A triangle has a base length of 6ac^2 and a height 3 centimeters more than the base length. Find the area of the triangle if a = 2 and c = 3.
Answers:
3,078cm^2
11,988cm^2
2,025cm^2
5,994cm^2
Answers
The area of the triangle if a = 2 and c = 3 is: D. 5,994 cm²
How to calculate the area of a triangle?In Mathematics and Geometry, the area of a triangle can be calculated by using this formula:
Area of triangle = 1/2 × b × h
Where:
b represent the base area.h represent the height.Based on the information provided above, the base area of this triangle can be modeled by the following mathematical expression:
Base area = 6ac²
Base area = 6 × 2 × 3²
Base area, b = 108 cm
Height, h = 3 + b
Height, h = 3 + 108
Height, h = 111 cm.
Now, we can determine the area of this triangle:
Area of triangle = 1/2 × 108 × 111
Area of triangle = 5,994 cm²
Read more on area of triangle here: brainly.com/question/12548135
#SPJ1
Related Questions
An independent-measures analysis of variance (ANOVA) is used to evaluate the mean differences for a research study comparing four treatments with a separate sample of n = 8 in each treatment.
If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision?
a) reject the null hypothesis with α=.05 but not with α=.01
b) reject the null hypothesis with either α=.05 or α=.01
c) fail to reject the null hypothesis with either α=.05 or α=.01
d) There is not enough information to make a statistical decision.
Answers
Comparingthe F-ratio of 4.60 to these critical values, we see that it is greater than the value for α = .05, but less than the value for α = .01. Therefore, the correct statistical decision is to reject the null hypothesis with α = .05, but not with α = .01. Option a) is the correct answer.
An independent-measures analysis of variance (ANOVA) is a statistical test used to evaluate the mean differences between two or more groups. In this case, we are comparing four treatments, each with a separate sample of n = 8.
The null hypothesis for an ANOVA is that there are no significant differences between the means of the groups being compared. The alternative hypothesis is that at least one of the means is different from the others.
To test this hypothesis, we use an F-ratio, which is the ratio of the variance between groups to the variance within groups. If the F-ratio is large enough, we can reject the null hypothesis and conclude that there are significant differences between the means.
In this case, the data produce an F-ratio of F = 4.60. To make a statistical decision, we need to compare this value to a critical value from an F-distribution table. The critical value depends on the degrees of freedom for the numerator and denominator of the F-ratio, as well as the level of significance (α) chosen for the test.
Since we have four groups, the numerator degrees of freedom are k-1 = 3, where k is the number of groups. The denominator degrees of freedom are (k-1)(n-1) = 21, where n is the sample size for each group.
For a two-tailed test with α = .05, the critical F-value for these degrees of freedom is 3.10. For α = .01, the critical value is 5.10.
To know more about null hypothesis visit:-
https://brainly.com/question/28098932
#SPJ11
Use the Distributive
Property to find 1/3 x 6 1/2
Answers
a x (b + c) = a x b + a x c
To apply this property to 1/3 x 6 1/2, we can rewrite 6 1/2 as the sum of 6 and 1/2:
1/3 x 6 1/2 = 1/3 x (6 + 1/2)
We can then use the distributive property to distribute 1/3 to each term inside the parentheses:
1/3 x (6 + 1/2) = 1/3 x 6 + 1/3 x 1/2
Simplifying this expression, we get:
1/3 x 6 + 1/3 x 1/2 = 2 + 1/6
Therefore, 1/3 x 6 1/2 = 2 1/6.
if a short-day (long-night) plant flowers, you know that it received if a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period. fewer consecutive hours of darkness than its critical period. fewer consecutive hours of light than its critical period. more consecutive hours of light than its critical period.
Answers
If a short-day (long-night) plant flowers, you know that it received more consecutive hours of darkness than its critical period.
This is because short-day plants (also known as long-night plants) require a certain period of uninterrupted darkness (usually around 12-16 hours) to trigger flowering. If the plant receives more hours of darkness than its critical period, it will flower.
If it receives fewer hours of darkness than its critical period, it will not flower. Similarly, long-day (short-night) plants require a certain period of uninterrupted light to trigger flowering. If they receive more hours of light than their critical period, they will flower, but if they receive fewer hours of light than their critical period, they will not flower.
To learn more about critical here:
https://brainly.com/question/30168469
#SPJ4
According to the 2010 Census, 11.4% of all housing units in the US were vacant. A county supervisor wonders if her count is different from this. She randomly selects 850 housing units in her county and finds that 120 of them are vacant. Use a significance level of a = 0.05.
a) State the hypotheses in symbols. (2 points)
b) Write the letter next to each assumption and condition that must be present in order to run the 1-Proportion z-Test. (2 points) A. Randomization Condition: The county supervisor conducts the survey randomly. B. 10% Condition: I will assume that this county has more than 8500 housing units. C. Independence Assumption: I will assume that one housing unit being vacant does not affect whether another housing unit is vacant, but I need to be careful here. D. Success/Failure Condition: Both N ∙ P = 850 ∙ 0.114 = 96.9 and n times q = 850 ∙ 0.886 = 753.1 are greater than 10. E. The Nearly Normal Condition: The sample size is 850 so it’s reasonable to say that this condition has been met.
c) Use your calculator to perform a 1-Proportion z-Test and report the test statistic and p-value. Do not make these calculations by hand. Instead, use the 1-PropZTest command in your graphing calculator found under STAT – TESTS. Write out what you entered in your calculator. (3 points)
d) Make a sketch of the test distribution. Your graphing calculator will make this sketch for you if your choose "Draw" instead of "Calculate" in the test input screen. However, your calculator will not label the graph for you. You must label the test statistic along the x-axis and the area under the curve as the p-value. For a two-tailed test such as this one, you will need to divide the pvalue in half and use that value to label each half of the area under the curve. (2 points)
e) Write a full conclusion for this test in the context of the problem (See #2b for format). (4 points)
Answers
a) State the hypotheses in symbols:
H₀: p = 0.114 (null hypothesis: the county's proportion of vacant housing units is equal to the national proportion)
H₁: p ≠ 0.114 (alternative hypothesis: the county's proportion of vacant housing units is different from the national proportion)
b) Assumptions and conditions for 1-Proportion z-Test:
A. Randomization Condition
B. 10% Condition
D. Success/Failure Condition
E. Nearly Normal Condition
c) To perform a 1-Proportion z-Test, enter the following in your calculator:
1-PropZTest(0.114, 120/850, 850)
Test statistic (z): ≈ 2.24
P-value: ≈ 0.025
d) Sketch of the test distribution:
- Label the x-axis with the test statistic (z ≈ 2.24)
- For a two-tailed test, divide the p-value in half (0.025/2 = 0.0125) and label each half of the area under the curve
e) Conclusion:
Since the p-value (0.025) is less than the significance level (α = 0.05), we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of vacant housing units in the county is different from the national proportion of 11.4%.
Learn more about hypotheses here:
https://brainly.com/question/18064632
#SPJ11
Which ordered pair makes both inequalities true?
y>-2x + 3
y
Answers
12. Write the MATLAB statements required to calculate f(t) using the following equation for values of t € [-9,9] in steps of 0.5. f(t) = { (-3t² +5 t 20 3t² +5 t < 0 13. Write a MATLAB function named UniGen that generates a specified number (n) of random values that are uniformly distributed on any given interval specified by values a and b, that is, [a, b].
Answers
12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`
13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`
MATLAB code to calculate f(t) using the given equation:
t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5
f = zeros(size(t)); % Initialize f(t) vector
for i = 1:numel(t)
if t(i) < 0
f(i) = -3*t(i)^2 + 5*t(i) + 20;
else
f(i) = 3*t(i)^2 + 5*t(i);
end
end
% Display the results
disp('t f(t)');
disp('--------');
disp([t' f']);
```
This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.
13. MATLAB function UniGen to generate uniformly distributed random values:
function random_values = UniGen(n, a, b)
% n: Number of random values to generate
% a: Start of the interval
% b: End of the interval
random_values = (b - a) * rand(n, 1) + a;
end
This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.
Learn more about MATLAB code
brainly.com/question/12950689
#SPJ11
35°
46"
65"
30"
2x
What is the perimeter? This is a little tougher problem,
and to solve it you'll need to know the lengths of the
segments on either side of the perpendicular height
(which is whyt I gave you the numbers in smaller font).
Submit
Answers
The perimeter of the triangle is 170 inches.
How to calculate the valueTo solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:
sin(35°) = 46/x
x = 46/sin(35°) = 65 inches
Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:
cos(35°) = 65/x
x = 65/cos(35°) = 75 inches
The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:
P = 65 + 75 + 30
= 170 inches
Learn more about perimeter on
https://brainly.com/question/19819849
#SPJ1
The time, T (seconds) it takes for a pot of water to boil is inversely proportional to the cooker setting, H , applied to the pot. When H = 7 , T = 90 . Work out T when H = 3
Answers
\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)
\(\stackrel{\textit{T varies inversely with H}}{T = \cfrac{k}{H}}\hspace{5em}\textit{we also know that} \begin{cases} H=7\\ T=90 \end{cases} \\\\\\ 90=\cfrac{k}{7}\implies 630=k\hspace{5em}\boxed{T=\cfrac{630}{H}} \\\\\\ \textit{when H = 3, what's "T"?}\qquad T=\cfrac{630}{3}\implies T=210\)
Data collected at Toronto International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration.
Answers
The probability that the duration is at least 2 hours is 0.435 and for 3 hours is 0.611, probability that the duration is between 2 and 3 hours is 0.176.
The probability that the duration of a particular rainfall event at Toronto Pearson International Airport is at least 2 hours can be calculated using the exponential distribution with a mean of 2.725 hours. To find this probability, we need to calculate the cumulative distribution function (CDF) of the exponential distribution.
The CDF of an exponential distribution is given by: CDF(x) = 1 - exp(-λx), where λ is the rate parameter. In this case, since the mean is 2.725 hours, we can calculate the rate parameter λ as \(1/2.725.\)
a) To find the probability that the duration is at least 2 hours, we need to calculate CDF(2) = 1 - exp\((-1/2.725 * 2).\)
b) To find the probability that the duration is at most 3 hours, we can calculate CDF(3) = 1 - exp\((-1/2.725 * 3).\)
c) To find the probability that the duration is between 2 and 3 hours, we can subtract the probability calculated in part (a) from the probability calculated in part (b).
For example, if we calculate the CDF(2) to be 0.435 and the CDF(3) to be 0.611, then the probability of the duration being between 2 and 3 hours is \(0.611 - 0.435 = 0.176.\).
In summary: a) The probability that the duration is at least 2 hours is 0.435.
b) The probability that the duration is at most 3 hours is 0.611.
c) The probability that the duration is between 2 and 3 hours is 0.176.
To know more about exponential distribution visit-
brainly.com/question/33722848
#SPJ11
Given question is incomplete. Hence, the complete question is :
Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2.725 hours is a good model for rainfall duration (Urban Stormwater Management Planning with Analytical Probabilistic Models, 2000, p. 69).
a. What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours?
Point M is the midpoint of line segment CD,
shown below.
What are the coordinates of point M?
C (6,10)
M
D (20, 18)
Answers
Answer:
M(13, 14)-------------------------
Each coordinate of the midpoint is the average of endpoints:
x = (6 + 20)/2 = 26/2 = 13y = (10 + 18)/2 = 28/2 = 14Therefore M is (13, 14).
IM SICK OF ALL THE FAKE LINKS! Can I get help?
Answers
Answer:
equation: 28 = 2h+ h + h or you could say 28 = 4h
h= 7
Step-by-step explanation:
since both lines are the same length they equal each other.
to get h = 7 you have to solve the equation you made.
28 = 4h
28/4 = 4h/4
7 = h
mark as brainliest please :)
How do news paper work?
Answers
Exit Find the digit 5 in each of these numbers. 15.2 3.5 The 5 in 3.5 is 1 place to the right of the 5 in 15.2. Which sentence correctly compares the values? A. The value of the 5 in 3.5 is times the value of the 5 in 15.2. B. The value of the 5 in 3.5 is times the value of the 5 in 15.2. C. The value of the 5 in 3.5 is 10 times the value of the 5 in 15.2. D. The value of the 5 in 3.5 is 100 times the value of the 5 in 15.2.
Answers
Answer:
The value of the 5 in 3.5 is 1/10 times the value of the 5 in 15.2
Step-by-step explanation:
15.2
2 = tenth = 2/10 = 0.2
5 = unit = 5
1 = tens = 10
3.5
5 = tenth = 5/10 = 0.5
3 = units =3
5 tenth ÷ 5 units
= 5/10 ÷ 5
= 5/10 × 1/5
= 5/50
= 1/10
Check:
1/10 × 5
= 5/10
= 0.5
The Wheelers’ bill at a restaurant is $63.00. How much total money is Mr. Wheelers' lunch if he plans to tip 15%?
asap besties
Answers
we know that
when you want to figure out a tip, you take your total bill and multiply it by the percentage you would like to tip them
so
15%=15/100------> 0.15
$63*0.15=$9.45
the answer is
$9.45
X
The table below shows the number of gallons of water in a fish tank after the tank has been leaking
water at a steady rate.
Water Leaked
Minutes Leaking
Gallons of Water
Remaining in Tank
у
0
75
3
67.5
7
57.5
15
37.5
21
22.5
26
10
2
When these data are graphed on a coordinate grid, the points all lie on the same line. What are the
slope and y-intercept of this line?
slope = 3, y-intercept = 30
slope - y-intercept = 30
o slope = - , y-intercept = 75
o slope = .y-intercept = 75
Answers
Find the length of the second leg of the triangle round to the nearest hundredth
Answers
Answer:
\(\displaystyle \frac{3\sqrt{230}}{5}\)
Step-by-step explanation:
Use the Pythagorean Theorem:
\(\displaystyle a^2 + b^2 = c^2 \\ \\ 9,7^2 + b^2 = 13,3^2; \sqrt{82,8} = \sqrt{b^2} \\ \\ \frac{3\sqrt{230}}{5}\:[or\:9,0994505329...] = b\)
So, you have this:
\(\displaystyle 9,1 ≈ b\)
I am joyous to assist you at any time.
A restaurant customer left $3.50 as a tip. The tax on the meal was 7% and the tip was 20% of the cost including tax.
Answers
Answer:
17.50
Step-by-step explanation:
you really don't need to know the tax amount.
20% of x = 3.50
(20/100) x = 3.50 Divide top and bottom of the left number by 20
(20÷20) / (100÷20) * x = 3.50
(1/5) x = 3.50 Multiply both sides by 5
x = 3.50 * 5
x = 17.50
The meal cost 17.50
HOPE THIS HELPS
A rectangle has vertices a(1, 1), b(1, 4), c(8, 4), and d(8, 1). find the perimeter of the rectangle.
Answers
The perimeter of the rectangle is 20 units.
What is the total length of the rectangle's sides?The given rectangle has vertices at points A(1, 1), B(1, 4), C(8, 4), and D(8, 1). To find the perimeter, we need to calculate the sum of the lengths of all four sides.
Using the distance formula between two points in a coordinate plane, we can find the length of each side:
Side AB:
AB = √((\(x_2 - x1)^2\) + (\(y_2\) - y1)²)
AB = √((1 - 1)² + (4 - 1)²)
AB = √(0² + 3²)
AB = √(0 + 9)
AB = 3 units
Side BC:
BC = √((x₂ - x1)² + (y₂ - y1)²)
BC = √((8 - 1)² + (4 - 4)²)
BC = √(7² + 0²)
BC = √(49 + 0)
BC = √49
BC = 7 units
Side CD:
CD = √((x₂ - x1)² + (y₂ - y1)²)
CD = √((8 - 8)² + (1 - 4)²)
CD = √(0² + (-3)²)
CD = √(0 + 9)
CD = 3 units
Side DA:
DA = √((x₂ - x1)² + (y₂ - y1)²)
DA = √((1 - 8)² + (1 - 1)²)
DA = √((-7)² + 0²)
DA = √(49 + 0)
DA = √49
DA = 7 units
To find the perimeter, we add up the lengths of all four sides:
Perimeter = AB + BC + CD + DA
Perimeter = 3 + 7 + 3 + 7
Perimeter = 20 units
Learn more about Perimeter
brainly.com/question/30252651
#SPJ11
35 more than a number x is 73
Answers
Answer:
38
Step-by-step explanation:
X+35=73
x=73-35
x=38
Answer:
X=38
Step-by-step explanation:
x+35=73
-35 -35
I need this question answered ASAP
Answers
The ordered pair that gives the location of point B is given as follows:
(2, f(2)).
What are the ordered pairs?The notation of an ordered pair is given as follows:
(x-coordinate,y-coordinate).
For a function given by f(x), we have that the y-coordinate is the numeric value at point x, hence the format of the ordered pair is given as follows:
(x, f(x)).
In this problem, the x-coordinate of the point B is of:
x = 2.
Hence the ordered pair is given as follows:
(2, f(x)).
Then the numeric value of the function at x = 2 will be given by:
f(2).
Hence the ordered pair will be of:
(2, f(2)).
Meaning that the bottom right option is the correct option among the options given on the image.
More can be learned about ordered pairs at https://brainly.com/question/1528681
#SPJ1
6+3(6x-7)=ax+b make A and B make the problem have infinitely many solution. if you could pleases hurry
Answers
Answer:
sry
"j3ewqdusifqj43we0q9d8uq-idw30oasc[k-0q239ifk09eqwi,dci-0kew-f328rufj34uewdcm3riy4hg0n38ry2vn7
Answer:
A = 18 and B = -15
Explanation:
\(6+3(6x-7)=ax+b\\6+18x-21=ax+b\\18x-15=ax+b\\\) An equation that is equated to itself has infinitely many solutions, because every point on its line is a solution.A company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". Which of the following statements is true? She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The rcent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.
Answers
The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:
Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:
She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.
To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:
S(n) = 70000(1.2)
S(n) = 84000
The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)
S(1) = 84000
The percent increase of her salary is: S(n) = 70000(1.2)n
S(n) - S(n-1) / S(n-1) × 100%
S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%
S(n) - S(n-1) / S(n-1) × 100% = 20%
Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.
To know more about salary visit:
https://brainly.com/question/14371457
#SPJ11
bank of america's consumer spending survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. using data from a sample of credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). using the difference data, the sample mean difference was , and the sample standard deviation was . a. formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out. - select your answer - - select your answer - b. use level of significance. can you conclude that the population means differ? - select your answer - what is the -value? (to 6 decimals) c. which category, groceries or dining out, has a higher population mean annual credit card charge? - select your answer - what is the point estimate of the difference between the population means? round to the nearest whole number. what is the confidence interval estimate of the difference between the population means? round to the nearest whole number. ,
Answers
a. Null hypothesis: The population means credit card charges for groceries and dining out are equal.
Alternative hypothesis: The population means credit card charges for groceries and dining out are not equal.
b. Using a level of significance of 0.05, we can conclude that the population means differ since the calculated p-value is less than 0.05.
c. The point estimate of the difference between the population means is also not provided in the question. Therefore, we cannot calculate the confidence interval estimate of the difference between the population means.
a. To formulate the null and alternative hypotheses, you can use the following notation:
H0 (null hypothesis): μ1 - μ2 = 0 (There is no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
Ha (alternative hypothesis): μ1 - μ2 ≠ 0 (There is a difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out)
b. To determine if the population means differ at a given level of significance (let's say α), you would need to perform a hypothesis test using the sample mean difference, sample standard deviation, and sample sizes for both populations. Unfortunately, you didn't provide these values, so I cannot perform the test or calculate the p-value.
c. To determine which category has a higher population mean annual credit card charge, you would need to compare the point estimate of the difference between the population means. Since you didn't provide the sample mean difference, I cannot determine which category has a higher population mean annual credit card charge.
We cannot determine which category, groceries or dining out, has a higher population mean annual credit card charge without additional information such as the sample mean credit card charges for each category. The point estimate of the difference between the population means is also not provided in the question.
Additionally, to calculate the confidence interval estimate of the difference between the population means, you would need the sample mean difference, sample standard deviation, and sample sizes. Without this information, I cannot provide the confidence interval estimate.
Learn more about the null hypothesis:
brainly.com/question/28920252
#SPJ11
help solve 90 please
Answers
Answer:
c=263
Step-by-step explanation:
Algebra II 5.02: Solve Radical Equations
Answers
Radical Equations
Step 1
To demonstrate how to solve a radical equation, let's use the following equation as an example:
Find the measure of Angle 8
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Angle 8 = 99°Since they form corresponding Angle pair ~
There are 8employees on The Game Shop's sales team. Last month, they sold a total of g games. One of the sales team members, Chris, sold 17 fewer games than what the team averaged per employee. How many games did Chris sell? Write your answer as an expression.
Answers
Answer:
(g/8) - 17
Step-by-step explanation:
Given that:
Number of employees = 8
Employees sold a total of g games
Chris sale = 17 fewer than team Average
Number of games Chris sold :
Team average :
Total sales made / number of employees
Team average = g/ 8
Number of games sold by Chris:
(g/8) - 17
Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?
Answers
Answer:
There are 26 students in the class
Step-by-step explanation:
Let n millilitres be the solution in the beaker
Let x be the number of students in a class
He gives 3 millilitres of solution to each student . He will have 5 millilitres left over.
So, Solution distributed = 3x
Remaining solution = n-3x
So, n-3x = 5 ----1
In order to give each student 4 millilitres of solution, he will need an additional 21 millilitres.
So, n-4x=-21 -----2
Substitute the value of n from 1 in 2
So, 5+3x-4x=-21
5-x=-21
26=x
Hence There are 26 students in the class
Use cylindrical shells to find the volume of the cone generated when the triangle with vertices (0, 0), (0,r), (h, 0), where r> 0 and h> 0, is revolved about the x-axis. NOTE: Enter the exact answer. V =
Answers
To find the volume of the cone generated by revolving a triangle with vertices (0, 0), (0, r), and (h, 0) around the x-axis, we can use the method of cylindrical shells.
First, let's consider a vertical slice of the cone parallel to the y-axis. This slice forms a cylindrical shell when revolved around the x-axis. The height of the shell is given by h, the base radius is given by the distance from the y-axis to the point (0, r), which is r, and the circumference of the shell is given by the distance around the slice, which is 2πx, where x represents the distance along the x-axis.
The volume of the cylindrical shell can be calculated using the formula V_shell = 2πx(r)(h). Integrating this volume from x = 0 to x = h will give us the total volume of the cone.
Integrating the expression 2πx(r)(h) with respect to x over the interval [0, h] yields V = 2πrh²/2 = πrh²/2.
Therefore, the volume of the cone generated by revolving the triangle about the x-axis is V = πrh²/2.
Learn more about cylindrical here:
https://brainly.com/question/13721630
#SPJ11
Which equation shows the inverse property of multiplication?
Answers
Answer:
C
Step-by-step explanation:
Answer:
(a/b)*(b/a)=1.
Step-by-step explanation: