the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:
V = l × w × 10
We are also given that the prism requires 120 unit cubes to fill completely, which means:
V = l × w × 10 = 120
Dividing both sides by 10, we get:
l × w = 12
Now we need to find pairs of positive integers l and w that multiply to 12. These are:
1 × 12
2 × 6
3 × 4
Therefore, the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.
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Factor completely.
7b^2-63
Thank you :DDD
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]
Answer:[tex]7(b+3)(b-3)[/tex]using the net below find the area of the triangular prism
6 cm
3 cm
4 cm
6 cm
5 cm
2 cm
Answer:153
Step-by-step explanation:
I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
Round the answer to the nearest hundredth
Using trigonometric functions, the value of the side AC = 2.85 units.
What are trigonometric functions?The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.
The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.
Now in the given figure,
The angle is a right-angled triangle.
Now as per the trigonometric functions,
Sin 35° = AC/AB
⇒ 0.57 = x/5
⇒ x = 0.57 × 5
= 2.85.
The length of the opposite side AC is 2.85 units.
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The rectangular garden is 175 m long and 96 m broad . find the cost of fencing it at 17.50per m.also find the cost of ploughing it at 4.50 paise per square metre
Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.
Here,
The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:
2 × (length + width) = 2 × (175 m + 96 m) = 542 m
Therefore, the cost of fencing the garden at 17.50 per meter is:
Cost of fencing = length of fence × cost per meter
= 542 m × 17.50
= 9485
Hence, the cost of fencing the garden is ₹9485.
To find the cost of plowing the garden, we need to first calculate its area, which is given by:
Area = length × width
= 175 m × 96 m
= 16800 m²
Therefore, the cost of plowing the garden at 4.50 paise per square meter is:
Cost of plowing = area of garden × cost per square meter
= 16800 m² × 0.045
= 756
Hence, the cost of plowing the garden is ₹756.
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In a regular pentagon PQRST. PR intersects QS
at O. Calculate angle ROS.
Answer: 72°
Step-by-step explanation:
To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.
Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).
Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.
Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°
Darnel is studying the movement of glaciers, which are bodies of dense ice. The median
annual movement of the Blue Valley Glacier is about 300.2 feet, and the interquartile range is
14 feet. The median annual movement of the Silver Lake Glacier is about 300.4 feet, and the
interquartile range is about 14 feet.
4) What can you conclude from these statistics? Complete the sentence.
Over a year, the Blue Valley Glacier typically moves about
the Silver Lake Glacier, and Blue Valley has
its annual movement compared to Silver Lake.
as
▾ variability in its annual movement compared to silver lake
Over a year, the Blue Valley Glacier typically moves about the same distance as the Silver Lake Glacier, and Blue Valley has the same variability in its annual movement compared to Silver Lake.
How to interpret the statisticsThe median annual movement of the Blue Valley Glacier is 300.2 feet, and the interquartile range is 14 feet.
The interquartile range indicates the spread of the data within the middle 50% of the data
So we know that the annual movement of the Blue Valley Glacier falls within a range of 300.2 ± 7 feet (i.e. 293.2 to 307.2 feet)
Similarly, the median annual movement of the Silver Lake Glacier is 300.4 feet, and the interquartile range is also 14 feet
So the annual movement of the Silver Lake Glacier also falls within a range of 300.4 ± 7 feet (i.e. 293.4 to 307.4 feet)
Since the ranges for both glaciers overlap and have the same size, we can conclude that they typically move about the same distance over a year, and that the variability in the annual movement of Blue Valley is comparable to that of Silver Lake.
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Bella is splitting her rectangular backyard into a garden in the shape of a trapezoid and a fish pond in the shape of a right triangle. What is the area of her garden?
The Area of Bella's garden as required to be determined in the task content is the difference of the area of the rectangular backyard and the right triangular fish pond.
What is the area of Bella's trapezoidal garden?It follows from the task content that the area of Bella's trapezoidal garden is to be determined from the given information.
Since the garden and the fish pond are from the rectangular backyard; the sum of their areas is equal to the area of the backyard.
Ultimately, the area of the garden is the difference of the area of the rectangular backyard and the right triangular fish pond.
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Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Alfonso wants to purchase a pool membership
for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.
The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y
Identifying the system of inequalitiesLet's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,
Let S represent the total cost of purchasing a pool membership from the Swimming Hole.
Then we can write the following system of inequalities:
A = 75 + 20x (total cost of Aquatics Club membership)
S = 15 + 65x (total cost of Swimming Hole membership)
Alfonso has no more than y dollars to spend
So, we have
75 + 20x ≤ y
15 + 65x ≤ y
Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y
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Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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cala used 4 2/3 cups of watermelon and 2 1/6 cups of cherries to make a fruit bowl how many cups of watermelon and cherries were used in all
Answer:
6 5/6 cups
Step-by-step explanation:
Add.
4 2/3 = 4 4/6
4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.
Hope this helps!
HELP PLS ILL GIVE U POINTS
Answer:
i think 16 im not sure
Step-by-step explanation:
The village of Hampton has 436 families 238 of the families live within 1 mile of the village square use mental math to find how many families live farther than 1 mile from the square show your work
Answer: 198 families live farther than 1 mile from the square.
