you toss a pair of six-sided dice. (a) determine the number of possible pairs of outcomes. (recall that there are six possible outcomes for each die.)

Answer: 16

Step-by-step explanation:

32% of 50 = 16

Answer:
The light globe is 1.6 meters above the ground.

Explanation:

height of light globe = height of boy x distance from light globe to base of electric pole / distance from boy to base of electric pole

Plugging in the values given in the problem, we get:

height of light globe = 1.6 m x 8.1 m / 8.1 m

This simplifies to:

height of light globe = 1.6 m

Answer:Antonio drove 24 miles west

Step-by-step explanation: 50-26=24

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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Answer:

Tom will pay a total of $58,064 in interest over the 30 year loan.

Step-by-step explanation:

The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.

Therefore, Tom borrows $144,000 - $14,400 = $129,600.

Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.

Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:

I = P * r * t

Where:

I is the total interest

P is the principal (the amount borrowed)

r is the annual interest rate (in decimal form)

t is the number of payments

Plugging in the values, we get:

I = $129,600 * 0.045 * 360 payments

= $58,064

Answer:

6,561

Step-by-step explanation:

((3*3)²)²

((9)²)²

(81)²

6,561

Answer:

Step-by-step explanation

answer:6561

3 times 3 = 9

9^2=81

81^2=6561

Answer:

B. [tex]\triangle UVZ \cong \triangle VYX[/tex], SSS

The congruent statement and the reason why the triangles are congruent is (b) ΔUVZ ≅ ΔVYX, SSS

From the question, we have the following parameters that can be used in our computation:

Triangles = UVZ and VYX

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles UVZ and VYX have the same mark

UV and VY

UZ and VX

VZ and YX

This implies that these sides are congruent sides

Hence, the congruent statement on the congruency of the triangles is (b) ΔUVZ ≅ ΔVYX and the reason is by SSS

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Answer: y = 3x - 8

Step-by-step explanation:

      We will write a point-slope equation to help us write a slope-intercept equation.

y - 16 = 3(x - 8)

y = 3(x - 8) + 16

y = 3x - 8

      The slope-intercept form equation that represents this line is;

                        y = 3x - 8

The given quadratic equations are:

Is in fact a quadratic equation.

The options are:

(i) x^2 - x + 3 = 0

(ii) 2x^2 +5/2x - √3 = 0

(iii) √2x^2 + 7x + 5√2

(iv) 1/3x^2 + 1/5x - 2 = 0

(v) x^2 - 3x - √x + 4 = 0

(vi) x - 6/x = 3

A general quadratic equation is a polynomial of degree 2:

a*x² + b*x + c = y

Where the variable is x, and we can see that the maximum exponent on a power of x is 2.

In this case, we have the first equation:

x^2 - x + 3 = 0

You can see that we have a polynomial of degree 2 (the maximum exponent is 2 and we only have positive integers as exponents) then this is in did a quadratic equation.

The other quadratics are:

Where you also can see polynomials of degree 2.

(the third option also seems to be quadratic, but it is not an equation)

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The complete question is:

Which of the following are quadratic equation in x?

The options are:

(i) x^2 - x + 3 = 0

(ii) 2x^2 +5/2x - √3 = 0

(iii) √2x^2 + 7x + 5√2

(iv) 1/3x^2 + 1/5x - 2 = 0

(v) x^2 - 3x - √x + 4 = 0

(vi) x - 6/x = 3

Answer: M=1

Step-by-step explanation:

hope this help!

On solving the provided question, we got to know that 91/4 feet is the vertical distance that ball traveled.

What is equation?

An equation in algebra is a formula that proves two other formulas are equivalent. For instance, the equation 3x + 5 = 14 is produced when the two equations 3x + 5 and 14 are combined with an equal sign. Mathematical equations in algebra frequently have one or more variables.

If the balls land in a straight line:

dropped = 13 ft

rebounds 3/4 (13) ft  = 39/4 ft

vertical travel = 13 + 39/4 = 91/4 ft

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Answer:Bisect an angle :)

Step-by-step explanation:

Answer: Hugo should buy car A

Step-by-step explanation:

Car A

Take 702 divided by 12 = 58.5 miles per gallon of gas

Car B

Take 873 divided by 15 = 58.2 miles per gallon of gas.

So Hugo should buy car A

Answer:

x = 2

Step-by-step explanation:

The Unit Normal to the Surface cos(x. y) = e. z - 2 at (1,π,0) is -2 ≤ z ≤ 2.

Let F(x, y, z) = cos(x.y) − e.z + 2 .

A given surface is the same as the set of planes F(x, y, z) = 0.

Since the gradient vector ∇F( 1 , π, 0) is normal to this surface at (1, π, 0) , find this vector and normalize it to get the unit vector normal to this surface.

Differentiate:

∇F(x, y, z) = (−y sin(x y), −x sin(x y), e(z)

or

∇F(1, π, 0) = (0 , 0 , 1).

This vector is already of length 1, so this is sufficient. Alternatively, you can use the vector opposite. Therefore, the two vectors that satisfy the problem are ±k.  At problem point, the surface is flat horizontally.

We may want to see what this interface looks like. This is a computer-generated sketch corresponding to:

                      −4 ≤ x ≤ 4, −4 ≤ y ≤ 4, −2 ≤ z ≤ 2.

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The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

Time t = 11 sec

Initial velocity u = 25 kmph

u = (25 × 1000)/(60 × 60) = 6.9 m/s

final velocity v = 75 kmph

v = (75 × 1000)/(60 × 60) = 20.83 m/s

From the first equation of motion;

v = u + at

Put the values;

20.83 = 6.9 + 11a

20.83 - 6.9 = 13a

11a = 13.93

a = 13.93 / 11

a = 1.26 m/s²

Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

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Answer:

Step-by-step explanation:

12.1

Answer:

8 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{17}{20}[/tex] = [tex]\frac{34}{40}[/tex] Multiplied the numerator and denominator by 2

[tex]\frac{1}{2}[/tex] = [tex]\frac{20}{40}[/tex]  Multiplied the numerator and denominator by 20

[tex]\frac{3}{4}[/tex] = [tex]\frac{30}{40}[/tex]  Multiplied the numerator and denominator by 10

2 + 3 + 1 [tex]\frac{34}{40}[/tex] + [tex]\frac{20}{40}[/tex] + [tex]\frac{30}{40}[/tex]

6 [tex]\frac{84}{40}[/tex]  This can be written

6 + [tex]\frac{40}{40}[/tex] + [tex]\frac{40}{40}[/tex] + [tex]\frac{4}{40}[/tex]  another name for [tex]\frac{40}{40}[/tex] is 1

6 + 1 + 1 +[tex]\frac{4}{40}[/tex]

8[tex]\frac{4}{40}[/tex]  Divide the numerator and denominator by 4 to simplify

8 [tex]\frac{1}{10}[/tex]

The probability that all 3 will be vowels will be .01 to the nearest hundredth

Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.

There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.

First of all, we need to know the number of vowels in the 26 letters.

There are 5 vowels among the 26 letters,

probability (3 vowels of 3)

= (5/26)*(5/26)(5/26)    multiplication of probability of each letters

=0.1923*0.1923*0.1923

≈0.0071

≈0.71%

or .01 to the nearest hundredth

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a) The marginal cost MC at  x=9 units is $154.70.

b) The cost of producing 1 additional unit is $154.70.

c) The cost of producing 2 additional units is $309.40.

The Marginal Cost quantifies the incremental cost incurred from the production of each additional unit of a good or service. The marginal cost of production captures the additional cost of producing one more unit of a good/service.

The analysis of the marginal cost helps determine the “optimal” production quantity, where the cost of producing an additional unit is at its lowest point. The marginal cost of production must be lower than the price per unit for a company to be profitable – thus, the marginal cost pinpoints the output volume and pricing where incremental costs are reduced.

a) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

C(x) = 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18

MC = dC/dx

MC = d( 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18) / dx

      = 1/90 (3x²) + 8 (2x) + 8

      = 1/30x² + 16x + 8

At x = 9 units, we get

MC(x=9) = 1/30 (9²) + 16 (9) + 8

              = 154.7

Rounding off to two decimal places, we get 154.70.

Thus, the marginal cost MC at  x=9 units is $154.70.

b) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 1

Change in costs = 154.70

So, the cost of producing 1 additional unit is $154.70.

c) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)

154.70 = Change in costs/ 2

Change is costs = 309.40

So, the cost of producing 2 additional units is $309.40.

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Answer: I think its

x>-10/3

Step-by-step explanation:

The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time required to finish building the transmission if Jose and Luis works together be = A

Now , the equation will be

The time required by Jose to build a transmission = 10 hours

The time required by Luis to build a transmission = 8 hours

If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker

So ,

If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour

If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour

And ,

Together they build the transmission in

1/A = 1/10 + 1/8

where A is the total time required to finish building the transmission if Jose and Luis works together

So , the equation is

1/A = 1/10 + 1/8

1/A = 18/80

Taking reciprocals on both sides of the equation , we get

A = 80/18

A = 40/9

On simplifying the equation , we get

A = 4.44 hours

Therefore , the value of A is 4.44 hours

Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours

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The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.

As given in the question,

Number of six sided dice to be rolled = 4

Number of outcomes on one dice = 6

Total number of outcomes of 4 dice = 6⁴

                                                            = 1296

Conditions for the product of the numbers of top faces all four dice is prime:

Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),

( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)

Total number of favourable outcomes = 12

Required Probability = 12 / 1296

                                  = 1 / 108

Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.

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Answer:

18 tiles

Step-by-step explanation:

There are 20 tiles in total.  Red is 6 of the 20, or 6/20.  That is 3/10 or 30%

Each draw has a 30% chance of being red.  30% or 20 tiles is 1.8 tiles.  Over 30 draws, that would mean a total of 600 tiles are drawn,  The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:

 (0.30)*(600) = 18 tiles will be red.

Answer: 6 and 7

Step-by-step explanation: The square root of 41 is 6.4. Since you multiply it by itself, it’s the nearest square root to 41.

The time that it will take for the shadow to travel 1150 miles is; 30 minutes

Let y represent the distance in miles    

Let x represent the time in minutes

The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles

Thus, the coordinates are;

(60, 2300) and (20,  2300/3)

The slope is;

m = (2300 - 2300/3)/(60 - 20)

m = 115/3 mi/min

Thus, the linear equation in point slope form is;

y - 2300 = (115/3)(x - 60)

This gives;

y = (115/3)x

When y = 1150 miles, we have;

1150 = (115/3)x

x = 30 minutes

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The total amount of the monthly payments and the finance charge is 144.

Instalment is one of the regular payments that anyone can  make for anything until you have fully paid that full amount.

Using the appropriate interest relation, the solution to the problems posed are :

Down payment = 0.05k

144 monthly payments

Total monthly payment made = 144g

Down payment :

5% of total cost

Total cost = k

5% × k = 0.05k

B.)

Number of monthly payments :

Number of months per year = 12

Number of years = 12

Number of monthly payments = 12 × 12 = 144

C.)

Total charge :

Monthly payment = $g

Number of monthly payments × amount paid

g × 144 = 144g

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Part (a)

Part (b)

Yes, the triangles are congruent by RHS.

The possible temperatures for the north will be 4 degrees and 6 degrees. The correct option is D and E.

Mathematical statements with at least two terms connected by an operator and containing either numbers, variables, or both are referred to as expressions.

The direction that heat energy will spontaneously flow depends on temperature. Temperature is the degree to which a body is hot or cold. because it was mentioned that the north can occasionally experience temperatures below 3 degrees. D and E are the appropriate choices

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