V= 3,840 cm
Volume is L x W x H
and W is the same as Depth
So you would multiply those and multiply it again by four to make up for the other pieces of wood.
Final answer:
The total volume of wood used in making the square frame is 3840 cubic centimeters, which is calculated by finding the volume of one piece (960 cm³) and multiplying it by the number of pieces (4).
Explanation:
The question concerns the calculation of the total volume of wood used in making a square frame. Each piece of wood is a rectangular prism with given dimensions. To find the total volume, one must multiply the length, height, and depth of a single piece and then multiply the result by the number of pieces.
To calculate the volume of a single piece of wood, we use the formula for the volume of a rectangular prism, which is length × width × height. For one piece of wood:
Length = 40 cm
Width (depth) = 6 cm
Height = 4 cm
The volume of one piece of wood is therefore 40 cm × 6 cm × 4 cm = 960 cm³.
Since there are four pieces that make up the frame, the total volume of wood used is:
960 cm³/piece × 4 pieces = 3840 cm³
Thus, the total volume of the wood used in the frame is 3840 cubic centimeters.
Which of the following formulas would find the surface area of a right cone where s is the slant height r is the radius, LA is the lateral area, and BA is the base area?
Check all that apply.
Answer:
Option A and Option C
Step-by-step explanation:
The surface area of a cone can be calculated with this formula:
[tex]SA=\pi r^2+\pi rs[/tex] (This matches with the option A)
Where [tex]\pi rl[/tex] is the lateral area of the cone (Being "s" the slant height) and [tex]\pi r^2[/tex] is the area of the base of the cone (which is a circle).
You know that BA the is the area of the base and LA the lateral area of the cone.
Then, substituting into the formula for calculate the surface area of a cone, you get:
[tex]SA=BA+LA[/tex]
This matches with the option C
Answer:
a and c
Step-by-step explanation:
a p e x
A box contains 5 plain pencils and 5 pens. A second box contains 7 color pencils and 1 crayon. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
Write your answer as a fraction in simplest form.
Answer: 1 out of 5 for the first box and 1 out of 7 for the second box
( in simplest form)
Step-by-step explanation:
A dartboard has a diameter of 14 inches. What are its radius and circumference? Round to the nearest hundredth. Use 3.14 for π.
Answer:
The radius is 7, and the circumference is 43.96
Step-by-step explanation:
The radius is half of the diameter, and this would just be 14/2 which is 7. The circumference is found by C=pi(diamete) or 2pi(radius). This is found by 14*3.14 this is equals 43.96
The radius of the dartboard is 7 inches and the circumference is approximately 43.96 inches.
Explanation:Radius:
The radius of a circle is half of its diameter. So, in this case, the radius is 7 inches.
Circumference:
The circumference of a circle can be found using the formula C = 2πr, where r is the radius. So, the circumference of this dartboard is 2π(7) = 14π inches, which rounds to 43.96 inches when rounded to the nearest hundredth.
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please help!!! ive been stuck on this for 30 minutes now!
Answer:
f^-1 = 4(x-3)
Step-by-step explanation:
If f(x) = 1/4(x) + 3 we ned to find f^-1.
To find the inverse function, we need to solve the equation for "x", as follows:
f(x) = 1/4(x) + 3
y = 1/4(x) + 3
y-3 = 1/4(x)
4(y-3) = x
Now, change the "x" for an "y". And change the "y" for an "x":
4(x-3) = y
The solution is the last one.
Just 15
Determine whether the series is arithmetic or geometric, the find the indicated sum. Please help ASAP
Really hard to make it out, especially the upper limit of the sum, but I think it reads
[tex]\displaystyle\sum_{k=1}^n5k-42[/tex]
(not sure what [tex]n[/tex] is, but that's not very important)
Expand the sum as
[tex]\displaystyle5\sum_{k=1}^nk-42\sum_{k=1}^n1[/tex]
Recall that
[tex]\displaystyle\sum_{k=1}^n1=1+1+\cdots+1=n[/tex]
[tex]\displaystyle\sum_{k=1}^nk=1+2+\cdots+n=\dfrac{n(n+1)}2[/tex]
so that
[tex]\displaystyle\sum_{k=1}^n5k-42=\dfrac{5n(n+1)}2-42n[/tex]
Then just plug in whatever [tex]n[/tex] happens to be.
The coordinate grid above shows a pentagon. The pentagon is translated 1 unit to the left and 10 units down to create a new pentagon.
