What is the sum of the arithmetic series below? Use the formula for the sum of an arithmetic series.

Final answer:

The area of a rectangle with dimensions of 1/3 yards by 2/3 yards is calculated using the formula length × width, resulting in an area of 2/9 square yards. This value is already in simplest form.

Explanation:

The question asks us to find the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to calculate the area of a rectangle is length × width. Therefore, to find the area, we multiply 1/3 yards by 2/3 yards.

Area = (1/3) yd × (2/3) yd = 2/9 yd²

This calculation shows that the area of the rectangle is 2/9 square yards. It is important to express the answer in simplest form, as the question requests, and 2/9 is already in its simplest form.

Let us say Samantha spends $x for her school at lunch every week.

We are given that she can spend as much as $15 every week for her school at lunch every week.

As much as stands for maximum quantity that she can spend.

So $15 is the maximum she can spend.

Writing an inequality,

[tex] x \leq 15 [/tex]

Answer:

the answer is 2 and 2/3 if that doesn't pop up then 8/3 also works.

Step-by-step explanation:

Answer: Disjoint

Step-by-step explanation: Selecting specific colors in a m&m's pack is disjoint because the events cannot occur at the same time, i.e., when you take one m&m's, it can be blue and orange at the same time.

To determine the probability of disjoint or mutually exclusive events, you can find their probability by adding the probability of each event.

In the question, it is asked the probability of selecting a blue or an orange.

Probability of a blue:

P(b) = [tex]\frac{11}{51}[/tex]

Probability of an orange:

P(o) = [tex]\frac{11}{51}[/tex]

Probability of one OR the other:

P(b OR o) = P(b) + P(o)

P(b OR o) = [tex]\frac{11}{51} + \frac{11}{51}[/tex]

P(b OR o) = [tex]\frac{22}{51}[/tex]

P(b OR o) ≈ 0.44 or 44%

The probability of blue or orange m&m's is 44%, and the events are disjoint.

According to the provided probabilities on the M&M's website, the probability of choosing a blue or an orange M&M is a combined 44%. These outcomes are described as discrete, as they are distinct and countable events in the context of probabilities.

The question is based on probabilities related to the distribution of M&M colors in a package, particularly focusing on the number of orange M&Ms and the number of yellow M&Ms. When analyzing the distribution of M&M colors, we utilize concepts from statistics such as uniform distribution and binomial distribution to assess the likelihood of pulling a particular color from a bag. If the M&Ms had a uniform distribution, we would expect each color to appear with equal probability; however, the provided probabilities for each color do not align with a uniform distribution.

In the long run, the probability of selecting a blue or an orange M&M is 44% combined, based on the provided percentages on the M&M's website (24% blue and 20% orange). These outcomes are discrete, as they represent distinct countable outcomes. The terms 'finite', 'disjoint', and 'discrete' are all descriptions of different characteristics of statistical outcomes. 'Finite' refers to a set that has a limited number of outcomes, 'disjoint' indicates that the events cannot happen at the same time, and 'discrete' encompasses outcomes that are countable and not continuous.

Answer:

The given rectangle is not possible.

Step-by-step explanation:

The minimum perimeter of such a rectangle is 4√30 meters, about 21.9 meters. That is about 71.9 feet. The largest rectangle with a perimeter of 26 feet will have an area of about 3.93 square meters.

The rectangle described cannot exist.

Answer:

A. [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]

Step-by-step explanation:    

Let x be the measure of arc BD.

Since we know that an angle formed by two intersecting tangents equals one-half the difference of the measures of the intercepted  arcs (the major arc-minus the minor arc).  

[tex]\text{ Measure of tangent-tangent angle}=\frac{1}{2} (\text{measure of major arc-measure of minor arc})[/tex]

We can see from our given graph that the tangent-tangent angle's measure is 53 degree. The measure of its intercepting major arc equals 233 degrees and minor arc equals x.

Upon substituting our given values in above formula we will get,

[tex]53^{o}=\frac{1}{2} (233^{o}-x)[/tex]

[tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex]

Therefore, the equation that can be solved to find x (the measure of arc BD) will be [tex]\frac{1}{2} (233^{o}-x)=53^{o}[/tex] and option A is the correct choice.

Answer:

It is b

Step-by-step explanation:

Answer:

y≈3508.16

Step-by-step explanation:

Answer:

Measure of ∠A is 106°

Step-by-step explanation:

We are given that, 'Quadrilateral ABCD is inscribed in the circle'.

So, we get that,

'ABCD is a cyclic quadrilateral' i.e. The sum of the opposite interior angles is 180°.

Thus, we have,

∠A +∠C = 180°

i.e. ∠A + 74° = 180°

i.e. ∠A = 180° - 74°

i.e. ∠A = 106°

Thus, the measure of ∠A is 106°.

The value of x is x = -17.5.

The linear equation in question is -2x - 5 = 30. To complete a table of values for this equation, solve for x first:

Add 5 to both sides of the equation to isolate the term with x: -2x = 35.

Divide both sides by -2 to solve for x: x = -17.5.

Now that you have the value of x, you can fill in the table with x = -17.5, since a table of values typically includes various values for x and the corresponding values for the equation. However, in this case, the equation is simply solved for a single value of x without needing different values for it.

Final answer:

The patient should be given 0.25 mls of the medication.

Explanation:

To calculate the volume of medication a patient should be given, we can use a basic formula that relates the ordered dose, the concentration of the medication available, and the volume required to deliver the ordered dose. In this case, the student has been asked to determine how many milliliters (mls) of medication to administer when 0.5 mg is ordered and the medication concentration available is 2 mg/ml.

The formula to use is:

Dose ordered (mg) / Concentration of medication (mg/ml) = Volume to administer (ml)

So for this problem:

0.5 mg / 2 mg/ml = 0.25 ml

Therefore, the patient should be given 0.25 mls of the medication.

Answers:

She made __50__ grams of __20__% solution

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Work Shown:

There's 10+40 = 50 grams of stuff overall (that "stuff" being salt and water). Of this total, 10 grams are salt so 10/50 = 1/5 = 0.20 = 20% is salt. Therefore this is a 20% salt solution.

We can say "20% solution" or "20% salt solution" to be more specific of what kind of chemical mix it is.

Answer:

E2020

Step-by-step explanation:

The four successive terms of the given ap series by rule [tex]a_{n}[/tex] = 4 - 2n will be 2, 0, -2, and -4.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2.

Given the rule for nth term of ap series

[tex]a_{n}[/tex] = 4 - 2n

Now,

First term (n = 1) ⇒ 4 - 2(1) = 2

Second term  (n =2) ⇒ 4 - 2(2) = 0

Third term (n = 3)  ⇒ 4 - 2(3) = -2

Fourth term (n = 4)  ⇒4 - 2(4) = -4

Hence "The four successive terms of the given ap series by rule [tex]a_{n}[/tex] = 4 - 2n will be 2, 0, -2, and -4.".

For more about Arithmetic progression,

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Answer:

Answer is d

Step-by-step explanation:

sorry that im 4 years late

Answer:

y - 5 = 3 . (x - 2)

Step-by-step explanation:

A linear equation can be written in point-slope form.

y - y₁ = m. (x- x₁)

where

x is the independent variable

y is the dependent variable

(x₁, y₁) is an ordered pair representing a point through which the line passes

m is the slope

Given the slope is 3 (m = 3) and the line passes through the point (2, 5) (x₁ = 2, y₁ = 5), we can write the point-slope form of the linear equation.

y - 5 = 3 . (x - 2)

I think this might correspond to b, although it should have a parenthesis to be correct.

The correct answer is that Kersha worked as an office clerk for 35 hours and as a cashier for 20 hours.

To solve this problem, we can set up a system of equations based on the information given. Let's denote the number of hours Kersha worked as an office clerk as [tex]\( x \)[/tex] and the number of hours she worked as a cashier as [tex]\( y \).[/tex]

From the problem statement, we know the following:

1. Kersha earns $12.00 per hour at her office job.

2. Kersha earns $8.25 per hour at her cashier job.

3. Kersha worked a total of 55 hours in one week.

4. Kersha earned a total of $585 in one week.

Using this information, we can write two equations:

For the total number of hours worked:

[tex]\[ x + y = 55 \][/tex] (Equation 1)

For the total earnings:

[tex]\[ 12x + 8.25y = 585 \][/tex] (Equation 2)

Now we have a system of two equations with two variables. We can solve this system using substitution or elimination. Let's use the substitution method.

First, we can solve Equation 1 for [tex]\( x \):[/tex]

[tex]\[ x = 55 - y \][/tex]

Now we substitute [tex]\( x \)[/tex] in Equation 2 with [tex]\( 55 - y \):[/tex]

[tex]\[ 12(55 - y) + 8.25y = 585 \][/tex]

Expanding the equation, we get:

[tex]\[ 660 - 12y + 8.25y = 585 \][/tex]

Combining like terms, we get:

[tex]\[ -3.75y = 585 - 660 \][/tex]

[tex]\[ -3.75y = -75 \][/tex]

Dividing both sides by -3.75 to solve for [tex]\( y \)[/tex], we get:

[tex]\[ y = \frac{-75}{-3.75} \][/tex]

[tex]\[ y = 20 \][/tex]

Now that we have the value of [tex]\( y \)[/tex], we can find [tex]\( x \)[/tex] using Equation 1:

[tex]\[ x = 55 - y \][/tex]

[tex]\[ x = 55 - 20 \][/tex]

[tex]\[ x = 35 \][/tex]

Therefore, Kersha worked 35 hours as an office clerk and 20 hours as a cashier. The correct option is:

Office clerk: 35 hours; cashier: 20 hours.

By forming an algebraic equation based on the given information, we find that Elga's age is 29 years.

This question belongs to the category of Algebraic equations. We know that Alvin's age is two times Elga's, so we could represent Alvin's age as 2E, where E represents Elga's age.

The problem also tells us that the sum of their ages equals 87. That means we can form this equation: E + 2E = 87.

Combining like terms, we get 3E = 87. Finally, dividing each side by 3, we find the value of E (Elga's age).

So, Elga's age is 87 / 3, which equals 29 years.

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