Answer:
r = 8%
Step-by-step explanation:
Given that,
Interest, I = $24
Principal, P = $1200
Time, t = 90 days = 90/360 = 1/4 years
We need to find the rate.
We know that,
The simple interest is given by :
[tex]I=\dfrac{Prt}{100}[/tex]
Put all the values,
[tex]r=\dfrac{100I}{Pt}\\\\r=\dfrac{100\times 24}{1200\times \dfrac{1}{4}}\\\\r=8\%[/tex]
So, the rate is 8%.
A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 15 mph, find the speed of the plane in still air.
Answer:
161 speed of plain in still air
Mark in brainlist
If 5^3b-1 = 5^b-3, what is the value of b?
-2
-1
1
2
Answer:
3b-1 = b-3
2b = 4
b = 2
Step-by-step explanation:
parabola
Given that tanθ= [tex]-\frac{9}{4}[/tex] and [tex]\frac{\pi }{2\\}[/tex]<θ<π , find the exact values of the trigonometric functions.
9514 1404 393
Answer:
sin(θ) = (9√97)/97cos(θ) = (-4√97)/97csc(θ) = (√97)/9sec(θ) = (-√97)/4cot(θ) = -4/9Step-by-step explanation:
The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.
tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16 ⇒ sec = -(1/4)√97
cot(θ) = 1/tan(θ) = -4/9
csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81 ⇒ csc = (1/9)√97
sin(θ) = 1/csc(θ) = (9√97)/97
cos(θ) = 1/sec(θ) = (-4√97)/97
HELP MATH ANSWER QUESTION
Answer:
Last one.
Step-by-step explanation:
[tex]\sqrt{3}[/tex] is used in 30-60-90 triangles
[tex]\sqrt{2}[/tex] is used in 45-45-90 triangles
Base is x, leg is x[tex]\sqrt{3}[/tex], hypotenuse is 2x
Answer:
x = 20 ; y= 10√3
Step-by-step explanation:
30, 60 , 90 triangle ratio is
Side opposite to 30 is a
a = AC = 10
Side opposite to 60 is a[tex]\sqrt{3}[/tex]
AB = a[tex]\sqrt{3}[/tex] = 10√3
Side opposite to 90 is 2a
BC = 2a = 2* 10 = 20
Use the limit definition of the derivative to find the instantaneous rate of change of
f(x)=5x^2+3x+3 at x=4
[tex]f'(4) = 43[/tex]
Explanation:
Given: [tex]f(x)=5x^2 + 3x + 3[/tex]
[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]
Note that
[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]
[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]
[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]
Substituting the above equation into the expression for f'(x), we can then write f'(x) as
[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]
[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]
[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]
Therefore,
[tex]f'(4) = 10(4) + 3 = 43[/tex]
Match the metric measurement on the left with an equivalent unit of measurement on the right
Answer:
ans:
0.3 hectoliter = 3000 centiliters0.03 liter = 30 milliliterMatch the metric measurement on the left with an equivalent unit of measurement on the right are as follows;
0.3 hectoliter 3 deciliters
0.03 liters 30 milliliters
30 centimeter 3 Deciliters
3000 Milliliters 0.3 Decaliters
What is the unit measurement?A standard unit of measurement is a quantifiable language that describes the magnitude of the quantity.
Match the metric measurement on the left with an equivalent unit of measurement on the right is determined in the following steps given below.
1. 0.3 hectoliter = 0.3 × 10 = 3 deciliters
2. 0.03 liters = 0.03 × 1000 = 30 mililiters
3. 3 Centiliters = 0.3 Deciliters then 30 centimeter = 3 Deciliters
4. 3000 Milliliters = 0.3 Decaliters
Learn more about unit measurement here;
https://brainly.com/question/15402847
#SPJ2
please help thx steps too
Step-by-step explanation:
IN first triangle multiplier factor is 4
and IN second triangle multiplier factor is
[tex] \frac{3}{2} [/tex]
What is the domain of the function y=3 sqrt x?
