Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what is the probability that he will randomly select a blue marble, without replacement, and then a purple marble from the jar

Experimental Probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

Theoretical probability is equal to the number of favorable outcomes divided by the total number of possible outcomes.

In your case, when tossing a coin 15 times, you get the Pr(Heads)=2/5, this probability is experimental and the result is found by repeating an experiment.

Answer: correct option A.

The equivalent expression to \(\root(4)(x^{10})\) is \(x^{\frac{5}{2}}\), which is obtained by realizing that the fourth root of a number can be expressed as raising that number to the 1/4 power and then applying exponent multiplication.

To find an expression equivalent to \(\root(4)(x^{10})\), we need to apply the laws of exponents for roots and powers. The fourth root of a number is the same as raising that number to the 1/4 power, and we know from the properties of exponents that when we raise a power to another power, we multiply the exponents. Therefore:

\(\root(4)(x^{10}) = x^{\frac{10}{4}} = x^{\frac{5}{2}}\)

Thus, the equivalent expression is \(x^{\frac{5}{2}}\).

Answer:

76

Step-by-step explanation:

Answer:

Difference in cash and plan = $155 - $149.50 = $5.50

Interest Rate = 3.68%

Step-by-step explanation:

Given:A food processor for $149.50 cash, or $5.00 down and $10.00 per month for 15 months

A food processor by cash = $149.50

Payment plan =  Down payment + $10*15 months

= $5 + $10*15

= $5 + $150

Payment plan = $155

Difference in cash and plan = $155 - $149.50 = $5.50

Now we have to find the interest rate

= (difference/original)*100

= (5.50/149.50)*100

Interest Rate = 3.68%

Answer:

Step-by-step explanation:

The question is

if p(x)= 2x³-3x+5, what is the remainder of p(x) divided by (x-5)

We use the synthetic division to find the remainder,

x-5=0

x=5

Now, write the coefficients of polynomial.

5 | 2  0  -3    5

   | ↓ 10  50  235

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

     2 10  47  | 240→ is the remainder.

Quotient= 2x²+10x+47

Remainder= 240

The remainder of [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is

Explanation:

If division of a polynomial by a binomial result in a remainder of zero means that the binomial is a factor of polynomial.

The polynomial is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and [tex]\left( {x - 5} \right).[/tex]

The numerator of the division is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and the denominator is

Solve the given polynomial [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] by the use of synthetic division.

Now obtain the value of [tex]x[/tex] from the denominator.

[tex]\begin{aligned}x - 5 &= 0\\x&= 5\\\end{aligned}[/tex]

Divide the coefficients of the polynomial by [tex]5.[/tex]

[tex]\begin{aligned}5\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5} \,}} \right.  \hfill\\\,\,\,\,\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,50\,\,\,\,\,\,\,\,\,\,\,\,\,\,235}\hfill\\\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,47\,\,\,\,\,\,\,\,\,\,\,\,\,\,240\hfill\\\end{aligned}[/tex]

The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is [tex]240[/tex].Therefore, the remainder of the synthetic division is [tex]240.[/tex]

The remainder of [tex]p\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is [tex]\boxed{240}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Synthetic Division

Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.

Mary should buy 6 bags of 1 pound trail mix to provide each of the 15 club members with a 2/5 pound bag, resulting in no leftovers.

The task is to determine how many 1 pound bags of trail mix Mary should buy if each of the 15 members of her hiking club is to receive a 2/5 pound bag of trail mix without any leftovers.

First, calculate the total amount of trail mix needed by multiplying the number of members by the amount each member will receive: 15 members × 2/5 pound per member = 6 pounds.

Since trail mix is sold in 1 pound bags, Mary should buy 6 of these bags to provide the right amount of trail mix for her hiking club members without any leftovers.

Answer:

formula = n = t / p

Step-by-step explanation:

Final answer:

The probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12. There are 15 possible outcomes where the sum is less than 7 out of 36 total outcomes.

Explanation:

The question asks for the probability that the sum of the numbers shown by rolling a six-sided die twice is less than 7. To find this probability, we need to consider all the possible outcomes of rolling two dice.

Each die has 6 faces, so when you roll two dice, there are a total of 6 x 6 = 36 possible outcomes. To get the sum less than 7, we can have the following combinations:

(1,1) Sum = 2

(1,2) Sum = 3

(2,1) Sum = 3

(1,3) Sum = 4

(2,2) Sum = 4

(3,1) Sum = 4

(1,4) Sum = 5

(2,3) Sum = 5

(3,2) Sum = 5

(4,1) Sum = 5

(1,5) Sum = 6

(2,4) Sum = 6

(3,3) Sum = 6

(4,2) Sum = 6

(5,1) Sum = 6

Adding up the number of outcomes, there are 15 possibilities where the sum is less than 7. Therefore, the probability is 15 out of 36. This simplifies to 5/12 when reduced to its simplest form.

So, the probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12.

Answer:

B. [tex]x^2(4x^2 + 2x -9) -3x(4x^2 + 2x - 9)[/tex]

Step-by-step explanation:

The distributivity establish that in order to multiply these two polynomials, first you have to multiply [tex]x^2[/tex] by every element in  [tex]4x^2 + 2x - 9[/tex] and then multiply [tex]-3x[/tex] by every element in [tex]4x^2 + 2x - 9[/tex] as well.

That is exactly what the option B. says, since

in the expresion [tex]x^2(4x^2 + 2x - 9) - 3x(4x^2 + 2x - 9)[/tex] [tex]x^2[/tex] is being multiplied  by every element in  [tex](4x^2 + 2x - 9)[/tex] and also [tex]-3x[/tex] is being multiplied by every element in  [tex](4x^2 + 2x - 9)[/tex].

Answer:

This one is Right...

Step-by-step explanation:

Answer:

its 60

Step-by-step explanation:

Answer: It’s definitely 4.5, so D! Hope this helps someone! :>

The value for the sum of the squared residuals is SS(residuals) = (1 - r²) SS(y).

Residual value is defined as the difference of the value that we predicts with that of the observed value.

Given that,

The distance between the y value in the data and the y value predicted from the regression equation is known as the residual.

Sum of the squared residuals is used to measure the variance level in a regression model.

We know that,

r² = 1 - [SS(residuals) / SS(total)]

[SS(residuals) / SS(total)] = 1 - r²

SS(residuals) = (1 - r²) SS(total)

SS(residuals) = (1 - r²) SS(y)

Hence the value is SS(residuals) = (1 - r²) SS(y).

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The measure of spread that would be most appropriate to measure the amount of money that high school students spend on fast food per month is the range.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The amount of money that high school students spend on fast food each month can vary between $50 and $200, there is a considerable range of possible values.

Additionally, some students may not eat fast food at all, which could further increase the variability in the data.

The range is the difference between the maximum and minimum values in a dataset and provides a simple and straightforward measure of the variability of the data.

Therefore, the measure of spread that would be most appropriate to measure the amount of money that high school students spend on fast food per month is the range.

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Tony's total earnings for the week are $754.60, which includes his regular pay for 40 hours at an hourly rate of $15.40 and overtime pay for 6 extra hours at a rate of time and a half.

The subject of this question is Mathematics, specifically, it involves calculations relating to wage and overtime pay.

Calculating Regular and Overtime Pay

Tony earns an hourly wage of $15.40 for regular hours and is paid at a time and a half rate for any hours worked beyond 40 hours. Since he worked 46 hours last week, we can calculate his earnings as follows:

Calculate regular pay for 40 hours: 40 hours × $15.40 = $616.00.

Calculate the overtime pay rate: $15.40 × 1.5 = $23.10 per hour.

Calculate overtime pay for 6 hours: 6 hours × $23.10 = $138.60.

Add regular pay and overtime pay to get total earnings: $616.00 + $138.60 = $754.60.

Therefore, Tony's total earnings for the week, including overtime, are $754.60.

To have a test average between 85 and 90, inclusive, the scores on the next test should be greater than or equal to 85 and less than or equal to 100.

To have a test average between 85 and 90, inclusive, you need to find the possible scores on your next test. Let's assume the score on the next test is x. Then, the average of all three tests can be calculated as (82 + 88 + x) / 3. Now, we can set up an inequality to find the possible values of x:

(82 + 88 + x) / 3 ≥ 85 and (82 + 88 + x) / 3 ≤ 90

Simplifying each inequality, we get:

170 + x ≥ 255 and 170 + x ≤ 270

Subtracting 170 from both sides, we have:

x ≥ 85 and x ≤ 100

Therefore, the possible scores you can earn on your next test to have a test average between 85 and 90, inclusive, are any scores greater than or equal to 85 and less than or equal to 100.

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