Answer:
There is no correlation between age and purchase price
Step-by-step explanation:
In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.
It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
Two surveys are conducted to measure the effect of an advertising campaign for a certain brand of detergent.27 In the first survey, interviewers ask house- wives whether they use that brand of detergent. In the second, the interviewers ask to see what detergent is being used. Would you expect the two surveys to reach similar conclusions? Give your reasons.
Answer:
NO
Step-by-step explanation:
The objective of this surveys is to determine if the two surveys will reach a similar conclusion.
From the data given, we have two test surveys here:
The survey is to measure the effect of an advertising campaign for a certain brand of detergent.
Now in the first survey; interviewers ask house- wives whether they use that brand of detergent and in the second survey the interviewers ask to see what detergent is being used.
Let assume that the brand name of the detergent is KLIN ;
From this disparities of statement ; we anticipate that they will reach different conclusion. This is because; from the first survey people will either respond to the fact that they use the brand detergent (KLIN) or do not used the brand detergent. But in the second survey; when being asked to see what detergent that is being used. There are greater chance that they will bring out the detergent that is commonly used which will eventually result to the same detergent .
The total mass of the Sun is about 2×10^30 kg, of which about 76 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.
Part A
Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.
Express your answer using two significant figures.
Part B
The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.
Express your answer using two significant figures.
Part D
Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?
Express your answer using two significant figures.
Answer:
A. 1.8 ×[tex]10^{30}[/tex] Kg
B i. 3.0 × [tex]10^{17}[/tex] seconds
ii. 9.6 × [tex]10^{9}[/tex] years
C. After 9.2 × [tex]10^{9}[/tex] (9.2 billion) years
Step-by-step explanation:
Given that the mass of the Sun = 2× [tex]10^{30}[/tex] Kg.
Mass of hydrogen when Sun was formed = 76% of 2× [tex]10^{30}[/tex] Kg
= [tex]\frac{76}{100}[/tex] ×2× [tex]10^{30}[/tex] Kg
= 1.52 × [tex]10^{30}[/tex] Kg
Mass of hydrogen available for fusion = 12% of 1.52 × [tex]10^{30}[/tex] Kg
= [tex]\frac{12}{100}[/tex] × 1.52 × [tex]10^{30}[/tex] Kg
= 1.824 ×[tex]10^{30}[/tex] Kg
A. Total mass of hydrogen available for fusion over the lifetime of the sun is 1.8 ×[tex]10^{30}[/tex] Kg.
B. Given that the Sun fuses 6 × [tex]10^{11}[/tex] Kg of hydrogen each second.
i. The Sun's initial hydrogen would last;
[tex]\frac{1.8*10^{30} }{6*10^{11} }[/tex]
= 3.04 × [tex]10^{17}[/tex] seconds
The Sun's hydrogen would last 3.0 × [tex]10^{17}[/tex] seconds
ii. Since there are 31536000 seconds in a year, then;
The Sun's initial hydrogen would last;
[tex]\frac{3.04*10^{17} }{31536000}[/tex]
= 9.640 × [tex]10^{9}[/tex] years
The Sun's hydrogen would last 9.6 × [tex]10^{9}[/tex] years.
C. Given that our solar system is now about 4.6 × [tex]10^{9}[/tex] years, then;
[tex]\frac{9.6*10^{9} }{4.6*10^{9} }[/tex]
= 2.09
So that; 2 × 4.6 × [tex]10^{9}[/tex] = 9.2 × [tex]10^{9}[/tex] years
Therefore, we need to worry about the Sun running out of hydrogen for fusion after 9.2 × [tex]10^{9}[/tex] years.
Part(A): The total mass of hydrogen available 9.6 billion years.
Part(B): The total time is 5.10 billion years.
Part(D): The hydrogen will last [tex]5.04\times 10^9 \ years[/tex]
Mass of the sun:Our sun is the largest object in our solar system. The mass of the sun is approximately [tex]1.988\times 1030[/tex] kilograms
Part(A):
Given that,
The total mass of the Sun =[tex]2\times10^{30} kg[/tex]
Mass of hydrogen in Sun = [tex]2\times10^{30} \times0.76\ kg[/tex]
The mass of hydrogen ever available for fusion is,
[tex]2\times10^{30} \times 0.76 \times 0.12 kg = 1.824\times 10^{29}[/tex]
Mass of hydrogen fuses each second = 600 billion kg/second.
Time hydrogen will last in seconds=[tex]1.824\times 10^{29}seconds.[/tex]
[tex]= 0.00304\times 10^{29 }= 3.04\times 10^{17}.[/tex]
Time hydrogen will last in seconds =[tex]1 year = 31,536,000 seconds.[/tex]
[tex]31,536,000 x = 3.04\times 10^{17} = 9.6 \ billion \ years.[/tex]
(B) Present age of sun = [tex]9.6-4.5 \ billion \ years[/tex]
The time when we need to worry about Sun running out of hydrogen for fusion = 5.10 billion years.
(D) The solar system is 4.6 billion years old that is [tex]4.6\times 10^9\ years[/tex]
And in part (B) we have calculated that hydrogen will last [tex]9.64\times 10^9[/tex] then,
[tex]9.64\times 10^9-4.6\times 10^9=5.04\times 10^9[/tex]
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Gordon Miller's job shop has four work areas, A, B, C, and D. Distances in feet between centers of the work areas are: A B C D A − 5 9 7 B − − 6 8 C − − − 11 D − − − − Workpieces moved per week between work areas are: A B C D A − 900 900 500 B − − 500 200 C − − − 600 D − − − − It costs Gordon $22 to move 1 work piece 1 foot.What is the weekly total material handling cost of the layout?
Answer: $600,600
Step-by-step explanation:
Total handling cost :
Workpiece moved * cost * distance
Work area A :
-, (5 × 22 × 900), (9 × 22 × 900), (7 × 22 × 500)
-, 99000, 178200, 77000
Work area B:
-, -, (6 × 22 × 500), (8 × 22 × 200)
-, -, 66000, 35200
Work area C:
-, -, -, (11 × 22 × 600)
-,-,-, 145200
Work area D:
-, -, -, -
Total weekly handling cost :
(99000 + 178200 + 77000 + 66000 + 35200 + 145200)
= $600,600
Kindly check attached picture for more explanation
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
Simplify the expression and then evaluate it for the given value of the variable: (6−2x)+(15−3x) for x=−0.2
PLEASE HELP!!!!!!
Answer:
20
Step-by-step explanation:
The simplified expression is -5x+21
-5(0.2)+21=
-1+21= 20
Answer:
24
Step-by-step explanation:
f(x)= (6−2x)+(15−3x)
x=-0.2
f(-0.2)=(6−2(-0.2)+(15−3(-0.2))
f(-0.2)=(6+0.4)+(15+0.6)
f(-0.2)=6.4+15.6
f(-0.2)=22
Do not answer or report What is -6 plus -6
Answer:
-12Step-by-step explanation:
it is -12 because -6 plus -6 is also like 6 plus 6
and then you have to add the negative Sign.
pls brainliest me
-6 - 6 = - 12
Happy to help! Please mark as the brainliest!
A laptop producing company also produces laptop batteries, and claims that the batteries
it produces power a laptop for about 4:00 hours. But, you doubted the claim and collected
data from 500 laptop users of the same brand and battery, and you found out the battery
powers the laptop for about 3:00 hours and 30 minutes. Considering an alpha of 0.05,
prove the claim of the company is true or false or show whether you accept the
company’s claim or reject it? Please also write H0 and Ha statements for testing your
hypothesis
Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
Step-by-step explanation:
The question is incomplete: To test this claim a sample or population standard deviation is needed.
We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.
NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=500-1=499[/tex]
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-5.5902)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.
round 0.004198223 to 3 significant figures
I will give brainliest
Answer:
0.00420 is the answer
Step-by-step explanation:
The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
The rounding number of 0.004198223 to 3 significant figures is 0.0042
Here,
The number is 0.004198223.
We have to find, 0.004198223 to 3 significant figures.
What is Rounding number?
Rounding means making a number simpler but keeping its value close to what it was.
Here,
The number is 0.004198223.
To find 3 significant figures,
We round a number to three significant figures in the same way that we would round to three decimal places.
Then, We count from the first non-zero digit for three digits. We then round the last digit.
Here, the digit is 9 then it will be round.
We get, the number is;
0.0042
We fill in any remaining places to the right of the decimal point with zeros.
So, The rounding number of 0.004198223 to 3 significant figures is 0.00420
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A recent article1 claims that "Green Spaces Make Kids Smarter." The study described in the article involved
2623 schoolchildren in Barcelona. The researchers measured the amount of greenery around the children's schools, and then measured the children's working memories and attention spans. The children who had more vegetation around their schools did better on the memory and attention tests.
(a) What are the cases in this study?
(b) What is the explanatory variable?
(c) What is the response variable?
(d) Does the headline imply causation?
(e) Is the study an experiment or an observational study?
(f) Is it appropriate to conclude causation in this case?
