double b, then raise the result to the 5th power

Answer:

108quartz

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

If A cylindrical container can hold 4 quarts of water, then;

4 = πr²h ...... 1

Let the volume be x of the radius and height at tripled

h1 = 3h

r1 = 3r

X = πr1²h1

X = π(3r)²(3h)

X = 9πr²(3h)

X = 27πr²h .... 2

Divide 1 by 2

4/x = πr²h/27πr²h

4/x = 1/27

Cross multiply

x = 4×27

x = 108

Hence the container can hold 108quartz of water of the radius and height was tripled.

Answer:

400 balcony seats

Step-by-step explanation:

We know 170 tickets have been sold which is 1/5 of the total tickets

We have to find the total number of seats by doing 170x5

Now we know that there are 850 seats (170x5)

We have to subtract the lower seats from the total number of seats to find b (balcony seats)

850-450 = 400

Therefore, b is equal to 400 balcony seats

Answer:

We conclude that \(\sqrt{5}, \sqrt{5},\sqrt{10}\) is an isosceles right triangle.

Step-by-step explanation:

Given the sides of a triangle

\(\sqrt{5}, \sqrt{5},\sqrt{10}\)

Given that the two sides are equal. Thus, it must be an isosceles triangle.

Let us check whether it is an isosceles right triangle or not.

We know that for a right-angled triangle with sides a, b and the hypotenuse c is defined as:

\(c=\sqrt{a^2+b^2}\)

Given

\(a=\sqrt{5}\)

\(b=\sqrt{5}\)

now substituting \(a=\sqrt{5}\) and \(b=\sqrt{5}\) in the equation

\(c=\sqrt{a^2+b^2}\)

\(c=\sqrt{\left(\sqrt{5}\right)^2+\left(\sqrt{5}\right)^2}\)

\(c=\sqrt{10}\)

Thus,

\(a=\sqrt{5}\)

\(b=\sqrt{5}\)

\(c=\sqrt{10}\)

Which satisfies the given side lengths \(\sqrt{5}, \sqrt{5},\sqrt{10}\)

Therefore, we conclude that \(\sqrt{5}, \sqrt{5},\sqrt{10}\) is an isosceles right triangle.

To solve this question we need to do a rule of 3, this way:

0.5 h ---> 65people

5 h ------> x

650 people could ride the ferries wheel in 5 hours.

Answer:

Step-by-step explanation:

let, the length is z

thus the ratio will be 5z : 4z

perimeter = 2 (a + b)

360 = 2 ( 5z + 4z )

180 = 9z

z = 20 cm

length = 100 cm and width = 80cm

area = length * width

area = 100*80

area = 8000cm²

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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Step 1

The distribution given is a binomial distribution with following data:

\(n=25, \quad p=0.25\)

Step 2:

(a) Probability of at most 6 calls involving a fax message:

We have to add probabilities for x=0 to x=6

\(\begin{aligned}& P(X \leq 6)=\sum_{x=0}^6{ }^{25} C_x(0.25)^x(1-0.25)^{25-x} \\& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(1-0.25)^{25-0}+{ }^{25} C_1(0.25)^1(1-0.25)^{25-1} \\+{ }^{25} C_2(0.25)^2(1-0.25)^{25-2}+{ }^{25} C_3(0.25)^3(1-0.25)^{25-3} \\+{ }^{25} C_4(0.25)^4(1-0.25)^{25-4}+{ }^{25} C_{5 x}(0.25)^5(1-0.25)^{25-5} \\+{ }^{25} C_6(0.25)^6(1-0.25)^{25-6}\end{array}\right)\end{aligned}\)

\(\begin{aligned}& =\left(\begin{array}{l}{ }^{25} C_0(0.25)^0(0.75)^{25-0}+{ }^{25} C_1(0.25)^1(0.75)^{24} \\+{ }^{25} C_2(0.25)^2(0.75)^{23}+{ }^{25} C_3(0.25)^3(0.75)^{22} \\+{ }^{25} C_4(0.25)^4(0.75)^{21}+{ }^{25} C_{5 x}(0.25)^5(0.75)^{20} \\+{ }^{25} C_6(0.25)^6(0.75)^{19}\end{array}\right) \\& =\left(\begin{array}{l}0.0007525+0.006271+0.02508+0.06410 \\+0.1175+0.003171+0.182819\end{array}\right) \\& =0.5611\end{aligned}\)

Therefore,

\(P(X \leq 6)=0.5611\)

Step 3:

(b) Probability of exactly 6 calls involving a fax message:

We have to find probabilities for x=6\(\begin{aligned}& P(X=6)={ }^{25} C_6(0.25)^6(1-0.25)^{25-6} \\& ={ }^{25} C_6(0.25)^6(0.75)^{19} \\& =0.182819\end{aligned}\)

Therefore,

P(X=6)=0.182819

Step 4:

(c) Probability of at least 6 calls involving a fax message:

We have to add probabilities for x=0 to x=5 and subtract from 1\(\begin{aligned}& P(X \geq 6)=1-(P(X < 6)) \\& =1-(P(X \leq 6)-P(X=6)) \\& =1-(0.5611-0.1828) \\& =0.6217\end{aligned}\)

Therefore,\(P(X \geq 6)=0.6217\)

Step 5:

(d) Probability of more than 6 calls involving a fax message:

We have to add probabilities for x=0 to x=6 and subtract from 1\(\begin{aligned}& P(X \geq 6)=1-(P(X \leq 6)) \\& =1-(0.5611) \\& =0.4389\end{aligned}\)

Therefore,

\(P(X \geq 6)=0.4389\)

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The fraction of those who were cast got major roles is 1 / 5.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.

