The number of cells found in an average Koala is 1.30 x 10¹², under the condition that a cell is a sphere with radius 10 or 0. 001 centimeter.
Then the volume of a sphere with radius 10 cm is considered to be 4/3π(10)³ cubic cm that is approximately 4,188.79 cubic cm.
The evaluated volume of a sphere with radius 0.001 cm is 4/3π(0.001)³ cubic cm that is approximately 0.00000419 cubic cm.
Then the evaluated mass of a single cell is found by applying the formula
mass = density x volume
In case of larger cell, the mass will be
mass = 1.1 g/cm³ x 4,188.79 cubic cm
= 4,607.67 grams
In case of smaller cell, the mass will be
mass = 1.1 g/cm³ x 0.00000419 cubic cm
= 0.00000461 grams
As koalas measure an average of 6 kilograms or 6,000 grams², we can evaluate the number of cells in an average koala using division of the weight of the koala by the mass of a single cell
In case of larger cells
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 4,607.67 grams
≈ 1.30 x 10⁶ cells
For smaller cells:
number of cells = weight of koala / mass of single cell
number of cells = 6,000 grams / 0.00000461 grams
≈ 1.30 x 10¹² cells
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⁶
In ΔLMN, m = 2. 1 inches, n = 8. 2 inches and ∠L=85°. Find the length of l, to the nearest 10th of an inch
The length of l is approximately 6.1 inches to the nearest tenth of an inch.
To find the length of l, we can use the Law of Cosines which states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
where c is the side opposite angle C, and a and b are the other two sides.
In this case, we want to find the length of l, which is opposite the given angle ∠L. So we can label l as side c, and label m and n as sides a and b, respectively. Then we can plug in the values we know and solve for l:
l^2 = m^2 + n^2 - 2mn*cos(L)
l^2 = (2.1)^2 + (8.2)^2 - 2(2.1)(8.2)*cos(85°)
l^2 = 4.41 + 67.24 - 34.212
l^2 = 37.438
l = sqrt(37.438)
l ≈ 6.118
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Check each set of side lengths to see if it would be a
right triangle.
Remember plug the numbers into the Pythagorean
Theorem to see if they work!
Select ALL that are right traingles!
A 5,8, and 9
B 20, 21, and 29
C 9, 12, and 15
D 5, 6, and 11
Where the above figures are given, The right triangles are: B and C.
What is the explanation for the above response?Using the phythagoren theorem, we can determind the options that represent a right ttriangle.
A 5,8, and 9:
5^2 + 8^2 = 25 + 64 = 89
9^2 = 81
Not a right triangle.
B 20, 21, and 29:
20^2 + 21^2 = 400 + 441 = 841
29^2 = 841
It is a right triangle.
C 9, 12, and 15:
9^2 + 12^2 = 81 + 144 = 225
15^2 = 225
It is a right triangle.
D 5, 6, and 11:
5^2 + 6^2 = 25 + 36 = 61
11^2 = 121
Not a right triangle.
The right triangles are: B and C.
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Your family decides they have $400 per month to spend towards remodeling their house. the bank offers them a ten year(120 months) home equity loan for $30,000 with an interest rate of 6.5%. use p = p v ( i 1 − ( 1 + i ) − n ) to determine if your family can afford the monthly payment.
The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.
Money spend = $400
Time = 120 months
Loan amount = $30,000
Interest rate = 6.5%.
The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]
The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.
i = 0.065/12 = 0.00541667
Substituting the values into the formula,
P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]
P = $328.05
Therefore, we can conclude that the monthly payment for the loan is $328.05.
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5. A salesman bought a computer from a manufacturer. The salesman then sold the computer for
$15 600 making a profit of 25%. Unfortunately, he suffered a 5% loss due to damages when
assembling
a. What was his actual profit earnings? (10 marks)
The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.
Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.
Let the cost price of the computer be x.
Selling price = 125% of cost price
$15,600 = 1.25x
Solving for x, we get:
x = $12,480
So, the salesman's cost price of the computer was $12,480.
Now, the salesman suffered a loss of 5% due to damages when assembling the computer.
Loss = 5% of cost price
Loss = 5% of $12,480
Loss = $624
So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.
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13, 9, 17, 12, 18, 12, 17, 7, 16, 19
so what is the Mean Median_____ Range
Find f
f’’(θ) = sin (θ) +cos (θ), f(0) = 2, f’(0) = 4
F(θ) =
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
To find f, we need to integrate f''(θ) twice.
