The right rectangular prism is made of equally sized cubes. If the length of each cube is 1 meter, what is the volume of the right rectangular prism?
v

72 m3

13 m3

44 m3

36 m3

An equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

To find an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4, we can use the fact that parallel planes have the same normal vector.

Step 1: Find the normal vector of the given plane.
The normal vector of a plane with equation Ax + By + Cz = D is . So, in this case, the normal vector of the given plane is <3, -1, 3>.

Step 2: Use the normal vector to find the equation of the parallel plane.
Since the parallel plane has the same normal vector, the equation of the parallel plane passing through the origin is of the form 3x - y + 3z = 0.

Therefore, an equation of the plane through the origin and parallel to the plane 3x - y + 3z = 4 is 3x - y + 3z = 0.

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30% of the students in Ms. Goldwell's gym class are also in her science class.

What is the fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely the numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

To show the fraction of the students in Ms. Goldwell's gym class who are also in her science class, you can shade a part of a rectangle that represents the total number of students in the gym class.

If 12 out of 40 students are also in the science class, the fraction is 12/40.

To convert the fraction to a percentage, multiply it by 100. So, 12/40 x 100 = 30%.

Therefore, 30% of the students in Ms. Goldwell's gym class are also in her science class.

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Answer:

( x - 11 )^2 + ( y - 5 )^2 = 4^2

Step-by-step explanation:

The general form of equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.

h and k are the co-ordinates of the center of circle and r is the radius

We have,

r=4

(h,k)=(11,5)

( x - h )^2 + ( y - k )^2 = r^2

or, ( x - 11 )^2 + ( y - 5 )^2 = 4^2

If you simplify,

x^2-22x+121+y^2-10y+25=16

or, x^2+y^2-22x-10y+146-16=0

or,x^2+y^2-22x-10y+130=0

Answer:

( x - 11 )^2 + ( y - 5 )^2 = 4^2

Step-by-step explanation:

Answer:

x = 3 and y = 5

Step-by-step explanation:

y = x+2

3x+2(x+2)=19

3x+2x+4=19

5x+4=19

    -4   -4

5x=15

x=3

y=x+2

y=(3)+2

y=5

Answer:

x=3 and y=5

Step-by-step explanation:

Answer:

2 for 25

Step-by-step explanation:

all you have to do is divide money by the number of items.

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer:

a. 44 cm b. 126 cm

Step-by-step explanation:

a. it is semi circle

perimeter is πd

22/7*14

44 cm

b. it is equilateral triangle

so perimeter is side* 3

42 *3 = 126cm

Answer:

Step-by-step explanation:

(a)

The figure perimeter it is half of a circle with a diameter d₁=14 cm and two halfs of circle with a diameter d₂=14 cm÷2=7 cm.

The length of a circle is  L₀ = πd, where d is the diameter.

Therefore:

\(\bold{L=\frac12d_1+2\cdot\frac12d_2 = \frac12\cdot14\pi+\frac12\cdot2\cdot7\pi=14\pi\,cm\approx44\,cm}\)

(b)

A full circle it is 360°, so the circle sector of 60° is  \(\frac{60^o}{360^o}=\frac16\)  of the circle. So the arc of 60° is ¹/₆ of the full circle length.

The figure is an equilateral triangle and two 60°-sectors of circles with radiuses of length of the triangle's side (r=42 cm).

Its perimetr it's two radiuses, two arcs of 60° and one side of the triangle.

The length of a circle is  L₀ = 2πr, where r is a radius.

Therefore:

\(\bold{L=2r+2\cdot\frac16\cdot 2\pi r+r=3r+\frac23\pi r}\\\\\bold{L=3\cdot42+\frac23\pi\cdot42=(126+28\pi)\,cm\approx214\,cm}\)

Answer:

Step by step

Step-by-step explanation:

1. 0x2=0+5=9

1x2=2+5=7

2x2=4+5=9

the open parts are 3x2=6+5=11

and 17 because 3+14=17

2. do more of random numbers with the equasion 2x+5 and x+14

Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

Answer:

56

Step-by-step explanation:

(84÷3) · 2 = x

28 · 2 = 56

Hope that helps!

