Answer:
~ Sarah = b
!!!Michael = 1/2*b + 3
~~David = b/2 + 8
!!!Hannah = 3b + 28
~~~~~Sarah = 3b/2 + 14
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.
What is Loan interest ?Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.
Given data:
Principal = $1050 per month
Time = 30 year
= 30 × 12
= 360 months
Interest rate = 8%
= 0.08/12
= 0.006667 monthly
(a) We get here first maximum amount of loan by present value of annuity as
Present value of annuity = principal × [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex] .........(1)
Put here value we get
value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]
value of annuity = $143097.67
(b) Total amount = principal × time period
= $1050 × 360
= $378000
(c) Total amount of interest paid will be
interest amount = total amount paid - loan amount
interest amount = $378000 - $143097.67
interest amount = $234902.33
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R(x) = -40x^2 + 5000x
Determine the prices where the revenue is zero?
For each price where the revenue is zero, explain why the revenue is zero.
Answer:
The prices where the revenue is zero are $x = 0 and $x = 125.
When x = 0, the revenue is 0 since the function is equal to zero (R(0) = -40(0)^2 + 5000(0) = 0).
When x = 125, the revenue is 0 since the coefficient of the x^2 term is negative and the coefficient of the x term is positive. Since the equation is equal to zero, the two terms must cancel each other out, resulting in zero revenue (R(125) = -40(125)^2 + 5000(125) = 0).
Step-by-step explanation:
2. Sandra gets 2 dollars for every 50 aluminum cans she recycles. What is the ratio of dollars to
cans? How much money does she make per can?
Answer:
1:25
$0.04 or 4 cents per can
Step-by-step explanation:
The ratio of dollars to can is 2:50 = 1:25.
$1/25 = $0.04
She gets $0.04 or 4 cents per can
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is
μ=12.00
Mbps. The sample size is
n=25
and the test statistic is
t=2.376.
The p-value for the hypothesis test in this problem is given as follows:
0.0258.
How to obtain the p-value of the test?The first step in obtaining the p-value of the test is verifying the hypothesis that are test, to classify the test.
At the null hypothesis, it is tested if the mean carrier data speed is of 12 Mbps, that is:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if the mean carrier data speed is different of 12 Mbps, that is:
[tex]H_1: \mu \neq 12[/tex]
Then we have a two-tailed test, as we are testing if the mean is different of a value, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Test statistic of t = 2.376.Using a t-distribution calculator with these parameters, the p-value for the test is given as follows:
0.0258.
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Q4 Two consecutive numbers are such that the larger number when
added twice the smaller number gives a sum of 70. Find the two numbers.
Answer:
The answer is in the picture
Step-by-step explanation:
The explanation is in the picture
PLEASE HELP ASAP!!!! FULL ANSWER ONLY!!!
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
What is the maximum height of the ball 182.25 feet
How many seconds does it take until the ball hits the ground 6 seconds
How to find the maximum height of the ballThe maximum height will occur at the vertex v(h', k)
h' = -b/2a
From the equation h = − 16 t^2 + 84 t + 72
a = -16
b = 84
h' = -84/(2 * -16)
h' = t = 2.625
k = h = − 16 t^2 + 84 t + 72 at t = 2.625
= − 16 * 2.625^2 + 84 * 2.625 + 72
= 182.25 feet
The ball hits the ground when h = 0
0 = − 16 t^2 + 84 t + 72
solving the quadratic equation gives
t = 6 OR -3/4
Use the positive value
t = 6 seconds
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The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
The population of the state is 23.1 million
The population of the state will reach 28.3 million in 13.5 years
What is population ?
Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
So 13.5 years after 2000 the population will be 28.3 million.
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The length of rectangle is twice its width.How many times long as the width of the rectangle is the perimeter of the rectangle.
Step-by-step explanation:
w=x
l=2x
p=2(l+w)
p=2(2x+x)
p=6x
Find the slope of the line that passes through all of the points on the table.
I don’t understand this any help please answer and explain please
Answer:
25.5 inches.
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with legs of length 19 inches and 17 inches. The length of the hypotenuse is the square root of the sum of the squares of the other two sides. We can calculate this as follows:
hypotenuse = sqrt(19^2 + 17^2)
hypotenuse = sqrt(361 + 289)
hypotenuse = sqrt(650)
hypotenuse = 25.495097568 inches
Rounding to the nearest tenth, the length of the hypotenuse is 25.5 inches.
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6x^3+2x^2+3x -(3x^3-2x^2-3x)
The simplest form of the given expression is 3x³+4x²+6x
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
according to question ,
6x³+2x²+3x -(3x³-2x²-3x)
we need to simplify the given equation.
firstly opening the bracket and taking care of sign,
⇒6x³+2x²+3x -3x³ +2x² +3x
taking like terms seperately,
⇒6x³ -3x³ +2x²+2x²+3x+3x
⇒3x³+4x²+6x
Hence the simplest form of the given expression is 3x³+4x²+6x
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The packages a and b together weigh 6kg
Package a is twice as heavy as package b
Find the weight of package a and find the weight of package b
need help!!! with geometry
The value of r is 45 and the value of s is 29
Calculating value of missing variablesFrom the question, we are to solve the parallelogram for the missing variables.