Given that ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles.

The fraction will be calculated as below:-

Fraction of the students cast = 90 / 3 = 30

Fraction of the students selected for major roles = 6 / 30 = 1 / 5

Therefore, the fraction of those who were cast got major roles is 1 / 5.

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P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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(1) The value of x is determined as 16.8.

(2) The measure of length VX is calculated as 4.1.

(3) The measure of angle UWV is 69.5⁰.

The value of the missing lengths of the triangle is calculated by applying the following formula;

(1) For the two similar triangles, the value of x is calculated as follows;

20 / (28 - x) = 30 / x

20x = 30 (28 - x )

20x = 840 - 30x

20x + 30x = 840

50x = 840

x = 840 / 50

x = 16.8

(2) The measure of length VX is calculated by applying trig ratios.

tan 63 = 8 / VX

VX = 8 / tan 63

VX = 4.1

(3) The measure of angle UWV is calculated as follows;

angle T = 360 - (94 + 127) = 139

angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)

angle UWV = 69.5⁰

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The expression given xy²/⁹ is equivalent to x(⁹√y²)

An algebraic expression is an expression which consists of variables, coefficients, constants, and mathematical operators such as addition, subtraction, multiplication and division. Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged in the expression, both the expressions give the same result.

In the given expression;

xy²/⁹; This can be rewritten as x(⁹√y²)

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Answer:

Step-by-step explanation:

cosine is negative in 2nd and 3rd quadrant.

cotangent is negative in 2nd and 4th quadrant.

In the second quadrant, both cosine and cotangent are negative.

In the first quadrant all trig functions are positive, In the second quadrant sine and sec are positive in the third quadrant tan and cot are positive, and in the fourth quadrant cos and cosec are positive.

We know there are four quadrants in an XY plane.

We also know that sine is positive on 1st and second quadrants and cosine is positive on the first and fourth quadrants.

tan = (sin/cos).

So, cot = 1/tan = cos/sing.

∴ cotangent is negative if any one of sine and cosine is negative which is in the second and fourth quadrants because in the third quadrant both sine and cosine are negative making cotangent positive.

∴ In the second quadrant cosine and cotangent, both are negative.

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a. -79, -41, -31, 54, 57

b. -56, -55, -54, -43, -39, -37, 18, 22, 43, 44, 52

In both cases, I have put the integers in order from smallest to greatest by comparing each number and placing them in the correct order. Starting with the smallest number and moving to the largest.

Answer:

no

Step-by-step explanation:

if two numbers are co-prime that is not necessary that one of them must be a prime number

Answer:

10

Step-by-step explanation:

The formula for distance is [ √(x2 - x1)^2 + (y2 - y1)^2 ]

√(7 - (-1))^2 + (10 - 4)^2

√(8)^2 + (6)^2

√64 + 36

√100

10

Best of Luck!

Answer:

Step-by-step explanation:

\(f(x)=x^2+2x-4\\g(x)=3x+1\\\\g\circ f(x)=g(f(x)=3(x^2+2x-4)+1=3x^2+6x-11\)

Answer:

g(f(x)) = 3x^2 + 6x - 11.

Step-by-step explanation:

Replace the x in g(x) by f(x):

g(f(x)) = 3(x^2 + 2x - 4) + 1

= 3x^2 + 6x - 12 + 1

= 3x^2 + 6x - 11.

Answer:

The Poisson's ratio for the material is 0.0134.

Step-by-step explanation:

The Poisson's ratio (\(\nu\)), no unit, is the ratio of transversal strain (\(\epsilon_{t}\)), in inches, to axial strain (\(\epsilon_{a}\)), in inches:

\(\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}\) (1)

\(\epsilon_{a} = l_{a,f}-l_{a,o}\) (2)

\(\epsilon_{t} = l_{t,f}-l_{t,o}\) (3)

Where:

\(l_{a,o}\) - Initial axial length, in inches.

\(l_{a,f}\) - Final axial length, in inches.

\(l_{t,o}\) - Initial transversal length, in inches.

\(l_{t,f}\) - Final transversal length, in inches.

