Moses receives a gift that is wrapped in a cube shaped box. The volume of the box is 1331/8 cubic inches.Find the length of a side of the box

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, scalene, equilateral, acute, obtuse and right angled triangle. A right angle triangle is a triangle with one angle being 90°.

Trigonometric ratios is used to show the relationship between the angles and sides of a right angled triangle. Examples are:

sinΘ = opposite/hypotenuse; cosΘ = adjacent/hypotenuse; tanΘ = opposite/adjacent

From the question:

cos(62) = AB/12

AB = 12 * cos(62)

AB = 5.6 cm

Hello!

1) -3x - 4 = 23

-3x = 23 + 4

-3x = 27

x = 27 : (-3)

x = -9

2) x/2 - 12 = -4

x - 24 = -8

x = -8 + 24

x = 16

3) 6a + (-1) = 10

6a - 1 = 10

6a = 10 + 1

6a = 11

a = 11 : 6

a = 11/6

4) -(x + 2) = 12

x + 2 = -12

x = -12 - 2

x = -14

5) 7a + 12 = 10

7a = 10 - 12

7a = -2

a = -2 : 7

a = -2/7

6) -4(a + 2) = 12

a + 2 = -3

a = -3 - 2

a = -5

Good luck! :)

Answer:

[tex]791.7\:\mathrm{ft^3}[/tex]

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].

By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].

Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:

[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]

Answer:

Step-by-step explanation:

5 ) c

6) c

7) b

8) a

Answer:

hi, see mate the third angle is not in the photo, please upload another one

Answer:

the answer of r is 8 i hope it will help

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

( − ∞ , ∞ )

Set-Builder Notation:

{ x | x ∈ R }

Step-by-step explanation:

hope that helps bigger terms

Answer:

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

Step-by-step explanation:

For each shot, there are only two possible outcomes. Either they hit the target, or they do not. The probability of a shot hitting the target is independent of any other shot, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Each arrow with a probability 0.2

This means that [tex]p = 0.2[/tex]

First 10 arrows

This means that [tex]n = 10[/tex]

What is the probability that at most one of her first 10 arrows hits the target?

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1074 + 0.2684 = 0.3758[/tex]

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

Answer:

Step-by-step explanation:

Given function h(x).

Shift left:

Shift down:

Given function is,

→ h(x)

As we shift left,

→ h(x) = h(x + 3)

As we shift down,

→ h(x + 3) = h(x+3)-5

Then the equation is,

→ h(x+3)-5

It is correct answer.

Answer:

Step-by-step explanation:

f(x) = 3x² -5x - 1

f'(x) =2*3x - 5*1 +0

     = 6x - 5

f'(4) = 6*4 - 5

      = 24 - 5

      = 19

Answer:

Attached images

It was just easier for me this way.

Let me know in comments if you have questions.

Step-by-step explanation:

Answer Deleted

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Answer:

Not sure if this is right, but I hope it helps. Please see attached pic

Step-by-step explanation:

Answer:

0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A hotel manager calculates that 12% of the hotel rooms are booked.

This means that [tex]p = 0.12[/tex]

Sample of 556 rooms

This means that [tex]n = 556[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.12[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{556}} = 0.0138[/tex]

What is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%?

This is the p-value of Z when X = 0.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.1 - 0.12}{0.0138}[/tex]

[tex]Z = -1.45[/tex]

[tex]Z = -1.45[/tex] has a p-value of 0.0735

0.0735 = 7.35% probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%.

Answer:

D

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

Answer:

D.

Step-by-step explanation:

slope = m = rise/run = 2/1 = 2

The slope is 2.

Use point (-2, 1).

y - y_1 = m(x - x_1)

y - 1 = 2(x - (-2))

y - 1 = 2(x + 2)

Answer: D.

Answer:

the answer is c

Step-by-step explanation:

the answer is c

Answer:

About $150 billion US dollars to buy Venezuela

Step-by-step explanation:

It's a big place

Answer:

<A = 47.7°

<B = 99.4°

<C = 32.9

Step-by-step explanation:

When given the measurements of all three sides, you can calculate the angles using the Cosine Law.

c² = a² + b² - 2ab cos C

(based on Pythagorean Theorem)

If we say: a = 15

b = 20

c = 11

11² = 15² + 20² - 2(15)(20) cos C

121 = 625 - 2(15)(20) cos C

121 = 625 - 600 cos C

⁻504 = ⁻600 cos C

cos⁻¹ (504 ÷ 600) = C

< C = 32.9°

a² = b² + c² - 2bc cos A

15² = 20² + 11² - 2(20)(11) cos A

225 = 521 - 2(20)(11) cos A

225 = 521 - 440 cos A

⁻296 = ⁻440 cos A

cos⁻¹ (296 ÷ 440) = A

<A = 47.7°

Then, since we know the sum of all three angles of a triangle equals 180°:

180° - 32.9° - 47.7° = 99.4°

<B = 99.4°

Answer:

A saturated fat is a type of fat in which the fatty acid chains have all or predominantly single bonds. A fat is made of two kinds of smaller molecules: glycerol and fatty acids. Fats are made of long chains of carbon atoms. Some carbon atoms are linked by single bonds and others are linked by double bonds.

Saturated fats: a type of fat containing a high proportion of fatty acid molecules without double bonds, considered to be less healthy in the diet than unsaturated fat

Unsaturated fats: a type of fat containing a high proportion of fatty acid molecules with at least one double bond, considered to be healthier in the diet than saturated fat.

what's the difference between both?: saturated fats Contains a single bond, Excessive consumption leads to heart diseases,High melting point and Solid state in room temperature. While Unsaturated Contains at least one double bond, Good for consumption, but excessive may increase cholesterol,Low melting point and Liquid state in room temperature.

Answer:

[tex]y = 125.00x + 591.00[/tex]

Step-by-step explanation:

Given

See attachment for table

Required

Equation for Paris

From the table, we have:

[tex]flight = 591.00[/tex]

[tex]hotel = 125.00[/tex]

Let the number of nights be x.

So, the equation for the total amount (y) is:

[tex]y = flight + hotel * x[/tex]

[tex]y = 591.00 + 125.00 * x[/tex]

[tex]y = 125.00x + 591.00[/tex]

Answer:

60 degrees

Step-by-step explanation:

So we see there's a 90 degree angle and a 150 degree larger angle including it.

So to find out the part that the 150 degree large angle that's not a part of the 90 angle we would do: 150 - 90, and we get 60.

So the bottom right angle is 60 degrees.

Now since we have a straight line from the left to right horizontally, we know that one side has to equal 180 degrees. On the side which the x is on, we already have 2 angles: 90 and 30. 90 + 30 = 120.

Since a straight line equals 180, x + 120 has to equal 180.

So now we do simple algebra.

x + 120 = 180

x = 180 - 120

x = 60

So x is equal to 60 degrees.

Answer:

26.59 minutes

Step-by-step explanation:

Let's say the time needed to do the driveway combined is x. Sue does y parts of the driveway, and Tom does z parts of the driveway. Combined, y + z = 100% = 1, as they finish the whole driveway.

Next, Tom will take 45 * z minutes to do his part of the driveway. For example, if he did 50% = 0.5 of the driveway, he would take 45 * 0.5 = 22.5 minutes to do it. Similarly, Sue will take 65 *y minutes to do her part of the driveway. Since they will finish at the same time, we can say

45 * z = 65 * y

y + z = 1

Therefore, if we subtract y from both sides of the second equation, we have

z = 1-y

We can then plug 1-y in for z in the first equation to get

45 * (1-y) = 65 * y

45 - 45*y = 65*y

add both sides by 45 * y to separate the y values and their coefficients

45 = 110 * y

divide both sides by 110 to find y

y = 45/110 = 0.409

Use 1-y=z to get z = 1-0.409 = 0.59

Therefore, 45*z = 26.59 = 65*y

Answer:

Step-by-step explanation:

office at point A =(-7,-5)   ........................in the form (x1,y1)

supermarket and point B = (-2,-6)........in the form (x2,y2)

home Home at point C = (4,-6).............in the from (x3,y3)

find the total distance from A to B + B to C

ABdist= sqrt[ (x2-x1)^2 + (y2-y1)^2 ]

ABdist = sqrt[ (-2-(-7))^2 + (-6-(-5))^2 ]

ABdist = sqrt[ (-2 + 7)^2 + (-6 +5)^2]

ABdist = sqrt[ [tex]5^{2}[/tex] + [tex](-1)^{2}[/tex]]

ABdist = sqrt[ 25 + 1 }

ABdist = [tex]\sqrt{26}[/tex]

BCdist= sqrt[ (x3-x2)^2 + (y3-y2)^2 ]

BCdist = sqrt[ (4-(-2))^2 + (-6-(-6))^2]

BCdist = sqrt[ 4+2)^2  + -6+6)^2 ]

BCdist = sqrt [ [tex]6^{2}[/tex] + [tex]0^{2}[/tex] ]

BCdist = [tex]\sqrt{36}[/tex]

BCdist = 6

total distance = [tex]\sqrt{26}[/tex] +6

The first answer looks good

Answer:

The remainder is 3x - 4

Step-by-step explanation:

[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]

So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]

In this case our dividend is always P(x).

Part 1

When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]

When [tex]x = 1[/tex],

[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]

--------------------------------------------------------------------------------------------------------------

Part 2

When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]

When [tex]x = -3[/tex],

[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]

--------------------------------------------------------------------------------------------------------------

Part 3

When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]

We will call [tex]a + b = -1[/tex] equation 1

From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]

We will call [tex]3a - b = 13[/tex] equation 2

Now we can create a system of equations using equation 1 and equation 2

[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]

By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]

So equation 1 + equation 2:

[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]

Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.

So substituting [tex]a = 3[/tex] into equation 1:

[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]

Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.

So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:

[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]

Therefore, the remainder is [tex]3x - 4[/tex].

Answer:

The required probability is 0.1.

Step-by-step explanation:

red balls = 3

yellow balls =  2

blue balls = 5

Selected balls = 5

Number of elemnets in sample space = 10 C 5 = 1260

Ways to choose 1 red ball and 4 other colours =  (3 C 1 ) x (7 C 4) = 105

Ways to choose 5 balls of other colours = 7 C 5 = 21

So, the probability is

[tex]\frac{105}{1260} + \frac {21}{1260}\\\\\frac{126}{1260}=0.1[/tex]  

Answer:

B. 23

Step-by-step explanation:

BC = 32

CA = 44

To find the length of CD, apply the altitude of right triangle formula, (altitude-on-hypotenuse theorem) which is given as:

h = √(xy)

Where,

h = CB = 32

x = CA = 44

y = CD = ?

Plug in the values

32 = √(44 × CD)

Square both sides

32² = 44 × CD

1,024 = 44 × CD

Divide both sides by 44

1,024/44 = CD

CD = 23 units (nearest whole unit)

Answer:

Frustum Volume =

[PI * height * (small radius^2 + (small radius * large radius) * + large radius^2)] / 3

Frustum Volume = PI * 10 * ( 1.5^2 + 1.5*3.75 + 3.75^2 ) / 3

Frustum Volume = 31.41592654 * (2.25 +5.625 +14.0625) / 3

Frustum Volume = (31.41592654 * 21.9375) / 3

Frustum Volume = 689.1868884713 / 3

Frustum Volume = 229.72896282 cubic cm

Source: http://www.1728.org/volcone.htm

Step-by-step explanation: