given that a=2 and b=3, what is (ab)^2
Answers
Answer:
(ab)² = 36
Step-by-step explanation:
Plug in 2 for a and 3 for b:
(2·3)²
Multiply 2 and 3:
6²
Square the number:
36
(a x b)²
We know that a is 2 and that b is 3, so we substitute these into the expression:
(2 x 3)²
Then because of the Order of Operations we multiply INSIDE the brackets first:
(6)²
And when we square (²) a number we are simply multiplying it by itself:
(6)² = 6 x 6
So our final answer is:
6 x 6 = 36
Related Questions
The two lines below are parallel. If the slope of the red line is 3, what is the slope of the green line?
Answers
3 problems for 1 final answer. fairly easy 8th grade math.
Answers
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
Learn more about algebraic expression:
https://brainly.com/question/12518138
#SPJ1
Find the measure of the missing angle
Answers
Answer:
a = 115°
Step-by-step explanation:
Two angles are supplementary angles because they make a straight line.
The sum of two angles is equal to 180° then to find the measure of the missing angle we simply subtract 65 from 180:
180 - 65 = 115
Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
Answers
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
Learn more about Probability at:
https://brainly.com/question/24756209
#SPJ1
At a family reunion, each of Shamar's aunts and uncles is getting photographed once. The aunts are taking
pictures in groups of 5 and the uncles are taking pictures in groups of 10. If Shamar has the same total number
of aunts and uncles, what is the minimum number of aunts that Shamar must have?
Answers
The minimum number of aunts that Shamar must have based on the information provided is 10.
What are the possible number of uncles and aunts?It is known that uncles will take a photograph in groups of 10, while aunts will take a photograph in groups of 5. Based on this, the possible number for each are:
Uncles: 10, 20, 30, 40, 50
Aunts: 5, 10, 15, 20, 25
How to find the minimum number of relatives?In this case, the minimum number is the LCM or Least Common Multiple and based on the previous list, this number is 10.
Learn more about the Least Common Multiple in https://brainly.com/question/30060162
#SPJ1
Kelly simplified this power of a product.
(7w–9)–3
1. 7–3∙(w–9)–3
2. 1
343
w27
Use Kelly’s steps to simplify this expression.
(5w7)2
What is the simplified power of the product?
5w9
10w14
25w9
25w14
Answers
The solution is, 25w^14, is the simplified power of the product.
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that, expression.
(5w^7)^2
=5^2. (w^7)^2
=25.w^14
Hence, The solution is, 25w^14, is the simplified power of the product.
To learn more on exponent number click:
brainly.com/question/19467739
#SPJ6
Determine the simple interest when: principal: $9,500 interest rate: 5.8%, time: 30 year
Answers
Answer:
9500 times 5.8% times 30 years is $16,530
Step-by-step explanation:
Hope This Helps
can somebody help me please and thank you
Answers
1. 12/40 or 30% chance
2. 60
Explanation: 1. Not gonna lie i searched it up
2. x/200 times 12/40 = 2400/40
8 (b - 3)
what is the answer
Answers
Answer: =8b-24
Step-by-step explanation: hope this helps!
The answer would be 8B-24
for a special fully discrete 20-year term insurance on (30): the death benefit is 1,000 during the first ten years and 2,000 during the next ten years.
Answers
The cost of the 20-year term insurance will be based on age, health, smoking, and other factors to determine the premium.
The cost of a special fully discrete 20-year term insurance on a 30-year-old would depend on a range of factors, including the insured's age, health, smoking status, and lifestyle. These factors would be used to calculate the risk of death during the 20-year term. The death benefit of 1,000 during the first ten years and 2,000 during the next ten years would also be taken into account when calculating the cost of the policy. Depending on the risk of death and the death benefits, the premium could vary significantly. For example, a 30-year-old in good health with no smoking history could pay less for the policy than a 30-year-old with a pre-existing condition and a smoking history. The premium could also be higher for individuals with riskier lifestyles. Ultimately, the cost of the 20-year term insurance will depend on the risk of death and the death benefit offered by the policy.
