Lesson 10 Practice Problems
1. Andre bought a new bag of cat food. The next day, he opened it to feed his cat. The
graph shows how many ounces were left in the bag on the days after it was bought.
a. How many ounces of food were in
the bag 12 days after Andre bought
it?
b. How many days did it take for the
bag to contain 16 ounces of food?
c. How much did the bag weigh before
it was opened?
d. About how many days did it take for
the bag to be empty?
ounces of cat food
Using a linear function, it is found that:
a) 36 ounces of food were there after 12 days.
b) It took 24 days for the bag to contain 16 ounces of food.
c) The bag weighed 56 ounces before it was opened.
d) It took about 33 days for the bag to be empty.
What is the definition of a linear function?A linear function is defined according to the following rule:
y = mx + b
In which:
m is the slope of the function, also called the rate of change of the function, given by the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).From the graph of the function, we have that:
The intercept is of b = 56.The slope is of m = -40/24 = -1.6667, as in 24 days, the amount of food decayed from 56 ounces to 16 ounces, that is, it decayed 40 ounces.Hence the function for the amount of food after t days is given by:
A(t) = 56 - 1.6667t.
After 12 days, the amount is given by:
A(12) = 56 - 1.6667(12) = 36 ounces.
From the graph, we have that:
It took 24 days for the bag to contain 16 ounces of food.The bag weighed 56 ounces before it was opened. (y-intercept of the function = initial value).It took about 33 days for the bag to be empty. (x-intercept of the function).What is the missing information?The graph of the function is missing, and is given at the end of the answer.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
step by step
solve 3x + 4 = 5x + 28
Answer:
x = -12
Step-by-step explanation:
Step 1: Subtract 5x from both sides.
3x + 4 - 5x = 5x + 28 - 5x
-2x + 4 = 28
Step 2: Subtract 4 from both sides.
-2x + 4 - 4 = 28 - 4
-2x = 24
Divide both sides by -2.
-2x/-2 = 24/-2
x = -12
Answer:
x= -12
Step-by-step explanation:
whats the answer giving brainliest XD
Answer:
C.
Step-by-step explanation:
Keep, change, flip.
Keep the first number, change the division sign to a multiplication sign, and flip the numerator and denominator of the second number.
Answer:
C. 1/2 * 5/4
Step-by-step explanation:
Reciprocals
Somebody plz help me
Answer:
I am sorry thats a lot to type out.
Step-by-step explanation:
I will say that to know if its rational, you have to see if the integer can be written in a fraction (like 0.333, 89/10, -4, 0)
Answer:
Whole numbers: 3, [tex]\sqrt{4}[/tex], [tex]\frac{49}{7}[/tex], zero
Integer but not whole: -100, -34, -4, -[tex]\frac{8}{4}[/tex]
Rational number: 9.23456, [tex]\frac{1}{2}[/tex], [tex]\frac{89}{10}[/tex], 0.333_
Irrational number: [tex]\pi[/tex], 0.456783_, [tex]\sqrt{8}[/tex]
Step-by-step explanation:
Whole number is any number that does not have a decimal and is not negative. [tex]\sqrt{4}[/tex] = 2. [tex]\frac{49}{7}[/tex] = 7. 0 is not negative and does not have a decimal so it is also a whole number.
Integers are any number that does not have a decimal and can be both positive or negative. -[tex]\frac{8}{4}[/tex] = -2.
A rational number can have a decimal but the decimal digits must terminate or the digit must repeat. [tex]\frac{1}{2}[/tex] is 0.5. [tex]\frac{89}{10}[/tex] is 8.9 and 0.333_ repeats the digit 3 so it is rational.
An irrational number can have a decimal and the decimal digits must list on forever or not repeat. [tex]\pi[/tex] is naturally an irrational number as it does not repeat and it spreads on forever. 0.456783_ does not repeat and goes on forever due to the dash at the back. [tex]\sqrt{8}[/tex] is also not rational.
WILL GIVE A BRAINLIEST
1 fourth as a decimal?
1 fourth as a fraction?
1 fourth as a percent?
3 fourths as a decimal?
3 fourths as a fraction?
3 fourths as a percent?
