What type of triangle, if any can be formed with angle measures of 32 degrees, 126 degrees, and 32 degrees?


Answer 1 only an obtuse triangle

Answer 2 either an acute isosceles triangle or an obtuse isosceles triangle

Answer 3 only an acute isosceles triangle

Answer 4 no triangle

Answer: x = 3

Step-by-step explanation

This is a simultaneous equation. So to find x , we solve to ascertained the coordinate or point of intersection of the too lines.

y = 4x + 2, and 6x - y = 4

To solve , we need to rearrange first

y = 4x + 2 will be

4x - y = -2 -------------------------1

Equation 2 is in order

6x - y = 4 -------------------------- 2

Now solve the two equation for x by using any methods you are familiar with.

4x - y = -2

6x - y = 4, now subtract equation 2 from 1 in order to eliminate y,

we now have

-2x = -6, now divide through by 2

x = 3.

Hence y could be find by substitution for x in any of the equation above and now check.

4x - y = -2

4(3) - y = -2

12 - y = = -2

y = 12 + 2

y = 14.

Now let check

6x - y = 4

6(3) - 14

18 - 14

= 4.

Therefore, the value of x is 3

Answer:

Where's the triangle?

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Let

  \(W(t) = W_1 + W_2 + ... + W_n\)  

where W_i denotes the individual fare of the customer.

All W_i are independent of each other.

By formula for random sums,

E(W(t)) = E(Wi) * E(n)

  \(E(Wi) = \mu_G\)  

Mean inter arrival time =    \(\mu_F\)  

Therefore, mean number of customers per unit time =    \(1 / \mu_F\)  

=> mean number of customers in t time =    \(t / \mu_F\)  

=>    \(E(n) = t / \mu_F\)  

Answer:

  12,765

Step-by-step explanation:

The exponential formula for the population can be written as ...

  population = (initial population)(1 -decay rate)^t

where t is in years, and the decay rate is the loss per year.

The given numbers make this ...

  population = 100,000(0.9918^t)

In 250 years, the population will be about ...

  population = 100,000(0.9918^250) ≈ 12,765.15

There will be about 12,765 butterflies in 250 years.

In 250 years, there will be approximately 12,765 butterflies in the population.

This figure is obtained by applying the exponential decay formula with a 0.82% decrease rate per year from an initial population of 100,000 butterflies.

To determine the butterfly population in 250 years given a yearly decrease rate of 0.82%, we utilize the exponential decay formula:

[tex]\[ P(t) = P_0 \times (1 - r)^t \][/tex]

where:

- (P(t)) represents the population after (t) years,

- (P_0) is the initial population, which is 100,000,

- (r) is the annual decrease rate in decimal form, which is 0.82% or 0.0082,

- (t) is the time in years, here 250 years.

By substituting the given values into the formula:

[tex]\[ P(250) = 100,000 \times (1 - 0.0082)^{250} \][/tex]

Upon calculation, the population after 250 years is found to be approximately 12,765, rounding to the nearest whole number for practical purposes. This result is based on the principle of exponential decay, reflecting how a consistent percentage decrease affects the population over a prolonged period.

Answer:

crosses and touches is %100 RIGHT

Step-by-step explanation:

For the single roots -1 and 2,the graph crosses the x-axis at the intercepts

For the double root 3 the graph touches at the intercepts

"These are the point at which the graph of the function intersects the x-axis or Y-axis"

"These are the values for which the function equals zero."

For given question,

We have been given a function f(x) = (x + 1)(x - 2)(x - 3)²

To find the roots of function f(x)

⇒ f(x) = 0

⇒ (x + 1)(x - 2)(x - 3)² = 0

⇒ x + 1 = 0        or         x - 2 = 0      or      (x - 3)²=0

⇒ x = -1      or    x = 2   or x = 3

This means x = -1, 2, 3 are the roots of the function f(x)

From the graph of the function we can observe that the for the single roots -1 and 2,the graph of the function f(x)  crosses the x-axis at the intercepts x = -1 and x = 2 respectively.

And for the double root 3 the graph of the function f(x) touches at the intercept x = 3.

Therefore, For the single roots -1 and 2,the graph crosses the x-axis at the intercepts.

For the double root 3 the graph touches at the intercepts.

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Step-by-step explanation:

The bacteria is always doubled because in the sequence we multiply the number by 2

3 x 2 = 6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96

Answer:

  0.72

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation of interest is ...

  Cos = Adjacent/Hypotenuse

Then the cosine of angle C is ...

  cos(C) = CD/CB = 21/29

  cos(C) ≈ 0.72

Answer:

Step-by-step explanation:

The sample size needed with 99% confidence and 3% margin of error is 1843.

To estimate the sample size needed:

Determine the critical value for 99% confidence, which is 2.576.

Calculate the minimum sample size using the formula:

n = (Z^2 * p * q) / E^2

Substitute Z = 2.576, p = 0.5, q = 0.5, and E = 0.03.

Calculate to get the sample size, which is approximately 1843.

Answer:

Mrs. Potts needs 72 feet of fencing.

Step-by-step explanation:

You find the perimeter of the rectangular garden, which is 24 yards. You then convert the yards to feet. There are 3 feet in a yard. You multiply 24 by 3 to get your final answer of 72 feet.

Answer:

(a) The value of P (X = 4) is 0.1465.

(b) The probability that all 5 of them land heads up is 0.0313.

(c) The probability that the student answers correctly on less than 4 of these questions is 0.6980.

Step-by-step explanation:

A Binomial distribution is the probability distribution of the number of successes, X in n independent trials with each trial having an equal probability of success, p.

The probability mass function of a Binomial distribution is:

[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...,\ 0<p<1[/tex]

(1)

The information provided is:

X = 4

n = 8

p = 0.31

Compute the value of P (X = 4) as follows:

[tex]P(X=4)={8\choose 4}0.31^{4}(1-0.31)^{8-4}\\=70\times 0.00923521\times 0.22667121\\=0.146535\\\approx 0.1465[/tex]

Thus, the value of P (X = 4) is 0.1465.

(2)

The probability of heads, on tossing a single fair coin is, p = 0.50.

It is provided that n = 5 fair coins are tossed together.

Compute the probability that all 5 of them land heads up as follows:

[tex]P(X=5)={5\choose 5}0.50^{5}(1-0.50)^{5-5}\\=1\times 0.03125\times 1\\=0.03125\\\approx 0.0313[/tex]

Thus, the probability that all 5 of them land heads up is 0.0313.

(3)

There are 5 possible answers for every multiple choice question. Only one of the five options is correct.

The probability of selecting the correct answer is, p = 0.20.

Number of multiple choice questions, n = 14.

Compute the probability that the student answers correctly on less than 4 of these questions as follows:

P (X < 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

              [tex]=\sum\limits^{3}_{x=0}{{14\choose x}0.20^{x}(1-0.20)^{14-x}}\\=0.0439+0.1539+0.2501+0.2501\\=0.6980[/tex]

Thus, the probability that the student answers correctly on less than 4 of these questions is 0.6980.

The final probabilities are P(4 successes) ≈ 0.146, P(5 heads) ≈ 0.03125, and P(less than 4 correct answers) ≈ 0.5972.

Solutions to Probability Questions

Let's tackle each of your probability questions step-by-step:

Question 1 To find P(x) using the binomial probability formula, given n = 8, p = 0.31, and x = 4, we use the formula:

Where:

Calculating:

So, P(4) ≈ 70 * 0.009235 * 0.226981 ≈ 0.146.

Question 2 If 5 fair coins are tossed, the probability that all 5 of them land heads up is calculated as:

Question 3 For a student answering a multiple-choice quiz with 14 questions where each question has 5 possible answers, and we are to find the probability of correctly answering less than 4 questions, we use the binomial distribution with n = 14, p = 0.2 (since only one answer out of five is correct), and x < 4:

Answer:

A. (-3,4), (6,2), (-7,1), (2,2)

Step-by-step explanation:

Functions cannot have the x repeating. All the other answers have one of their x-values repeating, so they are not functions.

Answer:

0.5

Step-by-step explanation:

To subtract 143-79 by breaking apart, round 79 to 80, subtract it from 143 to get 63, and add 1 back for rounding to get the final answer of 64.

The question involves breaking apart numbers to subtract 143-79. This is a technique used in math to simplify subtraction by splitting numbers into parts that are easier to work with.

The final answer is 64.

Answer:

The Laplace transform of f(t) = 1 is given by

F(s) = (1/s) for all s>0

Step-by-step explanation:

Laplace transform of a function f(t) is given as

F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt

Find the Laplace transform for when f(t) = 1

F(s) = ∫∞₀ 1.e⁻ˢᵗ dt

F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀

= -(1/s) [1/eˢᵗ]∞₀

Note that e^(∞) = ∞

F(s) = -(1/s) [(1/∞) - (1/e⁰)]

Note that (1/∞) = 0

F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)

Hope this Helps!!!

In this exercise we have to use the knowledge of the Laplace transform to calculate the total value of the given function, thus we will find that:

[tex]F(s) = (1/s) \\for \ all\ s>0[/tex]

So we have that the Laplace transform can be recognized as:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt[/tex]

Find the Laplace transform for when f(t) = 1, we have that:

[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt \\\\ F(s) = \int\limits^\infty _0 { 1 e^{-st} \, dt[/tex]

[tex]F(s) = \int\limits^\infty _0 { e^{-st} \, dt = (1/s) [-e^{-st}] \\[/tex]

[tex]F(s) = -(1/s) [(1/\infty ) - (1/e^0)] \\F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)[/tex]

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Answer:

Mark will use 153 no of trays to accomplish his task.

Final answer:

Mark can use 9 trays to distribute 153 hot dogs and 171 hamburgers evenly by finding the Greatest Common Divisor (GCD) of the two numbers, which is 9.

Explanation:

Mark has 153 hot dogs and 171 hamburgers and wants to distribute them evenly across the greatest number of trays. To do this, Mark needs to find the Greatest Common Divisor (GCD) of the two numbers, which is the largest number that can evenly divide both 153 hot dogs and 171 hamburgers. The GCD of 153 and 171 is 9.

Therefore, Mark can use 9 trays, with 17 hot dogs and 19 hamburgers on each tray, to distribute them evenly.

Answer: Stocks will have the highest liquidity and convertability to cash

Answer:

If your asking what 4.7kg is to grams then it is 4700g

Answer:

4700 g

Step-by-step explanation:

1 kg = 1000g

Using this rule, 4.7 kg would be 4700g

4.7 x 1000 = 4700

Answer:

$38 + 15% off

Step-by-step explanation:

to do this, multiply each original price by the coupon percentage, (38 being .15, and 44 being .4,) and subtract the answers. when this is done and you compare, you will see that the $38 sweatshirt is less money by $2.90.

The cost of the sweatshirt both in-store and online after applying the respective discounts shows that it is better to buy the sweatshirt online, saving Nathan $2.90.

This problem relates to the mathematics field of percentage or discount calculations. To solve this problem, we need to calculate the cost of the sweatshirt after applying the discounts both in-store and online.

First, let's calculate the amount of the 20% discount for the in-store purchase. To find the discount, we multiply the cost of the sweatshirt by the discount rate: $44 * 20% = $8.80. So the total cost for the sweatshirt in-store after the discount would be $44 - $8.80 = $35.20.

Secondly, let's calculate the online price with a 15% discount. The discount on the online price would be calculated as: $38 * 15% = $5.70. Therefore, the cost of the sweatshirt online after the discount is $38 - $5.70 = $32.30.

Based on these calculations, buying online is the better deal by $35.20 - $32.30 = $2.90.