136.5 percent chance.

91 percent in one hour

how much percent in 1.5 hour?

we need to find how much percentage is in 0.5 hour

91 divided by 2 = 45.5

91 + 45.5 = 136.5

Am i bad? pls tell

Answer:

The coordinates of the vertex is (1, -6).

Step-by-step explanation:

Given the parabola, \(y = \frac{1}{2}(x - 1)^{2} - 6\), where a = \(\frac{1}{2}\), and the vertex is represented by (h, k) = (1, -6). Since it is an upward-facing parabola, the vertex is the minimum point in the graph.  

I came up with the formula for the quadratic equation by using the coordinates for the vertex (1, -6) and the y-intercept, (0, -5.5) from the given graph. The y-intercept is the point in the graph where the parabola crosses the y-axis, and the value of its x-coordinate is 0.  

I Plug the following values into the quadratic equation in vertex form: \(y = a(x - h)^{2} + k\).  

Let y = -5.5

x = 0

h = 1

k = -6

Since we need to find the value of a:

\(y = a(x - h)^{2} + k\)

\(-5.5 = a(0 - 1)^{2} - 6\)

\(-5.5 = a(- 1)^{2} - 6\)

\(-5.5 = 1a - 6\)

Add 6 to both sides to isolate 1a:

-5.5 + 6 = 1a - 6 + 6

0.5 = 1a

Divide both sides by 1 to solve for a:

\(\frac{0.5}{1} = \frac{1a}{1}\)

0.5 or 1/2 = a

The value of a determines whether the graph opens up or down. Since the value of a is positive, the graph of the parabola opens upward. Therefore, the formula of the parabola in vertex form is:

\(y = \frac{1}{2}(x - 1)^{2} - 6\)

The farmer will purchase five bags of kind A and six bags of type B.

Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.

Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.

The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.

Allow the farmer to mix type A feed = x pounds.

and feed type B = y pounds

(9x + 2y) pounds of oats when blended

Corn amount when combined: (3x + 10y) pounds

Oats equation: 9x + 2y = 57 ———— (1)

Corn equation: 3x + 10y = 75 ————- (2)

Subtract equation (2) from equation (2) by multiplying it by three (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 6 bags

derived from the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Because the business has 15 bags of each sort, each bag costs $4.

As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)

= 20 + 24

= $44

The farmer intends to buy five bags of kind A and six bags of type B.

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the minimum score needed to be in the top 7% is 85.48, which can be rounded to 85.4. To determine the minimum score needed to be in the top 7%, we need to use the properties of the normal distribution and the corresponding z-score.

First, we need to find the z-score that corresponds to the top 7%. This can be done by using the standard normal distribution table or a calculator with a normal distribution function. The z-score that corresponds to the top 7% is approximately 1.48.

Next, we can use the formula for transforming a z-score to a raw score:

raw score = z-score * standard deviation + mean    

Substituting the values given in the problem, we get:

raw score = 1.48 * 6.1 + 76.4

raw score = 85.48

Therefore, the minimum score needed to be in the top 7% is 85.48, which can be rounded to 85.4.

In conclusion, the minimum score needed to be in the top 7% is 85.4. This calculation was performed by finding the z-score that corresponds to the top 7%, and then transforming the z-score to a raw score using the mean and standard deviation of the distribution.

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a) 2,4,8 b) 1,3,9

A has a total sum of 16, and B has a total sum of 13.

Han's retirement account earns $247,163.25 in simple interest.

To find the simplest interest, we need to use the formula:

Simple Interest = Principal × Rate × Time

In this case, the Principal is $410,000 and the Rate is $15,785 per year. We don't know the time period, but we can solve for it using the formula:

Time = Simple Interest ÷ (Principal × Rate)

Plugging in the values, we get:

Time = $15,785 ÷ ($410,000 × 1) = 0.0385 years

Therefore, the simplest interest is:

Simple Interest = $410,000 × $15,785 × 0.0385 = $247,163.25

So Han's retirement account earns $247,163.25 in simple interest.

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Answer:

750 units.

Step-by-step explanation:

30 x 30 = 900 units (total space in the classroom)

2 x 3 = 6 units (how much space each desk takes up)

25 x 6 = 150 units (number of desks for each student)

900 - 150 = 750 units

Hope this helped!