First, we integrate sin(θ) + cos(θ) with respect to θ to get f'(θ):
f'(θ) = -cos(θ) + sin(θ) + C1
where C1 is the constant of integration.
Next, we integrate f'(θ) with respect to θ to get f(θ):
f(θ) = -sin(θ) - cos(θ) + C1θ + C2
where C2 is the constant of integration.
Using the initial conditions given, we can solve for C1 and C2:
[tex]f(0) = -1 - 1 + C2 = 2[/tex]
C2 = 4
f'(0) = -1 + 0 + C1 = 4
C1 = 5
Substituting these values into the expression for f(θ), we get:
f(θ) = -sin(θ) - cos(θ) + 5θ + 4
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The money in Maya's college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
A. 0. 0215
B. 11/5
C. 0. 022
D. 11/500
A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.
= 2 1/5% / 100
= (2 + (1/5)) / 100
= 0.022
A value that is less than 0.022 from the given data is 0. 0215.
Therefore, a value less than 2 1/5% is 0. 0215.
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[tex]4^3\sqrt{-88}[/tex]
Help I don't know where the negative goes.
if you meant simplification
[tex]4^3\sqrt{-88}\implies 64\sqrt{-88}\implies 64\sqrt{(-1)(2^2)(2)(11)}\implies 64(2)\sqrt{(-1)(2)(11)} \\\\\\ 128\sqrt{(2)(11)}\cdot \sqrt{-1}\implies 128\sqrt{22}~i[/tex]
Math geometry question please help
Answer:
LP is a raym∠LMO = 90°m∠LPO = 90°m∠MLP = 26°arc MP = 154°arc MNP = 206°Step-by-step explanation:
You want various angle and arc measures in the given figure.
RelationshipsThe relevant angle relationships are ...
a radius to a point of tangency makes a right angle with the tangentan arc has the same measure as its central anglethe sum of the arcs of a circle is 360°the sum of angles in a quadrilateral is 360°an angle is formed from two rays whose endpoints are the vertex of the angleThese answer the given questions as follows:
LP is a ray.
The angle at M is 90°.
The angle at P is 90°.
The angle at L is 360° -90° -90° -154° = 26°
Arc MP has the same measure as angle MOP, 154°
Arc MNP completes the circle, so is 360° -154° = 206°
A 4.0kg box slides with an initial speed of 3.0 m/s, end fraction towards a spring on a frictionless horizontal surface. when the box hits the spring, the spring compressed by 0.30m. what is the spring constant.
The spring constant is 180 N/m.
To solve for the spring constant, we can use the equation: k = (m * g) / x
where k is the spring constant, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s^2), and x is the compression distance of the spring.
First, let's get the final velocity of the box when it hits the spring. We can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial speed (3.0 m/s), a is the acceleration (which is constant and equal to -k/m since the force from the spring is in the opposite direction of the box's motion), and s is the compression distance of the spring (0.30 m).
Rearranging the equation, we get:
k/m = (u^2 - v^2) / (2s)
k/4.0 = (3.0^2 - 0^2) / (2 * 0.30)
k/4.0 = 45
k = 180 N/m
Therefore, the spring constant is 180 N/m.
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The hourly wages earned by 20 employees are shown in the first box-and-whisker plot below. The person earning $15 per hour quits and is replaced with a person earning $8 per hour. The graph of the resulting salaries is shown in plot 2. A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 15, and the box ranges from 8. 8 to 10. 2. A line divides the box at 9. 5. Plot 1 A box-and-whisker plot is shown. The number line goes from 7 to 15. The whiskers range from 8 to 11, and the box ranges from 8. 7 to 10. A line divides the box at 9. 6. Plot 2 How does the mean and median change from plot 1 to plot 2? The mean and median remain the same. The mean decreases, and the median remains the same. The mean remains the same, and the median decreases. The mean and median decrease.
The mean decreases, and the median remains the same from plot 1 to plot 2.
In the first box-and-whisker plot, the hourly wages earned by 20 employees are displayed, with a range from $8.70 per hour to $11.50 per hour. The median, which is the value that separates the higher half of the data from the lower half, is $10 per hour. The mean, which is the average of all the wages, is calculated by adding up all the wages and dividing the total by 20.
When one employee earning $15 per hour quits and is replaced by a new employee earning $8 per hour, the second box-and-whisker plot is created. The range of wages extends from $8 per hour to $15 per hour, with a median of $9.50 per hour. Since the new employee is earning a lower wage, the mean hourly wage decreases.
