Find the surface area of the prism

Step-by-step explanation:

sin(0) = 0.

sin^2(0) = sin(0) × sin(0) = 0 × 0 = 0.

∴ sin(0) / 1 - sin^2(0) = 0 / 1 - 0

= 0 / 1

= 0.

Answer: 0.032, 18, 4224, 7.58

Step-by-step explanation:

5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]

5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L

6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box

400/23 = 17.4 so it takes 18 balls to overflow the water

7. 1 mL = 1 [tex]cm^{3}[/tex]

(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL

(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]

22 x 12 = 264

2000/264 = 7.58 cm

The values represent the robot facing east, south, and west are 1, -i, -1.

To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.

given that,

The robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now,

It is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1.

(as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.

Hence,The values represent the robot facing east, south, and west are 1, -i, -1.

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Answer: Third Graph

Step-by-step explanation:

Given inequality

|x| + 1 > 2

Subtract 1 on both sides

|x| + 1 - 1 > 2 - 1

|x| > 1

Simplify the absolute value sign

x > 1 or x < -1

Apply the inequality to the graph

Since it is less than or greater than, the circle should be hollow

Since it is less than -1 or greater than 1, one line should point to the left and another should point to the right

Therefore, it should be the Third Graph

The expected values of the binomial distribution are given as follows:

1. 214.

2. 21.

3. 31.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For item 1, the parameters are:

p = 3/7, n = 500.

Hence the expected value is:

E(X) = np = 500 x 3/7 = 1500/7 = 214.

For item 2, the parameters are:

p = 0.083, n = 250.

Hence the expected value is:

E(X) = np = 250 x 0.083 = 21.

For item 3, the parameters are:

p = 1/13, n = 400.

Hence the expected value is:

E(X) = np = 400 x 1/13 = 31.

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The length of the railing needed is 31.4 feet

From the question, we are to determine the length of railing needed

To determine the length of railing needed, we will determine the length of the arc formed by the balcony

Using the formula,

l = θ/360° × 2πr

Where l is the length of the arc

θ is the angle subtended by the arc

and r is the radius

From the given information,

θ = 45°

r = 40 feet

Putting the parameters into the equation, we get

l = 45°/360° × 2 × 3.14 × 40

l = 1/8 × 2 × 3.14 × 40

l = 2 × 3.14 × 5

l = 31.4 feet

Hence, the length of the railing needed is 31.4 feet

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The region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.

In this question,

The curves are x = 4 - y^2 -------- (1) and

x = y^2 - 4 ------- (2)

The limits of the integral can be found by solving these two curves simultaneously.

On equating (1) and (2),

[tex]4 - y^2 = y^2 - 4[/tex]

⇒ [tex]4 +4 = y^2 +y^2[/tex]

⇒ [tex]8= 2y^2[/tex]

⇒ [tex]y^2=\frac{8}{2}[/tex]

⇒ [tex]y^2=4[/tex]

⇒ y = +2 or -2

The limits of y is {-2 < y +2} or 2{0 < y < 2}

The diagram below shows the region enclosed by the two curves.

The region enclosed by the given curves can be integrated with respect to y as

[tex]A=2\int\limits^2_0 {[(4-y^{2})-(y^{2}-4 )] } \, dy[/tex]

⇒ [tex]A=2\int\limits^2_0 {[4-y^{2}-y^{2}+4 ] } \, dy[/tex]

⇒ [tex]A=2\int\limits^2_0 {[8-2y^{2} ] } \, dy[/tex]

⇒ [tex]A=2[8y-\frac{2y^{3} }{3} ]\limits^2_0[/tex]

⇒ [tex]A=2[8(2)-\frac{2(2)^{3} }{3} ][/tex]

⇒ [tex]A=2[16-\frac{16}{3} ][/tex]

⇒ [tex]A=2[\frac{48-16}{3} ][/tex]

⇒ [tex]A=2[\frac{32}{3} ][/tex]

⇒ [tex]A=\frac{64}{3}[/tex]

⇒ [tex]A=21.33[/tex]

Hence we can conclude that the region enclosed by the given curve is integrated with respect to y and the area is 21.33 square units.

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Answer:

1/50

Steps:

Recall 2 can divide 100

therefore

2/100 = 1/50

For this expression, the variables are equal to:

An expression is a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.

Given the following expression:

[tex]\sqrt[4]{15^{7} }[/tex]

From the law of indices, we have:

[tex]\sqrt[c]{a^{b} } =a^{\frac{b}{c} } \\\\\sqrt[4]{15^{7} } =15^{\frac{7}{4} }[/tex]

For this expression, the variables are:

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Answer: A = 15, B = 7, C = 4, I got it right

:)

Part a

[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]

Part C

[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]

The frequency of the periodic function is given by: 0.0796.

From the graph, we have that the period is of 4pi hours, hence the frequency is:

f = 1/4pi = 0.0796.

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When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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Answer: sequence II, sequence I, sequence III

Answer:

By the definition of midpoints, AX and CX are congruent. By the definition of segment bisectors, X is the midpoint of BD, and therefore BX and DX are congruent. Since angle AXD and CXB are vertical angles, they are congruent by the vertical angles theorem. By SAS, triangles AXD and CXB are congruent. By CPCTC, angles A and C are congruent. By converse of alternate interior angles theorem, AD is parallel to CB.

Answer: Choice B

Work Shown:

[tex]\sqrt[3]{\text{x}^5\text{y}}\\\\(\text{x}^5\text{y})^{\frac{1}{3}}\\\\(\text{x}^5)^{\frac{1}{3}}*(\text{y})^{\frac{1}{3}}\\\\\text{x}^{\frac{5}{3}}\text{y}^{\frac{1}{3}}\\\\[/tex]

Answer:

320 pages.

Step-by-step explanation:

We can simply multiply and add to find how many pages are in the book.

So we have (13 pg * 20 d) + (6 pg * 10 d) = 260 + 60 = 320.

Another way of solving is to set up a proportion for both the 20 and 10 days, find how many pages are read on these days, and add:

[tex]\frac{13pg}{1d}=\frac{xpg}{20d}\\ x=260pages\\\\\frac{6pg}{1d} =\frac{xpg}{10d}\\ x=60pg\\260+60=320[/tex]

Answer:

Identity property of addition 8 + 0 = 8

Identity property of multiplication 8 x 1 = 8

Step-by-step explanation:

He mixed up his properties.  8 + 1  does not equal 8.  I want to know what I can add to 8 and that I would still get 8, the answer is zero.

The identity property of multiplication is showing that any number multiplied by 1 is itself.

Answer:

x^3+4x^2−23x+6

Step by Step:

(x−3)(x2+7x−2)

=(x+−3)(x2+7x+−2)

=(x)(x2)+(x)(7x)+(x)(−2)+(−3)(x2)+(−3)(7x)+(−3)(−2)

=x3+7x2−2x−3x2−21x+6

=x3+4x2−23x+6

Answer:

Step-by-step explanation:

answer is 1/2

An equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

An equation can be defined as a mathematical expression which is used to show and indicate that two (2) or more numerical quantities are equal.

Mathematically, the equation of a hyperbola in standard form is given by:

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1[/tex]

Given the following data:

Center (h, k) = (0, 0)

Vertex (h+a, k) = (-5, 0)

Foci, F = (h+c, k) = (-6, 0) and F' = (6, 0)

Also, we can logically deduce that the value of a and c are -5 and -6 respectively.

For the value of b, we would apply Pythagorean's theorem:

c² = a² + b²

b² = c² - a²

b² = (-6)² - (-5)²

b² = 36 - 25

b² = 9.

b = √9

b = 3.

Substituting the given parameters into the equation of a hyperbola in standard form, we have;

[tex]\frac{(y\;-\;k)^2}{a^2} - \frac{(x\;-\;h)^2}{b^2} = 1\\\\\frac{(y\;-\;0)^2}{-5^2} - \frac{(x\;-\;0)^2}{3^2} = 1\\\\\frac{y^2}{-5^2} - \frac{x^2}{3^2} = 1\\\\\frac{y^2}{25} - \frac{x^2}{9} = 1[/tex]

y²/25 - x²/9 = 1.

In conclusion, we can logically deduce that an equation in standard form for a hyperbola with center (0, 0), vertex (-5, 0), and focus (-6, 0) is given by y²/25 - x²/9 = 1.

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Answer:

1:52 PM

Step-by-step explanation:

It gains 4 min every hour so it gains    4 * 5.5 = 22 minutes

8 oclock   + 5.5 hrs   + 22 minutes =

1:52

Answer:

  628.0 mm²

Step-by-step explanation:

The total surface area of the figure is the sum of the inside lateral area, the outside lateral area, and the area of the donut bases.

The lateral area of a cylinder is ...

  A = 2πrh

The total lateral area of the inside and outside cylinders is ...

  A = 2π(r1)h +2π(r2)h = 2π(r1 +r2)h

  A = 2(3.14)(3 mm +7 mm)(6 mm) = 376.8 mm²

The area of one donut base is the product of the centerline length and the width.

  A = πdw = (3.14)(7 mm +3 mm)(4 mm) = 125.6 mm²

The total surface area of the composite figure is the sum of its lateral area and the area of the two bases.

  surface area = 376.8 mm² +2×125.6 mm² = 628.0 mm²

__

Additional comment

The radius of the centerline of the base donut is the average of the inside and outside radii: half their sum. The diameter of the centerline circle is twice that average radius, so is equal to the sum of the inside and outside radii. This is the value we used above.

The width of the donut is the difference in the radii.

The product of the sum and difference is the same as the difference of the squares of the radii. That difference of squares would be what you have if you compute the overall area and subtract the inner area.

Answer:

b.  2x^10y^12.

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

60 / 30 = 2

x^20 / x^10 = x^(20-10) = x^10

y^(24) / y^(12) = y^(24-12) = y^12.

Thus, the answer is:

2x^10y^12.

Answer:

b. 2x^(10)y^(12)

Step-by-step explanation:

(60x^(20)y^(24))/(30x^(10)y^(12)

when there is division we simplify that by subtracting the power

by using rules of indices

[tex] \frac{x^a}{x^b}=x^{a-b}[/tex]

and number can be divided easily

[tex] \frac{60}{30}*\frac{x^{20}}{x^{10}}*\frac{y^{24}}{y^{12}}[/tex]

[tex] 2*x^{20-10}y^{24-12}[/tex]

[tex] 2x^{10}y^{12}[/tex]

so answer is b. 2x^(10)y^(12)

[tex]f(x)=-\frac{3}{4}x-3[/tex]

A graph is a diagram that depicts the connections between two or more objects. A pie chart is a type of graph. 5. A mathematical function or equation is shown by a curve or line, usually represented using a Cartesian coordinate system.

The equation for f (x):

[tex]y=f(x)=mx+b[/tex]

The slope of the line is m.

The point of intersection of the line with the y-axis is b.

To find the slope first by the following formula:

[tex]=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Two points of the line: [tex](x_{1} ,y_{1})=(x_{2},y_{2} )[/tex]

[tex](x_{1} ,y_{1})=(-4,0)[/tex]

[tex](x_{2} ,y_{2})=(0,-3)[/tex]

Substituting:

[tex]m=\frac{-3-0}{0-(-4)}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Find the y-intercept Looking at the graph, we find the line intercepts the y-axis at y=-3.

Therefore, b=-3.

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After finding the intercept form of the graph of the given straight line, it can be obtained that [tex]f(x)=-\frac{4}{5}x-3[/tex].

If the graph of a straight line cuts the x-axis at the point [tex](a,0)[/tex] and the y-axis at the point [tex](0,b)[/tex], then the equation of the straight line in intercept form will be [tex]\frac{x}{a}+\frac{y}{b}=1[/tex].

Here, in the given figure, we can see that the graph of [tex]y=f(x)[/tex] is a straight line.

From the graph, we can see that the straight line cuts the x-axis at the point [tex](-3\frac{3}{4},0)=(-\frac{15}{4},0)[/tex] and cuts the y-axis at the point [tex](0,-3)[/tex].

So, here, [tex]a=-\frac{15}{4}[/tex] and [tex]b=-3[/tex].

Hence, the equation of the straight line in intercept form is

[tex]\frac{x}{a}+\frac{y}{b}=1\\\frac{x}{-\frac{15}{4}}+\frac{y}{-3}=1\\\frac{y}{-3}=1+\frac{4x}{15}\\y=-\frac{4}{5}x-3[/tex]

Therefore, finding the intercept form of the given straight line, we obtain that [tex]f(x)=-\frac{4}{5}x-3[/tex].

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The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

According to the statement

we have to find the condition of the expected values in the case of testing of goodness-of-fit test.

So, For this purpose we know that the

The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.

So, The main condition of the expected value for the goodness of fit test is

For each​ category, the expected frequency is at least 5.

Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.

So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

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Answer:

Find out how much each makes per hour and then compare.

Step-by-step explanation:

Phil: 112.70/14 = 8.05  Phil makes $8.05 per hour

Eva: 113.82/1 =8.13  Eva makes $8.13 per hour

Eva makes $0.08 more an hour.

Answer:

  A. -18·10^6

Step-by-step explanation:

The rules of exponents apply to powers of 10 used in scientific notation. The associative and commutative properties of multiplication also apply.

  (a^b)(a^c) = a^(b+c)

The numerical product is ...

  [tex](9\cdot10^9)\cdot(-2\cdot10^{-3})=(9)(-2)(10^{9-3})=\boxed{-18\cdot10^6}[/tex]

__

Additional comment

Expressed in scientific notation, the result would be ...

  [tex]-1.8\cdot10^7[/tex]

Your calculator can perform this multiplication for you.

The transformation of f(x) to g(x) would be 6 units upwards

To transform f(x) to g(x), the equation is; g(x) = f(x) + 6

We are told that f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.

f(x) passes through (1,3) and (3, 13).

Thus;

slope is; m =  (13 - 3) / (3 - 1) = 10/2 = 5

y-intercept is; b = y - mx

Thus;

b = 3 - 5*1 = -2

Equation of the line is;

f(x) = 5x - 2

g of x passes through negative 1, 3 and 1, 13. Thus, the slope is;

m = (13 - 3) / (1 + 1) = 10/2 = 5

y-intercept is; b = y - mx

Thus;

b = -1 - (5)(-1)

b = 4

Equation of the line is; g(x) = 5x + 4

part A: The transformation of f(x) to g(x) would be 6 units upwards

part B: k = 6

part C: To transform f(x) to g(x), the equation is;

g(x) = f(x) + k

g(x) = f(x) + 6

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