If A game is played using one die. If the die is rolled and shows 2 the player wins 40. If the die shows any number other than 2 the player wins nothing

There are two kinds of real numbers in mathematics, one is rational number and other is irrational number. Out of given options, π and √20 are irrational number. Therefore option A, D are correct option

Real numbers that can not be written in the form of fraction is called irrational number. Real number that can be written in form of fraction is called rational number.

In option (1)  π is an irrational number as it contains infinite decimals when we divide 22 by 7

In option (2)  1.33 is a fixed number so it can be written in fractions so this number is rational number

In option (3) √196, it is square root of 14 so it can be written in fraction so it is rational number.

In option (4) √20  is an irrational number as on finding its square root there will be infinite decimals so it cannot be written in form of fraction

Therefore π and √20 are irrational number.  Therefore option A, D are correct option

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Answer:

–5 with multiplicity 2 and 0 with multiplicity 4

Step-by-step explanation:

I just got it wrong on edge 2020

Answer:

2 1/2 for $6.25

Step-by-step explanation:

Hello

the unit price is the price that you pay for a unit of product, you must find each unit price and compare

the unit price is given by

[tex]Unit\ price = \frac{amount\ paid}{number\ of\ products} \\[/tex]

Step 1

find each unit price

1).2 for $5.08

[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 5.08}{2}\\\\Unit\ price =2.54[/tex]

unit price =2.54 $

2).5 for $12.70

[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 12.7}{5}\\\\Unit\ price =2.54[/tex]

unit price =2.54 $

3) 1/2 for $1.27 2

[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 1.27}{0.5}\\\\Unit\ price =2.54[/tex]

unit price =2.54 $

4) 2 1/2 for $6.25

[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 6.25}{2.5}\\\\Unit\ price =2.5[/tex]

unit price =2.5 $

Step 2

define

Now, we can define that the unit price of 2 1/2 for $6.25 is different to the others.

2.5 ≠ 2.54

Have a great day

Answer:

y = 1/3x - 2

Step-by-step explanation:

Answer with Step-by-step explanation:

Let x be the cost of 1 pen and y be the cost of 1 pencil

8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10

8x+7y= 3.37  -----------------(1)

and 5x+11y= 3.10  -----------------(2)

equation (1)×5-equation(2)×8

5(8x+7y)-8(5x+11y)=3.37×5-3.10×8

40x+35y-40x-88y= -7.95

-53y = -7.95

y= 0.15

Putting y=0.15 in equation (1), we get

8x+7×0.15=3.37

8x+1.05=3.37

8x=2.32

x=0.29

Hence, Cost of 1 pen=$ 0.29

Cost of 1 pencil= $ 0.15

The options that are equivalent to the given function are;

Option A

Option B

Option E

The correct options are;

A) f(x) = [tex]162^{x/4}[/tex]

B) f(x) = (3∜2[tex])^{x}[/tex]

C) f(x) = [tex]9\sqrt[4]{2^{x} }[/tex]

D) f(x) = [tex]162^{4/x}[/tex]

E) f(x) = [tex](3(2^{1/4}))^{x}[/tex]

We are given the function; f(x) = [tex](\sqrt[4]{162})^{x}[/tex]

Now, when we have something like; [tex]\sqrt[b]{2}^{a}[/tex]

This expression can also be expressed as; [tex]2^{a/b}[/tex]

Therefore our function can also be expressed as; f(x) = [tex]162^{x/4}[/tex]

Option A; This is correct because it is equal to our function gotten

Option B; f(x) = (3∜2[tex])^{x}[/tex]

From earlier, we will have;  (3 × [tex]2^{1/4}[/tex][tex])^{x}[/tex]

Now, 3 can also be expressed as [tex]81^{1/4}[/tex]

Thus, we now have;

([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]

Factorizing out the 1/4 exponent gives;

(81 × 2[tex])^{x/4}[/tex]

⇒ = [tex]162^{x/4}[/tex]

This is same with our function and it is correct

Option C; f(x) = (9∜2[tex])^{x}[/tex]

This is similar to our equation in option B which was correct but the difference here is 9 instead of 3 and clearly this option is not correct.

Option D; f(x) = [tex]162^{4/x}[/tex]

This is not the same with our function and so it is wrong

Option E; f(x) = [tex](3(2^{1/4}))^{x}[/tex]

As seen in option B;

3 can also be expressed as [tex]81^{1/4}[/tex]

Thus, we now have;

;([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]

Factorizing out the 1/4 exponent gives;

(81 × 2[tex])^{x/4}[/tex]

⇒ = [tex]162^{x/4}[/tex]

This is same with our function and it is correct

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The real square roots of 0.0625 are -0.25 and 0.25, as both of these numbers squared equal 0.0625.

The student has asked to find all the real square roots of 0.0625. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, equals 0.0625.

To find this, we can recognize that the square root of 0.0625 could be thought of in fraction form as the square root of 625/10000, which simplifies to the square root of 625 divided by the square root of 10000. This reduces to 25/100 because 625 is a perfect square (25 * 25) and 10000 is also a perfect square (100 * 100). Therefore, the principal square root of 0.0625 is 0.25.

However, since every positive number has two square roots, one positive and one negative, and because the square of both -0.25 and 0.25 gives 0.0625, we conclude that the real square roots of 0.0625 are -0.25 and 0.25.

Answer: the answer is too low i really hope this hepls

Step-by-step explanation:

The correct answer is B. y = -1/3x + 2

Sorry if I am wrong, but I believe that this is the correct answer.

I will just answer the problem about Pin numbers because the other questions lack other given values.

a. How many different pin numbers are there?

There are 26 letters in total and 10 numbers in total (including zero), therefore the total number of different pin numbers are:

Total possible = 26 * 26 * 10 * 10 * 10

Total possible = 676,000 different pins

b. What is the probability a pin number selected at random ends in 000

The total possible numbers with ending of 0 0 0 is:

Possible numbers = 26 * 26 * 1 * 1 *1

Possible numbers = 676

Therefore the probability is:

Probability = 676 / 676,000

Probability = 0.001 = 0.10%

c. What is the probability a pin number selected at random begins with AA?

The total possible numbers starting with A A is:

Possible numbers = 1 * 1 * 10 * 10 * 10

Possible numbers = 1000

Therefore the probability is:

Probability = 1000 / 676,000

Probability = 1.48 x 10^-3 = 0.148%

A unit test for the function addInventory() can be written in JavaScript using Jest. The test checks that the quantity of red sweaters increases correctly after calling addInventory(). If the test fails, an error message will be shown.

Based on the information given, you can create a unit test in many programming languages. Here we are going to illustrate with JavaScript and use the Jest testing framework.

Firstly, let's name the unit test file as redSweater.test.js. In this file, we call the addInventory() of the redSweater object with sweaterShipment as parameter.  Note that addInventory() is a method that increases the quantity of red sweaters in inventory by a certain amount provided by sweaterShipment.

Here is a sample unit test for your needs:

const redSweater = require('./redSweater'); // path to your redSweater.js file

test('addInventory() unit test', () => {

let initialQty = 10;

redSweater.qty = initialQty;

let shipmentQty = 50;

redSweater.addInventory(shipmentQty);

expect(redSweater.qty).toBe(initialQty + shipmentQty);

});

This script tests that the quantity of red sweaters increases correctly after calling the addInventory() method. If the quantity is not correct after the method call, the test will fail and show an error message.

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Answer:

9 full pieces.

Step-by-step explanation:

In order to solve this we have to divide the total feets of wood that Jessie has, by the size of the pieces that Jessie needs:

[tex]\frac{8}{\frac{7}{8} }\\\frac{\frac{8}{1} }{\frac{7}{8} }\\\frac{8*8}{7*1}\\\frac{64}{7} =9.14[/tex]

Since Jessie will be able to cut 9.14 pieces of wood, he will have only 9 full pieces, so the total amount of pieces that he would be able to cut will be 9.

To find the probability of not drawing a blue marble from the bag, one must divide the number of non-blue marbles by the total number of marbles, resulting in a probability of 3/4

The question asks to find the probability of not drawing a blue marble from a bag that contains 8 red marbles, 3 blue marbles, and 1 green marble. The total number of marbles is 8 + 3 + 1 = 12. The probability of not drawing a blue marble (P(not blue)) is the number of marbles that are not blue divided by the total number of marbles. This is (8 red + 1 green) / 12 total marbles. Calculated, the probability is 9/12, which simplifies to 3/4

-5.25, -5.09, 1.002

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Answer:

Option D

Step-by-step explanation:

The given function is

[tex]f(x)=4|x|[/tex]

It is given that the graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.

If a figure reflected across x-axis, then the rule of reflection is

[tex](x,y)\rightarrow (x,-y)[/tex]

Using the above rule, if the given function reflected across x-axis, then g(x)=-f(x).

[tex]g(x)=-(4|x|)[/tex]

[tex]g(x)=-4|x|[/tex]

The equation g(x)=-4|x| describes g(x).

Therefore, the correct option is D.

The sample mean for the given 90% confidence interval (65, 77) is 71. The margin of error is 6. The sample standard deviation cannot be specifically calculated without the t-value, but presuming a common t-value for such datasets (1.96), it approximates to 3.072.

The subject at hand pertains to confidence intervals and basic statistics calculations. Given a 90% confidence interval of (65, 77), we can find the sample mean by adding the two limits and dividing by 2. So (65 + 77) / 2 equals 71.

The margin of error for the confidence interval is calculated by subtracting the sample mean from the upper limit. That gives us 77 - 71 equals 6.

Unfortunately, without knowing the value of the t-statistic, we can't calculate the sample standard deviation, as it's calculated via the formula: standard deviation = margin of error / (t-value/sqrt(sample size)). But, usually, for a sample size of 25 observations and a 90% confidence level, the t-value is about 1.96. Using that assumed t-value, the standard deviation calculation gives us 6/(1.96/sqrt(25)) equals approximately 3.072.

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