simplify the ratio
60 cents: $2
The ratio 60 cents: $2 simplifies to 3:10 after converting dollars to cents and dividing both terms by the greatest common divisor, which is 20.
To simplify the ratio 60 cents: $2, we need to first express both quantities in the same units. Since 1 dollar is equal to 100 cents, $2 is equivalent to 200 cents. Thus, the ratio becomes 60 cents : 200 cents.
Next, we simplify the ratio by dividing both sides by the greatest common divisor. In this case, both 60 and 200 are divisible by 20, which is the greatest common divisor. So we divide both sides by 20:
[tex]\frac{60}{20}[/tex] = 3
[tex]\frac{200}{20}[/tex] = 10
Therefore, the simplified ratio is 3:10.
Solve (x + 2 < 5) (x - 7 > -6).
Please help
!!!!!!!!!!!!!!!!!!!!!!HELP ASAP!!!!!!!!!!!!!!!!!!!!
Jayden used the following steps to simplify the given expression.
-3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
What property of real numbers was used in step 3?
A)distributive property
B)associative property of addition
C)commutative property of addition
D)associative property of multiplication
Answer:
Option A -distributive property
Step-by-step explanation:
Given : expression -3 + 2(2 + x + 3)
Step 1: = -3 + 2(x + 2 + 3)
Step 2: = -3 + 2(x + 5)
Step 3: = -3 + 2x + 10
Step 4: = 2x + (-3) + 10
Step 5: = 2x + 7
In step 3 distributive property is applied i.e. c(a+b)=ca+cb
in step 2- 2(x+5) when we apply distributive property it became
2x+10
Therefore, option A is correct
Verify the identity.
tan(x+(pi/2)) = -cot x
Yen calculates the product 5/8 times 24/25. before he multiples he
Answer:
[tex]\frac{1}{1} \times \frac{3}{5}[/tex]
Step-by-step explanation:
The complete question is
Yen calculates the product 5/8 x 24/25. before he multiplies, he simplifies all the factors. what does the problem look like after he simplifies the factors?
The given product is
[tex]\frac{5}{8} \times \frac{24}{25}[/tex]
Then, Yen simplifies and the problem looks like
[tex]\frac{1}{1} \times \frac{3}{5}[/tex]
Because, we simplified 5 with 25 and 8 with 24.
Therefore, the result of the product is
[tex]\frac{3}{5}[/tex]
Can anyone show me steps on how to solve this equation.. I will upvote!
5x+7=4x+10
x^2-14x-4=0, solve by completing the square
The solution of the equation found by completing the square are;
x = 7 - √(53) and 7 + √(53)
What is the completing the square method?Completing the square method involves writing the quadratic expression of the form a·x² + b·x + c as (x + d)² + e, where d and e are constants.
Moving the constant to one side of the equation, we get;
x² - 14·x = 4
We complete the square on the left side of the equation by adding and subtracting the square of the half the coefficient of x term inside the parenthesis. Therefore, we add and subtract (-14/2)² = 49, as follows;
(x² - 14·x + 49) - 49 = 4
Therefore; (x - 7)² - 49 = 4
The -49 is moved to the right side of the equation to get;
(x - 7)² = 4 + 49 = 53
Taking the square root of both sides, we get;
x - 7 = ± √(53)
Therefore; x = 7 ± √(53)
The solution is; x = 7 + √(53) and 7 - √(53)
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Which of the following relations are functions?
A. {(a,b),(b,a),(c,c),(e,d)}
B. {(c,e),(c,d),(c,b)}
C. {(b,b),(c,d),(d,c),(c,a)}
D. {(a,b),(b,c),(c,d),(d,e)}
Solve log11 (y + 8) + log11 4 = log11 60. what is y?
Answer:
The value of y is 7.
Step-by-step explanation:
The given equation is
[tex]log_{11}(y+8)+log_{11}4=log_{11}60[/tex]
[tex]log_{11}[(y+8)4]=log_{11}60[/tex] [tex][\because log_ax+log_ay=log_axy][/tex]
[tex]log_{11}(4y+32)=log_{11}60[/tex]
Equating both sides.
[tex]4y+32=60[/tex]
[tex]4y=60-32[/tex]
[tex]4y=28[/tex]
Divide both sides by 4.
