The table shows the cost,c, of buying each number of boxes,b,of cookies. Write an equation that models this situation.
A. b=3c
B. c=3b
C. b=8c
D. c=8b
Answers
Answer:
B
Step-by-step explanation:
Each box of cookies is $3 since 4 x 3 =12, 6 x 3 = 18, and 9 x 3 = 27. So we want to multiply the number of boxes, b, by 3 to get the cost, c. The correct equation is c = 3b.
An equation that models this situation is c = 3b. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given the data is,
b c
4 12
6 16
9 27
c = kb
12 = k x 4
k = 12 / 4 = 3
c = 3b
Therefore, the equation that models this situation is c = 3b. The correct option is B.
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Related Questions
USING SUBSTITUTION, WHAT IS
Y=-×-6
Y=×-4
Answers
Answer:
x=-1, y=-5. (-1, -5).
Step-by-step explanation:
y=-x-6
y=x-4
----------
-x-6=x-4
-x-x-6=-4
-2x-6=-4
-2x=-4+6
-2x=2
x=2/-2
x=-1
y=-1-4
y=-5
Answer:
Step-by-step explanation:
Hajdiabndodisba djdk
Which of the following does NOT have a value of -5?
F. 1/4 - 5 1/4.
G. -10 ➗ 2
H. -20 x 0.25
J. -13 + 18
Answers
Answer:
J
Step-by-step explanation:
All of the other ones have a value of -5 except for J which has a value of 5.
More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled in a car. How many students were on each bus?
Answers
Answer:a total of 45 students per bus
Step-by-step explanation: 450-5= 445
445/10= 44.5
a total of 45 students per bus
6. Savannah leaves Redlands driving due north at
55 mph. Luke leaves Redlands at the same time
and drives due south at 62 mph. How far apart
are they after 3 hours?
Answers
Both people have rates: Savannah is driving at 55 mph; Luke is driving at 62 mph.
Since the question states that they both drive for 3 hours, all we have to do is multiply both rates by 3.
55(3) + 62(3) = ?
Multiply:
165 + 186 = ?
Add:
165 + 186 = 351
After 3 hours, Savannah and Luke are 351 miles apart.
-T.B.
What is the solution to this equation x/-3=6
Answers
Answer:
[tex]\frac{x}{-3} =6\\x=-18[/tex]
x= -18
Answer: X = -18
Step-by-step explanation: In this problem, notice that x is being divided by -3 so to get x by itself, we need to multiply both sides of the equation by -3.
Notice that on the left side, the -3 and -3 cancel each other out so we're just left with x.
On the right side, we have 6 × -3 which is -18 so X = -18.
Finally, we can check our answer by plugging a -18 back into the original equation.
So we have -18 ÷ -3 = 6, which is a true statement which means that our answer is correct.
Image provided.
Write in standard form (100 x 3)+(4 x 0.1)+(7 x 0.001)
Answers
Answer:
300.407
Step-by-step explanation:
100*3=300
4*0.1=0.4
7*0.001=0.007
----------------------
300+0.4+0.007
300.407
How many inches are equivalent to 2 meters?
Round your answer to the nearest tenth.
The measurement 2 meters is equivalent to
inches.
Answers
To convert 2 meters to inches, you multiply by the conversion factor of approximately 39.37, resulting in 78.7 inches when rounded to the nearest tenth.
The measurement 2 meters is equivalent to
78.7 inches.
To convert meters to inches, we know that 1 meter is approximately 39.37 inches. Therefore, 2 meters would be equal to 2 x 39.37 = 78.74 inches. Rounding to the nearest tenth, this equals 78.7 inches.
Should a denominator or numerator be bigger?
Answers
Answer: Usually, a denominator should be bigger. If the numerator was bigger, it would make the fraction inproper, which you should convert into a mixed number.
Answer:denominator
Step-by-step explanation:
Find the length of PQ if PQ parallel to BC and PQ is a midsegment of ABC
Answers
Answer:
4.924 units.
Step-by-step explanation:
See the attached diagram.
If P is the midpoint of AB and Q is the midpoint of AC, then PQ is parallel to BC and the length of PQ will be half of BC.
Now, the coordinates of B are (1,1) and that of C is (10,-3).
Therefore the length of BC is [tex]\sqrt{(10 - 1)^{2} + (- 3 - 1)^{2}} = 9.848[/tex] units (Approximate)
Therefore, the length of PQ = 0.5 × 9.848 = 4.924 units. (Answer)
We know that the distance between two given points ([tex]x_{1},y_{1}[/tex]), and ([tex]x_{2},y_{2}[/tex]) is given by the formula
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]
Gabriela has dinner at a cafe and the cost of her meal is
$
45.00
$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a
15
%
15%15, percent tip.