Learn more about terms here
https://brainly.com/question/26099230
#SPJ4
Use the information to answer the question. The table shows the amount of lemon juice and water that 4 students mix. Student Luca Kal Jenna Micah Lemon Juice Water (fluid ounces) (fluid ounces) 2 6 4 6 10 8 9 B Which two students mix the same ratio of lemon juice to water? Choose two students to show the answer.
Answers
The two students that mix the same ratio of juice to water is given as follows:
A. Luca.
D. Micah.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
Hence the ratio of juice to water for each person is given as follows:
Luca: 2/6 = 1/3.Kal: 6/10 = 3/5.Jenna: 4/8 = 1/2.Micah: 3/9 = 1/3.Hence Luca and Micah used the same ratio, meaning that options A and D are correct.
More can be learned about ratios at brainly.com/question/24372153
#SPJ1
A candy bar that originally sold for $.60 undergoes a 3% price increase each year.
Answers
Both calculations from part (1) and part (2) yield the same result of $0.86 for the new cost of the candy bar after 11 years.
Part 1 of 2:
The new cost of the candy bar after 11 years can be calculated by applying a 3% price increase each year to the original cost of $0.60.
To calculate the new cost after 11 years, we can use the formula:
New Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
New Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the new cost of the candy bar after 11 years is $0.86.
Part 2 of 2:
If the cost of the candy bar increased by 3% of the original cost each year for 11 years, we can calculate the final cost by multiplying the original cost by (1 + 3%) for each year.
Using the formula:
Final Cost = Original Cost * (1 + Percentage Increase)^Number of Years
Plugging in the values:
Final Cost = $0.60 * (1 + 3%)^11
≈ $0.60 * (1 + 0.03)^11
≈ $0.60 * (1.03)^11
≈ $0.60 * 1.432364654
Rounding to the nearest cent, the final cost would also be $0.86.
For more such questions on cost
https://brainly.com/question/25109150
#SPJ8
Note: The complete question is - What will be the cost of the candy bar after a specific number of years if it originally sold for $.60 and undergoes a 3% price increase each year?
Bean Seed Growth Temp 25 20 15 10 Days S 7 9 If the trend continues, how many days will it take at 10 degrees?
Answers
The needed number of days at 10 degrees is given as follows:
11 days.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:
m = -2/5
m = -0.4.
Hence the time needed for a temperature of 10 degrees is given as follows:
9 + 2 = 11 days.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
Carson wants to solve this system of equations.
y=x^2+5x−6
y=x−1
Use the drop-down menus to complete the explanation of why Carson’s work cannot be used to find the solution of the system of equations.
Answers
Carson's work is correct for solving the equations.
Given that;
Carson wants to solve this system of equations.
y = x² + 5x − 6
y = x − 1
Now, We can solve first equation as;
y = x² + 5x - 6
y = x² + 5x - 6 = 0
⇒ x = - 5 ± √5² - 4×1×- 6 / 2
⇒ x = - 5 ± √25 + 24 / 2
⇒ x = - 5 ± √49 / 2
⇒ x = - 5 ± 7/2
⇒ x = - 5 + 7 / 2
⇒ x = 2/2
⇒ x = 1
⇒ x = - 5 - 7 / 2
⇒ x = - 12 / 2
⇒ x = - 6
Hence, From (ii);
⇒ y = x - 1
At x = 1;
y = 1 - 1
y = 0
At x = - 6;
y = - 6 - 1
y = - 7
Hence, Carson's work is correct.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Only 40% of people between the ages of 18 and 24 read a daily
newspaper. Write the percent as a fraction in simplest form.