[tex]y=7[/tex]
Therefore the value of y is 7.
Given that f(x) = 3x + 1 and g(x) = the quantity of 4x plus 2
divided by 3, solve for g(f(0)).
2
6
8
9
What is 110.079 to the nearest hunderdths?
At first public inquiry showed there were 637000 women motorcyclists in the US up from 437000 just 8 years ago before it. Find the percent of increase in the number of women motorcyclists during these 8 years
The percent of increase in the number of women motorcyclists over the 8-year period is approximately 45.77%, calculated by finding the difference between the final and initial number of motorcyclists, dividing by the initial number, and converting the ratio to a percentage.
Explanation:To calculate the percent of increase in the number of women motorcyclists over the 8-year period provided, follow these steps:
Determine the initial and final values. Initial value: 437,000; Final value: 637,000.
Calculate the increase by subtracting the initial value from the final value: 637,000 - 437,000 = 200,000.
Divide the increase by the initial value to find the increase ratio: 200,000 / 437,000 ≈ 0.4577.
Multiply the increase ratio by 100 to convert it to a percentage: 0.4577 * 100 ≈ 45.77%.
Therefore, the percent of increase in the number of women motorcyclists during these 8 years is approximately 45.77%.
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Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents. ( 4 x 3 y −2 ) 3 (4x3y-2)3
What is the value of the sum 5 + 10 + 15 + ... + 95 + 100? ...?
Juan charges $3.50 per hour for babysitting. Write a rule to describe the amount of money (M) earned is a function of the number of hours (h) spent baby-sitting. HELP PLEASE
what number is 82% of 230
Which mathematical property is demonstrated?
5 + 3w + 2 = 5 + 2 + 3w
associative property of addition
commutative property of multiplication
associative property of multiplication
commutative property of addition
Answer:
commutative property of addition
Step-by-step explanation:
A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot?
a) 50.0 feet
b) 70.7 feet
c) 86.6 feet
d) 100.0 feet ...?
Answer:
the answer is b) 70.7 feet
Step-by-step explanation:
thank you for amazing answers on the board.
A number n is at least 7
The inequality would be equal to n ≥ 7.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that the phrase as;
"A number n is at least 7"
Therefore, the inequality would be;
n ≥ 7
Or
n = 7
Thus, the inequality would be equal to n ≥ 7.
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Maple Grove wants to include two types of maple trees, the namesake of the city,for their parks.Two varieties of maple trees have been selected.One variety costs $80 per tree; the other more colorful variety costs $85 per tree. The tree budget must not exceed $75,000. Citizens want more of the colorful $85 trees than the others if possible.
Let x be the number of $80 trees and y the number of $85 trees. Which system of inequalities represents the situation?
Options:
80x+85y>= 75,000 x<=y
80x+85y>=75,000 x>=y
80x+85y<=75,000 x>=y
80x+85y<=75,000 x<=y ...?
During a 52 week period, a company paid overtime wages for 19 weeks and hired temp help for 11 weeks. During 5 weeks, the company paid overtime AND hired temp help. If an auditor randomly examined the payroll for only one week, whats the probability that the payroll for that week contained overtime wages or temp help wages? ...?
The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\frac{10}{13}}[/tex].
Further explanation:
It is given that during a [tex]52[/tex] week period, a company paid overtime wages for [tex]19[/tex] weeks and hired temporary help for [tex]11[/tex] weeks.
During [tex]5[/tex] weeks, the company paid overtime and hired temporary help.
Calculation:
A company paid overtime wages for [tex]19[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.
Therefore, the probability of overtime wages [tex]P(O)[/tex] is calculated as follows:
[tex]\begin{aligned}P(O)&=\dfrac{19}{52}+\dfrac{5}{52}\\&=\dfrac{19+5}{52}\\&=\dfrac{24}{52}\end{aligned}[/tex]
The probability of overtime wages is [tex]\frac{24}{52}[/tex].
The same company hired temporary help for [tex]11[/tex] weeks and [tex]5[/tex] weeks during the [tex]52[/tex] week period.
Therefore, the probability of temporary help [tex]P(H)[/tex] is calculated as follows:
[tex]\begin{aligned}P(H)&=\dfrac{11}{52}+\dfrac{5}{52}\\&=\dfrac{11+5}{52}\\&=\dfrac{16}{52}\end{aligned}[/tex]
The probability of temporary help is [tex]\frac{16}{52}[/tex].
