The inequality representing Courtney's situation to buy air heads and popcorn is 0.25x + 2y ≤ 12.
Based on the situation of Courtney, we can conclude that she must get the combination in such quantity of each that it's total is less than or equal to 12. Creating the expression according to this statement.
Number of air heads × cost of one air head + number of popcorn × cost of one popcorn ≤ 12
Keep the values in formula to find the inequality
x×0.25 + y×2 ≤ 12
Performing multiplication between the constant and variable
0.25x + 2y ≤ 12
Thus, inequality representing this situation is 0.25x + 2y ≤ 12.
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The art teacher has 48 paintbrushes. She puts 8 paintbrushes on each table in her classroom. How many tables are in her classroom?
Answer:
6 Tables
Step-by-step explanation:
48 tables divided by 8 paintbrushes equals 6 tables.
chooe all of the following expreion which are even for all value of n
2n8
5n10
2n3
n2
4n-14
All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.
2n8, 5n10, n2, 4n-14
2n8 : This expression is even for all values of n because the coefficient of n is an even number (2).
5n10 : This expression is even for all values of n because the coefficient of n is an even number (5).
2n3 : This expression is even for all values of n because the coefficient of n is an even number (2).
n2 : This expression is even for all values of n because the coefficient of n is an even number (1).
4n-14 : This expression is even for all values of n because the coefficient of n is an even number (4).
All of the expressions 2n8, 5n10, 2n3, n2, and 4n-14 are even for all values of n because all of the coefficients of n are even numbers.
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The difference between the water levels for high and low tide was 3. 6 feet. Write and solve an equation to find the water level at high tide
The difference between the water levels for the high and low tide was 3. 6 feet. the equation to find the water level at high tide x = y + 3.6, where High Tide Water Level = x and Low Tide Water Level = y.
In simple form it will be High Tide Water Level = Low Tide Water Level + 3.6. To explain this equation, the water level at high tide is equal to the water level at low tide plus 3.6 feet. The variable 'x' represents the water level at high tide, while the variable 'y' represents the water level at low tide. By adding 3.6 feet to the water level at low tide, we can find the water level at high tide.
For example, if the water level at low tide is 4 feet, the water level at high tide would be 4 + 3.6 = 7.6 feet. To find the water level at high tide for any given low tide water level, one can simply add 3.6 feet to the known low tide water level. This equation can be used to accurately calculate the water level at high tide for any given low tide water level.
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5b-2c + 3)-d, a +2b-c+d, 2-d + 3c + a
The sum of the given expression will be 2a+7b+-d.
What are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now
Given expressions are 1.5b-2c+3-d 2.a+2b-c+d 3.2-d+3c+a
By adding these
=a+a+5b+2b-2c-c+3c-d+d-d
=2a+7b-d
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in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Lisa and Joe put $46 towards the gift
How much money did Lisa and Joe put towards the gift?Let's call the amount of money that Sara put in "x".
Joe put in twice that amount, so he put in 2x.
Lisa put in ten dollars more than Sara, so she put in x + 10.
Together, Sara, Joe, and Lisa put in x + 2x + (x + 10) = $58.
Evaluate the like terms, so we have
4x + 10 = 58.
Subtracting 10 from both sides, we get
4x = 48.
Dividing both sides by 4, we find that
x = $12.
So Sara put in $12, Joe put in $24, and Lisa put in $22.
The total amount put by Lisa and Joe is $24 + $22 = $46.
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Complete question
Three friends are put their money together to buy a $58 gift. Joe put in twice the amount of money as Sara. Lisa put in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Question
Two boxes need to be wrapped in paper (with no overlap). Both boxes are in the shape of right rectangular prisms.
Box A measures 0.8 feet high, 0.6 feet long, and 1 foot wide. Box B measures 1.4 feet high, 0.5 feet long and 1.2 feet wide.
The wrapping paper costs $6.79 per 80 square feet.
What is the cost of wrapping both boxes?
Enter your answer in the box.
