Answer:
$1100 at 9%$1300 at 12%Step-by-step explanation:
The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.
Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...
1100x +1300(x+0.03) = 255
2400x +39 = 255 . . . simplify
2400x = 216 . . . . . . subtract 39
x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x
Rosa invested $1100 at 9%, and $1300 at 12%.
Which values from the set {-8, -6, -2, 0, 2, 4, 8} satisfy the following inequality?
he was never late negative to affirmative
The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.
Answer:
[tex]A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524[/tex]
Step-by-step explanation:
Use the Washer Method [tex]A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx[/tex] where [tex]R(x)[/tex] is the outer radius and [tex]r(x)[/tex] is the inner radius.
If we sketch out the graph, we see that [tex]y=1[/tex] intersects points [tex](1,1)[/tex] and [tex](3,1)[/tex], which will be our bounds of integration.
Here, our outer radius will be [tex]R(x)=(-1-1)=-2[/tex] and our inner radius will be [tex]r(x)=-1-\frac{1}{x}[/tex].
Thus, we can compute the integral and find the volume:
[tex]A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2} \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\[/tex]
[tex]A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524[/tex]
In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!
please help me no links
Answer:
1. 4
2. 39.3700787 (just round it up)
Area compound shapes
Step-by-step explanation:
the area is the sum of the top square of 9×9 and the bottom parallelogram.
we know the length of the parallelogram is still also the square side length : 9ft.
but we don't need to bother about the lengths of the inclined sides, as the area of a parallelogram is
baseline × height
and the height we can see on the right hand side, as the height of the total shape is 14ft. given that the square side length is 9ft, that leaves us with 14-9 = 5ft as the height of the parallelogram.
so, the area of the square is
9×9 = 81 ft²
the area of the parallelogram is
9×5 = 45 ft²
the total area is then
81 + 45 = 126 ft²
Jayla just measured her pet snake and found out that it is 3.8 inches long, which is 52% longer than the last time Jayla measured. How long was the pet snake last time?
The sum of two numbers is 35. The smaller number is 11 less than the larger number. What are the numbers?
Answer:
12 & 23
Step-by-step explanation:
Let's make both of the statements into equations by making the numbers x & y.
"The sum of two numbers is 35" which means the two numbers added together is 35. So, x + y = 35.
"The smaller number is 11 less than the larger number." Let's make x the smaller number. So, x = y - 11.
So our equations are x + y = 35 and x = y -11. Using substitution, we can plug in (y-11) for x in the first equation.
y + y - 11 = 35. Combine the (y + y) to get 2y - 11 = 35. Add 11 to both sides of the equation, to get 2y = 46. Divide both sides by 2 to get y = 23.
Now, we can substitute 23 for y in either one of the equations, but I'm going to use the second one. x = y - 11 or x = 23 - 11 which equals 12.
Your 2 numbers are 12 and 23. Hope this helps! :)
3. In the accompanying diagram, a rectangular container with the dimensions 10 inches by 15 inches by 20 inches is to
be filled with water, using a cylindrical cup whose radius is 2 inches and whose height is 5 inches. What is the maximum
number of full cups of water that can be placed into the container without the water overflowing?
The maximum number of full cups of water that can be placed into the container without the water overflowing is 47 cups
How to calculate volume?Volume of the container = 10 * 15 * 20 = 3000 in³
The volume of the cylinder is:
Volume of cylinder = π * radius² * height = π * 2² * 5 = 62.83 in³
Number of cups that can be placed in container = 3000 in³ / 62.83 in³ = 47.74
The maximum number of full cups of water that can be placed into the container without the water overflowing is 47 cups
Find out more on volume at: https://brainly.com/question/1972490
If you want to be 99% confident of estimating the population mean to within a sampling error of 14 and the standard deviation is assumed to be 14, what sample size
is required?
The sample size required is
(Round up to the nearest integer.)
In
Help me solve this
View an example
Get more help
Clear all
Check answer
Answer:
16641
Step-by-step explanation:
Thank you!
(4a^2/3 b^1/2)(2a^1/3 b^3/2)
Answer:
8ab^2
Step-by-step explanation:
(4a^2/3 x 2a^1/3)(b^1/2 x b^3/2)
8a^(2/3+1/3) x b^(1/2+3/2) = 8a^1 x b^2
The length of the base of an isosceles triangle is x. The length of a leg is 2x - 2. The perimeter of the triangle is 71. Find
Answer:
x = 15
Step-by-step explanation:
x + 2x - 2 + 2x - 2 = 71
Solve for x, you get 15.
a) Work out
41/7 + 1 1/2
Answer:
11 5/4
Step-by-step explanation:
make the denominator the same then add.the common factor of 2 and 7 is 14 so make all the denominator to 14 then u can add.thus having the answer
What is the area of this figure?
