Answer:
see explanation
Step-by-step explanation:
(a)
given y is inversely proportional to x² then the equation relating them is
y = \(\frac{k}{x^2}\)
to find k use any ordered pair from the table
using (1, 4 ) and substituting into equation
4 = \(\frac{k}{1^2}\) = \(\frac{k}{1}\) , thus
k = 4
y = \(\frac{4}{x^2}\) ← equation of proportion
(b)
when y = 25 , then
25 = \(\frac{4}{x^2}\) ( multiply both sides by x² )
25x² = 4 ( divide both sides by 25 )
x² = \(\frac{4}{25}\) ( take square root of both sides )
x = ± \(\sqrt{\frac{4}{25} }\) = ± \(\frac{2}{5}\)
then
positive value of x when y = 25 is x = \(\frac{2}{5}\)
2. The population of a town was 7,250 in 2014
and 7,375 in 2015. What was the percent
increase from 2014 to 2015 to the nearest
tenth of a percent?
A) 1.5%
B) 1.6%
C) 1.7%
D) 1.8%
E) 2.0%
E
The percentage change of the population is P = 1.7 %
Given data ,
To calculate the percent increase from 2014 to 2015, we need to find the difference between the two population values, divide it by the initial value, and then multiply by 100 to get the percentage.
Population increase = 7,375 - 7,250 = 125
Percent increase = (Population increase / Initial population) * 100
Percent increase = (125 / 7,250) * 100 ≈ 1.7241
Rounding to the nearest tenth of a percent, the percent increase is approximately 1.7%.
Hence , the percentage change is P = 1.7 %
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1. AIDS is caused by a virus called HIV. True or false
Answer:
\(\huge\boxed{True\hookleftarrow}\)
⎆ AIDS (Acquired Immunodeficiency Syndrome) is caused by a virus named HIV (Human Immunodeficiency Virus). This disease can be transmitted through :-1) sexual contact2) transfer of blood etc.How many times does 1/4 go into 3/8
Answer:
3/2
Step-by-step explanation:
3/8 ÷ 1/4
Copy dot flip
3/8 * 4/1
12/8
Divide top and bottom by 4
3/2
marian has a savings account with $21,390 if she earns $4,100 per month, what is the maximum she can spend on a house?
The answer is: 4100x + 21390
We need to know the number of months Marian wants to save to get the specific value.
Step-by-step explanation:
In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.
We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.
Solve the problem:Marian earns $4,100.00 per month
Suppose Marian wants to save for x months, then the maximum amount that she can spend on the house is:
4100 * x + 21390
Draw the conclusion:The answer is: 4100x + 21390
We need to know the number of months Marian wants to save to get the specific value.
Hope this helps!
how are the probability of an event and the probability of its complement related mathematically
The relation between the probability of its complement is that their sum is 1.
Complement in probability theory is an essential concept that helps us understand the likelihood of an event not occurring. It is a mathematical term that refers to the opposite or negation of an event.
Complement refers to the probability of an event not occurring, given the probability of it occurring. It is often denoted as the complement of an event A and is represented by A’.
The complement of an event A is defined as the set of all outcomes in the sample space that are not in A.
The probability of the complement of A is equal to the probability of all the outcomes in the sample space that are not in A.
The most important properties of the complement of an event is that the probability of an event and its complement always add up to 1. This is known as the law of complementary probability, and is expressed as:
P(A) + P(A’) = 1
This means that if we know the probability of an event occurring, we can easily calculate the probability of its complement by subtracting the probability of the event from 1.
For example, if the probability of event A is 0.7, then the probability of its complement, A’, is 1 – 0.7 = 0.3.
Hence the relation between the probability of its complement is that their sum is 1.
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Suppose that the relation T is defined as follows. =T, , p9, , 0m, , 9p, 66 Give the domain and range of T. Write your answers using set notation.
domain=
range =
Answer:
Step-by-step explanation:
Set notation { } is used in this case, to represent the domain and the range.
The values that go into T are the domain while the values that come out of T are the range.
The domain comprises all x (independent) values while the range comprises all y (dependent) values.
This should be applied in the clear definition of the relation T.
A discount store normally sells DVDs for $14.44. If the DVDs go on sale for $13.72, which of the following is closest to the percent of decrease in the price?.049 or 4.99% or .052
First, calculate the decrease amount:
14.44-13.72 = $0.72
The original price multiplied by a percentage will be equal to the discount amount:
14.44 x = 0.72
x = 0.72 /14.44
x = 0.049
0.049 x 100 = 4.99 %
Correct options:
.049 and 4.99%
What does
non-proportional and
proportional
Answer: i don’t understand the question... are you asking what eacg of them mean?
Step-by-step explanation:
Answer:Proportional: ... How to tell the difference: A proportional graph is a straight line that always goes through the origin. A non-proportional graph is a straight line that does not go through the origin.
Step-by-step explanation:
The students in a gym class measured the length of their longest jump (in feet). The results were tallied and are reported in the following histogram. How many students jumped greater than 8.5 but less than 11.5 feet?
On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.
What is frequency?the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.
Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5
AND,
frequency of length of jump greater than 8.5 but less than 11.5 is -
Number of students jumped greater than 8.5 and less than 9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=
3+3+1=7 ( since, sum of respective frequencies of the three class)
so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.
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In the equation (x-3)²+(y-2)2=16, the radius of the circle is...
16
3
32
4
Step-by-step explanation:
This is of the form
(x-h)^2 + ( y-k)^2 = r^2 so r^2 = 16 means r = 4 units
leo le debe 15.00 pesos. Si su madre le da 60.00 pesos de paga y se gasta 20.00 con sus amigos
¿cuanto dinero le queda?
¿tendrá pendiente alguna deuda?
Answer:
Le quedan 25 pesos
No tendrá pendiente ninguna deuda
Step-by-step explanation:
60-15-20=25
PLEASE HELP WILL MARK BRAINLIEST
If A = (-infinity,3) and B
then find A n B
[0,9],
Answer:
A Π B = [0,3)
be careful with the brackets :))
A study team was discussing how to multiply 6x^10 by 12x^2.
Andrea said, "The answer is 72x^20"
Bernard said, "No, the answer is 18x^20"
Carmen disagreed and said, "No, the answer is 72x^12"
Finally, Diego concluded, "You are all wrong. The answer is 18x^12"
Are any of these students correct? How do you know? Explain.
The correct option is that C. Carmen disagreed and said, "No, the answer is 72x^12"
How to illustrate the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
It should be noted that when dividing exponents with same base, we will subtract the powers and when multiplying them, we will add the powers.
Here, the study team was discussing how to multiply 6x^10 by 12x^2. Therefore, this will be:
= 72 × x^(10 + 2)
= 72x^12.
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Devin measured his basketball rim. The radius of the rim is 6 inches. What is the circumference of the rim?
Your bank give you 6% annual interest compounded quarterly on all savings account balances. Which of the following is the multiplier used when modeling this situation
A. 1.015
B. 1.02
C. 1.04
D. 1.06
E. 0.94
stuck on this question
To make marbled paper, Shannon filled a rectangular 279/10cm by 178/10cm dish with water. Then they gently swirled paint on top of the water. let a represent the area of the dish.
Select 1 multiplication and 1 division equation to represent the relationship.
choose 2 answers
A) 178/10 x a = 279/10
B) 178/10 x 279/10 = a
C) 279/10 ÷ 178/10 = a
D) a ÷ 178/10 = 279/10
The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:
a = (279/10) cm x (178/10) cm
Simplifying this expression, we get:
a = 4953/100 cm^2
So, the correct equations are:
B) 178/10 x 279/10 = a
and
D) a ÷ 178/10 = 279/10
how do u graph the solution y=2x-1 iready
Answer:
Step-by-step explanation:
y=mx+b
m= slope and b= y intercept
you'll start with a point on the y axis on -1
and the slope will go up so towards the right corner up but 2/1 points
9+4f-7z use f=6 and z=5
Answer:
-2
Step-by-step explanation:
9 + 4f - 7z
Use what they have given you
f = 6
z = 5
Now that you have those, all you need to do is substitute them into the expression
9 + 4f - 7z
9 + 4 (6) - 7 (5)
9 + 24 - 35
33 - 35
-2
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Answer: -2
9 + 4f - 7z
Use what they have given you
f = 6
z = 5
Now that you have those, all you need to do is substitute them into the expression
9 + 4f - 7z
9 + 4 (6) - 7 (5)
9 + 24 - 35
33 - 35
-2
PLEASE HELPP ASAPPP pleaseeeee
answer: 28561^2in the area involves multiplying by the 4 sides of the shaded square and the shaded is the colored square.