Answer:
1/4=0.25
1/4
1/4=25℅
3/4=0.75
3/4
3/4=75℅
A teacher purchased 20 calculators and 10 measuring
tapes for her class and paid $495. Later, she realized
that she didn't order enough supplies. She placed
another order of 8 calculators and 1 measuring tape
and paid $178.50.
Write a system that can be used to model this situation
Answer:
pog
Step-by-step explanation:
answer the question with an explanation, please
The ratio of Amy's loan repayments to her earnings last year was 7/23
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Amy earned £18400 and her total loan repayments were £5600. Hence:
Ratio of repayments to earnings = £5600 / £18400 = 7/23
The ratio of Amy's loan repayments to her earnings last year was 7/23
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
which of the following represent 4%?
A. 400
B. 40
C. 0.4
D. 0.04
Answer:
D. 0.04
Step-by-step explanation:
Because 400 and 40 are whole numbers. 0.4 is a decimal meaning is 40% and 0.04 is in the hundreds so is 4%
a recent survey determined the iq score of a random selection of residents identify the class midpoints
The class Midpoint =( Lower class limit + Upper class limit )/2
What is class mid points?The “midpoint” (or “class mark”) of each class can be calculated as: Midpoint = Lower class limit + Upper class limit /2 . The “relative frequency” of each class is the proportion of the data that falls in that class.
If we look at the question attached below then
Upper class limit = 69
Lower class limit =50
class midpoints= 50+69/2
class midpoint= 59.5
Hence, the Midpoint =( Lower class limit + Upper class limit )/2
Learn more about mid point here:
https://brainly.com/question/28293974
#SPJ4
What is the solution to the equation 6n+7=55
Answer:
n = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
6n + 7 = 55
Step 2: Solve for n
Subtract 7 on both sides: 6n = 48Divide 6 on both sides: n = 8Step 3: Check
Plug in n into the original equation to verify it's a solution.
Substitute in n: 6(8) + 7 = 55Multiply: 48 + 7 = 55Add: 55 = 55Here we see that 55 does indeed equal 55.
∴ n = 8 is a solution of the equation.
Answer:
n =8 I hope this helped
Solution:
6n +7-7=55-7
I hope this helped
A jeweler has a watch for sale for $75.00. If she charges her customer $7.50 for sales tax, what is the percent of sales tax?
Answer:
10 percent
Step-by-step explanation:
7.5 times 10 = 75.
plez give me brainiest
if y directly with x, and y= -20 when x=3, what is y when x=15?
Step-by-step explanation:
you can ask questions for clarification
3. Based on the data within your schedule and curve, are you using your resources efficiently? Support your answer using the data presented. i used the numbers Combinations Running shoe inserts Hiking boot inserts
A 0 10
B 3 8
C 6 6
D 9 4
E 12 2
F 15 0
please help brainlyistttt
3. No, I am not using my resources very efficiently. This is because when we need to make more hiking boots you have to make fewer running shoes.
4. I would recommend for them to focus on the hiking boots more because they use less material to make them.
hope this is correct c:
Yes, my resources are being used efficiently if I choose point D, as then I will be making equal amounts of product (1 to 1 ratio).
What is a statistics?
'Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.'
According to the given problem,
This is the most efficient point by far compared to the others, because the two axes are the closest together out of all of the 7 points.
I would recommend that the Shoe Hut focus on both of them, as they have a perfect 1 to 1 ratio.
However, if needed, it is possible to allocate all production power towards running shoe insoles at a 15 to 0 ratio compared to hiking shoe insoles at10 to 0.
Hence, we concluded that, It would be better for the shoe hut to focus on running shoe insoles because they are easier to produce and there is less production of cost.
.Learn more about statistics here: https://brainly.com/question/17267403
#SPJ2
increase 300 by 12%.
Answer:
300, percentage increased by 12% (percent) of its value = 336
Step-by-step explanation:
Change the fraction to an equivalent fraction using multiplication.
\(\frac{5}{7}=\frac{?}{21}\)
Answer:
[tex]\frac{5}{7\\}[/tex] * [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{21}[/tex]
Step-by-step explanation:
To get an equivalent fraction, we multiply by a fraction that is equal to one. The purpose is to alter the denominator of the fraction. To get from a denominator of 7 to 21 we multiply by 3. Therefore we will multiply 5/7 by 3/3 to get the new equivalent fraction with a denominator of 21.
