[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]
A simple gable roof is to cover a span of 32 feet. If it is to have a 7:12 pitch, how tall will the ridgeline be above the house?
The ridgeline will be 18.67 feet above the house.
What will be the height of the ridgeline above the house?Generally, a height refers to the measurement of someone or something from head to foot or from base to top.
To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span
Given data:
Pitch = 7
Span = 32 feet
Inputting the values, we have:
Height = (7 / 12) * 32
Height = 0.5833 * 32
Height = 18.6656
Height = 18.67 feet.
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Find the value of 20x when x = 10.
(a) 200
(c) 2
(b) 30
(d) 5
6x + y = 8
y= -6x + 8
Answer:
y = -6x + 8
Step-by-step explanation:
\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}
I don't know why it came out like this
Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?
There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
How to solveThe Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.
Given:
The class has 42 students.
12 boys and 15 girls are said to know how to read three-letter words in English.
19 boys and 17 girls are said to know how to identify all letters of the alphabet.
None of the students in the class is able to write a sentence of five words if dictated to them.
There are in total 22 boys and 20 girls in the class.
Read three-letter words |
|____________|______________|
| | |
| Boys (12) | Girls (15) | Can read three-letter words
|____________|______________|
| | |
| Boys (10) | Girls (13) | Cannot read three-letter words
_______|____________|______________|
| | |
| Boys (9) | Girls (13) | Can identify all letters
|____________|______________|
| | |
| Boys (13) | Girls (7) | Cannot identify all letters
|____________|______________|
To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:
Boys who cannot read a letter or a three-letter word: 10 + 13 = 23
Girls who cannot read a letter or a three-letter word: 13 + 7 = 20
Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
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Kl and CaCl₂ particle diagram
Answer:
CaCL2 + KL → KCL + CaL2
Step-by-step explanation:
To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.
Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.
Ionic charges are not yet supported and will be ignored.
Replace immutable groups in compounds to avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.
Compound states [like (s) (aq) or (g)] are not required.
You can use parenthesis () or brackets [].Li + Ag = Li + Ag
KOH + KMnO4 + H2SO4 = KOH + KMnO4 + H2SO4
C6H6O + KOH = C6H7KO2
CUO + HNO3 = CU(NO3)2 + H2O
C4H6O4 + KOH = C2K2O4 + C2H6O2
Zn + Sr(OH)2 = Sr + Zn(OH)2
Al + Pb(No3)2 = Al(No3)3 + Pb
HNO3 + Zn = Zn(NO3)2 + H2
ZnO + CH3COOH + H2O + Al2O3 = Zn(CH3COO)2*2H2O + Al2O3
BeO + Zn(OH)2 = Be(OH)2 + ZnO
CH3COOK + CH3Br = CH3COOCH3 + KBr
Pb(NO3)2 + HBr = PbBr2 + NHO3
1. The Roth Family took out a $215,000 with a 15-year mortgage at an APR of 5.4%. The
monthly payment was $1,850. What will be their total interest charges after 15 years?
The total interest charges to the Roth Family, after 15 years, given the monthly payment would be $ 118, 000
How to find the total interest charges ?First, find the total amount paid over the 15 years by the Roth Family to be :
= Number of years x Monthly payment x Number of months per year
= 15 x 1, 850 x 12
= $ 333, 000
The total interest charges that the Roth Family paid would be :
= Total amount paid after 15 years - Total amount borrowed as mortgage
= 333, 000 - 215, 000
= $ 118, 000
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Pleaseee help me I’ve been stuck on this fool like 30 minutes can’t miss this or I restart the whole lesson pleease help
The properties of equality that shows justification of how the equation is solved is explained below.
How to Apply the Properties of Equality to Solve an Equation?Given the equation, 17/3 - 3/4x = 1/2x + 5, we have the following steps and justification which explains the property of equality that was used:
17/3 - 3/4x = 1/2x + 5 [given]
17/3 - 3/4x - 17/3 = 1/2x + 5 - 17/3 [subtraction property of equality]
3/4x = 1/2x - 2/3 [simplification]
3/4x - 1/2x = 1/2x - 2/3 - 1/2x [subtraction property of equality]
-5/4x = -2/3 [simplification]
-5/4x * -4/5 = -2/3 * -4/5 [multiplication property of equality]
x = 8/15 [simplification]
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Which of the following statements is true for ∠a and ∠b in the diagram?
A) m∠a = m∠b
B) m∠a + m∠b = 90°
C) m∠a + m∠b = 180°
D) m∠a – m∠b = 90°
Answer:
A
Step-by-step explanation:
If you look at the angles or use something to measure it you can tell that a and b are opposite sides that are parallel to each other. So they are equal.
One of the authors received a credit card bill for $2,559, but it included a charge of $1,825 th
values of the absolute and relative errors.
The value of the absolute error is $
The value of the relative error is%. (Round to the nearest integer as needed)
The absolute error is $1825, the relative error is 2
What is an absolute and relative error?An absolute error is a determinant of how large an error is. A relative error defines how good or bad an error is.
The formula for determining an absolute error is;
Absolute error = measured value - actual valueThe formula for determining a relative error is:
Relative error = absolute error ÷ actual valueFrom the parameters given:
The absolute error can be computed as:
Absolute error = 2559 - (2559 - 1825)
Absolute error = 2559 - 734
Absolute error = $1825
The relative error = 1825 ÷ 734
The relative error = 2.4
The relative error ≅ 2 (as an integer)
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Suppose that 15% of all American use CNN as their primary source of news. A random sample of 200 Americans is selected. What is the probability that is your sample of 200 Americans that proportion that us CNN as their primary news source is at least 0.21?
The probability that in a sample of 200 Americans, the proportion that uses CNN as their primary news source is at least 0.21 is 49.6%.
What is the probability?The probability is determined using the normal approximation to the binomial distribution.
Given that the sample size is large (n = 200) and the probability of success (p = 0.15) is not too close to 0 or 1, the mean (μ) and standard deviation (σ) of the binomial distribution, will be:
μ = n * p
μ = 200 * 0.15
μ = 30
σ = √(n * p * (1 - p))
σ = √(200 * 0.15 * (1 - 0.15))
σ ≈ 4.29
Then, the z-score corresponding to the proportion of 0.21 is:
z = (x - μ) / σ
z = (0.21 - 0.15) / 4.29
z ≈ 0.014
Using a calculator, the probability of a z-score of 0.014 is approximately 0.504.
Hence, the probability of obtaining a proportion at least 0.21, is:
Probability = 1 - 0.504
Probability ≈ 0.496
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here is my algebra 13 homework screenshot. can somebody please help me! QUICK
The function which has a range of real numbers is f(x) = -x + 2
Range is the set of the values that the function obtains this set is the values that the function obtains when we put an x value in the function.
In f(x) = -x + 2 when we put any value of x we get real number so the function range is ( -∞ , ∞ )
In g(x) = -x² when we put any value of x we get all negative number function range is (-∞ , 0]
In h(x) = [tex]2^{x}[/tex] + 1 when we put any value of x we get all positive number so the function range is (1 , ∞)
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Can someone please answer and provide an explanation for these problems?
The distance between each pair of points include the following:
44. 2.8 units.
45. 5.8 units.
46. 12.0 units.
47. 16.6 units.
48. 7.1 units.
49. 4.5 units.
How to determine the distance between two end points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Question 44.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(3 - 1)² + (2 - 4)²]
Distance = √[(2)² + (-2)²]
Distance = √8
Distance = 2.8 units.
Question 45.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 + 7)² + (0 - 3)²]
Distance = √[(5)² + (-3)²]
Distance = √34
Distance = 5.8 units.
Question 46.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-6 - 2)² + (-2 - 7)²]
Distance = √[(-8)² + (-9)²]
Distance = √145
Distance = 12.0 units.
Question 47.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(1 - 8)² + (-8 - 7)²]
Distance = √[(-7)² + (-15)²]
Distance = √274
Distance = 16.6 units.
Question 48.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-5 - 2)² + (-4 + 5)²]
Distance = √[(-7)² + (1)²]
Distance = √50
Distance = 7.1 units.
Question 49.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 - 3)² + (5 - 1)²]
Distance = √[(2)² + (4)²]
Distance = √20
Distance = 4.5 units.