The solution to the system is x = -2 and y = 2.

To solve the given system of equations using the method of elimination, we need to eliminate one variable by manipulating the equations. In this case, we can eliminate the variable "x" by multiplying the first equation by 5 and the second equation by 2, and then subtracting the resulting equations.

Multiplying the first equation by 5, we get:

10x + 25y = 40.

Multiplying the second equation by 2, we get:

10x + 16y = 20.

Subtracting the second equation from the first equation, we eliminate the variable "x":

(10x + 25y) - (10x + 16y) = 40 - 20.

Simplifying, we have:

9y = 20.

Dividing both sides by 9, we find the value of "y":

y = 20/9.

Substituting this value of "y" back into the second equation, we can solve for "x":

5x + 8(20/9) = 10.

5x + 160/9 = 10.

Subtracting 160/9 from both sides, we have:

5x = 10 - 160/9.

5x = 90/9 - 160/9.

5x = -70/9.

Dividing both sides by 5, we obtain the value of "x":

x = (-70/9) / 5.

x = -70/45.

x = -14/9.

So the solution to the system is x = -2 and y = 2.

By multiplying the equations and manipulating them, we eliminate the variable "x" to find that y = 20/9. Substituting this value back into the second equation, we can solve for "x" and find that x = -14/9. Therefore, the main answer to the system of equations is x = -2 and y = 2. These values satisfy both equations when substituted back into them. Thus, the solution is confirmed algebraically.

The method of elimination, also known as the method of addition or subtraction, is a technique used to solve systems of linear equations. It involves manipulating the equations by multiplying or adding/subtracting them in order to eliminate one variable and solve for the other. This method is particularly useful when the coefficients of one variable in the two equations are additive inverses of each other.

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By the Riemann-Roch theorem, we know that for any compact Riemann surface C, there exists a line bundle L on C such that h⁰(C, L) ≥ deg(L) + 1.

By the Riemann-Roch theorem, we know that for any compact Riemann surface C, there exists a line bundle L on C such that h⁰(C, L) ≥ deg(L) + 1. Consider the projective space P(H⁰(C, L)) associated with the space of holomorphic sections of L.

By the Kodaira embedding theorem, there exists an immersion f: C -> P(H⁰(C, L)) such that f(C) is an algebraic curve. Moreover, since f maps C into projective space, it naturally avoids triple points and higher.

f(C) only has double points or less as singularities, proving the desired result.

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The statement "Despite their efforts, the shoguns were unable to prevent Japan from becoming a colony of a European power" is true.

During the late 19th and early 20th centuries, Japan faced increasing pressure from European powers to open up to foreign trade and influence. Despite the efforts of the shoguns to resist foreign control and maintain their independence, Japan eventually succumbed to colonization by a European power. This marked a significant shift in Japan's political and social landscape, leading to the transformation of its feudal system and the emergence of a centralized imperial government.

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Let us assume a value, a for the other part of the base. thus, the length of the base of the triangle is d + a

Considering the right angle traingle containing y degrees,

opposite side = h

adjacent side = a

Tan# = opposite side/adjacent side

tan y = h/a

a = h/tany

Considering the right angle traingle containing x degrees,

opposite side = h

adjacent side = a + d

Tan# = opposite side/adjacent side

tan x = h/(a + d)

a + d = h/tanx

a = h/tanx - d

If we equate both a's, it becomes

h/tany = h/tanx - d

d = h/tanx - h/tany

Choose N such that 1/N < log2(ε). For all n > N, we have 1/n < 1/N < log2(ε). Thus, 2^(1/n) < ε, which proves the limit.

Choose N such that 1/N < log5(ε). For all n > N, we have 1/n < 1/N < log5(ε). Thus, 5^(1/n) < ε, which proves the limit.

For any ε > 0, we can find N such that for all n > N, -3n < 3n*sin^2(n) < 3n. This means that |3n*sin^2(n) - 0| < ε, which proves the limit.
When p > 0, the sequence approaches 1. When p = 0, the sequence is constant 1.

(a) To prove limn→∞ (-2^(1/n)) = 0, let's start by choosing ε > 0. We need to find N such that for all n > N, |(-2^(1/n)) - 0| < ε.

|(-2^(1/n)) - 0| = |-2^(1/n)| = 2^(1/n). To make this less than ε, we need (1/n)log2(2) < log2(ε). Simplifying, we get 1/n < log2(ε).

Now, choose N such that 1/N < log2(ε). For all n > N, we have 1/n < 1/N < log2(ε). Thus, 2^(1/n) < ε, which proves the limit.

(b) To prove limn→∞ (1 + 5n^(1/n)) = 1, let's choose ε > 0. We need to find N such that for all n > N, |(1 + 5n^(1/n)) - 1| < ε.

|(1 + 5n^(1/n)) - 1| = |5n^(1/n)| = 5^(1/n). To make this less than ε, we need (1/n)log5(5) < log5(ε). Simplifying, we get 1/n < log5(ε).

Choose N such that 1/N < log5(ε). For all n > N, we have 1/n < 1/N < log5(ε). Thus, 5^(1/n) < ε, which proves the limit.

(c) To prove limn→∞ (3n*sin^2(n)) = 0, let's choose ε > 0. We need to find N such that for all n > N, |3n*sin^2(n) - 0| < ε.

We know that -1 ≤ sin(n) ≤ 1. So, -3n ≤ 3n*sin^2(n) ≤ 3n. As n approaches infinity, -3n and 3n both approach infinity.

Therefore, for any ε > 0, we can find N such that for all n > N, -3n < 3n*sin^2(n) < 3n. This means that |3n*sin^2(n) - 0| < ε, which proves the limit.

(d) The sequence limn→∞ (np^(1/n)) converges if and only if p > 0. When p > 0, the sequence approaches 1. When p = 0, the sequence is constant 1. When p < 0, the sequence diverges to infinity or negative infinity depending on the sign of p.

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Answer:

The area of the shaded part of the rectangle is 28 m².

Step-by-step explanation:

The area of the shaded part of the rectangle can be calculated by subtracting the areas of the two unshaded triangles from the area of the rectangle.

The area of a rectangle is the product of its width and length.

From inspection of the given diagram, the width of the rectangle is 4 m and the length is 14 m. Therefore, the area of the rectangle is:

\(\begin{aligned}\textsf{Area of the rectangle}&=4\cdot 14\\&=56\; \sf m^2\end{aligned}\)

The area of a triangle is half the product of its base and height.

The bases of the two unshaded triangles are congruent (denoted by the double tick marks) and are 7 m.

The height of both triangles is the height of the rectangle, 4 m.

Therefore, the two triangles have the same area.

\(\begin{aligned}\textsf{Area of 2 unshaded triangles}&=2 \cdot \dfrac{1}{2} \cdot 7 \cdot 4\\&=1 \cdot 7 \cdot 4\\&=7 \cdot 4\\&=28\; \sf m^2\end{aligned}\)

To calculate the area of the shaded part of the rectangle, subtract the area of the 2 unshaded triangles from the area of the rectangle:

\(\begin{aligned}\textsf{Area of the shaded part}&=\sf Area_{rectangle}-Area_{triangles}\\&=56-28\\&=28\; \sf m^2\end{aligned}\)

Therefore, the area of the shaded part of the rectangle is 28 m².

Answer:

The hiking club's member count increased by 48%.

Step-by-step explanation:

We are given two data values: 25 members and 37 members. We need to determine how many members the club gained first. We can set up an equation where we solve for an unknown, or x, in this case.

\(25 + x = 37\\\\x = 12\)

The club increased by 12 members, so now we can divide this value by the initial amount of members and multiply the decimal we receive by 100 to express it in percentage form.

\(\frac{12}{25} =0.48\\\\0.48 \times 100 = 48\%\)

Therefore, the club's member count increased by 48%.

Answer:

25+12=37

There would be 48%.

Answer:

its always C trush me on this one

Step-by-step explanation:

Answer:

Its y=-x-3

Step-by-step explanation:

x+y=-3

You would subtract the x to make it a y equals statement

y=-x-3

the -3 stays the same all thats different is the x which you will subtract over since its added to the y.