd term)
step 3:find the common difference
d=3rd term- 2nd term, 2nd term-1st term
3rd term-2nd term
18-11=7
2nd term-1st term
11-4=7
therefore...d=7
step 4:find the general formula
we use the formula Tn=a+(n-1)d to find the general formula/ nth term
where: Tn is the nth term
a is the first term
n is the number of term
d is the common difference
Tn=a+(n-1)d
=4+(n-1)7
=4+7n-7
=7n-3
step 5:find the 9th term
Tn=a+(n-1)d
=7n-3
=7(9)-3
=60
The sequence below shows the number of raffle tickets that Samantha sold each day during a month.
3,7,11,15…
Which one explicit formula models the number of tickets Samantha sold on day x?
Answer:
C
Step-by-step explanation:
You are looking for the arithmetic sequence.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
In this case the formula is written:
t(x) = 3 + 4(x-1)
The 3 is the first term. The 4 is how much the sequence is increasing each time. (x-1) stands for the term we are looking for. If we were looking for the 15th term, we would have (15-1) in the parentheses.
Shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. What percent increase in sales does this represent?
If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.
Percentage increaseUsing this formula
Percentage increase= Percentage increase in share price / Initial percentage x 100%
Let plug in the formula
Percentage increase= 0.9% / 4.5% x 100%
Percentage increase=20%
Therefore If shareholders in an electronics company were informed that the company's market share increased from 4.5% to 5.4%, a rise of 0.9 percentage points. The percent increase in sales that this represent is: 20%.
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please answer with steps
txt: identify the domain and range of the following relation and determine if the relation is a function. Explain why or why not.
We need to know about relation and function to solve the problem. The domain of the relation is {-4,2,7,10} and the range is {-4}. The relation is a function.
Relation is a subset of Cartesian product or we can say that it is a set of points. It can also be described as a collection of ordered pairs.Function is a relation which follows that each input should have only one output. The domain of a relation or function is the set of values that the relation can accept, the range of a relation is the set of values that can be an output of the function or relation. The x values are the inputs and form the domain whereas the y values give the range. In the given relation the domain of the relation is {-4,2,7,10} and the range of the relation is {-4} since there is only one ouput value. The relation is a function since every input has only one output.
Therefore the domain of the relation is {-4,2,7,10} and the range is {-4} and the relation is function.
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write an equation of the line
I NEED HELP QUICK
In the image above angle 11 is 93 degrees, what is angle 11?
Answer:
angle 11 is an obtuse angle
Step-by-step explanation:
93 < 90
⬆️ ⬆️
obtuse right
Use what you know about addition and subtraction of polynomials to find the missing term represented by the question mark in each equation. (â€""4x2 6x 3) (8x 5 ?) = 2x2 14x 8 ? = (â€""b3 3b2 8) â€"" (? â€"" 5b2 â€"" 9) = 5b3 8b2 17 ? =
According to the given statement the value for:
A. = 6x²
B. = 6x³
What do you mean by Polynomials?An expression that only uses the same operations of addition, subtraction, multiplication, and non-negative integer exponentiation of factors is said to be a polynomial. It consists of indeterminates and coefficients. x²+4x + 7 is an illustration of a polynomial of one uncertain x.
According to the given data:Polynomials are added by combining like terms.
We can see that adding 6 and 8 together yields 14, and adding 3 and 5 together yields 8.
We also understand that adding something to -4x² yields 2x². We deduct to obtain the value that is missing:
2x²-(-4x²) = 2x²+4x² = 6x².
Similarly for the second equation on solving we get:
Polynomials are added by combining like terms.
We also understand that adding something to -b³ yields 5b³. We deduct to obtain the value that is missing:
5b³-(-b³) = 5b³+ b³ = 6x³.
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I understand that the question you are looking for is:
Use what you know about addition and subtraction of polynomials to find the missing term represented
by the question mark in each equation.
