Is the statement true or false? If false, give a counterexample.
For all real numbers a, b and c, a(b + c) = ab + bc.
A. true
B. false; a(b + c) = ab − ac
C. false; if a = b = c = 1, then 1(1 + 1) ≠ 1(1) + 1(1)
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Answer:
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Step-by-step explanation:
A is false, because the a is being distributed/ being multiplied to all terms inside the parenthesis, and not the term b.
B is also false. There is no indicated negative signs.
C is also false because 1(1 + 1) is EQUAL to 1(1) + 1(1)
D is true.
The weight, y, in pounds, of kittens was tracked for the first 8 weeks after birth where t represents the number of weeks after birth. The linear model representing this relationship is ŷ = 1.7 + 1.48t. Statler wanted to predict the weight of a kitten at 10 weeks. What is this an example of, and is this method a best practice for prediction? Explain your reasoning.
Answer:
Step-by-step explanation:
The mentioned relationship for the weight, in pounds, of the kitten with respect to time, in weeks, is
[tex]\hat y =1.7 +1.48t[/tex]
Weight of the kitten after 10 weeks
[tex]\hat y =1.7 +1.48\times 10[/tex]
[tex]\hat y =16.5[/tex] pounds
This modeled equation is based on the observation of the early age of a kitten where the kitten is in its growth period, but in the early stage the growth rate in the weight of the kitten was the same but the growth of any living beings continues till the adult stage. So, after some time, in real life situation, this weekly change in weight will become zero, So, this model is not suitable to measure the weight of the kitten over the larger time period.
Here, t= 10 weeks is nearby the observed time period, so the linearly modeled equation can be used to predict the weight.
Hence, the weight of the kitten after 10 weeks is 16.5 pounds.
)) Stefan estimates the income and expenses for renting
a phone accessory store in the mall. He enters the
amounts in the table shown. Should Stefan rent a
phone accessory store? Explain.
Estimated Income and Expenses
Type Amount Frequency
Sales
$950 Each week
Services
$2,875 Each month
Rent
-54,500 Each month
Travel
-$7.50 Each day
Merchandise -$1,650 Each month
Answer:
Stefan should rent a phone accessory store
Step-by-step explanation:
The given information are;
The total of the estimated income and expenses are given as follows;
Sales
Type [tex]{}[/tex] Amount [tex]{}[/tex] Frequency
Sales [tex]{}[/tex] $ 950 [tex]{}[/tex] Each week
Services [tex]{}[/tex] $2,875 [tex]{}[/tex] Each month
Rent [tex]{}[/tex] -$4,500 [tex]{}[/tex] Each month
Travel [tex]{}[/tex] -$7.50 [tex]{}[/tex] Each day
Merchandise [tex]{}[/tex] -$1,650 [tex]{}[/tex] Each month
Therefore;
Total sale = 4×950 = $3,800
Total services = $2,875
Total income = $3,800 + $2,875 = $6,675
Total expenses = $4,500 + $7.50×30 + $1,650 = $6,375
Total profit = Total income - Total expenses = $6,675 - $6,375 = $300
Therefore, the net profit = $300.
Therefore, given that Stefan is able to make a net profit from his investment, he should rent a phone accessory store.
if the cost of carpeting a floor is $2.50 per foot how much will it cost to carpet a rectangular floor that is 10 feet by 12 feet
Answer:
300 dollars
Step-by-step explanation:
Multiply 10 feet by 12 feet to get the total number of feet needed
10x12=120 feet
120 times $2.5= $300
The cost to carpet a rectangular floor is $300.
Given that,
The cost of carpeting a floor is $2.50 per foot A rectangular floor that is 10 feet by 12 feetBased on the above information, the calculation is as follows:
[tex]= 10 \times 12 \times \$2.50[/tex]
= $300
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2 5. 8 11 X 2 -4 8 у 14 What is the equation of the given table?
Answer:
8-6+-2
Step-by-step explanation:
When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, start text, space, m, L, end text of chocolate syrup for every 333 ounces of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, start text, space, m, L, end text of chocolate syrup for every 666 ounces of hot water. Which hot cocoa is more chocolatey? Choose 1 answer: Choose 1 answer:
Answer:
45mL hot cocoa is more chocolateyStep-by-step explanation:
When Arjun makes hot cocoa, if he add 20mL of chocolate syrup to 3ounces of water, let us know the equivalent chocolate in one ounces of water.