Now, the combined probability [tex]P[/tex] that the payroll for one week contained overtime wages or temporary help is calculated by adding the probabilities of overtime wages and temporary help as follows:
[tex]\begin{aligned}P&=\dfrac{24}{52}+\dfrac{16}{52}\\&=\dfrac{24+16}{52}\\&=\dfrac{40}{52}\\&=\dfrac{10}{13}\end{aligned}[/tex]
The probability that the payroll for one week contained overtime wages or temporary help is [tex]\boxed{\dfrac{10}{13}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, events, outcome, sample, experiment, equally likely, random, complementary events, joint probability, independent events, mutually exclusive events, conditional probability.
Tim is buying packages of paper plates and cups. He wants to have equal amounts of each, but plates come 24 per pack, and cups come 16 per pack. What is the least amount of plates and cups Tim will have to buy to get the same number of each?
8
16
24
48
Factors of 14 least to greatest
Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable.
1 × 12
A. numerical expression
B. variable expression; a is the variable.
C. variable expression; there is no variable.
D. variable expression; l is the variable.
Use the prime factoriations of 24 and 28 to find their greatest common factor
Bobby will buy coffe and hot chocolate for his co-workers each cup of coffe costs $2.25 and each cup of hot chocolate costs $1.50 .he pays a total of $15.75 for 8 cups
( please answer me as quickly as possible)
Final answer:
Bobby can buy 5 cups of coffee at $2.25 each and 3 cups of hot chocolate at $1.50 each to meet his budget of $15.75 for 8 cups in total. We find this by solving a system of equations.
Explanation:
Bobby wants to buy a total of 8 cups of coffee and hot chocolate for his co-workers with a budget of $15.75. Since each cup of coffee costs $2.25 and each cup of hot chocolate costs $1.50, we need to find out how many cups of each he can buy.
Let's denote the number of cups of coffee as C and the number of cups of hot chocolate as H.
The total cost for coffee will be $2.25 × C and for hot chocolate $1.50 × H.
The total amount spent is $15.75, and the total number of cups is 8, so we have two equations: 2.25C + 1.50H = 15.75 and C + H = 8.
We can solve this system of equations using substitution or elimination. For simplicity, we'll use substitution.
From C + H = 8, we can express H in terms of C: H = 8 - C.
Substitute H in the cost equation: 2.25C + 1.50(8 - C) = 15.75.
Simplify and solve for C: 2.25C + 12 - 1.50C = 15.75, which simplifies to 0.75C = 3.75, and therefore C = 5.
Now, plug C = 5 into H = 8 - C to find H: H = 3.
Bobby can buy 5 cups of coffee and 3 cups of hot chocolate.
The amount of weight that Sam loses is directly proportional to the number of hours he spends exercising. If Sam loses a pound of weight for each 3 hrs of exercise, how many hours must he spend exercising to lose 25 lbs?
A) 25 hrs
B) 50 hrs
C) 75 hrs
D) 80 hrs
Answer:
The answer is C. 75 hours.
Step-by-step explanation:
In order to determine the hours, we have to know about direct proportionality.
The direct proportionality happens when two variables increase at the same time and their rate is a constant. It means that if one variable is increased, so the other variable will be increased too.
I have attached an image that shows a graph of two variables with direct proportionality.
In this case, we can get the constant of both variables: losing weight and the spending time.
[tex]k=\frac{Weight}{Time}=\frac{1}{3} =0.33[/tex]
Then we need to know how many hours Sam will spend to lose 25 lbs:
[tex]\frac{25}{T}=k=0.33\\ T=\frac{25}{0.33}\\ T=75.76[/tex] hours.
Finally, Sam needs to spend 75 hours to lose 25 lbs.
Use one transformation to solve n-4.6=2.98
1. The figure attached is a regular octagon with radii and an apothem drawn. What is the measure of angle 1?
A. 22.5 degrees
B. 45 degrees
C. 60 degrees
D. 67.5 degrees
A rectangle has a length of x inches and a width 2 inches less than the length. If the dimensions were tripled what would be the area of the new rectangle in terms o x