Lily makes a triangular car scratcher for her pet cat.. If two of its sides, measure 8 inches and 15 inches, which of the following is the possible measure of its third side? Choose two.Show your work.
A. 18 inches
B. 7 inches
C. 22 inches
D. 23 inches
E. 12 inches

Answer:

a) {0,1,3,5,8}

b) -

Step-by-step explanation:

the composition cannot be performed cos 3 is mapped to 2 by g, but 2 is not in the domain of f

To find the percent decrease, we first need to find the amount of the decrease, which is the difference between the regular price and the sale price:

$550 - $456.50 = $93.50

So the amount of the decrease is $93.50.

To find the percent decrease, we divide the amount of the decrease by the original price and then multiply by 100:

($93.50 / $550) x 100 ≈ 17.0%

Therefore, the percent decrease of the sale price from the regular price is approximately 17.0%.

The result of each length of the sides of a right triangle is as follows:

5, 12 and 13: Yes

12, 35 and 20√5: No

5, 10 and 5√5: Yes

8, 12 and 15: No

20, 99 and 101: Yes

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

For 5, 12 and 13:

13² = 5² + 13²

169 = 169 (This is true)

YES

For 12, 35 and 20√5 :

(20√5)² = 12² + 35²

2000 = 1369 (This is false)

NO

For 5, 10 and 5√5 :

(5√5)² = 5² + 10²

125 = 125 (This is true)

YES

For 8, 12 and 15:

15² = 12² + 15²

225 = 369 (This is false)

NO

For 20, 99 and 101:

101² = 20² + 99²

10201 = 10201 (This is true)

YES

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The required measure of the unknown side in similar triangles is 4.

Similar triangles are two triangles that have the same shape but are not necessarily the same size. More specifically, two triangles are similar if their corresponding angles are congruent (i.e., have the same measure), and the corresponding sides are proportional (i.e., have the same ratio).

Here,
Two similar triangles are given in the figure,

Let the unknown side be x
For a similar triangle, the ratio of the corresponding sides are equal So,
a / 8 = 6 / 12
a = 8/2
a = 4

Thus, the required measure of the unknown side in similar triangles is 4.

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Answer:

Let's start by figuring out how many blue beads Ann had initially.

If Ann had a total of 285 red and blue beads, and she used 45 red beads, then she had 240 blue beads remaining.

If Ann used 40% of the blue beads, then she used:

0.40 x 240 = 96 blue beads

After using 45 red beads and 96 blue beads, Ann had the following number of red and blue beads remaining:

Red beads = 285 - 45 = 240

Blue beads = 240 - 96 = 144

At this point, the ratio of red beads to blue beads is:

Red beads : Blue beads = 240 : 144 = 5 : 3

However, we want the ratio to be 1 : 3. To achieve this ratio, we need to divide both the red beads and blue beads by 5. This gives us:

Red beads = 240 / 5 = 48

Blue beads = 144 / 5 = 28.8

Since we can't have a fraction of a bead, we need to round up the number of blue beads to the nearest whole number. This gives us:

Red beads = 48

Blue beads = 29

Therefore, Ann initially had 285 - 48 - 29 = 208 beads, with 48 red beads and 29 blue beads.

Step-by-step explanation:

The correct answers are

1)  2x^2 + 12

2) Option C.

3) Option B.

1. You must apply the Distributive property as following:

(-5x^2 - 2x +4) + (8x^2 -x -1) - (x^2 -5x + 2x -10)

2. Now, you must distribute the negative sign, then you have:

3. Finally, you must add the like terms. Then you obtain the polynomial:

2x^2 + 13

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).

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The height of the lighthouse is 48 feet.

To find the height of the lighthouse, we can use the concept of similar triangles. When two triangles are similar, it means that they have the same shape but different sizes. In this case, the two triangles are similar because they have the same angle to the sun. That is, the angle between the ground and the line from the top of the lighthouse to the sun is the same as the angle between the ground and the line from Zara to the sun.

This proportion is based on the fact that the two triangles are similar, so the corresponding sides are in proportion.

So, we have:

(height of lighthouse) / 36 feet = 4 feet / 3 feet

We can solve for the height of the lighthouse by cross-multiplying:

(height of lighthouse) = 36 feet × (4 feet / 3 feet)

Simplifying the expression, we get:

(height of lighthouse) = 48 feet

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The given question is incomplete, the complete question is

A lighthouse has a shadow that is 36 36 feet long. Zara is 4 4 feet tall, and has a shadow that is 3 3 feet long. The two triangles formed are similar because the angle to the sun is the same. Use this information to complete the statement about the lighthouse.

The height of the lighthouse is ___ feet .

To find the total distance of Alanah's trip to the arena, we need to add up the distances of each segment of her trip. We can use the distance formula to calculate the distances between the different points.

First, let's calculate the distance between Alanah's house (A) and Mia's house (M). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((4 - 2)^2 + (14 - 10)^2)

distance = sqrt(4 + 16)

distance = sqrt(20)

distance ≈ 4.5

So the distance between A and M is approximately 4.5 miles.

Next, let's calculate the distance between Mia's house (M) and Teresa's house (N). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((14 - 6)^2 + (16 - 12)^2)

distance = sqrt(64 + 16)

distance = sqrt(80)

distance ≈ 8.9

So the distance between M and N is approximately 8.9 miles.

Finally, let's calculate the distance between Teresa's house (N) and the arena. Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((16 - 10)^2 + (8 - 16)^2)

distance = sqrt(36 + 64)

distance = sqrt(100)

distance = 10

So the distance between N and the arena is exactly 10 miles.

Now we can add up the distances of the three segments to get the total distance of Alanah's trip to the arena:

total distance = 4.5 + 8.9 + 10

total distance ≈ 23.4

Therefore, the total distance of Alanah's trip to the arena is approximately 23.4 miles

Therefore, the regression equation best fits the data set is yˆ=0.728x2−20.213x+179.246.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, the left-hand side and the right-hand side, connected by an equal sign (=). The expressions on either side of the equal sign can be made up of numbers, variables, mathematical operations, and other mathematical symbols. Equations are used to represent various mathematical relationships and can be solved to find the value of one or more variables. Solving an equation involves manipulating the expressions on either side of the equal sign to isolate the variable being solved for. This is often done by applying a series of mathematical operations to both sides of the equation, with the goal of eventually isolating the variable on one side of the equal sign and obtaining a numerical value for it.

Here,

Using a graphing calculator, we can plot the data set of x and y values and use the regression feature to find the quadratic regression equation that best fits the data. Here's how we can do it:

Enter the x and y values into the calculator.

Plot the points on a scatter plot.

Choose the regression feature on the calculator.

Select the quadratic regression option.

The calculator will display the quadratic regression equation that best fits the data.

After performing these steps, we get the following quadratic regression equation:

yˆ=0.728x2−20.213x+179.246

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The domain of the function is (-∝, -3) ∪ (-3, +∝)

The range is (-∝, 3) ∪ (3, +∝) and the asymptotes are x = -3 and y = 3

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

f(x) = 2/(x + 3) + 3

Set the denominator to not equal to 0

So, we have

x + 3 ≠ 0

So, we have

x ≠ -3

As an interval notation, we have

(-∝, -3) ∪ (-3, +∝)

Here, we have

f(x) = 2/(x + 3) + 3

When x = -3, we have

f(-3) = undefined + 3

This means that

f(x) ≠ -3

As an interval notation, we have

(-∝, 3) ∪ (3, +∝)

In (a), we have

x ≠ -3

This means that

Vertical asymptote: x = -3

In (b), we have

f(x) ≠ -3

This means that

Horizontal asymptote: y = 3

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Answer:

12 teams means 6 games each match day. Each team can play all the 11 other teams so 11 match days. So 66 games.

The value of z is 27 when the value of w is 5, when w varies inversely with z.