The missing variables are r and s
Since opposite angles of a parallelogram are equal, we can write that
(r - 10)° = (3r - 100)°
Solve for r
r - 10 = 3r - 100
-10 + 100 = 3r - r
90 = 2r
r = 90/2
r = 45
Also,
We can write that
(5s)° = (4r - 35)°
Substitute the value of r and solve for s
5s = 4(45) - 35
5s = 180 - 35
5s = 145
s = 145/5
s = 29
Hence, r = 45, s = 29
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Find the measure of X
The measure of x = 64°
Vertical opposite angles:The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.
Here we have
Three lines are intersected and formed a triangle
Let's assume that the triangle formed is ΔABC
In ΔABC, ∠C = 34°
Since Vertical opposite angles are equal
=> ∠B = 30°
As we know the sum of angles in a triangle = 180°
=> ∠A + ∠B + ∠C = 180°
=> ∠A = 180° - 30° - 34°
=> ∠A = 116
From the line CL [ observe the given picture ]
=> ∠A + x = 180°
=> 116° + x = 180°
=> x = 180° - 116°
=> x = 64°
Therefore,
The measure of x = 64°
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Write an equation and solve for p. Show all work.
a) The equation is 10p + 80 = 180 and p = 10.
b) The three angles are 90°, 37°, 53°.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that, the angles of the triangles are 53°, 2p + 17°, and 8p + 10°.
The sum of all angles of a triangle is 53° + 2p + 17° + 8p + 10° = 80 + 10p
The sum of all angles of a triangle is 180°.
Therefore,
80 + 10p = 180
Subtract 80 from both sides:
10p = 100
divide both sides by 10:
p = 10.
Putting p = 10 in 2p + 17°, and 8p + 10°:
2p + 17° = 20° + 17° = 37°
8p + 10° = 80° + 10° = 90°
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Find the measure of angle b.
59°
A) 69°
C) 21°
B) 121°
D) 159
Answer:
he answer is B
Step-by-step explanation:
Total angle is 180°
angle a=59°angle b=180°-59°=121°
Help help help help help help
Answer:
Andre walks more steps
Step-by-step explanation:
Step-by-step explanation:
dawn step rate=8400/60=140step/he
dawn step=140×240=33600 steps
teddl step=142 ×240 =34080
Xavier is riding on his bike at a constant speed of 15
miles per hour. What is the closest approximation of
how long it will take Xavier to ride 5 miles?
A. 0.15 hour
B. 0.2 hour
C. 0.33 hour
D. 0.5 hour
Answer:
C. 0.33 hour
Step-by-step explanation:
15 miles = 1 hr
5 miles = x hr
cross multiply
5 = 15x
x = 5/15
x = 0.333 hr
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read the whole question and then answer it!!
1a. No, the value of 60% of 400 is 240.
1b. No, the value of 60% of 200 is 120.
1c. No, the value of 60% of 120 is 72.
2. The equation the express the relation 60%, x, and 87 is 0.6x = 87. The value of x is 145.
3a.The equation is0.6c = 43.2. The value of c is 72.
3b. The equation is0.38e = 190. The value of e is 500.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
1.a
Compute the vale of 60% of 400.
Using the formula a% = a/100
60% of 400 = 60/100 of 400
Replace of by multiplication:
60% of 400 = (60/100) × 400
60% of 400 = 240.
1b.
Compute the vale of 60% of 200.
Using the formula a% = a/100
60% of 200 = 60/100 of 200
Replace of by multiplication:
60% of 200 = (60/100) ×2 00
60% of 400 = 120.
1c.
Compute the vale of 60% of 120.
Using the formula a% = a/100
60% of 120 = 60/100 of 120
Replace of by multiplication:
60% of 120 = (60/100) × 120
60% of 400 = 72.
2.
Given that 60% of x is 87.
Compute the vale of 60% of x.
Using the formula a% = a/100
60% of x = 60/100 of x
Replace of by multiplication:
60% of x = (60/100) × x
60% of x = 0.6x
Therefore the relationship is 0.6x = 87
Now divide both sides by 0.6:
x = 87/0.6
x = 145.
3a.
Given that 60% of c is 43.2.
Compute the vale of 60% of c.
Using the formula a% = a/100
60% of c = 60/100 of c
Replace of by multiplication:
60% of c = (60/100) × c
60% of c = 0.6c
Therefore the relationship is 0.6c = 43.2
Now divide both sides by 0.6:
c = 43.2/0.6
c =72.
3b.
Given that 38% of e is 190.
