Answer:
y = [tex]\frac{96}{5}[/tex]
Step-by-step explanation:
given that y and x are proportional then the equation relating them is
y = kx ← k is the constant of proportionality
to find k use the given condition y = 12 when x = 5
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{5}[/tex]
y = [tex]\frac{12}{5}[/tex] x ← equation of proportionality
when x = 8, then
y = [tex]\frac{12}{5}[/tex] × 8 = [tex]\frac{96}{5}[/tex]
What quantity of salt would you need to make a double recipe? Alfredo sauce INGREDIENTS: 1 cup milk 1 cup cream cheese 1 cup Parmesan cheese 1 cup parsley 1 teaspoon garlic 1 teaspoon pepper 1 2 teaspoon salt Write your answer as a fraction or as a whole or mixed number. teaspoons Questions
To make a double recipe of Alfredo sauce, the quantity of salt required would be doubled from 1 1/2 teaspoons to 3 teaspoons.
Explanation:To determine the quantity of salt needed to make a double recipe of Alfredo sauce, we need to look at the original recipe. The original recipe calls for 1 1/2 teaspoons of salt. To make a double recipe, we simply multiply the quantity of each ingredient by two. So, for the salt component, that would be:
1 1/2 teaspoons × 2 = 3 teaspoons.
Therefore, you would need 3 teaspoons of salt to make a double recipe of Alfredo sauce.
Lila decided to make more baked goods for the bake sale she used 1/8 lb less flour to make the bread then to make the cookies. She used 1/4 pound more flour to make cookies than to make brownies. If she used a half pound of flour to make bread how much flour did she use to make brownies
Answer:
The total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.
Step-by-step explanation:
Let x lb flour is used to make brownies.
She used 1/4 pound more flour to make cookies than to make brownies. So, the total flour is used to make cookies is
[tex]x+\frac{1}{4}[/tex]
she used 1/8 lb less flour to make the bread then to make the cookies. So, the total flour is used to make bread is
[tex]x+\frac{1}{4}-\frac{1}{8}[/tex]
It is given that she used a half pound of flour to make bread.
[tex]x+\frac{1}{4}-\frac{1}{8}=\frac{1}{2}[/tex]
[tex]x+\frac{2-1}{8}=\frac{1}{2}[/tex]
[tex]\frac{8x+1}{8}=\frac{1}{2}[/tex]
[tex]8x+1=4[/tex]
[tex]8x=3[/tex]
[tex]x=\frac{3}{8}[/tex]
Therefore total [tex]\frac{3}{8}[/tex] lb flour is used to make brownies.
13. Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If Philadelphia and Pittsburgh are 305 miles apart how long will it take Rich and Michelle to meet?
Answer:
It would be 2 hours and 15 minutes
Step-by-step explanation:
Answer:2.26 hours
Step-by-step explanation:
Given
Rich is driving from Philadelphia to Pittsburgh at 70 mph
and Michelle speed is 65 mph
If Philadelphia and Pittsburgh is 305 miles apart
Let Rich travels x miles in t time
therefore
Michelle travels 305 -x
[tex]\frac{x}{70}=\frac{305-x}{65}[/tex]
[tex]13x=14\times 305 -14x[/tex]
27x=4270
[tex]x=\frac{4270}{27}[/tex]
[tex]x=158.148\approx 158.15 miles[/tex]
time taken t[tex]=\frac{158.15}{70}=2.259 \approx [/tex] 2.26 hours
The largest possible circle is cut out of a square whose side length is 12 feet. What will be the approximate area, in square feet, of the remaining board?
Answer:
31 ft²
Step-by-step explanation:
(1) Area of square
A = l²
A = 12²
A = 144 ft²
=====
(2) Area of circle
A = πr²
A = π × 6²
A = π × 36
A = 113 ft²
=====
(3) Remaining area
A = 144 – 113
A = 31 ft²
The area of the remaining board is 31 ft².
Answer:
Step-by-step explanation:
30
Please answer this for me!!! Thanks!
Answer:
18x - 32
combine the like terms and then you get this.
The slope of a roof is called its pitch. The parthenon, an ancient greek temple, has a roof with a rise of 3.6 meters and a run of 12 meters. What is the pitch of the roof
Answer:
The answer is 0.3.
Solve the following systems using the ELIMINATION METHOD.
y=4x-5
y=3x+7
[tex]\left\{\begin{array}{ccc}y=4x-5\\y=3x+7&|\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y=4x-5\\-y=-3x-7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=x-12\qquad\text{add 12 to both sides}\\\qquad\boxed{x=12}\\\\\text{Substitute the value of x to the first equation}\\\\y=4(12)-5\\y=48-5\\\boxed{y=43}\\\\Answer:\ x=12\ and\ y=43.[/tex]
find the equation of the line passes through the pints (-2,3) and (1,-4).
Answer:
[tex]3y+7x=-5[/tex] is the required equation.
Step-by-step explanation:
We have been given two points: (-2,3) and (1,-4)
We have a formula to find the equation with two points:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)[/tex]
Here, we have:
[tex]x_1=-2,x_2=1,y_1=3,y_2=-4[/tex]
On substituting the values in the formula we get:
[tex]y-3=\frac{-4-3}{1-(-2)}\cdot (x-(-2))[/tex]
[tex]\Rightarrow y-3=\frac{-7}{3}\cdot (x+2)[/tex]
On further simplification:
[tex]3y-9=-7(x+2)[/tex]
[tex]\Rightarrow 3y-9=-7x-14[/tex]
After rearranging the terms
[tex]3y+7x=-14+9[/tex]
After final simplification we get:
[tex]3y+7x=-5[/tex]
Answer:
m=[tex]\frac{-7}{3}[/tex]
Step-by-step explanation:
Given:
(-2,3)(1,-4)
(x₁,y₁)(x₂,y₂)
m=(y₂-x₂)÷(y₁-x₁)
m=(-4 - 3) ÷ (1+2)
m= [tex]\frac{-7}{3}[/tex]
What is the product? 3 1/2 × 2 2/3
Answer:
56/6
Step-by-step explanation:
3 1/2 * 2 2/3
first evaluate 3 1/2 = (6+1)/2=7/2
so for that multiply 2 * 3 and +1 and divide by 2
second evaluate 2 2/3 = (6+2)/3 = 8/3
now the product = 7/2 * 8/3 = (7*8) / (2*3) = 56 / 6
Kayla's age is 3 less than twive her brother's age. Kayla is 13 years old. How old is her brother?
Answer: 6
Step-by-step explanation:
3 times 2
The range of relation is
Answer:
A
Step-by-step explanation:
The range is the set of y values, that is the output
can someone please help me with this
You are on a cycling trip around Europe with friends. You are coming towards the end of your trip and have been asked by an online cycling blog to give some details about the cost of your trip, the places you visited and how many kilometres you have cycled. Look at your kilometres cycled record for each week:
Answer:
Based on the questions asked on the screen shot of the problem, the range of time spend cycling each week is 16 hours and the average number of calories burned per day in week 5 was 1200.
Step-by-step explanation:
Given the data in the problem for the number of weeks versus the amount of hours spent cycling, in order to find the range you would subtract the highest number of hours in a given day (22 - week 4) by the lowest number of hours in a given day (6 - week 1), or 16. For week 5, if you were to burn 8400 calories for the week, assuming that you cycled for all seven days, you would take your total calories burned and divide by the number of days to get approximately 1200 calories per day.
Which expression represents the difference of (8x-5y) and (2x-y)?
A. 10x - 9y
B. 10x - 8y
C. 6x - 4y
D. 6x - 6y
Answer:
C. 6x - 4y
Step-by-step explanation:
Difference means subtract
8x-5y - (2x-y)
Distribute the minus sign
8x-5y - 2x+y
Combine like terms
6x-4y
Answer:
C
Step-by-step explanation:
a social networking site recorded that 80 per-cent of people who became members of the site one month were between 30 and 40 years old the equation below represents information where X represents the total number of people who became members of the site that month
x=0.8x +72
how many people who became members of the site that wants where between 30 and 4 years of age
Answer:
x=360 30-40 yrs =288
Step-by-step explanation:
multiple 72 by .05 (36) to find 10 percent, then multiple 80 percent by that number(36) then add both numbers together to get total number of members that month
(72x.05)=36x2+(.80x36)=288
288+72=360
The Number of people who became members in month, x = 5 are 76
The equation given represents a linear expression representing :
x = total number of people who became members that monthTo obtain the number of people who became members in a particular month, we input the value of x into the equation and calculate the output :
For instance, if Number of month, x = 5
The Number of people who became members is :
y = 0.8(5) + 72
y = 4 + 72
y = 76
Hence, the Number of people who became members in month, x = 4 are 76
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98 POINTS AND BRAINLIEST FOR FASTEST AND RIGHT ANSWERS!!! 4 MULTIPLE CHOICE QUESTIONS!!!
A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. Find the absolute value inequality that describes the situation and solve it to find the range of rejected masses, x.
|x − 0.23| + 9.25 > 0; x < 9.02 or x > 9.48
|x − 9.25| > 0.23; x < 9.25 or x > 9.48
|x − 0.23| + 9.25 > 0; x < 9.25 or x > 9.48
|x − 9.25| > 0.23; x < 9.02 or x > 9.48
Almond trees yield 12 pounds per acre and macadamia nut trees yield 8 pounds per acre. Suppose Pippa's farm has a acres of almond trees, m acres of macadamia nut trees, and yields 250 pounds of nuts. What is the equation that represents this scenario?
8a + 12m = 250
20n = 250
12a + 8m = 250
a + m = 250
One of the fastest recorded speeds of an alligator on land is 8.8 m/s. Approximately, what is this speed in kilometers per hour? [1 kilometer = 1,000 meters] [1 hour = 60 minutes = 3,600 seconds]
2.444 km/h
6.336 km/h
31.68 km/h
0.244 km/h
In a certain county, the number of charter schools is 4 less than twice the number of alternative schools. We know that there are 48 charter schools in the county. How many alternative schools are in the county?
52
22
36
26
(RIGHT ANSWERS ONLY PLEASE!!!)
Answer:
Problem 1. Answer: D
Problem 2. Answer: A
Problem 3. Answer: C
Problem 4. Answer: D
Step-by-step explanation:
Problem 1:
A pack is targeted to weigh 9.25 oz.
A pack can be up to 0.23 oz off, either over or under weight.
The pack cannot weigh less than 9.25 oz - 0.23 oz or more than 9.25 oz + 0.23 oz.
The following compound inequality represents the rejected weights.
x < 9.25 - 0.23 or x > 9.25 + 0.23
Subtract 9.25 from both sides of both inequalities.
x - 9.25 < -0.23 or x - 9.25 > 0.23
Change to an absolute value inequality.
|x - 9.25| > 0.23
x - 9.25 < -0.23 or x - 9.25 > 0.23
x < 9.02 or x > 9.48
Problem 2:
Almond trees produce 12a
Macadamia nut trees produce 8m
Yield is 250
12a + 8m = 250
Problem 3:
8.8 m/s converted into km/h
1000 m = 1 km
60 sec = 1 min
60 min = 1 hr
8.8 m/s * (1 km)/(1000 m) * (60 s)/(1 min) * (60 min)/(1 hr) =
= 31.68 km/h
Problem 4.
Let number of alternative schools be a.
Let number of charter schools be c.
"the number of charter schools is 4 less than twice the number of alternative schools"
c = 2a - 4
There are 48 charter schools, so c = 48. Now we solve for a.
48 = 2a - 4
52 = 2a
a = 26
Answer:
Do the MAth yourself
Step-by-step explanation:
the box plots show the high temperatures in may and september for denver in degrees in fahrenheit. which can you tell about the mean temperatures for these two months?
