x = number of small boxes
y = number of large boxes
well, we know a total of 20 boxes, large and small were shipped, that means that whatever "x" and "y" may be, we know that x + y = 20.
so the volume of one small box is 8 ft³, so sticking to ft³, we can say that the volume of 1 box is 8(1) ft³, and the volume of 2 boxes will then be 8(2) and three is 8(3) ft³ and the volume of "x" boxes will then just be 8(x) ft³.
now, we can say the same thing about large boxes, volume of 1 is 21(1) ft³, for two is 21(2) ft³, for three 21(3) ft³, and for "y" boxes that'll just be 21(y) ft³.
that said, well hell their volume combined must be 8x + 21y, and we happen to know that's 264 ft³, namely 8x + 21y = 264.
[tex]\begin{cases} x+y=20\\\\ 8x+21y=264 \end{cases}\hspace{5em}\stackrel{\textit{using the 1st equation}}{x+y=20\implies }y=20-x \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{8x+21(\underset{y}{20-x})=264}\implies 8x+420-21x=264 \\\\\\ 8x+420=264+21x\implies 8x+156=21x\implies 156=13x \\\\\\ \cfrac{156}{13}=x\implies \boxed{12=x}\hspace{13em}\stackrel{20~~ - ~~12}{\boxed{y=8}}[/tex]
a certain statistic will be used as an unbiased estimator of a parameter. let r represent the sampling distribution of the estimator for samples of size 35, and let s represent the sampling distribution of the estimator for samples of size 15. which of the following must be true about r and s ? responses the expected values of r and s will be equal, and the variability of r will be less than the variability of s. the expected values of r and s will be equal, and the variability of r will be less than the variability of s . the expected values of r and s will be equal, and the variability of r will be equal to the variability of s. the expected values of r and s will be equal, and the variability of r will be equal to the variability of s . the expected values of r and s will be equal, and the variability of r will be greater than the variability of s. the expected values of r and s will be equal, and the variability of r will be greater than the variability of s . the expected value of r will be greater than the expected value of s, and the variability of r will be greater than the variability of s. the expected value of r will be greater than the expected value of s , and the variability of r will be greater than the variability of s . the expected value of r will be greater than the expected value of s, and the variability of r will be less than the variability of s.
Using the Central Limit Theorem, it is found that the correct option is
a. The expected values of R and S will be equal, and the variability of R will be less than the variability of S.
What is the Central Limit Theorem?
A sufficiently high sample size from a population with a finite level of variance will result in a mean of all samples from that population that is roughly equal to the population mean, according to the CLT, a statistical theory.
According to the central limit theorem, the distribution of the sample means will be roughly normally distributed if you take sufficiently large random samples from a population with mean and standard deviation and replacement.
The samples in this issue were drawn from the same population, thus they all had the same expected value.
R has less variability because there are more samples available.
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After spending many hours studying for your math class (I am being hopeful here!) you decide to reward yourself with a case of soda. Unfortunately the store only had a warm case left (the Kent students got there first and got all of the cold ones). You buy several bags of ice and decide to chill it at home. When you get home the temperature of the soda is 76 degrees F and you proceed to pack it in ice. After ten minutes the temperature has cooled to 70 degrees F. If the soda is best served at 60 degrees F or cooler, how much longer must you wait to enjoy your soda? Note that you have not been given the temperature of the surroundings, but you should be able to figure out what that should be (you are packing it in ice that is at the freezing point of water so...).
the difference between the two temperatures as 16 degrees F. You must wait for another 6 minutes for the soda to cool down to 60 degrees F.
Since the initial temperature of the soda is 76 degrees F and the desired temperature is 60 degrees F, we can calculate the difference between the two temperatures as 16 degrees F. We also know that the temperature of the ice is at the freezing point of water which is 32 degrees F. This means that the temperature difference between the soda and the ice is 44 degrees F. Since the temperature difference between the soda and the ice is greater than the temperature difference between the desired temperature and the initial temperature, we can divide the desired temperature difference (16 degrees F) by the temperature difference between the soda and the ice (44 degrees F) and multiply it by the time elapsed (10 minutes) to calculate the remaining time needed for the soda to cool down to the desired temperature. 16/44 * 10 = 6. Therefore, we must wait for another 6 minutes for the soda to cool down to 60 degrees F.
