Answer:
Below
Step-by-step explanation:
(2x+15) / ( 3x+15) = 11/14 cross multiply to get
28x + 210 = 33x + 165
45 = 5x
x = 9 so the larger number is 3 X 9 = 27
(smaller number is 2 x 9 = 18)
Help with these questions pls?
Answer:
76
Step-by-step explanation:
(16x3)+28
Its 16x3 because there's 3 half hours in 1.5hrs
Q: What is the result of adding
-3x²-5x +1 and 8x²-2x-9?
A. 5x²-3x-10
B. -5x²-3x-10
C. 5x²-7x-8
D. -5x²-7x+8
Answer:
C. 5x²-7x-8
Step-by-step explanation:
(-3x²-5x +1 ) + (8x²-2x-9)
Grouping like terms:
(- 3x² + 8x²) + (- 5x - 2x) + (1 - 9)
=> (5x²) + (-7x) + (-8)
=> 5x² - 7x - 8
Find the amount of money (Future Value) in an account where $5,100 is deposited (Present Value) at an interest rate of 8% per year compounded continuously and the money is left in the account for 13 years.
round to 2 decimal places.
Answer:
Step-by-step explanation:
The formula for calculating the future value of a continuously compounded investment is:
FV = PV * e^(rt)
where PV is the present value, r is the annual interest rate as a decimal, t is the time in years, and e is the mathematical constant approximately equal to 2.718.
Plugging in the given values, we get:
FV = 5100 * e^(0.08 * 13) = 5100 * e^1.04 = 5100 * 2.856116786 = 14536.86
So, the future value of the investment after 13 years at an 8% interest rate compounded continuously would be approximately $14,536.86. Rounded to 2 decimal places, this is $14,536.86.
The measure of angle 4 is 120°, and the measure of angle 2 is 35°.
Triangle A B C. Angle A is 2, angle B is 1, angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.
What is the measure of angle 5?
95°
105°
130°
155°
The measure of angle that is an exterior angle to B is 95°.
What are exterior angles?The angle created by any extended side of a triangle and its neighboring side is referred to as the external angle of a triangle. A triangle has three external angles. It should be noticed that every outside angle and corresponding interior angle constitute a linear pair. We are aware that a triangle's internal angle is created when its sides come together at its apex.
Given that,
The measure of angle 4 is 120°, and the measure of angle 2 is 35°.
Triangle A B C. Angle A is 2, angle B is 1, and angle C is 3. The exterior angle to angle B is 5, and the exterior angle to angle C is 4.
The sum of an interior and exterior angle is 180°,
∠4 + ∠3 = ∠1 + ∠5 = ∠2 + ∠6 = 180°
and ∠2+ ∠1 +∠3 = 180°
Also, ∠3 = 180 - ∠4
∠3 = 180 - 120 = 60°
Substitute the values,
∠2+ ∠1 +∠3 = 180°
35 + ∠1 + 60 = 180
∠1 = 180 - 95
∠1 = 85°
Now, ∠1 + ∠5 = 180
∠5 = 180 - 85
∠5 = 95°
Hence, the measure of angle that is an exterior angle to B is 95°.
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The correct question is:
Answer: A) 95 Degrees
Step-by-step explanation:
0.5(1.2)^x percentage
Answer:
20%
Step-by-step explanation:
1 + r = 1.2 = 1 + 0.2 = 1 + 20%
r = 20%
The percent growth is 20%.
A washer and a dryer cost $993 combined. The washer costs $43 more than the dryer. What is the cost of the dryer?
Answer:425
Step-by-step explanation:
993-43=950
950/2=425
Answer:
$475
Step-by-step explanation:
Let's call the cost of the dryer x. That means the cost of the washer is x + $43. The combined cost of the two is $993, so we can write the equation:
x + (x + $43) = $993
Expanding the right side:
2x + $43 = $993
Subtracting $43 from both sides:
2x = $950
Dividing both sides by 2:
x = $475
So the cost of the dryer is $475.
The temperature in a certain location was recorded each day for two months. The mean temperature was 28.8°F with a standard deviation 7.4°F. What can you determine about these data by using Chebyshev's Inequality with =K3?
Using Chebyshev's Theorem, it is found that at least 89% of days have a high temperature between 6.6ºF and 51ºF.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].Considering k = 3, the percentage is of at least 89% and the bounds are given as follows:
28.8 - 3 x 7.4 = 6.6ºF.28.8 + 3 x 7.4 = 51ºF.More can be learned about Chebyshev's Theorem at https://brainly.com/question/2927197
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Joel opened a
savings account and
deposited $3500 as
principal. The account
earns 7% interest,
compounded
semianually. What is the
balance after 48
months?
Answer:
Step-by-step explanation:
The balance of the savings account after 48 months can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the balance after t years
P is the principal (initial amount)
r is the interest rate (as a decimal)
n is the number of times compounded per year
t is the number of years
Step-by-step, the calculation is as follows:
Convert the interest rate from a percentage to a decimal:
r = 7% = 0.07
Determine the number of times compounded per year:
n = 2 (compounded semi-annually)
Determine the number of years:
t = 48 months / 12 months/year = 4 years
Plug the values into the formula:
A = P * (1 + r/n)^(nt)
A = $3500 * (1 + 0.07/2)^(2 * 4)
Calculate the balance using the formula:
A = $3500 * (1.035)^8
A = $3500 * 1.306769
A = $4588.72
So, the balance in the savings account after 48 months is $4588.72.
Some neighbors knows that you have very good geometry skills and asks for your help on their deck project. They did alright on the level pieces but the railing for the steps has them stumped. Help your neighbors determine how much wood is necessary to frame the outside of the railing. The railing height needs to be between 34 inches and 38 inches. Provide your answer in 3 to 5 sentences.
The length of the wood necessary to frame the outside of the railing will be 48.167 inches.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The length of the wood necessary to frame the outside of the railing will be given as,
l² = 32² + 36²
l² = 1,024 + 1,296
l² = 2,320
I = 48.167 inches
The length of the wood necessary to frame the outside of the railing will be 48.167 inches.
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I need help finding b
Step-by-step explanation:
You would find a the same way as finding B, just backwards
[tex]( {x}^{2} - 1)( {x}^{2} + 5)[/tex]
Distributing we get
[tex] {x}^{4} + 5 {x}^{2} - {x}^{2} - 5[/tex]
Simplifying it...
[tex] {x}^{4} + 4 {x}^{2} - 5[/tex]
In a certain college, 4 instructors are single out of 24 instructors employed. What is the ratio of single to married instructors?
A. 1 to 6
B. 1 to 5
C. 24 to 4
D. 20 to 24
Answer:
(B) "1 to 5."
Step-by-step explanation:
The ratio of single to married instructors is 1 to 5. Since 4 instructors are single out of 24 total instructors, the ratio of single instructors to married instructors is 4 to (24 - 4) = 4 to 20. Simplifying the ratio to its simplest form, we get 4:20 = 1:5, which is the answer choice (B) "1 to 5."
An online furniture store sells chairs for $150 each and tables for $350 each. Every day, the store can ship no more than 22 pieces of furniture and must sell at least $4800 worth of chairs and tables. If
x
x represents the number of tables sold and
y
y represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.

Answer: x+y=22; 150x+350y=4800
Step-by-step explanation:
The following information is available for Shanika Company for 20Y6: Inventories January 1 December 31 Materials $274,730 $346,160 Work in process 494,510 470,780 Finished goods 475,280 481,160
The Shanika Company's inventory levels changed during 20Y6. The materials inventory increased, the work in process decreased, and the finished goods slightly increased.
Inventory Changes at Shanika Company in 20Y6Based on the information provided, it appears that the Shanika Company has gone through some changes in its inventory levels during the 20Y6 period.
The company's materials inventory has increased from $274,730 on January 1 to $346,160 on December 31, indicating that the company has acquired more raw materials over the course of the year.
On the other hand, the work-in-process inventory has decreased from $494,510 to $470,780, suggesting that the company has been able to efficiently process its raw materials into partially completed goods over the year.
Finally, the finished goods inventory has increased slightly from $475,280 to $481,160, indicating that the company has been able to produce more finished products over the course of the year and has had sufficient demand for its products to keep the finished goods inventory at a relatively stable level.
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If 3250 was increased by 46%
Answer:
4745
Step-by-step explanation:
Answer: 4745
Step-by-step explanation:
3250 = 100%
Percent Increase = +46%
46% of 3250 = 1495
3250 (100%) + 1495 (46%) = 4745
Leila is walking from the park at point P to a restaurant at point R. She wants to stop for a break when the distance she has travelled and the distance she has left to travel has a ratio of 3:5, at which point should Leila stop for her break?
Answer: To determine the point where Leila should stop for her break, we need to find the midpoint of the line segment connecting points P and R, since the midpoint will represent equal distances from both points.
Let the distance between points P and R be d, and let's call the point where Leila stops for her break point B.
Since the ratio of the distance travelled to the distance remaining is 3:5, we know that the distance from B to P is 3/8 of the total distance d, and the distance from B to R is 5/8 of the total distance d.
Therefore, point B is the midpoint of line segment PR, and can be found by dividing the distance between P and R by 2.
Step-by-step explanation:
At the local grocery store, A 12 ounce bottle of stay clean shampoo costs 8 and an 8 ounce bottle of shampoo costs 6. Which size bottle has the lesser cost per ounce?
Using their unit rates, the 12-ounce bottle costs lesser per ounce than the 8-ounce bottle of stay clean shampoo.
What is the unit rate?The unit rate is the cost per unit.
The unit rate is computed as the quotient of the total cost and the number of units.
The cost of a 12-ounce bottle of stay clean shampoo = $8
The unit rate per ounce of the 12-ounce bottle = $0.67 ($8/12)
The cost of an 8-ounce bottle of stay clean shampoo = $6
The unit rate per ounce of the 8-ounce bottle = $0.75 ($6/8)
Thus, comparing the unit rate of the 12-ounce bottle with the 8-ounce bottle, we can conclude that it costs more per ounce to buy the 8-ounce bottle than the 12-ounce bottle.
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2023 Tax Year (Filing in 2024)
You are 25yr old and single with no kids/dependents.
You live in Florida.
Your job pays $84,649/yr.
You have no other sources of incomes.
Your itemized deductions come out to $10,211.
Your credits come out to $9.
Your tax-deffered retirement contributions come out to $3,288.
Calculate the total Federal Income Taxes and FICA paid.
If you are 25yr old and single with no kids/dependents. The total Federal Income Taxes is $11,218 and FICA paid is $6,478.
How to find the total Federal Income Taxes and FICA paid?First, you need to determine your taxable income.
Gross income: $84,649
Itemized deductions: $10,211
Tax-deferred retirement contributions: $3,288
Taxable income: $71,150
Next, you can use the tax brackets and rates for the 2023 tax year to calculate your federal income tax liability.
The first $10,950 is taxed at 10%: $1,095
The next $32,250 is taxed at 12%: $3,870
The next $28,425 is taxed at 22%: $6,253
The remaining $0 is taxed at 24%: $0
Total federal income tax liability: $11,218
b. For 2023, the Social Security tax rate is 6.2% on the first $147,000 of income, and the Medicare tax rate is 1.45% on all income.
Social Security tax: $5,240.80
Medicare tax: $1,237.20
Total FICA taxes: $6,478
Therefore the total Federal Income Taxes is $11,218 and FICA paid is $6,478.
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mrs.musick splits her students into 2 equal groups. 2/3 of the first group have an A and 40% of second group have an A. what fraction of the class has a A
Hi there, here's your answer:
Given a class is divided into 2 equal groups, i.e. Group A has 1 : 2 of the students in the class and group B has 1 : 2 of the students in the class.
Also [tex]\frac{2}{3} rd[/tex] of group A have an A
While 40% of group B have an A
To find:
Fraction of the class that has A
Solution:
First, we find the % of students in group A who have an A:
Since [tex]\frac{2}{3} rd[/tex] of group A have an A,
[tex]\frac{2}{3}[/tex] × [tex]50[/tex] (∵ 1 : 2 = 50 : 100)
[tex]= \frac{100}{3} = 33.33[/tex] (i)
Therefore, % of students in group A who have an A = 33.33%
Now, we find the % of students in group B who have an A:
Since 40% of group B have an A:
[tex]\frac{40}{100}[/tex] × [tex]50[/tex] (∵ 1 : 2 = 50 : 100)
= 4 × 5 = 20 (ii)
Adding (i) and (ii), we get
33.33 + 20 = 53.33%
Thus, the fraction of the class that has an A = [tex]\frac{53.33}{100}[/tex]
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Tamaya borrowed $8,500 to buy a car. After 42 months, she ended up paying $1,785 in interest on the car loan. What was the simple interest rate on Tamaya’s car loan?
Answer:
5%
Step-by-step explanation:
We can use the formula for simple interest to solve for the interest rate:
I = Prt
where:
I is the interest
P is the principal (the amount borrowed)
r is the interest rate
t is the time in years
We know the principal (P) is $8,500, the interest (I) is $1,785, and the time (t) is 42 months, or 42/12 = 3.5 years. So, we can plug in the values and solve for r:
I = Prt
$1,785 = $8,500 * r * 3.5
$1,785 / $8,500 / 3.5 = r
r = 0.05, or 5%
So, the simple interest rate on Tamaya's car loan was 5%.
Pieto brought a wristwatch for $250 and sold it for $300. What is his percentage gain.
Answer: 83%
Step-by-step explanation: Take 250 and divide it by 300
3) Find the sum of the first 50 terms. *
8 + 20+32 +44 + ...
15100
Step-by-step explanation :
Sum of first 50 terms for the AP:
[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]
where ,
Total no. of terms (n)= 50 Comman difference (d) = 20 - 8 = 12 First term (a) = 8On substituting the values , we get :
[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]
[tex] \therefore[/tex] Sum of the first 50 terms is 15100
The rate in the portion formula is not always expressed with a percent symbol?
That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.
What is the proportional and ratio formula?How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.