$
Answer:
0.82
Step-by-step explanation:
A： area =2( 0.8*0.6*+0.6*1+0.8*1) =2(0.48+0.6+0.8)=2*1.88 =3.76
B：area = 2(1.4*0.5+0.5*1.2+1.4+1.2) =2(0.7+0.6+1.68)=2*2.98=5.96
total 9.72
cost = $6.79* 9.72/80 =$0.82
Answer:
0.92
Step-by-step explanation:
3/5 less than a number, and the result is squared
Answer:
(n - 3/5)²
Step-by-step explanation:
(n - 3/5)²
PLEASE HELP
A restaurant plans to use a new food delivery service. The food delivery service charges $5.48 for every 2 meals delivered, plus a $3.50 service fee. What is the slope of this situation?
A.2.74
B.3.50
C.5.48
D. 6.24
glassdoor four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?
The expected value of the sum of the two extreme numbers is 1/2.
Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.
This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.
Therefore, the expected value of the sum of the two extreme numbers is 1/2.
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A ball is thrown upward at an angle of elevation of 28 degrees with a force of 19n. How much of that force is horizontal and how much of that force is vertical?
19N force act in upward direction with angle of elevation 28 degrees has horizontal and vertical force is given by 16.78N and 8.92N respectively.
Angle of elevation while thrown a ball upward 'α' = 28 degrees
Force 'F' is equal to 19N.
While throwing a ball force is applied in two possible direction are:
Horizontal direction and Vertical direction.
For horizontal direction :
let 'x' represents the horizontal direction
cosα = x / F
⇒ cos28° = x / 19
⇒ x = 19 cos 28°
⇒ x = 19 × 0.8829
⇒ x = 16.78N
For Vertical direction :
let 'y' represents the vertical direction
sinα = x / F
⇒ sin28° = y / 19
⇒ y = 19 sin 28°
⇒y = 19 × 0.4695
⇒ y = 8.92N
Therefore, the horizontal force and vertical force for the given angle of elevation is equal to 16.78N and 8.92N respectively.
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Simplify (4s+7 -2S) +4 (3s-5^2) 
Answer:
14S -93
Step-by-step explanation:
(4s+7 -2S) +4 (3s-5^2)
= 2S +7 +12S -4*25
=14S -93
What is the solution to this system of
equations?
s 6x – 2y = 8
1-3x + y = -4
According to the elimination method, the solution of the system of equation has infinite number of solutions.
In math the term elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables
Here we know that the equations are
=> 6x - 2y = 8 ---------------(1)
=> -3x + y = -4 ------------------(2)
when we simplify the equation (1) by dividing the terms by 2, then we get
=> 3x - y = 4
Now, we have to add the two equation then we get the result as,
=> (-3x + 3x) +( -y + y) = (-4 + 4)
=> 0 + 0 = 0
Hence the system has an infinite number of solutions.
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The point (6, -2) is reflected over the and-axis. What are the coordinates resulting point, A?
The population of a city in 2015 was 36,000. The population is increasing at 15% per year.
Part A: Write an exponential equation that models the population, P(x), where x represents the number of years since 2005.
Part B: Based on your equation, what was the population in 2020? Show how you obtained your answer.
A: The exponential function for the situation is P(t) = 36,000 × (1 + 0.15)^t.
B: The population in 2020 was 72,396.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The population of a city in 2015 is 36,000 and it is increasing at 15% per year.
Model this using an exponential equation of the form -
P(t) = P0 × (1 + r)^t
Where -
P(t) is the population after t years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
t is the number of years since 2015
So the exponential equation that models the population is -
P(t) = 36,000 × (1 + 0.15)^t
Part B:
To find the population in 2020, substitute t = 5 (2020 - 2015) into the equation -
P(5) = 36,000 × (1 + 0.15)^5
P(5) = 36,000 × 1.15^5
P(5) = 36,000 × 2.011
P(5) = 72396
Calculating this gives us a population of approximately 72,396 in 2020.
