Joseph borrows $10000 from his sister Katie at an annual interest rate of 10%. If the
interest is compounded twice a year, how much does he owe after 12 months? Give your answer in dollars.
Answer:
A = P ( 1 + r / n) ^( t * n)
where
A = the amt owed
P = amt borrowed
r = the interest rate as a decimal
n = the number of compoundings per year
t = the number of years
A = 10000 ( 1 + .10 / 2)^(2 *1) = 10000 ( 1.05)^2 = $11025
Step-by-step explanation:
If a product normal retails for $40, and a customer has a coupon for 15% off, what will the discounted price of the product be?
Answer:
$34
Step-by-step explanation:
price of the product = $40
coupon = 15% off
discount price = 15% of price of a product
=15/100 * $40
=$600/100
=$6
New price of the product = original price - discount
=$40 - $6
=$34
What is this function’s input if its output is 11?
f(x) = 2x + 5
Answer:
the input x is 3
Step-by-step explanation:
2x+5=11
2x=6
x=3
Factor completely, then place the factors in the proper location on the grid. a8 - 12a4 + 36
Answer:
[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]
What is the period of the graph of y = 5 sin (πx) + 4?
Answer:
I think it’s 2 hope my answer was good have a nice day as well
Step-by-step explanation:
The period of the given function y = 5 sin (πx) + 4 is π.
We have given that,
y = 5 sin (πx) + 4
We have to determine the period
What is the period?
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2π.
Therefore the period of the given function is π.
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If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?
Answer:
The correct answer is - 178.
Step-by-step explanation:
The standard deviation is a measure of the amount of dispersion in a set of values.
Given:
Mean of a normal distribution (m) = 154
Standard deviation (s) = 15
z-score = 1.6
Solution:
To find: value (x) that has a z-score of 1.6
z-score is given by = x-u/15
1.6*15 = x-154
=> 154+24 = x
x = 178
What is 5^-3?
Please I really need someone to explain to me what do you do when there is a negative sign in the exponent. Thank you :)
Answer: 1/125 or 0.008 (simplify 1.125 or should I do it?)
Step-by-step explanation:
Well, when there is a negative sign in the exponent you only move the negative exponents. Moving only negative exponents is recommended because using this rule, you multiply two exponents with the same base and add their powers.
Find the interest earned on $1,000 for 1 year at a 6% rate of interest when the interest is compounded quarterly.
Answer:
1060
Step-by-step explanation:
Find the value of x and show work
Answer:
20
Step-by-step explanation:
Differentiate the function. y = (2x - 5)^2 (5 - x)?
Answer:
[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x)
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor: [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4: [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative: [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x): [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms: [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor: [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!
Answer:
2, 3, 4, 7, 8, 10 I hope
Answers
Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent=================================================
Explanations:
As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).---------------
Acronyms
SSS = side side side
SAS = side angle side
ASA = angle side angle
AAS = angle angle side
Look at the illustration.
What is WX?
Answer:
O 0.5 units
Step-by-step explanation:
so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W'X' is:
W'X' = 3 units *(1/6) = 0.5 units
If you know two corresponding sides of two triangles and you know that the corresponding angles are equal, how can you find out if they are similar triangles? a. the other angles are proportional c. ratios of the sides will be equal b. the vertical angles will be congruent d. ratio of the sides will not be equal Please select the best answer from the choices provided A
Answer:
I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using
-SSS (side-side-side) which would tell you if all three corresponding sides are congruent
-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent
-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent
-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles
WILL MARK YOU IF YOU ANSWER SO PLEASE HELP
Answer:
x= 83
first take vertical opposite angle then take corresponding angles then you're done
Answer:
x value is 83 degree
because they both are alternate exterior angle
The volume of a cone with a diameter of 9 and a height of 120
Answer: 15268.1403 unit^3 (unit: cm,m,mm)
Step-by-step explanation:
volume of a cone= 1/2*pi*r^2*h
r= radius (unit: cm,m,mm)
h= perpendicular height (unit: cm,m,mm)
volume= 1/2*pi* (9)^2* 120 = 15268.1403 unit^3
what number must you add to complete the square? x^2+24x=50
Answer:
144
Step-by-step explanation:
Divide the b term which is 24 by 2
Gives you 12, then square it.
that's 144
formula for completing squares is [tex](b/2)^{2}[/tex]
100° - y А (x+2) units Match the values based on parallelogram ABCD, shown in the figure. length of BC value of y mZDAB value of I 56 4 44 2
Answer:
BC = 4 units
Value fo y = 44
∠DAB = 56°
Value of x = 2
Step-by-step explanation:
100 - y = 12 + y (opposite angles of parallelogram are equal)
2y = 88
y = 44
Similarly,
6-x = x+2 (opposite sides of parallelogram are equal)
2x = 4
x = 2
Last month Rudy’s Tacos sold 22 dinner specials. The next month they released a new commercial and sold 250% of last month’s dinners. How many dinner specials did they sell this month?
Answer:
the answer is 2
Step-by-step explanation: because 250 -22 is i dont even know
Answer:
55
Step-by-step explanation:
Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
Help me pls I don’t know how to do this
Answer:
[tex]radius=6.68cm[/tex]
Step-by-step explanation:
Formula to find radius:
[tex]r=\frac{C}{2\pi }[/tex]
[tex]r=42/2\pi[/tex]
[tex]r=42/2(3.14)[/tex]
[tex]r=6.68cm[/tex]
hope this helps......
What is the smallest number you should subtract from 456 to make it divisible by 9?
Solve for T: 10t-4x=3S Explanation plz
solve the following function 3x^{2x-7}=9.
Answer:
3x-2x+7=-9
We simplify the equation to the form, which is simple to understand
3x-2x+7=-9
We move all terms containing x to the left and all other terms to the right.
+3x-2x=-9-7
We simplify left and right side of the equation.
+1x=-16
We divide both sides of the equation by 1 to get x.
x=-16
76 is what percent of 79
Answer:
79
100
0.79%
76
100
0.76%
25. Approximate the sample variance and standard deviation given the following frequency distribution: Class Frequency 0–9 13 10–19 7 20–29 10 30–39 9 40–49 11
Sample variance = 228.408
Standard deviation = 15.113
Step-by-step explanation:The well formatted frequency table has been attached to this response.
To calculate the sample variance and standard deviation of the given grouped data, follow these steps:
i. Find the midpoint (m) of the class interval.
This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e
For class 0 - 9, we have
m = (0 + 9) / 2 = 4.5
For class 10 - 19, we have
m = (10 + 19) / 2 = 14.5
For class 20 - 29, we have
m = (20 + 29) / 2 = 24.5
For class 30 - 39, we have
m = (30 + 39) / 2 = 34.5
For class 40 - 49, we have
m = (40 + 49) / 2 = 44.5
This is shown in the third column of the attached table.
ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e
For class 0 - 9, we have
frequency (f) = 13
midpoint (m) = 4.5
=> f x m = 13 x 4.5 = 58.5
For class 10 - 19, we have
frequency (f) = 7
midpoint (m) = 14.5
=> f x m = 7 x 14.5 = 101.5
For class 20 - 29, we have
frequency (f) = 10
midpoint (m) = 24.5
=> f x m = 10 x 24.5 = 245
For class 30 - 39, we have
frequency (f) = 9
midpoint (m) = 34.5
=> f x m = 9 x 34.5 = 310.5
For class 40 - 49, we have
frequency (f) = 11
midpoint (m) = 44.5
=> f x m = 11 x 44.5 = 489.5
This is shown in the fourth column of the attached table.
iii. Calculate the mean (x) of the distribution i.e
This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e
x = ∑(f x m) ÷ ∑f
Where;
∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205
∑f = 13 + 7 + 10 + 9 + 11 = 50
=> x = 1205 ÷ 50
=> x = 24.1
Therefore, the mean is 24.1
This is shown on the fifth column of the attached table.
iv. Calculate the deviation of the midpoints from the mean.
This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint
For class 0 - 9, we have
midpoint (m) = 4.5
=> m - x = 4.5 - 24.1 = -19.6
For class 10 - 19, we have
midpoint (m) = 14.5
=> m - x = 14.5 - 24.1 = -9.6
For class 20 - 29, we have
midpoint (m) = 24.5
=> m - x = 24.5 - 24.1 = 0.4
For class 30 - 39, we have
midpoint (m) = 34.5
=> m - x = 34.5 - 24.1 = 10.4
For class 40 - 49, we have
midpoint (m) = 44.5
=> m - x = 44.5 - 24.1 = 20.4
This is shown on the sixth column of the attached table.
v. Find the square of each of the results in (iv) above.