[tex]a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\ [/tex]
[tex]a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\ [/tex]
[tex]a = 9 + \frac{33}{2} + 33 \\ [/tex]
[tex]a = 9 + 16.5 + 33[/tex]
[tex]a = 25.5 + 33[/tex]
[tex]a = 58.5 \: \: {ft}^{2} [/tex]
Solve the equation:
1. |x-7|=8
2. |x-9|=-14
Answer:
1. [tex]x=-1; x=15[/tex]
2. Impossible
Step-by-step explanation:
About #1.
There are two ways of reasoning.
Algebrically, you split the absolute value in two based on the sign of the quantity [tex]x-7[/tex]
[tex]x-7 = 8; x\ge7\\x=15\\x-7=-8; x < 7\\x=-1[/tex]
Geometrically, and it's a personal preference of mine, you're asking to find the numbers that are 8 units away from 7. One is to the right (15), and the other is to the left (-1).
#2 is impossible. The modulus of a number is by definition non negative, so it can never be equal to a negative number.
7 3/5 - 6 3/5
Pls help i can't do dis math
Step-by-step explanation:
[tex] = 7 \times \frac{3}{5} - 6 \times \frac{3}{5} \\ = \frac{7 \times 5 + 3}{5} - \frac{6 \times 5 + 3}{5} \\ = \frac{38}{5} - \frac{33}{5} \\ = \frac{38 - 33}{5} \\ = \frac{5}{5} [/tex]
Now convert into lowest term
[tex] \frac{1}{1} [/tex]
1/1 is the answer ....
What is the mean of the data set?
21.2, 15.3, 20.5, 16.8, 30.2
Question 1 options:
19.2
20.8
21.5
Answer:
B. 20.8 (second option)Step-by-step explanation:
The mean is calculated by adding up their values, and then dividing them into elements of a set.
All of them should first be added together.
21.2+15.3+20.5+16.8+30.2
Solve.
[tex]\sf{21.2+15.3+20.5+16.8+30.2=104}[/tex]
The sum of the data set is 104.
The number of terms in the data set is n=5.
Therefore, the mean of the data set is 20.8, which is our answer.
I hope this helps you! Let me know if my answer is wrong or not.
find rate
a)the interest of Re.1 of 1 month is 1 paisa.
b)the interest of re.1 of 1 month is 2 paisa
Step-by-step explanation:
A.) Correct Answer: 12%
Given , Principle = ₹ 1 , Time = 1 month = ( 1 / 12 ) year and SI = 1 paisa = ₹ ( 1 / 100 )
As we know that ,
Rate =SI × 100Principal × Time
Rate =(1 ÷ 100) × 100= 12% p.a.1 × (1 ÷ 12)
B.) Correct Answer:
Answer:
See below ↓
Step-by-step explanation:
a) I = Prt
r = I/Ptr = 0.01/1x(1/12)r = 0.12r = 12%b)
r = I/Ptr = 0.02/1x(1/12)r = 0.24r = 24%Elise is in a challenge with her gym class to run a total of 200 miles in one
school year. In the first month she ran 18 miles. If she wants to split the
remaining amount of miles over the
next seven months, how many miles will
she run each month?
Show your work.
Question
The sum of four times a number and two is 14. Find the number.
Answer:3
Step-by-step explanation:let the number be x
4x+2=14
4x=14-2
4x=12
divide both sides by 4
4x/4=12/4
x=3
At a student café, there are equal numbers of two types of customers with the following values. The café owner cannot distinguish between the two types of students because many students without early classes arrive early anyway (i.e., she cannot price-discriminate).
Students with Early Classes
Students without Early Classes
Coffee 73 63
Banana 53 103
The marginal cost of coffee is 5 and the marginal cost of a banana is 20.
The café owner is considering three pricing strategies:
1. Mixed bundling: Price bundle of coffee and a banana for 166, or just a coffee for 73.
2. Price separately: Offer coffee at 63, price a banana at 103.
3. Bundle only: Coffee and a banana for 126. Do not offer goods separately.
Assume that if the price of an item or bundle is no more than exactly equal to a student's willingness to pay, then the student will purchase the item or bundle.
For simplicity, assume there is just one student with an early class, and one student without an early class.
Price Strategy
Revenue from Pricing Strategy
Cost from Pricing Strategy
Profit from Pricing Strategy
1. Mixed Bundling
$
$
$
2. Price Separately
$
$
$
3. Bundle Only
$
$
$
Pricing strategy yields the highest profit for the café owner.
Based on the prices, the willingness to pay of the students and the costs, the profits will be:
Mixed bundling = 209.Price separately = 199.Bundle Only = 202.The pricing strategy that yields the highest profit is the Mixed bundling strategy.
What is the profit from Mixed bundling?First find the willingness to pay for both the students with early classes and those without.
Student with early classes: Students without early classes:
= 73 + 53 = 63 + 103
= 126 = 166
At a mixed bundling price of 166, only students without early classes will be able to afford the bundle as their willingness to pay is 166.