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Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
9x2 + xy + 9y2 = 19, (1, 1) (ellipse)
y = ________________?
The equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) is y = -18x + 19, which can be found using implicit differentiation.
We can find the equation of the tangent line to the ellipse 9x^2 + xy + 9y^2 = 19 at the point (1, 1) using implicit differentiation. Firstly, we take the partial derivatives of both sides of the equation with respect to x and y, which gives us y' = (9x + y)/(9y +x). Then, we plug in the given point (1,1) into the equation for y' and solve for y'. This gives us y' = (9 + 1)/(9 + 1) = 10/10 = 1. This means that the slope of the tangent line at this point is 1. We can then use the point-slope form of a line equation, y - 1 = 1(x - 1), to find the equation for the tangent line at this point, which is y = -18x + 19.
y' = (9x + y)/(9y +x)
At the given point (1,1):
y' = (9 + 1)/(9 + 1) = 10/10 = 1
Equation of the tangent line:
y - 1 = 1(x - 1)
y = -18x + 19
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martin is 6 years younger than his sister. the sum of their ages is no more than 22 years. enter an inequality that can be used to represent this situation in the box, where x represents martin's sister's age.
Answer:
x ≤ 14
Step-by-step explanation:
x = age of Sis
x - 6 = Martin's age
x + (x-6) ≤ 22
2x - 6 ≤ 22
2x ≤ 28
x ≤ 28/2
x ≤ 14
Which of the following is NOT one of the three main methods of inventory evaluation as described in your reading material? A. weighted average, B. straight average, C. FIFO, D. LIFO
Answer:
A or B
Step-by-step explanation:
I think it's B.. according to the people I know
the product of 3 and a number is twice 23
let z be a standard normal variable. find p(-0.86 < z < 2.25). a) 0.1980 b) 0.7898 c) 0.7929 d) 0.7884 e) 0.7742 f) none of the above.
Using the Z- Distribution table, The answer is c) that is 0.7929.
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What is Standard Normal Distribution?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
Following the Z-table,
P(-0.86<x<2.25) = 0.79288
The answer is c) 0.7929
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can someone help me figure out how to solve this problem
Answer:
To find the fourth term in the given sequence, we can use the formula for the nth term, which is a^n = 2 (a^n-1) + 4. We can then plug in the value of a^1, which is 3, and the value of n, which is 4, to find the fourth term:
a^4 = 2 (a^3) + 4
= 2 [2 (a^2) + 4] + 4
= 2 [2 [2 (a^1) + 4] + 4] + 4
= 2 [2 [2 (3) + 4] + 4] + 4
= 2 [2 [10] + 4] + 4
= 2 [24] + 4
= 52
Therefore, the fourth term in the sequence is 52.
Answer:
[tex]a_4 = 52\\[/tex]
Step-by-step explanation:
There is no way around this one. You just had to calculate each term until you got the fourth term.
[tex]a_2 = 2(a_1) + 4 = 2(3) + 4 = 10[/tex]
[tex]a_3 = 2(a_2) + 4 = 2(10) + 4 = 24[/tex]
[tex]a_4 = 2(a_3) + 4 = 2(24) + 4 = 52[/tex]
PLEASE HELP WITH THE QUESTION IN THE PICTURE
Answer:
(9.22 x 10⁻⁵) + (1.078 x 10⁻⁵)
You can take 10⁻⁵ as common from both terms and add the remaining ones.
(9.22 + 1.078) x 10⁻⁵
10.298 x 10⁻⁵
For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?
Answer:
f(x) = -3x + 6
Step-by-step explanation:
f(2)=0 point (2, 0)
f(4)=-6 point (4, -6)
m = slope = (y_2 - y_1)/(x_2 - x_1)
m = (-6 - 0)/(4 - 2) = -6/2 = -3
y = mx + b
y = -3 x + b
0 = -3 × 2 + b
0 = -6 + b
b = 6
y = -3x + 6
f(x) = -3x + 6
It would he quite risky for you to insure the life of a 21 -year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain $\$ 1250 dollars in premiums. But if he were to die, you would lose almost \$ 100,000$. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21 -year-old men. (b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the investment. We can measure the great risk of insuring $\mathrm{u}$ single person's life in Exercise 14 by computing the standard deviation of the income $Y$ that the insurer will receive. Find or using the distribution and mean found in Exercise 14.
The standard deviation of Y can be determined which is 9708.
Given in the question that the high probability would gain in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
According to the information, the gain around is 1250
Amount would lost in case of death is 100000.The expected value with its probability is:
E(X) = ∑x ×P(x)
=(-99750) × 0.00183 + ...+ (1250) × 0.99058
= 303.35
The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is
The standard deviation of Y can be determined as
α = under root {∑x2 × P(x) - (∑x × P(x) }
[tex]\sqrt{(-99750 - 303.3525)sq. X 0.00183 + .... + (1250 - 303.3525)sq. X 0.99058 }[/tex]
= 9708
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morgan bought new living room furniture for $6,500 on an installment plan. he made a down payment $500, and he has to make monthly payments of $210.00 for the next three years. how much interest will he pay?
Interest morgan will pay is $1560.
What is compound interest?Compound interest, also known as interest on principle and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given, Morgan used a payment plan to purchase brand-new living room furnishings for $6,500. He put down $500, and over the following three years, he must pay a monthly payment of $210.00.
Hence he has to total pay = 500 + 210*12*3
The total money morgan has to pay is $8060.
Therefore total interest morgan has to pay is 8060-6500 = $1560.
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the position of a particle moving along a coordinate line is s=√(3+6t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec.
The particle's velocity at time t = 1 seconds is equal to 3 meters per seconds.
What is a position vs time graph?In Mathematics, a position vs time graph can be defined as a type of graph that is used to graphically represent the distance traveled (covered) by an object from its starting position with respect to the time when it is started moving.
Generally speaking, the position of a physical object (body) in a position vs time graph is always plotted on the y-coordinate (y-axis) while time is always plotted on the x-coordinate (x-axis).
From the information provided about this particle on a position vs time graph, we have;
s =√(3 + 6t)
Where:
s in meters.t in seconds.Substituting the given parameters into the formula, we have;
s =√(3 + 6(1))
s =√(3 + 6)
s =√9
Distance, s = 3 meters.
Now, we can determine the velocity as follows;
Velocity = distance/time
Velocity = 3/1
Velocity = 3 meters per seconds.
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Which expressions are equivalent to
5^2/5^8
the accompanying data file shows the monthly closing stock price for a large technology firm for the first six months of the year.
The Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
What is a confidence interval?
A confidence interval is a range of values that is estimated to contain the true value of a population parameter with a certain level of confidence. It is a measure of the uncertainty associated with an estimate of a population parameter, such as the mean, the proportion, or the variance.
a)
sample mean = 75.67
sample std. dev. = 3.56
b)
Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015
[tex]CI = (xbar - tc * s/\sqrt{n} , xbar + tc * s/\sqrt{n})\\\\CI = (75.67 - 2.015 * 3.56/\sqrt{6} , 75.67 + 2.015 * 3.56/\sqrt{6})\\\\\CI = (72.74 , 78.60)[/tex]
Hence the Sample standard deviation would be 3.56 and the confidence interval is between72.74 to 78.60.
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Solve for d.
-10 = -2 + ½ d
d= -16.
Step-by-step explanation:1. Write the expression.[tex]-10=-2+\frac{1}{2}d[/tex]
2. Add "2" to both sides if the equation.[tex]-10+2=-2+\frac{1}{2}d+2\neq \\\\ -8=\frac{1}{2}d[/tex]
3. Divide both sides by "1/2".[tex]\frac{-8}{\frac{1}{2}} =\frac{\frac{1}{2}d}{\frac{1}{2}} \\ \\-8*2=d\\ \\-16=d\\ \\d=-16[/tex]
4. Verify.[tex]-10=-2+\frac{1}{2}(-16)\\ \\-10=-2-8\\ \\-10=-10[/tex]
That's correct! The answer is d= -16.
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The coefficient of determination of a set of data points is 0.83 and the slope of the regression line is -1.38. Determine the linear correlation coefficient of the data.
The linear correlation coefficient of the data is calculated to be -0.911 as the slope of the regression line is -1.38
As the coefficient of determination that is (R^2) = 0.83 and the slope of the regression line = - 1.38, we can determine the linear correlation coefficient of the data as follows;
The Coefficient of determination (R^2) is the square of the linear correlation Coefficient (R) and is used to acquire the proportion of explained variance of the regression line.
Hence. To get the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2 as follows;
R = √R^2
R = √0.83
R = 0.91104335791
R = 0.911
As the value of the slope is negative, therefore this represents a negative relationship between the variables, hence R will also be negative ;
Therefore, R = -0.911
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2. *
In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern?
a) P=3 n
b) P=n+3
c) P=2 n+1
d) P=3-n
A
B
C
Both A andC
In a table of values for a pattern, P=3 when n=1; the equations P=3n and 2n+1 might represent the pattern. So the option d "Both A and C" is correct option.
In the given question, In a table of values for a pattern, P=3 when n=1; which of the following equations might represent the pattern.
a) P=3n
b) P = n+3
c) P = 2n+1
d) P = 3-n
We find the pattern we firstly observe the given diagram closely.
We firstly check which option can given P=3 when n=1.
Firstly taking the option a.
P = 3n
Now put n=1, so
P = 3
Hence, the option one is following the condition.
Now taking the option b.
P = n+3
Now put n=1, so
P = 1+3
P = 4
Hence, the option b is not following the condition.
Now taking the option c.
P = 2n+1
Now put n=1, so
P = 2(1)+1
P = 2+1
P = 3
Hence, the option c is following the condition.
Now taking the option d.
P = 3-n
Now put n=1, so
P = 3-1
P = 2
Hence, the option d is not following the condition.
Hence, the option a and c is following the condition. So the option d "Both A and C" is correct option.
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the following data represent the running times of films produced by two motion-picture companies. company time (minutes) i 103 94 110 87 98 ii 97 82 123 92 175 88 118 compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. assume that the running-time differences are approximately normally distributed with unequal variances
The 90% confidence interval for the difference between the average running times of films produced by the two companies ≅ (- 35.5 , 10.8)
Given that:
Company (i) :
[tex]n_{1}[/tex] = 5 , [tex]x_{1}[/tex]bar = 98.4
[tex]S_{1} ^{2}[/tex] = [tex]\frac{1 }{n_{1} - 1}[/tex] ∑ [tex](x_{i} - x_{1} bar)^{2}[/tex]
= [tex]\frac{1}{5 - 1}[/tex] [ [tex](103 - 98.4)^{2}[/tex] + [tex](94 -98.4)^{2}[/tex]+........+ [tex](98 - 98.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ [tex](4.6)^{2}[/tex] + [tex](-4.4)^{2}[/tex]+..........+[tex](0.4)^{2}[/tex] ]
= [tex]\frac{1}{4}[/tex] [ 305.2]
= 76.3
Company (ii) :
[tex]n_{2}[/tex] = 7 , [tex]x_{2}[/tex] bar = 110.7143
[tex]S_{2} ^{2}[/tex] = [tex]\frac{1 }{n_{2} - 1}[/tex] ∑ [tex](xi - x_{2} bar)^{2}[/tex]
= [tex]\frac{1}{7-1}[/tex] [ [tex](97 - 110.7143)^{2}[/tex]+ [tex](82-110.7143)^{2}[/tex]+.........+[tex](118 - 110.7143)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ [tex](-13.7143)^{2}[/tex]+ [tex](-28.7143)^{2}[/tex]+.........+[tex](7.2857)^{2}[/tex] ]
= [tex]\frac{1}{6}[/tex] [ 6125.4274]
≅ 1035.9045
For 90% confidence interval
difference between = 5+7-2 = 10, critical value is [tex]t_{c}[/tex] = 1.812.
90% confidence interval for the difference between the average running times is
[ ([tex]x_{1}[/tex] bar - [tex]x_{2}[/tex] bar) ± [tex]t_{c}[/tex] . [tex]\sqrt{\frac{S_{1}^2 }{n_{1} } } + \sqrt{\frac{S_{2}^2 }{n_{2} }}[/tex] ]
= [(98.4 - 110.7143) ± 1.812 [tex]\sqrt{\frac{76.3}{5} } + \sqrt{\frac{1035.90457}{7} }[/tex] ]
= [-12.3143 ± 23.1515]
= (- 35.4658 , 10.8372)
≅ (-35.5 , 10.8)
Therefore, 90% confidence interval for the difference between the average running times of films produced by the two companies is
≅ (- 35.5 , 10.8)
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The vertex is (-4,-2) and the parabola opens up. What is the domain and range
Answer:
Domain: -∞ < x < ∞
Range: y ≥ -2
Step-by-step explanation:
The domain of a parabola graph is all real numbers, this is written as;
-∞ < x < ∞
The range of this parabola graph is all numbers greater than and equal to -2, since the parabola opens up and the vertex is at (-4, -2). This is written as;
y ≥ -2
Mario's current credit card balance is $2,673.19 with a minimum payment of $102.00. Over the next month, he plans to spend $626.00. If the APR is 26.99%, what will Mario's new balance be, including
interest? (2 points)
$3,201.98
$3,269.10
$3,197.19
$3,394.68
If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.
What is the APR?Annual percentage rate (APR) is the annual finance charge applied to a credit balance.
The APR includes interest and other fees for borrowing credit.
Current credit card balance = $2,673.19
Minimum payment within the month = (102.00)
Purchase payments 626.00
Finance Charge $71.91 ($3,197.19 x 26.99% x 1/12)
Ending credit card balance = $3,269.10 ($3,197.19 + $71.91)
Annual percentage rate = 26.99%
Monthly percentage rate = 2.25% (26.99% ÷ 12)
Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.
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Mrs.Lopez asked a Capenter to struck a rectangular bulletin board for her classroom . she told the carpenter that the board must be 12 square feet.
1.what are the possible length and width of bulletin board?Give at least 2 pairs
2. how did you determine the possible length and width of the bulletim board?
3.suppose the length of the board is 1 ft.longer that its width and let x be the width. how will you represent the length of bulletin board?
4. given the area of the illustration board which is 12 square feet,what equation represent the given Situation? hint. Area=(length) (width)
5. how would you describe the equation formulated?
6. do you think you can use the equation formulated to find the length and width of the bulletin board
Let us answer the individual questions as per the given conditions:
1. Since the area of the bulletin board is meant to be exactly 12 square feet, the 2 pairs for length and width would be 4feet and 3feet(first pair), 6 feet and 2 feet(second pair) respectively.
2. The possible length and width of the board were determined using trial and error method to find two numbers whose product equal to 12.
3. If width of the board were to be x , and the length be 1 greater than width, we can represent the length as x+1.
4. Given the area of illustration board as 12 sq ft. the equation that represents the given situation is :
5. The equation can be described as quadratic equation.
6. Yes, I think we can use the equation formulated to find the length and width of the bulletin board.
What is rectangle?
A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. Two dimensions, the length and breadth, define any rectangle form.
What is the formula for calculating area of rectangle?
The formula for calculating the area of rectangle is given by:
A = L * B
where A - area of rectangle
L - Length of the rectangle
B - Width of the rectangle
According to the given question:
1. Using the formula for area of rectangle(length * width) , the two pairs of length and breadth can be found by finding two real positive numbers whose product equals to 12. Hence , we get 4 feet and 3 feet as first pair and 6 feet and 2 feet as second pair for length and width respectively.
2. The possible length and width pairs were determined by using the equation of area, A = L*B which is equal to 12 sq ft.
3. Since the width is given to be x by the question and x is mentioned to be 1 greater than width, hence length will be equal to x+1.
4. Using the equation for area of rectangle:
A = L * B
substituting the values as per the given conditions,
12 = x(x+1)
or, x2 + x = 12
or, x2+x-12 =0
Which is the required equation.
5. Since the highest power in the equation is 2. Hence the equation is described as quadratic equation.
6. Yes , we can use the equation formulated to find the length and width of the bulletin word, Simply solving the quadratic equation given above.
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What is the range of the set of ordered points defined below?
{(–1 , 3), (2 , 3), (4 , 5)}
Answer:
Rang is the output values or the y values.
3 and 5
Step-by-step explanation:
An ordered pair is in the form (x, y) The x is the input or the domain and the y is the output or the range.
a convex mirror, like the passenger-side rearview mirror on a car, has a focal length of -2.8 m. an object is 5.6 m from the mirror.
The image's distance from the mirror is -1.87, by using the mirror equation.
Note:- Although the question is missing, I believe the issue is asking where the image is located.
To find the solution to the problem, the mirror equation can be used:
Mirror equation = [tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]
Where,
f = mirror's focal length
[tex]d_{o}[/tex] = object's distance from the mirror
[tex]d_{i}[/tex] = image's distance from the mirror
The focal length is assumed to be negative for a convex mirror in our problem.
f = -2.8 m
The object's distance (do) = 5.6m
By using the mirror equation, the image's distance from the mirror can be determined
[tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]
i.e, [tex]\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }[/tex]
= [tex]-\frac{1}{2.8} -\frac{1}{5.6}[/tex] = [tex]-\frac{3}{5.6}[/tex]
= - 0.5357
[tex]d_{i} =[/tex] [tex]-\frac{5.6}{3}[/tex]
= -1.87 m
The virtual nature of the image is indicated by the negative sign (located behind the mirror)
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This morning, Kenneth took a history test. He got 42 out of 56 problems right. What percentage did Kenneth get right?
\
help me with this question please
Answer:
Step-by-step explanation:
You just have to recall those rules in geometry. :/
for 1 RU = QT
the red single marks on the segment mean those are the same length
for 2 ∠T = ∠U
the red arc means they are the same angle
for 3 QT is parallel to RU
because of both red marks, same length, and same angles
for 4 RQT = SRU
because both of these angles come from the same line, and have the same length and angle below
for 5 triangle QRT = RSU
because of both red marks and starting from the same line.
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeA cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the center of the base. It is also called right circular cone.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneHowever, we have to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
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Kelly has the following income and expenses:
$200 per month paychecks
$50 cell phone
$40 gasoline
$40 Miscellaneous expenses
How much are Kelly's total planned expenses?
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Which linear function has the greatest initial value? Which has the greatest rate of change? Use the drop-down menus to show your answer.
The linear function that has greatest initial value is function C
The linear function that has greatest rate of change is function B
Consider the function A
The y intercept = 0
Consider two points (2, 5) and (4, 10)
The slope of the line = (10-5) / 4-2
= 5 /2
The equation will be
y = 5/2x + 0
Consider the function B
y = 3x - 1
Which is in the form of slope intercept form
The slope of the line = 3
The y intercept = -1
Consider the function C
y intercept = 2
Consider the points (0, 2) and (3, 3)
The slope of the function = 3-2 / 3 -0
= 1/3
The equation is
y = 1/3x + 2
Therefore, function C has greatest initial value and function B has greatest rate of change
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A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Question 26 options:
y = –x + 2
y = x
y = x + 3
y = –x – 7
y= - x + 2.
Step-by-step explanation:1. Find the slope of the given line.The slope of any linear equation will always be the coefficient of the "x" variable when the equation is solved for "y". Since there isn't any number written to the left of "x", the slope of the line is 1.
2. Find the slope of the new line.When looking for the slope of a line perpendicular do another, take the value of the slope and find its multiplicative inverse and change the sign of this value as well. This is how you do it:
Original slope value: 1.
Multiplicative inverse: 1/1= 1
Changing the sign: -1
3. Form the new equation.Using the calculated value of the slope "m", which is -1, use the formula for calculating linear equations with both the slope and the values of the ordered pair:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
Substitute the values and simplify.
[tex]y-(-3) =(-1)(x-(5) )\\ \\y+3=(-1)(x)-(-1)(5)\\ \\y+3=(-1x)-(-5)\\ \\y+3=-1x+5\\ \\y=-1x+2\\ \\y=-x+2[/tex]
4. Conclude.A line that passes through point (5, –3) and is perpendicular to the equation y = x is y= - x + 2.
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