Answers
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6
Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4
V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)
Related Questions
PLEASE HELP AS SOON AS POSSIBLE!!!!!!!!!!!!!!!!!! |r+3| ≥7 solve the inequality (please show work and steps )
Answers
r + 3 ≥ 7
r ≥ 4
|r+3| = -(r+3) when r < -3 so for r < -3
-(r + 3) ≥ 7
r + 3 ≤ -7
r ≤ -10
The answer to this question is r ≤ -10, r ≥ 4
|r+3| = (r+3)
r + 3 ≥ 7
r ≥ 4
|r+3| = -(r+3)
-(r + 3) ≥ 7
r + 3 ≤ -7
r ≤ -10
So the answer is r ≤ -10, r ≥ 4
A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. you choose one marble from the jar at random. what is the theoretical probability of choosing a white marble?
Answers
P(white)= 20/100 =1/5
P(white)=1/5
A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Answers
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:
[tex]V = xxy = x^{2}y[/tex]
We also know that the bin is constructed from 48 square feet of sheet metal, so:
Surface area of the square base = [tex]x^{2}[/tex]
Surface area of the rectangular sides = [tex]4xy[/tex]
Therefore, the total area of the cube is:
[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]
Isolating the variable y in terms of x:
[tex]y = \frac{48- x^{2} }{4x}[/tex]
Substituting this value in V:
[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]
Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:
[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]
Solving for x:
[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]
Solving for y:
[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]
Then, the dimensions of the largest volume of such a bin is:
Length = 4 ft
Width = 4 ft
Height = 2 ft
And its volume is:
[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]
From a point on a circle, two perpendicular chords are drawn. One is 6 cm from the center and the other one is 3 cm from the center. Find the lengths of these chords.
Answers
The two perpendicular chords will create a rectangle with the center. each side will be half of the parallel sides length.
The two perpendicular chords will create a rectangle with the center. each side will be half of the parallel sides length.
Students washed cars to raise funds for their school. they collected $291 by charging $3.00 per car. how many cars did they wash?
Answers
=$291 total ÷ $3 a car
=97 cars
ANSWER: They washed 97 cars.
Hope this helps! :)
Hamilton received a 75 on his algebra exam. The professor is allowing students to take a 7-question bonus quiz to improve their algebra exam score. Each question answered correctly on the bonus quiz will add 3 points to the exam score. Hamilton needs to receive at least a 90 on his exam score in order to make an "A" for the semester. If x represents the number of questions answered correctly on the bonus quiz, which of the following inequalities symbolizes this situation?
A. 3x + 75 < 90
B. 7x + 75 > 90
C. 3x + 75 > 90
D. 7x + 75 < 90
Answers
Since each question answered right would add 3 points, the amount of questions answered correctly would be x. You then going to add that to his original score, 75. He needs at least a 90, so 90 is the lowest test grade he can afford. Therefore, 90 is should be the greatest number since there are no less than, equal to and such. Knowing that, the answer would be A
Hope this helps!
Final answer:
The correct inequality should be 3x + 75 ≥ 90 to indicate Hamilton needs at least 90 on his exam. The closest option given, which is not entirely accurate, is C. 3x + 75 > 90.
Explanation:
To determine the inequality that represents Hamilton’s situation, we need to calculate how many points he requires to reach a score of at least an “A”, which is 90. Each correct bonus question adds 3 points to his exam score of 75. We need to find the number of questions, x, Hamilton must answer correctly to achieve a total score of 90 or more. Therefore, the inequality that encompasses this scenario is 3x + 75 ≥ 90 because each correct answer contributes 3 points towards closing the 15-point gap between his current score and the desired score of 90.
However, the options given do not include the correct representation which would be 3x + 75 ≥ 90. Instead, the closest option is C. 3x + 75 > 90, which would imply that Hamilton must score more than 90, which is not a requirement for making an “A” (as “A” can include exactly 90).
Find the surface area of the equilateral triangular pyramid.
Answers
1/2g^2 + 7/2 + 3g^2- 4/5g + 1/4
Answers
1 / 2g ^ 2 + 7/2 + 3g ^ 2- 4 / 5g + 1/4
The first thing we must do is to group terms with the same degree:
g ^ 2 (1/2 + 3) - 4 / 5g + (7/2 + 1/4)
Then, rewriting we have:
(7/2) g ^ 2 - (4/5) g + (15/4)
Answer:
(7/2) g ^ 2 - (4/5) g + (15/4)
The expression [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4[/tex]5/4 by combining like terms, which include the [tex]g^2[/tex]s and the constants.
Explanation:The student's question involves combining like terms and simplifying a polynomial expression in mathematics. The expression provided is [tex]1/2g^2 + 7/2 + 3g^2 - 4/5g + 1/4.[/tex]ed to combine like terms, which involves adding or subtracting the coefficients of terms with the same degree.
First, combine the g2 terms (1/2g2 + 3g2) to get 7/2g2. Next, the constant terms (7/2 + 1/4) are combined to yield 15/4. The term with g, which is -4/5g, does not have a like term, so it remains as it is. After combining like terms, the simplified expression is 7/2g2 - 4/5g + 15/4.
An investment of $450 increases at a rate of 6.5% per year. What is the growth factor, b?
Answers
What is the standard deviation of the following data set rounded to the nearest tenth? 52.1, 45.5, 51, 48.8, 43.6
Answers
[tex]\sigma = \sqrt{ \frac{1}{N} \sum (x_i - \mu)^2} [/tex]
where
N is the number of data (in this case, N=5)
[tex]x_i[/tex] are the data
[tex]\mu[/tex] is the average value
Let's calculate the average value:
[tex]\mu = \frac{52.1+45.5+51+48.8+43.6}{5}=48.2 [/tex]
And now we can apply the formula to calculate the standard deviation:
[tex]\sigma = \sqrt{ \frac{1}{5} \sum ( x_i - 48.2 )^2} =[/tex]
[tex]= \sqrt{ \frac{1}{5} ( (3.9)^2 + (-2.7)^2 + (2.8)^2 + (0.6)^2 + (-4.6)^2 ) } =[/tex]
[tex]= \sqrt{ \frac{1}{5} (51.86) } =3.2[/tex]
Answer:
Standard deviation is 3.2.
Step-by-step explanation:
Given data is,
52.1, 45.5, 51, 48.8, 43.6,
Let x represents the data points,
Now, mean of the data is,
[tex]\mu = \frac{52.1 + 45.5 + 51 + 48.8 + 43.6}{5}=48.2[/tex]
Population size, N = 5,
Hence, the standard deviation of the following data set is,
[tex]\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i-\mu )^2[/tex]
[tex]=\sqrt{\frac{1}{5}\sum_{i=1}^{5} (x_i-48.2 )^2[/tex]
[tex]=\sqrt{\frac{1}{5} (15.21+7.29+7.84+0.36+21.16)}[/tex]
[tex]=\sqrt{10.372}[/tex]
[tex]=3.2205589577[/tex]
[tex]\approx 3.2[/tex]
Need this geometry answer quick!
Answers
90 + 6x + 4x = 180
Combine like terms:
90 + 10x = 180
Subtract 90 from both sides:
10x = 90
Divide both sides by 10:
x = 9
Answer: 9
what is the volume , in cubic units , of a pyramid of height 8 and a square base of length 15?
Answers
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answers
48 = k* 16
k = 3
x=3*5
x=15
Answer:
15
Step-by-step explanation:
x =ky
48 = k16
divide by 16
k = 3
plug k into x=ky
x=3*5
x=15
Line RS is tangent to circle Q at point R.
What is the measure of ∠SQR ?
Enter your answer in the box.
Answers
Now that we know 2 angles, we can find the 3rd:
180 - 90 - 32 = 58
Using the tangent and radius theorem, the measure of ∠SQR is 58°.
What is Circle Geometry??From the question, we are to determine the measure of ∠SQR
In the given diagram, QR is a radius
By the tangent and radius theorem,
If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another
∴ ∠QRS = 90°
∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)
∠SQR + 32° + 90° = 180°
∠SQR + 122° = 180°
∠SQR = 180° - 122°
∠SQR = 58°
Hence, the measure of ∠SQR is 58°.
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Simplify the trigonometric expression.
Answers
[tex](1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha [/tex]
Now we can rewrite our expression using the common denominator:
[tex]\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha} [/tex]
Finally, we can use the trig identities: [tex]1-sin^2 \alpha =cos^2 \alpha [/tex] and [tex]sec \alpha = \frac{1}{cos \alpha } [/tex] to simplify our trig expression:
[tex]\frac{2}{cos^2\alpha}=2sec^2 \alpha [/tex]
We can conclude that the correct answer is the fourth one.
THe answer is letter D. 2 sec^2 theta
Hope it help! Goodluck!
Find the slope of the line on the graph
Answers
1st point ( -4,0)
2nd point (0,3)
slope = change in y over change in x
change in y = 3-0 = 3
change in x = 0 - -4 = 0+4 = 4
slope = 3/4
Quadrilateral ABCD has the following vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6). Quadrilateral ABCD is a
A. trapezoid
B. parallelogram
C. square
D. rectangle
Answers
Quadlirateral ABCDwith vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-4, -6) is s A. TRAPEZOID
the answer is TRAPEZOID
O is the center of the given circle. The measure of angle O is 128°. The diagram is not drawn to scale.
Assuming that lines that appear to be tangent are tangent, what is the value of x?
Answers
The measure of the external angle is the semi difference of the arcs that it covers.
so
see the picture attached to better understand the problem
m AB=128°--------> by central angle
m ACB=360°-128°-----> m ACB=232°
∠x=(1/2)*[m ACB-m AB]
∠x=(1/2)*[232-128]-----> ∠x=(1/2)*104°-----> ∠x=52°
the answer is
∠ x is 52°
Hope I helped :)
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
Answers
1 liter = 10 deciliters
therefore the amount of liters used in making the cake will be found as follows:
5.25/10×1=0.525 liters
Answer: 0.525 liters
Need help to write equations for 5, 6 & 7
Answers
The x-values go up by 1: -2, -1, 0, 1, 2
The y values are always 3 times the previous value.
This is an exponential function.
[tex] y = a(b)^x [/tex]
We need to find a and b.
Look at x = 0.
For x = 0, y = 4.
[tex] y = a(b)^x [/tex]
[tex] 4 = a(b)^0 [/tex]
Since b^0 = 1, this simplifies to
[tex] 4 = a [/tex]
Now we know a = 4. We have
[tex] y = 4(b)^x [/tex]
Look at x = 1. For x = 1, y = 12.
[tex] 12 = 4(b)^1 [/tex]
[tex] 12 = 4b [/tex]
[tex] b = 3 [/tex]
Now that we know a and b, we can write the function.
[tex] y = 4(3)^x [/tex]
Now that you have the function written out, notice the following.
In the exponential equation we found, the number raised to x
is the number you multiply each y value to get the next y value.
In this case, each y value is 3 times the previous one, so you have 3^x.
The way you find "a" in the exponential equation is to look at the y-coordinate
when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to
the y-value. In this case, when x = 0, y = 4, so "a" is 4.
With b = 3, and a = 4, you can quickly write:
y = 4(3)^x.
ANYONE WHO KNOWS SURFACE AREA!!!
I need help urgently!
Answers
What is cos 45? Please HELP !!!
Answers
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
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A carpenter earns $18 an hour for a regular work week (40) hours. He earns time and a half for overtime. The weekly wage function is W(h)={ 18h 040} where h is the number of hours worked for the week. Find the wage if the carpenter worked 42.5 hours in the week
Answers
18×1.5=27 overtime per hour
27×2.5= 67.5 overtime
$720+$67.50=$787.50
Final answer:
To find the carpenter's weekly wage after working 42.5 hours, we calculate the regular pay for 40 hours at $18 per hour, which is $720, and then add the earnings from 2.5 hours of overtime at time and a half ($27 per hour), which is $67.5. The total weekly wage is $787.5.
Explanation:
To calculate the weekly wage of the carpenter who worked 42.5 hours, with $18 per hour for the first 40 hours and time and a half for overtime, we will use the wage function provided: W(h) = 18h for hours up to 40, and for hours above 40, it's (18 × 1.5) × (h - 40). Let's apply this to the 42.5 hours worked.
The carpenter's earnings for the regular 40 hours are $720 (which is 40 hours × $18). For the 2.5 hours of overtime, he earns time and a half, which is $27 per hour (18 × 1.5). The overtime earnings are $67.5 (2.5 hours × $27). So, the total wage is:
$720 + $67.5 = $787.5
Therefore, the carpenter's weekly wage for working 42.5 hours at the given rate is $787.5.
The function f(x) = 12x + 50 gives the amount of money a worker earns for working x hours per week. What is the inverse function?
Answers
Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12
Answers
y = -33/2
Start by plugging in the second equation for y in the first equation. Then solve for x. After you can use that value to solve for y.
2=sqrt P solve for P
Answers
Square both sides;-
(sqrt P)^2 = 2^2
P = 4 Answer
2²=(√P)²
4=P
P=4
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?
Answers
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units
A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9
hence
the dimensions of the rectangle are
length is 9 units
width is 13 units
the area of rectangle is -----> 9*13-----> 117 units²
the answer is
117 units²
What is the y-intercept of the function f(x) = –2/9 + 1/5
Answers
- 2/9 + 1/5 >> - 10/45 + 9/45 = - 1/45
Your y-int is - 1/45 or (0, - 1/45)
Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
I understand the steps where I am stuck is how did you get 2/3/
Answers
Divide 2 3/4 acres by 4 1/8 hours:
Divide 2.75 acres by 4.125 hours:
2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs
If this is not entirely clear to you, please share the work you've done yourself and I will respond.
You buy a new yoga ball. The ball has a diameter of 26 inches. What is the volume of the ball? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
V = 4/3 x PI x r^3
we are told PI = 3.14
the diameter is 26 inches so r ( radius )= 26 / 2 = 13 inches
now we have V = 4/3 x 3.14 x 13^3
V = 9198.11 cubic inches
Answer:
The volume of the ball is [tex]9,198.11\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a sphere (yoga ball) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=26/2=13\ in[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}(3.14)(13^{3})=9,198.11\ in^{3}[/tex]