What is her total bill including tip?
Answers
Answer:
Step-by-step explanation:
Answer:
Total bill=$51.75
Step-by-step explanation:
Step 1: Determine the cost of her meal
Cost of meal=$45
Step 2: Calculate the amount of the tip
Tip amount=15% of the cost of meal
where;
cost of meal=$45
replacing;
Tip amount=(15/100)×45=6.75
The tip amount=$6.75
Step 3: Total bill
The total bill can be expressed as;
Total bill=tip amount+subtotal
where;
tip amount=$6.75
cost of meal=$45
replacing;
Total bill=(45+6.75)=51.75
Total bill=$51.75
4×=32 how do i solve this
Answers
Answer:
x=8
Step-by-step explanation:
You divide both sides by 4 to get x alone.
Answer:
x = 8
Step-by-step explanation:
4x divied by 4 is x. 32 divided by 4 is 8.x = 8At the Idaho Humane Society there is a ratio of 9 cats 13 dogs . If there are a total of 66 cats and dogs how many are cats ?
Answers
Answer:
27 cats.
Step-by-step explanation:
The fraction of cats = 9 / (9 + 13) and dogs = 13 / ( 9 + 130
= 9/22 and 13/22
So the number of cats = (9/22) * 66
= 9 *3
= 27.
=
A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns 7.5% interest per year, starting on the day your child is born. How much would you need to invest each year (rounded to the nearest dollar) to accumulate a million for your child by the time he is 35 years old? (Your last deposit will be made on his 34th birthday.)
Answers
Answer:
$12159 per year.
Step-by-step explanation:
If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.
So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by
[tex]x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})[/tex]
= [tex]35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1][/tex]
= [tex]35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)][/tex]
{Since sum of n natural numbers is given by [tex]\frac{1}{2} (n)(n + 1)[/tex]}
= 35x + 47.25x
= 82.25x
Now, given that the final amount will be i million dollars = $1000000
So, 82.25x = 1000000
⇒ x = $12,158. 05 ≈ $12159
Therefore. I have to invest $12159 per year. (Answer)
What is the only prime number that is a factor of 16
Answers
The only prime number that is a factor of 16 is 2, since 16 is a power of 2 (2⁴).
Explanation:The student has asked to identify the only prime number that is a factor of 16. To find the factors of 16, we can break it down into its prime factors. The prime factorization of 16 is 2×4×4, which reduces further to 2×2×2×2 or 24. Since the prime factors of 16 are all 2s, the only prime number that is a factor of 16 is 2. It's important to note that a prime number is defined as a number that has exactly two distinct positive divisors: 1 and the number itself. In the case of 16, 2 is the only prime number that fits this definition and is a factor.
How many times does 7 go into 18
Answers
Answer:
Twice.
Step-by-step explanation:
7 times 2 is 14.
So it can only go in 2x.
Answer:
Seven goes into 18 twice
Step-by-step explanation:
7×2=14
2(n +5)= -2
I need to find the value of n
Answers
Answer:
-6
Step-by-step explanation: 2(n+5)=-2
Remove the bracket(expanding):
2×n+2×5=-2
2n+10=-2
collect like terms:
2n=-2+(-10)
2n=-12
Dividing both side by the coefficient of n i.e 2
2n/2=-12/2
n=-6
Write an equation of the line that passes through the given point and is parallel to the given line.
40. (4,1);y=-2x+7 41. (0,6);y=5x-3 42. (-5,-2);y=2/3x+1
Answers
Answer:
Part 40) [tex]y=-2x+9[/tex]
Part 41) [tex]y=5x+6[/tex]
Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
Step-by-step explanation:
Remember that
If two lines are parallel, then their slopes are the same
Part 40) Write an equation of the line that passes through the given point
and is parallel to the given line
we have
Point (4,1)
Given line y=-2x+7
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=-2[/tex]
step 2
Find the y-intercept b
we have
[tex]m=-2[/tex]
[tex](4,1)[/tex]
substitute in the linear equation
[tex]1=(-2)4+b[/tex]
solve for b
[tex]b=1+8[/tex]
[tex]b=9[/tex]
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
[tex]m=-2[/tex]
[tex]b=9[/tex]
substitute
The equation of the line is
[tex]y=-2x+9[/tex]
Part 41) Write an equation of the line that passes through the given point
and is parallel to the given line
we have
Point (0,6)
Given line y=5x-3
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=5[/tex]
step 2
Find the y-intercept b
[tex]b=6[/tex] ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
[tex]m=5[/tex]
[tex]b=6[/tex]
substitute in the linear equation
[tex]y=5x+6[/tex]
Part 42) Write an equation of the line that passes through the given point
and is parallel to the given line
we have
Point (-5,-2)
Given line y=(2/3)x+1
step 1
Find the slope of the given line
The given line is a equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
so
The slope of the given line is
[tex]m=\frac{2}{3}[/tex]
step 2
Find the y-intercept b
we have
[tex]m=\frac{2}{3}[/tex]
[tex](-5,-2)[/tex]
substitute in the linear equation
[tex]-2=(\frac{2}{3})(-5)+b[/tex]
solve for b
[tex]-2=-\frac{10}{3}+b[/tex]
[tex]b=-2+\frac{10}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
step 3
Find equation of the line that passes through the given point and is parallel to the given line
we have
[tex]m=\frac{2}{3}[/tex]
[tex]b=\frac{4}{3}[/tex]
substitute
The equation of the line is
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]
Final answer:
To find the equation of a line that is parallel to a given line and passes through a specific point, use the fact that parallel lines have the same slope. Find the slope of the given line, substitute the slope and the point into the slope-intercept form of a line to find the y-intercept, and write the equation with the new slope and y-intercept.