PLEASE HELP! I JUST NEED TO KNOW HOW YOU SOLVE THIS!!! SEE ATTACHED!!! WILL MARK YOU BRAINLIEST!!! Surface Area
The surface area of the complex solid is 530 square yards.
How to determine the surface area of a complex solid
In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:
A = w · h
Where:
A - Area, in square yards.w - Width, in yardsh - Height, in yards.The surface area of the complex solid is:
A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)
A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²
A = 530 yd²
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Find all solutions to the system
5x − 3y = 2,
15x + 6y = 6.
Answer:
The answer I got was: (0.4,0)
Need help with this geometry question
Answer: C
Step-by-step explanation:
\(50 < 5x-10\\\\60 < 5x\\\\x < 12\)
However, the angle has to have positive measure, so:
\(5x-10 > 0\\ \\ 5x > 10\\\\x > 2\\\\\therefore \boxed{2 < x < 12}\)
A student ran a distance of 312 miles each day for 5 days. Then the student ran a distance of 414 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi
What is the total distance that the student ran on the 10 days?We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:
5*(3 + 1/2) mi = (15 + 5/2) mi
Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:
5*(4 + 1/4) mi = (20 + 5/4)mi
Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:
(15 + 5/2) mi + (20 + 5/4)mi
So we have a sum of mixed numbers, we can rewrite this as:
(15 + 5/2) mi + (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi
(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi
35mi + (10/4 + 5/4) mi = 35mi + 15/4mi
35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi
35mi + 12/4 mi + 3/4 mi = (38 + 3/4)mi
That is the total distance that the student ran on the 10 days.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
How to solve quadratic equation?8x² + 16x + 3 = 0
using Quadratic formula
The following steps are involved
\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)
\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)
\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)
\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)
\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)
\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)
\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
\(x = -0.209431\)
or
\(x = -1.79057\)
Therefore, the steps peter could follow will give the result
\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)
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Write a polynomial that represents the area of the shaded region
The polynomial that represents the area of the shaded region is given as follows:
x² - 3x + 36.
How to obtain the area of a rectangle?The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:
A = lw.
For the entire region, the area is given as follows:
A = (x + 1)(x + 1)
A = x² + 2x + 1.
The area of the white region is given as follows:
Aw = 5(x - 7)
Aw = 5x - 35.
Then the area of the shaded region is given as follows:
As = A - Aw
A = x² + 2x + 1 - (5x - 35)
A = x² + 2x + 1 - 5x + 35
A = x² - 3x + 36.
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 190 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.65 cm, y= 81.36 kg, r= 0.309, P-value= 0,002, and y= 106+1.15x. Find the best predicted value of y (weight) given an adult male who is 156 cm tall. Use a 0.10 significance level.
The best predicted weight of a person that is 156 cm is 285.4kg
We have the regression equation asy= 106+1.15
When the adult male is 156 cm tall the weight of this person would be calculated as:
y= 106+1.15*156
y = 106 + 179.4
y = 285.4
Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg
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Kevin and Randy Muise have a jar containing 54 coins, all of which are either quarters or nickels. The total value of the
coins in the jar is $6.50. How many of each type of coin do they have?
The jar contains__
quarters.
There are 35 nickels and 19 quarters in the jar.
What is an equation?
In mathematics, an equation is a statement that two expressions are equal, often denoted using the equal sign "=".
Let's assume that the number of nickels in the jar is x, then the number of quarters will be 54 - x.
The value of x nickels is 5x cents, and the value of (54 - x) quarters is 25(54 - x) cents.
According to the problem, the total value of the coins is $6.50, which is equal to 650 cents.
So we can write an equation:
5x + 25(54 - x) = 650
Simplifying and solving for x, we get:
5x + 1350 - 25x = 650
-20x + 1350 = 650
-20x = -700
x = 35
The jar contains = 54 - 35 = 19
Therefore, there are 35 nickels and 19 quarters in the jar.
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Why is the interest rate of a loan one of the most important things to consider when shopping around for loans?
a.
The interest rate should be ignored, because there’s nothing a consumer can do to change it.
b.
The interest rate is essentially how long you have to pay off your loan, and the shorter the better.
c.
The interest rate can drastically change the total amount paid to the lender, in the case of mortgages, up to thousands of dollars.
d.
The interest rate does not change, even between banks, so choosing the right time to borrow is essential.
Answer:
C
Step-by-step explanation:
trust me c is the correct answer
Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units
Answer:
I think B. 3.85 units
Step-by-step explanation: