Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true

Final answer:

To calculate Nicole Tobin's earnings for a week in which her sales totaled $3000, we first determine the total sales eligible for commission and then calculate 15% commission on that amount. Adding the resulting commission to her weekly salary of $250 gives us Nicole's total earnings for the week, which are $475.

Explanation:

Nicole Tobin receives a salary of $250 per week plus a commission of 15% on all sales over $1500. To calculate her earnings during a week in which her sales totaled $3000, we need to find out the commission on the sales exceeding $1500 and then add it to her weekly salary.

First, we calculate the amount eligible for commission:

Sales = $3000

Threshold for commission = $1500

Eligible amount for commission = Total sales - Threshold for commission = $3000 - $1500 = $1500

Next, we calculate the commission:

Commission rate = 15%

Commission = Eligible amount for commission × Commission rate = $1500 × 0.15 = $225

Finally, we find Nicole's total earnings:

Weekly salary = $250

Total earnings = Weekly salary + Commission = $250 + $225 = $475

Nicole's earnings for the week are $475.

Answer:

Tess is wrong and  Dan is correct because the tax is calculated after discount.

Step-by-step explanation:

Answer:

Given the functions:

[tex]f(x) = 3x^2+2[/tex]

[tex]g(x) = x-8[/tex]

we have to find [tex](f \cdot g)(2)[/tex]

[tex](f \cdot g)(2) = f(2) \cdot g(2)[/tex]         ....[1]

Substitute the value of x = 2 in f(x) and g(x) we have;

[tex]f(2) = 3(2)^2+2 =12+2 = 14[/tex] and

[tex]g(2) = 2-8 = -6[/tex]

Substitute these in [1] we have;

[tex](f \cdot g)(2) = 14 \cdot -6 = -84[/tex]

Therefore, the value of  [tex](f \cdot g)(2)[/tex] is, -84

Answer:

No, it's not possible

Step-by-step explanation:

We know that for various values of x , [tex]-1\leq \sin x\leq 1[/tex]

and [tex]-1\leq \cos x \leq 1[/tex]

For values of [tex]\alpha[/tex], [tex]-1\leq \sin \alpha\leq 1[/tex]

On multiplying all sides by 3, we get

[tex]-3\leq 3\sin \alpha\leq 3[/tex]

For values of [tex]\beta[/tex], [tex]-1\leq\cos \beta\leq 1[/tex]

On multiplying all sides  by 4, we get

[tex]-4\leq 4\cos \beta\leq 4[/tex]

On adding all sides of [tex]-3\leq 3\sin \alpha\leq 3\,\,,\,\,-4\leq 4\cos \beta\leq 4[/tex] , we get

[tex]-3-4\leq 3\sin \alpha+ 4\cos \beta\leq 3+4\\-7\leq 3\sin \alpha+ 4\cos \beta\leq 7[/tex]

Therefore, maximum value of [tex]3\sin \alpha+ 4\cos \beta[/tex] is 7.

So, it's not possible that [tex]3\sin \alpha+ 4\cos \beta=8[/tex]

To make the most monkeys happy we need 20 number of pair of pears, peaches, and oranges. and 20 number of pair of peaches bananas and oranges.

In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their actions accordingly.

Given, A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches, and 50 oranges. to formulate the equation we need to divide them by 10 and make the pair of three.

Hence,

2pears + 3 bananas + 4 peaches + 5 oranges

2(pears + oranges +  peaches)  + 2(banana + peach + oranges) + peach +1 orange.

Therefore to make the most monkey happy. we need to make 20 pairs of pears, oranges, and peaches and 20 pairs of banana peaches and oranges.

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3 is the number whose four times the square is equal to twelve times 3.

An equation is a relationship between two or more variables expressed in equal to sign. It is solved to find the value of variables. Equation of two variables will look like ax+ by=c.

Let the required number be x.

According to question we have to form an equation which will be:

4[tex]x^{2}[/tex]=12x

[tex]4x^{2} -12x=0[/tex]

4x(x-3)=0

4x=0, x-3=0

x=0, x=3

Non negative number=3

Hence 3 is the number whose 4 times square is equal to 12*3.

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Answer:

{174,000, 134,000, 420,000, 452,000, 474,000}

Among the given options, (c) 0.108 is the only number that lies between 0.10 (which is the decimal equivalent of 10%) and 0.111 (which is approximate decimal equivalent of 1/9).

To answer the question "Which of the following numbers has a value that is between 10% and 1/9?", we first need to convert 10% and 1/9 into decimal form. 10% is equivalent to 0.10, and 1/9 is approximately 0.111. We are therefore looking for a number between 0.10 and 0.111.

Reviewing the options, (a) 0.151, (b) 0.112, (c) 0.108, and (d) 0.019, we see that only (c) 0.108 fits because it falls between 0.10 and 0.111.

Therefore, the correct answer is (c) 0.108.

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Two numbers are 30 and 60 that have 2,3 and 5 as factors.

LCM is the least common multiple of two or more that two given numbers which is exactly divisible by these given numbers.

According to the given question we have to find two numbers that have 2, 3 and 5 as common factors.

To find least such number which have common factor of 2, 3 and 5 we have to take LCM of 2, 3 and 5.

The LCM of 2, 3 and 5 is 30.

The next such possible higher numbers will be of the form 30k, where k is an integer.

At k = 2,
The number 30k will be 30(2) which is

= 60.

We can find any such form of numbers by putting different integer value of k.

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y=5

5=1/4x^2+1

4=1/4x^2

16 = x^s

x = square root (16) = 4

x=3

y= 1/4(3)^2+1 = 3 1/4 = 13/4

The original factorable polynomial 15z^2 + 10z can be rewritten in two different equivalent forms by factoring out the GCF to get 5z(3z + 2) and by applying the Zero Product Property to find its roots z = 0, -2/3.

To begin, we will create a factorable polynomial with a Greatest Common Factor (GCF) of 5z. An example might be: 15z^2 + 10z. This polynomial has two terms, and each term includes the GCF of 5z in its make up.

Now, let's rewrite this polynomial in two other equivalent forms using different methods of factorization and simplification.

Form 1: Factor by GCF

In this form, we factor out the GCF from the original polynomial. For our provided example, the GCF is 5z, so we get: 5z(3z + 2).

Form 2: Use the Zero Property

We can also rewrite this polynomial using the Zero Product Property. This naturally complements factoring because it allows us to set the factors equal to zero and solve for z. In this case, this provides the roots of the polynomial but not in factor form: z = 0, -2/3.

Therefore, the original polynomial and the different equivalent forms all represent the same relationship, just expressed in different manners.

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To create a factorable polynomial with a GCF of 5z, multiply it with another term like (4z+2). The resulting polynomial is 20z² + 10z. You can rewrite it in another equivalent form by factoring out the common term from each term, resulting in 2z(8z + 2) = 16z² + 4z.

To create a factorable polynomial with a GCF of 5z, we can start by multiplying 5z with another term. Let's say we multiply it with (4z+2). The polynomial becomes 5z(4z+2), which can be expanded to 20z² + 10z. This is one form of the polynomial.

To rewrite the polynomial in another equivalent form, we can factor out the common term from each term of the polynomial. Doing so, we get 5z(4z+2) = 5z * 4z + 5z * 2 = 20z² + 10z. Thus, the second equivalent form is 20z² + 10z.

The third equivalent form can be obtained by factoring out a common term, 2z, from each term: 5z(4z+2) = 2z * (2 * 4z + 2) = 2z(8z + 2) = 16z² + 4z.

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multiply 8 by 1/3

8* 1/3 = 8/3 =2 2/3 hours

The inequality from the given graph is y≤-3x+5.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

From the graph, the coordinate points are (2, -1) and (1, 2).

Here, slope (m)=(2+1)/(1-2)

m=-3

Substitute m=-3 and (x, y)=(2, -1) in y=mx+c, we get

-1=-3(2)+c

-1=-6+c

c=5

Substitute m=-3 and c=5 in y=mx+c, we get

y=-3x+5

So, the inequality is y≤-3x+5

Therefore, the inequality is y≤-3x+5.

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Answer:

The correct option is D.

Step-by-step explanation:

The given equation is

[tex]\frac{Rs}{x}=\frac{1}{4}[/tex]

We need to solve the given equation for x.

On cross multiplication we get

[tex]Rs\times 4=1\times x[/tex]

On further simplification we get

[tex]4Rs=x[/tex]

The value of x is 4 times of Rs. Only option D represents this situation.

Therefore, the correct option is D.