Explanation:
To find the equation of a line that is parallel to a given line and passes through a specific point, we need to use the fact that parallel lines have the same slope. The given line, y = -2x + 7, has a slope of -2. So, the parallel line we need to find will also have a slope of -2.
Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope is -2 and the point (4,1) lies on the line, we can substitute these values into the equation to find the y-intercept:
y = -2x + b
1 = -2(4) + b
1 = -8 + b
b = 9
Therefore, the equation of the line that passes through (4,1) and is parallel to y = -2x + 7 is y = -2x + 9.
a. Original Price: $16.20
Increase by 40%
Final Price:
Proportional Constant:
How to find the final price and the constant of proportionality in this problem?
Answers
Answer:
The final price is $ 22.68 And Proportional constant is 1.4
Step-by-step explanation:
Given as :
The Original price = $ 16.20
The rate of increase = 40%
Let The final price = x
Now,
Final price after increase = initial price × ( 1 + [tex]\frac{\textrm Rate}{100}[/tex]
Or. Final price after increase = $ 16.20 × ( 1 + [tex]\frac{\textrm 40}{100}[/tex]
Or, Final price after increase = $ 16.20 × ( 1.4 )
∴ Final price after increase = $ 22.68
Now , Proportional constant = [tex]\frac{22.68}{16.20}[/tex]
I.e Proportional constant = 1.4
Hence The final price is $ 22.68 And Proportional constant is 1.4 Answer
Which change (in percent) is larger: losing weight from 100 lb to 90 lb or losing weight from 50 lb to 40 lb
Answers
Answer: losing weight from 50lb to 40lb
Step-by-step explanation:
Answer:
50lb to 40lb
Step-by-step explanation:
When you multiply 50 lb to 40lb by 2, it makes 100 lb to 80 lb. 50lb to 40 lb is 20 percent change while 100 lb to 90 lb is 10 percent
Kay has 28 coins which includes nickels and dimes if the total is 2.35$, how many of each coin does Kay have?
Answers
Answer:9 nickels and 19 dimes.
Step-by-step explanation:
Let [tex]n[/tex] be the number of nickels Kay has.
Let [tex]d[/tex] be the number of dimes Kay has.
Value of [tex]1[/tex] nickel is $[tex]0.05[/tex]
Value of [tex]n[/tex] nickels is $[tex]0.05n[/tex]
Value of [tex]1[/tex] dime is $[tex]0.1[/tex]
Value of [tex]d[/tex] nickels is $[tex]0.1dn[/tex]
Given that Kay has a total of [tex]28[/tex] coins.
So,[tex]n+d=28[/tex] ...(i)
Given that Kay has a total value of $[tex]2.35[/tex]
So,[tex]0.05n+0.1d=2.35[/tex] ...(ii)
Using (i) and (ii),
[tex]0.05n+0.1(28-n)=2.35\\0.05n+2.8-0.1n=2.35\\2.8-2.35=0.05n\\0.45=0.05n\\n=9[/tex]
[tex]d=28-n=28-9=19[/tex]
The National Zoo has T-shirts that regularly sell for $32. The shirts are marked 1/4 off during a Labor Day sale. What is the sale price of a T-shirt?
Answers
Answer:
The sale price of a T-shirt is $24.
Step-by-step explanation:
1/4 off=25%=0.25
0.25*32=8
32-8=24
Leonard it sells small watermelons for seven dollars each and large watermelons for $10 each one day the number of small watermelons he saw was 15 more than the number of large watermelons and he made a total of $394 how many small and how many large watermelons a did he sell?
Answers
He sold 32 small watermelons and 17 large watermelons.