Therefore, the correct answer to the question is that the mean decreases, and the median remains the same. It is important to note that while the median does not change in this case, it is not always the case in other situations where data is added or removed from a set. It is also important to note that box-and-whisker plots are helpful in visualizing the spread of data and identifying any outliers.
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Sam has 42 pencils and 56 pens.he will give all of them to a group of his classmates. each classmate will receive the same number of each item. what is the greatest number of classmates sam can give pencils and pens to? how many of each item will each classmate receive?
Sam can give pencils and pens to 14 classmates, with each classmate receiving 3 pencils and 4 pens (since 42 divided by 14 is 3, and 56 divided by 14 is 4).
Sam has 42 pencils and 56 pens, and he wants to distribute them equally among his classmates. To find the greatest number of classmates, we need to find the greatest common divisor (GCD) of 42 and 56.
The GCD of 42 and 56 is 14. Therefore, the greatest number of classmates Sam can give pencils and pens to is 14.
Each classmate will receive:
- 42 pencils / 14 classmates = 3 pencils per classmate
- 56 pens / 14 classmates = 4 pens per classmate
So, each of the 14 classmates will receive 3 pencils and 4 pens.
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Only a small percentage of Americans owned cars before the 1940s. By 2017, there were nearly 250 million vehicles for 323 million people, significantly increasing the need for roadways. In 1960, the United States had about 16,000 km of interstate highways. Today, the interstate highway system includes 77,000 km of paved roadways. What percent increase does this represent?
A. 381 percent
B. 792 percent
C. 38 percent
D. 79 percent
The percent increase in the interstate highway system from 1960 to now is 381%.
option A.
What is the percent increase?The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.
percent increase = 100% x (new value - old value) / old value
percent increase = 100% x (77,000 - 16,000) / 16,000
percent increase = 100% x 61,000 / 16,000
percent increase = 381.25%
Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.
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A pond of fish starts with 200 fish. The pond can sustain 460 fish, 40% of the fish die each year while the number of births is 60% of the current population. – 3.04174E+07 fish are harvested from the pond each year. Write a differential equation that models the problem
The differential equation that models the problem is: dN/dt = 0.2*N(t) - 3.04174E+07.
Let's denote the current number of fish in the pond by N(t), where t is time in years.
The rate of change of N(t) is given by the difference between the number of births and deaths, minus the number of fish harvested from the pond:
dN/dt = (0.6N(t)) - (0.4N(t)) - (3.04174E+07)
The first term represents the number of births, which is 60% of the current population N(t). The second term represents the number of deaths, which is 40% of the current population N(t). The third term represents the number of fish harvested from the pond each year.
Therefore, the differential equation that models the problem is:
dN/dt = 0.2*N(t) - 3.04174E+07
Note that we have simplified the expression (0.6-0.4)N(t) to 0.2*N(t) for simplicity.
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What is the equation of a circle with center (2,3) that passes through the point (5, 3)?
The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.
The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.
Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]
Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]
Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]
So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
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One day, Bill at the candy shop sold 210 bottles of cherry soda and grape
soda for a total of $230. 30. If the cherry soda costs $1. 15 and the grape
soda costs $0. 99, how many of each kind were sold?
Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
Let's assume that x is the number of bottles of cherry soda sold and y is the number of bottles of grape soda sold. We can set up a system of equations to represent the given information:
x + y = 210 (equation 1: the total number of bottles sold is 210)
1.15x + 0.99y = 230.30 (equation 2: the total cost of the sodas is $230.30)
We can use the first equation to solve for y in terms of x:
y = 210 - x
Substituting this expression for y into the second equation, we get:
1.15x + 0.99(210 - x) = 230.30
Simplifying and solving for x, we get:
1.15x + 207.9 - 0.99x = 230.30
0.16x = 22.4
x = 140
So Bill sold 140 bottles of cherry soda. Substituting this value into equation 1, we get:
140 + y = 210
y = 70
Therefore, Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
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Answer the following questions for the function
f(x) = x^3/x^2 - 4 defined on the interval (–18, 19) Enter the z-coordinates of the vertical asymptotes of f(x) as a comma-separated list. That is, if there is just one value, give it; if there are more than one, enter them separated commas; and if there are nono, enter NONE
There is a vertical asymptote at x = 0.
A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.
In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.
