Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temp. 174 176 177 178 178 179 180 181
Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74
Temp. 184 184 184 184 184 185 185 186
Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94
Temp. 186 186 186 188 188 189 190 192
Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16
A)
Using the online linear regression calculator, the lie of best fit which models the data above is :
ŷ = 0.09386X - 15.55523
Where ;
X = independent variable
ŷ = predicted or dependent variable
- 15.55523 = intercept
0.09386 = gradient / slope
B)
Point estimate when tank temperature is 186
ŷ = 0.09386(186) - 15.55523
ŷ = 17.45796 - 15.55523
ŷ = 1.90273
C)
Residual error (y - ŷ), ŷ = 1.90273 when x = 186
(0.94 - 1.90273) = −0.96273
(1.85 - 1.90273) = −0.05273
(2.02 - 1.90273) = 0.11727
(2.64 - 1.90273) = 0.73727
D)
To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.
Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Round to 3 decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]49.85 < \mu < 54.15[/tex]
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 52[/tex]
The population standard deviation is [tex]\sigma = 6[/tex]
Given that the confidence level is 95% then the level of confidence is evaluate as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]
[tex]E = 2.147[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]52 - 2.147 < \mu < 52 + 2.147[/tex]
[tex]49.85 < \mu < 54.15[/tex]
generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
Given that:
The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]
The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:
[tex]x = -3[/tex] or [tex]x = 3[/tex]
Equate both equations to 0
[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]
Multiply both equations to give y'
[tex]y' = (3 - x) \times (x + 3)[/tex]
Open bracket
[tex]y' = 3x + 9 - x^2 - 3x[/tex]
Collect like terms
[tex]y' = 3x - 3x+ 9 - x^2[/tex]
[tex]y' = 9 - x^2[/tex]
Integrate y'
[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]
[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]
[tex]y = 9x - \frac{x^3}{3} + c[/tex]
Express as a function
[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(-5) < 0[/tex] implies that:
[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]
[tex]-45 - \frac{-125}{3} + c < 0[/tex]
[tex]-45 + \frac{125}{3} + c < 0[/tex]
Take LCM
[tex]\frac{-135 + 125}{3} + c < 0[/tex]
[tex]-\frac{10}{3} + c < 0[/tex]
Collect like terms
[tex]c < \frac{10}{3}[/tex]
[tex]c <3.33[/tex]
We can then assume the value of c to be
[tex]c=3[/tex] or any other value less than 3.33
Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
See attachment for the function of f(x)
Read more about continuous and differentiable function at:
https://brainly.com/question/19590547
Officer Jacobi drove 180 miles in his patrol car during part of May. The distance represents 40% of May. How many miles did he drive all of May? a) 710 miles b) 420 miles c) 720 miles d) 450 miles Need Help on How to work this problem out, what formula would I use?
Answer:
D: 450 miles
Step-by-step explanation:
So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):
[tex]0.4D=180[/tex]
This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:
[tex]0.4D=180\\D=450[/tex]
So the answer is D or 450 miles.
Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.
A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
A researcher would like to test the claim that the mean lung capacity of middle-aged smokers is less than the mean lung capacity of senior citizen nonsmokers. Independent random samples of 34 middle-aged smokers and 34 senior citizen nonsmokers will be used in a hypothesis test of this claim, and it is believed that the standard deviations of the lung capacities in the populations of middle-aged smokers and senior citizen nonsmokers are the same. Which test statistic formula should be used for this test
Answer:
The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
You make 85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary.
Answer:
The question is incomplete, below is a possible match for the complete question:
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answer:
a.) The company will contribute $100
b.) The company will contribute $415
c.) maximum amount the company will be willing to contribute = $6,800 per year
Step-by-step explanation:
First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:
Annual salary = $85,000
Monthly salary = $7083.3333
maximum amount = 8% = 8/100 = 0.08 of salary
maximum amount = 0.08 × 7083.3333 = $566.67
a.) If you contribute $200 every month.
Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:
Company matches 50 cents for every dollar you deposit
1 dollar deposited = 50 cents from company
but 1 cent = $0.01
∴ 50 cents = 0.01 × 50 = $0.5
$1 deposited = $0.5 from company
∴ $200 deposited = 0.5 × 200 = $100 contributed by company
Therefore, if you contribute $200 every month, your company will contribute $100 each month.
from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.
b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:
half of $830 = 830 ÷ 2 = $415
Therefore, if you contribute $830 per month, your company will contribute $415 per month.
c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year
= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]
Therefore, the company will be willing to contribute $6,800 per year.
True or False. The statistician should use Printout C to perform a t-test on the GROUP variable in the regression model. g
Answer:
False
Step-by-step explanation:
Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.
Lori wants to buy a radio for 60 dollars.
She can pay $60 now, or she can pay $12
a month for 6 months. How much more will
she pay for the radio if she makes monthly
payments?
Answer:
Lori will pay $12 more if she makes monthly payments
Step-by-step explanation:
to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72
subtracting the amount she would pay as a down payment
$72 - $60 is $12
Lori will pay $12 more if she makes monthly payments
The manager of the video department at a department store plans to purchase a large number of DVDs of a recent movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling boxes of 14 DVD movies for $170. Only complete boxes of DVD movies can be purchased. Complete part a) and b) below. a)
a) If the manager can purchase boxes of DVD movies from either or both suppliers, determine the maximum number of DVD movies that can be purchased for $415. Indicate how many boxes of 20 and how many boxes of 14 will be purchased.
— box(es) of 20 and — box(es) of 14
b) How much will the DVD movies cost?
They will cost $—
Answer:
1 box of 20 and 1 box of 14
They will cost $410
Step-by-step explanation:
1. Find how many boxes of 20 DVD movies can be bought
415 - 240 = 175
1 box of 20 DVD movies can be sold
2. Find how many boxes of 14 DVD movies can be bought from $175
175 - 170 = 5
1 box of 14 DVD movies can be bought
3. Find the cost
240 + 170 = 410
You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 inhalers per month and a standard deviation of 21 due to a storm the next shipment of inhalers did not arrive. The pharmacy only has 163 inhalers currently in stock and available to sell for the current month. What is the z score corresponding to selling 163 inhalers?
Answer: -1.33 .
Step-by-step explanation:
Formula to find the Z-score :
[tex]Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}[/tex]
Given: Mean = 191 and Standard deviation = 21
Then , the z-score corresponding to the expected value of 163 will be :
[tex]Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33[/tex]
Hence, the z score corresponding to selling 163 inhalers is -1.33 .
Factor this trinomial completely. -6x^2 +26x+20
Answer:
Step-by-step explanation:
-6x²+26x+20
=-2(3x²-13x-10)
=-2(3x²-15x+2x-10)
=-2[3x(x-5)+2(x-5)]
=-2(x-5)(3x+2)
What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.For
90° < 0 < 270°
, which of the primary trigonometric functions may have positive values?
Answer:
sine and tangent
will be positive.
Nan lives 13 miles from the airport. Felipe lives 6 miles from the airport.
How many more miles does Nan live from the airport than Felipe?
Answer:
7
Step-by-step explanation:
it's simply 13 - 6
7 it the answer, that was easy
3. Solve 6 + 5 √ 2 4 9 − 2 x = 7
Answer:
please mark my answer brainliest
Step-by-step explanation:
question is unclear to give u correct answer
(08.01 MC)
The volume of a pyramid that fits exactly inside a cube is 9 cubic feet. What is the volume of the cube? (5 points)
Select one:
a. 3 cubic feet
b. 6 cubic feet
c. 18 cubic feet
d. 27 cubic feet
Answer:
d. 27 cubic feet
Step-by-step explanation:
volume of cube = s^3 = B * s
volume of pyramid = (1/3) * B * h
The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.
volume of pyramid = 9 cu ft
volume of cube = 3 * 9 cu ft = 27 cu ft
Answer: d. 27 cubic feet
Answer:
27 ft^3 (Answer d)
Step-by-step explanation:
Here the volume of the pyramid is (1/3) the volume of the cube:
Letting s represent the length of one side of the base,
(1/3)(s)^2(s) = 9 ft^3, equivalent to s^3 = 27.
Solving for s, we get s = 3 ft.
Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)
Find the value of x.
A. 22
B. 7.3
C. 3.6
D. 5.5
Answer:
x= 5.5
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
x*4 = 11*2
4x = 22
Divide each side by 4
4x/4 = 22/4
x =5.5
What number is the opposite of -3?
Explain your reasoning
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]
Cheers.
Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
What is composite functionThe composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.
In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.
Solving a composite function means finding the composition of two functions.
Function p(t)The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].
The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:
s(t)= q[p(t)]
4t -21= 4[p(t)]³ – 1
Solving:
4t -21 +1= 4[p(t)]³
4t -20 = 4[p(t)]³
(4t -20)÷ 4 = [p(t)]³
4t÷4 -20÷ 4 = [p(t)]³
t -5 = [p(t)]³
[tex]\sqrt[3]{t-5}=p(t)[/tex]
Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].
Learn more about composite function:
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#SPJ2
10. (01.02)
Given the function f(x)
3x - 4
5
which of the below expressions is correct? (1 point)
5x+4
f-1(x) =
3
f-1(x)
5x - 4
3
O f-'(x)
-344
-3x – 4
5
4–3x
f-1(x) =
5
Answer:
5x+4f-1(x)=3 this is short answer
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
The graph of y = −4x2 + 13x + 12 is shown below. What are the zeros of the function (as exact values), the y-intercept, and the maximum or minimum value of the function?
Answer:
zeros: -3/4, 4y-intercept: 12maximum: 22 9/16Step-by-step explanation:
The graph tells you the zeros of the function are x=-3/4 and x=4.
The y-intercept is the constant in the function: 12.
The maximum is 22.5625 at x = 1.625.
a kicker starts a football game by "kicking off". The quadratic function y = -10x^2 + 25x models football's height after x seconds. How long, in seconds, is the football in the air?
Answer: 2.5 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) for the ball to land on the ground (y = 0)
0 = -10x² + 25x
0 = -5x(2x - 5)
0 = -5x 0 = 2x - 5
[tex]0 = x\qquad \dfrac{5}{2}=x[/tex]
x = 0 seconds is when the ball was kicked
x = 5/2 --> 2.5 seconds is when the ball landed on the ground
the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi
Answer:
James town is 5 meters higher than Takoradi .
Step-by-step explanation:
Given:
Height of James town = 2 meters below sea level
Height of Takoradi town = 7 meters below sea level
To find:
How much higher is James town that Takoradi = ?
Solution:
As we can see the standard of height is how much the town is below the sea level.
So, the height of town having lesser value will be at a higher level.
Value of Height of James town is lesser than that of Takoradi town.
Therefore, James town is at a higher level.
Difference of height = 7 meters - 2 meters = 5 meters
So, the answer is:
James town is 5 meters higher than Takoradi.
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
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Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
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Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
