What is -2 1/6 + 3 5/8?
I’m really confused on adding and subtracting fractions, can someone please explain?

Selecting the "best" histogram width depends on your specific analysis goals and the characteristics of your data.

The width of a histogram determines the size of its bins, impacting the level of detail presented. A wider bin width provides a generalized overview, revealing broad trends and distribution shape.

This is useful for quick understanding. In contrast, a narrower bin width offers more granular information, allowing for detailed analysis of peaks, valleys, and patterns within the data.

The "best" histogram width depends on specific analysis goals and data characteristics. It requires striking a balance between capturing meaningful observations and avoiding excessive noise or oversimplification.

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Mathematics is a fundamental subject in education that is essential in the development of an individual’s critical thinking and problem-solving skills. It is one of the primary subjects that are taught in elementary schools and must be taught appropriately for children to understand and gain the required skills. One true statement about mathematics teaching in elementary schools is that it should be student-centered.

Teachers should focus on the child's understanding, individual learning abilities and styles, and progress.The learning experience should not be centered on the teacher but on the students. Teachers should also make the subject engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject. Besides, teachers should develop a personalized learning approach that allows students to learn and understand the subject at their own pace while creating opportunities for individual and group learning. Through such learning approaches, students can develop the required mathematical concepts and competencies such as critical thinking, problem-solving, and decision-making skills that will be beneficial in their future endeavors.

In elementary schools, mathematics teaching should be student-centered. It should be engaging and interactive to enable students to grasp the content easily and maintain their interest in the subject.

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The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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To calculate the expected number of people you would need to observe before finding one person with a certain genetic trait, we can use the formula:

expected number = 1 / probability

So, in this case, the probability of observing a person with the trait is 27%, or 0.27. Therefore, the expected number of people you would need to observe before finding one person with the trait is:

expected number = 1 / 0.27 ≈ 3.7

Rounding up, we get an expected number of about 4 people. Therefore, the answer is A) About 4.

Probability of genetic trait in the general population is 27%, the expected number of people is About 4, i.e., option A) is correct.

We need to find the number of people who need to be observed to find one person with this trait.

Probability of the event happening

(p) = 27% = 0.27

Let q be the probability of the event not happening, then

q = 1 - p

= 1 - 0.27 ⇒ 0.73

The expected number of trials is given by the formula

n = 1/p

n = 1/0.27

n = 3.703

The expected number of people we need to observe to find one person with this trait is 4.

Thus, the answer is (A) about 4.

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Answer:

He could save $ 165

Step-by-step explanation:

Discount = 30% of 550

\(=\frac{30}{100}*550\\\\=3*55\)

= $ 165

Answer:

the TV after the discount will cost 385.00 dollars and you would have saved 165.00 dollars! hope this helped :D

Answer:

Step-by-step explanation:

A triangular pyramid has a base with an area of 21.8 square meters, and lateral faces with bases of 7.1 meters and heights of 9 meters. Enter an expression that can be used to find the surface area of the triangular pyramid.

The expression is written as:

Surface Area = Area of the base + 1/2( Perimeter × Slant height)

Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

I hope it will help you .

Thank you.

^ - ^

Answer:

Cost with 45 songs: $46.75

Cost with s songs: $13 + (s * $0.75)

Step-by-step explanation:

First multiply the number of songs by the cost per song (45 * $0.75 = $33.75), then add the monthly service cost to that number ($13 + $33.75 = $46.75) to get the total monthly cost to Pedro.

Answer:

I think x equals 7.5

Step-by-step explanation:

Please let me know if this was correct or what you were looking for. Thanks!

Answer:

11°

Step-by-step explanation:

tan ∅ = 20/100 = 0.2

∅ = 11.31°

Answer:

Pitcher 2

Step-by-step explanation:

Pitcher 1  = 4 x 1.25 = 5ml concentration

Pitcher 2 = 5 x 2 = 10ml concentration

therefore, pitcher 2 has more concentration :)

hope this helped

Answer:

D

Step-by-step explanation:

If you match what the numbers say you will see the answer is D

Answer:

.27 or 27/100

Step-by-step explanation:

each tenth is equal to 10 one hundredths

\(k > 1\)

Step-by-step explanation:

1) Subtract 11 from both sides.

\(12 - 11 < k\)

2) Subtract 12 - 11 to 1.

\(1 < k\)

3) Switch sides.

\(k > 1\)

Therefor the answer is, k > 1.

Answer:

1700 - 700x

Step-by-step explanation:

assuming x is the number of weeks, the equation is 1700 - 700x equals the amount you are trying to solve for. You can say you are solving for y.

Answer:

\(x=1\,,\,y=-1\)

Step-by-step explanation:

Given: \(ax+by=a-b\,,\,bx-ay=a+b\)

To solve: the given linear equations

Solution:

Consider the equations:

\(A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0\)

By method of cross multiplication:

\(\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}\)

For equations: \(ax+by=a-b\,,\,bx-ay=a+b\)

\(ax+by-(a-b)=0\\bx-ay-(a+b)=0\)

Take \(A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)\)

So,

\(\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1\)

Data

• Morning: 156 times

• Lunch: x times

• Afternoon: 201 times

• Whole day: 562 times

Procedure

To know how many times did it ring at lunch, we have to build a relation, in which we know that the addition of the times in the morning, lunch, and afternoon equal the times it rang the whole day:

Then, we have to solve for x considering that it represents the times it rang during the lunch.

Answer: It rang 205 times during the afternoon.

Decimal degrees 45.5013 converts to 45 degrees, 30 minutes and 4.68 seconds, or 45° 30' 4.68"

Decimal degrees 168.7862 converts to 168 degrees, 47 minutes, 10.32 seconds, or 168° 47' 10.32".

Decimal degrees  87.2530 converts to 87 degrees, 15 minutes, 10.8 seconds, or 87° 15' 10.8".

To translate decimal degrees into DMS, take the following actions:

Converting the following angles from decimal degrees to degrees, minutes, and seconds.

A) 45.5013

The whole number is degrees. So 45.5013 gives you 45degrees.

Multiply the remaining decimal by 60.

0.5013*60 =30.078, so the whole number 30 equals minutes.

Multiply the remaining decimal by 60.

.078*60 = 4.68, so the whole number 4.68 equals seconds.

Decimal degrees 45.5013 converts to 45 degrees, 30 minutes and 4.68 seconds, or 45° 30' 4.68".

B) Similarly for this 168.7862.

Decimal degrees 168.7862 converts to 168 degrees, 47 minutes, 10.32 seconds, or 168° 47' 10.32".

C)Similarly for this  87.2530.

Decimal degrees  87.2530 converts to 87 degrees, 15 minutes, 10.8 seconds, or 87° 15' 10.8".

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The amount of money Patricio has in the savings account after 5 years is $537.50.

The formula for simple interest is i = Prt Where, i = simple interest P = principal or the deposited amount R = Rate of Interest in decimal formt = time in years.

Patricio puts $500 into a savings account that offers 1.5% simple interest in light of this. He doesn't make any additional deposits or withdrawals from the account. We need to find how much money does Patricio have in the savings account after 5 years?  

We know that, Principal(P) = $500Rate(R) = 1.5% = 0.015 (given in decimal form)Time(t) = 5 years.

Using the above formula, we can calculate the interest earned by Patricio as follows;i = Prt i = 500 × 0.015 × 5i = $37.5

Therefore, Patricio earns $37.5 as simple interest and hence the total amount in his savings account after 5 years = Principal(P) + Simple Interest(I) = $500 + $37.5 = $537.5Hence, the amount of money Patricio has in the savings account after 5 years is $537.50.

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Answer:

118

Step-by-step explanation:

inscribed angle = 1/2 intercepted arc, therefore an intercepted arc is twice its inscribed angle

\(59 \times 2 = 118\)

The answer is (C) StartFraction y Superscript one-half Baseline Over x z squared EndFraction.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

The expression equivalent to\((x^{1/2} y^{-1/4} z )^{-2}\) is:

StartFraction 1 Over (x Superscript one-half baseline y Superscript negative one-fourth Baseline z) squared EndFraction

= StartFraction 1}{x Superscript one-half baseline y Superscript negative one-half Baseline z squared EndFraction

= StartFraction x Superscript one-half baseline}{y Superscript negative one-half Baseline z squared EndFraction

Taking the reciprocal of the above expression, we get:

= StartFraction y Superscript one-half Baseline z squared}{x Superscript one-half baseline

Therefore, the answer is (C) StartFraction y Superscript one-half Baseline Over x z squared EndFraction.

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The interval of convergence of the series is (-5, 5).

Given the series ∑[infinity]n=1x^n/5n−1:A) Find the radius of convergence, R, of the series.The formula to find the radius of convergence is  R = 1/L, where L = Lim_n→∞ |a_n|^{1/n}Here, a_n = x^n/5n-1 |L_n| = |x^n/5n-1|^{1/n}By using root test, Lim_n→∞ |x^n/5n-1|^{1/n} = Lim_n→∞ (|x|/5^{1/n})^{n/ n - 1} = |x|/5Therefore, Lim_n→∞ |x^n/5n-1|^{1/n} < 1 for |x|/5 < 1, which is the interval (-5, 5).Then, Lim_n→∞ |x^n/5n-1|^{1/n} = 1 for x = ± 5.Thus, R = 5.

B) Find the interval, I, of convergence of the series. (Give an answer using interval notation.)The interval of convergence of a power series is the set of all x for which the series converges. The interval of convergence can be either an interval, a single point, or the entire real line.

The series will converge if x lies within the interval (-5, 5). So the interval of convergence is (-5, 5).Thus, the interval of convergence of the series is (-5, 5).Answer: The interval of convergence of the series is (-5, 5).

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Answer:

Quintic Trinomial (2nd option)

Step-by-step explanation:

We know that this is a quintic polynomial because the degrees add up to 5. If we expand the polynomial, we have \(-3x(x^2-4)(2x^2+5)=(-3x^3-12x)(2x^2+5)=-6x^5-45x^3-24x^3-60x=-6x^5-69x^3-60x\)

So, there are 3 terms, which is a trinomial.

Answer:

C and D

Step-by-step explanation:

They are both roots of the equation.

a. The minimum sample size needed is 601.

b. The minimum sample size needed using a prior study is 304.

c. The difference between the results from parts (b) and (a) shows that a preliminary estimation of the population proportion can lower the necessary minimum sample size.

The signed, fractional number of standard deviations above the mean value that an event is above is expressed by the dimensionless variable known as the z-score. Among other names, it is also referred to as the normal score, z-value, and standard score. Z-scores are indicative of values that are higher than the mean and lower than the mean.

(a) To find the minimum sample size needed assuming that no prior information is available, we can use the formula:

n = (Zα/2)² *\(\hat p \hat q\)/ E²

where Zα/2 is the z-score corresponding to the desired level of confidence (90% confidence corresponds to a z-score of 1.645), \(\hat p\) is the sample proportion (unknown), \(\hat q = 1 - \hat p\), and E is the maximum error of estimation (2% of the true proportion, or 0.02).

Plugging in the values, we get:

n = (1.645)² * 0.5*0.5 / 0.02² ≈ 601

Consequently, 601 is the required minimum sample size.

(b) To find the minimum sample size needed using a prior study that found that 42% of the respondents said they think Congress is doing a good or excellent job, we can use the formula:

n = (Zα/2)² * \(\hat p \hat q\) / E²

where now we have a preliminary estimate of the population proportion, \(\hat p = 0.42, and \hat q = 1 - \hat p.\)

Plugging in the values, we get:

n = (1.645)² * 0.42*0.58 / 0.02² ≈ 304

Therefore, the minimum sample size needed using a prior study is 304.

(c) The result from part (b) is smaller than the result from part (a), indicating that having a preliminary estimate of the population proportion can reduce the minimum sample size needed. This is because a preliminary estimate can provide a starting point for the sample size calculation, and reduce the variability of the sampling distribution.

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Answer:

no solution, you have "9x -" on both sides, so the equation is false and has no solution

Step-by-step explanation:

How many solutions are there to the equation below?

9x - 16 = 9x - 23

take off 9x from both side

-16 = -23

no solution, you have "9x -" on both sides, so the equation is false and has no solution

The given series terms can be described as follows:

From this, we are able to calculate and sum the rest of the terms until A10, as follows:

From the solution de developed above, we are able to conclude that the answer to the present question is:

Answer:

21/2 = 10.5

y = 10.5*hours

We can directly identify a pair of congruent triangles by selecting a postulate.

A statement that expresses that two triangles are congruent if they are made exactly in same shape and size. Hence, two triangles having equal corresponding side length and equal corresponding angles are congruent to each other.

A postulate is a mathematical statement that can claim an assumption as true without showing any proof.

We can claim the two triangles are congruent

if they contain three equal side lengths

if they have 2 equal side lengths along with 1 equal angle

the two triangles have 2 equal angles and 1 equal sides

if these are right angle triangles

Suppose we find two triangles which have exactly 3 side lengths to each other. In such case, we claim the triangles are congruent without any proof. And the situation is a postulate. Therefore, we identify a pair of congruent triangles without any verification.

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