Answer:
Russell: 40 pounds; Sarah: 100 pounds; and Terry: 160 pounds.
Step-by-step explanation:
The three different amounts of money are 2x, 5x and 8x, or 15x.
Terry gets 8x, whereas Russell gets 2x, and 8x - 2x = 120 pounds.
Solving for x, 6x = 120 pounds, and so x = 20 pounds.
Russell gets 2(20 pounds); Sarah gets 5(20 pounds); and Terry gets 8(20 pounds), or 40 pounds, 100 pounds and 160 pounds. Note that 40 pounds is 120 pounds less than 160 pounds, as required by the problem.
In this ratio problem, the total money is split into 15 portions. Each portion is worth 20 pounds. Russell gets 40 pounds, Sarah gets 100 pounds and Terry gets 160 pounds.
Explanation:The subject of this question is ratios and its application to practical problems. In this problem, Russell, Sarah and Terry share money in the ratio 2:5:8, meaning the total money is shared in 15 portions (2+5+8). As we know that Russell gets 120 pound less than Terry, which would be 6 portions (8 portions for Terry - 2 portions for Russell).
Therefore, each portion of money is equal to 120 pound divided by 6, which is 20 pound. So, Russell receives 2 portions which equals 40 pound (2 x 20), Sarah receives 5 portions which equals 100 pound (5 x 20) and Terry receives 8 portions which equals 160 pound (8 x 20).
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if the ratio of 7 less than a number and 7 more than the number 2, what is the number?
Answer:
Step-by-step explanation:
I assume you mean "if the ratio of 7 less than a number and 7 more than the number is 2".
Let x be the number.
Ratio is division.
(x-7)/(x+7)=2
Multiply by (x+7) on each side:
x-7=2(x+7) = 2x+14
Add 7 on each side
x=2x+21
Subtract 2
-x=21
x=-21
The bank charged Travis a $20 fee because his balance dropped below $0. He knows that he currently had an outstanding charge for $7.85 that he had not recorded yet. How much money will Travis have to deposit into his account so that the outstanding charge does not create another bank fee
Final answer:
Travis must deposit $27.85 to cover the $7.85 outstanding charge and the previous $20 overdraft fee, to avoid further overdraft fees and bring his account balance back to at least $0.
Explanation:
Travis needs to not only cover the outstanding charge to avoid further overdraft fees but also bring his account balance back to at least $0. If Travis currently has an outstanding charge of $7.85, and overdraft fees are typically $35 or higher, it's clear that merely covering the charge won't be enough; he must also compensate for any negative balance incurred from previous overdraft fees.
Assuming the $20 fee has already been applied to his account and his balance is now at -$20 (not considering any other transactions that have taken place), Travis would need to deposit enough money to cover both the fee and the outstanding charge. Therefore, he would need to deposit a total of $20 (to bring his balance to $0) plus the $7.85 outstanding charge, which sums up to $27.85. By depositing this amount, Travis would avoid a second overdraft fee and any additional monetary penalties.
It is worth noting that financial literacy is essential to manage personal finances effectively and avoid potential overdraft situations which could lead to a cycle of fees and negative balances.
Write the equation of a line with the slope of 2, which contains the point (4,-8).
Answer:
y = 2x-16
Step-by-step explanation:
To find a line when we know the slope and a point, we can use the point slope formula for a line
y-y1 = m(x-x1)
where the point is (x1,y1) and the slope is m. Substituting the known information in.
y--8 = 2 (x-4)
y+8 = 2(x-4)
We can manipulate this into slope intercept form by distributing the 2
y+8 = 2x-8
and subtracting 8 from each side
y+8-8 = 2x-8-8
y = 2x-16
what is the recursive formula for this geometric sequence? 4, -12, 36, -108, ...
Answer:
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = -108/36
a₄/a₃ = -3
r = -3
aₙ = 4(-3)ⁿ⁻¹
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
The (-1)ⁿ⁻¹ term makes even-numbered terms negative.
Answer:
answer is attached
Step-by-step explanation:
If (6 to the 0 power ) to x power = 1, what are the possible values of x? Explain answer
The value of x can be any real number because raising 1 to any exponent will always result in 1.
