Answer: 17.28
Step-by-step explanation:
18*12 =216*.02=4.32
18*12=216*.10=21.6
21.6-4.32=17.28
In a year, by opting for online e-checks at a rate of $.02 per check instead of paper checks at $.10 per check for an average of 18 checks per month, your savings amount to $17.28.
Explanation:The subject of your question is a practical application of mathematics, specifically an area often referred to as personal finance. To find out how much you've saved over a year by sending e-checks online instead of writing paper checks, we first need to calculate the cost of each method and then compare the two.
First, let's calculate how much it would cost for the e-checks. The bank charges you $0.02 for each e-check you send. If you send an average of 18 checks per month over a year (12 months), that's 18 checks/month x 12 months/year = 216 checks/year. At $0.02 a check, that comes out to 216 checks/year x $0.02/check = $4.32/year.
Now let's calculate the cost if you were writing paper checks. The bank charges $0.10 for each paper check you write, so that would have been 216 checks/year x $0.10/check = $21.60/year.
So, by choosing to send e-checks online instead of writing paper checks, you've saved $21.60/year - $4.32/year = $17.28/year.
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The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches. What is the height of the rectangle in inches?
The height of the rectangle in inches is 6.5 inches.
The area of a rectangle = lw
where
l = length
w = width
Therefore,
area = 45.5 in²
length = 7 inches
The height of the rectangle can be found below:
45.5 = 7h
divide both sides by 7
45.5 / 7 = h
h = 6.5 inches
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Based on the information given the height of the rectangle in inches is 6.5 inches.
Using this formula
Area of a rectangle = Length× Width
Where:
Area = 45.5 in²
Length = 7 inches
Hence,
Let solve for Length
45.5 = 7h
Divide both sides by 7
h=45.5 / 7
h = 6.5 inches
Inconclusion the height of the rectangle in inches is 6.5 inches.
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A bet on "black" in Roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin.
a. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.
b. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.
Answer:
Check the explanation
Step-by-step explanation:
let the money on bet is X.
probability of winning =18/38=9/19
probability of losing =(1-9/19)=10/19
expected outcome =[tex]\tiny \sum[/tex]probability *return =(
Expected value of return after one bet is =(9/19*x)-(10/19*x)=-1x/19
it is negative which is obvious cause casinos are there to earn money.
a) Our best strategy in this case as probability of winning is near by 50 %, we should place a bet of 1 $ each,and when we lose one bet consecutively we should bet twice the amount..
Cause two consecutive losses on black has less probability.
c) In case we have to reach 30 $ we have to use the same strategy as above.
Explaining the best gambling strategy using expected value in roulette scenarios.
Expected value is a key concept when determining the best strategy in gambling scenarios like this. In the given situation, if you want to play until you reach $20 starting with $10, the best strategy is to bet the maximum amount on each spin. This way, your expected value increases, giving you a higher chance of reaching $20.
On the other hand, if you aim to reach $30 starting with $10, it's better to bet smaller amounts on each spin to minimize the risk of going broke quickly. By betting conservatively, you increase your chances of eventually reaching $30.
A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 80 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h left parenthesis t right parenthesis equals negative 16 t squared plus 80 t plus 8. How long will it take the rocket to reach its maximum height? What is the maximum height?
The toy rocket will take 2.5 seconds to reach its maximum height, which is 108 feet above the ground.
Explanation:The question asks about the time it takes for a toy rocket to reach its maximum height and what that maximum height is, given the equation of its height h(t) = -16t2 + 80t + 8. This is a quadratic equation representing the height of the toy rocket as a function of time, which is a typical problem in physics or mathematics dealing with projectile motion. To solve for the time when the rocket reaches its maximum height, we need to find the vertex of the parabola shaped by the quadratic equation where the coefficient of t2 is negative indicating that the parabola opens downwards.
The formula to calculate the time to reach maximum height in a quadratic equation like this is t = -b/(2a), where a is the coefficient of t2 (-16) and b is the coefficient of t (80). Thus, t = -80/(2*(-16)) = 2.5 seconds. To find the maximum height, we plug this time into the height equation: h(2.5) = -16*(2.5)2 + 80*(2.5) + 8 = 108 feet.