Compute the vale of 38% of e.
Using the formula a% = a/100
38% of e = 38/100 of e
Replace of by multiplication:
38% of e = (38/100) × e
38% of e = 0.38e
Therefore the relationship is 0.38e = 190
Now divide both sides by 0.38:
e = 190/0.38
e = 500.
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One angle measures 160°, and another angle measures (3k + 61)°. If the angles are vertical angles, determine the value of k.
k = 14
k = 33
k = 74
k = 160
Answer:
Therefore, the value of k is 1.
Step-by-step explanation:
Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.
Answer:
k = 33
Step-by-step explanation:
20 + 4 (3x - 5) + 2x = 28
How can I get the answer and please explain step by step!
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Equation
[tex]20 + 4(3x-5)+2x=28[/tex]
Expand the brackets
[tex]20 + 12x- 20 + 2x=28[/tex]
Combine like terms
[tex]14x=28[/tex]
Solve
[tex]x=2[/tex]
I would appreciate it if you mark my answer as brainliest.
I need help badly.
0.000236 to 3 significant figures.
Answer:
It is rounded to 3 sig figs already
Step-by-step explanation:
fhyyyyyyyyyyyyyyyyyyyyytttttttttttttttttttttttttttttttttttttttttgsdddddddddddddtttttttt
Answer:
Step-by-step explanation:
there is no answer it just a bunch of f,h,y and t this is not math this is something
Q1 - Similar shapes and area
Work out the missing area in each pair of similar shapes.
The answer for the first shape would be 24cm^2.
The answer for the second shape would be 20cm^2.
The answer for the third shape would be 30cm^2. "30".
What are Shapes?
A shape in geometry can be characterized as an object's form, outline, outer border, or outer surface.
Every object we notice in the world has a form. The objects we see around us may be broken down into several fundamental forms, such as the two-dimensional square, rectangle, and oval, or the three-dimensional rectangular prism, cylinder, and sphere few types of Shape.Shapes establish an object's perimeter and may be distinguished in a variety of ways depending on their characteristics. In a Shape a border that is created by merging the curves, points, and line segments surrounds these forms. The name of each form depends on the structure. Circle, square, rectangle, triangle, and other simple forms are few types of Shape.The first shape seems to be scaling up. From 3cm to 12cm. So for this you need to multiply. Using the formula that I gave you last time.
3cm times ___ = 12cm. 4 fits in there,
therefore 6cm^2 times 4 = 24cm^2.
The answer for the first one would be 24cm^2. "24" in the blank.
The second shape seems to be scaling down. From 16cm to 8cm. So for this you need to divide.
16cm divided by ___ = 8cm. 2 fits in there,
therefore 40cm^2 divided 2 = 20cm^2.
The answer for the second one would be 20cm^2. "20" in the blank.
The third shape seems to be scaling up.
From 3cm to 4.5cm.
So for this you need to multiply. 3cm times ___ = 4.5cm.
Now since we're dealing with decimals, not whole numbers this time you can't really use guess and check as efficiently. So you do the opposite operation, which in this case the opposite of multiplication is division.
You take 3cm (the original shape's number) and divide it into 4.5cm. So 4.5cm divided by 3cm = 1.5. 1.5 fits in there,
therefore 20cm^2 times 1.5 = 30cm^2.
The answer for the third one would be 30cm^2. "30" in the blank.
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A sample of 200g of an isotope decays to another isotope according to the function A(t)= 200е⁻⁰⁰⁵⁴⁺ ,where t is the time in years
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about __g of the sample will be left.
(Round to the nearest hundredth as needed.)
The amount of initial sample will be left in the sample after 25 years is $771.49.
What is isotope decay?
An unstable atomic nucleus loses energy via radiation during the process of radioactive decay. A substance is regarded as radioactive if it has unstable nuclei. The three most frequent types of decay are alpha decay, beta decay, and gamma decay, all of which involve the emission of one or more particles.
Given:
A sample of 200g of an isotope decays to another isotope according to the function [tex]A(t) = 200e^-^0^.^0^5^4^t[/tex],where t is the time in years.
We have to find the amount of initial sample will be left in the sample after 25 years.
Plug t = 25 in the given equation.
[tex]A(25) = 200e^-^0^.^0^5^4^(^2^5^)\\A(25) = 771.4851\\A(25) = 771.49[/tex]
Hence, the amount of initial sample will be left in the sample after 25 years is $771.49.
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√3 + (4 + √x + 3)² / 6 = 3
Answer: x = 1
Step-by-step explanation:
El primer término en una serie geométrica es 64 y la razón común es 0.75
Answer:
Si...
En una progresión geométrica se conocen a1 = 64 y r = 0,75
The figure below is reflected over the y-axis. What are the coordinates of the image of point R after this transformation?
solution set of a compound inequality
The solution of a compound inequality is the common region or intersection region of two inequalities.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.
For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.
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