The question needs us to solve for x in the equation [tex](6 to the 0 power)^x[/tex]= 1. We know that any non-zero number raised to the 0 power is 1 (e.g.,[tex]10^0[/tex] = 1). Thus, 6 to the 0 power is 1 regardless of the value of 6. From this, we have[tex]1^x[/tex], which is still 1 for any value of x because 1 raised to any power is always 1. Hence, the equation remains true for any real number value of x.
Someone help me with this question ASAP and show work please and thank you
Answer:
g(f(x)) = x
Step-by-step explanation:
You are given f(x) = -4x - 1 and g(x) = [tex]\frac{x+1}{-4}[/tex]. Keep in mind that f(x) or g(x) is the same as a y = equation, but two separate equations.
You are trying to find g(f(x)), which means that you will use f(x) and substitute this value into the x value in the equation of g(x).
It will look like: g(-4x - 1) = [tex]\frac{x+1}{-4}[/tex]
[tex]\frac{(-4x-1)+1}{-4}[/tex]
Now evaluate the expression to solve the problem. Start by combining like terms.
[tex]\frac{(-4x)}{-4}[/tex]
You are left with -4x/-4. We can simplify this even further by dividing both sides of the fraction by -4/-4. The -4's cancel out and become 1's, so you are left with:
[tex]x[/tex]
Answer:
Step-by-step explanation:
g(f(x)) means that wherever you see an x in g(x) you put f(x) in it's place. Read that sentence a couple of times until it makes sense.
g(x) = (x + 1)/-4
g(f(x)) = (f(x) + 1) / - 4 Now wherever you see f(x), put in -4x - 1
g(f(x)) = [(-4x - 1) + 1] / - 4 Remove ( )
g(f(x)) = [-4x - 1 + 1 ] / - 4
g(f(x)) = [-4x] / - 4 Do the division
g(f(x)) = x
Neat problem. thanks for posting.
3. The population of Detroit, MI was 673,104 in 2018. The population of the United States was about 325.7 million in 2017 (a) Write each population in scientific notation. (2 points) (b) About how many times larger was the population of the United States than the population of Detroit, MI? Show your work
Answer:
a) 6.73104 x 10⁵
b) about 480 times larger
Step-by-step explanation:
a) 673,104 people in scientific notation is 6.73104 x 10⁵
b)325.7 million is the same as 325700000 = 3.257 x 10⁸
so (3.257 x 10⁸) divided by (6.73104 x 10⁵) ≈ 0.48 x 10³
480 times larger
What are the zeros of the polynomial function f(x)=x^3+2x^2-24x?
Immediately, we can factor an x out of each term to simplify the polynomial.
x(x^2 + 2x - 24)
In doing this, we know the first zero will be x = 0.
Using the AC method, we can find the next two zeros.
x(x - 4)(x + 6)
The zeros, or x-intercepts of the polynomial, are 0, 4, and -6.The zeros of the polynomial function f(x) = x^3 + 2x^2 -24x are x = -6, 0, and 4.
Explanation:The question requires finding the zeros of the polynomial function f(x) = x^3 + 2x^2 -24x. The zeros of this function can be found by setting the function equal to zero and solving for x. So, we have 0 = x^3 + 2x^2 - 24x. All terms have an 'x', so we can factor out 'x' to give: 0 = x (x^2 + 2x - 24). The quadratic formula (which is used for expressions of the form ax^2 + bx + c = 0) to solve x^2 + 2x - 24 = 0, we get x = -6 and x = 4. Therefore, the zeros of the function are x = -6, 0, and 4.
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A special paint requires a mixture of paints: A, B and C. The ratio is: 60% A, 25% B, and 15% C. If you want 20 gallons of the special color, how many gallons of paint A will you need?
You would need 12 gallons of paint A. You can find this answer by finding what 60% of 20 is, and do that by multiplying 20 • (0.6). This is what gives you 12. Following that, you’ll need 3 gallons of C, and 5 gallons of B.
In a certain year, brand A of heart-rate watch cost $39.99 and brand B cost $59.99. A nonprofit community health organization purchased 34 heart-rate watches for use at a wellness center. If the organization spent $1619.66 for the watches, how many of each type did they purchase?
Answer:
Brand A = 21 heart-rate watches.
Brand B = 13 heart-rate watches.