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√x+3
a.3x^1/2
b.(x+3)^1/2
c.x^1/2+3
d.(3x)^1/2
Answer:
b
Step-by-step explanation:
The expression √x+3 means the square root of x+3. We can rewrite this as (x+3)^(1/2), using the exponent rule that says taking the square root is the same as raising to the power of 1/2.
So the options become:
a. 3x^(1/2)
b. (x+3)^(1/2)
c. x^(1/2) + 3
d. (3x)^(1/2)
None of the other options match the given expression. So the correct answer is (b) (x+3)^(1/2).
Find the value of x that will make aiib.
4x 2x
x=
The value of x that will make a parallel to b is 30. We solved the equation 4x + 2x = 180 and obtained x = 30.
According to the definition of interior consecutive angles, when a transversal intersects two parallel lines, the sum of the measures of the two interior consecutive angles formed on the same side of the transversal is always 180°.
In this case, we are given that lines A and B are parallel, and line q intersects these lines at two distinct points, forming two interior consecutive angles with measures 4x and 2x, respectively.
Since the two angles are consecutive and on the same side of the transversal, their sum is equal to 180°. Therefore, we can set up the following equation
4x + 2x = 180
Simplifying the equation, we get
6x = 180
Dividing both sides by 6, we get
x = 30
Therefore, the value of x that will make a parallel to b is 30.
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--The given question is incomplete, the complete question is given
" Find the value of x that will make a parallel to b.
Lines A and B are parallel lines and a transverse line is intersecting these lines at two distinct points, making the angle 4x and 2x
x= "--
Debra has these snacks from a birthday party in a bag.
4 bags of chips
5 fruit snacks
6 chocolate bars
3 pieces of bubble gum
Debra will randomly choose one snack from the bag. Then she will put it back and randomly choose another snack. What is the probability that she will choose a chocolate bar and then a piece of gum?
A. 1/2
B. 1/3
C. 1/9
D. 1/18
Your answer is D. 1/18 is the probability that she will choose a chocolate bar and then a piece of gum
First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks
Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.
Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.
Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18
So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.
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Copy and complete the equation of line B below. y = — 84 NWPца - 0 7- 6+ 5- 4- 3- 2- 1/ -11 -2- -8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 ܢܐ ܚ ܩ ܘ ܘ ܢ -3 -4- -5 -6 x +_ -7 -8- Line B 19
The equation of the line passing through the given points is y = 3x-1.
Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),
Therefore, the required equation is =
y+1 = -1-2/-1 (x-0)
y+1 = 3x
y = 3x-1
Hence, the equation of the line passing through the given points is y = 3x-1.
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From a distance of 300 m, Susan looks up at the top of a lighthouse. The angle of elevation is 5',
Determine the height of the lighthouse to the nearest meter,
If Susan stands 300 m away from the lighthouse and looks up at it with an angle of elevation of 5 degrees, the height of the lighthouse is approximately 26 meters. This calculation is important for navigation and other purposes.
To determine the height of the lighthouse, we can use trigonometry. We know that the angle of elevation, which is the angle between Susan's line of sight and the ground, is 5'. We also know the distance between Susan and the lighthouse, which is 300 m.
We can use the tangent function to find the height of the lighthouse:
tan(5') = height/300
To solve for height, we can cross-multiply and simplify:
height = 300 x tan(5')
Using a calculator, we get that the height of the lighthouse is approximately 26.2 m.
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Given: AB=CD, AD|| BC, BF=HD, CGE=AHF and AE=FC.
Prove: BAE=DCF
The ∠BAE ≅ ∠DCF by SAS congruence of triangles. The solution has been obtained by using the congruence of triangles.
What is congruence of triangles?
If all three corresponding sides and all three corresponding angles of two triangles have the same size, the triangles are said to be congruent. These triangles can be moved, flipped, twisted, and turned to achieve the same result. They are parallel to one another when moved.
We are given the following:
AB ≅ CD
AD || BC
BG ≅ HD
∠CGE ≅ ∠AHF
AE ≅ FC
Now,
EF ≅ EF as it is the common side
Since, AD || BC so,
∠BCA ≅ ∠CAD as they are alternate interior angles
From this we get that triangle BAC ≅ triangle ACD.
So, the ∠BAE ≅ ∠DCF.
Hence, the ∠BAE ≅ ∠DCF by SAS congruence of triangles.
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Find the error. A class must find the area of a sector of a circle determined by a ° arc. The radius of the circle is cm. What is the student's error?
The student's error could be in the wrong formula he used. The area of the sector is 245.043 sq.
