Gordon rolls a fair dice 162 times.
How many times would Gordon expect to roll a number greater than 3?

Simplest form of expression is an expression written in its simplest of terms without changing the original value of the expression. There should be no like terms or parentheses.

In the given expression, there are two like terms and no parentheses. Hence, we solve for eliminating the like terms to find the simplest form of expression.

In order to eliminate the like terms, we need solve the square root terms to its simplest form.

√32=√2x2x2x2x2=4√2  

√72=√2x2x2x3x3=6√2

Hence, the expression becomes,

2*4√2 x2+3*6√2 x2

Simplifying,

8√2 x2+18√2 x2

Adding the like terms,

(8+18)√2 x2

26√2 x2

Hence, the simplest form of expression 2 √32 x²+3 √72 x² is 26√2 x2.

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Answer:c=7

Step-by-step explanation:

The rocket moves really fast with high speed.

A projectile that receives thrust from a rocket engine is known as a rocket (from the Italian rocchetto, which means "bobbin/spool"). All of the propellant carried by the rocket is used to create the exhaust from its engine.

In actuality, the absence of an atmosphere in space allows rockets to operate more effectively.

Due to their ability to reach Earth's escape velocity, multistage rockets can reach any maximum altitude. Rockets may produce significant accelerations and are powerful, light, and lightweight when compared to airbreathing engines.

In order for rockets to go forward and function in the vacuum of space, their action-reaction engines quickly discharge exhaust in the opposite direction.

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Adult tickets costs $63.8

Children tickets costs $13.2

Let x represent the adult tickets and y to represent the cost of children tickets

x + y= 77..........equation 1

36x + 17y= 2,297........equation 2

From equation 1

x= 77-y

Substitute 77-y for x in equation 2

36(77-y) + 17y = 2297

2772 - 36y= 2297

-36y= 2297-2772

-36y= -475

y= 475/36

y= 13.2

Substitute 13.2 for y in equation 1

x + 13.2 = 77

x= 77-13.2
x= 63.8

Hence adult tickets costs $63.8 and children tickets costs $13.2

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Answer:

The answer is supposedly 0.25

Answer:

f(10) = 905

Step-by-step explanation:

f(x) = 9x² +5; find f(10)

~Substitute x with 10

9(10)^2 + 5

~Solve exponent first

9(100) + 5

~Multiply

900 + 5

~Add

905

Best of Luck!

The answer is:

Work/explanation:

To evaluate the given function, plug in 5 for x:

[tex]\bf{f(x)=9x^2+5}[/tex]

[tex]\bf{f(10)=9(10)^2+5}[/tex]

Remember, exponents first. So we square 10 first.

[tex]\bf{f(10)=9\cdot100+5}[/tex]

Multiply, then add:

[tex]\bf{f(10)=900+5}[/tex]

[tex]\bf{f(10)=905}[/tex]

The measure of PQT = 142.

We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.

So we can set up and solve the following equation as such:

2(8x-25) = 9x +34

16x - 50 = 9x +34

7x -50 = 34

7x = 84

x = 12

Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.

8(12) - 25

96 -25

71

So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.

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Answer:

A. & B.

Step-by-step explanation:

Square root of 4 is 2, and the square root of 9 is 3. These are rational, and adding fractions keeps them rational.

But the square root of 2 is irrational, and subtracting or dividing will not make them rational.

Hope this helps! :)

The equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.

It should be noted that there's a constant relationship between the figures that are given.

This can be illustrated as:

= 25/10

= 2.5

Therefore, the equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.

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1. 10 * 10 * 10 = 1000 = 10^3

2. 10 * 10 * 10 * 10 = 10,000 = 10^4

3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5

4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7

5. Summary

Multiplication   Exp on first factor   Exp on 2nd factor    Exp on product

10^1 * 10^2                 1                                    2                             3

10^1 * 10^3                 1                                    3                              4

10^2 * 10^3               2                                   3                              5

10^4 * 10^3               4                                   3                              7

6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.

This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.

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According to the question, the given rational expression is as follows:

Expression =  [tex]\frac{x^{2} +8x+16}{x^{2} -2x-24}[/tex]

Simplify the numerator as well as denominator by doing factors which is shown below:

[tex]x^{2} +8x+16=x^{2} +4x+4x+16=(x+4)(x+4)[/tex]

Similarly, denominator factors are as follows:

[tex]x^{2} -2x-24=x^{2} -6x+4x-24=(x-6)(x+4)[/tex]

Now, substituting these values in the given expression, we get:

[tex]\frac{x^{2} +8x+16}{x^{2} -2x-24} = \frac{(x+4)(x+4)}{(x-6)(x+4)}=\frac{x+4}{x-6}[/tex]

Therefore, the final answer for the given expression is [tex]\frac{x+4}{x-6}[/tex].

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Answer:5

Step-by-step explanation:

4x + 5 = 5.. if its addition you take away the number if its subtraction you add the number.. take away 5 from 25.. 4 times 5 is 20

Answer:

Step-by-step explanation:

Depreciation means value falling

10 is the scrap value which means the value that will remain after the product is properly used up.

depreciation for one year will be calculeted through

(original value - scrap value)/ no of years of use

(500 - 10)/3

= 163 is the annual rate of depreciation

If no scrap value is given, then you will simply divide the value by the no. of years of use

b. annual depreciation = 163

original value = 500

500 - 163(x) = worth of the poster after x years

worth remaining after a certain no. of years is also known as net book value.

The exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .

Given : height = 5 feet

            rebound on first bounce = 35 inches

            rebound on second bounce = 21.5 inches

To find :  exponential function that would be a good model for the                      bouncing ball

Calculation :

at x = 0

ht. = 5 feet = 60 inches

at x = 1

ht. = 35 inches

at x = 2

ht. = 21.5 inches

( 21. 5 / 35 ) * 100 = 60 % approx.

Since , the ht. rebounded is about 60% of the previous ht. rebounded , the exponential function that would be used would be of the form y = a * ( [tex]b^{x}[/tex] ) .

Therefore , the exponential function that would be a good model for the bouncing ball is [ 60 * [tex]0.6^{x}[/tex]] .

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Answer:

Due to the fact that the denomonator is the same your answer will be 8/9 but if there was a different denominator you would need to find the least common multiple. Dont forget anything you do to the bottom has to be done to the top

Step-by-step explanation:

Hope this helps!!

The actual distance that is represented by 4 centimeters on the map is 16 kilometers

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the scale used on the map is:

1 cm = 4 km

Hence, for 4 cm represented on the map:

Actual distance = 4 cm * 4 km per 1 cm = 16 km

The actual distance that is represented by 4 centimeters on the map is 16 kilometers

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The inverse of the function y=5x+7 is y = (x-7)/5.

So,

All we have to do to find the inverse of an equation is switch the variables x and y.

Now, solve for y as follows:

Therefore,  the inverse of the function y=5x+7 is y = (x-7)/5.

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Answer:

-8x^2+2x+5

Step-by-step explanation:

Distributive Property

We need to know about logarithm to solve this problem. The greatest integer that is less than log 0.08 is -2.

Logarithm is the exponent which is raised to a base to get a certain number. There are a few rules of logarithm, log a + log b can be written as log ab, log a- log b can be written as log a/b, when the number for which the logarithm is calculated is raised to a power, then the power can be directly multiplied to the log itself. Logarithms when written as log has a base of 10 and the logarithm of a number same as its base is always 1, log of 1 is zero.

log 0.08= log 8/100= log 8- log 100 = [tex]log 2^{3} -log 10^{2}[/tex]

=3 log2 -2log10=3x0.30-2=0.9-2=-1.1

Therefore the greatest integer that is less than the value of log 0.08 is -2.

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According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.

Therefore, the given expression is [tex]ln2+ln3=2[/tex]

The values get multiplied in addition. Therefore, the above expression can be written as:

Expression = [tex]ln(6)=2[/tex]

Using logarithmic definition, we can write:

[tex]6 = e^{2}\\e = \sqrt{6},-\sqrt{6}[/tex]

The solution for the given expression is [tex]e = \sqrt{6},-\sqrt{6}[/tex]

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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After evaluating the expression we get 12.

Given, x³ ₊ x²

Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.

A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.

substitute the value of x =2

2³ ₊ 2²

= 8 ₊ 4

= 12

hence we get the answer as 12.

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Kloe can make 4 flower arrangement

The number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations.

The number of flower arrangements can be calculated as follows;

The first step is to calculate the HCF between the three numbers

24= 6 × 4

16= 4 × 4

48= 12 × 4

The HCF is 4

Hence the number of flower arrangement is 4  and the number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations

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ΔT= 313.5k-240.3k = 73.2k.

Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius. Temperature indicates the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).

One unit increase in the Kelvin scale is the same as a one-degree increase in the Celsius scale. The only difference between these two scales is zero points of the thermometer.

ΔT= highest T° in k - lowest T° in k

40.5°c+273= 313.5k

-32.7°c+273= 240.3k

therefore the difference will be 73.2k

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Answer:

125 small boxes

Step-by-step explanation:

[tex]n = { \tt{ \frac{volume \: of \: big \: box}{volume \: of \: small \: boxes} }} \\ \\ { \tt{n = \frac{(20 \times 10 \times 5)}{(2 \times 2 \times 2)} }} \\ \\ { \tt{n = \frac{5 \times 5 \times 5}{1} }} \\ \\ { \tt{n = 5 {}^{3} }} \\ \\ { \tt{n = 125}}[/tex]

If we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that there are two numbers which are  -√7 and 3.12345.

Let's compare the,.

We know that an irrational number is a number which can't be expressed other than using roots.

Here -√7 is an irrational number and if we represent that in decimal form then it can be written as :

-√7 = - 2.6467

Now , as this number is negative decimal number it is less than the other number given which is 3.12345 because 3.12345 is a positive decimal number. And we know that value of a positive number is always greater than a negative number.

i.e.,

3.1245 > -√7

Therefore , if we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

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The missing value of the inverse variation is 8

The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to inverse variation

k = xy or y = k/x

In the given question,

Take the order pair (4,6)

As it is an inverse variation, we can substitute it

y=k/x  

6=k/4

K=24

Now find the inverse variation equation

Y=k/x

Also, k=24

Solve this equation for the second pair (x,3)

As, y=24/x

    x = 24/3 = 8

Therefore, missing value is 8

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Answer:

The required number is 6. 6+6=12. 6×6=36.

Step-by-step explanation: