Answer:
D) 4176 unit cubes
Step-by-step explanation:
Length of the right rectangular prism [tex]=7\frac{1}{4}[/tex] inches
Width of the right rectangular prism [tex]=8[/tex] inches
Height of the right rectangular prism [tex]=9[/tex] inches
Then volume of the right rectangular prism = (Length)(Width)(Height)
[tex]=\left(7\frac{1}{4}\right)\left(8\right)\left(9\right)[/tex]
[tex]=\left(7.25\right)\left(8\right)\left(9\right)[/tex]
[tex]=522[/tex] cubic inches
Now volume of the small cubic prism [tex]=(Length)^3=\left(\frac{1}{2}\right)^3=\frac{1}{8}[/tex]
Then number of cubes that can fit into the right rectangular prism [tex]=\frac{522}{\left(\frac{1}{8}\right)}=522*8=4176[/tex]
Hence correct choice is D) 4176 unit cubes
I need to find the measure of each angle indicated and round to the nearest tenth.
45.2 (for question 1/#19)
To find the angle, you need to use the cosine because you have the adjacent and the hypotenuse.
Cosine 0 = 9.3/13.2
Cosine 0 = 9.3/13.2 = 0.705
Arccos 0.705
Angle 0 = 45.2
Line AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to ?
A.
5x − 3y = 0
B.
-x + 3y = 0
C.
-5x − 3y = 0
D.
3x + 5y = 0
E.
-3x + 5y = 0
Answer:
3y+5x=0
Step-by-step explanation:
The question is on equations of parallel lines
Finding the gradient m of line AB
m=change in y coordinates/change in x-co-ordinates
Given points A(-3,0) and B (-6,5)
m=Δy/Δx Δy=5-0=5 Δx=-6 - -3= -3 ⇒m= - 5/3
Equation
The line will have its gradient equal to - 5/3
m=-5/3
point is the origin (0,0)
m=Δy/Δx
y-0/x-0 = -5/3
3(y-0)=-5(x-0)
3y-0= -5x+0
3y=-5x
3y+5x=0
Answer:
c is the correct answer
Step-by-step explanation:
-5y = -5
7x + 6y = 7
Is (5,1) a solution of the system?
Choose 1 answer.
A. Yes
B. No
-5y = -5 = 1
7x + 6y = 7
=-1.167
your answer is B) no
The given coordinate (5,1) is not a solution to the system of equations -5y = -5 and 7x + 6y = 7. Both equations do not hold true when 5 and 1 are substituted for y and x respectively.
Explanation:In Mathematics, to confirm if the given set of numbers ((5,1)) are a solution to the system, we substitute these values back into both system equations. In this case, 5 for y and 1 for x. As a result, the equation -5y = -5 becomes -5*5= -25, which is not equal to -5. Therefore, 5 is not a solution for y. Similarly, solving 7x + 6y = 7 after substituting the values becomes 7*1 + 6*5= 37, which is not equal to 7. So, 1 is not a solution for x. Therefore, the provided answer (5,1) is not a solution for the given system of equations. Thus, the answer is B. No.
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How is using the Pythagorean theorem in a rectangular prism similar to using it in a rectangle
The Pythagorean theorem is used in a similar manner to compute the diagonal of a rectangle and a rectangular prism. In both cases, the theorem is utilized to find the length of a line connecting two opposite corners across the shape or space.
Explanation:In the field of Mathematics, the Pythagorean theorem presents a fundamental relationship within a right triangle which expresses that the square of the hypotenuse (the side opposite the right angle) is equivalent to the sum of the squares of the other two sides. This theorem is represented mathematically as a² + b² = c².
When applying this theorem in a rectangle, consider a diagonal drawn from one corner to the opposite corner, which gives us a right triangle. To find the length of this diagonal (hypotenuse), we use the Pythagorean theorem, considering the two sides of the rectangle as the other two sides of the triangle.
In a rectangular prism, the same principle applies. However, instead of two sides (as in a rectangle), we now have three dimensions (length, width, and height) to consider. When one wishes to find the distance from one corner to the opposite corner (a diagonal cutting through the prism), the Pythagorean theorem can be employed. First, a right triangle is considered in the base of the prism, and the Pythagorean theorem is used to find the length of the diagonal of the base. Next, a second right triangle is constructed using the height of the prism and the diagonal of the base. Once again, the Pythagorean theorem can be implemented to calculate the length of the longest diagonal of the prism.
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The Pythagorean theorem applies similarly in both rectangular prisms and rectangles, using right triangles to calculate distances.
The Pythagorean theorem is fundamentally the same in both a rectangular prism and a rectangle, as it relies on the properties of right triangles. For a rectangle, the theorem states that the sum of the squares of the two shorter sides (a and b) equals the square of the hypotenuse (c), or a² + b² = c².
When applied to a rectangular prism, the theorem is used in three dimensions to find the length of the diagonal (d) stretching between opposite corners. In a rectangular prism, by applying the Pythagorean theorem successively across two-dimensional planes, we first calculate the diagonal of one face of the prism (b² = x² + y²).
Then, we incorporate the third dimension z to find the space diagonal: d² = x² + y² + z². This sequential application of the Pythagorean theorem leverages its two-dimensional principle to solve for three-dimensional distances.
Steps to Apply Pythagorean Theorem in a Rectangular Prism:
Identify the three side lengths of the prism: x, y, and z.Calculate the face diagonal using: b² = x² + y².Apply the theorem again to incorporate the third dimension: d² = x² + y² + z².This demonstrates how the Pythagorean theorem's consistent application in both two and three dimensions allows calculation of diagonals and distances in various geometric contexts.
A basketball player made 11 out 100 attempted free throws. What percent of free throws was made ?
Answer:11%
Step-by-step explanation:
A percent is always a number over 100, so 11/100 = 11%
Answer:
11%
Step-by-step explanation:
Mr. McGee mowed 4/5 of his lawn. His three sons finished the mowing. Each son mowed the same amount. How much of the lawn did each son mow?
Answer:
1 fifteenth, or 1/15
Step-by-step explanation:
If there are 3 sons multiply the fraction by 3 and then you have 12/15 because 12/15 is equal to 4/5, so the remaining is 3 out of 15, so divide that between the 3 sons and boom, 1/15th per son.
Which of these are factors of 121?
11, 11 •11 equals 121 which makes it a factor
pls help i need to finish all my khan academy work or else i fail my grade, plsssss help
Answer:
Start by dividing things up so that you know them. Use the dotted line to make a square a 2 triangles. Base and height for the square is 4 so that total is 16. Then the triangles have a base an height of 4 as well so that ((4•4)/2)= 8. Then add them together = 24
Hope this helps.
Answer:
Step-by-step explanation:
im lost . . .. . . ????????
Answer:
f(x) = 3x - 1
Step-by-step explanation:
The line can be represented in the form f(x) = mx + b, where m is the rate of change of the line and b is the value of the function when x = 0.
Looking at the graph, we can tell that when x = 0 the function = -1. (The point on the line and the y-axis).
We can also tell that when x increases by 1, y increases by 3. The points (0,-1) and (1, 2) are both on the line and their difference in x is 1 and their difference in y is 3.
The formula for slope (rate of change) is [tex]\frac{change\ in\ y}{change\ in\ x}[/tex], so m = [tex]\frac{3}{1}[/tex] or 3.
Now we have the equation for the line is f(x) = 3x - 1
what is the surface of a cylinder that has a height of 8 and a radius of 10
Answer:
Surface area I'm guessing. 1,130.4
Step-by-step explanation:
The formula for the surface area of a cylinder is: 2*pi*r^2 + 2*pi*r*h.
Plug in the values given.
2*pi*10^2 + 2*pi*10*8
628 + 502.4 = 1,130.4
(If you want the most precise value, use a calculator for pi instead of just 3.14.)
ANSWER
[tex]S A = 1130.4[/tex]
square units.
EXPLANATION
The given cylinder has a height of 8 and a radius of 10.
The formula for calculating the surface area of a cylinder is
[tex]S A = 2\pi \: r(r + h)[/tex]
We substitute r=8 and h=10 into the formula to get:
[tex]S A = 2\pi \: 10(10+ 8)[/tex]
[tex]S A = 360\pi [/tex]
Or using π=3.14
[tex]S A = 1130.4[/tex]
units square.
y=2x square root of 2
Answer:
Step-by-step explanation:
Divide both sides by 2.
you get
y /2=x (2) (2)
y/2 =x (4)
Divide both sides by 4
y/2
------ = x
4
PLEASE HELP 10 POINTS
Answer:
Area: 4069.44
Circumference: 226.08
Step-by-step explanation:
The equation for the area of a circle is:
pi(r^2)
So they told us to use 3.14 for pi, the r (radius)is found by dividing the diameter (72) by 2 since
r = d/2
r = 72/2 = 36
plug this into the equation for the area of a circle:
3.14(36^2) = 4069.44
——————————————————————————————————
To find the circumference, use the equation for it:
2 x pi x r or pi x d
Let’s use the second equation, since the diameter is already given
2(3.14)(72) = 226.08
Answer:
Area is 4069.44 m². Circumference is 226.08 m.
Step-by-step explanation:
Area:
a = r²π
a = 36²π
a = 4069.44
Circumference:
c = dπ
c = 72 × 3.14
c = 226.08
A simplified algebraic expression for the expression, x decreased by 9
I think the answer is in the question itself
x-9
If this triangle is translated backwards through space, what three dimensional figure will be formed?
A) square pyramid
B) triangular prism
C)rectangular prism
D) triangular pyramid
Answer:
triangular prism
Step-by-step explanation:
the space translated will form straight lines
Answer:
a triangular prism
Step-by-step explanation:
because when a triangle forms a 3d shape it either a prism or cone since it goes backwards it is d
suppose you rolled a six sided number cube 120 times how many times woul you roll a 6
Answer:
You would roll a 6 about 20 times
Step-by-step explanation:
First you have to find the probability of rolling a 6 one time
There is one 6 and 6 total number
That is a probability of 1/6
Multiply this by the amount of times you roll the cube
1/6 * 120 = 20
The answer is 20
Using 3.14 for pie what is the area of the circle to the nearest tenth of an inch
[tex]area = \pi {r}^{2} \\ r = \frac{1}{2} \times 7.5 = 3.75 \\ 3.14 \times 3.75 {}^{2} \\ 3.75 {}^{2} = 14.06 \\ 3.14 \times 14.06 = 44.1484 \: inches {}^{2} [/tex]
hope that helped
[tex]A = \pi {r}^{2} \\ \\ r = \frac{7.5}{2} = 3.75[/tex]
So
[tex]A = (3.14)({3.75}^{2} ) \\ A = (3.14)(14.0625) \\ A = 44.15625 \\ A =44.16[/tex]
Mean of the integers 10,-27,4,-9
Answer:
-5.5
Step-by-step explanation:
Add all numbers and divide by 4 (the total amount of numbers)
10+(-27)+4+(-9)=-22
-22/4 = -5.5
-5.5
In order to find the mean, you add up all numbers and then divide by the amount of numbers
1. What’s the answer to this question?
Answer: I think its no correlation; the dots are scattered...
Hey there!
The answer to this would be C.
There is no correlation.
Notice that the points in the graph are all spread out so we can't draw a line of best for to represent the given data.
In order for there to be a correlation, positive or negative, we need to see a change either down or up.
What is the measure of angle C
Answer:
C = 77°
Step-by-step explanation:
From the intercepted arc theorem, we can say that Angle ABC (angle B) is HALF of the arc intercepted (which is 110).
Hence, angle ABC = 55.
Now, looking at triangle ABC, we know that sum of 3 angles of a triangle is 180. We already know Angle A to be 48 and Angle B to be 55, thus Angle C is:
A + B + C = 180
48 + 55 + C = 180
103 + C = 180
C = 180 - 103
C = 77
The Bulldogs, a baseball team, has nine starting players. The heights of the starting players are 72 in., 71 in ., 78 in., 70 in., 72 in., 72 in., 73 in., 70 in., and 72 in. Which term BEST describes the data value 78 in.?
A) mean
B) median
C) mode
D) outlier
By looking at this data, you can see that while most of the data is in between 70 and 73, the only number that isn't in that range is 78. Therefore, the term outlier describes 78in the best.
Answer:
D) Outlier
Step-by-step explanation:
The manager of an online news service received the report given in the table on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be half the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?
table:
2012: 5,600
2013: 5,880
Answer:
= 5880 +
= 5880 + (0.10 × 5880)
= 5880 + 588
= 6,468
In 2014 subscriptions would be sold 6,468.
Step-by-step explanation:
There are 5 white balls, 8 red balls, 7 yellow balls and 4 green balls in a container. A ball is chosen at random. What is the probability of picking a red
Answer:
8/24=1/3
There are 24 balls in total and 8 of them are red. So you get 8/24 but you need to simplify it to its simplest form which is 1/3
Final answer:
The probability of picking a red ball from a container with 5 white, 8 red, 7 yellow, and 4 green balls is 1/3, because you divide the number of red balls (8) by the total number of balls (24).
Explanation:
The subject of this question is probability, a branch of mathematics concerned with the likelihood of an event occurring. To find the probability of picking a red ball, we need to divide the number of red balls by the total number of balls in the container.
In the question, there are 5 white balls, 8 red balls, 7 yellow balls, and 4 green balls, which means there are a total of 24 balls. The probability of picking a red ball is calculated by taking the number of red balls and dividing it by the total number of balls:
Probability of picking a red ball = Number of red balls / Total number of balls = 8 / 24 = 1/3.
Kenisha tried to subtract two polynomials her work is shown below. At which step did Kenisha make an error, If at all?
A. Step 1
B. Step 2
C. Step 3
D. Kenisha’s work is correct
Answer:
Step 1
Step-by-step explanation:
When you subtract a polynomial in parentheses, you have to remove them from the parentheses first, which Kenisha did right. The problem is that because the numbers are being subtracted, all of the signs switch, which they forgot to do. Step one should look like: 2b² + 3b + 11 - 7b² + 5b - 1
Which graph represents the function f(x)=-x2+5?
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]f(x)=-x^2+5[/tex] .... (1)
We need to find the graph of the function.
The vertex form of the quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex] .... (2)
On comparing (1) and (2) we get
[tex]h=0,k=5[/tex]
It means the vertex of the function is (0,5).
The table of values is
x y
-2 1
-1 4
0 5
1 4
2 1
Plot all ordered pairs on a coordinate plane and connect them by a free hand curve.
The graph of given function is shown below.
What is the mean of this data set? 12,17,16,10,20,13,14,14,12,12,19,18
Answer:
14.75 :) please give me brainliest :)
Step-by-step explanation:
Hello There!
Mean: Average of numbers in a set of data.
STEP 1: Add the numbers up. In this case, we would add
12 + 17 + 16 + 10 + 20 + 13 + 14 + 14 + 12 + 12 + 19 + 18 = 177
STEP 2: Divide the sum of the number by the number of digits you added.
We would divide 177 "sum of numbers" by 12 "number of digits" and would
get a quotient of 14.75
The mean for this set of data is 14.75
what is the perimeter of a hexagon with an apothem of 10
Assuming that said hexagon is regular then triangles formed (split in half by the apothem) are 30-60-90 triangles. The side that you'd get would be 10√3/3. Multiplied by two, you'd get 20√3/3. The perimeter would be 120√3/3, which would be 40√3 as the answer.
The perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.
What is hexagon?A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.
From the figure, we can calculate the side length of the hexagon:
We know each interior angle of the hexagons = 120 degree
Half of the angle = 120/2 = 60 degree
From the tan ratio:
tan30 = (s/2)/10
1/√3 = s/20
s = 20/√3
Perimeter = 6×(20/√3) = 120/√3 = 40√3
Thus, the perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.
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Find the correct value to fill in the space below.
cos 50° = 2 cos^2 ____° -1
Answer:
25.
Step-by-step explanation:
Use the identity cos 2x = 2 cos^2 x - 1
So cos 50 = 2 cos^2 25 - 1
So the space = 25.
Answer:
25°
Step-by-step explanation:
Using the double angle trigonometric identity for cosine
• cos2x = 2cos²x - 1
Here 2x = 50° ⇒ x = 25°, thus
cos50° = 2cos²25° - 1
AB has endpoints at (-1, -1) and (-2, -4). Its transformation A'B' has endpoints at (-2, -2) and (-4, -8). What type of transformation occurred? Are lengths of segments affected by this
A) rotation; no; The lengths of the two segments are the same.
B) reflection; yes; The length of segment A'B' is longer than the original segment AB.
C) dilation by a scale factor of 2; yes; The length of segment A'B' is longer than the original segment AB.
D) dilation by a scale factor of 1/2; The length of segment A'B' is shorter than the original segment AB.
type of transformation? Justify.
will mark brainliest if correct and give 50 pts.
The correct answer is C
Solve -4/3x+1/6<7/9
< or >
A. -34/27
B. -17/24
C. -11/24
D. -22/27
EDIT THE ANSWER IS >-11/24 I TOOK THE TEST
Answer:
[tex]\large\boxed{x>-\dfrac{11}{24}}[/tex]
Step-by-step explanation:
[tex]-\dfrac{4}{3}x+\dfrac{1}{6}<\dfrac{7}{9}\qquad\text{multiply by common denominator}\to18\\\\18\!\!\!\!\!\diagup^6\left(-\dfrac{4}{3\!\!\!\!\diagup_1}x\right)+18\!\!\!\!\!\diagup^3\left(\dfrac{1}{6\!\!\!\!\diagup_1}\right)<18\!\!\!\!\!\diagup^2\left(\dfrac{7}{9\!\!\!\!\diagup_1}\right)\\\\(6)(-4x)+(3)(1)<(2)(7)\\\\-24x+3<14\qquad\text{subtract 3 from both sides}\\\\-24x<11\qquad\text{change the signs}\\\\24x>-11\qquad\text{divide both sides by 24}\\\\x>-\dfrac{11}{24}[/tex]
Jerry has invested $1500 into a savings account that paid him 8.25% interest, what will the balance of his account be after 6 years?
Please Explain!
answer: $2413.50
y=original amount of money(1+ the percent divided by 100)^the number of years is the power
we do this with the 1+ ... because the original amount plus the extra 8.25%
so the equation would be ...
y=1500(1+0.0825)^6
y=1500(1.60904218428)
y=1500(1.609) (I rounded)
y=$2413.50