To obtain this answer, the exponential equation that models the population, P(t), is used where t represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for t.
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Use the Bisection Method up to five iterations and find the root to 3 decimal places for the following:
f(x) = x2 − 3x + 1 in the interval [0, 1]
A.
0.375
B.
0.438
C.
0.406
D.
0.391
Answer:
D. 0.391
Step-by-step explanation:
You want the approximate solution to f(x) = x² -3x +1 = 0 on the interval [0, 1] using 5 iterations of the Bisection Method.
IterationThe Bisection Method makes one iteration by finding the function value at the midpoint of the interval. The midpoint replaces the end of the interval whose function value has the same sign. At the end of one iteration, the midpoint of the halved interval is calculated.
Start:
f(0) = 1, f(1) = -1. Interval: [0, 1]; midpoint: 1/2
First iteration:
f(1/2) < 0. Interval: [0, 1/2]; midpoint: 1/4
Second iteration:
f(1/4) > 0. Interval: [1/4, 1/2]; midpoint: 3/8
Third iteration:
f(3/8) > 0. Interval: [3/8, 1/2]; midpoint: 7/16
Fourth iteration:
f(7/16) < 0. Interval: [3/8, 7/16]; midpoint: 13/32
Fifth iteration:
f(13/32) < 0. Interval: [3/8, 13/32]; midpoint: 25/64
SolutionThe approximate solution after 5 iterations is x ≈ 25/64 ≈ 0.391.
__
Additional comments
The approximate solution in the interval to full calculator precision is 0.38196601125. The exact solution is 1.5-√1.25.
You will notice that the function values for the ends of the interval [0, 1] are [positive, negative]. So, when the function value at the midpoint is negative, that point replaces the right end of the interval.
Of course, the midpoint is the average of the interval end values.
On average, it takes about 3.3 iterations to improve the accuracy of the solution by 1 decimal place.
Given the two functions, which statement is true?
f(x) = e^x, g(x) = e^x-2
g(x) is translated down 2 units compared to f(x)
g(x) is translated right 2 units compared to f(x)
g(x) is translated left 2 units compared to f(x)
g(x) is translated up 2 units compared to f(x)
WHICH one doesn’t belong
9 16
25 43
NUMBER 1
from Pam Wilson
From the set of numbers 9, 16, 25, 43 , the number does not belong to the group is prime number 43.
Set of numbers are 9, 16 , 25, 43.
9 is the composite number with 1, 3, 9 as factor.
It is perfect square of 3 also.
16 is the composite number with 1, 2, 4, 8,16 as factors.
It is perfect square of 4 also.
25 is the composite number with 1, 5, 25 as factors.
It is perfect square of 5 also.
43 is not a composite number.
It has only two factors 1, 43.
43 is a prime number.
It is not a perfect square of any number.
Here 43 does not belong to the group.
Therefore, the number which does not belong to the group from 9,16, 25, 43 is 43.
The above question is incomplete, the complete question is :
Which number does not belongs to group ?
9, 16, 25, 43.
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on a fair die whose faces are numbered consecutively starting from 1, the probability of rolling an even number is less than twice the probability of rolling a multiple of 3. which could be the number of sides on the die?
Answer:
iam sorry
i don't know the answer
Can anyone help?- I need it by 11:30.
Answer:
See Below
Step-by-step explanation:
5. [tex]3.1 + (8.6 + m)\\3.1 + 8.6 + m\\11.7 + m[/tex]
take expression out of brackets by distribution (multiplying both by 1), then add
6. [tex]((\frac{2}{3})(t)) (1\frac{1}{2})\\(\frac{2}{3}t) (1\frac{1}{2})\\(\frac{2}{3}t) (\frac{3}{2})\\\frac{6}{6} t\\t[/tex]
Simplify the expression in the brackets by multiplying them together, once done turn the mixed fraction back into improper fraction in order to multiply the two together. Once done, simplify the expression
7. [tex]4(x + 8)\\4x + 32[/tex]
I would argue that factored form is the most simplified but regardless using the distribution rule you multiply both numbers within the bracket in order to get rid of it
8. [tex]4t + 7 + 2t - 2\\6t + 5[/tex]
This is just combining like terms and simplifying
The sum of the ages of Jaren and his brother, Daniel is 40. Four years ago, Daniel was 3 times as old as Jaren. Calculate
(i) Jaren's present age
(ii) the age of Daniel when Jaren was born
Answer:
(i) Let's call Jaren's current age J. According to the problem, the sum of J and Daniel's age is 40.