How do we calculate?The formula for area of a sector is
A = (θ/360) * π * r^2
where:
θ is the central angle of the sector in degrees
r is the radius of the circle
In this case, the central angle θ is 45 degrees and the radius r is 25 cm. So the area of the sector should be:
A = (45/360) * π * (25)^2
A = (1/8) * π * 625
A = 78.125π ≈ 245.043 sq. cm
The student could have made an error during any step of the calculation.
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What is the image of the point (-3,8) after a rotation of 180 counterclockwise about the origin
The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)
What is transformation?Transformation is the movement of a point in the coordinate plane from one location to another. Transformation can either be reflection, rotation, translation and dilation.
Rotation is the flipping of a figure about a point in the coordinate plane; this point of rotation is usually origin.
(x, y) → (-x, -y) represents a rotation 180° counterclockwise.
The image of point (-3, 8) after a rotation of 180 counterclockwise about the origin is (3, -8)
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Every day, Carmen walks to the bus stop and the amount of time she will have to wait for the bus is between 0 and 12 minutes, with all times being equally likely (i. E. , a uniform distribution). This means that the mean wait time is 6 minutes, with a variance of 12 minutes. What is the probability that her total wait time over the course of 60 days is less than 5. 5 hours
The probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.
The total wait time over 60 days will have a mean of 360 minutes (6 minutes per day x 60 days) and a variance of 720 minutes (12 minutes per day x 60 days). Since the wait times are uniformly distributed, the total wait time over 60 days will follow a normal distribution.
To find the probability that the total wait time over 60 days is less than 5.5 hours, we need to standardize the value using the z-score formula:
z = (x - μ) / σ
where x is the total wait time in minutes, μ is the mean total wait time in minutes, and σ is the standard deviation of the total wait time in minutes.
Substituting the values, we get:
z = (330 - 360) / sqrt(720) = -1.4434
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.4434 is 0.0746.
Therefore, the probability that Carmen's total wait time over the course of 60 days is less than 5.5 hours is approximately 0.0746.
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A triangular prism is 40 yards long and has a triangular face with a base of 32 yards and a height of 30 yards. The other two sides of the triangle are each 34 yards. What is the surface area of the triangular prism?
The surface area of the triangular prism is 4800 square yard.
How to find the surface area of the triangular prism?The surface area of a triangular prism is sum of the areas of the faces that make the prism.
The surface area of a triangular prism is given by:
SA = (a + b + c)L + bc
Where a and b are the bases of the rectangular faces, c is the height of the triangle and h is the total length of the prism
In this case:
L = 40, a = 34, b = 32 and c = 30
SA = (34 + 32 + 30)40 + (32 * 30)
SA = 3840 + 960
SA = 4800 square yard
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Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer
Alexander stacked 16 unit cubes required to build the rectangular prism.
What is a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
Here we need to find the number of cubes required to build the rectangular prism.
Here first we need to find how many cubes stack in the base layer
Number of unit cubes in the base layer = Number of cubes along the length * Number of cubes along the width
The number of unit cubes in the base layer = 2 * 4 = 8 cubes.
Total number of unit cubes in prism =Number of unit cubes in the base layer *Number of layers = 8 * 2 = 16 unit cubes
So, there are 16 unit cubes are required to build the rectangular prism.
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Complete question :
Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer the question.
How many cubes are required to build the rectangular prism?
PLEASEEEEEEEEEEEEEEEEEEE
Answer:
< 3 = 3x + 105°
Step-by-step explanation:
There is remot angle theory which is the exterior angle is congrent to the other non adjecent angle in triangle.
so <1 + <EDF = <3
(3x + 15 ) ° + 90° = <3
3x°+ 105° = <3
< 3 = 3x + 105° .... so the measur of angle 3 interms of x is 3x + 105°
Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
To find the volume of a cone, we use the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.
In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.
First, we need to find the slant height of the cone. We can use the Pythagorean theorem:
[tex]l = \sqrt{(r^2 + h^2)[/tex]
[tex]l = \sqrt{(6^2 + 10^2)[/tex]
[tex]l = \sqrt{\\(36 + 100)[/tex]
[tex]l = \sqrt{136[/tex]
[tex]l = 11.66 ft[/tex]
Now we can substitute the values into the formula for the volume:
[tex]V = (1/3)\pi r^2h[/tex]
[tex]V = (1/3)\pi (6^2)(10)[/tex]
[tex]V = 120\pi /3[/tex]
[tex]V = 40\pi[/tex]
[tex]V= 125.6 cubic feet[/tex]
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