Answer:
Cases : 2623 school children , Explanatory Variable : Greenery or Vegetation around school , Response Variable : Children's Memory & attention spans , Yes causation, Observational study
Step-by-step explanation:
a) Cases refers to the people or units of population studied in the research. In this case, it is sample of 2623 school children in Barcelona
b) Explanatory variable is variable which leads to, or causes the change in other variable. In this case, it is greenery or vegetation around researched students' schools
c) Response variable is the variable which is affected due to change in independent explanatory variable. In this case, it is children's working memory & attention spans
d) Yes, the headline implies causation. As it implies cause effect relationship of greenery around children's school on their working memory & attention spans.
e) It is an observational study, as it observes the variables relationship as it is, without any specific experimental intervention.
a line has a slope of -3/4 and passes through the point (-5, 4). what is the equation of the line?
Answer:
y = -3/4x-1/4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = -3/4x +b
We have a point (-5,4)
4 = -3/4 (-5) +b
Changing to a common denominator
16/4 = 15/4 +b
subtracting 15/4 from each side
16/4-15/4 = -15/4 +15/4 +b
1/4 = b
y = -3/4x-1/4
Answer:
book
Step-by-step explanation:
kmgktn
simplify (51/3)^3
i will give brainlist
Answer: D. 5
Step-by-step explanation:
Typically when you have exponents in a form like this, you would multiply 1/3 with 3 to get 1/3 * 3/1. The threes cancel out and you're left with an exponent of 1. And 5 to the 1 power is 5.
how do you add 9 1/6 + 2 1/12
Answer:
11 1/4
Step-by-step explanation:
first make the fractions equal. So 9 1/6 would be 9 2/12 so that we canadd them together.
9 2/12 + 2 1/12 = 11 3/12
but u can simplify the answer so itll be 11 1/4
[tex]answer = 11 \ \frac{3}{12} \\ solution \\ 9 \ \frac{1}{6} + 2 \ \frac{1}{12} \\ = \frac{55}{6} + \frac{25}{12} \\ = \frac{55 \times 2 + 25}{12} \\ = \frac{110 + 25}{12} \\ = \frac{135}{12} \\ = 11 \ \ \frac{3}{12} \\ hope \: it \: helps[/tex]
A company that manufactures toothpaste is studying five different package designs.Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs (to 2 decimals)
Answer:
The selection probability to be assigned to each of the package designs is 0.20
Step-by-step explanation:
Firstly, we need to assume that one design is just as likely to be selected by a consumer as any other design
so the probability of selecting any of the design is same and that is 1/5 = 0.20
Thus, what we are trying to say is that each of the package designs have an equal selection probability of 0.20
Please answer this correctly
Answer: 1-20=2 and 60-80=4
Step-by-step explanation:
the first is 2 number of building
and the third one is 4 number of buldings
Hope this helps :)
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
Please answer this correctly
Answer:
24.99
Step-by-step explanation:
If the area of the quarter circle is 38.465, then the equation to find this would be
3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.
Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4
Plugging 7 in as the radius, r, we get 24.99 as our final answer.
if jm = 5x - 8 and lm = 2x - 6, which expression represents jl
Answer:
7x -14 = jl
Step-by-step explanation:
Assuming a straight line
jm+ ml = jl
5x-8 + 2x-6 = jl
Combine like terms
7x -14 = jl
Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio): • Independent variable = ______________ • Condition A = ______________ • Condition B = ______________ • Dependent variable = _______________ • How do you know this DV is measured on a continuous scale? • How would you word the null hypothesis for your sample study? • How would you word the alternative hypothesis for your sample study? • What alpha level would you set to test your hypothesis? Why?
Answer:
Step-by-step explanation:
A possible study is to compare the prices of items in a two different online auction platform: the Dutch auction and the first-priced sealed auction.
Independent variable = the two types of auction
• Condition A = Dutch auction
• Condition B = First-price sealed auction
The Dependent variable in my case study is the prices for each pair of identical items I place in each auction using a known pair sample. The depends variable is measured in the continuous scale because prices are in numbers and these numbers vary continuously, it is not fixed.
The null hypothesis for my study would be: there is no difference in the prices of identical items in the two different auction.
The alternative hypothesis for my study would be: there is a difference in the prices of identical items in the two different auction.
I would set it to the 0.05 level of significance because this is the standard level of significance normally set in a study although this varies.
Lily paints 3 trees for a wall mural. The middle tree is 2 1/2 ft tall. The tree on the left is 3/4 as tall as the middle tree. The tree on the right is 1 3/4 times as tall as the middle tree. How tall is each tree?
Answer:
middle is 2.5 ft
right is 4375 ft
left is 1875 ft
Step-by-step explanation:
I promise brainieliest for the first to answer What is the solution to the inequality 2x ≥ -4? Click the number line until the correct answer is shown.
Answer:
x ≥ -2
Step-by-step explanation:
Divide both sides of the inequality by 2.
2x ≥ - 4
2x / 2 ≥ -4 / 2
x ≥ -2
Answer:
the answer is the arrow going to the right because its not a negative number and a closed circle
Step-by-step explanation:
so that means that 2x is at LEASt more than -4 opposed to this sign> wich just means greater than
because when you work with variables you usually cannot find the exact amount especially when you are rounding so you know that its biigger than no less than or at least -4
Find the area of the triangle
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
If p(x) = 2x2 - 4x and q(x) = x - 3, what is (pºq)(x)?
Answer:
Step-by-step explanation:
p(x)=2x^2
q(x)=x-3
(p•q)(x)=2(x-3)^2
2(x^2-6x+9)
2x^2-12x+18
2- = - 6 – 4.0
Solve for x:
Which is the same as asking:
To what power must 5 be raised to get 3,125?
Answer: 5^5
Step-by-step explanation:
Since 5x5x5x5x5 = 3,125
Express loga 6 + loga 70 as a single logarithm
Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
A survey was sent out to compare the proportion of adults who use their car horns when driving for two age populations (1=younger adults, defined as between 20 and 39 years old and 2 =older adults, defined as over 60 years old). The following data was obtained from those who responded.
Calculate the 90% confidence interval using the standard normal distribution. Note that 1 =0.52. P2= 0.35, and s.e.(P1-P2) =0.0338. Round to the fourth decimal point. Please enter you answer in the following format: (lower value, upper value)
Use the horn Use the horn
Group Yes No Total
1= younger adults 261 240 501
2= older adults 123 229 352
Answer:
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
As the value 0 is not included in the interval, we can conclude that there is significant difference in the proportion of youger adults that use the horn and older adults that use the horn.
Step-by-step explanation:
We want to calculate the bounds of a 90% confidence interval.
For a 90% CI, the critical value for z is z=1.645.
The sample 1 (younger adults) , of size n1=501 has a proportion of p1=0.521.
[tex]p_1=X_1/n_1=261/501=0.5210[/tex]
The sample 2 (older adults), of size n2=352 has a proportion of p2=0.3494.
[tex]p_2=X_2/n_2=123/352=0.3494[/tex]
The difference between proportions is (p1-p2)=0.1715.
[tex]p_d=p_1-p_2=0.5210-0.3494=0.1715[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{261+123}{501+352}=\dfrac{384}{853}=0.4502[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.4502*0.5498}{501}+\dfrac{0.4502*0.5498}{352}}\\\\\\s_{p1-p2}=\sqrt{0.0005+0.0007}=\sqrt{0.0012}=0.0346[/tex]
Then, the margin of error is:
[tex]MOE=z \cdot s_{p1-p2}=1.645\cdot 0.0346=0.0569[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.1715-0.0569=0.115\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.1715+0.0569=0.228[/tex]
The 90% confidence interval for the difference between proportions is (0.115, 0.228).
Simplify (1+√3) (2-√3).
Answer:
[tex] \sqrt{3} - 1[/tex]
Step-by-step explanation:
[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]
If y = x² + 2x,
find the value of y when x = 5
_____________________________
Hey!!
Solution,
X=5
Now,
y=x^2+2x
=(5)^2+2*5
=25+10
= 35
So the value of y is 35
hope it helps
Good luck on your assignment
___________________________
For the given equation y = x² + 2x, the value of y when x = 5 is, 35
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation, y = x² + 2x
The value of y when x is equal to 5 = ?
after putting value of x in a equation
⇒ y = 5² + 2 × 5
⇒ y = 25 + 10
⇒ y = 35
Hence, the value of y is 35
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Ben bought 4 volleyballs and 5 footballs for $352.65 altogether. If Ben’s brother bought 2 volleyballs and 4 footballs for $249.12 altogether, what was the price of each football?
Answer:
$48.53
Step-by-step explanation:
The purchases can be written in equation form as ...
4v +5f = 352.65
2v +4f = 249.12
Doubling the second equation and subtracting the first gives ...
2(2v +4f) -(4v +5f) = 2(249.12) -(352.65)
3f = 145.59 . . . . simplify
f = 48.53 . . . . . . divide by 3
The price of each football was $48.53.