Step-by-step explanation:
We know that there are 238 families that live within 1 mile of the village square. To find the number of families that live farther than 1 mile from the square, we can subtract 238 from the total number of families:
436 - 238 = 198
Therefore, 198 families live farther than 1 mile from the square. We can do this subtraction mentally without needing a calculator.
Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (B nC), and on the other, shade the region that represents (A -B) U (A C). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BnC) and (A -B)U (A -C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a).
In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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The graph shows the velocity, v metres per second, of a car at time t seconds. Work out an estimate for the distance the car travelled for the first 8 seconds. Use 4 strips of equal width. -1-500- -1000- -500 0 V t
please help!!!
To estimate the distance traveled we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.
Define velocity-time graph?A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.
The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.
Using the trapezium rule, the estimated area of each strip is:
Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s
Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s
Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s
Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s
The total estimated area is the sum of the areas of the 4 strips:
Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s
Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:
Estimated distance traveled is = |-4000| = 4000 meters
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machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
PLEASE HELP WILL GIVE BRAINLIEST.
Given f(x)=sin x and g(x)=cos x show that f(g(pi/2))=0. Show all your steps.
Answer:
Step-by-step explanation:
xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc
First, we need to find the value of g(pi/2):
g(pi/2) = cos(pi/2) = 0
Now we can substitute this value into f(x):
f(g(pi/2)) = f(0) = sin(0) = 0
Therefore, f(g(pi/2)) = 0.
an equation of a circle is given by (x+3)^2+(y_9)^2=5^2 apply the distributive property to the square binomials and rearrange the equation so that one side is 0.
The equation of the circle is [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex].
Given:
Equation of the circle is [tex](x+3)^2+(y-9)^2=5^2[/tex]
Expand the equation
[tex](x+3)^2 = (x+3)(x+3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9[/tex]
[tex](y-9)^2 = (y-9)(y-9) = y^2 - 9y - 9y + 81 = y^2 - 18y + 81[/tex]
[tex]5^2 = 25[/tex]
Then, substitute the expanded expressions into the equation
[tex](x+3)^2+(y-9)^2=5^2\\(x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\[/tex]
Simplify and combine like terms
[tex](x^2 + 6x + 9) + (y^2 - 18y + 81) = 25\\x^2 + y^2 + 6x - 18y + 90 = 25[/tex]
Rearrange the equation so that one side is 0
[tex]x^2 + y^2 + 6x - 18y + 90 = 25\\x^2 + y^2 + 6x - 18y + 90 - 25 = 0\\x^2 + y^2 + 6x - 18y + 65 = 0[/tex]
Thus, the equation of a circle [tex](x+3)^2+(y-9)^2=5^2[/tex] can be rearranged using the distributive property to form [tex]x^2 + y^2 + 6x - 18y + 65 = 0[/tex], with one side equaling 0.
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What is an equation for the quadratic function represented by the table shown?
The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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20x50x30x50 = ?
Please answer someone!!
Answer: 1500000
Step-by-step explanation:
use a calculator
Answer:
1,500,000
Step-by-step explanation:
Breaking it up into an easier problem:
20x50 = 1,000
30x50=1,500
1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.
Thus, the answer is 1,500,000
The interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan
find the formula relating I and P
a) I when P = 800 b)P when I = 72
The formula relating I and P is I = kP
a) When P= $800, then I = $48
b) When I = $72, then P = $1200
If the interest $I on a loan of $P for a year at a rate of 6% varies directly as the loan, we can write:
I = kP
where k is a constant of proportionality. To find the value of k, we can use the given information that the interest rate is 6%, or 0.06 as a decimal. We know that when P = 100, the interest I = 0.06 × 100 = 6. Therefore:
I/P = 6/100 = 0.06 = k
Now we can use this value of k to answer the given questions,
a) When P = 800, the formula relating I and P is:
I = kP
I = 0.06 × 800
I = 48
Therefore, the interest on a loan of $800 for a year at a rate of 6% is $48.
b) When I = 72, the formula relating I and P is:
I = kP
72 = 0.06P
Solving for P:
P = 72/0.06
P = 1200
Therefore, a loan of $1200 for a year at a rate of 6% would have an interest of $72.
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Please help quick with this question.
Answer:
b = [tex]\frac{S-2la}{h+l}[/tex]
Step-by-step explanation:
S = bh + lb + 2la ( reversing the equation )
bh + lb + 2la = S ( subtract 2la from both sides )
bh + lb = S - 2la ← factor out b from each term on the left side
b(h + l) = S - 2la ← divide both sides by (h + l)
b = [tex]\frac{S-2la}{h+l}[/tex]
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. what is the effect on the weight when the distance is multiplied by 2?
The weight becomes 1/4 of its original value when the distance is multiplied by 2.
According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.
Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,
w = k / d²
When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:
w' = k / (2d)²
w' = k / 4d²
w' = w / 4
Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.
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write down the name of shape W
A hexagon with two lines
hope helped you please make me brainalist and keep smiling dude
I hope you are form India
Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Bonny has 3 cards and a standard rolling cube. She wants to pick a card and spin the rolling cube at random. How many outcomes are possible?
There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
How to calculate How many outcomes are possibleThere are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:
Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube
Total number of outcomes = 3 x 6 = 18
Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
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