The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value. Direct variation and inverse variation are two different sorts of this relationship.

Given that, w is 15 when z is 9, and w varies inversely with z.

This can be represented as:

w = k (1 /z)

where, k is the proportionality constant.

Substituting the value of w = 15 and z = 9 we have:

15 = k(1/9)

k = 15(9)

k = 135

Substituting the value of k and w = 5:

5 = 135(1/z)

z = 135/5

z = 27

Hence, the value of z is 27 when the value of w is 5.

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Answer:

Step-by-step explanation: To expand the algebraic expression using the distributive property, we distribute the 3 to each term inside the parentheses:

3(3d + 2) = 33d + 32

Simplifying, we get:

3(3d + 2) = 9d + 6

Therefore, the expanded form of the expression 3(3d+2) is 9d + 6.

Let w = x^3

Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6

In short: w^2 = x^6

The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2

Set this equal to zero and use the quadratic formula. We'll plug in

So,

[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]

If w = -2/3, then that rearranges to the following

w = -2/3

3w = -2

3w+2 = 0

This makes (3w+2) a factor of -3w^2+w+2

If w = 1, then it rearranges to w-1 = 0.

This makes (w-1) a factor of -3w^2+w+2

--------------------

To summarize the previous section, we found the factors of -3w^2+w+2 were:

It leads to (3w+2)(w-1)

We must stick a negative out front because the leading coefficient is negative.

Therefore, -3w^2+w+2 = -(3w+2)(w-1)

You can use the FOIL rule to confirm.

--------------------

Recall we made w = x^3

Let's replace each w with x^3

-(3w+2)(w-1)

-(3x^3+2)(x^3-1)

This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)

The next task is to factor x^3-1 using the difference of cubes factoring rule.

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)

x^3 - 1 = (x-1)(x^2 + x + 1)

--------------------

So,

2+x^3-3x^6

-3x^6 + x^3 + 2

-(3x^3+2)(x^3-1)

-(3x^3+2)(x-1)(x^2 + x + 1)

-(2 + 3x^3)(-(1-x))(1 + x + x^2)

(2 + 3x^3)(1 - x)(1 + x + x^2)

Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.

6 cups of dal may be used to make eight bowls of sambar.

The ratio can be defined as the number that can represent one quantity as a percentage of another. They can be compared only when the two numbers in a ratio have the same unit. Ratios are used to compare two objects.

Given, One bowl of sambar is made the use of 3/four cup dal.

If 1 bowl of sambar is made using 3/4 cup of dal, then the number of bowls of sambar that can be made from 6 cups of dal can be found by dividing 6 cups by 3/4 cup per bowl:

6 cups / (3/4 cup per bowl)

We can simplify by multiplying the numerator and denominator by the reciprocal of 3/4:

6 cups / (3/4 cup per bowl) * (4/3)

Simplifying, we get:

8 bowls

Therefore, 6 cups of dal can be used to make 8 bowls of sambar.

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Answer:

x = 40° , y = 43° , z = 97°

Step-by-step explanation:

∠ DAC = y = ∠ ACB = 43°

• opposite angles in a parallelogram are congruent , then

z = ∠ D = 97°

the sum of the 3 angles in Δ ACD = 180° , that is

x + y + 97° = 180°

x + 43° + 97° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

then

x = 40° , y = 43° , z = 97°

Answer:

3000 x 1.02^10 = 3656.98.. = 3656 people

The probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

To calculate the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb, we can use the complementary probability. That is, we can calculate the probability that a 23-watt bulb is obtained within the first 5 selections and then subtract this from 1 to get the probability that at least 6 bulbs must be examined.

The probability of obtaining a 23-watt bulb on the first selection is 1/50. If a 23-watt bulb is not obtained on the first selection, the probability of obtaining one on the second selection is 49/50 x 1/49 = 1/50.

Similarly, the probability of obtaining a 23-watt bulb on the third, fourth, or fifth selection is also 1/50.

Therefore, the probability of obtaining a 23-watt bulb within the first 5 selections is:

P(23-watt bulb in first 5 selections) = P(23-watt bulb on first selection) + P(23-watt bulb on second selection) + P(23-watt bulb on third selection) + P(23-watt bulb on fourth selection) + P(23-watt bulb on fifth selection)

= 1/50 + 1/50 + 1/50 + 1/50 + 1/50

= 1/10

The probability of needing to examine at least 6 bulbs before obtaining a 23-watt bulb is therefore:

P(need to examine at least 6 bulbs) = 1 - P(23-watt bulb in first 5 selections)

= 1 - 1/10

= 9/10

Therefore, the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

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According to the information, we can infer that the equation expressed by the parable symmetry axis is x = −b2a.

The symmetry axis of a parable is a term that refers to a vertical line that divides the parable into two congruent halves. The axis of symmetry always passes through the vertex of the parable.

To find the symmetry axis of this parable we must perform the following procedure taking into account the following information:

Additionally, we must compare the equation with y = ax2+bx+c to find the values of a, b, and c. Then these values would be like this:

According to the above, we can replace these values to solve the equation of axis of symmetry. then, the graph of a quadratic equation in the form Y = Ax2+Bx+C has ss its axis of symmetry the line X = −B2a.

Note: This Question is incomplete. Here is the complete information:

Attached Image

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Answer:Mike has $100. He wants to buy a bike that costs $75 and three speakers that cost $30 each. trade of is example of Opportunity cost

Step-by-step explanation:

Answer:

5 = $ 5.25.    10= $ 6.50.   20= $9.00

Step-by-step explanation:

if this is wrong you can completely write me a really rude email or message or something

The values for this problem are given as follows:

a) lim x -> 2^- f(x) = 3.

b) lim x -> 2^+ f(x) = 1.

c) lim x -> 2 f(x) is not defined.

d) f(2) = 3.

e) lim x -> 4 f(x) = 4.

f) f(4) is not defined.

To the left of x = 2, the graph of f(x) approaches x = 2 at y = 3, hence:

lim x -> 2^- f(x) = 3.

To the right of x = 2, the graph of f(x) approaches x = 2 at y = 1, hence:

lim x -> 2^+ f(x) = 1.

As the lateral limits are different, the limit of f(x) as x -> 2 is not defined.

Due to the closed circle, at x = 2, the function has a numeric value of f(2) = 3.

At x = 4, the graph of the function approaches x = 4 both left and right at y = 4, hence:

lim x -> 4 f(x) = 4.

Due to the open circle at x = 4, we have that f(4) is not defined.

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We do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

Probability is a method for assessing how likely something is to happen. Many occurrences cannot be foreseen with 100% accuracy. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

We cannot determine whether the probability of an adult being a full-time college student and 65 or older is nonzero based on the given information alone.

To see why, consider the following two scenarios:

Scenario 1: The proportion of adults who are both full-time college students and 65 or older is 0%.

In this case, the events "full-time college student" and "65 or older" are mutually exclusive. That is, no adult can be both a full-time college student and 65 or older. Therefore, P(full-time college student and 65 or older) = 0%.

Scenario 2: The proportion of adults who are both full-time college students and 65 or older is greater than 0%.

In this case, the events "full-time college student" and "65 or older" are not mutually exclusive. That is, there may be some adults who are both full-time college students and 65 or older. Therefore, P(full-time college student and 65 or older) is greater than 0%.

Since we do not have information about whether the two events are mutually exclusive or not, we cannot determine whether P(full-time college student and 65 or older) is nonzero.

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Answer:based on the student's work?A Each side of the equation, in one variable, can be found by isolating the x-variable of each equationin the s

Step-by-step explanation:

Chart that arranges all of the known elements in a particular order.

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation: [tex]x-2x = -4 - 3[/tex]

Combine like terms: [tex]-x = -4-3[/tex]

Calculate the sum or difference: [tex]-x = -7[/tex]

Divide both sides of the equation by the coefficient of variable: [tex]x = 7[/tex]

The ratio of people waiting in line for the slingshot is 2:21

A ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.

From the question, the total number of people is 15 + 4 + 12 + 11 = 42

The number of people waiting for slingshot is = 4

The ratio of slingshot waiting in line = 4/42

The ratio = 2:21

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The equation and solution to find the length of mis teak wood piece is x=3*8 and 24.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The length of oak wood=8inches

Teak wood= 3* oak wood

Now,

Let the length of teak wood be x

Then,

x=3*8

x=24

Therefore, by algebra the answer will be 24.

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The average from 1986 to 2000 was 46.250 million and circulation was closest to 46.250 in 1994.

What is the definition of average?

An average of a list of data is a mathematical expression for the centre value of a set of data. It is defined mathematically as the ratio of the sum of all the data to the number of units in the list. The average of 2, 3, and 4 equals (2+3+4)/3 = 9/3 = 3.

Average = Sum of Values divided by Number of Values

Now,

As  The newspaper circulation between 1986 and 2000 can be modeled as:

n(x)=0.00692x³-0.42x²+3.557x+51.588 million newspaper, where x is the number of years since 1980.

1. We will determine the circulation by finding x (subtracting 1980 from the said year) and substitute it in the formula.

n(6)=59.305, n(7)=59.281, n(8)=58.707, n(9)=57.626, n(10)=56.078, n(11)=54.106, n(12)=51.750, n(13)=49.052, n(14)=46.054, n(15)=42.798, n(16)=39.324, n(17)=35.675, n(18)=31.891, n(19)=28.015, n(20)=24.088

2. We will add the values: Sum of n=693.750

3. Average newspaper circulation=Sum of circulation each year/No of years

   Average=693.750/15=46.250

4. Compare each year circulation to the average.

   The circulation in 1994 i.e.,46.054 was closest to the average i.e.,46.250

As a result, the average newspaper circulation from 1986 to 2000 was 46.25 million. Additionally, the year with the closest average circulation from 1986 to 2000 was 1994.

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Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

In the first scenario where we have imperfect throwers, the probability that a ball lands in a particular bin is (1-pm)/n, where pm is the probability that the ball misses all the bins. The probability that a ball does not land in a particular bin after k throws is (1- (1-pm)/n)^k.

Let X_i be a random variable representing the number of throws required to fill the ith bin for the first time. We know that X_i follows a geometric distribution with probability of success p_i = (1-pm)/n.

The expected value of X_i is given by:

E[X_i] = 1/p_i = n/(n - (1-pm))

Now, let X be the random variable representing the number of throws required to fill all n bins for the first time. We want to find the expected value of X, denoted as E[X].

Since each bin is being filled independently, the number of throws required to fill all n bins is given by the maximum of the X_i. Therefore, we have:

X = max(X_1, X_2, ..., X_n)

Using the formula for the expected value of the maximum of n independent and identically distributed random variables, we can write:

E[X] = n * E[X_i] - (n-1) * E[X_i, X_j]

where E[X_i, X_j] is the expected value of the minimum of X_i and X_j.

Since the X_i are identically distributed, we have E[X_i, X_j] = E[X_i]^2.

Substituting the value of E[X_i] in the above equation, we get:

E[X] = n * (n / (n - (1-pm))) - (n-1) * (n / (n - (1-pm)))^2

This is the expected number of throws required to fill each bin at least once, accounting for the probability that the balls may miss all bins with probability pm.

Therefore, Simplifying this expression, we get: E[X] = n * (1 + (1-pm)/(n-1)) * H_{n-1} where H_{n-1} is the (n-1)th harmonic number.

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Answer: el enunciado cinco veces la diferencia de un numero y 3 es 17

Step-by-step explanation:

Answer:

ATQ, 5( x -3 ) = 17

5 x - 15 = 17

5x = 17 + 15

x = 32 /5

x = 6.4 ,