Mar’s, In. claims that its M&M candies are distributed with the color percentages of 20% brown, 20% yellow, 30% red, 10% orange, 10 % green, and 10% blue. A classroom exercise involving a random sample of 460 M&M’s resulted in the observed frequencies were: 90 brown, 94 yellow, 99 red, 64 orange, 51 green, and 62 blue. Test the claim that the color distribution is as claimed by Mars, Inc (α= 0.05). What can you conclude if the test statistic is greater than the critical value?
Answer:
Null hypothesis is rejected. There is no or little evidence to support the claim made by Mars.In
Step-by-step explanation:
Solution:-
- A claim is made by Mars.In that the M&M candies in a packet are distributed by color percentage given below.
- A random sample of N = 460 M&M's was taken and the frequencies of different colors were observed as given below.
- We are to test a claim made by the Mars.In regarding the color distribution of M&Ms at significance level α = 0.05.
- Compute the expected frequency of distribution for color as per Mars.In claim. Use the following formula for expected outcome:
Expected = N*pi
Where, pi : The percentages for each color.
- The table for expected and observed frequencies for each color is tabulated below.
Colors Percentage Expected Observed
Brown 20% 460*0.2 = 92 90
Yellow 20% 460*0.2 = 92 94
Red 30% 460*0.3 = 138 99
Orange 10% 460*0.1 = 46 64
Green 10% 460*0.1 = 46 51
Blue 10% 460*0.1 = 46 62
- To test the claim for color distribution of M&Ms using X^2 - test. We will state the Null and Alternate hypothesis as follows:
Null Hypothesis: The distribution is colors is as its claimed by the company
Alternate Hypothesis: The distribution is colors is not its claimed by the company
- We will first determine the X^2 statistics value using the following relation:
[tex]X^2-test = Sum [ \frac{(Oi- Ei)^2}{Ei} ]\\\\X^2-test = \frac{(90- 92)^2}{92} + \frac{(94- 92)^2}{92} + \frac{(99- 138)^2}{138} + \frac{(64- 46)^2}{46} + \frac{(51- 46)^2}{46} + \frac{(62- 46)^2}{46} \\\\X^2-test = \frac{4}{92} + \frac{4}{92} + \frac{1521}{138} + \frac{324}{46} + \frac{25}{46} + \frac{256}{46} \\\\X^2-test = 0.04347 + 0.04347 + 11.0217 + 7.04348 + 0.54348 + 5.56522\\\\X^2-test = 24.2608[/tex]
- The rejection region is defined by the significance level ( α ) = 0.05 and degree of freedom. The bound ( critical value ), X^2-critical is determined using the look-up table:
degree of freedom = number of observation category - 1 = 6 - 1 = 5
P ( X < X^2 - critical ) = 0.025
X^2 - critical = 12.8
- All the test values of X^2 > X^2-critical lie in the rejection region.
24.2608 > 12.8
X^-test > X^2-critical
Hence, Null hypothesis is rejected.
Conclusion: As per Chi-square test the claim made by the Mars.In has little or no evidence to be true; hence, the color distribution of M&M is not what is claimed.
Parallelogram ABCD has vertices at A(-2,3), B(4,3), C(-1,1). What is the length of side AB? Answer choices ;
A) 2 units
B) 3 units
C) 4 units
D) 6 units
Answer:
D)6 units
Step-by-step explanation:
the answer is D because since side AB have the same y coordinate then you would have to either subtract or add the x. if one point on x is negative and the other is positive then you would add. but if they were both positive or both negative then you would subtract the x.
what is the axis of symmetry for the graph of a quadratic function whose zeros or -2 and 4?
Answer:
x = 1
Step-by-step explanation:
As you might guess, the zeros are symmetrical about the axis of symmetry. That is, the axis of symmetry is midway between the zeros, so will be their average value:
x = (-2 +4)/2 = 1
The axis of symmetry is x = 1.
The population of a community was 200 people 10 yrs ago. Today the population is 550 people. Using an exponential growth function when will the population be 1000?
Answer:
in 6 years
Step-by-step explanation:
Using t=10 to represent today, we can write the exponential growth function as ...
p(t) = 200(550/200)^(t/10)
Then we can set p(t) = 1000 and solve for t:
1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor
1000/200 = (11/4)^(t/10) . . . . divide by 200
log(5) = (t/10)log(11/4) . . . . . . take logs
t = 10·log(5)/log(11/4) ≈ 15.91
That is, about 16 years from 10 years ago, the population will reach 1000.
The population will reach 1000 in about 6 years.
A group of high school seniors took a scholastic aptitude test. The resulting math scores had a mean 504.7 with a standard deviation of 191.4, verbal scores had a mean 491.5 with a standard deviation of 168.9, and the correlation between verbal and math scores was r 0.824. Answer the questions below a) What is the correlation?b) Write the equation of the line of regression predicting verbal scores from math scores (Round to three decimal places as needed) d) A person tells you her math score was 387. Predict her verbal score.
The correlation is 0.824. The equation of the regression line is Y = -12.6 + 0.722X. The estimated verbal score for a math score of 387 can be calculated by inputting 387 in place of X in the regression equation.
Explanation:The subject of this question is regression analysis, which is a type of statistical modeling technique.
A) The correlation, as given in the question, is 0.824. This number tells us the degree to which the math and verbal scores vary together.
B) The regression equation predicting verbal scores from math scores can be calculated as follows:
Regression line equation is Y = a + bX. 'a' is Y intercept, 'b' is the slope, 'X' is the value of the independent variable (in this case math scores), and 'Y' is the predicted value of the dependent variable (in this case, verbal scores). We calculate the slope 'b' using the formula b = r*(Sy/Sx), where r is the correlation coefficient, Sy is the standard deviation of Y (verbal scores) and Sx is the standard deviation of X (math scores).
Inserting our values in gets us: b = 0.824 * (168.9/191.4) = 0.722 (rounded to three decimal places). And a = My - b*Mx = 491.5 - 0.722*504.7 should give us our Y intercept. Plugging in your calculator should give you a roughly around -12.6.
The equation of the regression line would then be Y = -12.6 + 0.722X.
D) To predict the verbal score from a math score of 387, we substitute X = 387 into the regression equation: Y = -12.6 + 0.722 * 387, giving us a predicted verbal score when calculated.
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what's the least common denominator of 4 and 16
Answer:16
Step-by-step explanation:
The lcm of 4 and 16 is 16.
16
the lcm of 4 and 16 is 16
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 4 days? How long is it until there are 10,000 mosquitoes?
Answer: 3,917 days
Step-by-step explanation:
-2/3p + 1/5 -1 + 5/6p
Hey there!
All you have to COMBINE YOUR LIKE TERMS and you have your answer!
-2/3p + 1/5 - 1 + 5/6p
(-2/3p + 5/6p) + (1/5 - 1)
-2/3p + 5/6p = 1/6p
1/5 - 1 = -4/5
Answer: 1/6p + (- 4/5) ✅
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
39% of what is 118.9?
Answer:
39% of 118.9=46.371
Step-by-step explanation:
Final answer:
To find out what 39% of a certain amount is equal to 118.9, we can set up an equation and solve for x. To solve "39% of what is 118.9?", we use the equation 0.39x = 118.9 and find that x, which represents the original number, is equal to 305.
Explanation:
To find 39% of a certain number that equals 118.9, we set up the equation where 0.39 (which is 39% as a decimal) times the unknown number (let's call it x) equals 118.9:
0.39x = 118.9
To find the value of x, we divide both sides of the equation by 0.39:
x = 118.9 / 0.39
x = 305
Therefore, 39% of 305 is equal to 118.9.
The slope of a pipe with a 1/4 inch of drop has a run of 1 foot. What is the run of a pipe that has a 3/4 inch drop?
Answer:3 foot
Step-by-step explanation:
put these numbers in order 55, 52, 46, 52, 46, 43, 49, 56, 42
Answer: 55
Step-by-step explanation:
Answer:
42,43,46,46,49,52,52,55,56
Step-by-step explanation:
Use the table. Which inference can you make by comparing the measures of center?
Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Answer: the average speed of the runners increased since last year.
Step-by-step explanation:
The table is:
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Looking at this table we can see that this year, the mean time is smaller than the one from last year, so the runners are faster in average.
The mean absolute deviation is bigger, but the change in the mean is bigger.
difference of the mean 16.2 - 14.7 = 1.5
difference of the MAD 1.9 - 1.2 = 0.7
This means that the average speed of the runners increased since last year, and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike like last year.
Answer:
this guy above me is a genuies it correct
Step-by-step explanation:
If you had $500 to put into a savings account with 8% interest , how would you know which bank to choose, if you plan to withdraw everything after 10 years—one that pays simple interest or compound interest? Explain.
Answer:
Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.
Step-by-step explanation:
Simple interest formula:
The simple interest formula is given by:
[tex]E = P*r*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), r is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
Compound interest formula:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this problem:
[tex]P = 500, r = 0.08, t = 10[/tex]
So
Simple interest:
[tex]E = P*r*t = 500*0.08*10 = 400[/tex]
In total:
[tex]T = E + P = 500 + 400 = 900[/tex]
Using simple interest, you would withdraw an amount of $900.
Compound interest
We use n = 1
[tex]A = P(1 + \frac{r}{n})^{nt} = 500(1 + \frac{0.08}{1})^{10} = 1079.46[/tex]
You would withdraw $1079.86. Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.
Simplify the expression.
Answer:
(2x)(-2x+5)(x+2)
Step-by-step explanation:
Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these households. Suppose Nielsen reports that American Idol had 6565% of the TV audience. Interpret this result with a 95% confidence interval, based on a sample size of 12 comma 00012,000 people.
Answer:
We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%
Step-by-step explanation:
-From the given information, [tex]\hat p=0.65[/tex].
-We calculate the confidence interval using this value at 95% confidence level:
[tex]CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585][/tex]
So, the 95% confidence interval is (0.6515,0.6585).
Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.
A tanker that ran aground is leaking oil that forms a circular slick about 0.2 foot thick. To estimate the rate dV/dt (in cubic feet per minute) at which oil is leaking from the tanker, it was found that the radius of the slick was increasing at 0.31 foot per minute (dR/dtequals0.31) when the radius R was 400 feet. Find dV/dt, using pi almost equals 3.14 .
Answer:
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Step-by-step explanation:
Since it is circular slick, it's volume can be modeled as,
[tex]V = \pi R^{2}h[/tex]
Where R is the radius in feet and h is the thickness of slick.
taking derivative of the above equation with respect to time yields,
[tex]\frac{dV}{dt} = \pi 2Rh \frac{dR}{dt}[/tex]
Where the rate of change of radius of the slick (dR/dt) is given,
[tex]\frac{dV}{dt} = \pi 2(400)(0.2)(0.31)[/tex]
[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]
Therefore, the rate of change of volume is 155.82 cubic feet per minute.
The value of dV/dt using pi almost equal to 3.14 gives; dV/dt = 155.82 ft³/min
dV/dt = 155.82 ft³/min
We are given;
Radius; R = 400 ft
Height; h = 0.2 ft
Rate of Increase of radius; dr/dt = 0.31 ft/min
Formula for Volume of a cylinder is;
V = πr²h
Differentiation of both sides of V and r with respect to t gives;
dV/dt = 2πrh(dr/dt)
Plugging in the relevant values gives;
dV/dt = 2π × 400 × 0.2 × 0.31
dV/dt = 155.82 ft³/min
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64= 4^3 in logarithmic form
g The tangent plane to z=f(x,y) at the point (1,2) is z=5x+2y−10. (a) Find fx(1,2) and fy(1,2). fx(1,2)= Number fy(1,2)= Number (b) What is f(1,2)? f(1,2)= Number (c) Approximate f(1.1,1.9). f(1.1,1.9)= Number
Answer:
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Approximation at points (1.1,1.9) is 0.7
Step-by-step explanation:
Given:
Tangent plane to a surface z=5x+2y-10 as the function at point (1,2)
To find :
f(x,y) at (1,2)
partial derivatives of function w.r.t. (x and y) and value of that function at given points.
Solution:(refer the attachment also)
Now we know that
the equation of tangent plane at given points to the surface is given by,
f(x1,y1,z1) and z=f(x,y)
z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)
here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.
now
taking partial derivative w.r.t. x we get
Fx(x1`,y1)=[tex]\frac{d}{dx} (5x+2y-10)[/tex]
=5.
Then w.r.t y we get
Fy(x1,y1)=
[tex]\frac{d}{dy}(5x+2y-10)[/tex]
=2.
The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.
Using the Linearization or linear approximation we get
L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)
=-1+5(x-1)+2(y-2)
=5x+2y-10
Approximation at F(1.1,1.9)
=5(1.1)+2(1.9)-10
=5.5+3.8-10
=0.7
Approximation at points (1.1,1.9) is 0.7
Final answer:
The partial derivatives of f(x, y) at (1, 2) are fx(1,2) = 5 and fy(1,2) = 2. The function value f(1,2) is 0. An approximation for f(1.1, 1.9) using the tangent plane is 0.5.
Explanation:
The question concerns the computation of partial derivatives and the evaluation of a function f(x, y) given its tangent plane at a specific point. Given the tangent plane to z=f(x,y) at the point (1, 2), which is z=5x+2y−10, we have:
fx(1,2) is the partial derivative of z with respect to x at the point (1,2), equivalent to the coefficient of x in the tangent plane equation, which is 5.
fy(1,2) is the partial derivative of z with respect to y at the point (1,2), equivalent to the coefficient of y in the tangent plane equation, which is 2.
To find f(1,2), we substitute x=1 and y=2 into the tangent plane equation to get z = 5(1) + 2(2) − 10 = 0.
The value f(1.1,1.9) can be approximated by using the tangent plane equation. By plugging x=1.1 and y=1.9 into the equation, we obtain z = 5(1.1) + 2(1.9) - 10 = 0.5, for an approximate value of f(1.1, 1.9).
Summary of Answers:
fx(1,2) = 5
fy(1,2) = 2
f(1,2) = 0
f(1.1,1.9) ≈ 0.5
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 9 min and standard deviation 4 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Round your answer to four decimal places.)
Answer:
u know this carol
Step-by-step explanation:
For what value(s) of k is k-3/2k+5 undefined?
Answer:
The expression is undefined where the denominator equals
0 , the argument of an even indexed radical is less than
0 , or the argument of a logarithm is less than or equal to 0 . k = − 2 , k = 0 , k = 2 , k = 6
Step-by-step explanation:
I'm not rocket scientist but I hope this helps in anyway, if not i'm so sorry i tried. :)
12. Find the perimeter of the triangle below:
please help show steps thank you :)
Given:
The lengths of the three sides of the triangle are [tex]\frac{3}{x-4}[/tex], [tex]\frac{16-x}{x^{2}-2 x-8}[/tex] and [tex]\frac{x+5}{x+2}[/tex]
We need to determine the perimeter of the triangle.
Perimeter of the triangle:
The perimeter of the triangle can be determined by adding all the three sides.
Thus, we have;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{x^{2}-2 x-8}+\frac{x+5}{x+2}[/tex]
Factoring the term [tex]x^2-2x-8[/tex], we get, [tex](x-4)(x+2)[/tex]
Substituting, we get;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{(x-4)(x+2)}+\frac{x+5}{x+2}[/tex]
Taking LCM , we have;
[tex]Perimeter=\frac{3(x+2)+16-x+(x+5)(x-4)}{(x-4)(x+2)}[/tex]
Simplifying the numerator, we get;
[tex]Perimeter=\frac{3x+6+16-x+x^2-4x+5x-20}{(x-4)(x+2)}[/tex]
Adding the like terms in the numerator, we get;
[tex]Perimeter=\frac{x^2+3x+2}{(x-4)(x+2)}[/tex]
Factoring the numerator, we get;
[tex]Perimeter=\frac{(x+2)(x+1)}{(x-4)(x+2)}[/tex]
Cancelling the common terms, we have;
[tex]Perimeter=\frac{x+1}{x-4}[/tex]
Thus, the perimeter of the triangle is [tex]\frac{x+1}{x-4}[/tex]
The solution of the equation 2^x-1 - 7 = 9
IS X =
Answer:
x = log∨2 (17)
Explanation:
Calculate the difference
Move the constant to the right
Add the numbers
Then take the logarithm of both sides of the equation
Answer:
5
Step-by-step explanation:
The x-intercept and y-intercept
Answer:
x intercept = (1.2 , 0)
y intercept = (0 , 0.75)
Step-by-step explanation:
You wan to get it into whatever formula makes it easiest for you to understand. I put it into standard slope formula ax + by = c
5x +8y = 6
6/5 = x
x= 1.2
6/8 = y
y = 0.75
Newberg is 5 miles due north of the airport, and Rockport is 12 miles due east of the airport. How far apart are Newberg and Rockport?
Step-by-step explanation:
No of miles Newberg is north of airport = 5
No of miles Rockport is east of the airport = 12
No of miles Newberg and Rockport are apart = 12+5 =17
Answer:
I did this now and was not 12 it was 13
PLEASE HELP !!!!!!
If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning. (4 points—2 points for finding the length of the diagonal; 2 points for explanation)
Answer:
[tex]50\sqrt{2} feet[/tex]
Step-by-step explanation:
Given the vertices (1, 5) and (11, 15) for the corners labeled with red stars, the diagonal of the square C will be the length of the line joining the two vertices.
Using the Distance Formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)=(1, 5) \:and\: (x_2,y_2)=(11, 15)[/tex]
[tex]Distance=\sqrt{(11-1)^2+(15-5)^2}\\=\sqrt{10^2+10^2}\\=\sqrt{200}\\=10\sqrt{2}[/tex]
Since 1 Square Unit = 25 Square Feet
1 Unit =5 feet
Therefore, the length of the diagonal
[tex]=5*10\sqrt{2} \\=50\sqrt{2} \:feet[/tex]
Answer:
50 with 2 squared
Step-by-step explanation:
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The pair of variables have a significant correlation. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent or a test and their scores on the test are shown below.Hours spend studying, x 1 2 3 3 4 6 (a) x = 2 hours (B) x = 3.5 hrsTest score, y 37 41 51 48 65 69 (c) x = 12 hours (d) x = 1.5 hrsFind the regression equation : Y (hat) = _____x +(_____) round to 3 decimal placesPlot the grapha. predict the value of y for x = 2b. predict the value of y for x = 3.5c. Predict the value of y for x = 12d. predict the value of y for x = 1.5
Answer:
(a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Step-by-step explanation:
If you use a regressor calculator you will find that
y = 6.542x + 28.933
then for (a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Regression equations are used to represent scatter plots
The regression equation is [tex]\^y = 6.54\^x + 28.94[/tex]The predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75The table is given as:
x | 1 2 3 3 4 6
y | 37 41 51 48 65 69
To determine the regression equation, we make use of an graphing calculator.
From the graphing calculator, we have:
Sum of X = 21 Sum of Y = 311 Mean X = 3.5 Mean Y = 51.8333 Sum of squares (SSX) = 17.5 Sum of products (SP) = 114.5The regression equation is represented as:
[tex]\^y =b\^x + a[/tex]
Where:
[tex]b = \frac{SP}{SS_x}[/tex] and [tex]a = M_y - bM_x[/tex]
So, we have:
[tex]b = \frac{SP}{SS_x}[/tex]
[tex]b = \frac{17.5}{114.5}[/tex]
[tex]b = 6.54[/tex]
[tex]a = M_y - bM_x[/tex]
[tex]a = 51.83 - (6.54*3.5)[/tex]
[tex]a = 28.94[/tex]
Substitute values for (a) and (b) in [tex]\^y =b\^x + a[/tex]
[tex]\^y = 6.54\^x + 28.94[/tex]
The predicted values when x = 2, 3.5, 12 and 1.5 are:
[tex]\^y = 6.54 \times 2 + 28.94 = 42.02[/tex]
[tex]\^y = 6.54 \times 3.5 + 28.94 = 51.83[/tex]
[tex]\^y = 6.54 \times 12 + 28.94 = 107.42[/tex]
[tex]\^y = 6.54 \times 1.5 + 28.94 = 38.75[/tex]
Hence, the predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75
Read more about regressions equations at:
https://brainly.com/question/5586207
This cake was sliced parallel to the base. What shape will the cross-section make?
The shape of the cross-section of the cake is a square.
What is cross-section?In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections.
Given that, a cake was sliced parallel to the base, we need to find the shape of the cross section,
we see that the shape of the cake is a square base pyramid,
That means if we cut it horizontally parallel to its base, we will always find a square,
Therefore, the cross-section is a square.
Hence, the shape of the cross-section of the cake is a square.
Learn more about cross-section, click;
https://brainly.com/question/15541891
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When slicing a cake parallel to its base, the resulting cross-section will be a circle, mirroring the shape of the base of the cake.
The question pertains to the shape of the cross-section resulting from slicing a cake parallel to its base. When you slice a three-dimensional object like a cake in this way, the cross-section will mirror the shape of the object's base. As the base of a cake is typically a circle, the cross-section in this case will be a circular shape. To understand this better, imagine a cylinder, which is similar to a circular cake. When you slice a cylinder parallel to its base, you always obtain a circular cross-section. This concept is consistent across different objects, given that the slice is parallel to the base, such as slicing a cylindrical polony or cutting a slice of brick-shaped bread.