Which rule describes this transformation?
A) (x, y) → (x − 1, y − 10)
B) (x, y) → (x + 1, y − 10)
C) (x, y) → (x − 1, y + 10)
D) (x, y) → (x + 1, y + 10)
The pentagon is translated 1 unit to the left, so the points move to the left by 1 unit. Moving left or right changes the x value, when you move right, the x value increases, when you move left, x decreases. Since x is going left 1 unit:
So x - 1
10 units down. Moving up down or up changes the y value, when you move down, y decreases, when you move up, y increases. Since the pentagon is going down 10 units:
y - 10
Your answer is A
The rule that describes the given transformation is (x, y) → (x - 1, y - 10). It is given that the pentagon is translated by 1 unit to the left and 10 units down.
What are the transformations on the graph?The graph is transformed into a new graph by applying certain operations like,
translationrotationreflectiondilationHow the given graph is translated?It is given that a pentagon in the graph is translated as 1 unit to the left and 10 units to the down.
Here the translation is towards the negative axes.
Towards left means subtracting the given number of units from the x-coordinateTowards down means subtracting the given number of units from the y-coordinateSo, the rule for this transformation we can write as (x, y) → (x - 1, y - 10)
Translating the points of the pentagon from the graph using this rule:
Actual coordinates Translated coordinates
(-1, 3) ((-1 - 1), (3 - 10)) = (-2, -7)
(1, 5) ((1 - 1), (5 - 10)) = (0, -5)
(2, 2) ((2 - 1), (2 - 10)) = (1, -8)
(4, 6) ((4 - 1), (6 - 10)) = (3, -4)
(5, 3) ((5 - 1), (3 - 10)) = (4, -7)
So, the new pentagon will be plotted in the graph with these translated coordinates.
The graph of the translated pentagon is shown below.
So, option A (x, y) → (x − 1, y − 10) describes the given transformation correctly.
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Without graphing, describe the end behavior of the graph of the function.
As x → ∞, f (x) → −∞.
As x → −∞, f (x) → ∞.
As x → ∞, f (x) → −∞.
As x → −∞, f (x) → −∞.
As x → ∞, f (x) → ∞.
As x → −∞, f (x) → −∞.
As x → ∞, f (x) → ∞.
As x → −∞, f (x) → ∞.
if Judy completes a puzzle by herself, it takes her 3 hours. working with sal, it only takes them 2 hours.
what is the missing value from the table that represents Judy's rate?
A) r
B)3-r
C)1/3
D)3
Answer:
C. [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.
We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.
Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be [tex]\frac{1}{3}[/tex], therefore, correct choice is option C.
Answer:
C.
Step-by-step explanation:
The graph of f(x) = x^2 is shown.
Compare the graph of f(x) with the graph of d(x) = x^2 - 25
Answer:
D. The graph of d(x) is 25 units below the graph of f(x)
ANSWER
D. the graph of d(x) will be 25 units below the graph of f(x).
EXPLANATION
The graph of
[tex]f(x) = {x}^{2} [/tex]
is the base function.
The graph of
[tex]d(x) = {x}^{2} - 25[/tex]
is a vertical translation of the base function 25 units down.
This implies that, the graph of d(x) will be 25 units below the graph of f(x).
Therefore the correct answer is D.
You play a gambling game with a friend in which you roll a die. If a 1 or 2 comes up, you win $8. Otherwise you lose $2. What is your expected value for this game?
Answer:
you expect to win on average $1.33 per round
Step-by-step explanation:
The expected value is the sum of products of probability and value:
2/6×$8 + 4/6×(-$2) = $8/3 - 4/3 = $4/3 ≈ $1.33
The expected value of the gambling game is calculated by taking into account the probability of winning $8 and losing $2. The final expected value is $1.33, which means on average, you would gain $1.33 per game played.
Explanation:To calculate the expected value for the gambling game where you roll a die, you need to account for the different outcomes and their associated probabilities. In this game, rolling a 1 or 2 means you win $8, and there are two outcomes out of six that result in a win, giving a probability of 2/6 or 1/3 for each of these outcomes. Rolling any other number (3, 4, 5, or 6) results in losing $2, with a probability of 4/6 or 2/3 for each of these losing outcomes.
The expected value (EV) can be calculated using the formula:
EV = (Probability of Winning × Amount Won) + (Probability of Losing × Amount Lost)
Substituting the values into the formula:
EV = (1/3 × $8) + (2/3 × -$2)
EV = ($2.67) + (-$1.33)
EV = $1.33
This means that the average gain per game, after many plays, is expected to be $1.33.
What is the value of C in C = 3x - 2 if x = 5
Answer:
C = 13
Step-by-step explanation:
C = 3(5) - 2
C = 15 - 2
C = 13
Answer:
C = 13
Step-by-step explanation:
Substitute x = 5 into the expression for C
C = (3 × 5) - 2 = 15 - 2 = 13
Ms . Sanchez is opening a shop that sells coats . She buys enough coat racks to hold 338 coats . Each rack holds 19 coats . How many racks should Ms. Sanchez buy ?
Answer:
18 racks
Step-by-step explanation:
338/19=17.78 so if you round up you get 18 racks
Ms. Sanchez needs to buy 18 coat racks to accommodate 338 coats, as each rack holds 19 coats and we round up the result of the division 338/19 to the nearest whole number.
The question asks us to determine how many coat racks Ms. Sanchez should buy if she wants to hold 338 coats and each rack holds 19 coats. To find out the number of racks needed, we divide the total number of coats by the number of coats that one rack can hold, which is a straightforward division problem.
We calculate this by dividing 338 (the total number of coats the racks need to hold) by 19 (the number of coats each rack can hold):
338 / 19 = 17.7895...
Since we cannot have a fraction of a coat rack, we round up to the nearest whole number because Ms. Sanchez needs enough racks to hold all the coats, and you cannot purchase a fraction of a rack. Therefore, Ms. Sanchez should buy 18 coat racks to accommodate all 338 coats.
Find the probability of randomly choosing the letter A or E from a board that contains the letters CANDLE.
Answer:
Step-by-step explanation:
There are 6 letters all together. There 2 letters that if you draw them, you will be successful.
2/6 = 1/3
That means that 1 in 3 times you should draw an A or an E.
Simple Personal fianance
Alex back into a light pole and damaged his bumper. he decided to file a claim for the body damage. what deductible would he have to pay before he receives a payment from the insurance company?
A. he would not have to pay any deductible because he was not at fault
B. Premium
C. Collision
D. Comprehensive
I was between B and C
Answer:
The answer is : Collision
Step-by-step explanation:
Alex would have to pay collision deductible before he receives a payment from the insurance company.
A deductible is any amount that you have to pay out of pocket when you make a claim.
Collision deductible comes to effect when your vehicle is damaged in an accident. This pays the cost of repairing the vehicle minus the amount of your deductible.
John’s employer will match his contributions into his retirement plan, but only up to 3% of his salary. John decides to invest 5% of his $42,000 salary into the retirement plan. Find the future value of the annuity in 5 years if it earns 8% compounded quarterly.
$62,406.79
$20,409.79
$255,122.39
$9,909.79
I need help with this plz, im confused and im watching videos but idk how to do it. i will mark brainliest
Answer:
$20,409.79
Step-by-step explanation:
First find John’s quarterly salary. ;$42,000 / 4 = $10,500 ;Total Contributions = John’s + Employer’s ;Total Contributions = $10,500 x 0.05 + $10,500 x 0.03 ;Total Contributions = $840 ;Find the interest rate per compounding period and the number of compounding periods. ;8% / 4 = 2% ;5 x 4 = 20 periods ;The factor from the table for 2% and 20 is 24.29737. ;Amount = $840 x 24.29737 ;Amount = $20,409.79
Line graphs are used to show trends in categorical data. True False
Answer:
ezpz false
Step-by-step explanation:
What are the new vertices of the triangle under the translation (x, y) (x − 1, y − 3)?
ANSWER
(-1,-1), (-4,-5), (-8,0)
EXPLANATION
We have a triangle with vertices:
(0,2), (-3,-2) and (-7,3).
The rule for the translation is
[tex](x, y) \to (x - 1,y - 3)[/tex]
The new vertices of the triangle will be;
[tex](0, 2) \to (0 - 1,2- 3) = ( - 1, - 1)[/tex]
[tex]( - 3, - 2) \to (- 3-1, - 2- 3) = ( -4, - 5)[/tex]
[tex]( - 7, 3) \to ( - 7 - 1,3- 3) = ( - 8, 0)[/tex]
The new vertices are:
(-1,-1), (-4,-5), (-8,0)
The angle of elevation from point A to point B measures 5(x-2) The angle of depression from point B to point A measures (x+14). Find the measure of each angle.
Answer:
It's the first choice (20 degrees).
Step-by-step explanation:
These angles will be equal ( by The Alternate Angle Theorem).
5(x - 2) = x + 14
5x - 10 = x + 14
4x = 24
x = 6.
So the measure of each angle = 5(6 - 2) = 6 + 14 = 20 degrees.
The angles of elevation and depression are equal because they are alternate interior angles. Solving the given expressions yields x = 6. Therefore, both the angle of elevation and the angle of depression measure 20 degrees.
First, let's set up the problem:
The angle of elevation from point A to point B is given by the expression 5(x-2).The angle of depression from point B to point A is given by the expression (x+14).In any scenario involving angles of elevation and depression, these angles are equal because they are alternate interior angles formed by a horizontal line and a transversal.
Therefore, we can equate the two expressions:
5(x-2) = (x+14)
Now, solve for x:
Distribute the 5 on the left side: 5x - 10 = x + 14Subtract x from both sides: 4x - 10 = 14Add 10 to both sides: 4x = 24Divide both sides by 4: x = 6Now substitute x back into the expressions to find the angle measures:
For the angle of elevation: 5(x-2) = 5(6-2) = 5*4 = 20 degrees
For the angle of depression: (x+14) = (6+14) = 20 degrees
Therefore, both the angle of elevation and the angle of depression measure 20 degrees.
This confirms that our setup and calculation are correct.
is this right? In the triangle the ratio that represents cot 0 equals 3/4
For this case we have to define trigonometric relations in a rectangular triangle that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.
So, we have:
cos (Θ) = [tex]\frac {9} {15} = \frac {3} {5}[/tex]
Answer:
False
What is the angle of the elevation from the ground to the top of a 45-foot tree from 65 feet away? Round to the nearest tenth of a degree.
Answer:
34.7 degrees
Step-by-step explanation:
This is a right triangle trig problem. The angle in question, the angle of elevation, is the base angle that is NOT the right angle. The height of the tree is the side opposite the angle of elevation, and the distance away from the tree is the measure of the base of the right triangle. So the question, then, is "What is the angle that has a ratio equal to the side opposite the angle over the side adjacent to the angle?" This is the definition of the tangent of an angle. The equation will be set up as follows:
[tex]tan\beta =\frac{45}{65}[/tex]
Your calculator needs to be in degree mode when you do this operation. Press 2nd on your calculator then tan and you'll get tan^-1 on your display. This means you are looking for a missing angle. Enter the fraction as 45/65 inside the parenthesis and hit enter and you'll get an angle of 34.69515353. Round to the nearest tenth for 34.7
You will always use the 2nd and sin/cos/tan buttons to find missing angles.
The angle elevation is 34.6 9 degree.
What is Angle of Elevation?When it lies between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
Given:
Height of tree= 45 foot
Distance= 65 feet
Now, Using Trigonometry
tan [tex]\theta[/tex] = P/ B
= 45/65
= 9/ 13
= 0.6923
[tex]\theta[/tex] = 34.69 degrees.
Hence, the angle elevation is 34.6 9 degree.
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20 POINTS TO ANYONE! HURRYYYY HURRY HURRY
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
21.63
use the Pythagorean theorem.
a^2+b^2=c^2
Segment AB is being dilated with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4). What is the scale factor of the dilation and the coordinates of point B"
The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 1.25 and the coordinates of point B" are (–3.2, –4.8).
The scale factor is 0.8 and the coordinates of point B"are (–5, –7.5).
The scale factor is 1.25 and the coordinates of point B" are (–5, –7.5).
Answer: The correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation: Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).
We are to find the scale factor of the dilation and the co-ordinates of the point B''.
From the given graph, we note that
the co-ordinates of point A are (4, 8).
Now, If S is the scale factor of dilation, then we must have
[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]
So, the scale factor is 0.8.
Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be
[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]
Thus, the correct option is
(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Answer:
A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).
Step-by-step explanation:
If a computer depreciates at a rate of 24% per year, what is the monthly depreciation rate?
8.17%
6.33%
4.33%
2.00%
I believe the correct answer is 4.33%.
Answer:
2.00%
Step-by-step explanation:
Identify the volume of the sphere in terms of π. PLEASE HELP!!!
Answer:
its B
Step-by-step explanation:
Using your equation, estimate the number of daylight hours in this city on the 220th day of the year.
My equation = y = 2.15sin(2pi/12)x + 10
Answer:
The answer, using your equation is: 11 hours, 51 minutes and 44 seconds, that is the number of daylight hours in that city
Step-by-step explanation:
Ok, in a normal year, the 220th day is the 8 of august, that is 08-08.
So, using x=220, we can estimate the number of daylight hours in that city:
[tex]y=2.15sin(\frac{2\pi }{12}x)+10= 2.15sin(\frac{2\pi }{12}(220))+10[/tex]
Then using a calculator in radians:
[tex]y=2.15(sin(0,524*220))+10[/tex]
[tex]y=2.15(sin(115.192))+10[/tex]
[tex]y=2.15(0,866)+10[/tex]
[tex]y=1.862+10[/tex]
[tex]y=11.862[/tex]
Then, you have that is 11 hours, but what about the 0.862 hours? We convert the to hours knowing that 1 hour has 60 minutes. Then 0,862*60 minutes= 51,72 minutes. And we do this for the 0,72 minutes as well, knowing that 1 minute has 60 seconds, then 0,72*60= 44 seconds.
The number of hours is 11 hours, 51 minutes and 44 seconds
Select the functions that have identical graphs.
Answer:
c. 1 and 3
Step-by-step explanation:
To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.
Please see the attached image below, to find more information about the graph
s
The equations are:
1) y = sin (3x + π/6)
2) y = cos (3x - π/6)
3) y = cos (3x - π/3)
Looking at the graphs, we can see that the identical ones
are equations one and three
Correct option:
c. 1 and 3
Dr. Potter provides vaccinations against polio and measles. Each polio vaccination consists of 444 doses, and each measles vaccination consists of 222 doses. Last year, Dr. Potter gave a total of 606060 vaccinations that consisted of a total of 184184184 doses. How many polio vaccinations and how many measles vaccinations did Dr. Potter give last year? Dr. Potter gave polio vaccinations and measles vaccinations.
x - number of polio vaccinations
y - number of measles vaccinations:
x + y = 60 / * ( - 2 )
4 x + 2 y = 184
--------------------------
- 2 x - 2 y = - 120
+
4 x + 2 y = 184
--------------------------
2 x = 64
x = 64 : 2
x = 32
32 + y = 60
y = 60 - 32
y = 28
Answer: There were 32 polio and 28 measles vaccinations.
Answer:
32 and 28
Step-by-step explanation:
Given the points P(2,-1) and Q(-9,-6), what are the coordinates of the point on directed line segment PQ that partitions PQ in the ratio 3/2?
ANSWER
[tex]( - \frac{23}{5} , - 4)[/tex]
EXPLANATION
Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by
[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]
[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]
Where m=3 and n=2
[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]
[tex]x = \frac{ - 23}{5} [/tex]
[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]
[tex]y= \frac{ - 20}{5} = - 4[/tex]
The point is
[tex]( - \frac{23}{5} , - 4)[/tex]
The coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2 are (-21/5, -17/5).
Explanation:To find the coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2, we can use the section formula. The section formula states that the coordinates of a point dividing a line segment with endpoints (x1,y1) and (x2,y2) in the ratio m:n are given by:
x = (m*x2 + n*x1)/(m+n)
y = (m*y2 + n*y1)/(m+n)
Plugging in the values from the given points P(2,-1) and Q(-9,-6) into the formula, we get:
x = (3*(-9) + 2*2)/(3+2) = -21/5
y = (3*(-6) + 2*(-1))/(3+2) = -17/5
So, the coordinates of the point are (-21/5, -17/5).
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Abigail has 5 cousins her friend suki has 3 fewer than 4 times as many cousions as abigail has write an expression for the number of cousions suki has
5=(5 x 4)-3
Hope I helped! Sorry if I'm wrong!
~Potato
^^ What they said I think that’s right but I may be wrong
7.
Find the missing lengths of the sides.
Answer:
[tex]a=9\ in\\b= 9\ in[/tex]
Step-by-step explanation:
This straight triangle has two angles equal to 45 ° and two equal sides.
We know that the side opposite the 90 degree angle is:
[tex]c =9\sqrt{2}\ in[/tex]
Since the triangle has two equal angles, then it is an iscoceles triangle.
This means that
[tex]a = b[/tex]
We use the Pythagorean theorem to find b
[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]