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Which system is equivalent to
O
O
O
[5-x=9x²
y = 5-x
[y=9y²-90y+225
1x=y-5
[5+x=9x²
y = 5+x
y = 3x
x+3x=5
y=9x²?
x+y=5
The first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The system that is equivalent to:
O
O
O
[5-x=9x²
y = 5-x
is: x = -2, y = 7
In the given system, the first equation is a quadratic equation, and the second equation is a linear equation. The solution to the system is x = -2 and y = 7, which satisfies both equations.
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Work out the integer values
Please help, I attached a photo.
Step by step explanation if possible :)))
The integers that satisfy the inequality are -1, 0, 1, and 2.
To find the integer values that satisfy the inequality x < 6/(x - 1), we can start by analyzing the domain of the expression.
First, note that the denominator (x - 1) cannot be equal to zero since division by zero is undefined. Therefore, we must exclude x = 1 from the domain.
Next, consider the sign of the expression 6/(x - 1). When the denominator (x - 1) is positive, the expression will be positive. Similarly, when the denominator is negative, the expression will be negative.
Considering the inequality x < 6/(x - 1), we can divide the problem into two cases based on the sign of (x - 1):
Case 1: (x - 1) > 0
In this case, the expression 6/(x - 1) is positive. To satisfy the inequality x < 6/(x - 1), x must be less than the positive value of 6/(x - 1). Since the denominator is positive, we can drop the absolute value sign. Therefore, the inequality becomes:
x < 6/(x - 1)
Case 2: (x - 1) < 0
In this case, the expression 6/(x - 1) is negative. To satisfy the inequality x < 6/(x - 1), x must be greater than the negative value of 6/(x - 1). Since the denominator is negative, we need to flip the inequality sign and change the direction. Therefore, the inequality becomes:
x > 6/(x - 1)
Now, let's solve each case separately:
Case 1: (x - 1) > 0
Since the denominator (x - 1) is positive, we can multiply both sides of the inequality by (x - 1) without changing the direction of the inequality. This gives:
x(x - 1) < 6
Expanding the left side:
x² - x < 6
Rearranging the inequality:
x² - x - 6 < 0
Now we can factorize the quadratic:
(x - 3)(x + 2) < 0
To determine the solution, we need to consider the sign of the expression for different intervals:
When x < -2, both factors are negative, so the expression is positive.
When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.
When x > 3, both factors are positive, so the expression is positive.
Therefore, the solution to Case 1 is:
-2 < x < 3
Case 2: (x - 1) < 0
Since the denominator (x - 1) is negative, we need to flip the inequality sign. Multiplying both sides of the inequality by (x - 1) changes the direction of the inequality. This gives:
x(x - 1) > 6
Expanding the left side:
x² - x > 6
Rearranging the inequality:
x² - x - 6 > 0
Factoring the quadratic:
(x - 3)(x + 2) > 0
Considering the sign of the expression for different intervals:
When x < -2, both factors are negative, so the expression is positive.
When -2 < x < 3, the first factor (x - 3) is negative, and the second factor (x + 2) is positive, so the expression is negative.
When x > 3, both factors are positive, so the expression is positive.
Therefore, there are no solutions in Case 2.
Combining the solutions from both cases, we find that the integer values satisfying the inequality x < 6/(x - 1) are:
-2 < x < 3
In other words, the integers that satisfy the inequality are -1, 0, 1, and 2.
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Me mason likes to work around the yard during the weekends
A) One way to write mixed fractions [tex]6\frac{2}{4} \\[/tex] is 3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]
B) Saturday: 3 to 4 hours work = trim bushes and weed garden
Sunday: 4 to 5 hour work = paint sheet and mow lawn
A) [tex]6\frac{2}{4} \\[/tex] can be written as a simple fraction 6 + [tex]\frac{2}{4}[/tex]
This can be further broken into and written as
3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]
B) Saturday : 3 to 4 hours of work
Trim bushes + Weed garden
[tex]1\frac{1}{6} +2\frac{2}{6}[/tex]
1 + [tex]\frac{1}{6}[/tex] + 2+ [tex]\frac{2}{6}\\[/tex]
3 + [tex]\frac{3}{6}[/tex]
3 + [tex]\frac{1}{2}[/tex]
[tex]3\frac{1}{2}[/tex]
Sunday: 4 to 5 hours of work
Paint sheet + mow lawn
[tex]1\frac{3}{6} +3 \frac{4}{6}[/tex]
1 + 3 + [tex]\frac{3}{6} +\frac{4}{6}[/tex]
4 + [tex]\frac{8}{6}[/tex]
[tex]4\frac{8}{6}[/tex]
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The Given question is incomplete the complete question is :
Mr. mason likes to work around the yard during the weekends
can some one
factor 7a10 - 112a2
The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
How to find the factor 7a10 - 112a2To factor the expression [tex]7a^{10} - 112a^2[/tex] we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:
The coefficients 7 and 112 have a common factor of 7.
The lowest power of "a" in each term.
In this case, the lowest power of "a" is 2.
Factoring out [tex]7a^2[/tex] from both terms, we get:
[tex]7a^2(a^8 - 16)[/tex]
Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
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PLEASE HELP ME ITS DUE TODAY!!!
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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how do I change 1/4 to a percentage .
Answer: You divide it, get your answer, move the decimal point to the right twice, and that's you're percent.
Step-by-step explanation:
1/4=.25
.25 > 25%
Answer:
The answer is 25%
Step-by-step explanation:
To change decimal to percentage multiply by 100
1/4×100%
=25%
Write a sin function that has a midline of y=3, and amplitude of 2, and a period of 3/4.
The required sine function is
y = 2 sin (3π/4 (x) + 3
For given function,
A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4
A = 2
T = 3π/4
Since we know
The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
In this case, the midline is 3
⇒ D = 3
Using the generalized equation of sine function,
y = A sin (B (x + C)) + D
y = 2 sin (3π/4 (x + 0) + 3
y = 2 sin (3π/4 (x) + 3
Therefore, the required sine function is
y = 2 sin (3π/4 (x) + 3
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6
Select ALL the true statements about 388.33.
The value of the tens digit, 80, is 10 times the value of the ones digit, 8.
The value of the hundredths digit, 0.03, is 10 times the value of the tenths
digit, 0.3.
C. The value of the ones digit, 8, is the value of the tens digit, 80.
D.
The value of the hundredths digit, 0.03, is to the value of the tenths
digit, 0.3.
A.
B.
E. O The value of the tenths digit, 0.3, is 10 times the value of the hundredths
digit, 0.03.
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
We have,
The statement "The value of the tens digit, 80, is 10 times the value of the one's digit, 8" is incorrect. The tens digit is actually 3, not 80.
The statement "The value of the hundredths digit, 0.03, is 10 times the value of the tenths digit, 0.3" is true.
The hundredth digit is 3 times smaller than the tenth digit, which means that the tenth digit is 10 times larger than the hundredth digit.
The statement "The value of the one's digit, 8, is the value of the tens digit, 80" is incorrect.
The tens digit is 3, not 80.
The statement "The value of the hundredths digit, 0.03, is to the value of the tenths digit, 0.3" is unclear and not a proper comparison, so it cannot be determined whether it is true or false.
Thus,
The true statements about 388.33 are:
The value of the hundredth digit, 0.03, is 10 times the value of the tenth digit, 0.3.
The value of the tenth digit, 0.3, is 10 times the value of the hundredth digit, 0.03.
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Find the slope of the line.
A. 3/2
B. -2/3
C. 4/3
D. -3/4
Answer:
-3/4, answer D
Step-by-step explanation:
Slope = rise/run. The equation is (y2-y1)/(x2-x1).
So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.
slope = (2-(-4))/(-2-6)
slope = (2+4)/(-2-6)
slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.
slope = -3/4
Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.
Answer:
Step-by-step explanation:
Use 2 points from the line: (-2, 2) and (6, -4)
slope = y2 -y1 = -4 - 2 = -6 = - 3
x2 - x1 6 - -2 8 4
The slope is choice D -3/4
A family drove 592 miles during their trip this summer. In the winter they drove 376 miles during their trip . How many more miles did the family drive over the summer than over the winter . Explain !
Answer: 216
Step-by-step explanation:
592-376
592-300= 292
292-70= 222
222-6= 216
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
Polygon D is similar to polygon ABCD.
Dana had to pay her friend $900, 3 months ago and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month, what single payment would settle both payments today?
