[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{5}~,~\stackrel{y}{8})\qquad \implies 8=k(5)\implies \cfrac{8}{5}=k[/tex]
Evaluate the expression for the given value of x
7x + 8 for x = 2
Answer:
22
Step-by-step explanation:
Since x = 2, we can tell that x is equal to 2.
So this is basically asking 7 times 2 plus 8
7(2) + 8 = ?
14 + 8 = 22
Hope this helps!
8 is greater than w and 0 is less than w
So the variable w is less than 8 and greater than 0.
8>w>0
Jorge's cell phone plan costs $20.00 each month plus $0.15 per minute. If his bill for the month is
58420, how many minutes did Jorge use? (Round to the nearest whole number).
10
64
428
561
Answer:
Step-by-step explanation:
20 + .15x = 35 + .10x
.05x = 15
x = 300 minutes
CL 1-148. The county-fair prize wheel has equally spaced sections with the following colors:
one is golden, two are silver, three are green, four are blue, six are red, and nine are yellow.
a) What is the probability of landing on gold? Give your answer as a fraction and as a
percent.
b) If the probability of landing on yellow is 36%, what is the probability of not landing on
yellow?
b) If the wheel is spun 100 times, how many times would you expect to land on silver?
Answer:
A. [tex]\dfrac{1}{25}=0.04[/tex] or 4%
B. [tex]\dfrac{16}{25}=0.64[/tex] or 64%
C. 8 times
Step-by-step explanation:
The county-fair prize wheel has equally spaced sections with the following colors: 1 is golden, 2 are silver, 3 are green, 4 are blue, 6 are red, and 9 are yellow, 25 sections in total.
A. The probability of landing on gold is
[tex]P_1=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}=\dfrac{1}{25}=0.04[/tex]
or 4% as a percent.
B. If the probability of landing on yellow is 36% (or 0.36 as decimal), then the probability of not landing on yellow is
[tex]P_2=1-0.36=0.64[/tex]
or 64% as a percent.
C. If the wheel is spun 1 time, the probabilty of landing on silver is
[tex]P_3=\dfrac{2}{25}=0.08[/tex]
or 8% as a percent.
If the wheel is spun 100 times, the expected number of landing on silver is
[tex]100\cdot 0.08=8[/tex]
Final answer:
Explaining the probability of landing on different colors on a prize wheel and the expected outcomes in 100 spins.
Explanation:
a) What is the probability of landing on gold?
There is 1 golden section out of a total of 25 sections on the prize wheel.
Probability of landing on gold: 1/25 or 4%
b) If the probability of landing on yellow is 36%, what is the probability of not landing on yellow?
If the probability of landing on yellow is 36%, then the probability of not landing on yellow is 64%.
c) If the wheel is spun 100 times, how many times would you expect to land on silver?
Since there are 2 silver sections on the wheel, the probability of landing on silver is 2/25. Therefore, expected number of times to land on silver in 100 spins is 100 x 2/25 = 8 times.
What is the inverse of f(x) = one-thirdx + 2?
Answer:it is option D
Step-by-step explanation:
+
Simplify the following expression. Assume that each variable is positive.
[tex] \sqrt[3]{88 {x}^{11} {y}^{15} \div 64 {x}^{4} {y}^{6} } [/tex]
aaron drives 45 miles per day on average his car averages 28 miles per gallons if gasoline cost 3.80 per gallon how much will aaron spend on gasoline in one year
Answer:
2229.08
Step-by-step explanation:
Step 1: Calculate miles travelled in one year
Miles travelled per day = 45 miles
Miles travelled in one year = 45 x 365 = 16,425 miles
Cost of gasoline per gallon = 3.8 for every 28 miles
Step 2: Divide total miles in one year by per gallon miles
16,425 ÷ 28
= 586.6 miles
Step 3: Multiply the answer by cost of gasoline
586.6 x 3.8
= 2229.08
Therefore, Aaron will spend 2229.08 on gasoline in one year.
Answer:
Aaron spend Rs.1642.4996 on gasoline in one year
Step-by-step explanation:
Aaron drive in 1 day = 45 miles
1 year = 365 days
So, Aaron drives in 365 days = [tex]45 \times 365[/tex]
= [tex]16425 miles [/tex]
We are given that his car averages 28 miles per gallons .
His car travels 28 miles in gallons = 1
His car travels 1 miles in gallons =[tex]\frac{1}{28}[/tex]
His car travels 16425 miles in gallons =[tex]\frac{1}{28} \times 16425[/tex]
=[tex]586.607[/tex]
Cost of 1 gallon = 2.80
Cost of 586.607 gallons = [tex]2.80 \times 586.607=1642.4996[/tex]
Hence Aaron spend Rs.1642.4996 on gasoline in one year
The total cost C ( in dollars) to participate in a triathlon series is given by the literal equation C =90x+35 where x is the number of triathlon in which you participate. If your maximum annual triathlon cost is 1000 what is the maximum number of triathlons in who you could prarticipate?
Answer:
The answer is below in the photo.
Answer:
We can participate in 10 triathlons.
Step-by-step explanation:
Total cost C to participate in x number of triathlon is given by the expression
C = 90x + 35
If the maximum cost of the annual triathlon is = $1000
Then we can find the maximum number of triathlons by putting C = $1000 in the expression
1000 = 90x + 35
90x = 1000 - 35
90x = 965
x = [tex]\frac{965}{90}[/tex]
x = 10.72
Therefore, we can participate in 10 triathlons.
A race car travels 3.6 hours at an average speed of 205.7 miles per hour. How far does the car travel? Include unit of measurement
Answer:
The car traveled 740.52 miles
Step-by-step explanation:
The only thing you need to do in this problem is to multiply the hours by the rate (mph).
3.6 × 205.7 = 740.52
When buying an object on sale, the _______ is the decrease in the price of the item.
Final answer:
A discount represents the decrease in the item's price during a sale, leading to consumer savings. When a shopper gets a "good deal," they experience the substitution and income effect, which typically results in an increased quantity demanded of the product.
Explanation:
When buying an object on sale, the discount is the decrease in the price of the item. Economists may refer to the situation of getting a "good deal" on a product when the consumer is able to purchase something at a price lower than what it normally sells for, leading to consumer saving. This occurs due to the substitution effect and the income effect. The substitution effect indicates that when a product is cheaper relative to other products, consumers are likely to purchase more of it. On the other hand, the income effect explains that the decrease in price allows the consumer to buy the same amount of goods while still having extra money to purchase even more goods. Due to both these effects, a decrease in price typically leads to an increase in quantity demanded, which might suggest that the demand for a product is elastic if the quantity demand decreases significantly more than the price increase.
What is the simplified fractional equivalent of the terminating decimal 0.78
Answer:
39/50.
Step-by-step explanation:
0.78 = 78/100
= 39/50.
Answer:
39/50
Step-by-step explanation:
The original expression can be restated as follows:
0.78 = 0.70 + 0.08
Convert:
0.70 = 7/10
0.08 = 8/100
Add 7/10 + 8/100:
7/10 + 8/100
Find least common multiple, which is 100:
=(70+8)/100
=78/100
Now, simplify by dividing by 2 for both top and bottom:
39/50
jody has 3 red marbles 7 blue marbles and 8 yellow marbles what is the ratio red to blue marbles
Answer:
3/7
Step-by-step explanation:
The ratio is the number of red marbles and the number of blue marbles in a fraction, so the ratio would be 3/7
What is 14/18 in simplist form
Which angles are acute?
An acute angle is any angle smaller than 90 degrees. A right angle is an angle that measures 90 degrees.
Solve the following systems using substitution.
X - 9y = 25
6x - 5y = 3
Answer:
x = -2, y = -3
Step-by-step explanation:
Multiply eqn1 by the LCM of 1 and 6 i.e coefficients of x
We get:
6x - 54y = 150 (eqn1)
6x - 5y = 3 (eqn2)
- 49y = 147
y = 147
-49
y = -3
Substitute y in eqn2
6x - 5(-3) = 3
6x + 15 = 3
6x = -12
x = -2
Is the perpendicular bisector of a line segment also an angle bisector?
Answer:
yes
Step-by-step explanation:
In an isosceles triangle, one perpendicular bisector is also an angle bisector.
Factorise the following.
49g^2 - 36h^2 - 28g - 24h
Answer: -4(7g - 6h)(7g + 6h)
Step-by-step explanation:
Separate the 4 terms into two groups of 2 terms. Then factor out the GCF of each group. You should end up with a common factor in each group - that is one of the factors. The other factor is what you factored out from each term.
49g² - 36h² - 28g - 24h
(7g - 6h)(7g + 6h) -4(7g + 6h)
They both have a common factor of (7g + 6h)
The terms factored out are (7g - 6h) and -4
So, the factorization is: -4(7g - 6h)(7g + 6h)
how much does 4 5/7 kg of candy cost if 5/6 kg costs $7.50
To find the cost of 4 5/7 kg of candy, we divide the cost of 5/6 kg by 5/6 to find the cost of 1 kg. Then, we multiply the cost of 1 kg by 4 5/7 to find the total cost.
Explanation:To find the cost of 4 5/7 kg of candy, we need to find the cost of 1 kg of candy and then multiply it by 4 5/7. Given that 5/6 kg of candy costs $7.50, we can find the cost of 1 kg by dividing $7.50 by 5/6. So, the cost of 1 kg of candy is $9.00. To find the cost of 4 5/7 kg, we multiply $9.00 by 4 5/7.
To multiply a whole number and a fraction, we first convert the whole number to a fraction by placing it over 1. So, 4 can be written as 4/1. Then, we multiply the numerators (4 x 7 + 5) and the denominators (1 x 7). This gives us 33/7. Finally, we multiply $9.00 by 33/7 to find the cost of 4 5/7 kg of candy.
The cost of 4 5/7 kg of candy is $38.57.
A delivery truck travels 278 miles each day.How far does it go in 25 days
Answer:
6950
Step-by-step explanation: multiply 278 times 25
Two hoses are used to fill a swimming pool. Together they fill the pool at a rate of 3 gallons every 5
seconds. An equation representing this is g = 1, where is the time in seconds and g is the number of
gallons. About how many hours will it take to fill the pool if it holds 80,000 gallons?
A.4
B.7
C. 13
D. 37
Help ASAP !
Answer:13
Step-by-step explanation:
There are hours 2 will it take to fill the pool if it holds 80,000 gallons.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Two hoses are used to fill a swimming pool.
And, Together they fill the pool at a rate of 3 gallons every 5 seconds.
Hence, Time for to fill 80,000 gallons are,
⇒ Time = 80,000 × 3 / 5
⇒ Time = 16,000 × 3
⇒ Time = 48,000 seconds
⇒ Time = 48,000 / 36,000 hours
⇒ Time = 1.33 hours
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hey i need help i need it done soon plz help it is 3/8 and you add 1/2
Answer:
Add: 3
8
+ 1
2
= 3
8
+ 1 · 4
2 · 4
= 3
8
+ 4
8
= 3 + 4
8
= 7
8
The common denominator you can calculate as the least common multiple of the both denominators - LCM(8, 2) = 8. The fraction result cannot be further simplified by cancelling.
In words - three eighths plus one half = seven eighths.
Answer:7/8
Step-by-step explanation:The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(3/8, 1/2) = 8
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(3/8×1/1)+(1/2×4/4)=?
Complete the multiplication and the equation becomes
3/8+4/8=?
The two fractions now have like denominators so you can add the numerators.
Then:
3/8+4/8=7/8
This fraction cannot be reduced.
What is the answer to this problem 12(3-7)=x-7
Answer:
dang that one was hard wish I could help
Step-by-step explanation:
write an equation parallel to x - 3y = 9 that passes through the point ( 3, -1 )
Answer:
x - 3y = 9
-3y = -x + 9
y = (1/3)x - 3
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
y = (1/3)x - 2
3y = x - 6
-x + 3y = -6
x - 3y = 6
To find an equation parallel to x - 3y = 9 that passes through the point (3, -1), rearrange the equation to slope-intercept form, determine the slope of the given line, and substitute the slope and coordinates into the point-slope form equation.
Explanation:To find an equation parallel to x - 3y = 9 that passes through the point (3, -1), we need to determine the slope of the given line and then use it to form the equation of the parallel line.
First, we rearrange the given equation to find the slope-intercept form: y = (1/3)x - 3. We know that the slope of the parallel line will be the same as the slope of the given line, which is 1/3.
Using the point-slope form, we substitute the slope and the coordinates of the given point into the equation: y - (-1) = (1/3)(x - 3). Simplifying, we get the equation of the parallel line as y = (1/3)x + 2.
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Irrational number between 2 and 3
Answer:
2.084...
Step-by-step explanation:
Just write an non repeating string of any numbers that you think of but not in a pattern which will lie between decimal value of your 2 numbers
Irrational numbers between 2 and 3 include √2, which is approximately 1.414.
Irrational numbers are numbers that cannot be expressed as a ratio of integers. An example of an irrational number between 2 and 3 is √2, which is approximately 1.414. It is not possible to represent √2 as a fraction of two integers.
A product costs $60 today. How much will the product cost in t days if the price is reduced by $4 a day
Answer:
[tex]C=60-4t[/tex]
Step-by-step explanation:
A product costs $60 today.
The price is reduced by $4 a day, so
a product will cost $60 - $4 = $56 tomorrow;a product will cost $56 - $4 = $52 after 2 days;a product will cost $52 - $4 = $48 after 3 days;and so onThe genaral formula for the price of the product after t days will be
[tex]C=60-4t[/tex]
Penny used 2/5 lb of flour to bake a vanilla cake. She used another 3/4 lb of flour to bake a chocolate cake. How much flour did she use altogether?
Answer:
she use altogether flour is [tex]1 \frac{3}{20}[/tex] lb
Step-by-step explanation:
given data
flour to bake a vanilla cake = [tex]\frac{2}{5}[/tex] lb
flour to bake a chocolate cake = [tex]\frac{3}{4}[/tex] lb
to find out
How much flour did she use altogether
solution
we know here flour use to make cake
so total flour is used = add both flour for vanilla and chocolate cake
total flour is used = [tex]\frac{2}{5}[/tex] + [tex]\frac{3}{4}[/tex]
total flour is used = [tex]\frac{23}{20}[/tex]
she use altogether flour is [tex]1 \frac{3}{20}[/tex] lb
Answer: [tex]\frac{23}{20}\ lb[/tex] or [tex]1\frac{3}{20}\ lb[/tex]
Step-by-step explanation:
For this exercise you need to add fractions.
To bake the vanilla cake, Penny used [tex]\frac{2}{5}\ lb[/tex] of flour and to bake the chocolate cake she used [tex]\frac{3}{4}\ lb[/tex] of flour.
Then, the total flour she used can be found by solving this addition:
[tex]\frac{2}{5}\ lb+\frac{3}{4}\ lb[/tex]
Since the denominators are different, you must find the Least Common Denominator (LCD).
Descompose the denominators into their prime factors and multipy the commons and non-commons with the highest exponent.
Then:
[tex]5=5\\\\4=2*2=2^2[/tex]
[tex]LCD=5*2^2=20[/tex]
So, the sum is:
[tex]\frac{2}{5}+\frac{3}{4}=\frac{4(2)+5(3)}{20}=\frac{23}{20}[/tex]
That improper fraction can be written as a mixed number.
When you divide the numerator 23 by the denominator 20 you get;
A quotient of 1 (This will be the whole number).A remainder of 3 (This will be the numerator of the fraction).The denominator will not change.Then:
[tex]\frac{23}{20}\ lb=1\frac{3}{20}\ lb[/tex]
a village parking lot is 120 feet wide by 180 feet long, and it has room for 75 cars. the village plans to increase the length by 30%.
A. what will be the new length of the parking lot?
B. how much greater is the new area?
C. if each cars needs about 288 square feet in a parking lot, will the new parking lot be able to fit 20 more cars than the original parking lot? explain.
Answer:
A) 234 feet
B) Area of new parking lot = 28080 square feet
C) The new parking lot will be able to fit 20 more cars than the original parking lot.
Step-by-step explanation:
We are given the following information:
Length of parking lot = 180 feet
Width of parking lot = 120 feet
Number of cars that can be parked = 75
A) Increase in length = 30%
New length =
[tex]\text{original length} + 30\%(\text{original length})[/tex]
[tex]= 180 + \bigg(\displaystyle\frac{30}{100}\times 180\bigg) = 180 + 54 = 234~feet[/tex]
B) New area =
[tex]\text{New length}\times Breadth\\= 234\times 120 \\= 28080~ square~feet[/tex]
C) Space required by 1 car = 288 square feet
Number of cars we want to fit = 75 + 20 = 95
Area required =
[tex]\text{Number of cars}\times \text{Space occupied by 1 car}[/tex]
[tex]= 95\times 288 = 27360~square~feet[/tex]
Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.
A. This results in a new length of 234 feet.
B. The difference in area is 6480 square feet.
C. The new parking lot's area can only accommodate a fraction of a car more than the original lot's capacity of 75 cars, so it cannot fit 20 more cars.
How to find the new length of the parking lotA. The new length of the parking lot after a 30% increase is calculated by adding 30% of the original length (180 feet) to it.
= 180 * 1.3
= 234 feet
This results in a new length of 234 feet.
B. To find the greater area of the new parking lot compared to the original:
Original area: 120 feet (width) * 180 feet (original length) = 21600 square feet.
New area: 120 feet (width) * 234 feet (new length) = 28080 square feet.
The difference in area: 28080 square feet - 21600 square feet = 6480 square feet.
C. To check if the new parking lot can fit 20 more cars:
New area of the parking lot: 120 feet (width) * 234 feet (new length) = 28080 square feet.
Maximum number of cars in new area: 28080 square feet / 288 square feet per car ≈ 97.5 cars.
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Use mental math to determine whether each number is
divisible by 1, 2, 3, 5, 9, or 10.
9. 126
10. 257
11. 430
12. 535
13. 745
14. 896
15. 729
16. 945
17. 4,580
18. 6,331
19. 7,952
20. 8,000
21. 19,450
22. 21,789
23. 43,785
24. 28,751
Step-by-step explanation:
you can divide every number by 1
if a number is even you can always divide it by 2
if the number ends in an odd number that isn't 5, you will most likely be able to divide it by 1, 3, or 9
if a number can be divided by 3, it can most likely be divisible by 6 if its an even number
if it ends in 5, you will be able to divide it by 5
if the number is over 10 and ends in a 0 it will be divisible by 10 and/or 5
I hope this helps
casey bought sandwiches and a bag of chips. Each sandwich cost three times as much as bag of chips. She bought 5 sandwiches for 6 dollars each and spent 42 dollars. How many bags of chips b did she buy?
Final answer:
Casey spent $12 on chips that cost $2 per bag, so she bought 6 bags of chips.
Explanation:
Casey bought 5 sandwiches at $6 each, totaling $30 spent on sandwiches. Since she spent $42 in total, we subtract the amount spent on sandwiches from the total amount to find out how much she spent on bags of chips: $42 - $30 = $12 spent on chips. Each sandwich cost three times as much as a bag of chips, so one bag of chips costs $6 / 3 = $2. To find out the number of bags of chips b she bought, we divide the total spent on chips by the cost of one bag: $12 / $2 = 6 bags of chips.
3x = 15 - 2х
Help me
Answer:
Step-by-step explanation:
you have to move the x’s to one side. so the equation would look like
5x = 15
then you have to divide both side of the equation by 5 to get the x by itself which leaves you with
x = 3
Answer is provided in the image attached.