Step-by-step explanation:
Let A be the number of Brand A heart watches and B be the number of Brand B heart watches.
We have been given that a nonprofit community health organization purchased 34 heart-rate watches for use at a wellness center.
We can represent this information in an equation as:
[tex]A+B=34...(1)[/tex]
We have been given that in a certain year, brand A of heart-rate watch cost $39.99 and brand B cost $59.99 and the organization spent $1619.66 for the watches.
We can represent this information in an equation as:
[tex]39.99*A+59.99*B=1619.66...(2)[/tex]
We will use substitution method to solve our system of equations.
From equation (1) we will get,
[tex]A=34-B[/tex]
Substituting [tex]A=34-B[/tex] in equation(2) we will get,
[tex]39.99*(34-B)+59.99*B=1619.66[/tex]
[tex]1359.66-39.99*B+59.99*B=1619.66[/tex]
[tex]-39.99*B+59.99*B=1619.66-1359.66[/tex]
[tex]20*B=260[/tex]
[tex]B=\frac{260}{20}[/tex]
[tex]B=13[/tex]
Therefore, the organisation purchased 13 heart-rate watches of brand B.
Now let us substitute B=13 in equation (1).
[tex]A+13=34[/tex]
[tex]A+13-13=34-13[/tex]
[tex]A=21[/tex]
Therefore, the organisation purchased 21 heart-rate watches of brand A.
write 423% as a decimal
[tex]p\%=\dfrac{p}{100}\\\\423\%=\dfrac{423}{100}=4\dfrac{23}{100}=4.23\\\\\boxed{423\%=4.23}[/tex]
Answer:
4.23
Step-by-step explanation:
423%
Percent means out of 100
423/100
Pt the decimal 2 places to the left of the 3
4.23
What is the slope of this line
There are 1600 kilocalories in 5 cups of dog food that mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food. How many kilocalories are there in this 2-cup serving?
Answer:
640 kilocalories are there in this 2-cup serving.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the given statement: There are 1600 kilocalories in 5 cups of dog food that mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food.
Let x kilocalories are there in 2-cup serving.
then, by definition of proportion;
[tex]\frac{1600}{5} =\frac{x}{2}[/tex]
Multiply both sides by 2 we get;
[tex]x = \frac{1600}{5} \times 2[/tex]
Simplify:
[tex]x = 320 \times 2 = 640 kilocalories[/tex]
Therefore, 640 kilocalories are there in this 2-cup serving.
A petri dish has 246 bacteria. It grows at a rate of 7% per month. How many bacteria will there be in 5 months? Round your answer to the nearest whole number. Question 20 options:
A.253
B.345
C. 171
D.281
Answer:
B 345
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the slope for (-3,14)(5,10)
Answer:
slope = -1/2
Step-by-step explanation:
The formula for slope is (y2-y1)/ (x2-x1)
m = (10-14)/(5--3)
= (-4)/(5+3)
= -4/8
= -1/2
In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?
Answer:
The number of problems solved = 2000
Step-by-step explanation:
Let us assume the monthly quota of problems be x
number of problem solved in first week = 25 % of x =[tex]0.25x[/tex]
number of problems solved in 2nd week = 110% of (problems solved in 1st week)
= [tex]1.10 (0.25x)[/tex]
=[tex]0.275x[/tex]
number of problem solved 3rd week= 60% of ( problems solved in 1st and 2nd week)
= [tex]0.60(0.25x+0.275x)[/tex]
=[tex]0.60(0.525x)[/tex]
=[tex]0.315x[/tex]
number of problem solved in 4th week = [tex]320[/tex]
now we have
number of problems solved in ll 4 weeks = x
[tex]0.25x +0.275x+0.315x+320=x[/tex]
[tex]0.84x+320=x[/tex]
[tex]320=x-0.84x[/tex]
[tex]320=0.16 x[/tex]
[tex]x=\frac{320}{0.16}[/tex]
[tex]x=2000[/tex]
Hence the number of problems solved = 2000
Final answer:
In the third week they solved 60% of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. The total number of problems solved in the four-week month is 492.
Explanation:
To solve this problem, we need to find the number of problems solved in each week and then add them together to get the total number of problems solved in the four-week month.
In the first week, the students solved 25% of their monthly quota of problems. Let's say their monthly quota is 'x'. So, they solved 0.25x problems in the first week.
In the second week, they solved 110% of the number of problems solved in the first week. That means they solved 1.1 * 0.25x = 0.275x problems in the second week.
In the third week, they solved 60% of the number of problems they had solved in the first two weeks. So, they solved 0.6 * (0.25x + 0.275x) = 0.345x problems in the third week.
In the fourth week, they solved the remaining 320 problems. This means the total number of problems solved in the first three weeks is 0.345x, and we can set up the following equation to find x: 0.345x + 320 = x.
Solving this equation, we get x = 491.429. Since we can't have a fractional number of problems, we can round x up to 492. Therefore, the students solved a total of 492 problems in the four-week month.
during a hoagie sale fundraiser a ski club sold 42 Italian hoagies and 53 roasted beef Hoagies what is the ratio of Italian hoagie sold to the total number of Hoagies sold
Answer:
42:53 would be the answer
Step-by-step explanation:
In a ski club fundraiser, the ratio of Italian hoagies sold to the total number of hoagies sold, when the numbers of Italian and roast beef hoagies are 42 and 53 respectively, is 42:95.
Explanation:The student is asking for the ratio of Italian hoagies sold to the total number of hoagies sold at a ski club fundraiser. To calculate this ratio, one must add the number of Italian hoagies to the number of roast beef hoagies to determine the total hoagies sold. In this case, 42 Italian hoagies were sold, and 53 roast beef hoagies were sold, yielding a total of 95 hoagies sold. Thus, the ratio of Italian hoagies sold to total hoagies sold is 42:95. In ratio terms, this expresses that for every 42 Italian hoagies sold, there were 95 total hoagies sold.
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What is the value of 3b when b = 18?
Answer:
54
Step-by-step explanation:
to evaluate substitute b = 18 into 3b
3b = 3 × 18 = 54
[ Answer ]
54
[ Explanation ]
B = 18
Substitue B for 18
3 * 18
= 54
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Which value in the replacement set is a solution to this equation? 2n + 5 = 27 Replacement set: {11, 12, 13} Drag the solution into the box.
What is $4.99 x 0.5lb + $6.99 x 0.25lb?
Answer:
$3.77
Step-by-step explanation:
$4.99 x 0.5lb + $6.99 x 0.25lb?
First we multiply
2.495+1.725
Then we add
3.77
We will spend $3.77
(02.06) The table below shows that 1 day equals 24 hours. Notice that 12 hours is one-half of that. Use the table to help you determine how many days are equal to 42 hours. 1 day 24 hours 12 hours 12 hours (3 points) 1 and 1 over 4. days 1 and 1 over 2. days 1 and 3 over 4. days 2 days
Answer:
1 and 3/4 days are equal to 42 hours
Step-by-step explanation:
42 hours = (42 hours) (1 day / 24 hours)
42 hours = 42/24 days
Simplyfing the fraction: Dividing the numerator and denominator by 6:
42 hours = (42/6) / (24/6) days
42 hours = 7/4 days
42 hours = (4+3)/4 days
42 hours = (4/4+3/4) days
42 hours = 1 3/4 days
To determine how many days are equal to 42 hours, you divide 42 by 24 which results in 1.75. Therefore, 42 hours is equivalent to 1 and 3/4 days.
Explanation:In this mathematics problem, we are asked to convert 42 hours into a measurement of days. To begin with, we know that 1 day equals 24 hours. Therefore, to convert 42 hours into days we will divide 42 by 24.
The result of this division is 1.75. In terms of a day fraction, this value represents 1 and 3/4 days. As such, we can say that 42 hours is equivalent to 1 and 3/4 days.
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In math, how do you solve 2h<200?
Answer:
h < 100
Step-by-step explanation:
isolate h by dividing both sides by 2
h < 100
What is the slope of the line that passes through (5,4) and (7,10)?
(10-4)/(7-5)=6/2=3.
The slope of the line that passes through those two points is 3.
The slope of the line that passes through (5,4) and (7,10) is 3.
Given that,
It passes through (5,4) and (7,10).We need to find out the slope of the line.Based on the above information, the slope of the line is:
[tex]= \frac{y_2 - y_1}{x_2 - x_1} \\\\= \frac{10-7}{5-4} \\\\= \frac{3}{1}\\[/tex]
= 3
Therefore we can conclude that the slope of the line that passes through (5,4) and (7,10) is 3.
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help please. its math. please explain your answer
Answer:
Step-by-step explanation: 20 percent
:)
You invest 23,400 annual interest rate of 4% compounded annually for seven years what is the balance of the account at the end of that time
Answer: 30792.80
=====================================
Work Shown:
We deposit P = 23400 dollars for t = 7 years, which is compounded n = 1 times per year at an interest rate of r = 4% = 0.04 (we'll use the decimal form of the interest rate)
So this means...
A = P*(1+r/n)^(n*t)
A = 23400*(1+0.04/1)^(1*7)
A = 23400*(1+0.04)^(7)
A = 23400*(1.04)^(7)
A = 23400*1.31593177923584
A = 30792.8036341187
A = 30792.80
DONT KEEP SCROLLING PLEASE
Please I don’t understand 50 POINTS BRAINLIEST
Answer:why didn’t you want me to scroll down ? Can you answer my question
Step-by-step explanation:
1)Not necessarily a parallelogram
2)parallelogram
3)parallelogram
4)parallelogram
How determine if a quadrilateral is a parallelogramTo classify a shape as a parallelogram, the following four conditions must be satisfied
1. Opposite sides are equal in length.
2. Opposite angles are equal.
3. Consecutive angles are supplementary
4. Diagonals bisect each other.
Each of these conditions contributes to the definition of a parallelogram, and all of them must be satisfied for a shape to be considered a parallelogram.
From the figures
1) Not necessarily a parallelogram
The opposite sides are not equal.
GH is congruent to Gl and HJ is congruent to IJ. These are adjacent sides instead of opposite sides equality.
2) Given
RS is parallel to TU
SU is parallel to R(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
3) Given PQRS
PQ||RS(given)
PR||QS(Converse of the Opposite Sides Are Congruent (OSAC) Theorem)
Since the both pairs of opposite sides of the quadrilateral are congruent, then the quadrilateral is a parallelogram.
4) <ABC ≅ DCB(alternate angles, AB||CD BC is transversal)
<ACB ≅ DBC(alternate angles,AC||BD,BC is transversal)
Therefore
Opposite angles are equal.
Pairs of opposite sides are parallel.
Adjacent angles are supplementary.
so, the quadrilateral is a parallelogram.
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A scientist builds a Mars rover that can travel 4.9 centimeters per second on flat ground. If the rover continues at the same rate, how many centimeters will it travel in 15 1/2 seconds?
Answer:
The rover would travel 75.95 centimeters in 15 1/2 seconds.
Step-by-step explanation:
Simply multiply 4.9 by 15 1/2.
Hope it helps!
Answer:
75.95 cm
Step-by-step explanation:
We know that distance = rate times time
d =rt
We know the rate = 4.9 cm/s
and time = 15 1/2 s = 15.5 s
Substituting these into d=rt
d = (4.9 cm/s) * 15.5 s = 75.95 cm
problem 1: two numbers add together equals 47. their difference is 13. write and solve a system to find the two numbers
problem 2: the sum of two numbers is 54 and their difference is 12. write and solve a system to find the two numbers
Answer:
34+13= 47
Step-by-step explanation:
47-34=13
please help me with these im stuck
Answer:
Is it 15?
Step-by-step explanation:
Since it is asking for the sites, aren't you just supposed to count the dots...?
Answer:
15
Step-by-step explanation:
The question is asking how many sites are shown in this data set. So, on the side of the rectangle, it says "Number of Sites" & the dots represent the number of sites. So, there are 15.
Sorry if I'm incorrect...
If the number 38,469 is rounded to the nearest thousand, how many zeros does the rounded number have?
This rounded number has three zeros. The number 38,469 rounded to the nearest thousand is 38,000.
To find the number of zeros in 38,469 when rounded to the nearest thousand, we first need to round the number appropriately. We look at the hundreds place (the third digit from the right), which is '4'. Since 4 is less than 5, we do not round up.
Identify the digit in the hundreds place of 38,469 (which is '4').Since 4 is less than 5, do not round up.Change all the digits after the thousands place to zero.The rounded number is 38,000, which contains three zeros.