The total cost of painting and tiling a community hall shaped as a cuboid with the given dimensions is £972. This is based on calculating the surface area for paint and the floor area for tiles, then multiplying by the respective costs per m².
Explanation:To solve this problem, we first need to figure out the total surface area of the cuboid, which will include the floor area for the tiles, and all sides for the paint.
Surface area of the cuboid involves calculating area for all six sides, which totals to 2*(lb + bh + hl), where l is length, b is breadth, and h is height.
Substituting the values given, the total surface area of the cuboid is 2*(40*15 + 15*3 + 3*40) = 2*(600 + 45 + 120) = 2*765 = 1530m2.
The floor area is length * breadth i.e., 40m * 3m = 120 m2.
Next, we calculate the cost of painting and tiling. We know 10 liters of paint covers 25 m2 and costs £10.
So, 1 litre covers 25/10 = 2.5m2 and similarly costs £10/10 = £1.
Therefore, the paint costs for 1530 m2 are 1530/2.5 = 612 litres * £1/litre = £612.
For tiling, the cost for 1m2 is £3, so for a 120 m2 floor, the cost will be 120m2*£3/m2 = £360.
Therefore, the total cost for paint and tiles is £612 + £360 = £972.
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Nina made two investments: Investment \text{A}A has a value of \$50$50 at the end of the first year and increases by 8\%8% per year. Investment \text{B}B has a value of \$60$60 at the end of the first year and increases by \$3$3 per year. Nina checks the value of her investments once a year, at the end of the year. What is the first year in which Nina sees that investment \text{A}A's value exceeded investment \text{B}B's value?
Answer: 7 years
Step-by-step explanation:
A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you? need?
Answer:
[tex]13\frac{1}{3}[/tex] cups
Step-by-step explanation:
We are told that a recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B.
To find the number of cups of ingredient B we will use proportions.
[tex]1\frac{2}{3}=\frac{5}{3}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{\frac{1}{2}}{\frac{5}{3}}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
Now let us substitute our amount of Ingredient A =4 in our proportions.
[tex]\frac{4}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
[tex]\frac{\text{Number of cups of ingredient B}}{4}=\frac{10}{3}[/tex]
Multiplying both sides of our equation by 4.
[tex]4*\frac{\text{Number of cups of ingredient B}}{4}=4*\frac{10}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=\frac{40}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=13\frac{1}{3}[/tex]
Therefore, we need [tex]13\frac{1}{3}[/tex] cups of ingredient B to make our recipe.
Answer:
Proportion states that the two ratios are equal.
Given statement: A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A.
By using proportion definition to find ingredients B;
[tex]\frac{\frac{1}{2} }{1\frac{2}{3} } = \frac{4}{B}[/tex]
Simplify:
[tex]\frac{\frac{1}{2} }{\frac{5}{3}} = \frac{4}{B}[/tex]
By cross multiply we get;
[tex]B \cdot \frac{1}{2} = 4 \cdot \frac{5}{3}[/tex]
or
[tex]\frac{B}{2} = \frac{20}{3}[/tex]
Multiply both sides by 2 we get;
[tex]B = \frac{20}{3} \times 2 = \frac{40}{3} = 13\frac{1}{3}[/tex]
Therefore, [tex]13\frac{1}{3}[/tex] cups of ingredients B needs.
Which expression is equivalent to [tex]\frac{4-2}{2^{2}}[/tex]?
A: −16
B: −8
C: 8
D: 16
Answer:
1/2
Step-by-step explanation:
(4-2)
----------
2^2
The numerator is 4-2 = 2
The denominator is 2^2 = 4
2
------
4
1/2
Elvie can type 4,200 words in 30 minutes givr the ratio of the time in minutes to the number of words
Answer:
1 : 140
Step-by-step explanation:
Ratio is 30 : 4200
Divide both numbers by 30:-
= 1 : 140 (answer)
To calculate the ratio of time to words, divide the minutes by the number of words, resulting in a 30:4200 ratio. This ratio highlights the efficiency of typing, useful for productivity analysis.
Explanation:The question involves calculating the ratio of time in minutes to the number of words typed. Elvie can type 4,200 words in 30 minutes. To find the ratio of time in minutes to the number of words, we divide the number of minutes by the number of words.
First, express both quantities in their simplest forms: 30 minutes and 4,200 words. Then, create the ratio as follows:
Time in minutes : Number of words = 30 : 4,200
For easier comparison or further calculations, the ratio can be simplified by dividing both terms by the greatest common divisor. However, in this case, presenting the ratio in its initial form already communicates the relationship clearly, showing how many words are typed in a given amount of time. The ratio can be crucial for understanding productivity and efficiency in typing or other time-bound tasks.
Colby and Danielle clean pools for extra money over the summer. Colby's income is determined by f(x) = 3x + 12, where x is the number of hours. Danielle's income is g(x) = 5x + 10. If Colby and Danielle were to combine their efforts, their income would be h(x) = f(x) + g(x). Create the new function h(x). If Colby works 4 hours and Danielle works 4 hours, and if they each get half of the money when they work together, will Colby make more money working alone or by teaming with Danielle?
Answer:
Colby makes more money by teaming with Danielle
Step-by-step explanation:
Colby's income =f(x) = 3x+12
and Danielle's income = g(x) = 5x+10
If they combine their efforts the combined income would be
h(x) = 3x+12+5x+10 = 8x +22
If shared equally between them
Colby would get 1/2(8x+22) = 4x+11 and
Danielle would get 1/2(8x+22) = 4x+11
Since given they worked each for 4 hours
Colby income = Danielle income= 4(4) +11 = 27
If not combined, then
Colby income 3(4) + 12=24 and
Danielle income= 5(4) +10 = 30
Because of combining Colby makes more money by teaming with Danielle.
The difference is 3 for 4 hours work.
Answer:
B
Step-by-step explanation:
team with Danielle , h(x)=8x+22
please help on this one? :)
Answer:
62 kg: A
Step-by-step explanation:
The black line is called line of best fit. This line shows the points plotted and how they compare to the predicted amounts. The reason why A is the correct answer is because all of the other blue points line up with the line of best fit. Since the point 62kg is NOT on the line of best fit, that is the point where experimental error may have occurred.
Rectangle ABCD is similar to rectangle WXYZ. What is the value of AB if WX is & feet, AD is 12 feet, and WZ is 16 feet?
Answer:
Similar rectangles states that the corresponding sides are in proportion.
As per the statement:
Rectangle ABCD is similar to rectangle WXYZ.
WX = 8 feet, AD = 12 feet and WZ = 16 feet.
Since. Rectangle ABCD and rectangle WXYZ are similar
then;
their corresponding sides are in proportion:
[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]
To find the value of AB:
[tex]\frac{AB}{WX}=\frac{AD}{WZ}[/tex]
Substitute the given values we have;
[tex]\frac{AB}{8}=\frac{12}{16}[/tex]
Multiply both sides by 8 we have;
[tex]AB = \frac{12}{16} \times 8 = \frac{96}{16}=6[/tex]
Therefore, the value of AB is 6 units.
The value of AB in the similar rectangles ABCD and WXYZ, given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, is calculated as 6 feet by using the property of similar rectangles that the ratios of their corresponding sides are equal.
Explanation:The subject in question deals with similar rectangles. Since rectangle ABCD is similar to rectangle WXYZ, the ratio of their corresponding sides will be equal. This means that the ratio of side AB to side WX should be the same as the ratio of side AD to side WZ.
Given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, we can set up the proportion as AB/WX = AD/WZ. Substituting the known values into this proportion we get AB/8 = 12/16.
To find the value of AB, we can cross multiply and solve for AB to get AB = (8 * 12) / 16 = 6 feet.
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You are a space alien. You visit planet Earth and abduct 97 chickens, 47 cows, and 77 humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected.
Create a probability model to show how likely you are to select each type of Earth creature.
Input your answers as fractions or as decimals rounded to the nearest hundredth.
Chicken estimated probability:
Cow estimated probability:
Human estimated probability:
Answer:
Chicken=97/221=0.44
Cow=47/221=0.21
Human=77/221=0.35
Step-by-step explanation:
Two numbers have a difference of 34. What is the sum of their squares if it is a minimum?
[tex]a,b-the\ numbers\\\\a-b=34\to a=34+b\\\\a^2+b^2\to minimum\\\\\text{substitute:}\\\\(34+b)^2+b^2\to minimum\\\\f(b)=(34+b)^2+b^2\qquad\text{use}\ (x+y)^2=x^2+2xy+y^2\\\\f(b)=34^2+(2)(34)(b)+b^2+b^2\\\\f(b)=1156+68b+2b^2\to f(b)=2b^2+68b+1156\\\\y=ax^2+bx+c\\\\if\ a>0\ then\ a\ parabola\ op en\ up\\if\ a<0\ then\ a\ parabola\ op en\ down\\\\if\ a>0\ then\ a\ parabola\ has\ a\ minimum\ at\ a\ vertex\\if\ a<0\ then\ a\ parabola\ has\ a\ maximum\ at\ a\ vertex[/tex]
[tex]\text{We have}\ a=2>0.\ \text{Therefore the parabola has the minimum at the vertex.}\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a};\ k=f(h)\\\\\text{We have}\ a=2\ \text{and}\ b=68.\ \text{Substitute:}\\\\h=\dfrac{-68}{2(2)}=\dfrac{-68}{4}=-17\\\\k=f(-17)=2(-17)^2+68(-17)+1156=2(289)-1156+1156=578[/tex]
[tex]\text{Therefore}\ b=-17\ \text{and}\ a=34+b\to a=34+(-17)=17.\\\\Answer:\ a^2+b^2=17^2+(-17)^2=289+289=578[/tex]
The minimum sum of their squares is [tex]\(578\)[/tex].The sum of their squares is a minimum when each number is half the difference between them.The sum of their squares is[tex]\(2 \times \left(\frac{34}{2}\right)^2\)[/tex].
Let the two numbers be [tex]\(x\)[/tex] and [tex]\(y\)[/tex], where [tex]\(x > y\)[/tex]. Given that the difference between the numbers is 34, we can express [tex]\(y\)[/tex] in terms of [tex]\(x\) as \(y = x - 34\)[/tex].
We want to find the minimum value of the sum of their squares, which is [tex]\(x^2 + y^2\)[/tex]. Substituting [tex]\(y\)[/tex] with [tex]\(x - 34\)[/tex], we get:
[tex]\[S = x^2 + (x - 34)^2\] \[S = x^2 + x^2 - 68x + 1156\] \[S = 2x^2 - 68x + 1156\][/tex]
To find the minimum value of [tex]\(S\)[/tex], we take the derivative of [tex]\(S\)[/tex] with respect to [tex]\(x\)[/tex] and set it equal to zero:
[tex]\[\frac{dS}{dx} = 4x - 68\][/tex]
Setting the derivative equal to zero gives us:
[tex]\[4x - 68 = 0\] \[x = \frac{68}{4}\] \[x = 17\][/tex]
Since [tex]\(y = x - 34\)[/tex], we substitute [tex]\(x = 17\)[/tex] to find [tex]\(y\)[/tex]:
[tex]\[y = 17 - 34\] \[y = -17\][/tex]
So the two numbers are 17 and -17. The sum of their squares is:
[tex]\[17^2 + (-17)^2 = 289 + 289\] \[= 578\][/tex]
However, since we are looking for the minimum sum of squares, we can also use the property that the sum of squares is minimum when the numbers are equidistant from their mean. The mean of the two numbers is [tex]\(\frac{34}{2}\)[/tex], so the numbers would be [tex]\(\frac{34}{2}\)[/tex] and [tex]\(-\frac{34}{2}\)[/tex]. The sum of their squares is:
[tex]\[2 \times \left(\frac{34}{2}\right)^2 = 2 \times 289\] \[= 578\][/tex]
Please help!!!!
Leonard wants to restrict the domain of the tangent function so that its inverse is a function. Which description best describes how he could restrict the domain?
A) Choose any interval between consecutive asymptotes.
B) Choose any interval that includes two asymptotes.
C) Choose any interval of length 2π radians.
D) Choose any interval of length π radians.
Answer:
Correct choice is A
Step-by-step explanation:
If a function has an inverse, then there is at most one x-value for each y-value.
The tangent function is periodic with period [tex]\pi.[/tex] Hence, at each value for which [tex]f(x)=\tan x[/tex] is defined, [tex]f(x+n\pi )=\tan x[/tex] for each integer n. Therefore, the function [tex]f(x)=\tan x[/tex] does not have an inverse. Since tangent is not a one-to-one function, the domain must be limited. From examining the graph of the tangent function, we see that in each interval of the form
[tex]\left((2k−1)\dfrac{\pi}{2},(2k+1)\dfrac{\pi}{2}\right)[/tex]
where k is an integer, the tangent function assumes every value in its range. Moreover, in each such interval, each y-value is achieved exactly once. Hence, we can create an invertible function by restricting the domain tangent function to one such interval. Such interval is an interval between two consecutive vertical asymptotes [tex]x=(2k−1)\dfrac{\pi}{2}[/tex] and [tex]x=(2k+1)\dfrac{\pi}{2}.[/tex]
Glen has three pairs of shoes, five shirts, and four pairs of pants. How many outfits considering one pair of shoes, one shirt, and one pair of pants can he make?
Answer:
3
Step-by-step explanation:
To have full outfits he can only make three
Answer:
she can make 12: A
Step-by-step explanation
add up the numbers of pants, shoes , shirts you will get 12
the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days what is the probability of randomly selecting a pregnant woman whose length of pregnancy is less than 260 days
a.0.2981
b.0.7019
c.0.8186
d.0.1814
Answer:
a. 0.2981
Step-by-step explanation:
We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
Let us find z-score for 260 days.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
[tex]x[/tex] = Sample score,
[tex]\mu[/tex] = Mean
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula we will get,
[tex]z=\frac{260-268}{15}[/tex]
[tex]z=\frac{-8}{15}[/tex]
[tex]z=-0.53[/tex]
Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.
From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.
Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.
Jack has $55 and Emily has $28. Jack is saving $4 per day, and Emily is saving $13 per day. After how many days will Jack and Emily have the same amount of money.
Answer:
About 4
Step-by-step explanation:
Answer: B: 3 Days
Step-by-step explanation:
Let x be the number of days when Jack and Emily have the same amount of money.
Then, the total amount saved by Jack =4x+55
The total amount saved by Emily = 13x+28
According to the question,
13x + 28 = 4x + 55
13x - 4x = 55 - 28
9x = 27
x = 3
Brainiest PLZ
Calculate s24 for the arithmetic sequence in which a13=1.9 and the common difference is d=3.7.
Answer:
The correct answer option is 42.6.
Step-by-step explanation:
We know that in a arithmetic sequence, [tex]a_{13}=1.9[/tex] and the common difference is [tex](d)=3.7[/tex].
The standard form of an arithmetic sequence is given by:
[tex]a_n=a_1+(n-1)d[/tex]
So we will substitute the given values in this formula to find the value of [tex]a_1[/tex].
[tex]a_{13}=a_1+(13-1)3.7[/tex]
[tex]1.9=a_1+(12)3.7[/tex]
[tex]1.9=a_1+44.4[/tex]
[tex]a_1=-42.5[/tex]
Now finding the 24th term"
[tex]S_{24}=a_1+(n-1)d\\\\S_{24}=-42.5+(24-1)3.7\\\\\\S_{24}=42.6[/tex].
Therefore, the 24th term of the given arithmetic sequence is 42.6.
Answer:
Just took this test the correct answer is 1.2
At the movie theatre 30% of the audience members were children. If the number of children at the movie theatre was 210, what was the total number of people at the movie theatre?
Answer:
The total number of people at the movie theatre is 700.
Step-by-step explanation:
Formula
[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]
As given
At the movie theatre 30% of the audience members were children.
If the number of children at the movie theatre was 210.
Percentage = 30%
Part value = 210
Put in the formula
[tex]30 = \frac{210\times 100}{Total\ value}[/tex]
[tex]Total\ value = \frac{21000}{30}[/tex]
Total value = 700
Therefore the total number of people at the movie theatre is 700.
3x x 2x
IS THE ANSWER 6x^2???
Answer:
yes
Step-by-step explanation:
3x × 2x can be broken down as
3 × x × 2 × x = 3 × 2 × x × x = 6 × x² = 6x²
How do the graphs of the function differ from the graph of f(x)=1.5x^3
Answer: p(x) = steeper
q(x) = less steep and reflection
r(x) = reflection
Step-by-step explanation:
The parent graph is: f(x) = 1.5x³
If the absolute value of the coefficient in front of x³ is greater than 1.5, then it is steeper (the graph is stretched).If the absolute value of the coefficient in front of x³ is less than 1.5, then it is less steep (the graph is shrunk/compressed).A negative sign in front of the coefficient represents a reflection over the x-axis.p(x): 2 > 1.5 , so it is stretched (steeper).
p(x): coefficient has a positive sign, so it is NOT a reflection
q(x): 1 < 1.5 , so it is shrunk/compressed (less steep).
q(x): coefficient has a negative sign, so it is a reflection over x-axis
r(x): 1.5 = 1.5 so it is neither a stretch or a shrink
r(x): coefficient has a negative sign, so it is a reflection over x-axis
The graph of the function f(x) = 1.5x^3 has a steep increase or decrease, exhibits symmetry, and passes through the origin.
Explanation:When comparing the graphs of different functions, it's important to analyze their key characteristics. In the case of the function f(x) = 1.5x^3, the graph will be a cubic function. Here are three significant differences between the graph of f(x) = 1.5x^3 and other functions:
The graph will have a steep increase if x > 0 and a steep decrease if x < 0, due to the positive coefficient of the x^3 term.The graph will exhibit symmetry with respect to the y-axis because the power of x is odd.The graph will pass through the origin (0, 0) since there is no constant term in the function.Learn more about Graphs here:https://brainly.com/question/26215563
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Find the inverse.
f(x)= 2x-5/3x+4
To find the inverse of the function f(x) = 2x - 5/3x + 4, swap x and y and solve for y. The inverse function is f-1(x) = (x - 4) / (2 - 5/3).
Explanation:To find the inverse of a function, we need to swap the variables x and y and solve for y. Let's start:
f(x) = 2x - 5/3x + 4
Replace f(x) with y:
y = 2x - 5/3x + 4
To find the inverse, solve for x:
x = (y - 4) / (2 - 5/3)
Now, swap x and y to find the inverse function:
y = (x - 4) / (2 - 5/3)
Therefore, the inverse of f(x) = 2x - 5/3x + 4 is f-1(x) = (x - 4) / (2 - 5/3).
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1960, the U.S. per capita personal income was $2283. in 2000, it was $30,069. find an exponential function to model this data
f(t) = 2283·(30069/2283)^(t/40) . . . . . t = years after 1960
Step-by-step explanation:In simplest terms, the exponential function can be written from the initial value, the ratio of given values, and the time period over which that ratio was effective. The form is ...
... f(t) = (initial value) · (ratio of values)^(t/(time period))
This works for both increasing and decreasing exponentials.
_____
Using e as a base
It can be converted to an exponential with "e" as the base by taking logarithms.
ln(f(t)) = ln(2283) + (t/40)·ln(30069/2283) = ln(2283) + 0.06445011·t
Taking antilogs, this is ...
... f(t) = 2283·e^(0.06445011·t)
_____
Comment on accuracy
The final number (30,069) when including cents (30,069.00) has 7 significant digits. In order to get the function f(t) to reproduce that number to 7 significant digits, the multiplier of t in the exponential function must be accurate to 7 significant digits. (Fairly commonly, you will see it rounded to 2 or 3 significant digits. It cannot give 30069 even to 5 digits in that case.)
I need help with this problem
Answer:
D
Step-by-step explanation:
Because it's saying what is the shape of the "Square" inside of the cylinder.
Answer:
C) rectangle, would be the best answer beacuse the shape of the dotted line clously resembles a rectangle
Step-by-step explanation:
I could probably figure this out, but it lists A, B, and C as points and I don't see them. I assume I'd have to place them somewhere, but I don't know where I would put them.
Answer: Choice D) Opposite sides of a parallelogram are congruent
Likely a typo has been made because A, B, C, and D aren't shown. I think your teacher meant to say PQ = RS and QR = PS
A parallelogram has properties that the opposite sides are parallel, and it can be proven that the opposite sides are congruent as well.
Answer:
D is the right answer hope this helps!!!!!!!!
A cheerleading squad consists of ten cheerleaders of ten different heights. How many ways are there for the cheerleaders to line up for a photo in two rows of five people each so that each cheerleader in the back row is taller than the one immediately in front?
Final answer:
The cheerleaders can be lined up in 3,628,800 ways.
Explanation:
To solve this problem, we need to consider the arrangement of the cheerleaders in two rows of five people each. Since each cheerleader in the back row must be taller than the one immediately in front, we can start by arranging the taller cheerleaders in the back row.
There are 10 different heights, so we have 10 choices for the tallest cheerleader in the back row. After choosing the tallest cheerleader in the back row, there are 9 choices for the second tallest cheerleader, 8 choices for the third tallest cheerleader, and so on, until there are 6 choices for the shortest cheerleader in the back row.
Once we have arranged the back row, there are 5 cheerleaders left to be arranged in the front row. Since the heights of the cheerleaders in the front row are smaller than the heights of the cheerleaders in the back row, we can simply arrange them in any order. There are 5! (5 factorial) ways to arrange the cheerleaders in the front row.
Therefore, the total number of ways to line up the cheerleaders is: 10 x 9 x 8 x 7 x 6 x 5! = 10! = 3,628,800 ways.
Mark solved 18 out of 20 problems correctly on his math quiz. What percent of the problems were correct?
Final answer:
Mark solved 90% of the problems correctly on his math quiz, calculated by dividing 18 (correct answers) by 20 (total questions) and then multiplying by 100%.
Explanation:
To calculate the percent of problems Mark solved correctly on his math quiz, we use the formula for percentages, which is: (Number of items of interest ÷ Total number of items) × 100%
In this case, Mark solved 18 out of 20 problems correctly. So, we set up the calculation as follows:
(18 ÷ 20) × 100% = 0.9 × 100% = 90%
Therefore, Mark got 90% of the problems correct on his quiz.
Bryan and Seth are both members of the same private social networking site. Bryan’s membership plan can be expressed with the function y = 9.50x + 22, where x is the number of months that he is a member and y is the total cost. Seth’s membership fees are shown in the graph.
If x represents the number of months that they are members of the social networking site, how much will Bryan and Seth each pay after 15 months of membership?
Answer:
After 15 month of membership, Brian will pay $164.5 and Seth will pay $100.
Step-by-step explanation:
Brian
y=9.50(15)+22
y=142.5+22
y=164.5
Seth
(15,100)
please help
The volume V of a pyramid is given by the formula V=13Bh, where B is the area of the base and h is the height.
a. Solve the formula for h.
h=
b. Find the height h of the pyramid.
The height is centimeters.
Answer:
(a). [tex]h=\frac{3V}{B}[/tex]
(b). 18 cm.
Step-by-step explanation:
We have been given the volume of pyramid is given by the formula [tex]V=\frac{1}{3}Bh[/tex], where B is the area of the base and h is the height.
(a). Let us solve the given formula for h as:
[tex]V=\frac{1}{3}Bh[/tex]
Multiply both sides by [tex]3[/tex]:
[tex]3\cdotV=3\cdot\frac{1}{3}Bh[/tex]
[tex]3V=Bh[/tex]
Divide both sides by B:
[tex]\frac{3V}{B}=\frac{Bh}{B}[/tex]
[tex]\frac{3V}{B}=h[/tex]
Switch sides:
[tex]h=\frac{3V}{B}[/tex]
(b). To find the height for the given pyramid, we will substitute the given values as:
[tex]h=\frac{3(216\text{ cm}^3)}{36\text{ cm}^2}[/tex]
[tex]h=\frac{648\text{ cm}}{36}[/tex]
[tex]h=18\text{ cm}[/tex]
Therefore, the height of the pyramid is 18 cm.
All 150 eighth grade students at a local middle school were asked how many hours they studied during the week. Each row of the table represents one sample from the population. Find the mean of each sample.
Population Data
Row 1
6
5
3
0
4
Row 2
4
5
3
5
6
Row 3
7
1
4
5
3
Row 4
4
2
5
6
3
Which row has the greatest mean?
Answer:
Row 2
Step-by-step explanation:
To find the mean, we add all the numbers and divide by the number of numbers
Row 1:
(6+5+3+0+4)/5 = 18/5 = 3.6
Row 2:
(4+5+3+5+6)/5 = 23/5 = 4.6
Row 3:
(7+1+4+5+3)/5 = 20/5 = 4.0
Row 4:
(4+2+5+6+3)/5 = 20/5 = 4.0
The greatest mean , or the largest mean is 4.6 or Row 2
Answer:
The answer is B) Row 2
Step-by-step explanation:
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Help plz!!
I've already answered question #4.
Answers: 1h, 2e, 3d, 4a, 5f, 6b, 7c, 8g
Statement Reason
1. JKLM is a rectangle 1. Given
2. ∠K and ∠L are right angles 2. Definition of rectangle
3. ΔJKM and ΔMLJ are right angles 3. Definition of right triangles
4. [tex]\overline{JM}[/tex] ≅ [tex]\overline{JM}[/tex] 4. Reflexive Property
5. [tex]\overline{JK}[/tex] ≅ [tex]\overline{LM}[/tex] 5. Definition of rectangle
6. ΔJKM ≅ Δ MLJ 6. HL congruency theorem
Consider the quadratic equation below. Determine the correct set-up for solving the equation using the quadratic formula.
Answer:
--3 ±sqrt((-3)^2 -4(4)(-9))
-------------------------------
2(4)
Step-by-step explanation:
4x^2-5=3x+4
We need to get this in standard form to answer the question
Subtract 3x from each side
4x^2-3x-5=3x-3x+4
4x^2-3x-5=+4
Subtract 4 from each side
4x^2-3x-9 =0
a = 4
b = -3
c = -9
-b ±sqrt(b^2 -4ac)
---------------------------
2a
--3 ±sqrt((-3)^2 -4(4)(-9))
-------------------------------
2(4)
Answer:
--3 ±sqrt((-3)^2 -4(4)(-9))
Step-by-step explanation:
jason is training for a marathon bike ride. His average speed increase from 3 miles per hour to 6 miles per hour in 3 months find the rate of change in the miles per hour that jason bikes
Answer:
The rate of change is 1 mile per hour per month
Step-by-step explanation:
We are given
initial speed = 3 mph
final speed =6 mph
total number of months =3
now, we can use rate of change formula
we know that
rate of change = ( final speed - initial speed)/(total number of months)
now, we can plug values
and we get
Rate of change is
[tex]=\frac{6-3}{3}[/tex] mph per month
=1 mph per month
Jason's rate of change in biking speed is 1 mile per hour per month.
Jason is training for a marathon bike ride. His average speed increases from 3 miles per hour to 6 miles per hour in 3 months. To find the rate of change in the miles per hour that Jason bikes, we use the formula:
Rate of Change = (Final Speed - Initial Speed) / Time Period
The final speed is 6 miles per hour, the initial speed is 3 miles per hour, and the time period is 3 months. Therefore:
Rate of Change = (6 - 3) mph / 3 months
Rate of Change = 3 mph / 3 months
Rate of Change = 1 mph per month
Therefore, Jason's rate of change in biking speed is 1 mile per hour per month.
Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}{cb} = \dfrac{1}{2}$ and the point $d$ is such that $\dfrac{da}{ba} = 3$ and $\dfrac{db}{ba} = 2.$ if $c = (0, 4),$ $d = (4, 0),$ and $a = (x, y),$ what is the value of $2x + y$?
Start with a line segment connecting two points, A and B. [tex]\dfrac{DA}{BA}=3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.
But with [tex]\dfrac{DB}{BA}=2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.
Finally, [tex]\dfrac{AB}{CB}=\dfrac12[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.
Now let [tex]d[/tex] be the length of AB. Then the length of CD in terms of [tex]d[/tex] is [tex]4d[/tex]. We have the coordinates of C and D, and the distance between them is [tex]\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2[/tex]. So
[tex]4d=4\sqrt2\implies d=\sqrt2[/tex]
The slope of the line through C and D is
[tex]\dfrac{0-4}{4-0}=-1[/tex]
and so the equation of the line through these points is
[tex]y-4=-(x-0)\implies x+y=4[/tex]
So the coordinates of A are [tex](x,y)=(x,4-x)[/tex]. The distance between C and A is [tex]d=\sqrt2[/tex], so we have
[tex]\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1[/tex]
Since A falls to the right of C (in the [tex]x,y[/tex] plane, not just in the sketch), we know to take the positive value [tex]x=1[/tex]. Then the [tex]y[/tex] coordinate is [tex]y=4-1=3[/tex].
All this to say that A is the point (1, 3), so
[tex]2x+y=2+3=5[/tex]
The value 2x + y of is 5.
Start with a line segment connecting two points, A and B. [tex]\frac{DA}{BA} =3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.
But with [tex]\frac{DB}{BA} =2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.
Finally, [tex]\frac{AB}{CB} =\frac{1}{2}[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.
Now let be the length of AB. Then the length of CD in terms of is . We have the coordinates of C and D, and the distance between them is
[tex]\sqrt{(4-0)^2+ (4-0)^2} =4\sqrt{2}[/tex]
So
4d= 4√2 = d= √2
The slope of the line through C and D is
[tex]\frac{0- 4}{4-0} = -1[/tex]
and so the equation of the line through these points is
y- 4 = -(x- 0) =x + y =0
So the coordinates of A are (x, y) = (x,4 -x). The distance between C and A is d= √2, so we have
[tex]\sqrt{(x-0)^2+(4- x - 4)^2} = \sqrt{2x^3} = |x| \sqrt{2} = \sqrt{2} = |x| = 1[/tex]
Since A falls to the right of C (in the x, y plane, not just in the sketch), we know to take the positive value . Then the coordinate is .
All this to say that A is the point (1, 3), so 2x + y= 2+3=5
for such more question on coordinates
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Question
Let us have four distinct collinear points a, b, c, and d on the cartesian plane. the point c is such that [tex]\dfrac{ab}{cb} = \dfrac{1}{2}[/tex] and the point d is such that [tex]\dfrac{da}{ba} = 3[/tex] and [tex]\dfrac{db}{ba} = 2[/tex] c = (0, 4), d = (4, 0), and a = (x, y), what is the value of 2x + y?