Question 2 of 10
Solve (x – 4)2 = 5.
O A. x=-4+25
O x X
O B. x=514
O C. x = 9 and x= -1
O D. x = 4+15

To use polar coordinates, we need to first express the equations of the surfaces in polar coordinates.

In polar coordinates, we have x = r cosθ and y = r sinθ. Therefore, the equation x^2 + y^2 = 1 becomes r^2 = 1.

To find the volume of the solid, we can integrate over the region in the xy-plane bounded by the circle r=1. For each point (r,θ) in this region, the corresponding point in 3D space has coordinates (r cosθ, r sinθ, r^2+3)

Thus, the volume of the solid can be expressed as the double integral:

V = ∬R (r^2+3) r dr dθ

where R is the region in the xy-plane bounded by the circle r=1.

We can evaluate this integral using the limits of integration 0 to 2π for θ, and 0 to 1 for r:

V = ∫₀^¹ ∫₀^(2π) (r^3 + 3r) dθ dr

= ∫₀^¹ [(r^3/3 + 3rθ)]₀^(2π) dr

= ∫₀^¹ (2πr^3/3 + 6πr) dr

= 2π[(1/12) + (1/2)]

= 2π(5/12)

= (5/6)π

Therefore, the volume of the solid is (5/6)π.

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Answer:

3 , 2.96 , 1/5 (0.2)  
3.48 , 3 , 1/4 (0.25)

Step-by-step explanation:

descending order

Answer: \(\dfrac14\)

Step-by-step explanation:

Given: The factory produces equal quantities of four flavors cherry lemon orange and strawberry.

Let  orange candy= cherry = lemon = strawberry  = x

Total candies = x + x + x + x= 4x

The probability that a randomly selected candy is orange = \(\dfrac{x}{4x}=\dfrac14\)

Hence, the probability that a randomly selected candy is orange = \(\dfrac14\)

Answer:

x+3

I hope this helps you

The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.

Given that,

At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.

To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)

R-bar = 1.05 Degrees

X-bar = 45.25 Degrees

Sample Size , n=5

D3=0

D4=2.114

3 Sigma control limits of Range Chart

LCLR = D3*R-bar = 0*1.05 =0

UCLR =D4*R-bar = 2.114*1.05 = 2.22

The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.

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Check the picture below.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-4}\\ b=\stackrel{opposite}{-5}\\ \end{cases} \\\\\\ c=\sqrt{(-4)^2 + (-5)^2}\implies c=\sqrt{41} \\\\[-0.35em] ~\dotfill\)

\(cos(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{\sqrt{41}}}\implies \cfrac{-4}{\sqrt{41}}\cdot \cfrac{\sqrt{41}}{\sqrt{41}}\implies -\cfrac{4\sqrt{41}}{41} \\\\\\ sec(\theta )\cfrac{\stackrel{hypotenuse}{\sqrt{41}}}{\underset{adjacent}{-4}}\implies -\cfrac{\sqrt{41}}{4}~\hfill cot(\theta )\implies \cfrac{\stackrel{adjacent}{-4}}{\underset{opposite}{-5}}\implies \cfrac{4}{5}\)

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer g(x)=x2 + 2

Step-by-step explanation:

Answer:

Step-by-step explandation:

d

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Answer:

\( {( \frac{2}{5}) }^{ - 4} = {( \frac{5}{2} )}^{4} = \frac{625}{16} \)

Answer:

15, 21, 27

Step-by-step explanation:

\(a_n}\) = \(a_{1}\) + (n-1)d  

\(a_{n}\) is the number in the sequence we are looking for

\(a_{1}\)  This is the first term in the sequence that we do not know and we are looking for

n stands for the number of the term and d is the common difference.  We will put in all that we know and solve for the first term.

609 = \(a_{1}\) + (100-1)6  

609 =\(a_{1}\) + (99)6

609 = \(a_{1}\) + 594  Subtract 594 from both sides of the equation

15 = \(a_{1}\)

Now that we know that the first term is 15 we just add 6 to get the next term which is 21 and then add 6 again to get the last term 27.

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Answer:

answer is c

Step-by-step explanation:

The true statements about the data collected are option 1. The mode of the data set is 9 and option 3. The data shows the preferred activities of 40 students.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition to mean and median, it is one of the three measures of central tendency. For instance, the set "3, 7, 8, 8, 9" has an 8 as its mode. Hence, we can quickly determine the mode given a finite number of observations. There might be one mode, several modes, or none at all for a given collection of values.

From the given dot plot we see that the maximum dots are on the activity dance, that is there are 9 dots.

Thus, the mode of the data is 9.

The total number of students represented on the graph are 40.

Hence, the true statements about the data collected are option 1. The mode of the data set is 9 and option 3. The data shows the preferred activities of 40 students.

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The complete question is:

Step-by-step explanation:

2400/100=24

24×10.5=252

252×5= 1260

Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

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Answer:

see explanation

Step-by-step explanation:

the error in the question is that

sec²x = \(\frac{1}{cos^2x}\) ≠ \(\frac{1}{sin^2x}\) , and

csc²x = \(\frac{1}{sin^2x}\) ≠ \(\frac{1}{cos^2x}\)

have been used incorrectly in simplifying the expression

then

\(\frac{tan^2x+1}{1+cot^2x}\)

= \(\frac{sec^2x}{csc^2x}\)

= \(\frac{\frac{1}{cos^2x} }{\frac{1}{sin^2x} }\)

= \(\frac{1}{cos^2x}\) × \(\frac{sin^2x}{1}\)

= \(\frac{sin^2x}{cos^2x}\)

= tan²x

As per the remainder that the greatest possible value of 17

The term remainder in math defined as if a number is not completely divisible by another number  then we are left with a value once the division is done

Here we have if x is a positive integer, then r is the remainder when x is divided by 4 and r is the remainder when x is divided by 9.

As we all know that the remainder is always smaller than the divisor.

Here we have also know that it will be 0 if the dividend is evenly divisible or a positive integer less than the divisor.

So, when we divided by 4 then the largest remainder will be 3 and then here we have to  divided by 9, then the largest remainder will be written as

=> r² + R = 32 + 8

=> 9 + 8 = 17

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Answer:

$44.31

Step-by-step explanation:

5.5/100 = x/42 (5.5% is what of 42) (%/100=is/of)

(5.5)(42) / 100 = $2.31(tax) (cross multiply)

42 + 2.31 = $44.31

Answer:

Step-by-step explanation:

hope this helps

The figure below shows a line graph and two shaded triangles that are similar:

A line is shown on a coordinate grid. The x axis values are from negative 20 to positive 20 in increments of 4 for each grid line. The y axis values are from negative 5 to positive 5 in increments of 1 for each grid line. The line passes through the ordered pairs negative 16, 4, and 0, 0, and 16, negative 4. A shaded right triangle is formed so that its hypotenuse is from ordered pair 0, 0 labeled as O to negative 8, 2 labeled as A, one leg is from 0, 0 to negative 8, 0, and the second leg is from negative 8, 0 to negative 8, 2. Another shaded right triangle is formed with the hypotenuse from negative 8, 2 to negative 12, 3 labeled as B, one leg is from negative 8, 2 to negative 12, 2, and the second leg is from negative 12, 2 to negative 12, 3.

Which statement about the slope of the line is true?

The slope from point O to point A is fraction 1 over 4 times the slope of the line from point A to point B.

The slope from point O to point A is 4 times the slope of the line from point A to point B.

It is fraction negative 1 over 4 throughout the line.

It is −4 throughout the line

Step-by-step explanation:

not my answer found it on a different page but it should help.

The probability of the region not flooding the next year is 19/20.

Given that a region is prone to flooding once every 20 years, we can calculate the probability of flooding in any one year as:

Probability of flooding in any one year = 1/20 = 0.05

Since the probability of flooding in any one year is greater than 0, the probability of not flooding in any one year would be:

Probability of not flooding in any one year = 1 - 0.05 = 0.95

Therefore, the probability of not flooding the next year in this region would be 0.95 or 95%.
Hi, I'd be happy to help you with your probability question.

The probability of flooding in the region any one year is 1/20 (once every 20 years). To find the probability of not flooding the next year, we need to find the complement of the probability of flooding.

Step 1: Determine the probability of flooding.
P(Flooding) = 1/20

Step 2: Find the complement probability.
P(Not Flooding) = 1 - P(Flooding)

Step 3: Calculate the probability of not flooding.
P(Not Flooding) = 1 - (1/20) = 19/20

The probability of the region not flooding the next year is 19/20.

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We can approach this problem using the concept of probability and complement rule.

Given that a region is prone to flooding once every 20 years, we can assume that the probability of flooding in any given year is 1/20 or 0.05 (since once in 20 years means once in 20 trials, and the probability of success in any one trial is 1/20).

Now, the probability of not flooding in the next year can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

Therefore, the probability of not flooding in the next year can be calculated as follows:

P(not flooding) = 1 - P(flooding)

P(not flooding) = 1 - 0.05

P(not flooding) = 0.95

So, the probability of not flooding in the next year is 0.95 or 95%. This means that there is a high likelihood that the region will not experience flooding in the next year.

However, it's important to note that the probability of flooding in any given year is still greater than 0, which means that there is always a possibility of flooding occurring, regardless of whether it occurred in the previous year or not.

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The total cost of the camera with sales tax included is $811.47.

The total cost refers to the summation of all the cost involved from the manufacturing to sales, it majorly involves the fix cost and variable cost.

To find the total cost we need to derive a formula

total cost = listed price + ( listed price x sales tax rate)

now by placing the values given in the question we can calculate the the total cost

listed price = $761. 98

sales tax rate = 6. 5%

then,

total cost = 761.98 + (761.98 x 0.065)

total cost = 761.98 + 49.49

total cost = $811.47

The total cost of the camera with sales tax included is $811.47.

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In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer:

1/3

Step-by-step explanation:

Alice can select any ball from her bag and it goes into Bob's bag. Then bob has 6 balls including two of one color.

Suppose they are {A,B,B,C,D,E}

Now Bob must draw one of the two balls of the same color (B) in order to have the same content of the two bags.

P(bags same content)= 2/6= 1/3

The probability that the bags content are the same= 1/3

The appropriate transformation to increase the hourly wage is a vertical stretch of the function.

The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:

P(h) = mh + b.

In which the coefficients of the payment function are listed as follows:

To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.

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The appropriate transformation to increase the hourly wage is a vertical stretch of the function.

What is the definition of the payment function?

The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:

P(h) = mh + b.

In which the coefficients of the payment function are listed as follows:

m is the slope of the linear function, which is equivalent to the hourly pay of the students.

b is the intercept of the linear function, which is equivalent to the fixed pay of the students.

To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.

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