Using a Net to Find the Surface Area of a Triangular Prism.

Answer:

27

32

27

Step-by-step explanation:

1) limit x->2 1/3[f(x)]^2= 27

2) limit x->2 3f(x)+5= 32

3) limit x->2 [f(x)]3/2= 27/2

"A limit is the value that a function approaches as the input approaches some value."

If limit f(x) = m and constant 'a',

limit a (f(x)) = a × m

limit (f(x))^n = (m)^n

limit (a) = a

limit (f(x) + a) = m + a

Given: limit x->2 f(x)=9.

We need to evaluate each limit.

1) limit x->2 1/3[f(x)]^2

⇒ \(\lim_{x \to 2} \frac{1}{3} (f(x))^2\)

= \(\frac{1}{3} \lim_{x \to 2} (f(x))^2\)

= \(\frac{1}{3} (\lim_{x \to 2} f(x))^2\)

= \(\frac{1}{3} \times (9)^2\)

= \(\frac{81}{3}\)

= 27

2) limit x->2 3f(x)+5

⇒ \(\lim_{x \to 2} (3f(x)+5)\)

= \(\lim_{x \to 2} 3f(x)+ \lim_{x \to 2} 5\)

= \(3\lim_{x \to 2} f(x) + 5\)

= \((3 \times 9)+5\)

=\(\bold{32}\)

3) limit x->2 [f(x)]3/2

⇒ \(\lim_{x \to 2} (f(x))\frac{3}{2}\)

= \(\frac{3}{2} \times (\lim_{x \to 2} f(x))\)

= \(\frac{3}{2} \times 9\)

= 27/2

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Answer:

Believe it's just a

Step-by-step explanation:

Because

Answer:  Distributive Property of Multiplication.

Step-by-step explanation:

The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.

Here we want to find the solution set of the inequality below:

x ≤ -4

First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so  we need to have a closed set at that end)

This is written as:

(-∞, -4]

The use of the symbols [ ] means that the element belongs to the set.

Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.

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Answer:

True; True; False; True

Step-by-step explanation:

Answer:

The unit rate is 6 pieces or candy per child.

Step-by-step explanation:

you would divide the number of pieces by the amount of children. 36÷6=6 candies. 6 candirs per child

Answer:

6

Step-by-step explanation:

36 pieces of candy among 6 children so 6 pieces for each

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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In a right angled triangle, the base is 17 and the angle between base and hypotenuse is 29°, then the hypotenuse x is equal to 19.4 after rounding off to the nearest tenth.

From the given figure, we have to find the missing length x

In the figure we can see that,

For the angle, θ = 29°

Base = 17

and, hypotenuse = x

We know that by the cosine of the angle in the given triangle can be written as,

cos θ = \(\frac{base}{hypotenuse}\)

⇒ cos 29° = \(\frac{17}{x}\)

⇒ x = \(\frac{17}{cos \ 29\textdegree}\)

⇒ x = 19.437

Rounding to the nearest tenth, x = 19.4

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Answer:

10x + 6(0.5) = 10

Step-by-step explanation:

1) We know that there are 6 apples, each costing $0.50

We can write this portion of the equation as 6(0.5)

2) There are 10 oranges, but we don't know the amount they each cost
We can write this portion of the equation as 10x

x= amount each orange costs

3) The total will add up to $10

10x oranges + 6($0.5) apples = $10.00

Answer:

45 minutes

Step-by-step explanation:

If its 1 mile above the ground in 15 min from 1 ½, that means it descended ½ mile in 15 min, and if you multiply ½*3, you get 1 ½ miles, so multiply 15 minute * 3 and it would take 45 minutes for the entire descent to last

The entire descent lasts for 7.5 minutes, when it begins its descent at 1 1/2 miles above the ground.

Let's break this problem into two parts:

1. Find the change in height of the airplane.

2. Determine how long the entire descent lasts.

Part 1: Find the change in height

The airplane begins its descent at 1 1/2 miles above the ground, which is equivalent to 1.5 miles.

After 15 minutes, it is 1 mile above the ground.

To find the change in height, subtract the final altitude from the initial altitude:

Change in Height = Initial Altitude - Final Altitude

                                = 1.5 miles - 1 mile

                               = 0.5 miles

So, the change in height of the airplane is 0.5 miles.

Part 2: Determine how long the entire descent lasts

As, the airplane descends 0.5 miles in 15 minutes.

Set up a proportion:

(0.5 miles / 15 minutes) = (Total Descent / Total Time)

Now, solve for Total Time:

Total Time = (0.5 miles * 15 minutes) / 0.5 miles

Total Time = 7.5 minutes

So, the entire descent lasts for 7.5 minutes.

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Answer:

If you're saying Jan ate 1/4 of what was left. How much of the pie did Jan eat?

then the answer is 5/32

Step-by-step explanation:

Answer:

Step-by-step explanation:

m-(n+(p-(m+n-p)))

Final Result :

     2 • (m - p)

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

64 ways

Step-by-step explanation:

Let n = 8

The number of ways a person can take one stair = n^P1 = 8^P1

The number of ways a person can take two stairs = n^P2 = 8^P2

∴ The number of ways the person who can take one stair or two stairs at a time = 8^P1 + 8^P2 = 8 + 56 = 64 ways

Answer:

x(7y)x(7y)

Step-by-step explanation:

The given expression: 7(xy)7(xy)

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication :-

a\times b=b\times aa×b=b×a for any numbers a and b.

Associative property of multiplication :-

a\times(b\times c)=(a\times b\times c)a×(b×c)=(a×b×c) for any numbers a , band c.

Now, 7(xy)=(7x)y7(xy)=(7x)y [Associative property of multiplication]

=(x7)y=(x7)y [Commutative property of multiplication]

=x(7y)=x(7y) [Associative property of multiplication]

Answer:

Step-by-step explanation:

we just have to substitute 0 in place of x

1-(0)³, 0³ is still 0, so we're left with 1-0=1

mark me brainliest of it helped

The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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a. The secant slope through (-2,4) and (0,0) is -2.

b. The secant slope through (-1.5,2.25) and (-0.5,0.25) is -2.

The estimated slope of the tangent line to f(x) = x^2 at x = -1 is approximately -2.

To estimate the slope of the tangent line to the function f(x) = x^2 at x = -1, we can find the slopes of the secant lines through different pairs of points.

a. (-2,4) and (0,0):

The coordinates of the two points are (-2, 4) and (0, 0). We can calculate the slope of the secant line passing through these points using the formula:

msec = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

msec = (0 - 4) / (0 - (-2))

= -4 / 2

= -2

So, the slope of the secant line passing through (-2, 4) and (0, 0) is -2.

b. (-1.5, 2.25) and (-0.5, 0.25):

The coordinates of the two points are (-1.5, 2.25) and (-0.5, 0.25). Using the slope formula, we can calculate the slope of the secant line passing through these points:

msec = (0.25 - 2.25) / (-0.5 - (-1.5))

= (-2) / (1)

= -2

So, the slope of the secant line passing through (-1.5, 2.25) and (-0.5, 0.25) is -2.

By finding the slopes of the secant lines, we have estimated the rate of change of the function f(x) = x^2 at x = -1. The slope of the tangent line at this point will be very close to these secant slopes, particularly as the two points used to calculate the secant lines get closer together.

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The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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Answer: x=5, DF=12

Step-by-step explanation:

By the triangle proportionality theorem,

(x+7)/16 = 3/4

(x+7)/16 = 12/16

So x+7=12 -> x=5

Meaning DF=5+7=12

Answer:

12

Step-by-step explanation:

Two triangles are similar so we can find the length of DF using the sides' proportion:

BC/EC = DC/FC

7/4 = (x+7+16)/16 cross multiply expressions:

112 = 4x + 92 subtract 92 from both sides

20 = 4x divide both sides by

5 = x

since DF is x+7 then its length is 12

Answer:

$0.75 per song

Step-by-step explanation:

Given that the relationship between variable s and c is a proportional relationship, and is represented by the equation, c = 0.75s.

Where,

c = total costs

s = number of songs

The constant of proportionality, k, = 0.75.

Thus, 0.75 represents the cost per sing downloaded.

The answer is:

✔️$0.75 per song

Answer:

Prime Factors of 545 are 5, 109, and usually expressed as 5 x 109. 4.

hope this is right! :) -liaa

A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

Answer:

Probability is 0.831727

Step-by-step explanation:

The probability can be calculated as below

There are multiple scenarios

Scanerio 1

0 occurance & No damage = 1 - 0.2 - 0.03 - 0.001 = 0.769

Scanerio 2

1 occurance & No damage = 0.2 x ( 1 - 0.7 ) = 0.06

Scanerio 3

2 occurance & No damage = 0.03 x ( 1 - 0.7 )^2 = 0.0027

Scanerio 4

3 occurance & No damage = 0.001 x ( 1 - 0.7 )^3 = 0.000027

P(structure will not suffer any damage) = Scanerio 1 + Scanerio 2 + Scanerio 3 + Scanerio 4 = 0.769 + 0.06 + 0.0027 + 0.000027 = 0.831727

The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

\(P(x) = (x^2 - 3x + 4x - 12)(x - 5)\)

\(= (x^2 + x - 12)(x - 5)\)

\(= x^3 - 5x^2 + x^2 - 5x - 12x + 60\)

\(= x^3 - 4x^2 - 17x + 60\).

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For the first part of the ID number (consisting of digits) we have the following number of permutations

The first part 9 takes into consideration that the first digit is non-zero, so we only have 1-9 to choose from, while the other succeeding 5 digits we have 10 to choose from (0 - 9).

The second part of the ID number (two letter part) will have the number of permutations

First multiplied by 5, and then 4, since we cannot repeat the previous letter.

Therefore the number of different student numbers is solved as

18,000,000 possible student ID numbers.

Answer:

It's 8 yuan per hour in company A and 9 yuan per hour in company B

Specific individuals in a population are unfairly left out of a study, which is known as exclusion bias. When researchers design a study that inadequately represents specific segments of the community, undercoverage bias emerges.

When a sample is not chosen that accurately represents the full population of data, a statistical error known as sampling error arises. As a result, the sample's findings do not accurately reflect the outcomes that the complete population would produce.

When a sample is chosen from a population based on the idea of randomization, this practise is known as probability sampling.

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