How many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/2 cm, 1/6 cm, and 1/2 cm respectively ?

Answer:

Its C just got it right.

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Given that at the end of each semester in college, a survey is given to students to get feedback on the course. One of the questions on the survey is shown below.

The course met my expectations.

1. Strongly Agree

2. Slightly Agree

3. Agree

4. Slightly Disagree

5. Strongly Disagree

The problem in this survey is the difference in people's mind set about saying the answer. One person may say strongly agree for agree also while other person may do the reverse.

Hence option C is right

C. The answer choices could be interpreted differently by different students.

Answer:

The correct answer option is D) 2.

Step-by-step explanation:

We are given the value of x and f(x) in a table and we are to find the average rate of change for the given function from x = 1 to x = 4.

To find that, we will calculate the ration of change in y to change in x.

Average rate of change = [tex] \frac { 1 0 - 0 } { 4 - ( - 1 ) } = \frac { 1 0 } { 5 } [/tex] = 2

The average rate of change of the function from x = 1 to x = 4 is calculated by subtracting the function values at these points and dividing by the difference in x-values, which results in 2.

To calculate the average rate of change, you subtract the values of the function at the two points, and then divide by the difference in the x-values. For the function given with range x = 1 to x = 4, the average rate of change is calculated as follows:

[f(4) - f(1)] / (4 - 1) = (10 - 4) / (4 - 1) = 6 / 3 = 2.

Therefore, the average rate of change for the specified range is 2

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Answer:

C

Step-by-step explanation:

The area of the sector and the whole circle are proportional to the central angles.

a / A = x / 360°

a = (x / 360°) A

So the answer is C.

Find the missing side of the right triangle using Pythagorean Theorem:

10^2 =8.7^2 +x^2;

x^2=100-75.69=24.31

x= sqrt 24.31~ 4.93

Area of trapezoid is area of triangle+area of a rectangle.

A=(8.7x4.93/2)+(12x4.93)

A=80.6055 ~81 ft^2

Ok so you do height times width

Answer:

141.12 cm^2

Step-by-step explanation:

   Since the area of a trapezoid is the average of the bases multiplied by the height, we can just plug these numbers into the equation! Since the average of 10.2 and 12.2 is 11.2, and the height is 12.6, we multiply them to get the area to be 141.12 cm^2.

Answer:

141.12cm^2

Step-by-step explanation:

I do not know if this is the correct way to do it, but I split the trapezoid in half, then putting it on top of each other to create a rectangle, which is (10.2cm+12.2cm)(12.6cm/2)

Answer:

y = 8

Step-by-step explanation:

Since the 2 triangles are similar then the ratio of corresponding sides are equal, that is the sides 15 and 10 and y + 4 and y, thus

[tex]\frac{15}{10}[/tex] = [tex]\frac{y+4}{y}[/tex] ( cross- multiply )

10(y + 4) = 15y ← distribute left side

10y + 40 = 15y ( subtract 10y from both sides )

40 = 5y ( divide both sides by 5 )

8 = y

Step-by-step answer:

The maximum and minimum values are the positive sum and difference of the two magnitudes.  The magnitude of u+v can range between these two limits, namely 5+4=9, and 5-4=1.

Therefore among the given choices, the possible values of u+v are 1 unit and 9 units.  11 and 13 are greater than the maximum so do not apply.

Answer:

1 unit

9 units

Step-by-step explanation:

PLATO

Answer:

option D

[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}[/tex]

Step 1

Divide and multiple by [tex]\sqrt{x}+\sqrt{x-3}[/tex] to remove radical sign from denominator.

[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}*\frac{\sqrt{x} +\sqrt{x-3}}{\sqrt{x} +\sqrt{x-3}}[/tex]

Step 2

Apply a² - b² = (a+b)(a-b)

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{\sqrt{x^{2}}-\sqrt{(x-3)^{2}}}}[/tex]

Step 3

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{x-x+3}[/tex]

Step 4

[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{3}[/tex]

Step 5

[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]

No specific question was provided. Therefore, a clear question related to a specific subject and grade needs to be put forward for a detailed, example-filled explanation.

Since there is no specific question provided, it is not possible to provide an accurate and factual answer. Therefore, in order to give a comprehensive answer, a clear and specific question related to a given subject like Mathematics, History, English, Biology, Chemistry, Physics, etc., and grade (Middle School, High School, College) needs to be provided. Once the question is presented, I would be delighted to provide a detailed explanation, using relevant examples and details to help you understand the concept.

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Answer:

1553 cm^2.

Step-by-step explanation:

Surface area of the top part = area of the lateral part of the cylinder + area of the top circle

= 2π*6*10 + π*6^2 = 490.09 cm^2

Surface area of the bottom part

= surface area of the cube - surface area of the bottom of the cylinder

= 6 * 14^2 - π*6^2 = 1062.90

Total surface area = 490.09 + 1062.90 = 1553 cm^2.