If we know that \(l_{a,o} = 61.2\,in\), \(l_{a,f} = 61.235\,in\), \(l_{t,o} = 2.7\,in\) and \(l_{t,f} = 2.69953\,in\), then the Poisson's ratio is:

\(\epsilon_{a} = 61.235\,in - 61.2\,in\)

\(\epsilon_{a} = 0.035\,in\)

\(\epsilon_{t} = 2.69953\,in - 2.7\,in\)

\(\epsilon_{t} = -4.7\times 10^{-4}\,in\)

\(\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}\)

\(\nu = 0.0134\)

The Poisson's ratio for the material is 0.0134.

A. The equation that relates these variables is:

d = s * t. B. The biker would travel 10 miles in 20 minutes. C. The biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

a. Let's define the variables:

t = time in minutes

d = distance traveled by the biker in miles

s = speed of the biker in miles per minute

The equation that relates these variables is:

d = s * t

b. If the biker travels for 20 minutes, we can use the equation above to find the distance traveled:

d = s * t

d = s * 20 (since t = 20 minutes)

We need to know the speed of the biker to calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent to 30 miles per hour):

d = 0.5 * 20

d = 10

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can rearrange the equation above to find the time:

d = s * t

t = d / s

We need to know the speed of the biker to calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:

t = 48 / 0.5

t = 96

Therefore, the biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

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⠀⠀⠀⠀

⠀⠀⠀⠀

━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀

For solving such questions we need to know ratio and proportion .

⠀⠀⠀⠀

We know that in a : b : c = x : y : z ;

⠀⠀⠀⠀

a : b = x : y

⠀⠀⠀⠀

b : c = y : z

⠀⠀⠀⠀

c : a = z : x

━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀

⠀⠀

let the unknown value be x and y ;

⠀⠀⠀⠀

Therefore ;

⠀⠀⠀⠀

Required ratio = 6 : x : 15 = y : 20 : 10

➠ x : 15 = 20 : 10

Now, we will change it into fraction

⠀⠀⠀⠀

➠ x / 15 = 20 / 10

➠ x = 20 × 15 / 10

➠ x = 2 × 15

➠ x = 30

⠀⠀⠀⠀

Now the ratio becomes ;

⠀⠀⠀⠀

6 : 30 : 15 = y : 20 : 10

➠ 6 : 30 = y : 20

➠ 6 / 30 = y / 20

⠀⠀⠀⠀

➠ y = 6 × 20 / 30

⠀⠀⠀⠀

➠ y = 6 × 2 / 3

⠀⠀⠀⠀

➠ y = 2 × 2

⠀⠀⠀⠀

➠ y = 4

⠀⠀⠀⠀

\(\sf{\underline{\boxed{\large{\blue{\mathsf{Required \: ratio = 6 : 30 : 15 = 4 : 20 : 10 }}}}}}\)

━━━━━━━━━━━━━━━━━

Answer:

30 degree

Step-by-step explanation:

x + x + 60 + 60 = 180 degree (being sum of interior angles of a triangle )

2x  120 = 180

2x = 180 - 120

x = 60/2

x = 30 degree

Answer:

I'm not quite sure but there is 180 degrees in a triangle and they give us two 60 degrees which add up to 120. So, I'm assuming x = 60 or either 30 degrees if we're solving for both the x's at the top.

I'm really sorry if this is wrong.

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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The pairs of triangles can be proven similar through SSS similarity is given by Third pair.

We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.

1. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

2. KL / EG = HL / DG = HK / DE

3/10 ≠ 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

3. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 = 5/10

Thus, SSS similarity follow.

4. All three angles are congruent.

Thus, SSS similarity does not follow.

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The only true mathematical statement is the one in option C.

1 +1  = 2

Here we have some mathematical statements that are equations.

An equation is only true if both sides of the equation are equal.

So:

A = B

Is true only if A and B have the same value.

From the given options, the only one that is true is the one in option C, which gives:

1 +1  = 2

If wesimplify the left side we willget:

2 = 2

Which is true.

So that is the only true statement.

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Answer:

$98.44

Step-by-step explanation:

You already know how much the actual dinner was so all you have to do is figure out how much 15% of the $85.60 is which is $12.84 meaning that they left a tip of $12.84 for the waiter. Then you would just add the cost of the dinner with the tip to get the total amount they spent. $85.60 + $12.84 = $98.44. So the total amount the Wiggins spent is $98.44

Answer:

Multiplication, Division, Fractions, Decimals, Multipling Fractions, Divide Large Numbers

Step-by-step explanation:

The angle measures are given as follows:

The sketch is given by the image presented at the end of the answer.

We have a right triangle, hence one of the angle measures is given as follows:

90º.

The sum of the measures of the internal angles of a triangle is of 180º, hence the sum of the remaining measures is given as follows:

90º, as 180 - 90 = 90.

The smallest angle is one fifth the medium size angle, hence:

x + 5x = 90

x = 15.

The measures are:

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Answer:

Step-by-step explanation:

CACA POOP

Answer:

464

Step-by-step explanation:

hwe

Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

I think it's 5 with a remainder of 89. Hope this helps! :)

Step-by-step explanation:

K=7,

F+G=K+7

F+G=7+7

F=7, G=7 proved