x^2-3x-40=0 solve for x

Answer:

To factor 4x³-10x²-14x, we can first factor out the greatest common factor, which is 2x:

4x³-10x²-14x = 2x(2x² - 5x - 7)

Next, we can factor the quadratic expression 2x² - 5x - 7 using either factoring by grouping, completing the square, or the quadratic formula. Here, we'll use factoring by grouping:

2x² - 5x - 7 = 2x² - 7x + 2x - 7

= (2x² - 7x) + (2x - 7)

= x(2x - 7) + (2x - 7)

= (2x - 7)(x + 1)

Therefore, the factored form of 4x³-10x²-14x is:

4x³-10x²-14x = 2x(2x - 7)(x + 1)

The equation of the line is y = -3x + 4.

The equation of a line can be represented in slope intercept form as follows:

y - mx + b

where

Hence, using (1, 1) and (0, 4)

Therefore,

m = 4 - 1 / 0 - 1

m = 3 / -1

m = -3

Hence, the y-intercept of the line is as follows:

y = -3x + b

4 = -3(0) + b

b = 4

Therefore, the equation of the line is y = -3x + 4

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The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol “%” and is used to compare values or express change. It can be used to compare two or more numbers, to show how much one number is a percentage of another, or to indicate the rate of change. In mathematics, percentages are often used to compare the size of one number to the size of another number.

The bar chart shows that the percentage of people who responded “yes” to listening to audiobooks increases with age. Only 18% of people aged 18-24 said they listen to audiobooks, while 30% of people aged 25-34 and 44% of people aged 35-44 responded positively. The percentage continues to increase with age, with the highest percentage of people aged 45-54 saying they listen to audiobooks (54%).
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).

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No, since the ratios do not constitute a whole. Option(a) is the required response to the posed query.

A collection of categorical data can be summarised using a bar chart, and continuous data can be made categorical using auto-binning. The bar chart uses several bars to show data, with each bar denoting a distinct category.

A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarise a collection of nominal data. This kind of chart consists of a circle with numerous parts. A specific group is represented by each segment. A pie chart is useful for organising and displaying data by proportion of the total.

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The rest of the question is,

Would it be appropriate to display the data with a pie chart?

a). No, because the proportions are not parts of a whole.

b). No, because the data categories are too broad.

c). Yes, because the data are grouped into categories.

d). Yes, because the data can be represented by a relative frequency compared to the whole.

Answer:

6y

Step-by-step explanation:

because if u divde

Answer:

 (2,0). First use a graphing calculator called demos. graph the y=5x-10

Once you graph the equation. Look for the cooordinates of the graph. One the coordinates are 2,0

Step-by-step explanation: Hope this helps!! Mark me brainliest!! Have a great spring break!! :))

Answer:

2/3 is the answer .......mmm..

Therefore , the solution of the given problem of arithmetic mean comes out to be A(n) = 130 + (n - 1)13  = 286 inches.

The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.

Here,

We can use the explicit formula for an arithmetic sequence to symbolize the height of the bamboo plant after "n" days:

=> A(n) = a + (n - 1)d

Therefore, the following explicit method can be used to determine the height of the bamboo plant after "n" days:

=> A(n) = 130 + (n - 1)13

Adding "n = 13" to the calculation will yield the height of the bamboo plant after 13 days:

=> A(13) = 130 + (13 - 1)13

=> A(13) = 130 + 12(13)

=> A(13) = 286

As a result, the bamboo growth will reach a height of 286 inches after 13 days.

The right response is thus:

=> A(n) = 130 + (n - 1)13 , or 286 inches.

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Answer:

In a circle, an exterior angle is formed when a side of a triangle is extended. The measure of the exterior angle is equal to the sum of the measures of the two intercepted arcs.

Let x be the measure of the exterior angle. Then we have:

x = 84° + 108°

x = 192°

Therefore, the measure of the exterior angle is 192°.

Answer:

a. After 10 minutes of hiking, Kiran will have covered a distance of:

distance = rate × time

distance = 0.04 mile/min × 10 min

distance = 0.4 mile

So, his remaining distance on the trail will be:

remaining distance = total distance - covered distance

remaining distance = 1.8 mile - 0.4 mile

remaining distance = 1.4 miles

Therefore, Kiran's remaining distance on the trail after 10 minutes of hiking is 1.4 miles.

b. We can use the same formula to find out how far Kiran will have walked after a certain amount of time:

distance = rate × time

We know that Kiran walks at a rate of 0.04 mile a minute, and we want to find out how much time it will take him to cover the remaining distance of 0.2 mile. So we can rearrange the formula to solve for time:

time = distance / rate

time = 0.2 mile / 0.04 mile/min

time = 5 minutes

Therefore, Kiran will have 0.2 mile left on the trail after 5 minutes of walking.

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Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

The elements of the sequence that are divisible by 5 occur every third term, while the elements divisible by 13 occur every fourth term. There are no elements of the sequence that are divisible by 65, since there are no elements that are divisible by both 5 and 13.

To find which elements of the sequence are divisible by 5, we need to find the remainder of each element when divided by 5. Using the first few terms of the sequence, we get:

a₁ = -1, a₂ = 0, a₃ = 5, a₄ = 13, a₅ = 29, a₆ = 61, a₇ = 125, a₈ = 253, ...

To check if an element is divisible by 5, we only need to look at the units digit of the number, since any multiple of 5 ends in 5 or 0. From the sequence, we can see that the units digit of a₃ is 5, so a₃ is divisible by 5. To find any other elements that are divisible by 5, we can look for a pattern in the units digits of the terms. We can see that the units digits of the terms cycle through 5, 3, 1, and 9. Since 5 appears in the cycle, every third term of the sequence will be divisible by 5. Therefore, the only elements of the sequence that are divisible by 5 are a₃, a₆, a₉, a₁₂, and so on.

To find which elements of the sequence are divisible by 13, we can use a similar approach. We need to find the remainder of each element when divided by 13. From the sequence, we can see that the units digit of a₄ is 3, so a₄ is not divisible by 13. To find any other elements that are divisible by 13, we can look for a pattern in the remainders of the terms. We can see that the remainders cycle through 3, 8, 6, and 10. Since 10 appears in the cycle, every fourth term of the sequence will be divisible by 13. Therefore, the only elements of the sequence that are divisible by 13 are a₄, a₈, a₁₂, a₁₆, and so on.

To find if any elements of the sequence are divisible by 65=5.13, we need to find elements that are divisible by both 5 and 13. From our analysis above, we can see that a₃ is the only element of the sequence that is divisible by 5, and a₄ is the only element that is divisible by 13. Therefore, there are no elements of the sequence that are divisible by 65, since the only way a number can be divisible by 65 is if it is divisible by both 5 and 13.

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Complete question:

Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5? What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?​

Answer:

216.8

Step-by-step explanation:

Pi times 13-Pi times 100

Answer: x= 71

Step-by-step explanation:

Since each triangle has a sun of all the angles to equal 180, we can figure what is X.

If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.

To solve this problem, we can use the formula for the surface area of a pyramid:

Surface area = base area + (1/2) x perimeter of base x slant height

First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:

Area = (square root of 3) / 4 x (side length)^2

Substituting the given values, we get:

Area = (square root of 3) / 4 x 9^2

Area = (square root of 3) x 20.25

Area = 11.06 (rounded to two decimal places)

Next, we need to find the perimeter of the base, which is simply 3 times the side length:

Perimeter = 3 x 9

Perimeter = 27

Finally, we can use the given slant height to find the surface area:

Surface area = 11.06 + (1/2) x 27 x 8.1

Surface area = 11.06 + 109.35

Surface area = 120.41 square feet (rounded to two decimal places)

Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.

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Cinderella would weigh either 187 or 153 pounds this morning.

Unit cοnversiοn is the prοcess οf cοnverting a quantity expressed in οne unit οf measurement tο anοther equivalent quantity expressed in a different unit οf measurement. It invοlves using cοnversiοn factοrs that relate the twο units οf measurement. This is dοne by multiplying οr dividing the οriginal quantity by a cοnversiοn factοr, which is a ratiο οf the twο units οf measurement that is equal tο οne.

Cinderella's weight increased or decreased by 10%, we can find her weight this morning by multiplying her previous weight by 1.10 (to find a 10% increase) or 0.90 (to find a 10% decrease).

For a 10% increase, Cinderella's weight this morning would be:

170 x 1.10 = 187 pounds

For a 10% decrease, Cinderella's weight this morning would be:

170 x 0.90 = 153 pounds

So depending on whether her weight increased or decreased by 10%, Cinderella would weigh either 187 or 153 pounds this morning.

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The answer would be  a) With Replacement 16,807 points will be in the sample space if batteries are selected.

The sample space with replacement would be 7^5 = 16,807 points. This means that when selecting five batteries from a bag of seven with replacement, the total number of points would be 16,807. This is because each of the five batteries could potentially be from the same brand, so the sample space would include all 16,807 possibilities of the combination of 5 batteries from the 7 available.

B) Without Replacement: The sample space without replacement would be 7P5 = 21,053 points. This means that when selecting five batteries from a bag of seven without replacement, the total number of points would be 21,053. This is because each of the five batteries must be from a different brand, so the sample space would include all 21,053 possibilities of the combination of 5 batteries from the 7 available.

In conclusion, the sample space would have more points if the batteries are selected without replacement compared to when the batteries are selected with replacement. This is because when batteries are selected without replacement, each of the five batteries must be from a different brand, whereas when batteries are selected with replacement, the same brand could be chosen multiple times.

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Option B) H o: p = 0.5, H₁: p ≠ 0.5. This is a two-tailed test where the null hypothesis states that the proportion of people in the town who like chocolate ice cream is equal to the national average of 0.5.

The alternative hypothesis states that the proportion is either greater than or less than 0.5. This test is appropriate because it is comparing a single proportion (people in the town who like chocolate ice cream) to a known population proportion (the national average). The test statistic used would be a z-score, calculated using the sample proportion and the population proportion.

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Complete question is in the image attached below

Diameter = 16 mm

Radius = Diameter/2

= 16/2

= 8 mm

Total height of figure = 32 mm

Height of cylinder = 19 mm

Height of cone = 32 - 19

= 13 mm

Volume of cylinder = πr²h

Substituting the values of r and h in above formula,,

[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]

Hence, Volume of cylinder is 3820.17 mm³

Now,

Volume of cone = 1/3 πr²h

[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]

Hence, Volume of the cone is 871.26 mm³

Volume of composite figure = Volume of cylinder + Volume of cone.

= 3820.17 + 871.26

= 4691.43 mm³

Therefore, Volume of the composite figure is 4691.43 mm³.

As a result, the carer will deliver 0.38 mL of methylprednisolone.

Milliliter is what the ml stands for. When pronouncing the characters aloud, the word ml is usually pronounced millilitre. It's good to keep this in mind. Simply imagine to yourself, "l = liquid," whenever you see the small "l".

To determine how many milliliters of methylprednisolone injection the nurse will administer, we need to know the concentration of the medication. Let's assume the concentration is 40 mg/mL.

We can use the following formula to calculate the amount to administer:

Amount (mL) = Dose (mg) / Concentration (mg/mL)

Plugging in the values from the order, we get:

Amount (mL) = 15 mg / 40 mg/mL

Amount (mL) = 0.375 mL

Rounding the answer to the nearest hundredth gives us:

Amount (mL) = 0.38 mL

Therefore, the nurse will administer 0.38 mL of methylprednisolone injection.

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Answer:

Step-by-step explanation:

It is possible if your friend has a bigger glass than you.

(a) Probability that both numbers are odd = 0.4932

(b) Probability that both numbers are less than 12 = 0.4545

(c) Probability that the same number is chosen twice = 1/60

(a) To find the probability that both numbers are odd, we need to count the number of ways to choose two odd numbers between 1 and 60, and divide by the total number of possible outcomes.

There are 30 odd numbers between 1 and 60, so there are 30 choices for the first number and 29 choices for the second number (since the two numbers can be the same). The total number of possible outcomes is 60 choose 2, which is

60 choose 2 = (60 × 59) / 2 = 1770

So the probability that both numbers are odd is

(30 × 29) / 1770 = 0.4932

(b) To find the probability that both numbers are less than 12, we need to count the number of ways to choose two numbers between 1 and 11, and divide by the total number of possible outcomes.

There are 11 choices for each number, so there are 11 × 11 = 121 possible outcomes. The number of ways to choose two numbers less than 12 is

11 choose 2 = (11 × 10) / 2 = 55

So the probability that both numbers are less than 12 is

55 / 121 = 0.4545

(c) To find the probability that the same number is chosen twice, we need to count the number of ways to choose a number, and then multiply by the probability that the same number is chosen again.

There are 60 choices for the first number, and only 1 choice for the second number if we want it to be the same as the first. So the probability that the same number is chosen twice is

1/60

So the probability that the same number is chosen twice is

(1/60) × 60 = 1/60

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The density of the textbook which is in the rectangular prism with dimensions is 0.0738 grams per cubic centimeter.

Define density.

Density is the mass of a component per unit volume.

       →d = M/V,

where d is density, M is mass, and V is volume, is the expression for density. Grams per cubic centimeter are a standard unit of measurement for density.

 The volume of a component = length*breadth*height

Given:

length = 16cm; breadth = 10cm; height = 5cm; Mass = 59grams

The volume of the book = 16 * 10 * 5

                                         = 800 cm³

The density of the textbook = Mass/volume

                                               = 59/800

                                  Density = 0.07375 g/cm³

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The least upper bound of the elements {8, 12} under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.

To find the least upper bound of a set of elements under a relation, we look for the smallest element in the set that is greater than or equal to all of the elements in the set.

Under the divisibility relation, an element a is said to be divisible by an element b (written as b divides a) if a is a multiple of b, that is, a = b * k for some integer k. For example, 8 divides 24 because 24 = 8 * 3.

We want to find the least upper bound of the elements {8, 12} under this relation on the set {1, 2, 3, 6, 8, 12, 24, 36}. That means we want to find the smallest element in the set that is a multiple of both 8 and 12.

We can list the multiples of 8 and 12 in the set as follows:

Multiples of 8: 8, 24

Multiples of 12: 12, 24, 36

We can see that the smallest element in the set that is a multiple of both 8 and 12 is 24.

Therefore, the least upper bound under the divisibility relation on the set {1, 2, 3, 6, 8, 12, 24, 36} is 24.

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The function f(x) has a decreasing end behaviour on the right when its leading coefficient is negative and its degree is greater than or equal to 2.

This means that the terms in the function must be decreasing from left to right and the last term must be negative. To illustrate, an example of a function with a decreasing end behaviour on the right could be

f(x) = -2x2 + 3x + 4.

The leading coefficient is -2, which is negative, and the degree is 2, which is greater than or equal to 2. The terms decrease from left to right, and the last term is negative, which both fulfil the requirements for the function to have a decreasing end behaviour on the right.

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The factors that could be part of the function so that the function has a decreasing end behavior on the right are as follows: - A negative coefficient of the highest degree term.

- An odd degree of the highest degree term and a negative coefficient.
- An even degree of the highest degree term and a negative coefficient.
Explanation:
A function's end behavior refers to what happens to the function's values as x approaches positive or negative infinity. A function's end behavior is said to be decreasing if the values of the function decrease as x approaches infinity, and increasing if the values of the function increase as x approaches infinity.
There are three cases when the function has a decreasing end behavior on the right:

1. If the highest degree term has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -2x³ - 4x² + 3x + 6 will have a decreasing end behavior on the right.
2. If the highest degree term is odd and has a negative coefficient, the function will have a decreasing end behavior on the right.

For example, the function f(x) = -x⁵ + 2x³ - x will have a decreasing end behavior on the right.
3. If the highest degree term is even and has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -4x⁶ + 3x⁴ - 2x² + 1 will have a decreasing end behavior on the right.

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Answer:

11.52 feet

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.

We can rearrange the formula to solve for the radius:

r = (3V/4π)^(1/3)

Substituting the given volume V = 7,234.56 ft³, we get:

r = (3(7,234.56)/(4π))^(1/3) ≈ 11.52 ft

Therefore, the radius of the sphere is approximately 11.52 feet.

Hence, the likelihood is 11/80, or roughly 0.138 as the player represented Spain, the likelihood that a randomly chosen athlete.

The likelihood or chance of an event occurring is measured by probability. It is a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. By dividing the number of favorable outcomes by the total number of possible outcomes, one can determine the probability of an occurring. Because there is only one desirable result (rolling a 3) out of six potential outcomes, the probability of rolling a 3 when using a fair six-sided die is 1/6. (rolling a 1, 2, 3, 4, 5, or 6).

given

The number of gold, silver, and bronze medals each player from each nation has earned is displayed in the table.

We need to utilize conditional probability to determine the likelihood that a randomly chosen player won a bronze medal provided that the player represented Spain.

The following formula determines the conditional probability of an event B given an event A:

P(A and B) = P(B|A) (A)

where P(A) is the likelihood that event A will occur and P(A and B) is the likelihood that events A and B will both occur.

In this instance, event A was the player representing Spain, and event B was the bronze medal the player took home.

The table reveals that 11 bronze medals were won by Spanish athletes. Moreover, the total number of medals won by Spanish athletes is:

20 + 18 + 42 = 80

Hence, given that the player represented Spain, the likelihood that a randomly chosen athlete would have earned a bronze medal is:

P(B|A) = 11/80

Hence, the likelihood is 11/80, or roughly 0.138 as the player represented Spain, the likelihood that a randomly chosen athlete.

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There would be a problem with taking readings from the right side of a sphere if the diameters of the spheres were different because the right side of a sphere is not a fixed point, but rather a relative term.

If the diameters of two spheres were different, the right side of one sphere would not be the same as the right side of the other sphere. This means that taking readings from the right side of each sphere would not be a fair comparison, as the points being measured are not equivalent.

For example, imagine two spheres with diameters of 5cm and 10cm, respectively. If we were to take readings from the right side of each sphere, we would be measuring points at different distances from the center of each sphere. This would result in inaccurate measurements and an unfair comparison.

To avoid this problem, it is important to define a consistent point of measurement on each sphere that is equivalent, regardless of the diameter. For example, measuring from the center of each sphere would provide a consistent and fair comparison.

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If 7 cards are dealt from an ordinary deck of 52 playing cards, the probability that (a) exactly 2 of them will be face cards is 0.3601. and  (b) at least 1 of them will be a queen is 0.0008.

A) The probability that exactly 2 of the 7 cards dealt from an ordinary deck of 52 playing cards will be face cards is as follows:

      We need to use the formula for probability here. The probability formula is given by,

       Probability = Number of favorable outcomes/ Total number of possible outcomes.

The total number of possible outcomes = Number of ways 7 cards can be selected from 52 =  ₅₂C₇

A number of favorable outcomes = Number of ways 2 face cards can be selected from 12 face cards * Number of ways 5 nonface cards can be selected from 40 non-face cards

                                                      = ₁₂C₂ * ₄₀C₅

      Putting these values in the formula,

      Probability =  ₁₂C₂ * ₄₀C₅ / ₅₂C₇.

      Simplifying this gives Probability = 0.3601. (Rounded to four decimal places)

b) The probability that at least 1 of the 7 cards dealt from an ordinary deck of 52 playing cards will be a queen is as follows:

         Here, we can use the complement rule. i.e. we can calculate the probability of none of the 7 cards being a queen and subtract that from

  1. Total number of possible outcomes = Number of ways 7 cards can be selected from

                                                           52  =  ₅₂C₇

Number of favorable outcomes = Number of ways 7 non-queen cards can be selected from 48 non-queen cards = ₄₈C₇

Putting these values in the formula,

      The Probability of none of the cards being a queen = ₄₈C₇ / ₅₂C₇

Therefore, the Probability of at least 1 of the 7 cards being a queen

                     = 1 - ₄₈C₇ / ₅₂C₇ Probability of at least 1 queen

                     = 1 - 0.9992

                     = 0.0008 (rounded to four decimal places).

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Answer:

x = 118.5°

Step-by-step explanation:

the measure of the chord- chord angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

x = [tex]\frac{1}{2}[/tex] (27 + 210)° = [tex]\frac{1}{2}[/tex] × 237° = 118.5°

The value of x in the given circle by secant lines is 118.5 degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

A straight line that intersects a circle in two points is called a secant line

A chord is in a unique secant line and every secant line defines a unique chord.

The measure of the angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle

x=1/2(210+27)

x=1/2(237)

Divide two hundred thirty seven by two

x=118.5

Hence, the value of x in the given circle by secant lines is 118.5 degrees.

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The probability of spotting 3 imperfections plates in 3 minutes is .3352.

The probability of spotting 3 imperfections plates in 3 minutes can be calculated using the binomial probability formula. This formula is used to calculate the probability of getting a certain number of successes in a certain number of trials (n), given a certain probability of success (p) for each trial.

In this case, the probability of success (p) is .15 and the number of trials (n) is 3. The formula for this is:

[tex]P(X = 3) = 3C3(.15)^3(1-.15)^(3-3)[/tex]

P(X = 3) = .3352

Therefore, the probability of spotting 3 imperfections plates in 3 minutes is .3352.

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The probability that the ball that rolled out of the pit is red is 0.2 or 20%.

Now, let's apply this concept to Jose's ball pit problem. We know that Jose put 40 red balls, 55 purple balls, 45 yellow balls, and 60 green balls into the ball pit. The total number of balls in the pit is therefore:

Total number of balls = 40 + 55 + 45 + 60 = 200

Next, we know that one ball has rolled out of the pit. We want to find the probability that this ball is red. To do this, we need to calculate the probability of selecting a red ball from the total number of balls in the pit.

Probability of selecting a red ball = Number of red balls / Total number of balls

= 40 / 200

= 0.2 or 20%

This means that for every 10 balls that roll out of the pit, 2 of them are expected to be red.

To know more about probability here

https://brainly.com/question/11234923

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