Answer:
Step-by-step explanation:
y=3√x
domain : all real values≥0
Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?
To maximize his income, Dr. Lum should teach_______classes for Hilltop College and __________classes for Serra College. His maximum income would be________.
Answer:
z (max) = 34500 $
x₁ = 2
x₂ = 3
Step-by-step explanation:
Hilltop College
3 hours per week preparing lessons and grading papers
Serra College
4 hours per week preparing lessons and grading papers
Total hours to spend per week preparing lessons 18
Let´s call x₁ numbers of class at Hilltop College
and x₂ numbers of class at Serra College then:
Objective function
z = 6000*x₁ + 7500*x₂
Constraints:
1.- x₁ + x₂ ≤ 5 the total number of class
2.- 3*x₁ + 4*x₂ ≤ 18
3. General constraints x₁ ≥ 0 x₂ ≥ 0 integers
After 6 iteration optimal solution is: From on-line solver
z (max) = 34500 $
x₁ = 2
x₂ = 3
A bag contains 9 red marbles, 6 white marbles, and 8 blue marbles. You draw 4 marbles out at random, without replacement. Find the following probabilities and round to 4 decimal places.
a. The probability that all the marbles are red is
b. The probability that none of the marbles are red is
Step-by-step explanation:
here are the answers bae. Feel free to ask for more
The list price on slacks is $22, and the list price on jumpers is $37. If Petit’s Clothing Store orders 30 pairs of slacks and 40 jumpers at a discount rate of 11%, what is the trade discount on the purchase?
Answer: $235.4
Step-by-step explanation:
Given
Price list on slacks is $22
Price list on jumpers is $37
Store ordered 30 pairs of slacks and 40 Jumpers
Total price becomes
[tex]\Rightarrow 22\times 30+37\times 40\\\Rightarrow \$2140[/tex]
for a discount of 11%
Trade discount is [tex]2140\times 11\%[/tex]
[tex]\Rightarrow 2140\times 0.11\\\Rightarrow \$235.4[/tex]
As preparation for designing a new line of business wear, a clothing manufacturer asked a large sample of department store customers, "What is your favorite
color of dress shirt?" The ple chart below summarizes their responses.
(a) Which color was chosen by approximately one fourth of
the customers?
Answer:
white
Step-by-step explanation:
if you cut the shape in half both ways it makes white take up a fourth.
Consider random samples of size 86 drawn from population A with proportion 0.43 and random samples of size 60 drawn from population B with proportion 0.15
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
(b) Are the sample sizes large enough for the Central Limit Theorem toa
Yes or No?
Answer:
a) The standard error is s = 0.071.
b) Yes, as both sample sizes are above 30.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Samples of size 86 drawn from population A with proportion 0.43
This means that [tex]n = 86, p = 0.43[/tex]. So:
[tex]s_A = \sqrt{\frac{0.43*0.57}{86}} = 0.0534[/tex]
Samples of size 60 drawn from population B with proportion 0.15:
This means that [tex]n = 60, p = 0.15[/tex]. So:
[tex]s_B = \sqrt{\frac{0.15*0.85}{60}} = 0.0461[/tex]
(a) Find the standard error of the distribution of differences in sample proportions A - B Round your answer for the standard error to three decimal places. Standard error=
This is:
[tex]s = \sqrt{s_A^2 + s_B^2}[/tex]
[tex]s = \sqrt{(0.0534)^2 + (0.0461)^2}[/tex]
[tex]s = 0.071[/tex]
The standard error is s = 0.071.
(b) Are the sample sizes large enough for the Central Limit Theorem. Yes or No?
Yes, as both sample sizes are above 30.