What does a ratio example look like?An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.
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7x + 14y = 28
5x+10y= 20
Solve for x and y using elimination
The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.
What is elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.
We are given two equations as
7x + 14y = 28 ....(1)
5x + 10y = 20 ....(2)
Now, on multiplying equation (1) by 10, we get the equation as
70x + 140y = 280 ....(3)
On multiplying equation (2) by 14, we get the equation as
70x + 140y = 280 ....(4)
Since, we are getting the same equations so, the system has infinitely many solutions.
Hence, the value of x is [0,∞] and y is [0,∞].
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Solving linear equations by substitution y=5x-7 -3y-2y=-12
By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.
How to solve this system of linear equations?In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:
y = 5x - 7 .......equation 1.
3y - 2x = -12 .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
-3(5x - 7) - 2x = -12
-15x + 21 - 2x = -12
-17x = -12 - 21
17x = -33
x = -33/17 or -1.94
For the value of y, we have:
y = 5(-33/17) - 7
y = -165/17 - 7
y = 2.71
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What is the slope of the line that passes through the points ( 6 , 7 ) (6,7) and ( 16 , 22 ) (16,22)? write your answer in simplest form.
Answer:
Step-by-step explanation:
The slope of a line is the change in y (the vertical axis) divided by the change in x (the horizontal axis).
Given the two points (6,7) and (16,22), we can calculate the slope as follows:
Change in y = 22 - 7 = 15
Change in x = 16 - 6 = 10
Therefore, the slope of the line passing through the two points is:
slope = change in y / change in x = 15 / 10 = 3/2
So the slope of the line is in its simplest form, 3/2.
Regenerate response
Which of the following is the midsegment for A ACE?
A. AC
B. BC
C. DB
D. CE
Explanation:
Points B and D are midpoints of segments AC and CE respectively. This is because of the tickmarks indicating congruent segment pieces (AB = BC and CD = DE)
Joining the midpoints together forms a midsegment. The midsegment is half as long as the side parallel to it. This means BD is half as long as AE. Flip things around to say that AE is twice as long as BD.
Solve the following equation for y. 22x+2y=-14
Step-by-step explanation:
22x + 2y = -14
2y = -22x - 14
y = -11x - 7
Metalworking Twelve equally spaced holes are to be drilled in a metal strip 3414-in. long, with 2 in. remaining on each end. What is the distance, to the nearest hundredth of an inch, from center to center of two consecutive holes.
Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.
How would you define distance?How far apart or how far away items or locations are from one another is measured numerically as distance. A physical quantity, it is typically stated in terms of meters, kilometers, miles, or feet. Given that it simply has magnitude and no direction, distance is a scalar quantity.
Usually, a formula is used to determine the distance between two points. One example is the distance formula in Euclidean geometry, which includes computing the square root of the sum of the squares of the coordinate differences between the two points.
Distance can be measured in a variety of contexts, including physics, where it is used to describe an object's displacement through time, and geography, where it is used to define the separation between two points on the surface of the Earth. It is also frequently used in daily life when people go for walks or runs or when they drive from one area to another to calculate the distance they travel.
There are no holes in the first and last 2 inches of the metal strip, leaving 3410 inches (3414 - 2 - 2) as the remaining length.
We can divide the total remaining length by the number of gaps between the holes to determine the distance between the centers of two adjacent holes. The distance between the 12 holes is determined by the fact that there are 11 gaps between them.
distance = (total length - length of 2 end pieces) / (number of gaps)
distance = (3410 in.) / 11
distance ≈ 310.91 in.
Rounded to the nearest hundredth of an inch, the distance is 310.91 inches.
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Hassan finds the product of two multiples of 10 the answer is 6000 list 5 different calculations Hassan could write
The two ways of writing the number 6000 will be 10 x 600 and 100 x 60.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Multiplication is the process of determining the product of two or more numbers in mathematics.
Given that Hassan discovers that the result of two multiples of 10 is 6000.
The two ways can be calculated as:-
10 x 600 = 6000
100 x 60 = 6000
Hence, the two ways are 10 x 600 = 6000 and 100 x 60 = 6000.
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A radioactive element decays by 40% every year. A scientist started an experiment with 5 grams of the radioactive material. Write a function that models the amount of radioactive material remaining after x years.
The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.
What is Exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
here, we have,
An exponential function is in the form:
y = abˣ
where y,x are variables, a is the initial value and b is the multiplicative factor.
Let y represent the amount of substance remaining after x hours. Hence:
a = 9375, at x = 4, y = 15:
15 = 9375(b)⁴
b = 0.2
y = 9375(0.2)ˣ
For the 7th hour, x = 7:
y = 9375(0.2)⁷
= 0.12
The amount of radioactive material that would remain by the 7th hour of decay is 0.12 grams.
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