Answers
Answer:
2/5
Step-by-step explanation:
40% = 40/100 = 4/10 = 2/5
Answer:
2/5
Step-by-step explanation:
40%/100% =2/5
you just take the 40% and divide with one hundred %
Assume that the amount of water that Mario uses for irrigation at his vineyard in inversely proportional to the amount of rainfall. if he uses 40,000 gallons during a month in which there is 6" of rain, how much water would be used in a month that has 7" of rain? (round to nearest integer as needed)
Answers
34,286 gallons
Explanations:Let the amount of water that Mario uses for irrigation be A
Let the amount of rainfall be "r"
If the amount of water that Mario uses for irrigation at his vineyard in inversely proportional to the amount of rainfall, this is expressed as:
\(\begin{gathered} A\alpha\frac{1}{r} \\ A=\frac{k}{r} \end{gathered}\)If he uses 40,000 gallons during a month in which there is 6" of rain, this means that A = 40,000 and r = 6"
Substitute the given values into the formula:
\(\begin{gathered} 40,000=\frac{k}{6} \\ k=6\times40,000 \\ k=240,000 \end{gathered}\)In order to know how much water would be used in a month that has 7" of rain, this means that;
A = ?, r = 7"
Get the value of "A"
Recall that:
\(\begin{gathered} A=\frac{k}{r} \\ A=\frac{240,000}{7} \\ A=34,285.7 \end{gathered}\)This shows that about 34,286 gallons of water would be used in a month that has 7" of rain.
Mrs. Peters purchased 120 flowers. The total cost was $55.20. After planting all of the flowers, Mrs. Peters decided she needed an additional 18 plants. About how much should she expect to pay total for the additional flowers.
Answers
Answer: 39.13 for 18 plants
Step-by-step explanation:
120/55.20= 2.17 dollars per plant
18*2.17=39.13
Help please!!! Tyyyyy
Answers
Answer:
D) 60 degree
Step-by-step explanation:
Let's connect the remaining diagonal, which forms a triangle containing angle x.
As a property of regular hexagon, all diagonals are equal.
=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.
A company created a new container in the shape of a
triangular prism that will hold sunflower seeds. A three-
dimensional image of the container is shown below, as
well as a two-dimensional image of the base.
6 in.
3.2 in.
2 in.
3.2 in.
1 in.
square inches
1 in.
The container will be made from cardboard. How many
square inches of cardboard are needed to make one
container? Assume there are no overlapping areas.
Answers
The number of square inches of cardboard that are needed to make one
the container is 18.
We have,
The volume of the triangular prism.
= Area of the triangle x height
Now,
Height = 6 in
And,
To find the area of a triangle, we can use Heron's formula.
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.
Let's calculate the area using Heron's formula:
s = (3.2 + 3.2 + 2) / 2 = 4.2
A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))
A = √(4.2 x 1 x 1 x 2.2)
A = √(9.24)
A ≈ 3.04 square inches
Now,
The volume of the triangular prism.
= Area of the triangle x height
= 3.04 x 6
= 18.24 in²
Now,
Area of one cardboard.
= 1² in²
= 1 in²
Now,
The number of square inches of cardboard that are needed to make one
container.
= The volume of the triangular prism / Area of one cardboard
= 18.24 in² / 1 in²
= 18.24
= 18
Therefore,
The number of square inches of cardboard that are needed to make one
the container is 18.
Learn more about Prism here:
https://brainly.com/question/12649592
#SPJ1
Describe the slope of the line
Find the slope
m=??
Answers
Slope formula (y2-y1)/(x2-x1) ride over run (4+3)/(5-2) = answer: 7/3 or 2 1/3
Answer: 2.333333...
Step-by-step explanation:
If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)
samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. the result is120 grams 15% sugar syrup. how many grams of 25% sugar syrup did samantha use?
Answers
Answer:
Final mixture is 120 gm
x = 10% then (120-x) = 25%
.25(120-x) + .1 (x) = .15 (120) solve for x= 10% amount
then 25% amount = 120-x
Step-by-step explanation:
What is qualitative data? Give an example.