This is done by finding (m-x)²
For class 0 - 9, we have
=> (m - x)² = (-19.6)² = 384.16
For class 10 - 19, we have
=> (m - x)² = (-9.6)² = 92.16
For class 20 - 29, we have
=> (m - x)² = (0.4)² = 0.16
For class 30 - 39, we have
=> (m - x)² = (10.4)² = 108.16
For class 40 - 49, we have
=> (m - x)² = (20.4)² = 416.16
This is shown on the seventh column of the attached table.
vi. Multiply each of the results in (v) above by their corresponding frequencies.
This is done by finding f(m-x)²
For class 0 - 9, we have
=> f(m - x)² = 13 x 384.16 = 4994.08
For class 10 - 19, we have
=> f(m - x)² = 7 x 92.16 = 645.12
For class 20 - 29, we have
=> f(m - x)² = 10 x 0.16 = 1.6
For class 30 - 39, we have
=> f(m - x)² = 9 x 108.16 = 973.44
For class 40 - 49, we have
=> f(m - x)² = 11 x 416.16 = 4577.76
This is shown on the eighth column of the attached table.
vi. Calculate the sample variance.
Variance σ², is calculated by using the following relation;
σ² = ∑f(m-x)² ÷ (∑f - 1)
This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.
∑f(m-x)² = sum of the results in (vi)
∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192
∑f - 1 = 50 - 1 = 49 {Remember that ∑f was calculated in (iii) above}
∴ σ² = 11192 ÷ 49 = 228.408
Therefore, the variance is 228.408
vii. Calculate the standard deviation
Standard deviation σ, is calculated by using the following relation;
σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]
This is done by taking the square root of the variance calculated above.
σ = [tex]\sqrt{228.408}[/tex]
σ = 15.113
Therefore, the standard deviation is 15.113
A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.
Answer:
The current value of the stamp collection is of $2,191.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A stamp collection is purchased for $1,000.
This means that [tex]P = 1000[/tex]
The rate of return on the stamp collection is 4% per year
This means that [tex]n = 1, r = 0.04[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]
[tex]A(t) = 1000(1.04)^{t}[/tex]
What is the current value of the stamp collection?
This is A(20). So
[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]
The current value of the stamp collection is of $2,191.
Answer:
Step-by-step explanation:
y = 1000(1+0.04)^20
y = 1000(1.04)^20
Rounded to the nearest hundredth
y = 1000(2.19)
y = $2190
Find the 23rd term of the arithmetic sequence with the terms a1 27 and d = 16.
Answer:
379
Step-by-step explanation:
a23 = 27 + (23-1)(16)
= 27 + (22)(16)
= 27 + 352
= 379
solve for x 6(x-3)=8(x-4)
Answer:
7=x
Step-by-step explanation:
6(x-3)=8(x-4)
Distribute
6x -18 = 8x-32
Subtract 6x from each side
6x-18 -6x = 8x-32-8x
-18 = 2x-32
Add 32 to each side
-18+32 = 2x-32+32
14 = 2x
Divide by 2
14/2 =2x/2
7=x
[tex]\sf\purple{x= 7}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
[tex]➺\:6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6x - 18 = 8x - 32[/tex]
[tex]➺ \: 6x - 8x = - 32 + 18[/tex]
[tex]➺ \: - 2x = - 14[/tex]
[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the value of [tex]x[/tex] is 7.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]
[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]
[tex]➺ \: 24 = 24[/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
This is for my brother’s test
What are the measures of L1 and L2? Show your work or explain your answers.
Answer:
angle 2 is 75°osjdiajsjoasnndosnsnd
Jill calls a plumber to her house to fix the leaking faucets . The plumber charges a one-time fee of $50 plus an additional $35 per hour of labor. What are the independent and dependent variables
Answer:
independent=$50
dependent=$35X
Step-by-step explanation:
50 is the independent variable because it doesn't change.
35X is the dependent variable because it does change.
In this scenario, the independent variable is the number of hours of labor and dependent variable is the total cost.
The independent variable is the number of hours. It is the variable that we can control or change.
The dependent variable is the total cost charged by the plumber.
It depends on the number of hours of labor and is determined by the plumber's fee structure, which includes a one-time fee of $50 plus $35 per hour of labor.
The total cost is calculated based on the number of hours of labor, making it the dependent variable in this situation.
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