To determine two numbers where their difference is 16, and their ratio is 5:7, we let the smaller number be 5x and the larger one be 7x, solve for x with the equation 7x - 5x = 16, and find that the numbers are 40 and 56.
Explanation:To find two numbers with a difference of 16 and a ratio of 5:7, first let's denote the smaller number as 5x and the larger number as 7x. The difference between the two numbers is 16, so we can write the equation 7x - 5x = 16.
Solving for x gives us 2x = 16 or x = 8. Thus, the two numbers we are looking for are 5x = 5 × 8 = 40 and 7x = 7 × 8 = 56.
Check: The difference between 56 and 40 is indeed 16, and the ratio of 40 to 56 simplifies to 5:7, confirming our solution.
PLESEEE HELP I WILL GIVE THE BRAINLIEST TO THE BEST ANWSERS
Which word sentence represents the equation?
6(x + 3) = 42
A)The sum of 3 and six times some number is 42.
B)Three plus 3 times some number is 42.
C)Six times some number plus 3 is 42.
D)Six times the sum of a number and 3 is 42.
What is the solution set for 3x + 2 = 14, given the replacement set {1, 2, 3, 4} ?
A)x = 1B)x = 2C)x = 3D)x = 4Eric and his work crew have 50 trees o plant. In 8 hours today, they planted 40 trees. If the work at the same rate tomorrow, how long will it take to finish planting the trees?
The length of a rectangle is four times its width. If the perimeter is at most 100 centimeters, what is the greatest possible value for the width? Question 17 options:
If the length of the rectangle is twice the width and the perimeter of the rectangle is 30 cm find its area
Simplify 7t · s · 3rt.
10rst
10rst2
21rst2
An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 7t · s · 3rt, when simplified will be equal to 21rst². The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 7t · s · 3rt can be written as,
7t · s · 3rt
= 7 × t × s × 3 × r × t
= 21rst²
Hence, the given expression 7t · s · 3rt, when simplified will be equal to 21rst².
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Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything
PLEASE HELP ASAP!! Will give brainliest!
In a class of 10, there are 2 students who forgot their lunch.
If the teacher chooses 2 students, what is the probability that both of them forgot their lunch?
Answer:2/10
Step-by-step explanation: 10 students, 2 of them forgot their lunch. So 2/10 of the students will be chosen by the teacher
Solve the inequality
7x ≥ -7
a. x ≤ -1
b. x > -14
c. x ≥ -1
d. x ≥ 14
Answer:
A: x ≥ -1
its rightc bc
List an example of two events that are independent. (b) list an example of two events that are dependent. (a) list an example of two events that are independent. choose the correct answer below.
a. a father having hazel eyes and a daughter having hazel eyes
b. selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck
c. rolling a die twice
d. not putting money in a parking meter and getting a parking ticket (b) list an example of two events that are dependent. choose the correct answer below.
a. tossing a coin and getting a head, and then rolling a six-sided die and obtaining a 6
b. selecting a ball numbered 1 through 12 from a bin, replacing it, and then selecting a second numbered ball from the bin
c. rolling a die twice
d. drawing one card from a standard deck, not replacing it, and then selecting another card
When two events are dependent, this means that one event cannot occur without the other, or simply put the two events are connected to each other in one way or the other.
When two events are independent, this means that the two events can occur separately, with one event having no effect on the occurrence of the other.
Therefore the dependent and independent events are as follows:
Independent event:
c. rolling a die twice
The outcome of the first die does not affect the outcome of the second die, hence independent.
Dependent event:
d. drawing one card from a standard deck, not replacing it, and then selecting another card
By the act of not replacing the drawn card, we are changing the probability of selecting another card, hence dependent.
Each digit in the division example has been replaced with the same letter throughout (r stands for remainder) the digits used were 1, 2, 3, 4, 5, 7, and 9 find the numbers clue u is 5
This is a cryptarithm problem where every unique letter represents a unique digit. Given that 'u' equals 5, we would navigate the problem by dividing numbers out front and subtracting the exponents.
Explanation:This question is about a form of a cryptarithm. Cryptarithms are mathematical puzzles where the digits are replaced by letters of the alphabet or other symbols. If the same letter appears more than once, it represents the same digit each time. Your question implies that each letter corresponds to a unique digit and that division is involved. Therefore, we need to figure out which numbers are represented by the remaining letters. You've already been given that 'u' represents 5. Since there isn't a complete problem provided, I can't offer a step by step guide on how to solve it. However, I can suggest to you to start the cryptarithm solution by dividing numbers out front and subtracting the exponents.
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The question involves substituting the given number for a letter in a division problem and then solving it. It's a step-by-step process of trial and error.
Explanation:In this problem, you are asked to find the numbers that replace the same letter throughout a division problem. Given that 'u' is 5, you know that wherever 'u' appears in your division equation, you can replace it with 5. Solve the division problem accordingly. Do not forget, each distinct letter represents a distinct number. It is a process of trial and error until you come up with the right numbers that fit the equation and abides by the division rules.
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To take a taxi , it cost $3.00 plus an additional $2.00 mile traveled. you spent exactly $20 on a taxi, which includes the $1tip you left. how many miles did you travel?
Reuben drove 576 miles in 8 hours.
At the same rate, how long would it take him to drive 936 miles?
Reuben's driving rate is 72 miles per hour. At this same rate, it would take him 13 hours to drive 936 miles.
To determine how long it would take Reuben to drive 936 miles at the same rate, we first need to find his driving rate. Reuben drove 576 miles in 8 hours. To find his rate, we divide the distance by the time:
Rate = Distance / Time
Rate = 576 miles / 8 hours = 72 miles/hour
Next, we use this rate to find out how long it will take him to drive 936 miles:
Time = Distance / Rate
Time = 936 miles / 72 miles/hour = 13 hours
Thus, it would take Reuben 13 hours to drive 936 miles at the same rate.
Calc Question :fuel cost Please help me.
vertical angles are opposite angles with the same vertex
true or false
An air cargo plane can transport as many as 15 regular shipping containers. One supersize container takes up the space of 3 regular containers.
Robert climbed 775 steps in 12 1/2minutes. how many steps did he average per minute?
Evaluate the function f(x)=−4x−3 f(x)=−4x−3 for x=−6x=−6.
Is 81 a multiple of 3 explain why
Convert 7 4/7 to a mixed decimal and rounded to the nearest thousandth.
Rob cuts 15-foot wire into 8 equal pieces. About how long is each piece
Does a negative minus a negative equal positive
The expression 3x² represents
Final answer:
The expression 3x² signifies a quadratically powered variable (x) that is multiplied by the coefficient 3, commonly seen in algebraic equations.
Explanation:
The expression 3x² represents a mathematical formula where the variable x is squared (multiplied by itself) and then multiplied by 3. The squaring of a variable is a fundamental concept in algebra that symbolizes a number raised to the power of 2.
The coefficient 3 in this case indicates that the square of x is being tripled. Therefore, if x is 2, x² would be 4, and 3x² would be 12. This type of expression is essential in solving quadratic equations and appears frequently in various mathematical contexts.
A shop has a sale that offers 20% off all price. On the final day they reduce all the sale prices by 25%. Linz buys a radio on the final day. Work out the overall percentage reduction on he price of the radio.
To calculate the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. The second discount of 25% off reduces the price by 25/100 = 0.25. The overall percentage reduction is 40%.
Explanation:To find the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. So, the price after the first discount is 1 - 0.2 = 0.8 times the original price. The second discount of 25% off reduces the price by 25/100 = 0.25. So, the final price after both discounts is 0.8 * (1 - 0.25) = 0.8 * 0.75 = 0.6 times the original price.
To calculate the overall percentage reduction, we can subtract the final price from the original price, divide by the original price, and multiply by 100. The overall percentage reduction is ((1 - 0.6) / 1) * 100 = 40%.
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What’s the reciprocal of 7/2a
2a/7
-2a/7
7/2a
-7/2a
A jet travels 510 miles in 2 hours. At this rate, how far could the jet fly in 15 hours? What is the rate of the speed of the jet?
Which term describes gross pay that is calculated based on the number of hours an employee has worked?
Answer: Hourly wage
Step-by-step explanation:
The term "hourly wage" describes the gross pay that is calculated based on the number of hours an employee has worked.
The hourly wage is the amount of money that is earned by a employee for every hour worked or it is the amount of money paid by employer for every hour worked.
Here, the gross pay is calculated by multiplying the hourly wage to the number of hours worked.
How to solve the second equation
Odette deposited $3,624.40 into a savings account with an interest rate of 2.1% compounded annual. About how long will it take for the account to be worth $7,000?
A. 31 years, 9 months
B. 30 years, 9 months
C. 28 years, 4 months
7000 = 3624*(1+0.21)^x
7000 = 3624 *1.021^x
7000/3624 = 1.021^x
875/453 = 1.021^x
xlog(1.021 = log(875/453
x = 31.677
31 years 9 months
Answer:
Option A is the answer.
Step-by-step explanation:
p = 3624.40
r = 2.1% or 0.021
n = 1
t = ?
A = 7000
Compound interest formula is :
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]
Substituting the values in formula:
[tex]7000=3624.40(1+\frac{0.021}{1})^{t}[/tex]
=> [tex]\frac{7000}{3624.40} =(1.021)^{t}[/tex]
=> [tex]1.93135=(1.021)^{t}[/tex]
[tex]t=\frac{log1.93135}{log1.021}[/tex]
=> t = 31.670 years.
Closest to option A.
I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $20. Then it occurred to me that, if my nickels were dimes and my dimes were quarters, I would have $46.25. How many dimes and nickels are in the box?
There are 150 nickels and 125 dimes in the box.
Let x = the number of nickels in the box
Let y = the number of dimes in the box
Firstly, we have to convert value of nickels and dimes into cents.
Value of 1 nickel = 5 cents
Value of 1 dime = 10 cents
Value of 1 dollar = 100 cents
Thus, the equation (1) (in cents) can be written as:
x + 2y = 400 Equation (1)
If my nickels were dimes and dimes were quarters:
A quarter is worth 25 cents.
Thus, the equation (2) (in cents) can be written as:
5x+10y =2000
5(x+2y)= 2000
x+2y = 2000/5
2x + 5y = 925 Equation (2)
Multiply Equation (1) by "2", we get:
10x +25y= 4625
5(2x+5y)=4625
2x+5y=4625/5
2x + 4y = 800 Equation (1)
Subtraction Equation (1) from Equation (2):
2x +5y-2x -4y=925-800
y= 125
2x + 5y = 925
2x + 5 × 125 = 925
2x + 625 = 925
2x = 925 - 625
2x = 300
x = 150
There are 150 nickels and 125 dimes in the box.
Here, we can check it by putting the value of x and y in Equation (1):
5x + 10y = 2000
5× 150 + 10 × 125 = 2000
750 + 1250 = 2000
2000 = 2000
There are 150 nickels and 125 dimes in the box.