To find the approximate side length of a square game board with an area of 151 in², take the square root of 151.
Explanation:To find the approximate side length of a square game board with an area of 151 in2, we can use the formula for the area of a square, which is length x width. Since all sides of a square are equal, we can represent the side length as 's'. So, s x s = 151. To find the side length, we can take the square root of 151, which is approximately 12.29 inches. Therefore, the approximate side length of the square game board is 12.29 inches.
Factor the expression.
d2 + 10d + 9
Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%? $117 $680 $760 $820
Answer:
The correct option is B) $680.
Step-by-step explanation:
Consider the provided information.
Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest.
Let she invested x amount with 8% interest rate.
Total amount she invested was $1,500, thus the amount she invested with 6% interest rate was 1500-x.
Total interest she earn was $106.40
Write this information into mathematical form.
[tex]x\times \frac{8}{100}+\frac{6}{100}(1500-x)=106.40[/tex]
[tex]x\times 0.08+0.06(1500-x)=106.40[/tex]
[tex]0.08x+90-0.06x=106.40[/tex]
[tex]0.08x-0.06x=106.40-90[/tex]
[tex]0.02x=16.4[/tex]
[tex]x=820[/tex]
Hence, she invested $820 with 8% interest rate.
The amount she invested with 6% interest rate was 1500-x.
Substitute the value of x in above.
1500-820=680
Hence, she invested $680 with 6% interest rate.
The correct option is B) $680.
Simplify 1/3 (9a+b)-1/2 (4a+2b)
Find the midpoint of the segment between the points (15,3) and (2,-14)
The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 6in. width is 5/6 and the height is 1 2/6 the cube side is 1/6
The number of cubes should be 1.440.
The calculation is as follows:Calculate the volume of each shape is as follows:
Volume of rectangle = [tex]6 \times 5\div 6 \times 1\ 2\div 6 = 6\ 2\div 3[/tex] cubic inches.
And,
Volume of cube =[tex] 1\div6 \times 1\div6 \times 1\div6 = 1\div216[/tex] cubic inch.
Now
divide the volume of the rectangle by the volume of the cube:
So,
[tex]= (6\ 2\div 3) \div (1\div 216)[/tex]
= 1.440
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given (x-1)^2=50, select the values of x
A. x = -49
B. x = 51
C. x = 1+5√2
D. x = 1-5√2
Value of x is 1 + 5√2
Given that;
(x - 1)² = 50
Find:
Value of x
Computation:
(x - 1)² = 50
By taking square root both side
x - 1 = √50
x - 1 = 5√2
x = 5√2 + 1
x = 1 + 5√2
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*PLEASE ANSWER*
The function y=2x+4 has a domain of 2,3,5,7, and 8...
That number is not in the range of the function?
A. 8
B. 12
C. 18
D. 20
Simplify 3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28.
a.2 square root of 12
b.2 square root of 2
c.6 square root of 5 end root minus 4 square root of 7
d. 6 square root of 10 end root minus 4 square root of 14
Answer: Simplifying the square roots and adding the similar square roots the answer is option c. 6 square root of 5 end root minus 4 square root of 7
Solution:
3√5-2√7+√45-√28
45=9*5 and 28=4*7. Replacing in the equation above:
3√5-2√7+√(9*5)-√(4*7)
Using √(a*b)=√a√b
3√5-2√7+√9√5-√4√7
√9=3 and √4=2. Replacing in the equation above:
3√5-2√7+3√5-2√7
Adding similar square roots:
(3+3)√5+(-2-2)√7=
(6)√5+(-4)√7=
6√5-4√7
A catering service offers 8 appetizers, 11 main courses, and 4 desserts. A banquet chairperson is to select 5 appetizers, 9 main courses, and 2 desserts for a banquet. In how many ways can this be done?
What is the distance from (−3, 1) to (−1, 5)? Round your answer to the nearest hundredth.
A.3.60
B. 4.12
C.4.47
D.5.66
pls
Answer:
c 4.47
Step-by-step explanation:
got it right on my test
The distance from (−3, 1) to (−1, 5) is 4.47
What is slope of line?
Slope of line is defined as the angle of line.
The distance between two points is found by
[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]
[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]
[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]
[tex]d=\sqrt{(4+16)}[/tex]
[tex]d=\sqrt{(20)}[/tex]
d = 4.472135955
Rounding to the nearest hundredth
d = 4.47
Hence, the distance from (−3, 1) to (−1, 5) is 4.47
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PLEASE HELP I'M BEING TIMED!!!!
if the diameter of a youth softball is 3.5 inches and the diameter of an adult softball is 3.8 inches, what is the approximate difference in their volumes? Use 3.14 for pi . Round to the nearest tenth of a cubic inch.
Question: Rationalize the denominator
Joyce saved $90 on an item that was 75 % % off What was the original price?
How does the area of triangle RST compare to the area of triangle LMN? The area of △RST is 2 square units less than the area of △LMN. The area of △RST is equal to the area of △LMN. The area of △RST is 2 square units greater than the area of △LMN. The area of △RST is 4 square units greater than the area of △LMN.
The answer would be B
The profit on the sale of a small bag of popcorn is $1, while the profit on the sale of a medium bag of popcorn is $2. The Glee Club expects to sell fewer than 100 total bags of popcorn, but they hope to make more than $100 in profit. The system that represents this is s+m<100 and s+2m>100. The graph of the boundary lines is shown below. Which regions should be shaded (to form the solution)?
Which conversions from scientific notation to standard notation are true? Check all that apply.
The correct conversion from scientific notation to standard notation are:
b) [tex]8.05\times 10^5[/tex]
e) [tex]7.09\times 10^{-6}[/tex]
Step-by-step explanation:We know that when we have a power of 10 as positive then the decimal is shifted to the right and if the power of 10 is negative then we shift the decimal to the left.
a)
[tex]1.71\times 10^3[/tex]
As the power of 10 is positive hence we shift the decimal to the right 3 places.
Hence, the conversion is:
[tex]1.71\times 10^3=1710[/tex]
b)
[tex]8.05\times 10^5[/tex]
Again the power of 10 is positive and hence we will shift the decimal 5 places to the right and the conversion is done as follows:
[tex]8.05\times 10^5=805000[/tex]
c)
[tex]2.4\times 10^4[/tex]
Since, the power of 10 is positive and hence we will shift the decimal 4 places to the right and we convert the number to standard notation as:
[tex]2.4\times 10^4=24000[/tex]
d)
[tex]8.25\times 10^{-3}[/tex]
Since, the power of 10 is negative and hence we will shift the decimal 3 places to the left and we convert the number to standard notation as:
[tex]8.25\times 10^{-3}=0.00825[/tex]
e)
[tex]7.09\times 10^{-6}[/tex]
Since, the power of 10 is negative and hence we will shift the decimal 8 places to the left.
Hence, we convert our number to standard notation:
[tex]7.09\times 10^{-8}=0.00000709[/tex]
It is accurate to convert scientific notation to standard notation in the following ways:
B [tex]8.05x10^5=805,000[/tex]
C [tex]2.4x10^4= -24,000[/tex]
E [tex]7.09x10^-^6=0.0000070[/tex]
To solve this problemFirstly, Let's evaluate each conversion one by one:
[tex]1.71x 10^3=0.00171[/tex]
This conversion is not true. The correct value of[tex]1.71x 10^3[/tex] is 1710.
[tex]8.05x10^5=805,000[/tex]
This conversion is true.
[tex]2.4x10^4= -24,000[/tex]
This conversion is true.
[tex]8.25x10^-^3=-8,250[/tex]
This conversion is not true. The correct value of [tex]8.25x 10^-^3[/tex] is 0.00825.
[tex]7.09x10^-^6=0.0000070[/tex]
This conversion is true.
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FIRST CORRECT ANSWER GETS BRAINLIEST
The equation A=p(1+r)^t can be used to calculate compound interest on a savings account. A = future balance, p = current balance, r = rate of interest, and t = time in years. If you deposit $2,000 at 10% each year, how much money will be in your account in 10 years
Using the formula for compound interest, if you deposit $2,000 at 10% each year, the future balance in your account after 10 years would be approximately $5,187.12. This is due to the effect of compounding where the interest is calculated on both the principal and the accumulated interest.
Explanation:The subject of this question is compound interest which is a Mathematics topic typically covered in High School. The formula A=p(1+r)^t is used to calculate the future balance in your savings account considering compound interest. Here, 'A' represents the future balance, 'p' is the current principle or balance, 'r' is the rate of interest, and 't' is time in years.
To answer your specific question: If you deposit $2,000 at a 10% rate each year, how much money will be in your account in 10 years? Let's plug the numbers into the formula. In this case, p=$2000, r=0.10 (as 10% equals 0.10 in decimal), and t=10 years.
So, A = 2000*(1 + 0.10)^10. Solving this, the future balance in your account after 10 years would be approximately $5,187.12. This is significantly more than simple interest ($100 × 0.05 × 3 = $15 in your example) due to the effect of compounding, as the interest is calculated on the principal plus the accumulated interest.
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Brian is selling cookies at a bake sale. He earns $2.75 for each bag of cookies he sells. Write an equation to represent this scenario.
Find the Unknown that you're looking for. What is happening to that variable?
Explain the method for determining the correct degree and classification of a polynomial?
I think it is Monomials, Binomials and Trinomials
am i correct?
Help I don't know this answer
11 POINTS GUYS PLZ
Answer 12 and 14
12) 10.77 + 2.09 + 0.75 = 13.61
13.61 x 1.07 = $14.56
total amount = $14.56
14) C shows the possible combinations
Determine the theoretical probability of rolling a number larger than 3 on a standard 6-sided cube. 1/2, 1/6, 1/4, 1/3
Answer:
Option A is correct.
Step-by-step explanation:
Given: A 6-sided cube is rolled.
To find: Probability of getting a number greater than 3.
Total number of outcome when a 6-sided cube is rolled = 6
Favorable outcome = { 4 , 5 6 }
Number of favorable outcome = 3
Theoretical Probability is a probability based on reasoning written as a ratio of the number of favorable outcomes to the number of possible outcomes.
[tex]Probability=\frac{Number\:of\:favorable\:outcome}{Number\:of\:Total\:outcome}[/tex]
[tex]Probability=\frac{3}{6}=\frac{1}{2}[/tex]
Therefore, Option A is correct.
With _______ insurance, the insured agrees to pay a specific premium each year until death. half life
With whole life insurance, the insured agrees to pay a specific premium each year until death.
Whole life insurance is a plan that requires you to pay premiums for you entire life, thus it is known as "whole life."
The profit function for a new product is given by p(x) = -4x^2+28x-40, where x is the number sold in thousands. How many items must be sold for the company to break even?
Final answer:
The company must sell either 2,000 or 5,000 items to break even, as determined by setting the profit function to zero and factoring the resulting quadratic equation.
Explanation:
To determine how many items must be sold for the company to break even, we need to set the profit function p(x) equal to zero and solve for x. In this case, the profit function is given by p(x) = -4x^2 + 28x - 40. Setting this to zero, we have:
-4x^2 + 28x - 40 = 0
Now, we need to solve this quadratic equation for x. To do this, we can factor the equation, use the quadratic formula, or complete the square. Since the coefficients are manageable, we'll try to factor first:
-4(x^2 - 7x + 10) = 0
Let's look for two numbers that multiply to 10 and add up to 7, which are 5 and 2. We can now factor further:
-4(x - 5)(x - 2) = 0
From the factored form, we get two potential solutions for x when the profit is zero:
x = 5
x = 2
Since x represents the number of items sold in thousands, the company must sell either 2,000 or 5,000 items to break even.
What is the next value 4 D 7 G 10 J 13
One lap around a dirt track is 1/3 mile. It takes Bryce 1/9 hour to ride one lap. What is Bryce's unit rate, in miles, around the track?
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
800 grams =
pounds
700 grams =
pounds
The weight of each tire in pounds is approximately:
Full steel bead tire: 1.76 pounds.
Lighter wheel: 1.54 pounds.
Given that the weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams.
We need to convert the weights into pound.
To convert the weight of each tire from grams to pounds, we'll use the conversion factor that there are 453.592 grams in one pound.
Weight of a full steel bead tire in pounds:
800 grams x (1 pound / 453.592 grams) ≈ 1.76 pounds
Weight of a lighter wheel in pounds:
700 grams x (1 pound / 453.592 grams) ≈ 1.54 pounds
Rounded to 2 decimal places:
Weight of a full steel bead tire = 1.76 pounds
Weight of a lighter wheel = 1.54 pounds
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The price of a share of stock started the day at $37. During the day it went down $3, up $1, down $7 and up $4. What was the price of a share at the end of the day
A taxi driver makes $24.50 in an hour, but uses $6.75 worth of gas during that time. What will the driver's total earnings for the hour be, after paying for gas?