Answers
Answer:
it is data that you can see or describe such as he is a boy
Step-by-step explanation:
The ratio table below shows the ratio of cups of blueberries to cups of ice needed to make a smoothie at a local smoothie place.
Answers
When cup of blueberries is 3 , cup of ice is 6
when cup of ice is 10, cup of blueberries is 5 and
when cup of ice is 20, cup of blueberries is 10
What is ratio?A variation is a relation between a set of values of one variable and a set of values of other variables.
let cup of blueberries be x and cup of ice be y
it is discovered that as y increase x also increase
this means x varies directly as y
x= ky
k= x/y
therefore when x = 1 and y= 2
k = 1/2
therefore when x = 3, y= x/k= 3/½= 3×2= 6
when y = 10 , x= ky = 1/2 × 10= 5
When y = 20, x= ky = 1/2×20= 10
Therefore it is deduced that x varies directly as y and x =y/2
learn more about variation from
https://brainly.com/question/6499629
#SPJ1
A recipe for chocolate chip cookies calls for 3 1/3 cups of flour. If you are making 2 1/4 recipes, how many cups of flour are needed.
Answers
Answer:
THIS IS THE ANSWER
Step-by-step explanation:
1 1/2 = 3/2
2 1/3 = 7/3
3/2 * 7/3 = 21/6 = 3 3/5 = 3 1/2 cups
PLEASE MARK ME AS A BRAINLIST!Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answers
Answer:
6.14 inches
Step-by-step explanation:
The one side of the dollar bill is 6.14 inch. The 6.14 inches of the dollar approximates the 156.1 mm. When Malia measures the longer side of a dollar bill from her rule it will be approximately 6.14 inches in length. The ruler normally has inches and cm sides. Very few rulers have mm scales. The most probable scale that malia would have measure is in inches.
Which expressions will produce an answer with the fewest significant figures?A. 12.2 - 4.7B. 22.3 - 9.7C. 23.51 * 56.2D. 3460 - 1790
Answers
Considering all the options
A. 12.2 - 4.7 = 7.5
B. 22.3 - 9.7 = 12.6
C. 23.51 * 56.2 = 1321.262
D. 3460 - 1790 = 1670
From the results above, option A has the fewest significant figures
A shop makes a profit of £2 750 in March
It has an Easter sale and the profit for April is £3 162.50
Work out the profit percentage increase
Answers
The percent increase of the profit is 15%
How to determine the percent increase of the profit?In this question, the figures are given as
Profit in March = £2750
Profit in April = £3162.50
The percentage of the increase of the profit is then calculated using the following equation
Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%
Substitute the known values in the above equation, so, we have the following representation
Increase percentage = (3162.50 - 2750)/2750 * 100%
Evaluate
Increase percentage = 15%
Hence, the increase in percentage is 15%
Read more about percentage at
brainly.com/question/15056889
#SPJ1
Please help me out with this!!!
Answers
Answer:
\(0.455\)
Step-by-step explanation:
Divide the number of round blue blocks in the box from the total number of round blocks in the box. Remember that only the round blocks are in the box.
\(\dfrac{\# \textrm{ of blue blocks}}{\textrm{total }\# \textrm{ of blocks}} = \dfrac{5}{5 + 2 + 4}\)
\(= \dfrac{5}{11}\)
\(\approx 0.455\)
Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answers
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
In November, 26 students at Monarch High School had contracted the flu. Each month, the number of students who have contracted the flu increases by 36%. Write and use an exponential growth function to find the total number of students who have contracted the flu by May.
Answers
Answer: 25.64
Step-by-step explanation:
165 students who have contracted the flu by May.
What is Exponential function?A mathematical function with the formula f(x) = \(a^x\) is an exponential function. where a is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
As, there are 6 months from November to May.
Let the number of months be x.
So, the total is= 26\(( 1 + 36)^x\)
when x= 6
So, total= 26\(( 1 + 36)^6\)
Total = 6.328 x 26
Total = 164.5
Total = 165 people
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ5