Five times the sum of some number plus 3 is equal to 9 times the number minus 9.
5 (x + 3) = 9x - 9
expand left side:
5x + 15 = 9x - 9
subtract 15 from both sides:
5x + 15 - 15 = 9x - 9 - 15
5x = 9x - 24
subtract 9x from both sides:
5x - 9x = 9x - 24 - 9x
-4x = -24
divide both sides by -4:
-4x/(-4) = -24/(-4)
x = 6
Which of the following is logically equivalent to ∼(∼p⇒q)? a.p^q b. p^~q c. ~p^q d. ~p^~q
Answer:
Step-by-step explanation:
Solution
verified
Verified by Toppr
Correct option is D)
p p
∼p⇒q ∼(∼p⇒q)
T T T F
T F T F
F T T F
F F F T
p q p∧q p∧∼q ∼p∧q ∼p∧∼q
T T T F F F
T F F F F F
F T F T T F
F F F F F T
So we see the given relation is logically equivalent to option D, as shown in last column.
two of the nine insist on sitting side-by-side. in how many ways can the nine be seated together in a row?
A group of nine people can now be seated in a row in 40320 different ways.
The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.
As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.
In this situation, the two people who dislike each other can be seated in
(7-1)! different ways.
The remaining seven people can be seated in seven different ways.
As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.
A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.
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A typical tip in a restaurant is 15% of the total bill. If the bill is $150, what would the typical tip be?
he typical tip would be $
Answer:
22.5
Step-by-step explanation:
total bill =$150
tip percentage =15%
now,
tip money = 15% of $150
=150×15/100
=2250/100
=$22.5
If X + 2 y = 5, then X + 2 (3 + y) =
Answer:
11
Step-by-step explanation:
x + 6 + 2y
x + 2y + 6
x + 2y = 5
5 + 6 = 11
Ticket to a play cot $4 in advance and $5 at the door. The theater club preident want to raie at leat $400 from the ticket ale. If the club ell 40 ticket in advance, what i the leat number of ticket the club need to ell at the door to reach the preident’ goal?
the number of tickets sold in advance to the number of tickets needed to be sold at the door is 88 .The club needs to sell at least 160 tickets at the door to reach their goal of $400.
1. Calculate the total amount of money raised from the tickets sold in advance: 40 tickets x $4 = $160
2. Subtract the total amount from the goal of $400: $400 - $160 = $240
3. Calculate the number of tickets needed to be sold at the door to reach the goal: $240 / $5 = 48 tickets
4. Add the number of tickets sold in advance to the number of tickets needed to be sold at the door: 40 + 48 = 88
Therefore, the club needs to sell at least 88 tickets at the door to reach their goal of $400.
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Solve the word problem below. Enter your answer as a fraction in simplest
terms, using the slash (/) as the fraction bar.
One week a student exercised 3 hours at school and another of an hour at
home. If of the student's total exercise came from playing basketball, how
much time did the student spend playing basketball that week? Enter your
answer in hours; do not include units in your answer.
The number of hours in a week a student played basketball is [tex]11\frac{3}{8}[/tex].
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, One week a student exercised 3 hours at school and another 1/4 of an hour at home.
Also given that 1/4 of the exercise of a student came from playing basketball.
Therefore, Time playing basketball is one-fourth of the total time exercised which is,
= (3 + 1/4)×(1/4).
= (13/4)×(1/4).
= (13/8).
Therefore, In a week the student played (13/8)×7.
= 91/8.
= [tex]11\frac{3}{8}[/tex].
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Translate the phrase "the product of fifteen and negative three decreased by twelve into a numerical expression then evaluate.
After solving, the expression as per the given statement will be equal to 135.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given information in the question,
The given statement is, the product of fifteen and negative three decreased by twelve.
Let the other number be x.
Negative 3 is decreased by 12.
x = 12 - 3 = 9
Then, the product of 15 and another number will be,
= 15 × 9
= 135
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w is proportional
to √x
x is decreased by 9.75%
Work out the percentage decrease in
W.
Answer:
To determine the percentage decrease in W when x is decreased by 9.75%, we need to first determine the relationship between w and x. Since w is proportional to the square root of x, we can write an equation to represent this relationship as follows:
w = k * √x
where k is the proportionality constant.
If the value of x is decreased by 9.75%, we can write the new value of x as follows:
x' = x * (1 - 0.0975) = x * 0.9025
Substituting this expression for x' into the equation above, we get:
w' = k * √(x * 0.9025)
To determine the percentage decrease in w, we can divide the new value of w by the original value of w and multiply by 100% to get the percentage change, or:
percentage decrease in w = (w' / w) * 100%
Substituting the expressions for w' and w into this equation, we get:
percentage decrease in w = [(k * √(x * 0.9025)) / (k * √x)] * 100%
Simplifying this expression, we get:
percentage decrease in w = (√(0.9025)) * 100%
Since the square root of 0.9025 is approximately 0.95, we can say that the percentage decrease in w is approximately 5%. This means that the value of w decreases by approximately 5% when the value of x decreases by 9.75%.
HELP PLEASE Note: For questions 22-25, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday she restocked her supply and sold 0.85 of the boxes of cheeses. On which day did Marietta sell more boxes? Explain.
She sold more cheese boxes on Tuesday.
What is comparison?Comparing numbers in maths is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.
Given that, Marietta is selling cheeses for the holiday fundraiser. On Monday, she sold seven-ninths of the boxes of cheeses. On Tuesday, she restocked her supply and sold 0.85 of the boxes of cheeses.
On Monday = 7/9 = 0.777
On Tuesday = 0.89
Since, 0.89 > 0.777
Hence, she sold more on Tuesday.
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solve ½ + ¼ in two ways
Answer:
3/4
Step-by-step explanation:
First way:
We can find a common denominator for the fractions and then add the fractions:
½ + ¼ = (2/4) + (1/4)
= (2 + 1)/4
= 3/4
Second way:
We can convert the fractions to decimals and then add the decimals:
½ + ¼ = 0.5 + 0.25
= 0.75
In both methods, the result is 3/4 or 0.75.
A ladder is leaning against the side of a 10 m. House. If the base of the ladder is 3 m. Away from the house, how tall is the ladder?.
The length of ladder leaning against the side of a house is 10.44 m .
As shown in the figure below h is the length of the house so we have to find h .
the ladder form a right angled traingle where base of the ladder is 3 m.
and the height of wall to which ladder is leaning against is 10m. and the ladder is the longest side of the right angled traingle i.e Hypotenuse
so we wil use Pythagoras theorem to find the longest side of ladder + wall system
so for a right angled traingle Pythagoras theorem states that
[tex]h^2 = p^2 + b^2[/tex]
where h=Hypotenuse ,p=perpendicular , b=base.
so we have to find h given p= 10m ,b=3m
so putting the values of p and b in the above equation we get
[tex]h^2 = 10^2 +3^2 =109[/tex]
so
[tex]h=\sqrt{109} = 10.44 m[/tex]
so the length of ladder is 10.44 m
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This number line models the division problem 13÷6 . What is the quotient?
Answer: About 2.2
Step-by-step explanation: Since 13 divided by 6 is 2.16 repeating, you can use the 6 to round up the 1, making it about 2.2
Which ratio is equivalent to 3/15 ?
Greg is paddling his canoe
upstream, against the current, to
a fishing spot 10 miles away. If he
paddles upstream for 2.5 hours
and his return trip takes 1.25
hours, find the speed of the current
and his paddling speed in still
water.
The speed of the current and his paddling speed in still water will be 5.33 miles per hour and 1.33 miles per hour, respectively.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
Let 'x' be the paddling speed in still water and 'y' be the current of water. Then the equations are given as,
x - y = 10 / 2.5
x - y = 4 ...1
x + y = 10 / 1.5
x + y = 6.667 ...2
Add both equations, then we have
x + x = 4 + 6.667
x = 5.33 miles per hour
Then the value of 'y' is given as,
x - y = 4
5.33 - y = 4
y = 1.33 miles per hour
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Barry has 17 more than two-thirds of the number of cards in his brother’s baseball card collection. If x represents the number of baseball cards his brother has, which expression represents the number of baseball cards Barry has?
Two-thirds x minus 17
Two-thirds x + 17
17 x minus two-thirds
17 x + two-thirds
Answer:
2/3x + 17
Step-by-step explanation:
2/3x represents the 2/3, then add the additional 17 at the end
Based on the graphs of f (x) and g(x), in which interval(s) are both functions increasing? Polynomial function f of x, which increases from the left and passes through the point negative 5 comma negative 4 and goes to a local maximum at negative 4 comma 0 and then goes back down through the point negative 3 comma negative 2 to a local minimum at the point negative 2 comma negative 4 and then goes back up through the point negative 1 comma 0 to the right, and a rational function g of x with one piece that increases from the left in quadrant 2 asymptotic to the line y equals 1 passing through the points negative 6 comma 2 and negative 3 comma 5 that is asymptotic to the line x equals negative 2 and then another piece that is asymptotic to the line x equals negative 2 and increases from the left in quadrant 3 passing through the point negative 1 comma negative 3 and 2 comma 0 that is asymptotic to the line y equals 1
The intervals in which both functions f(x) and g(x) are increasing are given as follows:
(-∞, -3) U (-1, ∞).
How to determine the behavior of the function?The behavior of a function is classified as either increasing, decreasing or constant, as follows:
Increasing: as x increases the function increases, that is, the graph moves up and right.Decreasing: as x increases the function decreases, that is, the graph moves down and right.Constant: as x increases the function remains constant, that is, the graph moves right while staying constant.From these bullet points and the functions given at the end of the answer, we have that the behavior of each function is given as follows:
Function f(x) is increasing over it's entire domain.Function g(x) is decreasing over the interval (-3,-1), and increasing over the remainder of the domain.Thus, both functions are increasing on the interval, (-∞, -3) U (-1, ∞), which is the first option.
Missing InformationThe problem is given by the image shown at the end of the answer.
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x² : (x + 6) = 1 : 2
Find the possible values of x
Answer:
x= 2 and x= -(2/3)
Step-by-step explanation:
Step 1 :Multiply all terms by the same value to eliminate fraction denominators
x^2/ x+6 = 1/2
2(x+6)*(x^2/x+6) = 2(x+6) * 1/2
Step 2: Cancel multiplied terms that are in the denominator
2x^2= x+6
Step 3: Move terms to the left side
2x^2 - (x+ 6) = 0
Step 4: Distribute
2x^2 - x - 6 = 0
Step 5: Use the quadratic formula
x= ( - (-1) +- Squar((-1)^2-4*2(-6)) ) / 2*2
Step 6: Simplify
x= (1+- 7)/ 4
Step7: Separate the equations
x= (1+7)/ 4 and x= (1- 7)/ 4
Step 8: Solve that 2 small equation
x= 2 and x= -(3/2)
Answer:
x = - [tex]\frac{3}{2}[/tex] , x = 2
Step-by-step explanation:
x² : x + 6 = 1 : 2
express the ratio in fractional form
[tex]\frac{x^2}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x² = x + 6 ( subtract x + 6 from both sides )
2x² - x - 6 = 0 ← in standard form
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 6 = - 12 and sum = - 1
the factors are - 4 and + 3
use these factors to split the x- term
2x² - 4x + 3x - 6 = 0 ( factor the first/second and third/fourth terms )
2x(x - 2) + 3(x - 2) = 0 ← factor out (x - 2) from each term
(x - 2)(2x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]
Which division problem is represented in this model?
Answer:
try 5/15 or 1/15
Step-by-step explanation:
this is because it shows one shaded box we know it's a third out of just that one column
so you multiple a third by 5 and you get 15 what ever you do to the denominators you do to the numerator
2√21 can be written in the form √p. Where p is an integer. What is the value of p?
Answer:
The answer is √84.
Step-by-step explanation:
To find the value of p, we need to square the expression 2√21 to get rid of the square root. When we do this, we get 4 * 21 = 84, so the value of p is 84. This means that 2√21 can be written as √84.
Answer:
p = 84
Step-by-step explanation:
2[tex]\sqrt{21}[/tex] ( place the 2 inside the radical by squaring it , that is
= [tex]\sqrt{2^2(21)}[/tex]
= [tex]\sqrt{4(21)}[/tex]
= [tex]\sqrt{84}[/tex]
in a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
The probability that the proportion surviving for at least five years will exceed 80% is 0.00084.
It is given to us that -
65% of the total dialysis patients can survive for at least 5 years
A simple random sample consists of 100 new dialysis patients
We have to find out the probability that the proportion surviving for at least five years will exceed 80%.
From the given information, we have -
Probability, p = 65% = 0.65
=> Population mean, μ = 0.65
Number of patients in the sample, n = 100
The raw data, x = 80% = 0.80
Now, we know the standard deviation of a given sample can be calculated as -
σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
=> σ = [tex]\sqrt{\frac{0.65(1-0.65)}{100} }[/tex]
=> σ = [tex]\sqrt{\frac{0.2275}{100} }[/tex]
=> σ = 0.04770 ----- (1)
We also know that the z-score can be calculated by the formula -
z = (x-μ)/σ
Substituting all the values in the above formula for z-score, we have -
z = (x-μ)/σ
=> z = (0.80-0.65)/0.04770
=> z = 3.14
From the normal distribution table, we can find out the corresponding area for the value of z = 3.14 which is equal to 0.99916.
For a value of the raw data, x to be more than 80%, the area to the right of normal distribution table for z = 3.14 is required.
=> P(x>80%) = 1-0.99916
=> P(x>80%) = 0.00084
Therefore, the probability that the proportion surviving for at least five years will exceed 80% is 0.00084.
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Convert 6 centimeters into yards. Round your answer to the nearest hundredth.
Answer:
6 centimeters is equal to 0.07 yards.
Step-by-step explanation:
To convert 6 centimeters into yards, we need to first convert the distance from centimeters to meters by dividing the distance in centimeters by 100:
Distance in meters = Distance in centimeters / 100
Distance in meters = 6 cm / 100
Distance in meters = 0.06 m
Next, we can convert the distance from meters to yards by dividing the distance in meters by 0.9144, which is the number of meters in a yard:
Distance in yards = Distance in meters / Meters per yard
Distance in yards = 0.06 m / 0.9144 m/yard
Distance in yards = 0.0654 yards
Rounded to the nearest hundredth, 6 centimeters is equal to 0.07 yards.
Answer:
Step-by-step explanation:
0.0656168
round to the nearest hundredth is:
0.07
jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup. a quick search told her that this was 173.3 cubic inches. she hoped the soup pot below would be big enough. the soup pot is 8 inches tall with a radius of 3 inches. what is the volume of the soup pot?
The volume of the soup pot is 226.08 cube inches.
Jayla bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 12 cups of soup.
A quick search told her that this was 173.3 cubic inches. she hoped the soup pot below would be big enough.
The soup pot is 8 inches tall with a radius of 3 inches.
We have to find the volume of the soup pot.
Since the cup is in the shape of cylinder.
So the volume of cylinder = πr^2h
from the question, r = 3 inches and h = 8 inches
π = 3.14
The volume of cylinder = πr^2h
The volume of cylinder = 3.14 * (3)^2*(8)
The volume of cylinder = 226.08 cube inches
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Question 3
The figure below is a rectangular shipping bax Name two different pla
b
C
d
plane FBC, plane ADC
plane ADE, plane FBC
plane ADC, plane CGH
plane ADE, plane CGH
DH
The answer is d. plane ADE, plane CGH.
which document do you need to have on hand when preparing to file your tax return? a. auto insurance card b. birth certificate c. driver’s license d. form w-2 e. form w-4
The document do you need to have on hand when preparing to file your tax return is W-2
What is a tax return?A tax return is a form or forms filed with a tax authority that reports income, expenses, and other pertinent tax information.
To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year, but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.
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A contractor bought 10.8 ft2 of sheet metal. he has used 2.3 ft2 so far and has $153 worth of sheet metal remaining. The equation 10.8x - 3.2x= represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
10.8 - 2.3 = 8.5ft2 amount of $153
Can i use proportion for this?
8.5/153 : 1/x
8.5x = 153
x = 18
The cost of metal per square foot is $18.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-A car travels along the x-axis with increasing speed. We don’t know if to the left or the right. Which of the graphs in Fig. 2–34 most closely represents the motion of the car?
A car travels along the x-axis with increasing speed. Among the given graphs. the graph given in (a) most closely represents the motion of the car.
The slope of graphs (b) and (e) remains constant.
Here, the distance increases with time.
Graph (c) shows decreasing the velocity of the vehicle.
In graph (d) the velocity of the vehicle increases and then slows down.
In graph (a), speed is increased which means that as time passes the slope of the graph becomes steeper. here, the slope of the graph increases with time.
Hence, the speed of the car increases.
Therefore, the correct representation of the motion of the car is the graph (a).
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The question diagram is missing in the question,
The diagram is like (As attached below)
The box plot shows the times for sprinters on a track team. A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds. Which value does 50% of the data lie above, and what is it called? 48, the lower quartile 50.5, the median 56, the median 53, the upper quartile
The value does 50% of the data lie above is 50.5 and is called the median.
What is median?The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.
Given that, The box plot shows the times for sprinters on a track team. A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot.
Data we get from the graph is
Minimum (min) = 44
Lower 1 (Q1) = 48
Median (med) = 50.5
Upper 3 (Q3) = 53
Maximum (max) = 56
The median is considered the second quartile (Q2).
The median cuts the data set in half. Half of the answers lie below the median and half lie above the median.
Hence, The value does 50% of the data lie above is 50.5 and is called the median.
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Evan practices the piano 329 minutesbc in 1 weeks. Assuming he practices the same amount every week, how many minutes would he practice in 2 weeks?
The number of minutes of practice in two weeks is 658.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total minutes of practice in one week = 329.
Total minutes of practice in two weeks.
= 2 x 329
= 658 minutes.
Thus,
658 minutes was the practice in two weeks.
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15 < -5x
Help I need it for khan academny
[tex]\huge \boxed{\sf x < -3} \\\\\\ \displaystyle \sf 15 < -5x \\\\ Divide\ each\ side\ by\ -5\ and\ switch\ the\ symbol. \\\\ \frac{15}{-5} > \frac{-5x}{-5} \\\\-3 > x[/tex]
PLEASE PLEASE PLEASE HELP(attached image)
Answer:
The answer is D.
Step-by-step explanation:
Test each multiply choice to see if given the x-axis points.
(x+1)(x+2)(x-3)=0
(x+1) = 0 , (x+2) = 0 , (x-3) = 0
x = -1 , x = -2 , x = 3
(-1 , 0) , (-2 , 0) , (0 , 3)