USING THE DRAWING BELOW IDENTIFY THE FIGURES REPRESENTED BY THE LETTERS,

A
B
C
E
D


​

The answer is D) 5/4.

To find the limit of the given function as x approaches 2, we can plug the value of 2 directly into the function. However, since the denominator of the function becomes 0 when x=2, we need to simplify the function first.

(x^2 + x - 6)/(x^2 - 4) can be factored as [(x+3)(x-2)]/[(x+2)(x-2)].

We can then cancel out the common factor of (x-2) in the numerator and denominator, leaving us with (x+3)/(x+2) as the simplified function.

Now, we can plug in the value of 2 into this simplified function:

limx→2 (x+3)/(x+2)

= (2+3)/(2+2)

= 5/4

Therefore, the answer is D) 5/4.

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The solution set of 6 ㏑ e = e ^ ㏑ 2x is 3

What is relation between Exponents and logarithms ?

Exponents and logarithms are inverse functions, you can use exponents to "undo" logarithms and use logarithms to "undo" logarithms. Exponents specify the number of times you must multiply a value, while logarithms specify which exponent to apply to obtain a certain value.

The given expression is,

6 ㏑ e = e ^ ㏑ 2x

we know, ㏑ (e) = 1 and e ^ ㏑(x)  = x

Put these values,

6 * 1 = 2x

Now, find x

6 = 2x

x = 3

Hence, the solution set of 6 ㏑ (e) = e ^ ㏑ (2x)  is 3

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The y-intercept of the equation is (0,6)

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. In English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics.

The given equation is 15x + 5y = 30

or, 5y = -15x + 30

or, y = -3x + 6

So, y-intercept of the equation is (0,6)

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Answer:

80.5

Step-by-step explanation:

True/False question cannot be answered with a "main answer". However, the archaeologists do believe that the cities of Sodom and Gomorrah were near the Dead Sea.

The location of Sodom and Gomorrah is a subject of debate among archaeologists and scholars. Some believe that they were located near the Dead Sea, while others propose different locations. However, the prevailing theory is that they were situated near the Dead Sea, which is a salt lake bordered by Jordan to the east and Israel and Palestine to the west.

The true/false question you have posed cannot be answered with a long answer as it is a binary question. However, if you want to know more about the archaeology and history of Sodom and Gomorrah, there is a wealth of information available online and in scholarly articles and books. The story of Sodom and Gomorrah is a biblical tale that recounts the destruction of two cities by God due to their wickedness. The story appears in both the Book of Genesis in the Hebrew Bible and in the Quran. Archaeological evidence suggests that there were settlements in the area of the Dead Sea around the time the story of Sodom and Gomorrah is said to have occurred, but there is no conclusive proof that these were the cities referred to in the Bible. Some scholars argue that the story is a myth, while others believe that there is a historical basis for it. Regardless of the veracity of the tale, the story of Sodom and Gomorrah has captured the imagination of people for centuries and continues to be a subject of scholarly inquiry.

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Let,

Now,

The probability is:

→ \(P(xq) = 0.35\times 0.15\)

             \(= 0.0525\)

→ \(P(yp) = (1-0.35)\times 0.85\)

             \(= 0.65\times 0.85\)

             \(= 0.5525\)

hence,

The likelihood that perhaps the factory's carbon emissions were well within the allowable range:

= \(\frac{0.5525}{(0.5525+0.0525)}\)

= \(\frac{0.5525}{0.605}\)

= \(0.9132\)

Thus the above response is right.

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Answer: 0.098%

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Using the property that the angle of a line is always 180°, we solved for x and found its value as -5.

What is a straight angle?

A straight angle in geometry is an angle with a vertex point that is at 180 degrees. In essence, it creates a straight line with sides that face away from the vertex. Essentially, two rays linked end to end create an angle according to the definition of angles in mathematics. As a result, where the rays are linked at endpoints, the two 180-degree angle rays are subtended in the opposite direction. A 180-degree is also seen as an addition. Because it measures 180 degrees, a straight angle differs from a straight line, which connects two points.

It is shown that there are two parallel lines. Another line cuts both parallel lines.

The sum of angles of a straight line is always 180°.

So the sum of angles (98+x)° and (x+92)° should be 180° as it is the angle of the first parallel line.

W can then solve for x.

98 + x + x + 92 = 180

190 + 2x = 180

2x  = 180 - 190 = -10

x = -10/5 = -5

Therefore using the property that the angle of a line is always 180°, we solved for x and found its value as -5.

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The probability of A1 occurring given B1 is approximately 0.375, rounded to three decimal places.

To find the probability of P(A1|B1), we can use Bayes' theorem:

P(A1|B1) = (P(B1|A1) * P(A1)) / P(B1)

Given that A1 and A2 are complements, P(A2) can be calculated as 1 - P(A1), which means P(A2) = 0.7.

We are given P(B1|A1) = 0.6 and P(B1|A2) = 0.5.

