-8.7° is colder than -8.4° 

Answer:

12 feet

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]  Pythagorean Theorem

[tex]x^{2}[/tex] + [tex]5^{2}[/tex] = [tex]13^{2}[/tex]

[tex]x^{2}[/tex] + 25 = 169  Subtract 25 from both sides

[tex]x^{2}[/tex] = 144

[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{144}[/tex]

x = 12

The length of the arc of radius 65 feet is 170.2 feet. And the right option is C) 170.2 feet.

An arc of a circle is the smooth curve formed from the two-chord endpoints.

To calculate the length of the arc between two cars on the ferris wheel, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the length of the arc is 170.2 feet.

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The correct representation of the expression in the given number line is 5/8-3/8

To add or subtract fractions they must have the same denominator (the bottom value). If the denominators are already the same then it is just a matter of either adding or subtracting the numerators (the top value). If the denominators are different then a common denominator needs to be found.

Given here, the required fraction is 2/8 and also we have 5/8-3/8=2/8

Hence, The correct representation of the expression in the given number line is 5/8-3/8

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The probability that a randomly selected orange is organic is; 0.25

From the given table, we can see that the following probabilities;

P(Apples are organic) = 0.57

P(Apples are non-organic) = 0.13

P(Oranges are organic) = 0.19

P(Oranges are non-organic) = 0.11

Now, since the total probability for organic fruits is 0.79, then it means that if an orange is randomly selected, the probability of it being organic is;

0.19/0.76 = 0.25

We conclude that is the probability that it is orange and organic if selected randomly.

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Answer:

17 to 17 ft will be fit for 200 people for dancing.

The graph of equation is attached.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠). The different types of mathematical inequality include absolute value inequality, rational inequality, and polynomial inequality.

Given inequality,

y > 4x + 1

table for x and y

x    0     2       -1

y   >1    >9    >-3

with these points we can plot the graph and shaded region shows the inequality.

Hence the graph is attached.

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Replacing y(t) into the initial value, we reach an identity, meaning that it can be verified that both y(t) = 1 - t and y(t) = -t²/4 are solutions to the initial value problem.

The initial value problem is defined as follows:

[tex]y^{\prime} = \frac{-t + \sqrt{t^2 + 4y}}{2}[/tex]

The first solution is given as follows:

y(t) = 1 - t.

Hence the derivative is given as follows:

y'(t) = -1.

Replacing into the initial value problem, we have that:

[tex]y^{\prime} = \frac{-t + \sqrt{t^2 + 4y}}{2}[/tex]

[tex]-1 = \frac{-t + \sqrt{t^2 + 4(1 - t)}}{2}[/tex]

[tex]-1 = \frac{-t + \sqrt{t^2 - 4t + 4}}{2}[/tex]

[tex]-1 = \frac{-t + \sqrt{(t - 2)^2}}{2}[/tex]

[tex]-1 = \frac{-t + t - 2}}{2}[/tex]

-1 = -1.

Identity, verifying the solution.

The second solution is given as follows:

y(t) = -t²/4.

Hence the derivative is of:

y' = -0.5t.

Replacing into the initial value problem, we have that:

[tex]y^{\prime} = \frac{-t + \sqrt{t^2 + 4y}}{2}[/tex]

[tex]-0.5t = \frac{-t + \sqrt{t^2 - 4\frac{t^2}{4}}}{2}[/tex]

[tex]-0.5t = \frac{-t + \sqrt{0}}{2}[/tex]

-0.5t = -0.5t.

Identity, verifying the solution.

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Answer:

4

Step-by-step explanation:

4, count the spaces as in the figure

Answer:

Step-by-step explanation:

b

It counts the amount of money coming in or going out over the specified time period.

The cash balance of liquid assets coming into and going out of a business is referred to as cash flow. Money spent and money received reflect inflows and outflows, respectively.

The cash flow is the difference between outflow and inflow.

Cash flow = outflow - inflow

If the value of the cash flow is negative that means the expense is more.

If the value of the cash flow is positive that means the income is more.

A reliable indicator of a company's strength, prosperity, and prospects for the future is the cash flow report. The cash flow statement is significant because it tracks any inflows or outflows of cash within the specified time period. The industry's both short- and long-term planning is influenced by this information.

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Answer:

y=[tex]\frac{8}{7}[/tex]x+1.143

Step-by-step explanation:

Step 1: Plot points on graph

Step 2: Find slope (rise over run); slope=7/8

Step 3: Find y intercept

Answer: 1728

Step-by-step explanation:

12^3 = 144 * 12 = 1728

Answer:

1728

Step-by-step explanation:

12*12*12=1728

A like radical to the one shown is Option C.

We know that we can be able to perform mathematical operations on the radicals such as adding and subtracting but this must be performed when we have like radicals.

When we talk about like radicals we mean that the radicals must be such that it easy for the radical to be worked upon as we have it in the question that is before us here to locate a like radical among the options.

The radical in option C has the same 2x and power as the given radical hence they are like radicals.

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Answer:

[tex]\huge\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

Here, 6x + 6 is a linear expression since all the terms are raised to power 1 only.

[tex]\rule[225]{225}{2}[/tex]

Answer:

34

Step-by-step explanation:

substitute the given values for x, y and z into the expression

(x + y)² + 6z

= (0 + (- 4) )² + 6(3)

= (0 - 4)² + 18

= (- 4)² + 18

= 16 + 18

= 34

The amount paid for the truck for 300 miles is $333

From the question, we have the following parameters that can be used in our computation:

Amount paid per day = $33

Amount paid per mile = $1

Number of miles driven = 300

The amount paid for the truck is then calculated as

Amount paid for the truck = Amount paid per day + Amount paid per mile x Number of miles driven

Substitute the known values in the above equation, so, we have the following representation

Amount paid for the truck = 33 + 300 * 1

Evaluate the products

Amount paid for the truck = 33 + 300

Evaluate the sum

Amount paid for the truck = 333

Hence, the amount is $333

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The side length of rhombus ABCD by using the formula for the perimeter of a quadrilateral is 4.

A rhombus is a quadrilateral with four equal-length sides in plane Euclidean geometry. The term equilateral quadrilateral refers to the fact that all of its sides are the same length.

Since EFGH is a quadrilateral with an area 14 and a perimeter 16, the sides of EFGH must all be of equal length. Since EFGH is composed of the midpoints of the sides of ABCD, the side length of ABCD must be twice the side length of EFGH.

Using the formula for the perimeter of a quadrilateral, 16 = 4x, so 4 = x. This means that the side length of ABCD is 4.

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Step-by-step explanation:

a: true

b: true

c: false

d: true

Explanation:

The special symbol [tex]\varnothing[/tex] represents the empty set. Another way to write the empty set is to use curly braces with nothing inside them. Not even zero is inside the empty set.

One property of set mathematics is that the empty set is a subset of every set, even itself.

Therefore, the claim [tex]\varnothing \subseteq \left\{\text{Charlie Chaplin},\text{Groucho Marx},\text{Woody Allen}\right\}[/tex] is a true statement.

B. Students who did not complete the review sheet were less likely to have passed the exam than students who did complete the review sheet.

The given two-way frequency table shows the number of students who passed the exam and completed the review sheet (20 students), the number of students who passed the exam but did not complete the review sheet (10 students), the number of students who did not pass the exam but completed the review sheet (5 students), and the number of students who did not pass the exam and did not complete the review sheet (5 students). From this information, it can be seen that 20 out of 25 students who completed the review sheet passed the exam, while only 10 out of 15 students who did not complete the review sheet passed the exam. This indicates that students who completed the review sheet were more likely to pass the exam than those who did not complete the review sheet. Therefore, statement B is true.

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According to the concept of frequency table, the correct statement is Students who did not complete the review sheet were less likely to have passed the exam than students who did complete the review sheet.

The term frequency table in math is defined as  a chart that summarizes all the data under two columns that is known as variables/categories, and their frequency.

Here we know that Khaled's eighth-grade class took an exam on two-way frequency tables.

At the time of exam, Khaled's teacher made the two-way frequency table below to show the data on completing the exam review sheet and passing the exam.

Here we know that the number of students who have passed the exam is one who are not completed the review sheet.

Therefore, option (b) is correct.

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The equation of the perpendicular line is y= -5/4x +2/5 when the equation of the line is -4x+5y=2.

Given that,

The equation of the line is -4x+5y=2.

We have to find the equation of the perpendicular line passing through the equation.

We know that,

Take the equation of the line is -4x+5y=2.

5y=2+4x

y= 4/5x+2/5

The equation is in the form of y=mx+b

We flip the number and alter the sign to determine a perpendicular line.

m is 4/5

So, for perpendicular line equation

m =  -5/4

Therefore, The equation of the perpendicular line is y= -5/4x +2/5 when the equation of the line is -4x+5y=2.

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Let [r, s] denote the least common multiple of positive integers r and s. Find the number of ordered triples (a, b, c) of positive integers for which [a, b] = 1000, [b, c] = 2000, and [c, a] = 2000.

Solution 1

It's clear that we must have a = 2^j5^k, b = 2^m^6 and c = 2^p5^q for some nonnegative integers j, k, m, n, p, q. Dealing first with the powers of 2: from the given conditions, max(j, m)=3, max(m, p) = max(p, j) = 4. Thus we must have p = 4 and at least one of m, j equal to 3. This gives 7 possible triples (j,m,p): (0, 3, 4), (1, 3, 4), (2, 3, 4), (3, 3, 4), (3, 2, 4), (3, 1, 4) and (3, 0, 4).

Now, for the powers of 5: we have max (k, n) = max(n, q) = max(q, k) = 3. Thus, at least two of k, n, g must be equal to 3, and the other can take any value between 0 and 3. This gives us a total of 10 possible triples: (3, 3, 3) and three possibilities of each of the forms (3, 3, n), (3, n, 3) and (n, 3, 3).

Since the exponents of 2 and 5 must satisfy these conditions independently, we have a total of 7. 10= 70 possible valid triples.

Solution 2

1000=2³5³ and 2000= 2⁴5³. By looking at the prime factorization of 2000, c must have a factor of 2¹. If c has a factor of 53, then there are two cases: either (1) a or b = 5³2³, or (2) one of a and has a factor of 5³ and the other a factor of 2³. For case 1, the other number will be in the form of 2^x5^y, so there are 4 4 16 possible such numbers; since this can be either a orb there are a total of 2(16)-1=31 possibilities. For case 2, a and b are in the form of 2³5^x and 2^y5³, with a x<3 and y<3 (if they were equal to 3, it would overlap with case 1). Thus, there are 2(3-3)= 18 cases.

If c does not have a factor of 5³, then at least one of a and b must be 2³5³, and both must have a factor of 5³. Then, there are 4 solutions possible just considering a = 2353, and a total of 4.2-17 possibilities. Multiplying by three, as 0<=c<=2, there are 7.3 = 21.

Together, that makes 31 +18+21= 70 solutions for (a, b, c).

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The estimated answer for 212 divided by 18 is 12.

Estimation means approximating a quantity to the required accuracy.

This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer. It is used to find a value that is close enough to the right answer.

Estimation in math is done by rounding off the numbers to their closest whole value to get a quick and simple rough answer. It saves time and effort.

Dividing 212 by 18

= 212/18

= 11.77777

Estimated to be 12

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The diagonal intersection and the midpoint of both diagonal lies on the same point.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

As per the given parallelogram,

The midpoint of diagonal through J(4,-2) and H(-2,2) will be as,

x = (4 - 2)/2 = 1

y = (-2 + 2)/2 = 0

So it will be (1,0)

The midpoint of diagonal through K(-2,-3) and I(4,3) will be as,

x = (-2 + 4)/2 = 1

y = (-3 + 3)/2 = 0

So it will also be (1,0).

Since both midpoints are the same thus it will be the intersection point.

Hence "The midpoint of both diagonals and the diagonal intersection is located at the same location".

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The expressions that are equivalent to 0.3(9n + 22) are:

(a)

Apply the Distributive Property: 0.3 x 9n + 0.3 x 22

Multiply the monomials: 2.7n + 0.3  x 22

Calculate the product or quotient: 2.7n + 6.6

Determine whether 0.3(9n + 22) and -2.7n - 6.6 are equivalent.

FALSE.

b.

Apply the Distributive Property: 0.3 x 9n + 0.3 x 22

Multiply the monomials: 2.7n + 0.3  x 22

Calculate the product or quotient: 2.7n + 6.6

Determine whether 0.3(9n + 22) and 2.7n + 6.6 are equivalent.

TRUE

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The total number of candle that Maya sold to her neighbor is 60 candles

The number of candles Maya sold to her neighbor is solved using the concept of multiplication

Since there are 6 candles in each box and Maya sold 2 boxes each. the number of candle sold to each neighbor is solved by

= 6 candles * 2 neighbors

= 12 candles

Because Maya has 5 neighbors the total number of candle Maya sold is

= 5 neighbors * 12 candles

= 60 candles

we can therefore say that Maya sold a total of 60 candles to her neighbors

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Ling is now 17 feet off the ground if she is climbing a rock wall.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

She begins by climbing 12 feet. Then she descends 3 feet to take a different path. She climbs another 8 feet from there.

Ling started 12 feet off the ground and climbed down 3 feet, so she is now 12 - 3 = 9 feet off the ground.

Then she climbed up another 8 feet, so she is now 9 + 8 = 17 feet off the ground.

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a. The intervals of equal width must be used because it allows for a fair comparison.

b. Some of the data can be left out of the frequency polygon if it is not relevant to the analysis.

a) For a frequency polygon to accurately display the distribution of data, intervals of equal width must be used because it allows for a fair comparison between different parts of the data. If the intervals are not equal in width, it can give the impression that there are more or fewer data points in a particular interval, which can be misleading.

For example, if we have data on the heights of 100 people and we want to create a frequency polygon to display this data, we would first need to decide on the intervals that we want to use. If we use intervals of equal width, such as 1 inch, it would allow us to fairly compare the number of people who are between 5'0" and 5'1", 5'1" and 5'2", and so on. However, if we use intervals of unequal width, such as 1 inch for heights between 5'0" and 5'3", and 2 inches for heights between 5'3" and 5'6", it would give the impression that there are fewer people in the second interval than in the first, even if that is not the case.

b) Some of the data can be left out of the frequency polygon if it is not relevant to the analysis that we are trying to perform. For example, if we are interested in understanding the distribution of heights among people who are between the ages of 18 and 25, we could exclude data on the heights of people who are outside of this age range from our frequency polygon.

However, it is important to be careful about which data we choose to exclude, as it can significantly affect the interpretation of the results. If we exclude too much data, it could lead to a distorted view of the distribution of the data.

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The 95% confidence interval for the amount spent on the child's last birthday gift is between  $44.5 and $55.5.

To construct a 95% confidence interval, we first calculate the margin of error, which is equal to 1.96 times the standard deviation divided by the square root of the sample size.

In this case, the margin of error is 1.96 x 13/√14 = $5.5. Then, we add the margin of error to the mean to obtain the upper bound of the confidence interval, which is 50 + 5.5 = $55.5. We subtract the margin of error from the mean to obtain the lower bound of the confidence interval, which is 50 - 5.5 = $44.5.

Finally, we round the upper and lower bounds to the nearest decimal place, which gives us the 95% confidence interval of (36.4, 63.6).

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The expression that represents how much money that will be in the account is A = 800.00(1 + 0.015)⁴.

The expression that represents how much money you will have in one year if 6% is compounded quarterly on a 800$ for one year is as follows:

Hence, using the compound interest formula,

A = P + I

where

Hence,

r = 6/100

r = 0.06 rate per year

Then solve the equation for A

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

A = 800(1 + 0.06/4)⁴ˣ¹

Therefore, the expression is  A = 800(1 + 0.015)⁴

A = $849.09

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