Answer:
The mean temperature for May is higher than September's mean.
The mean temperature of May is higher than the mean temperature of September.
Step-by-step explanation:The mean is calculated from the box-plot as follows:
It is the ratio of Sum of (Least value, greatest value, Lower quartile i.e. [tex]Q_1[/tex] , Median i.e. [tex]Q_2[/tex] and Upper quartile i.e. [tex]Q_3[/tex] ) to the number of points i.e. 5.
Hence, From the Box plot of May we have:Least value=52
Greatest value=79
Lower quartile or first quartile i.e. [tex]Q_1[/tex]=63
Middle quartile or Median i.e. [tex]Q_2[/tex]=71
Upper quartile or Third quartile i.e. [tex]Q_3[/tex]=73
[tex]Mean=\dfrac{52+63+71+73+79}{5}\\\\\\Mean=67.6[/tex]
Hence, From the Box plot of September we have:Least value=47
Greatest value=88.5
Lower quartile or first quartile i.e. [tex]Q_1[/tex]=52
Middle quartile or Median i.e. [tex]Q_2[/tex]=62
Upper quartile or Third quartile i.e. [tex]Q_3[/tex]=77.5
[tex]Mean=\dfrac{47+88.5+52+62+77.5}{5}\\\\\\Mean=65.4[/tex]
Hence, the mean of May is higher as compared to September.
Name three other common mutiples or 8 and 12.
Answer:
24
48
72
96
Step-by-step explanation:
I just know
Of maceo’s $750 salary,he puts 10% in his savings account,1/8 towards rent,and 1/3 for food. How much of his salary was left (in dollars) for other expenditures
Answer:
413.44 but the whole decimal is 413.4375
Step-by-step explanation:
first I turned the fractions into percents...
1/3- 30% and 1/8- 12.5
$750-10%= $675
675-12.5%= 590.63 (or 590.635)
590.63-30%= 413.441
Hope it helps some!
How many significant digits does the measurement 2000 feet have
A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the computer?
Answer:
$3200
Step-by-step explanation:
Let price of computer be [tex]c[/tex] and price of software be [tex]s[/tex]
From this statement, we can write: [tex]c+s=4000[/tex]
"The computer costs 4 times as much as the software"From this statement, we can write: [tex]c=4s[/tex]
Substituting 2nd equation into the first and solving for [tex]s[/tex]:
[tex]c+s=4000\\(4s)+s=4000\\5s=4000\\s=\frac{4000}{5}=800[/tex]
We want to know price of computer, which is 4 times this, so we have:
[tex]c=4(800)=3200[/tex]
Thus, the computer costed $3200
Erica babysits for 4.5 hours and is paid $27. If the people she babysits for have $34 to pay her, how long can they stay out?
Find the algebraic equation
Answer:
5 hours 40 minutes can they stay out.
An algebraic equation, y =6x
Step-by-step explanation:
Unit rate defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
Let x represents the hours and y represents the cost.
As per the statement: Erica babysits for 4.5 hours and is paid $27.
Unit rate per hour(m) = [tex]\frac{27}{4.5}= $6[/tex]
Line of equation with no intercept is given by:
y = mx .....[1]; where m represents the slope or unit rate.
Also, it is given if the people she babysits for have $34 to pay her.
⇒ y = $34
substitute the given values in [1] to solve for x;
[tex]34 = 6 \times x[/tex]
Divide both sides by 6 we get;
[tex]x = \frac{34}{6} = 5\frac{4}{6}[/tex] hours
or
x = 5 hours 40 minutes
Therefore, 5 hours 40 minutes can they stay out.
Also, algebraic equation: y =6x
In a pet rescue shelter, 50% of the animals are cats and 40% of the cats are black. What percentage of the animals at the shelter are black cats?
Answer:
20% are black cats.
Step-by-step explanation:
This is 40% of 50%
= 0.40 * 0.50
= 0.20
= 20%
20% of the animals at the shelter are black cats.
What is described in the question ?In a pet rescue shelter, 50% of the total number of animals are cats.