Now, to calculate P(B1), we can use the law of total probability:

P(B1) = P(B1|A1) * P(A1) + P(B1|A2) * P(A2)

Substituting the given values, we get:

P(B1) = (0.6 * 0.3) + (0.5 * 0.7)

= 0.18 + 0.35

= 0.53

Finally, we can calculate P(A1|B1) using Bayes' theorem:

P(A1|B1) = (P(B1|A1) * P(A1)) / P(B1)

= (0.6 * 0.3) / 0.53

≈ 0.375

Therefore, the probability of A1 occurring given B1 is approximately 0.375, rounded to three decimal places.

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Answer: 57285

Step-by-step explanation:   I can't show the work digitally but all you do is multiply.

Answer:

X = 24

Step-by-step explanation:

First you need to find the third angle for the farthest angle to the right (the big triangle), I'm going to label this angle as Y for now. Since all triangle angles = to 180 we can do 94 + 41 + Y = 180 We will find x as 45. Now we have to plug it in. 45 + 111 + x = 180. 156 + x = 180. X = 24

Hope this helps!!!

Answer:

24°

Step-by-step explanation:

180° - 41° - 94° = 45°

180° - 111° - 45° = 24°

Answer:

6.4% of the lights are faulty

Step-by-step explanation:

Well you can make a proportion out of this question.
so lets do faulty/total

16/250 = x/ 100

Since x/100 is basically finding the percent since percent means out of a hundred.

Cross multiply to solve.

250x= 1600

SOlve for x

X=6.4

6.4 percent of the lights are faulty.

Answer:

M = 1

Step-by-step explanation:

Based on the information given regarding the trips taken by the boat, the speed of the current is determined as: approximately 6.94 miles per hour.

Upstream trip:

Distance = Speed * Time

Distance = (14 - c) * 0.95 miles

Downstream trip:

Distance = Speed * Time

Distance = (14 + c) * 0.32 miles

Equating the distances:

(14 - c) * 0.95 = (14 + c) * 0.32

Expanding the equation:

13.3 - 0.95c = 4.48 + 0.32c

Rearranging the equation:

0.95c + 0.32c = 13.3 - 4.48

Combining like terms:

1.27c = 8.82

Solving for 'c':

c = 8.82 / 1.27

Calculating the value of 'c':

c ≈ 6.94

Therefore, the speed of the current is approximately 6.94 miles per hour.

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Answer:

Step-by-step explanation:

<A and <B are corresponding angles

< A = < B

plugging the values

\(7x + 24 = 3x + 92\)

Move variable to L.H.S and change its sign

\(7x - 3x + 24 = 92\)

Move constant to R.H.S and change its sign

\(7x - 3x = 92 - 24\)

Calculate

\(4x = 68\)

Divide both sides of the equation by 4

\( \frac{4x}{4} = \frac{68}{4} \)

Calculate

\(x = 17\)

Replacing value

<A = \(7x + 24\)

\( = 7 \times 17 + 24\)

\( = 119 + 24\)

\( = 143\)

hope this helps...

Answer:

You would eliminate Y

Step-by-step explanation:

Options aren't avaible

Answer:

(1 ÷ 1/6) * 6

36 pieces of pizza

Step-by-step explanation:

Given that :

Number of pizzas ordered = 6

Divisions per pizza = 1/6 ;

Hence, 1 full pizza is divided into 1 ÷ 1/6 = 1 * 6/1 = 6 pieces

6 * 1/6(1)

The total pieces of pizzas equals :

6 pieces per pizza * number of pizzas

6 * 6

= 36 pieces of pizza

The expression which represents the number of miles Mary rode in 5 days is 5*(2 + 2).

A fraction represented with its quotient and remainder is a mixed fraction.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

According to the given question.

Distance between Mary's house and school = \(1\frac{3}{4} =\frac{7}{4}\)

Number of days Mary rode her bicycle to school and back = 5

⇒ Distance travelled by Mary in one day = \(2(\frac{7}{4} )=\frac{7}{2}\)

Therefore, the expression which represents the number of miles she rode in 5 days = \(5(\frac{7}{2} )=\frac{35}{2}=17.5 miles\) ≈ 20 miles

Hence, the expression which represents the number of miles Mary rode in 5 days is \(5\) *(2+2).

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Cumulative Frequency is used to calculate a class's relative frequency.

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its forerunners.. Since all frequencies have already been added to the prior total, the final value will always be equal to the sum of all observations.

What is Relative frequency?

The ratio of the total number of outcomes in an experiment, also known as the number of trials, to the number of times an event occurs is called relative frequency.

Each class's "relative frequency" refers to the percentage of the data that belongs to that class. For a set of data of size n, it can be calculated by: Class frequency equals relative frequency Sample size equals f n. The frequencies of that class and all prior classes are added together to form the "cumulative frequency."

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Answer:

nice

Step-by-step explanation:

Answer:

Ok..kid..I mean yeh.

Step-by-step explanation:

btw wassup

Ik you but you don't know me lol..

