Answer:
length: 75 ftwidth: 72 ftStep-by-step explanation:
Length: (25 yd)(3 ft/yd) = 75 ft.
Width: (8 lanes)(3 yd/lane)(3 ft/yd) = 72 ft.
The length and width are 75 ft and 72 ft, respectively.
Answer:
length; 75 ft
width; 72 ft
Step-by-step explanation:
find the measure of the angle
Answer: 86
Step-by-step explanation:
This is a cyclic quadilateral in which opposite angles adds upto 180.
Let the unknown angle be x
ATQ
x + 94 = 180
x = 180 - 94
x = 86
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7 students are running for student council. how many different ways can their names be listed on the ballot
Step-by-step explanation:
7! = 5040 ways
A
B
C
D
37. What is the length of side P in the figure below?
6.7 cm
11 cm
15 cm
45 cm
20 cm
25 cm
P
The length of the side P is 15 cm. And the right option is C.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
To calculate the length of side P we use Pythagoras theorem's formula
Pythagoras formula:
a² = b²+c²......................... Equation 1Where:
a = Diagonal of the rectangleb = Length of the rectanglec = Width of the rectangleFrom the diagram,
Given:
a = 25 cmb = 20 cmc = p cmSubstitute these values into equation 1
25² = 20²+p²p² = 25²-20²p² = 225p = √225p = 15 cmHence, the right option is C 15 cm.
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Neal invested $120,000 in stocks and bonds. He earned 18% on his stock investments and 12% on his bond investments. If Neal's combined profits on both types of investments were $17,400, how much did he invest in stocks?
Answer:
$50,000
Step-by-step explanation:
The given relations can be used to write and solve an equation for the amount invested in stocks.
SetupLet s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...
0.18s +0.12(120,000 -s) = 17,400
SolutionSimplifying the equation, we have ...
0.06s +14,400 = 17,400
0.06s = 3000 . . . . . . . . . . subtract 14,400
s = 50,000 . . . . . . . . . . . . divide by 0.06
Neal invested $50,000 in stocks.
__
Additional comment
The amount invested in bonds was 70,000. The profit earned was ...
0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400
Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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The measure of one angle of a right triangle is 26°. Find the measure of the other angle.
Enter an integer or decimal number [more...]
Question Help:
Post to forum
Calculator
Answer:
64°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the third angle be x , then
x + 90° + 26° = 180°
x + 116° = 180° ( subtract 116° from both sides )
x = 64°
the other angle is 64°
lineal or no?1) 2x+y=52) y= x + 6 --- 2thanks
1) 2x+y=5 ...... It is a linear equation
2) y= x + 6 ....... It is a linear equation
Because they are of first degree and they contain x and y (equations of a line)
What is the area of the quadrilateral?
Answer:
\( 16 \: {m}^{2} \)
Step-by-step explanation:
Area of the quadrilateral
\( = \frac{1}{\cancel 2} \times 8 \times \cancel 2 + \frac{1}{\cancel 2} \times 8 \times \cancel 2 \\ \\ = 8 + 8 \\ \\ = 16 \: {m}^{2} \)
Which slope description best compares the graph given by the equations 3x - y = 5 and 2x + 6y = 24
The description best compares the graph given by the equations 3x - y = 5 and 2x + 6y = 24 will be intersecting but not perpendicular. Option D is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation of the line is 3x - y = 5 and 2x + 6y = 24.
The graph for the function is plotted on the paper below and it is observed that the lines are intersecting.
Thus, the description best compares the graph given by the equations 3x - y = 5 and 2x + 6y = 24 will be intersecting but not perpendicular. Option D is correct.
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Amy bought a new car for $21,000
. She paid a 10%
down payment and financed the remaining balance for 36
months with an APR of 3.5%
. Determine the monthly payment that Amy pays. Round your answer to the nearest cent, if necessary.
Answer:
Step-by-step explanation:
To determine the monthly payment Amy pays, we can use the formula for calculating the monthly payment on a loan. The formula is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate
n = Number of monthly payments
Given information:
Principal amount (loan amount) = $21,000
Down payment = 10% of $21,000 = $2,100
Remaining balance = $21,000 - $2,100 = $18,900
APR = 3.5%
Number of monthly payments (n) = 36
To calculate the monthly interest rate (r), we divide the annual interest rate by 12 (number of months in a year):
Monthly interest rate (r) = APR / (12 * 100)
Substituting the values into the formula:
r = 3.5 / (12 * 100) = 0.0029167 (rounded to 7 decimal places)
M = (18,900 * 0.0029167 * (1 + 0.0029167)^36) / ((1 + 0.0029167)^36 - 1)
Using a calculator to evaluate the expression within the formula:
M ≈ $539.26
Therefore, the monthly payment that Amy pays is approximately $539.26.
If 2n + m = 10 and 3n - m = -5, then what is m?
Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the
sample is less than 0.7.
The probability that the third largest observation in the sample is less than 0.7 is 0.2401 = 24.01%.
How do we calculate?The sample size n = 5,
Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.
Probability that X₃ is less than 0.7:
Since X₃ is the third largest observation = (X₁ and X₂) < 0.7.
The probability that X₃ is less than 0.7 is (0.7)² = 0.49.
The Probability that X₁ and X₂ < or equal to 0.7 is found as:.
The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.
We then get the product of both cases:
Probability = 0.49 * 0.49 = 0.2401
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You have $500,000 saved for retirement. Your account earns 7% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 25 years?
$3,244.21 can be withdrawn each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.
Formula to calculate the present value of the annuityPV = PMT × [1 - (1 + r)⁻ⁿ] / r
where:
PV is the present value of the annuity
PMT is the payment amount per period
r is the interest rate per period
n is the total number of periods
In this case, we want to withdraw a fixed amount each month for 25 years, which represents 12 ×25 = 300 periods.
The interest rate per period is 7% / 12 = 0.5833%.
Let's assume that you want to withdraw a fixed amount each month, and you want the withdrawals to last for 25 years. To calculate the amount you can withdraw each month,
PV = PMT × [1 - (1 + r)⁻ⁿ] / r
500,000 = PMT × [1 - (1 + 0.005833)⁻³⁰⁰] / 0.005833
Solving for PMT, we get:
PMT = PV × r / [1 - (1 + r)⁻ⁿ]
PMT = 500,000 × 0.005833 / [1 - (1 + 0.005833)⁻³⁰⁰]
PMT = $3,244.21
Therefore, you can withdraw $3,244.21 each month for 25 years, assuming an interest rate of 7% and a starting principal of $500,000.
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The cost of one t-shirt is 128. How much will be the cost of 20
The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.
When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.
Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.
We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.
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9)By selling an article for $96 a profit of $16 was made on the cost price. The profit as a
percentage of the cost price is
(a)16%
(b)17%
(c)20%
(d)25%
Answer:
A
Step-by-step explanation:
Simplify: 7/8 - 17/24
Simplify:
7/8 - 17/24
To complete the operation, we need to have both denominators with the same value.
One denominator is 8 and the other one is 24
Note 24 is a multiple of 8 (24=8*3).
Thus, to make both denominators be equal, we just multiply the first fraction by 3. This is called amplification
The expression is now:
21/24 - 17/24
Please note the first fraction was amplified by 3: 7*3= 21 and 8*3=24
Now we have both denominators the same, we just subtract the numerators:
(21-17) / 24
Operating:
4 / 24
This fraction can be simplified by 4:
1/6
This is the final result
What is the exact volume of the cone?
225π cm3
405π cm3
90π cm3
675π cm3
A dairy farmer wants to mix a 70% protein supplement and a standard 20% protein ratio to make 1900 pounds of a high grade 55% protein ration how many pounds of each should he use
The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.
To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.
Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.
The total weight equation is given by:
x + y = 1900
The protein content equation is given by:
(0.70x + 0.20y) / 1900 = 0.55
Simplifying the second equation, we get:
0.70x + 0.20y = 0.55 × 1900
0.70x + 0.20y = 1045
Now, we can solve this system of equations to find the values of x and y.
Rearrange the first equation to solve for x:
x = 1900 - y
Substitute this expression for x in the second equation:
0.70(1900 - y) + 0.20y = 1045
1330 - 0.70y + 0.20y = 1045
1330 - 0.50y = 1045
-0.50y = 1045 - 1330
-0.50y = -285
y = -285 / -0.50
y = 570
Now substitute this value of y back into the first equation to find x:
x + 570 = 1900
x = 1900 - 570
x = 1330
Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.
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i need help asap
than you!
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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What is the purpose of data? Answer below.
The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.
Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.
By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.
For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.
Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.
Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.
Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.
Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.
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Solve the inequality below.
2x < 12
To solve the inequality 2x < 12, we need to isolate x on one side of the inequality sign. We can do this by dividing both sides by 2:
2x < 12
x < 6
Therefore, the solution to the inequality is x < 6. This means that all values of x that are less than 6 satisfy the inequality. We can represent this graphically on a number line:
<=======()------6-------------->
The open circle () indicates that x cannot be equal to 6, but can be any value less than 6. The arrow indicates that the inequality is true for all values of x to the left of the open circle.
In summary, the solution to the inequality 2x < 12 is x < 6.
I'm 15 BTW
What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
help me pls i need this immediatrly
Answer:
AB = 146°
Step-by-step explanation:
The measure of the arc is equal to the angle it subtends at the centre, thus
measure of arc AB = 146°
Answer:
mAB = 214
Step-by-step explanation:
A circle has 360 degree all around
mAB = 360-146 = 214 degree
1. Global warming creates local problems. Projections forecast that even a moderate air temperature increase of only 1.8 °F could cause brook trout distributions to decrease dramatically. For example, such a temperature increase would take Washburn county's 19 ponds that support brook trout down to 10 ponds. What would be the percent decrease in the number of ponds that support brook trout?
The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.
To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.
Initial number of ponds: 19
Final number of ponds: 10
To calculate the percent decrease, we can use the following formula:
Percent Decrease = (Difference / Initial Value) * 100
Let's apply this formula to the given data:
Difference = Initial number of ponds - Final number of ponds
Difference = 19 - 10
Difference = 9
Percent Decrease = (9 / 19) * 100
Now, let's calculate the percent decrease:
Percent Decrease = (9 / 19) * 100
Percent Decrease ≈ 47.37%
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For 2021, Gourmet Kitchen Products reported $22 million of sales and $19 million of operating costs (including depreciation). The company has $14 million of total invested capital. Its after-tax cost of capital is 9% and its federal-plus-state income tax rate was 25%. What was the firm's economic value added (EVA), that is, how much value did management add to stockholders' wealth during 2021?
The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
Net operating profit = (22 million - 19 million)*(1 - 0.36)
= $1.92 million
EVA = net operating profit after taxes - invested capital*WACC
= 1.92 million - 15 million*0.10
= $0.42 million
Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.
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Which number is divisible by 10? 148 99 121 100
Answer:
100
Step-by-step explanation:
100/ 10
= 10
2q-3p and 2(p+q)/q
When p=8and q=4
Answers:
Step-by-step explanation:
Part 1.) To solve for the first one:
Replace the variables with the given numbers. 2 x 4 = 8^2 (= 64), and 3 x 8 = 24. (P.S, the carrot symbol ^ means exponent, or to the power of, just to let you know.)
So, 8 - 24 = (-16).
Part 2.) To solve for the second part of the equation:
Replace the variables with the given numbers, and distribute the coefficient (2) into the parentheses. 2 x 8 = 16, 2 x 4 = 8.
Now add the two sides and then place them over a fraction. 16 + 8 = 24, 24/4 = 6.
Part 3.) So, the answer is -16 < 6. Six is the larger number.
I hope this helps.
The area is about? Sorry I’m asking this but I just can’t figure it out I need the step PLEASE HELP im not good at this!!
Answer:
area = 113.04 ft²
Step-by-step explanation:
area = πr²
r = 1/2diameter so:
r = 6 ft
π = 3.14
area = (3.14)(6²) = (3.14)(36) = 113.04 ft²
Answer:
The area is about 113.04 ft² square feet
Step-by-step explanation:
Hope this helps
need help writing a function
n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.
Roots : -3(mult . 2), 4(mult.2)
the function is given as
f(n) = (n + 3)² (n - 4)²
= (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)
= (n² + 6n + 9) (n² - 8n + 16 )
= n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1
collecting like term,
f(n) = n⁴ - 2n³ - 23n² + 24n + 144
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Choose the correct answer below
The correct statement is;
False, because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be x = 2π/3 + 2nx and x = 4π/3 + 2nx.
Option D
How to determine the statementFrom the information given, we have that;
All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx
There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx
Such that n is an integer.
This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.
The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.
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