(-4x² + 6x + 3) + (8x + 5 + ?) = 2x² + 14x + 8
? =
(-b³ + 3b2 + 8) – (? - 562 - 9) = 5b³ + 8b2 + 17
? =
Write two number so that the value of the digit 9 in the second number is 10 times the value of digit 9 in the first number ?
The two numbers with the value of 9 in the first digit being 10 times the value of 9 in the second digit are 98 and 9.
Given that the value of the digit 9 in the second number is 10 times the value of digit 9 in the first number .
The first number will be 9 and the second number will be 98.
In the second number, the 9 is in the tens position which means that it has the value of 90.
In the first number, the value of 9 is simply 9.
90 is 10 times the value of 9 which means that 9 and 98 satisfy the requirements.
The first number will be 9 and the second number will be 98.
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Lots took one hour to drive from his apartment to philips arena and back. the return drive took 8 minutes less than the trip to the arena. if x represents the time it took llya to drive from his apartment to the arena, which equation would you use to determine how long he drove each way
The equation would use to determine how long he drove each way is 2x - 8 = 60.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that Lots took one hour to drive from his apartment to Philips arena and back. the return drive took 8 minutes less than the trip to the arena.
Since the return trip took 8 minutes less, the complete equation must be written in minutes.
Here x - 8 represents the time it took to return to Philips Arena.
The total travel time, including both directions, was 60 minutes;
thus, add x and x - 8 and set them both equal to 60.
So 2x - 8 = 60
Therefore, the equation would use to determine how long he drove each way is 2x - 8 = 60.
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Jorge, sandra, danny, and valeria each mowed lawns after school and on the
weekends for a month. sandra mowed one-third of the number of lawns as jorge
and danny mowed half as many lawns as jorge. if valeria mowed 16 lawns and
the group mowed a total of 49 lawns in the month, how many did jorge mow?
Jorge mowed 18 lawns.
Let the number of lawns mowed by Jorge =x
So according to the question
Number of lawns mowed by sandra = x/3
Number of lawns mowed by Danny =x/2
Number of lawns mowed by Valeria =16
sum of total lawns mowed = lawns mowed by Jorge + lawns mowed by sandra + lawns mowed by Danny + lawns mowed by Valeria.
[tex]x+\frac{x}{3} +\frac{x}{2} +16=49[/tex]
taking LCM as 6 and solving further we get
[tex]\frac{6x+2x+3x+96}{6} =49[/tex]
By cross Multiplying we get
11x+96=294
11x=198
Solving further for x,
x=198/11
x=18
Therefore, the number of lawns mowed by Jorge is 18 .
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Select all the correct answers.
Grace's work is x miles from her house. She drives to work every day of a 5-day workweek. Grace also goes to the gym every day after work, which increases her daily drive by 8 miles. The following expression shows the number of miles Grace puts on her car during the workweek.
Which of the following descriptions are equivalent ways to write this problem?
-----------------------------------------------------
1, Grace's work is x miles from her house. During the workweek, she drives the x miles between her house and work 7 times. She also goes to the gym to work out which increases her driving by 13 miles per workweek.
2. Grace's work is x miles from her house. To get to work and back, she drives 2x miles. She does this 5 times during the workweek. She also goes to the gym to work out which increases her daily driving by 8 miles. She does this 5 times.
3. Grace's work is x miles from her house. To get to work and back, she drives x miles. She does this 5 times during the workweek. She also goes to the gym to work out which increases her daily driving by 8 miles. She does this 5 times.
4. Grace's work is x miles from her house. During the workweek, she drives the x miles between her house and work 10 times. She also works out which increases her driving by 40 miles per workweek.
(this problem is multiple choice btw)
Answer: 54
Step-by-step explanation:
54
Answer: The 4 one is correct, The 2 one is correct
Step-by-step explanation:
-lukelaws hope i helped if i did please make me brainliest and if im wrong i am so sorry:(
HELPPPPP ASAPPP PLssss
Answer:
<
Step-by-step explanation:
Negative numbers are always smaller than positive numbers, and "<" is the smaller than symbol, so < is the correct choice. We can eliminate = immediately because a negative number can't equal a positive number (excluding the weird number 0)