If we also know that four years ago, Daniel was 3 times Jaren's age, we can set up the following equation:
J + (J+4) = 40
Solving for J, we find that Jaren's present age is 18.
(ii) When Jaren was born, Daniel would have been 18 + 4 = 22 years old.
The price of a new car was $22,800 in April. However, the price of the car was reduced by 5% in May. Find the price in May.
In May, the price of the car was ? % as compared to
the price of the car in April.
Answer: To find the price of the car in May, we can use the formula:
New price = Original price - (Original price x Discount rate)
In this case, the original price is $22,800, and the discount rate is 5%, which can be written as 0.05.
So, the new price in May is:
New price = 22700 - (22700 x 0.05)
New price = 22700 - 1135
New price = $21,565
So, the price of the car in May was $21,565.
To find the percentage of the price of the car in May as compared to the price of the car in April, we can use the formula:
(New price / Original price) x 100
In this case, the new price is $21,565 and the original price is $22,800
(21565 / 22700) x 100 = 0.95 x 100 = 95%
Therefore, in May, the price of the car was 95% as compared to the price of the car in April.
Step-by-step explanation:
You can model the arch of the fireplace using the equation y =-1/9(x+18)(x-18) when x and y are measured in inches. The x-axis represents the floor. Find the width of the arch at floor level
The width of the arch at floor level is 18 inches.
Substitute x = 0 into the equation.
y = -1/9(0+18)(0-18)
Solve for y.
y = -1/9(-18)(18)
y = 18
Therefore, the width of the arch at floor level is 18 inches.
A linear system can be algebraically solved using the substitution approach. One y-value is substituted for another in the substitution procedure. Finding the value of the x-variable in terms of the y-variable is the method's most straightforward step.
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in a negatively skewed distribution of exam scores, bender scored at the mean, fry scored at the median, and lela scored at the mode. who had the highest score?
Lela had the highest score.
Now, According to the question:
A skewed distribution is neither symmetric nor normal because the data values trail off more sharply on one side than on the other. In business, you often find skewness in data sets that represent sizes using positive numbers.
In a negatively skewed distribution, higher values are more frequent than lower values causing the distribution to present a longer left-tail. This implies in a median higher than the mean and in a mode higher than the median:
mean < median < mode.
Therefore, since Lela scored at the mode, Lela had the highest score.
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a car magazine is comparing the top speed in miles per hour of 15 different sports cars. the speeds are included in the table below. top speeds 267.71 253 187 247.16 188 250.4 240.10 224 195 212 248.5 190 205 202 245 use a calculator to create a histogram for the data. use the default window size. what is the result?
The result of a histogram of the given data is 0.8.
There are a few steps to use a TI-83, TI-83 plus, or TI-84 calculator is used to create the histogram.
1. First, the process is to press the STAT key and then press ENTER.
2. Enter the data into column L1.
3. In the third step with all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu.
4. After that press ENTER and make sure that Plot1 is set to On.
5. Use the directional keys to navigate to the Type selector, move the selection to the third type in the top row, and press ENTER.
6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1.
7. Finally, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is finished, the correct histogram will display on the calculator.
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Use the figure shown for Items 1–4. In the figure, m∠IJL=0.5 m∠JIK.
Triangle I J K with side I J congruent to side J K. Segment J L is drawn from vertex K perpendicular to base I K such that it bisects the base. Segment I L has length 3 x and is congruent to segment L K which has length 2 x plus 5.