I'm not a stalker ok..soooo..don't worry

The probability of a patient scoring above 192 on the endurance test is approximately 40.90%. A patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability that a patient will score above 192, we need to use the Z-score formula. The Z-score measures the number of standard deviations a data point is from the mean. In this case, the formula is Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

First, calculate the Z-score: Z = (192 - 185) / 30 = 7/30 ≈ 0.23.

Next, we need to find the probability of scoring above this Z-score. Using a Z-table or a calculator, we find that the probability is approximately 0.4090, or 40.90%.

b. To find the score that corresponds to the 80th percentile, we need to find the Z-score that has an area of 0.80 to the left. Using the Z-table or a calculator, we find that the Z-score is approximately 0.84.

Now, we can use the Z-score formula to find the corresponding score: X = Z * σ + μ. Plugging in the values, we get X = 0.84 * 30 + 185 = 208.2.

Therefore, a patient at the 80th percentile receives a score of approximately 208.2.

a. To find the probability of a patient scoring above 192 on the endurance test, we first calculate the Z-score. This allows us to standardize the score by measuring how many standard deviations it is from the mean. We then use a Z-table or calculator to find the probability corresponding to this Z-score, which is approximately 0.4090 or 40.90%.

b. To find the score at the 80th percentile, we first need to find the Z-score that corresponds to an area of 0.80 to the left. Using a Z-table or calculator, we find this Z-score to be approximately 0.84. We then use the Z-score formula to find the corresponding score, which is approximately 208.2.

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Let 185lb equate to 100%

20lb of fat will be ?

= 10.81%

Dave has 10.81% of body fat and it falls at the athlete category.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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To find the equation of the tangent line to the curve x^2+6xy+12y^2=28 at point (2,1), we need to find the slope of the tangent line at that point using implicit differentiation. After finding the derivative, we substitute the values of x and y from the given point to get the slope. Then, we use the point-slope formula to find the equation of the tangent line.

The first step is to take the derivative of the equation using the chain rule and product rule, which yields:

2x+6y+6xy'+24yy'=0

Next, we substitute x=2 and y=1 to get the slope of the tangent line at point (2,1):

2(2)+6(1)+6(2)y'+24(1)(y')=0

Solving for y', we get:

y'=-2/9

This is the slope of the tangent line at point (2,1). Finally, we use the point-slope formula to find the equation of the tangent line:

y-1=(-2/9)(x-2)

The equation of the tangent line to the curve x^2+6xy+12y^2=28 at point (2,1) is y-1=(-2/9)(x-2).

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The awnser is number 3,4,and 6 hope this helps

Answer:

346

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Subtract 200 from 180

200 - 180 = 20

2. Divide the difference of the number of bookmarks by last years

20 / 200 = 0.1

3. Multiply 0.1 by 100 to get the percentage

0.1 x 100 = 10 %

4. Since this is a reduction in number of bookmarks sold, then it would be a -10% change in the number of bookmarks sold.

From the z-score calculated which is 1.94, we reject the null hypothesis and accept the alternative hypothesis.

To determine the value of the standardized test statistic and make decisions for the hypothesis test, we need to perform the following steps:

Step 1: State the null and alternative hypotheses:

H₀: μ = 1040 (Null Hypothesis)

H₁: μ > 1040 (Alternative Hypothesis)

Step 2: Calculate the standardized test statistic:

The standardized test statistic, also known as the z-score, is given by:

z = (x - μ) / (σ / √n)

Where:

Plugging in the values, we have:

z = (1084.1 - 1040) / (210 / √85) = 1.94

The value of the standardized test statistic is approximately 1.94.

Step 3: Determine the rejection region:

Since the alternative hypothesis is one-tailed (μ > 1040), and the significance level α is 0.1, we need to find the z-score that corresponds to the upper tail area of 0.1.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to an upper tail area of 0.1 is approximately 1.28.

Therefore, the rejection region for the standardized test statistic is z > 1.28.

Step 4: Calculate the p-value:

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Since the alternative hypothesis is μ > 1040, the p-value corresponds to the area under the standard normal curve to the right of the calculated z-score 1.94.

Using a standard normal distribution table or calculator, we find that the p-value is approximately 0.018.

Step 5: Make a decision for the hypothesis test:

Comparing the p-value (0.018) with the significance level α (0.1), we can make a decision.

Since the p-value (0.018) is less than the significance level α (0.1), we reject the null hypothesis H₀ and conclude that there is sufficient evidence to support the alternative hypothesis H₁.

Therefore, the decisions for the hypothesis test are:

A. Reject H₁

B. Reject H₀.

C. Do Not Reject H₁.

D. Do Not Reject H₀.

In this case, the decision is to Reject H₀ and accept H₁.

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Answer:

\text{The area of the trapezoid is 92.4 m}^{2}.

The area of the trapezoid is 92.4 m 2.

Step-by-step explanation:

\text{The area of the trapezoid is 92.4 m}^{2}.

The area of the trapezoid is 92.4 m 2.

Answer: 50

Step-by-step explanation:

Answer:

which language is this can you translate?

Answer:

y = x - 6

Since the slope is 1, it can be put as x .