Select all the angle relationships in △
△
ABC that are correct.

The distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

The the distance can be observed to be of the side of a right triangle with the hypotenuse as the radius of the circle and the base side half of the chord, if x is used to represent the distance of the chord from the centre of the circle.

so by Pythagoras rule we can write:

12² = x² + 8²

144 = x² + 64

x² = 144 - 64 {collect like terms}

x² = 80

x = √80 {take square root of both sides}

x = 8.9443

Therefore, the distance of the chord from the center of the circle is derived to be equal to √80 cm or 8.9 cm to the nearest tenth using the Pythagoras rule.

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The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.

To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.

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Common denominator of 5/12 and 3/8 is 24.

To rename 5/12 and 3/8 using a common denominator, we need to find the least common multiple (LCM) of the denominators 12 and 8, which is 24.

To convert 5/12 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 2 to get:

5/12 = (5 x 2)/(12 x 2) = 10/24

To convert 3/8 to an equivalent fraction with a denominator of 24, we can multiply both the numerator and denominator by 3 to get:

3/8 = (3 x 3)/(8 x 3) = 9/24

So, 5/12 and 3/8 can be renamed as 10/24 and 9/24, respectively, using a common denominator of 24.

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Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:

Cost = 2.5 kg x $1.50/kg

   = $3.75/kg x 2.5 kg

   = $9.38

So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.

Step-by-step explanation:

Answer:

r = 8

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

given a₁ = 3 and a₃ = 192 , then

a₁ = 3 → (1)

a₁r² = 192 → (2)

divide (2) by (1) on both sides

[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then

r² = 64 ( take square root of both sides )

r = [tex]\sqrt{64}[/tex] = 8

Answer:

83%

Step-by-step explanation:

To find the percentage divide 40 by 48

40/48 = 0.83333333333333

Round to 0.83

Multiply by 100

The patient has only eaten 83% of her daily intake.

The p-value of the test statistic is 0.0401, which is less than the commonly used significance level of 0.05.

In statistical analysis, hypothesis testing is an essential method used to make inferences about population parameters using sample data. In this case, a hospital director wants to test a claim that the percentage of insured patients is less than the expected percentage.

The alternative hypothesis is that the percentage of insured patients is less than the expected percentage. To test this hypothesis, the director will use a one-tailed z-test for proportions. The test statistic is calculated as:

z = (p - P) / √(P(1-P) / n)

where p is the sample proportion, P is the expected proportion under the null hypothesis, and n is the sample size.

In this case, the sample proportion is 115/230 = 0.5, and the expected proportion is not specified. However, since the null hypothesis is that the percentage of insured patients is equal to the expected percentage, we can use the observed percentage of 55% as a reasonable estimate of the expected percentage. Thus, P = 0.55.

Plugging in these values, we get:

z = (0.5 - 0.55) / √(0.55 * 0.45 / 230) = -1.74

p-value = -1.74/0.069 = 0.0401

Trough this one we have identified that the test statistic's p-value is 0.0401, indicating that it is below the widely accepted significance level of 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

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The height of the rectangle must be greater than 4 inches if the perimeter of the rectangle is greater than 30 inches.

In geometry, a rectangle is a quadrilateral with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the total distance around it.

Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.

Now, we can calculate the perimeter of the rectangle using the formula:

Perimeter = 2(length + width)

In a rectangle, the length and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:

Perimeter = 2(x + (x + 7)) = 4x + 14

As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the inequality:

4x + 14 > 30

Solving for x, we get:

4x > 16

x > 4

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The given statement about the disjunction is true.

A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.

Given is the statement -

(S~T) v (~U.W)

The given statement about the disjunction is true.

Therefore, the given statement about the disjunction is true.

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The measures of angles of a rhombus are ∠KNL = 90° , ∠KJL = 50° , ∠MLK = 100° and ∠JKM = 40°

A Rhombus has four sides of the same length, its perimeter can be determined using the formula Perimeter = 4a, where "a" stands for the side's length.

When the two diagonals of a rhombus are known,

The perimeter = 2√p² + q²

where 'p' and 'q' are the diagonals.

Given data ,

Let the rhombus be represented as JKLM

where MK and JL are the diagonals and N is the midpoint of intersection

The measure of MK = 24

The measure of JL = 20

The measure of NK = 12

The measure of ∠MJL = 50°

Now , the diagonals of a rhombus bisect each other , so

NK = MK/2 = 12

And , NL = JL / 2 = 10

Now , to calculate the measure of ML ,

In triangle MNL, ∠N = 90°

MN = NK = 12 , NL = 10

Using Pythagorean theorem of triangles , we get

ML² = MN² + NL²

ML² = 12² + 10²

ML² = 244

ML = √244

On simplifying the equation , we get

ML = 2√61 = 15.62

The measure of ML = measure of JM = 15.62 ( all sides are equal )

The measure of ∠KNL = 90° ( diagonals of a rhombus are perpendicular bisectors )

∠KJL = ∠MJL (diagonals bisect angles)

The measure of ∠KJL = 50°

∠MJK = ∠KJL + ∠MJL = 50 + 50 = 100°

∠MJK = ∠MLK (opposite angles are equal)

The measure of ∠MLK = 100°

∠NJK + ∠JNK + ∠JKM = 180° (sum of angles in triangle)

50 + 90 + ∠JKM = 180

The measure of ∠JKM = 40°

∠JKL = 2 x ∠JKM (diagonal bisect angle)

The measure of ∠JKL = 2 x 40

The measure of ∠JKL = 80°

∠JKL = ∠JML (opposite angles are equal)

The measure of ∠JML = 80°

Hence , the measures of rhombus is solved

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The value of $×$ is 3.14 units

Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

The perimeter of a square is expressed as 4l

The circumference of a circle = 2πr

This means that;

4l = 2πr

4l = 2× 3.142 × 2

4l = 12.57

divide both sides by 4

l = 12.57/4

l = 3.14 units(nearest hundredth)

therefore the value of the side length is 3.14 units

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To get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if a student spends no time on homework is 55.

What is meant by a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."

It is given that y = 7.2x + 55

where y is the expected quiz score.

x is the number of hours spent on homework that week.

If the value of y=77

77=7.2x+55

22=7.2x

x is approximately 3 hrs.

If the student spends no time on their homework:

x=0

y=0+55

y=55.

Therefore to get 77 marks on a quiz the student has to spend approximately 3 hrs.

The expected quiz score if the student spends no time on home work is 55.

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Answer:

x = 1/3

Step-by-step explanation:

64^2x+1 = 1024
4^3(2x+1) = 4^5

Since the bases are the same, two expressions are only equal if the exponents are also equal.

3 (2x + 1) = 5

Divided each term by 3

2x + 1 = 5/3

2x = 2/3

x = 1/3

The angle that completes the law of cosines is 62°.

Option D is the correct answer.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

The law of cosines in a triangle states that,

c² = a² + b² - 2ab cos C

Where c is the side opposite to ∠C.

Similarly,

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

Now,

289 + 64 - 272 cos __ = 15²

17² + 8² - 2 x 17 x 8 cos 62 = 15²

289 + 64 - 272 cos 62 = 15²

Thus,

The angle that completes the law of cosines is 62°.

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The complete question.

289 + 64 - 272 cos __ = 15²

The graplh shows that it will take 3.33 weeks to pay up the money borrowed

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = money borrowed from your parents =  $50.00

m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15

x = number of weeks

y = amount remaining

The equation is

y = 15x - 50

From the graph the pay will be completed at x = 3.33 (3.33, 0)

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The circumference of a circle is equal to 2π multiplied by its radius. Therefore, the circumference of a circle with a radius of 15 cm is equal to 2π multiplied by 15 cm, or 30π cm.

Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.

Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.

Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.

Reimbursement = miles driven x rate per mile

Filling the value in above equation.

So,

Reimbursement = 982 miles x $0.75/mile

Reimbursement = $736.50

Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.

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Bob needs to buy 500 kg of sand.

What is the ratio?

A ratio is a quantitative relationship between two numbers, quantities, or values that expresses how many times one is contained in the other. Ratios are typically expressed in the form of "a to b" or "a:b" and can be represented as fractions or decimals.

Since the ratio of cement to sand to stone is 1:2:3 by weight, the total weight of the ingredients needed to make one bag of dry concrete is:

Cement: 1/6 of 30 kg = 5 kg

Sand: 2/6 of 30 kg = 10 kg

Stone: 3/6 of 30 kg = 15 kg

To make 50 bags of dry concrete, Bob will need 50 times these amounts:

Cement: 5 kg x 50 = 250 kg

Sand: 10 kg x 50 = 500 kg

Stone: 15 kg x 50 = 750 kg

Hence, Bob needs to buy 500 kg of sand.

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Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.

Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.

Here, in this triangle by Pythagorean theorem

[tex]A^2 = B ^2 + c^2[/tex]

AC = [tex]\sqrt{14^2- 9^2}[/tex]

AC = [tex]\sqrt{196- 81}[/tex]

Ac = [tex]\sqrt{115}[/tex]

Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.

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The probability of the selected coin showing heads is 0.77, or 77%.

Probability is the measure of the likelihood of an event occurring. In this scenario, we have three coins in a box, each with different properties.

To calculate the probability of an event occurring, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are three possible coins we could select, each with a different probability of showing heads.

Now, we need to determine the total number of possible outcomes, which is simply the number of coins we have, which is three.

Next, we need to determine the number of favorable outcomes. For Coin 1, the probability of showing heads is 1 (since it has two heads). For Coin 2, the probability of showing heads is 0.5 (since it is a fair coin with equal probability of heads and tails). For Coin 3, the probability of showing heads is 0.8.

To calculate the probability of showing heads when we randomly select one of these coins, we need to weigh the probabilities of each coin being selected with their corresponding probabilities of showing heads.

Let's say that the probability of selecting each coin is equal (since we have no information to suggest otherwise). Then, the probability of selecting Coin 1 is 1/3, the probability of selecting Coin 2 is 1/3, and the probability of selecting Coin 3 is 1/3.

To calculate the overall probability of showing heads, we can use the following formula:

P(heads) = (P(Coin 1) * P(heads on Coin 1)) + (P(Coin 2) * P(heads on Coin 2)) + (P(Coin 3) * P(heads on Coin 3))

= (1/3 * 1) + (1/3 * 0.5) + (1/3 * 0.8)

= 0.77

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3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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Answer:

The angle is 180°

Step-by-step explanation:

[tex]{}[/tex]

Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer:

x= 39.549°

Step-by-step explanation:

please review answer.

a. The percentage of the department faculty have 5 or more years of service is 76%

b. Probability that a faculty member chosen at random has between 5 and 35 years of service is 0.4.

c. The probability the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.

The histogram is used to estimate probability of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.

(a) The per cent of the department faculty have 5 or more years of service is calculated as follows,

The number of department faculty have 5 or more years of service is 38 and total frequency 50, therefore the required probability is:

P(x > 5) = 38/50 = 0.76 = 76%

(b) The probability (in decimal form) of representative will have between 5 and 35 years of service is given as,

P(5 < X < 35) = 20/50 = 0.4 = 40%

(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of service is calculated as follows,

P(X < 5 | X < 15) = 28/40 = 0.7

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For complete question, see the figure.

Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.

We use the division of polynomials to find the quotients of two polynomials. Two polynomials can be divided by simply multiplying and dividing by the largest power in each term.

The two different ways to divide polynomials are 1. Long division method and 2. The synthetic division method. The synthetic division method is the quickest way to divide polynomials between these two approaches.

Advantages of performing a Synthetic Division:

Therefore,

We can say

Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.

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Answer:

To find out which rental car company is cheaper, you need to compare the cost for the same number of miles driven. Let's say you drive a total of "m" miles.

The cost for renting a car from Lou's Garage is 50 + 0.1m dollars.

The cost for renting a car from Jerry's Garage is 25 + 0.05m dollars.

To determine which option is cheaper, you need to compare these two expressions and find out which one is less. To do this, you can subtract the second expression from the first expression:

50 + 0.1m - (25 + 0.05m) = 25 + 0.05m

This equation shows that the cost of renting a car from Lou's Garage is 25 + 0.05m dollars more expensive than renting a car from Jerry's Garage for the same number of miles driven. Therefore, Jerry's Garage is the cheaper option.

Answer:

13.0898597466511 or 13.09

Step-by-step explanation:

Answer:

20×5=100

380-100=280

280÷120=2 and 40 remain

40÷20=2

Answer:

2,2 but i could be wrong

Just wanted to say he's correct, it's 2, 2