Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°. 250.4° 63.2° 70.4° 19.6°

The total distance traveled by him is 60 ft

In this question, apply the Pythagorean relationship

Let's assume, the climbing, sliding and walking back to the base form a right-angle triangle

The tower height = the height of the triangle, h=10f

The sliding lane= the hypotenuse of the triangle=?

The distance covered to the base= base of the triangle=24f

Applying the relation ;

a²+b²=c²

10²+24²=c²

100+576=c²

676=c²

[tex]\sqrt{626}[/tex]=c

26=c

Distance traveled in all=26+24+10=60 feet

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Answer:

  b. Square -2

Step-by-step explanation:

You want to know the first step in evaluating 1/2 |2x² - 3| for x = -2.

The Order of Operations tells you the first step is to evaluate expressions inside the innermost grouping symbols. Here, that means you want to evaluate the expression 2x² - 3.

Once you have identified that expression, you start by evaluating terms with exponents. That term here is x². When x=-2, the first step is to square -2.

__

Additional comment

After you get x² = 4, then you evaluate the product 2(4) = 8, and then the difference 8 -3 = 5. Then the absolute value is determined |5| = 5, and finally the product with 1/2: (1/2)(5) = 5/2.

The correct option is option b. It can be obtained by following the order of operation BODMAS.

What is the order of operation?
To solve any mathematical expression, the BODMAS rule is used. The full form of BODMAS is Bracket Order DIvision Multiplication Addition Subtraction. It can be simplified as, to solve the Mathematica expression first open all brackets, then powers, then division, then multiplication, then addition, and finally subtraction.

Now, consider the following expression:

1/2 |2x² - 3|

Now, substitute -2 for x in the above expression.

1/2 |2(-2)² - 3|

In the above expression there is no bracket hence the next step is solve power of -2.

Hence, the first step of solving the above expression is square -2.

Hence, the correct option is b. It can be obtained by following the order of operation BODMAS.

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The expression equivalent to the given expression  -2(3x + 5y) is

given that

-2(3x + 5y)

expanding the parenthesis

-6x - 10y = 0

10y = 6x

y = 6x/10

y = 3x / 5

we can conclude that y = 3x/5 is equivalent to  -2(3x + 5y)

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Answer:

B)  f(5) = 8

Step-by-step explanation:

Remainder Theorem

When a polynomial f(x) is divided by (x − c) the remainder is f(c).

Therefore, if f(x) is divided by (x - 5) the remainder is f(5).

As the remainder is 8, then f(5) = 8.

Melitta found out that if she walks really fast during her morning exercise, she can cover 2 1/4 miles in 3/4 of an hour.

Mellita is walking with a coverage of 2.8  miles per hour. We simply need to know how far she covers in an hour to calculate her walking speed in miles per hour.

Time taken to complete 2~1/4 miles is 3/4 of an hour. This is the time she can beat, so we have to find for the remaining 1/4th half of 2~1/4 miles i.e

Miles she can cover in 1/4 of hour = 1/4 * 2~1/4

    = 1/4  * 9/4

    = 9/16 miles.

Now, Add this to the miles that she can cover, i.e 2~1/4

= 2~1/4 + 9/16

= 9/4 + 9/16

= (36+9)/16

= 45/16

= 2.8 miles.

Hence, Melitta can walk 2.8 miles per hour.

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Using linear regression, it is found that:

a) The equation is: y = -0.00408x + 16.

b) The interpretation of each coefficient is:

The linear regression equation is obtained inserting the points given on the table at the end of the answer in a linear regression calculator.

Then the equation will have the following format of a linear function:

y = mx + b.

In which the coefficients are as follows:

The points are given as follows:

(0, 16), (242, 14.8), (519, 14.1), (698, 13.5), (825, 12.7), (1009, 11.6).

Using the calculator, the equation is:

y = -0.00408x + 16.

The problem is given by the image at the end of the answer.

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Answer:

1. 2x + 3y

2. 15m -6n

Step-by-step explanation:

Combine like terms.

Answer:

1) 2x+3y

2) 15m-6n

Step-by-step explanation:

Lets first simplify 1.

1) open parentheses

9x+3y-7x

2)combine like terms

2x+3y

Simplify 2.

1) open parentheses

8m-6n+7m

2) combine like terms

15m-6n

Answer: C / .33

Step-by-step explanation:

Answer:

r = -37

Step-by-step explanation:

Step 1: Write out what is known

Step 2: Set up an equation to solve for r

Step 3: Solve for r

The probability of getting 2 white balls is 2/11.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. It has a range from 0 to 1.

Probability(Event) = Favorable Outcomes / Total Outcomes

Main body:

total balls = 5+6 =11

1st try:

P(white balls) = 5/11

2nd try:

as there is no replacement,

no. of white balls = 4

total balls =10

P( white ball) = 4/10

Now multiplying both the result = (5/11)*(4/10)

P( WHITE BALLS) = 2/11

Hence answer is 2/11.

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The final balance after 1 year with initial value $1000 if the interest is compounded quarterly will be $1215.5

What is compound interest?

Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. The power of compound interest is the creation of "interest on interest."

We are given that she initially invested $1000 and that she get 5% and interest is compounded quaterly.

After 3 months the interest will be

I = 1000*(5/100)

I = 50

So the total amount becomes

$1050 after 3 months

Now after 3 months again 5% interest will be credited

Hence the amount becomes

I1 = 1050*(5/100)

I1 = 52.5

Hence the total amount becomes

1102.5 after 6 months

After 9 months the interest will be

I2 = 1102.5*(5/100)

I2 = 55.12

Hence the total amount becomes

$1157.62 after 9 months

After 1 years the interest will be

I3 = 1157.62*(5/100)

I3 = 57.88

Hence the total amount becomes $1215.5

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There are ΔABC and ΔXYZ triangles that are congruent due to the SAS congruence postulate.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

As per the given question,

In ΔABC and ΔXYZ,

Side BC = Side YZ

m∠C = m∠Z

Side AC = Side XZ

According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

Thus, both triangles are congruent.

Hence, there are ΔABC and ΔXYZ triangles congruent due to the SAS congruence postulate.

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The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment.

What is a Perpendicular bisector?
A line that divides another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to draw a perpendicular bisector. When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.
So, In the given question, We can say that A bisector that divides the line segment into two parts is called a perpendicular bisector;
We can also, find the proof of it: as: It divides AB into two equal halves or bisects it. It makes right angles with (or is perpendicular to) AB.
Every point in the perpendicular bisector is equidistant from points A and B.A ruler and compass are needed. The process for creating a line segment's perpendicular bisector is as follows:

Draw the first segment of the line PQ.

Step 2: Set the compass to a length that is a little longer than half of PQ's length.

Draw arcs above and below the line by positioning the compass pointer at point P in step 3.

Step 4: Set the compass pointer at point Q while maintaining the same length. Draw two arcs above and below the line, in the same manner, maintaining the compass's pointer at Q.
Hence, The perpendicular bisector is a line that bisects the line segment into two equal halves and forms a right angle with the line segment

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The first figure is an example of a solid polyhedron,

Name of the bases: PONMQ, KJIHL

Name of the faces: HINM, IJON, JKPO, KPQL, LNMQ.

Name of the edges: HI, IN, MN, MH, LH, LQ, QM, LK, KP, PQ, KJ, JO, OP, JI, IN, ON

Name of the vertices: H, I, J, K, L, M, N, O, P, Q.

what is a solid polyhedron?

If all of the sides of a 3-dimensional solid are flat, it is a polyhedron. Soccer balls, prisms, bricks, houses, and pyramids are all real-world polyhedrons. These shapes all have flat sides. If a shape has any curved sides, it is no longer a polyhedron.

As the definition of the solid polyhedron says that if any shape has any curved sides, then it cannot be a solid polyhedron.

The second figure has curved surface, so it can't be a solid polyhedron.

Hence, the first figure is an example of a solid polyhedron,

Name of the bases: PONMQ, KJIHL

Name of the faces: HINM, IJON, JKPO, KPQL, LNMQ.

Name of the edges: HI, IN, MN, MH, LH, LQ, QM, LK, KP, PQ, KJ, JO, OP, JI, IN, ON

Name of the vertices: H, I, J, K, L, M, N, O, P, Q.

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600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

Given:

standard deviation σ = 0.01

margin of error e = 0.0008

For 95% confidence interval:

z value = 1.96

we know that:

e = z * σ/[tex]\sqrt{n}[/tex]

0.0008 = 1.96*0.01/[tex]\sqrt{n}[/tex]

0.0008 = 0.0196/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex] = 0.0196/0.0008

= 24.5

n = 24.5^2

n = 600.25

Therefore 600 large should n be so that a 95% confidence interval for has a margin of error of ± 0. 0008.

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Step-by-step explanation:

8m + 20 - 6m - m + 7

We combine 8m and -6m to get 2m. Now we combine 2m and -m to get m.

This gives us:

m + 20 + 7.

We combine 20 and 7 to get 27.

This gives us the answer of

m + 27

Answer: I think the answer is 71.98

Step-by-step explanation:

Answer:

area = base x height

Step-by-step explanation:

You multiply the base of the square and the height of the square and you get the area of it.

The equivalent equation of the given equation 3(x-4) = 18+2x-11 is given by,

x=19.

Given the mathematical equation is,

3(x-4) = 18+2x-11

Evaluating the equation we get,

3x-12 = 18+2x-11

3x-2x = 18-11+12, separating the variable and numbers

x = 19

Hence the equivalent equation of the given equation is x=19.

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Answer:

9 peppers

Step-by-step explanation:

A dozen is 12

so 3t + t = 12

4t=12  /3

t=3

He planted 9 peppers

Answer:

tomatoes are T so T3 is how many peppers he planted.

PS: if you are looking for a direct question you need to give the number of tomatoes or peppers.

Step-by-step explanation:

Answer: I don't know if I'm 100% spot on but I belive it may be 6.32.

There are calculators for this online, try get home (unless it's a test) and use them.

The given statement is false.

Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods.

The given statement is false: A p-value is the probability of obtaining a sample statistic less extreme than the one observed under the assumption that the statement in the null hypothesis is true.

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The answer is no, and the below explanation is given with a counter-example.

An integer is a number that includes both negative and positive numbers, including zero. It has no decimal or fractional parts. Here are a few examples of integers: -5, 0, 1, 5, 8, 97, and 3,043

P(n) is a condition that is true for P(0), P(1), and P(2), but P(3k) is true when P(k) is true for all numbers k0.

P(n) is thus not always true for all nonnegative integers n because 4 is not a multiple of 3.

For example, consider the property P(n): "n is 0 or 1, or n is a multiple of 3." Then P(0), P(1), and P(2) are trivially true, however, P(3k) is true for all numbers k because 3k is a multiple of 3. However, P(4) is false because 4 is not a multiple of 3.

As a result, no.

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The complete question is:

"Suppose P(n) is a property such that 1. P(0), P(1), P(2) are all true, 2. for all integers k≥0, if P(k) is true, then P(3k) is true. Must it follow that P(n) is true for all integers n≥0?

If yes, explain why; if no, give a counterexample".

By using unitary method it is obtained that Jennifer is at a distance of 8 km to her destination

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here unitary method is used

The scale on a map is stated as 1: 100 000

So 1 cm on the map is equivalent to 100000 cm on the ground

8 cm on the map is equivalent to 100000 [tex]\times[/tex] 8 cm on the ground

8 cm on the map is equivalent to 800000 cm on the ground

8 cm on the map is equivalent to [tex]\frac{800000}{1000 \times 100}[/tex] km on the ground

8 cm on the map is equivalent to 8 km on the ground

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No. of concert the stadium host to  earn the revenue of 200000 is 8.

acc to our question-

hence,No. of concert the stadium host to  earn the revenue of 200000 is 8.

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The problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation is y = 5x + 3.

(a) Problem: I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) Solution: The person gets $5 every month, therefore, he will have $5x after x month.

The person has $3 initially, therefore, the total money he will have after x month is:

y = 5x + 3

To find how much money will the person have after 6 months, substitute x=6 into the above equation:

y = 5(6) + 3

y = 30 + 3

y = 33

The person will have $33 after 6 months.

Hence, the problem and solution are:

(a) I have $3, and I get $5 every month as my pocket money. How much money will I have after 6 months?

(b) The person will have $33 after 6 months.

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The angle of elevation is 18. 43 degrees

Angle of elevation can be described as an angle formed between a horizontal line and the line of sight above the line.

From the information given, we have that;

Using the tangent identity, we have;

tan θ = opposite/ adjacent

tan  θ = 1/ 3

Divide the values

tan θ =0. 3333

Find the tan inverse of the value to determine  θ

θ = tan^-1(0. 3333)

θ = 18. 43 degrees

Hence, the value is 18. 43 degrees

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Answer: -8

Step-by-step explanation:

The line has a slope of 1/8, so the x increases by 8 for every 1 the y increases, and vice versa for a decrease.

The difference between the x coordinates 8 and -8 is 16. We then need to divide this by 8, because the x increases by 8 for every 1 the y increases, and we need to find the increase/decrease in y.

16/8 = 2

We need to subtract 2 from -6, giving us our answer, -8.

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance([tex]\sigma[/tex])= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]

So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]

where n=sample size

We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of [tex]z_{\alpha /2}[/tex].

Te given interval is 99%=99/100=0.99

The value of [tex]\alpha[/tex] =1−0.99

The value of [tex]\alpha[/tex] =0.01

Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005

From the standard table of z

[tex]z_{0.005}[/tex] =2.58

Now putting in the value in formula of sample size.

n[tex]=(2.58\times\frac{1.55}{0.25})^2[/tex]

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55

Standard deviation of resistance([tex]\sigma[/tex])= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n[tex]=(2.58\times\frac{3.1}{0.5})^2[/tex]

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

f(5) = 22; f(9) = 34

Step-by-step explanation:

f(5) = 3(5) +7

f(5) = 22

f(9) = 3(9) +7

f(9) = 34