20mL = 3 ounces
x = 1 ounce
cross multiply
3x = 20
x = 20/3
x = 6.67 mL
This means he must have add 6.67mL of chocolate to 1 ounce of water.
Similarly, if 45mL is added to every 6 ounces
45mL = 6ounces
x = 1 ounce
cross multiply
6x = 45
x = 45/6
x = 7.5mL
This means he must have add 7.5mL of chocolate to 1 ounce of water.
The hot cocoa that is more chocolatey is the one with the highest amount of chocolate in 1 ounce. That is 45mL hot cocoa
Answer:
eli's cocoa is more chocolately. i would show proof (on khan academy), but I just skipped the q. :|
Step-by-step explanation:
Which of the following statements is true?
The number 0 is a natural number.
The number is an integer.
The value π is a rational number.
The number -5 is a real number.
Answer: the number -5 is a real number
Real numbers are both negative and positive numbers. -5 is a negative number. Since real numbers include negative numbers, -5 is the answer.
Hope this helps!
Answer:
the number -5 is a real number
Step-by-step explanation:
what is the answer for −3x−6+(−1)
Answer:
-3x-7
Step-by-step explanation:
Combine like terms
-6+-1 = -6-1 = -7
Hence, it's -3x-7
people wont solve my question i need it ASAP
Answer:
A pig has 10,000 kg mass more than a mass
Step-by-step explanation:
[tex]\frac{2*10^{2}}{2*10^{10}}=\frac{10^{2}}{10^{-2}}\\\\=10^{2}*10^{2}\\\\=10^{2+2}\\\\=10^{4}\\\\=10000[/tex]
2(5x+5) + 9(x-10) + 9-squared
Step-by-step explanation:
We'll use BODMAS to solve this
Open the brackets :
2(5x+5)+9(x-10)+9sq = 10x+10+9x-90+81Then we arrange them accordingly :10x+9x+10-90+81 We then calculate :19x+10-90+81BODMAS :19x+91-90 = 19x+1ANSWER :19x+1A can run 3 miles in 30 minutes. How long will it take
the runner to run 2.5 miles? Use the diagram to explain.
Answer:
It will take her about 25 minutes.
Step-by-step explanation:
30 divided by 3 is ten.
It takes ten minutes to run each miles.
I don't have a diagram, but try drawing a graph with the information.
Buddy downloaded 16 apps in 24 seconds. At this rate, how many apps could he download in one minute? (24 seconds = 2/5 of a minute) (1-1 Unit Rate)
Ben and Ella are filling goodie bags for a party. Each goodie bag needs an eraser, a bubble wand, and a few candy bar bites. Ben filled 25 goodie bags in 20 minutes. Ella filled 27 goodie bags in 24 minutes. Who filled goodie bags at a faster pace?
Answer:
Ben
Step-by-step explanation:
25 goodies = 20 minutes
27 goodies = 24 minutes
Let's use ratio, divide both of them by their minute
25/20 = 20/20
27/24 = 24/24
1.25 goodies = 1 minute
1.12 goodies = 1 minute
1.25 is bigger than 1.12.
Answer:Ben
Step-by-step explanation:
Can someone please help
Answer:
( -1 , 0.5)
Step-by-step explanation:
I need help what is -0.5 _ -0.2
Write 2.08 x 10^2 in standard form.
Answer:
208
Step-by-step explanation:
If you multiply 2.08 by ten to the second power (100) Then you get 208
Scientific notations are the way through which a very small or a very large number can be written in shorthand. The given expression can be written in the standard form as 208.
What are Scientific notations?Scientific notations are the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5e+12.
The given expression can be written in the form of an expression as shown below.
2.08 x 10²
= 2.08 × 100
= 208
Hence, the given expression can be written in the standard form as 208.
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EASY You make a salad to share with friends. Your sister eats 1/3 of it before your friends arrive. You want to divide the leftover salad evenly among six friends. Which expression describes the situation? *
A. 6 ÷ 2/3
B .2/3 ÷ 6
Answer:
b
Step-by-step explanation:
Answer:
I would have to say B, because 2/3 divided by 6 = 1/9. Plus, I think this would make sense considering we're dealing with a fraction problem. I hope this will help m8! ;)
Step-by-step explanation:
EASY MATH QUESTION PLEASE I NEED HELP!
Answer:
x=8/3
Step by step
determine the defined range
remove parentheses
move the terms
collect like terms and calculate
divide both sides
Kay needs to fix part of her fence.She can buy 6 feet of fencing for $32.00 at a fencing store or 10 feet of fencing for $52.50 at a home store.She visits another store that sells 8 feet of fencing for a certain cost.The cost per foot is between that at the fencing store and the home store.How much the store charge for 8 feet of fencing?
Answer
42.66
Step-by-step explanation:
each foot is 5.33 so 5.33 x 8 is 42.66
help TWT ;-;-;-;-;-;-;
Answer:1
Step-by-step explanation:
Answer:
the answer is 1
Step-by-step explanation:
Joe and Carmen are partners in a business. Joe makes $2.00 profit for every $5.00 profit that Carmen makes. If Carmen makes $20 on the first item they sell, how much profit will Joe make?
what is $3 as a decimal
Answer:
3.00
Step-by-step explanation:
Answer:
3.00
Step-by-step explanation:
Since three is a whole number, that means it would be in front of the decimal.
What is 78x6 =
please let me know if you have the asers
Answer:
468
Step-by-step explanation:
and this is how you spell answers
The value of 78 × 6 is 468
What is multiplication?Multiplication is the process of calculating the product of two or more numbers. The result of multiplication is called product.
If a × b = c , this means that a and b are the factors and c is the product.
For example if each student has 5 apples and there are 100 students in the camp, the total number of apples in the camp is
100 × 5 = 500 mangoes.
Similarly, 78 × 6
= 70 × 6 + 8 × 6
= 420 + 48
= 468
Therefore the product of 78 and 6 is 468
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What single decimal multiplier would you use to decrease by 6% followed by a 19% increase?
Answer: 13% increase?
Step-by-step explanation: 19-6=13 which means it would be 1.13 the original amount?
Answer:
1.13
Step-by-step explanation:
A 6% decrease would be 0.94 and a 19% increase after that would be 1.13
Jen bought 5 CD's for $57.50. What was the unit price?
Answer:
$11.50 per CD
Step-by-step explanation: u have to make 5 into 1, thats divinding. Then u divide $57.50 by 5, there's your unit price :)
-5n-3(n+2)=18
what is n?
Please show all work
Answer:
n=-3
Step-by-step explanation:
Look at the attachment below
Hope this helps (:
· Evaluate f(2a + b), where f(x) = 4x2 – 3x.
Answer:
2af+bf = 2af+bf
Step-by-step explanation
f(x) = 4x2 – 3x. = x(4x−3)
Convert y = x2 - 4x + 1 to vertex form by completing the square.
O y= (- 1)2 + 4
O y= (1 - 2)2 +5
O y= (x - 2)2 – 3
O y = (x - 4) + 1
Answer:
vertex: (-2, -3)
Step-by-step explanation:
y = x2 + 4x + 1
y = x2 + 4x + 22 + 1 - 22
y = (x + 2)2 + 1 - 4
y = (x + 2)2 - 3 in y = (x - h)2 + k, (h, k) is the vertex.
Answer:
y = (x - 2)² - 3
Step-by-step explanation:
Given
y = x² - 4x + 1
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 4x
y = x² + 2(- 2)x + 4 - 4 + 1
= (x - 2)² - 3
what is the equation of a line parallel to y=3x-2 and goes through the point (-1,1)
Answer:
y = 3 x − 29
Step-by-step explanation:
First, let's find the slope of the line
y = 3 x + 2
As the equation is already in slope-intercept form
y = m x + c
Slope = 3
Let a point ( x , y ) be on the new line.
By finding the slope again,
y − 1 x − 10 = 3
y − 1 = 3 ( x − 10 )
y − 1 = 3 x − 30
Which can then be converted to different forms:
Standard form:
3 x − y = 29
Equation form:
3 x − y−29 = 0
Slope-intercept form:
y = 3 x − 29
graph{3x-y=29 [-32.3, 47.7, -34.1, 5.9]}
for how many tickets is the cost the same for club members and non-members?
Answer:
The cost will be the same for 2 club members as for 1 non-member.
Step-by-step explanation:
There will never be a number of tickets where the price for a given number of club members is the same for the same number of non-members.
However, if two club members purchase tickets, their cost is 2($3) = $6.
If one non-member purchases a ticket, the cost is 1($6) = $6.