Also 40% of the total number of cats are black.
What percentage of all sheltered animals are black cats ?Percentage of cats in all sheltered animals is 50%
Percentage of black cats in all sheltered animals is 40% of all cats,
i.e. 40% of 50% of the animals at the shelter are black cats.
= [tex]\frac{40}{100}[/tex]×[tex]\frac{50}{100}[/tex] of the animals at the shelter are black cats.
= [tex]\frac{20}{100}[/tex] of the animals at the shelter are black cats.
= 20% of the animals at the shelter are black cats.
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One high speed internet provider and has a $30 setup fee and charges $40 per month. Another provider has a $60 setup fee and charges $30 per month. In how many months will the cost be the same?
A radio station uses 1/6 of it's time for the news. In a 24 hour day, how many are used for music and entertainment? Wouldn't it be 20 hours for music and entertainment?
Wouldn't it be 20 hours?
Since they used 4 hours for news, so 24 - 4 = 20 for music and entertainment?
Someone else is telling me it's 4 hours but I'm confused on their reasoning.
Arrange the fractions in order, beginning with the smallest. 9/7,2/9,2/7,2/3
Hope this helps!
2/9, 2/7, 2/3, 9/7
Answer:
2/9, 2/7, 2/3, 9/7
Step-by-step explanation:
9th are smaller than 7th so 2/9 goes first.
7th are smaller than thirds so 2/7 goes second
9/7 is an improper fraction so it is more than one, so 2/3 goes third
Then 9/7
If 2 is added to the square of an integer, the result is 7 less than 10 times that integer. Find the integer(s). (Enter your answers as a comma-separated list. Simplify your answer completely.)
Final answer:
The integers that satisfy the given condition of the equation x^2 + 2 = 10x - 7 are 1 and 9. To find these integers, the quadratic equation x^2 - 10x + 9 = 0 was factored and solved.
Explanation:
To find the integer(s) that satisfies the given condition, we need to set up an equation based on the description. The condition states: if 2 is added to the square of an integer x, the result equals 10 times that integer minus 7. Mathematically, this can be expressed as x2 + 2 = 10x - 7. To solve this, first rearrange the terms to one side to form a quadratic equation:
x2 - 10x + 9 = 0
Now we factor the quadratic equation:
(x - 1)(x - 9) = 0
Setting each factor equal to zero gives us the solutions:
x - 1 = 0 ⇒ x = 1
x - 9 = 0 ⇒ x = 9
The integers that satisfy the given condition are 1 and 9.
In March Delphine’s house had 40% more snowfall than in February. Delphine’s house has F centimeters of snowfall in February
Answer: In March Delphine's house has 1.4*F centimeters of snow.
Step-by-step explanation:
We know that in March, the snow was 40% more than in Februray.
First we need to write 40% in decimal form, for this we divide it by 100%
40%/100% = 0.4
Now, in Februray Delphine's house has F centimeters of snow.
If F corresponds to the 100%, 0.4*F corresponds to the 40%
Now, in march we have a 140% of snow, this is:
Snow = F + 0.4*F = 1.4*F
In March Delphine's house has 1.4*F centimeters of snow.
Write the percent as a fraction or mixed number in simplest form. 72.5
The fraction form of the given expression is 29/40.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
The expression in the percentage form is given as 72.5%.
Divide by 100 to obtain fraction as,
72.5%
= 72.5/100
= 725/1000
= 29/40
Hence, the given expression can be written in fraction as 29/40.
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Write the equation of the line that passes through point (-10, -5) and is parallel to the line represented by the equation y = -2x + 7.
Answer:
y + 5 = -2(x + 10)
Step-by-step explanation:
To make the line parallel, we need the same slope as the line. Because it is in slope-intercept form, we know that the slope, or [tex]m[/tex], equals -2.
Also, because we have the point that it passes through, we have enough information to put the values into point-slope form, which is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
y + 5 = -2(x + 10)
The reason I made the subtraction signs to addition signs is because a negative times a negative equals a positive.