Step-by-step explanation:
Let,
Small watermelons = x
Large watermelons = y
Cost of one small watermelon = $7
Cost of one large watermelon = $10
According to given statement;
x = y+15 Eqn 1
7x+10y=394 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
[tex]7(y+15)+10y=394\\7y+105+10y=394\\17y=394-105\\17y=289\\[/tex]
Dividing both sides by 17
[tex]\frac{17y}{17}=\frac{289}{17}\\y=17[/tex]
Putting y=17 in Eqn 1
[tex]x=17+15\\x=32[/tex]
He sold 32 small watermelons and 17 large watermelons.
Keywords: linear equations, substitution method
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The table below shows the scores of a group of students on a 10-point quiz.
Test Score Frequency
3 0
4 1
5 1
6 1
7 2
8 1
9 5
10 5
The mean score on this test is:
The median score on this test is:
Help
Answers
The mean score on this test is 8.8, and the median score is 9.4.
Explanation:In order to find the mean of the scores, we use the formula:
[tex]\[ \text{Mean} = \frac{\sum (X \cdot f)}{N} \][/tex]
where X is the score, f is the frequency, and N is the total number of scores. Applying this formula to the given data:
[tex]\[ \text{Mean} = \frac{(4 \cdot 1) + (5 \cdot 1) + (6 \cdot 1) + (7 \cdot 2) + (8 \cdot 1) + (9 \cdot 5) + (10 \cdot 5)}{1 + 1 + 1 + 2 + 1 + 5 + 5} \][/tex]
[tex]\[ \text{Mean} = \frac{4 + 5 + 6 + 14 + 8 + 45 + 50}{15} \][/tex]
Mean = [tex]\frac{132}{15}[/tex]
Mean = 8.8
So, the mean score is 8.8.
To find the median using the formula:
[tex]\[ \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times w \][/tex]
where:
- L is the lower class boundary of the median group,
- N is the total number of observations,
- F is the cumulative frequency of the group before the median group,
- f is the frequency of the median group,
- w is the width of the median group.
First, arrange the data and calculate cumulative frequencies:
Test Score Frequency Cumulative Frequency
3 0 0
4 1 1
5 1 2
6 1 3
7 2 5
8 1 6
9 5 11
10 5 16
The median position is [tex]\( \frac{N}{2} = \frac{16}{2} = 8 \)[/tex] with a score of 9. The cumulative frequency before the median group is 6, and the frequency of the median group is 5.
Now, using the formula:
Median= 9 + [tex]\frac{8 - 6}{5} \times 1[/tex]
Median= 9 + [tex]\frac{2}{5}[/tex]
Median = 9 + 0.4
Median = 9.4
Therefore, the median score is 9.4.
please help!!! due tonight
Answers
Answer:
[tex]A=10^0[/tex]
Step-by-step explanation:
Number 2.247 has 2 in ones place, 2 in tenths place, 4 in hundredths place and 7 in thousandths place.
This means you can rewrite this number as
[tex]2.247=2\times 1+2\times 0.1+4\times 0.01+7\times 0.001\\ \\2.247=2\times 10^0+2\times \dfrac{1}{10^1}+4\times \dfrac{1}{10^2}+7\times \dfrac{1}{10^3}[/tex]
So,
[tex]A=10^0\\ \\B=\dfrac{1}{10^1}\\ \\C=\dfrac{1}{10^2}\\ \\D=\dfrac{1}{10^3}[/tex]
The following ratios form a proportion. 5/18 = 10/90
True or False
13 pts.
Answers
Answer:
False
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Find the slope and reduce.
P=(4.5,-1) Q=(5.3,2)
Answers
Answer: slope m = (y2 - y1)/(x2 - x1) so that m = (2-(-1))/(5.3-4.5)
m = 3 / .8 = 3.75 or 15/4
Step-by-step explanation:
Find the output, h, when the input, x, is -18. h = 17+x\6
Answers
Answer:
[tex]17 + \frac{ - 18}{6} = 17 - 3 = 14[/tex]
10.
Your brother has $2000 saved for a vacation. His airplane ticket is $637. Write and solve an
inequality to find how much he can spend for everything else.
Answers
Answer:
He can spend $1363 for everything else.
Step-by-step explanation:
x+637<=2000
x<=2000-637
x<=1363
[tex]\frac{x^{\frac{5}{6} } }{x^{\frac{1}{6} } }[/tex]
Answers
Answer:
x^2/3
Step-by-step explanation:
(x^5/6)/(x^1/6)=x^(5/6-1/6)=x^4/6
simplify 4/6, you get 2/3.
The lunch lady has 8 pounds of lasagna. If she makes 1/5-pound servings using this amount of lasagna, how many servings can she make?
Answers
Answer:
40
Step-by-step explanation:
8 / (1/5)
When dividing fractions, the second fraction just flips upside down. Then you just multiply.
So it's now 8 * 5 = 40