Dana had to pay her friend $900, 3 months ago, and she has to pay $580 in 3 months. If her friend was charging her an interest rate of 1.50% per month. $1499.45, single payment would settle both payments today.
Given:
The principal of a loan is the original sum borrowed.The interest rate per period is known as rate.The loan's duration is expressed in terms of time.Simple interest = Principal × Rate × Time
Simple interest = $900 × 0.015 × 3
Simple interest = $40.50
Present Value = Future Value / (1 + Rate x Time)
Present Value = $580 / (1 + 0.015 × 3)
Present Value = $580 / 1.045
Present Value = $558.95
Total amount $580 loan is $558.95.
Total amount owed = $940.50 + $558.95
Total amount owed = $1499.45
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
It would take 21 weeks for the population to surpass 16,000.
The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.
For the population to surpass 16,000, we can set up the following equation:
15,000 + 2500 sin(πt/52) = 16,000
Subtracting 15,000 from both sides, we get:
2500 sin(πt/52) = 1000
Dividing both sides by 2500, we get:
sin(πt/52) = 0.4
We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:
πt/52 = sin⁻¹(0.4)
Multiplying both sides by 52/π, we get:
t = (52/π) sin⁻¹(0.4)
Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.
t = (52/π) (0.4115)
t = 21.02
Therefore, it would take 21 weeks for the population to surpass 16,000.
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{NEEDED A.S.A.P.} What is the surface area of the square pyramid represented by the net?
Enter your answer in the box.
[25 Point Reward.]
Answer:
4(1/2)(3)(5) + (3^2) = 30 + 9 = 39 ft^2
Please help with this I am struggling bad thank you all
p = speed of the plain in still air
w = speed of the wind
when going headwind, the plane is not really going "p" fast, is really going slower, is going "p - w", because the wind is subtracting speed from it, likewise, when going with the wind the plane is not going "p" fast, is really going faster, is going "p + w", because the wind is adding its speed to it.
we also know that on the way over he flew 2000 miles and on the way back he flew again the same 2000 miles back.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&2000&p-w&10\\ \textit{with the wind}&2000&p+w&8 \end{array}\hspace{3.5em} \begin{cases} 2000=(p-w)(10)\\\\ 2000=(p+w)(8) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{2000=(p-w)10}\implies \cfrac{2000}{10}=p-2\implies 200=p-w\implies \boxed{200+w=p} \\\\\\ \stackrel{\textit{using the 2nd equation}}{2000=(p+w)8}\implies \cfrac{2000}{8}=p+w\implies 250=p+w \\\\\\ \stackrel{\textit{substituting "p" from above}}{250=(200+w)+w}\implies 250=200+2w\implies 50=2w\implies \cfrac{50}{2}=w \\\\\\ \boxed{25=w}\hspace{10em}\stackrel{ 200+(25) }{\boxed{225=p}}[/tex]
Find the simple interest owed if $340 is borrowed at 6.6% for 9 years
The simple interest owed on a $340 loan at 6.6% interest for 9 years is $201.96.
How to find simple interest?The simple interest formula is expressed as;
I = P × r × t
Where I is interest, P is principal, r is interest rate and t is time.
Given that:
Principal P = $340
Interest Rate r = 6.6%
Time t = 9 years
First convert the interest rate from percent to decimal:
Rate = r/100
Rate = 6.6/100
Rate = 0.066
Now, plug the values into the above formula and solve for interest.
I = P × r × t
I = $340 × 0.066 × 9
I = $201.96
Therefore, the simple interest is $201.96.
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A certain manufacturing concern has total cost function C = 15+9x-6x²+x? Find x, when the total
Answer:
Step-by-step explanation:
Total cost function, C = 15+9x-6x²+x
By differentiation,
dc/dx= 9-12x²+1
but
dc/dx= 0
9-12x²+1 = 0
-12x = -10
x=10/12
x=5/6
The EPA fuel economy estimates for automobiles models tested recently found them to be
normally distributed with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What is
the percentile rank of an automobile that has a fuel economy of 35 mpg?
90th Percentile
O 5th Percentile
O 95th Percentile
10th Percentile
Step-by-step explanation:
(35-24.8) / 6.2 = z-score of + 1.645 corresponding to .9495 =
~ 95th percentile