Can someone please help me
Answer:
8,889
Step-by-step explanation:
1 twig = 10 leaves
1 branch = 10 twigs = 100 leaves
1 trunk = 10 branches = 1000 leaves
1 tree = 10 trunks = 10,000 leaves
The complete tree has 10,000 leaves
The woodcutter cut off:
1 trunk = 1000 leaves
1 branch = 100 leaves
1 twig = 10 leaves
1 leaf
Total number of leaves that were cut:
1000 + 100 + 10 + 1 = 1111
Leaves left on tree:
10,000 - 1,111 = 8,889
Arrange the following numbers in order from smallest to largest. 0.89, 0.098 ,0.98
Answer:
0.098 , 0.89, 0.98
Step-by-step explanation:
0.098 is the smallest, 0.98 is the closest to 1 so it's the biggest
On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units.
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Yes, because corresponding sides are parallel and have lengths in the ratio Four-thirds
Yes, because both figures are rectangles and all rectangles are similar.
No, because the center of dilation is not at (0, 0).
No, because corresponding sides have different slopes.
Answer:
im doing the same one, i believe it is D
Step-by-step explanation:
Answer:
a- yes because corresponding sides are parallel and have lengths in the ration 4/3
Step-by-step explanation:
just did the test
What is the future value of a R 75 000 deposit made every 6 months for 3 years using an annual rate of 10% compounded semi-annually?
Answer:
The future value is: RS 132867.075
Step-by-step explanation:
Given
[tex]PV = 75000[/tex] --- present value
[tex]r = 10\%[/tex] --- annual rate
[tex]n = 6[/tex] --- number of times compounded (3 years/ 6 months)
Required
The future value
This is calculated as:
[tex]FV =PV * (1 + r)^n[/tex]
[tex]FV = 75000 * (1 + 10\%)^6[/tex]
[tex]FV = 75000 * (1 + 0.10)^6[/tex]
[tex]FV = 75000 * (1.10)^6[/tex]
[tex]FV = 132867.075[/tex]
Hence, the future value is: RS 132867.075
|x| =3 means that the distance between x and 0 is 3 / true or false
Answer:
True
Step-by-step explanation:
if |x| is 3 then x is either -3 or 3. Either way, the distance from 0 is 3.
Hole this helps! :)
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
The sample space,S,of a coin being tossed three times is shown below, where H and T denote the coin landing on heads and tails respectively.
Answer: Bottom left corner
=======================================================
Explanation:
There are only four possible outcomes here
A) we get all tails, ie getting 0 headsB) we get exactly one head (the rest tails)C) we get exactly 2 headsD) we get all three headsBased on this so far, the answer is either the table in the bottom left corner or in the top right corner. It's not possible for X = 4 since we only flipped 3 coins.
The probability of case A happening is 1/8 since we have 1 scenario that's all tails (TTT) out of 8 items in the sample space. Similarly, the probability for case D is the same probability. We only have one HHH out of 8 total items.
The probabilities of cases B and C are the same. Both are 3/8. Note that for case B, we have HTT, THT, TTH which is three occurrences in which we get exactly 1 head. So that explains the 3/8.
ASAP!!! There are three marbles in a bag. One is red and two are black. What is the probability of picking a red marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answer:
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Step-by-step explanation:
Hey there!
The probability of first getting a red marble is 1/3 since we have 1 red marble out of 2 + 1 = 3 total.
We put the marble back. The probability of then choosing a black marble is 2/3, since we have 2 black marbles out of 3 total.
So we get 1/3 * 2/3 = 2/9
The probability of picking a red marble first then replacing it and getting a black marble is 2/9. (The last option.)
Hope this helps, please mark brainliest if possible. Have a nice day. :)
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Shari drew several lines. Which lines are perpendicular to AC ?
Select all that apply.
How is the graph of y = 8x2 − 1 different from the graph of y = 8x2?
It is shifted 1 unit down.
It is shifted 1 unit to the right.
It is shifted 1 unit to the left.
It is shifted 1 unit up.
Answer:
since it's the lhs we are concerned about, i. e., Y axis, so it must be either up or down. now look at the question, it says 8x2 - (1), it means one lower value of y i. e., 1 unit down
Answer:It is shifted 1 unit down.
Step-by-step explanation:
please help out
3/2÷5
Answer:
0.3Step-by-step explanation:
[tex] \frac{3}{2} \div 5[/tex]
[tex] = \frac{3}{2} \times \frac{1}{5} [/tex]
[tex] = \frac{3}{10} [/tex]
= 0.3 (Ans)
Answer:
3/10
Step-by-step explanation:
3/2÷5
3/2÷5/1
3/2÷10/2 ( LCM of denominators)
3/2×2/10 ( Reciprocal of 10/2)
3/10 (Cancelling 2 by 2)
How to Factor 4n^3-49n
Answer:
n (2n-7) (2n+7)
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
the probabilities that Kojo and Adwoa will pass an examination are 3/4 and 3/5 respectively. Find the probability that both will fail the examination
An College student complained that the cost of textbooks was too high. She randomly surveyed 36 other students and found that the mean amount of money spent for textbooks was $121.60. If the standard deviation of the population was $6.36, find the best point estimate. Show your work.
Answer:
The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.
Step-by-step explanation:
Best point estimate:
The best point estimate of a population mean is the sample mean.
In this question:
The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
Assume that you take out a $2000 loan for 30 months at 8% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
$
Answer:
13.33
Step-by-step explanation:
Because it's only payment one we can easily figure out the interest portion
we first need the effective rate
.08/12= .006666667
We the just mulitply this by loan amount
2000*.006666667= 13.33
Step-by-step explanation:
its your answer
I hope it's help you
Consider the following data representing the price of plasma televisions (in dollars).
1325, 1266, 1123, 1233, 1387, 1249, 1120, 1140, 1347, 1337, 1402, 1259, 1421, 1351, 1452, 1277, 1309, 1232, 1112, 1243, 1429
Copy Data Price of Plasma Televisions (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency
1067–1126 1127–1186 1187–1246 1247–1306 1307–1366 1367–1426
Determine the class width of the classes listed in the frequency table.
Answer:
[tex]Width = 59[/tex]
Step-by-step explanation:
Given
The above data
Required
The class width
To do this, we simply calculate the difference between the class limits of any one of the classes.
Taking 1187–1246 as a point of reference, the class width is:
[tex]Width = 1246 - 1187[/tex]
[tex]Width = 59[/tex]
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side JK. Round your answer to nearest tenth if necessary,
Answer:
JK ≈ 12.3
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{FI}{JM}[/tex] = [tex]\frac{FG}{JK}[/tex] , substitute values
[tex]\frac{59}{26}[/tex] = [tex]\frac{28}{JK}[/tex] ( cross- multiply )
59 JK = 728 ( divide both sides by 59 )
JK ≈ 12.3 ( to the nearest tenth )
4. Write an equation for the line that is parallel to the given line and that passes
through the given point.
y = 5/2x-10;(-6,-29)
Answer:
[tex]y=\frac{5}{2}x-14[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]y=\frac{5}{2}x-10[/tex]
In the given equation, [tex]\frac{5}{2}[/tex] is in the place of m, making it the slope. Because parallel lines have the same slope, the line we're currently solving for therefore has a slope of [tex]\frac{5}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{5}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{5}{2}x+b[/tex]
Plug in the given point (-6,-29) and solve for b
[tex]-29=\frac{5}{2}(-6)+b[/tex]
Simplify -6 and 2
[tex]-29=\frac{5}{1}(-3)+b\\-29=(5)}(-3)+b\\-29=-15+b[/tex]
Add 15 to both sides to isolate b
[tex]-29+15=-15+b+15\\-14=b[/tex]
Therefore, the y-intercept is -14. Plug this back into [tex]y=\frac{5}{2}x+b[/tex]:
[tex]y=\frac{5}{2}x-14[/tex]
I hope this helps!