Answer:
a0 - 15
Step-by-step explanation:
What will the date be in 2 months and 3 weeks? current date: December 13, 2020.
Answer: March 6th, 2021
Today everything at a store is on sale the store offers a 20% discount the regular price of the t shirt is 10 dollars what price is the discount if the regular price of an item is x dollars what is the equation
Answer:
[tex]P= x-0.2x[/tex]
Step-by-step explanation:
Step one:
given
Everything at a store is on sale the store offers a 20% discount
The regular price of the t-shirt is $10
Required
The price of an item that cost $x
Step two:
the cost of the discount will be
= 20/100*x
= 0.2x
let the new price be P
[tex]P= x-0.2x[/tex]
12 - 3a for a=3. if a=3, 12 - 3a= ?
Answer:
3
Step-by-step explanation:
if a=3 then 12-3a = 12-9 = 3
what is the result of converting 60 ounces to pounds remember there are 16 ounces in a pound brainly
The 60 ounces equals 3.75 pounds.
We are given in question the relation between pound and ounce. So, using that to find out the result of converting 60 ounces to pound. We will simply divide the given number of ounces by number of ounces in a pound.
Representing the given relation in equation form -
16 ounces = 1 pound
Thus, 1 ounce = [tex]\frac{1}{16}[/tex] pounds
Rewriting the equation for 60 ounces
So, number of pounds in 60 ounces will be = [tex]\frac{1*60}{16}[/tex]
Performing multiplication and division to find the number of pounds in 60 ounces to
Number of pounds in 60 ounces = 3.75
Thus, the result of converting 60 ounces to pounds is 3.75 pounds.
Learn more about ounce to pound conversion -
https://brainly.com/question/16306917
#SPJ4
During the first week of school Andrew purchased two pounds of Jellies and two pounds of Bonbons for $38. The second week of school he purchased two pounds of Jellies and four pounds of Chocolates for $74 and the third week he purchased two pounds of Jellies, two pounds of Bonbons and one pound of Chocolates for $53. What is the cost of one pound of Chocolates?
Answer:
j = $7
b = $12
c = $15
Step-by-step explanation:
Let
j = cost of one pound of jelly
b = cost of one pound of Bonbon
c = cost of one pound of chocolate
First week:
two pounds of Jellies and two pounds of Bonbons for $38.
2j + 2b = 38
Second week:
two pounds of Jellies and four pounds of Chocolates for $74
2j + 4c = 74
Third week:
two pounds of Jellies, two pounds of Bonbons and one pound of Chocolates for $53.
2j + 2b + c = 53
Recall,
2j + 2b = 38
So,
38 + c = 53
c = 53 - 38
= 15
c = $15
Substitute c = 15 into
2j + 4c = 74
2j + 4(15) = 74
2j + 60 = 74
2j = 74 - 60
2j = 14
j = 14/2
= 7
j = $7
Substitute j = 7 into
2j + 2b = 38
2(7) + 2b = 38
14 + 2b = 38
2b = 38 - 14
2b = 24
b = 24/2
= 12
b = $12
Which expression represents the volume, in cubic
units, of the composite figure?
O (8)(6)6) + (8)(6)(4)
O (8)(6)(10) + (8)(6)(4)
O (8X6)\4)-(ex6)X6)
O (8X6)(4) –eX6)10)
Given:
The composite figure.
To find:
The volume of the given composite figure.
Solution:
Given composite figure contains a cuboid and a pyramid.
Length, breadth and height of the cuboid are 8, 6 and 4 respectively.
Volume of a cuboid is
[tex]V_1=length\times breadth\times height[/tex]
[tex]V_1=(8)(6)(4)[/tex]
Length and breadth of the pyramid is same as the cuboid, i.e., 8 and 6 respectively.
Height of pyramid = 10 - 4 = 6
Volume of a pyramid is
[tex]V_2=\dfrac{1}{3}\times length\times breadth\times height[/tex]
[tex]V_2=(\dfrac{1}{3})(8)(6)(6)[/tex]
The volume of composite figure is
[tex]V=V_1+V_2[/tex]
[tex]V=(8)(6)(4)+(\dfrac{1}{3})(8)(6)(6)[/tex]
It can be written as
[tex]V=(\dfrac{1}{3})(8)(6)(6)+(8)(6)(4)[/tex]
Therefore, the correct option is A.
PLEASE LOOKS AT PHOTO it’s due tonight i’m struggling badly :(
Answer:
y = 6.32
Step-by-step explanation:
7^2-3^2= 40
hope it helped
Amir solved the following equation. describe the first mistake he made.
2x-2=14
-2 -2
2x =12
2. 2
X=6
Answer:
he faked too much
Step-by-step explanation:
An environmentalist tracks the total number of trees y in a park after x years of a planting program. The line of best fit for the data is represented by the equation y = 4x + 15. What is the percent change in the total number of trees from x = 3 to x = 6? Round your answer to the nearest percent.
Answer:
44.4%
Step-by-step explanation:
Given that:
Equation of best fit : y = 4x + 15
Where, y = number of trees x years after a planting program
When x = 3
y = 4(3) + 15 = 12 + 15 = 27 trees
When x = 6
y = 4(6) + 15 = 24 + 15 = 39 trees
Percentage change in total number of trees:
((39 - 27) / 27) * 100%
(12 / 27) * 100%
0.44444 * 100%
= 44.4%
HELP PLEASE ILL GIVE 27 POINTS
120% of x is 96. What is x?
Answer:
Step-by-step explanation:
You can do this using a small equation.
120% x = 96 Change 120% to a decimal
120/100 * x = 96 Multiply by 100
120x = 96 * 100
120x = 9600 Divide by 120
x = 9600/120
x = 80
Look what you got. 20% more than 80 is 96. x is smaller than 96.
If you take 20/100 * 80 = 16
if you add 16 to 80, you get 96
Answer:
x = 80
Step-by-step explanation:
120 % of x = 96
or, 120/ 100 × x = 96 change percentage to 100 and devide
or, 6 / 5 × x = 96
or, 6x / 5 =96. multiply 6 and x
or, 6x = 96 × 5. change devide sign to multiply
or, 6x = 480. multiply
or, x = 480 / 6. change multiply sign to devide
therefore, x = 80
hope this answer will help you.
have a great time
Emily wins 22000$. She has to pay 10% for charity and then she decides to buy a car for 10800$. She divides the rest of them between her son and daughter in the ratio 1:4. How much does her daughter get.
Answer:
$7 200
Step-by-step explanation:
Amount of money paid for charity = [tex]\frac{10}{100}[/tex] × $22 000
= $2 200
Remaining money left for children = $22 000 - $2 200 - $10 800
= $9000
Let the amount of money her son receives be x and the amount her daughter gets be 4x.
Son's $ + Daughter's $ = $9000
x + 4x = 9000
5x = 9000
Amount of money her daughter gets (4x) = [tex]\frac{4}{5}[/tex] × 9000
= $7 200
The bill for the repair of a computer was $179. The cost of parts was $44, and labor charge was $45 per hour. How many hours did it take to repair the computer?
Step-by-step explanation:
44 + 45h = 179
45h = 179 - 44
45h = 135
h = 135/45
h = 3 It took 3h to repair
I hope that help's
Find the measure of the missing angle
Answer:
33
Step-by-step explanation:
90-57 = 33
Answer:
33 degrees
Step-by-step explanation:
its a right triangle which is 90 degrees so if you just subtract 90-57 you'll get your answer which is 33.
9. Which of the following vary inversely with each other?
(a) speed and distance covered.
(b) distance covered and taxi fare.
(c) distance travelled and time taken.
(d) speed and time taken.
8th class maths . please explain your answer
Answer:
speed and distance covered
Step-by-step explanation:
when the distance is a constant, the time is related inversely.
Easy math problems help!!!!
Answer:
x = ±7
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
[tex]x^2+24^2=25^2[/tex]
[tex]x^2+576=625[/tex]
[tex]x^2=49[/tex]
x = ±7
Answer:
x = ±7
Step-by-step explanation:
i did this before