Select all the statements that must be true.
A. KL=15
B. JL bisects IK
C. ΔIJK is equilateral.
D. JL is the perpendicular bisector of IK
E. JL=2LK
The true statements are:
A. KL=15
B. JL bisects IK
D. JL is the perpendicular bisector of IK
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular sign, ⊥ , can be used to visually depict the state of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
Given:
We have a triangle IJK.
m∠IJL=0.5 m∠JIK.
Side IJ ≅ side JK.
JL ⊥ IK.
It bisects the base.
That means,
JL bisects IK and JL is the perpendicular bisector of IK.
So, IL = LK.
3x = 2x + 5
x = 5
KL=15.
Therefore, A, B and D are the true statements.
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The total cost (in dollars) of a cell phone plan after x months can be represented by c(x) = 35x + 20. Find the inverse function. Then find the number of months
when the total cost is $1700.
The number of months when the total cost is $1700 is 48 months
What is a function?
A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.
These variables are;
Dependent variableIndependent variableFrom the information given, we have that;
The function for the total cost is c(x) = 35x + 20x represents the number of monthsNow, substitute the values, we have;
1700 = 35x + 20
collect like terms
35x = 1700 - 20
subtract the like terms
35x = 1680
Make 'x' the subject of formula
x = 48 months
Hence, the value is 48 months
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Chris opens up a new visa credit card and credit line with U. S. Bank. He is paying a 15% annual percentage rate (APR) on all new purchases. If he has a current balance of $2,800 on this credit card, how much does he owe in interest to the back next month?
Chris owes $35 in interest to the back next month.
We know that a credit card's interest rate is nothing but the price one pay for borrowing money. This is called the annual percentage rate (APR).
The Interest paid is calculated by the formula:
I = PTR ÷ 100
where P = Principal amount ,
R= rate of interest in percentage ,
and T= period.
Here, P = $2800,
R = 15%
T= 1 year
Using above formula,
I = (2800 x 15 x 1) ÷ 100
I = 420.
He will pay an interest of 420 ÷ 12= $35 per month.
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dilate figure ABCD by a cale factor of 3 with the center of dilation at the origin
the slope of A'B' is= 1.2 ,The length of A'C' in triangle is = 3q unit.
When we dilate a triangle and the center of the dilation is at the center of the triangle, the only thing that changes are the coordinates of the summits of the triangle.
The angles remain the same, so do the slope.
So, since the slope of AB is equal to -1.2, the slope of A'B' will also be -1.2.
They say the dilation factor was 3, that means the length of every side was multiplied by 3. So, if the length of AC is q units, the length of A'C' is 3q units.
The complete question is-
ΔABC is dilated by a scale factor of 3 with the origin as the center of dilation to form ΔA′B′C′. The slope of AB is -1.2. The length of AB is p units, the length of AC is q units, and the length of BC is r units.
The slope of AB is (?). The length of is (?) units.
the slope of AB is?
A. 1.2 B. -1.2 C. -3.6
The length of AC is ?
A. 1/3q
B. 3q
C.-1.2p
D. (p+q+r)
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At the end of each month, Bianca deposits $100 into an account with an interest rate of 4.25%, compounded monthly. If no money is withdrawn from the account, what will her balance be after 5 years?
Answer:
123.630189899 or A. $1,257.72
Step-by-step explanation:
[tex]\frac{4.25}{100}=0.0425\\ 100(1 + \frac{0.0425}{12})^{12(5)} \\= 123.630189899[/tex]
Nicole is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 18 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 41^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 44^{\circ} ∘ . If her eyes are 1.68 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.
The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,
we shall evaluate for the height of the antenna AB as follows:
tan 44° = AB/18m {opposite/adjacent}
AB = 18m × tan 44° {cross multiplication}
AB = 18m × 0.9657
AB = 17.3826m
Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.
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Answer:
2 meters
I got it correct in my hw (check the photos)
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