Student with early classes will only take the coffee at 73 because their willingness to pay of 126 is lower than the 166 bundle price.
Profit is:
= (Bundle price + Coffee price) - (Marginal cost of two coffees + Marginal cost of banana)
= (166 + 73) - (2 x 5 + 20)
= 209
What is the profit from pricing separately?At separate only pricing students without early classes will be able to afford the both things at 166.
Student with early classes will only take the coffee at 63 because their willingness to pay of 126 won't allow them to take both items.
Profit:
= (63 + 63 + 103) - (2 x 5+ 20)
= 199
What is the profit from price separately?At a bundle only price of 126, both the students with early classes and those without early classes will be able to afford the bundle as their willingness to pay, match the price.
Profit will be:
= (126 + 126) - (2 x 5 ) for coffee - (2 x 20) for bananas
= 202
In conclusion, the woman should go with the Mixed bundling as it gives the highest profit of 209.
Find out more on pricing strategies at https://brainly.com/question/7303679.
given determinant of a (a b c,d e f ,g h i) is -2 find determinant of ( g h i ,a b c ,d e f)
ANSWER:-
-2
Step-by-step explanation:
(abc, def, ghi) is -2
BRAINLIEST AND 100 POINTS!
The equation yˆ=−5.131x2+31.821x−3.333 approximates the number of people standing in line to catch a commuter train x hour after 5 a.m.
What is the best estimate for the number of people in line at 7 a.m.?
23
27
32
40
Answer:
The answer is 40. I'm 100% sure.
Answer:
D.40
Step-by-step explanation:
what is the parallelogram base b?
Answer:
10
Step-by-step explanation:
The area if a parallelogram is given by the equation, Area = base * height
In this case, area = 200, and the actual height = 20
So, let's say the base is x
Plug these values in to the Area equation
200 = 20 * x
200 = 20x
Divide both sides by 20 to get x alone
200 / 20 = 20x / 20
10 = x
The base is 10
Find the measures of the interior angles?
Answer:
Angle C = 35
Step-by-step explanation:
Angles A and B are already given to you, so I will not be explaining how to find them. If you have any questions, let me know.
There are 2 ways to solve this problem; you can either use the sum of the interior angles or isosceles triangles.
Sum of Interior Angles
The interior angles of all triangles equal 180 degrees. We can use this information to create an equation.
First, set up the equation.[tex]110+35+x=180[/tex]Then, combine like terms.[tex]145+x=180[/tex]Next, subtract 145 from both sides[tex]x=35[/tex]This means that angle C equals 35 degrees.
Isosceles Triangles
The image shows marks on 2 sides. These marks show that the sides are congruent. If a triangle has 2 congruent sides then it is isosceles. Isosceles always have 2 congruent angles as well. In addition, these congruent angles are always the angles opposite of the congruent sides.
In this case, the angles opposite of the congruent sides are angle A and angle C. Thus, angles A and C are congruent. If angle A is equal to 35, then angle C must also be 35.
A snack bar weighs 61g, and 10% of the weight is apple. How many
grams of apple are in the snack bar?
Answer:
61×10/100
=610/100
=6.1 g
Answer:
6.1g
Step-by-step explanation:
Snack bar: 61g
Apple: 10% of 61g
10/100 = 0.1
0.1 * 61 = 6.1g
There are 6.1g of apple in the snack bar.
Hope this helps!
Find the numbers whose difference is five and whose product is 266
Answer: 19 and 14
Step-by-step explanation:
19-14 = 5
19x14 =266
Help picture below problem 11
Answer:
128° is the correct answer...
Step-by-step explanation:
mark me brainliest
Award: 1.00 point Exercise 6-10A (Static) Why is it important to prepare the benefit analysis report or the total compensation report? [You may select more than one answer. Single flick the box with the question mark to produceea check marka forma correct answer and doubye-click the both with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) The reports may be used to accompany benefits billing. The reports may be used as employee contracts. The reports promote employee education about the total value of their salary and benefits. The reports inform labor planning and employer cost strategies. References Check All That Apply Difficulty: 1 Easy Exercise 6-10A (Static) Learning Objective: 06-06 Complete Benefit Analysis as a Function of Payroll
Answer:
i think its option one
Step-by-step explanation:
PLEASE HELP ME
A triangle has one angle that measures 29 degrees, one angle that measures 131 degrees, and one angle that measures 20 degrees.
What kind of triangle is it?
Answer:
obtuse angled triangle
Step-by-step explanation:
one angle is more than 90
Help anybody please help me
Answer:
3 units
Step-by-step explanation:
you count how many blocks they are from each other
In the grocery store, eggs are sold in cartons of 12. Write five
ordered pairs made from the corresponding terms of these
two patterns, based on selling 0 to 4 cartons of eggs.
Pattern A: number of cartons sold
Pattern B: number of eggs sold
Plot the points on the plane to the right.
Describe the relationship between the coordinates of the ordered pairs.