Answer:

x = 58.0

Step-by-step explanation:

We can use the inverse of cos to solve for x once you set up the equation

[tex]cosx = \frac{9}{17}[/tex]

This is as 9 is the adjacent side and 17 is the hypotenuse of the triangle.

We can then solve for x using the inverse of cos

[tex]x= cos^{-1} (\frac{9}{17} )[/tex]

When plugged into a calculator you get

x= 58.03 degrees

this rounds to 58.0 degrees

Answer:

False

Step-by-step explanation:

The surface area of the cone is

[tex]V=\pi r^2 +\pi rl[/tex]

[tex]SA=\pi r^2 +\pi\times r\times 2r[/tex]

[tex]SA=\pi r^2 +2\pi\times r^2[/tex]

[tex]SA=3\pi r^2[/tex]

The surface area of the cylinder is:

[tex]SA=2\pi r^2 +2\pi rh[/tex]

[tex]SA=2\pi r^2 +2\pi\times r\times r[/tex]

[tex]SA=4\pi r^2 [/tex]

Answer:

[tex]\large\boxed{y^\frac{1}{5}=\sqrt[5]{y}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\to a^\frac{1}{n}=\sqrt[n]{a}\\\\y^\frac{1}{5}=\sqrt[5]{y}[/tex]

The equivalent expression for y^1/5 using radicals is √(y) where y is the base and 5 is the index of the radical.

The expression

y^1/5

is the fifth root of y. In mathematics, when we talk about roots, we're essentially talking about the inverse operation of exponentiation. If we represent the expression y^1/5 using radicals, it would be written as

√(y)

. Here, the number inside the radical sign (y) is the base, and the index of the radical (in this case 5) is the root. Thus, √(y) and y^1/5 are equivalent expressions.

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Answer:

Step-by-step explanation:

[tex]P(A|B)=\dfrac{P(A\ \cap\ B)}{P(B)}\\\\\text{A and B are independent events. Therefore}\ P(A\ \cap\ B)=P(A)\cdot P(B).\\\\\text{Substitute:}\\\\P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}\qquad\text{cancel}\ P(B)\\\\P(A|B)=P(A)\to P(A|B)=0.3[/tex]

Final answer:

Since A and B are independent events, P(A/B) is equal to P(A), which is 0.30.

Explanation:

The student is asking for the calculation of P(A/B), which is the probability of event A given that event B has occurred. However, since A and B are independent events, the occurrence of B does not affect the probability of A happening. Hence, P(A/B) is simply P(A), which is 0.30.

For independent events, the probability of A occurring given B has occurred is the same as the probability of A occurring on its own, because the two events do not influence each other:

P(A/B) = P(A) = 0.30

Answer:

5/8 pounds of butter

Step-by-step explanation:

You have to subtract 3 1/4 and 2 5/8. Once you get them in common denominators, you get 3 2/8 - 2 5/8. Next you turn 3 2/8 into 2 10/8. Then when you subtract it, you get 5/8 pounds of butter.

Answer: Third Option

-2

Step-by-step explanation:

I want to find the minimum value of a function with the form

[tex]y = asin (x-c)[/tex]

But we do not know the value of the coefficient "a", which is the amplitude, nor of the constant c.

However, in the attached graph we have the function.

The minimum value of a function is the lowest value of the variable y that the function can reach.

Observe in the graph that the function is periodic and reaches its maximum value at [tex]y = 2[/tex] and its minimum value at [tex]y = -2[/tex]

Therefore the minimum value would be [tex]y = -2[/tex]

Answer:

N=N(sub o)e^-kt  

N/N(sub o)=e^-kt  

70/100=e^-kt  

ln .7=-.0001t  

t=ln .7/-.0001

ur welcome that is your Answer.

Step-by-step explanation:

Answer: THE ANSWER IS R(x)=9x+69

Step-by-step explanation:

Answer:

[tex]R(x)= 20x^2+300x+1080[/tex]

Step-by-step explanation:

The number of teams who entered in  basketball tournament

[tex]T(x)=4x+24[/tex]

The entire fee paid by each team to enter the tournament

[tex]F(x)=5x+45[/tex]

Total entry fees = Number of teams * fee paid by each term

[tex]R(x)= T(x) * F(x)[/tex]

[tex]R(x)= (4x+24) *(5x+45)[/tex]

USe FOIL method to multiply it

[tex]R(x)= 20x^2+180x+120x+1080[/tex]

combine like terms

[tex]R(x)= 20x^2+300x+1080[/tex]

Answer:

4.62%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

If you see the Row labeled "AB" and go to the last column labeled "Total", we can see that 33 patients have blood type AB.

If you look at the right most block, we see the grand total of all patients of all blood types, which is 714 patients.

To find our answer, we divide 33 by 714 and multiply by 100 to get percentage.

Percentage of patients with blood type AB = [tex]\frac{33}{714}*100=4.62[/tex]

Answer:

4.6%

Step-by-step explanation:

To find the percentage of patient with AB blood type, we would need:

total number of patients with blood type AB

total number of all patients of all blood types

(33/714)* 100 = 4.6%

1. [tex]P(X<5)[/tex] is the area under the curve to the left of [tex]x=5[/tex], which is a trapezoid with "bases" of length 2 and 5 and "height" 0.2, so

[tex]P(X<5)=\dfrac{5+2}2\cdot0.2=0.7[/tex]

2. Find the area under the curve for each of the specified intervals:

[tex]P(X\le2)=\dfrac{2\cdot0.2}2=0.2[/tex] (triangle with base 2 and height 0.2)

[tex]P(X\ge4)=\dfrac{1\cdot0.4}2=0.2[/tex] (triangle with base 1 and height 0.4)

[tex]P(2\le X\le4)=\dfrac{0.2+0.4}2\cdot2=0.6[/tex] (trapezoid with "bases" 0.2 and 0.4 and "height" 2)

[tex]P(1\le X\le3)=\dfrac{0.1+0.3}2\cdot2=0.4[/tex] (trapezoid with "bases" 0.1 and 0.3 and "height" 2)

The required probabilities are found using the  given graphs of the

probability distributions.

Response:

1) P(X< 5) is D) 0.7

2) The probability equal to 0.2 are;

The probabilities are given by the area under the curve of the graph of

the probability distribution, which are found as follows;

1) The given figure is a trapezium, which gives;

[tex]Area \ of \ a \ trapezium = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]

Where;

a, and b are the parallel sides of the trapezium

h = The height

Therefore;

[tex]P(X < 5) = \dfrac{5 + 2}{2} \times 0.2 = \mathbf{0.7}[/tex]

2) The probabilities equal to 0.2 are found as follows;

1) At P(X ≤ 2), the area is a triangle, which gives;

[tex]Area \ of \ a \ triangle = \mathbf{\dfrac{1}{2} \times Base \ length \times Height\sqrt{x}}[/tex]

[tex]P(X \leq 2) = \dfrac{1}{2} \times 2 \times 0.2 = \mathbf{0.2}[/tex]

2) At P(X ≥ 4), has a triangular area, which gives;

[tex]P(X \geq 4) = \mathbf{\dfrac{1}{2} \times 1 \times 0.4}= 0.2[/tex]

3) P(2 ≤ X ≤4) has a trapezoidal area, which gives;

[tex]P( 2 \leq X \leq 5) = \mathbf{\dfrac{0.2 + 0.4}{2}} \times 0.2 = 0.6[/tex]

P(2 ≤ X ≤4) = 0.6 ≠ 0.2

4) P(1 ≤ X ≤ 3) has a trapezoidal area, which gives;

[tex]P( 1 \leq X \leq 3) = \dfrac{0.1 + 0.3}{2} \times 2 = 0.4[/tex]

P(1 ≤ X ≤ 3)  = 0.4 ≠ 0.2

Therefore;

The probabilities that are equal to 0.2 are;

Learn more about probability distributions here:

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Answer:

we know that

surface area=2*area of the base+perimeter of base*height 

area of the base=b*h/2

b=8 ft

h=15 ft

so

area of triangle=8*15/2-------> 60 ft²

perimeter of base=a+b+c

a=15 ft

b=8 ft

c=?

applying the Pythagoras theorem

c²=a²+b²------> c²=15²+8²------> c²=225+64------> 289

c=√289------> c=17 ft

perimeter=15+8+17=40 ft

height of the prism=20 ft

surface area=2*60+40*20------> 920 ft²

the answer is the option

B. 920 ft 2

Answer: OPTION C

Step-by-step explanation:

You need to use this formula for calculate the surface area of the right cylinder:

[tex]SA=2\pi r^2+2\pi rh[/tex]

Where "r" is the radius and "h" is the height.

You can identify in the figure that:

[tex]r=6units\\h=14units[/tex]

Knowing this, you can substitute these values into the formula [tex]SA=2\pi r^2+2\pi rh[/tex], therefore you get that the surface area of this right cylinder is:

[tex]SA=2\pi (6units)^2+2\pi (6units)(14units)[/tex]

[tex]SA=240\pi\ units^2[/tex]

Answer is C

A=2πrh+2πr^2

A=2π*6*14+2π*(6)^2

A=π*(2*6*14+2*6^2)= 240 π

Answer:

$25.20

Step-by-step explanation:

Find 21% of $960

.21*960=201.6

Since there are 8 years, the cost per year will be the total cost divided by 8.

201.6/8=25.2

The cost per year is $25.20 on the extended warranty.

Answer:

50

Step-by-step explanation:

Answer:

  8.89 feet

Step-by-step explanation:

The square of the side length is 79 ft², so the side length is the square root of that:

  √(79 ft²) ≈ 8.88819 ft ≈ 8.89 ft

Answer:

A. 176

Step-by-step explanation: First, to find the surface area to each triangle, you multiply the base times the height by 1/2. It is 28 for each triangle. Multiply that by 4, and you get 112. Then, the surface area of the square on bottom is 64. When added together, you get 176. No rounding needed. Hope it helped and is correct!

Answer:

Step-by-step explanation:

First, to find the surface area to each triangle, you multiply the base times the height by 1/2. It is 28 for each triangle. Multiply that by 4, and you get 112. Then, the surface area of the square on bottom is 64. When added together, you get 176. No rounding needed. Hope it helped and is correct!

Answer: 30r

Step-by-step explanation:

2(8r2+r)-4r

2(17r)-4r

34r-4r

30r

Answer:

16r^2-2r

Step-by-step explanation:

2(8r^2+r)-4r

(16r^2 +2r)-4r               Distribute the 2

16r^2+(2r-4r)                Regroup like terms

16r^2-2r

Hope this helps!

Answer:

D) 168 ft3

Step-by-step explanation:

The formula to find the volume of a cone is V=π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex].

We need to plug in the radius, 4, and the height, 10, into this equation.

V=π[tex](4)^{2}[/tex][tex]\frac{10}{3}[/tex]

V=π16[tex]\frac{10}{3}[/tex]

V=π53.33

V=167.55

If we round up to the nearest whole number, we get 168 [tex]ft^{3}[/tex]. Therefore, the correct answer is D) 168 ft3.

I hope I helped!

The volume of a cone is calculated using the formula V = (1/3)πr²h. For a cone with a radius of 4 ft and a height of 10 ft, the volume rounds to approximately 168 ft³. Hence, the correct answer is D) 168 ft³.

The question asks for the volume of a cone with a radius of 4 ft and a height of 10 ft. The formula for the volume of a cone is V = (1/3)πr²h, where π (π approximately equals 3.14) is Pi, r is the radius of the base, and h is the height of the cone. Plugging the given values into this formula, we calculate the volume as follows:

V = (1/3)π(4 ft)²(10 ft) = (1/3) ∗ 3.14 ∗ 16 ft² ∗ 10 ft ≈ 167.55 ft³, which rounds to roughly 168 ft³.

Therefore, the correct answer is D) 168 ft³, rounding to the nearest cubic foot as requested.

ANSWER

See below

EXPLANATION

Given

[tex]f(x) = \frac{ {x}- 9 }{x + 5} [/tex]

and

[tex]g(x) = \frac{ - 5x - 9}{x - 1} [/tex]

[tex](f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5} [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} } [/tex]

Expand:

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} } [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} } [/tex]

[tex](f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} } [/tex]

Since the denominators are the same, they will cancel out,

[tex](f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x[/tex]

Answer:

1 5/9

hope it helped

Step-by-step

divide 5 1/4 by 3 3/8 to get 1 5/9

Answer:

Step-by-step explanation:

It's a quadratic function. The graph is a parabola.

The coefficient of x² is equal 1 > 0. Therefore the parabola is open up.

Conclusion: The minimum is in a vertex.

[tex]f(x)=ax^2+bx+c\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a},\ k=f(h)[/tex]

We have

[tex]g(x)=x^2-6x-12\to a=1,\ b=-6,\ c=-12\\\\h=\dfrac{-(-6)}{2(1)}=\dfrac{6}{2}=3\\\\k=g(3)=3^2-6(3)-12=9-18-12=-21\\\\(3,\ -21)-vertex[/tex]

Final answer:

After spending $37 on pizza and $89 on concert tickets, John overdrawn his account by $26. This calculation subtracts the total expenses from his initial amount, resulting in a negative balance.

Explanation:

John initially has $100, and we need to calculate how much money he will have on Monday after his expenses over the weekend. He bought pizza for $37 and concert tickets for $89, totaling $126 in expenses. To find out how much money John has left, we subtract his total expenses from his initial amount:

Initial Amount: $100
Total Expenses (Pizza + Concert Tickets): $37 + $89 = $126

Now, subtract the total expenses from the initial amount:

$100 - $126 = -$26

This means John will have a deficit of $26. Since he spent more than what he initially had, it implies he has overdrawn his account by $26.