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Answer:

The probability of  the student will pass the quiz = .0546

Step-by-step explanation:

Given -

Total no of question = 10

If the student guesses on each question there are two outcomes true of false

the probability  of guesses  question correctly =  [tex]\frac{1}{2}[/tex]

the probability  of success is (p) =  [tex]\frac{1}{2}[/tex]

the probability  of guesses  question incorrectly = [tex]\frac{1}{2}[/tex]

the probability  of failure is (q) = 1- p = [tex]\frac{1}{2}[/tex]

If the student guesses on each question he must answered at least 8 question correctly

the probability of  the student will pass the quiz = [tex]P(X\geq8 )[/tex]

= P(X = 8 ) + P(X = 9) + P(X = 10 )

= [tex]\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}[/tex]

= [tex]\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}[/tex]

= [tex]45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}[/tex]

= [tex]\frac{56}{2^{10}}[/tex]

= .0546

Final answer:

The probability of a student passing the true or false quiz by guessing and getting at least 8 out of 10 questions correct is 7/128. This is calculated by finding the binomial probabilities for 8, 9, and 10 correct guesses and summing them.

Explanation:

To determine the probability that the student passes the quiz by guessing, we need to calculate the chances of them getting at least 8 out of 10 true or false questions correct. Since each question can only be true or false, there's a 1/2 chance of guessing each question correctly, and therefore, a 1/2 chance of guessing incorrectly.

The scenarios in which a student can pass are by getting 8, 9, or 10 questions correct. We will use the binomial probability formula, which is P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k), where 'n' is the number of trials (questions), 'k' is the number of successes (correct answers), and 'p' is the probability of success on an individual trial (1/2 for true/false questions).

The probability of getting exactly 8 questions right is (10 choose 8) * (1/2)^8 * (1/2)^(10-8).

The probability of getting exactly 9 questions right is (10 choose 9) * (1/2)^9 * (1/2)^(10-9).

The probability of getting all 10 questions right is (10 choose 10) * (1/2)^10 * (1/2)^(10-10).

We add these individual probabilities together to find the total probability of passing the quiz.

Using a calculator or the binomial coefficients, we find:

P(getting 8 right) = 45 * (1/2)^10,

P(getting 9 right) = 10 * (1/2)^10,

P(getting 10 right) = 1 * (1/2)^10.

Adding these together gives us the total probability:
P(8 or more correct) = [45 + 10 + 1] * (1/2)^10 = 56 * (1/2)^10

After simplifying, we find that the probability of passing the quiz with at least 8 correct answers is thus 56/1024, which can be reduced to 7/128.

The opposite of a coordinate in mathematics is obtained by changing the sign of the given number. Without the specific coordinate for point D, the opposite cannot be determined from the provided options.

The question seems to refer to the notion of opposite coordinates in a coordinate system. In mathematics, particularly in the context of a coordinate plane, the opposite of a coordinate is simply the same number with its sign changed. If the original coordinate for point D is not given in the question, it's impossible to determine the correct opposite coordinate from the options provided.

Answer:

The answer is x=5, −9

Answer:

There are NO parallel sides.

Step-by-step explanation:

Look at them.

Answer: Bottom left, lamins have no parrellel sides

Step-by-step explanation: All of them have no parrellel sides. Hope this helps!

The average number of people per car visiting the national park is approximately 2.91.

In order to find the average number of people per car, you would first multiply the number of cars by the number of people in each.

Therefore, 57 cars had 4 people (57*4=228), 61 cars had 2 people (61*2=122), 9 cars had 1 person (9*1=9), and 5 cars had 5 people (5*5=25). After this, add all the results (228+122+9+25 = 384).

The total number of cars is the sum of all cars, which is (57+61+9+5 = 132).

Now, to find the average number of people per car, you would divide the total number of people, which is 384 by the total number of cars, which is 132. Therefore, the average number of people per car is 384 / 132 = about 2.91 people per car.

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Answer:

A = πr²

Step-by-step explanation:

Answer:

  6

Step-by-step explanation:

Freda lives in house 6. Lamar lives 3 houses from Freda, so lives in house 3. Jay lives next to Lamar, but not in house 2, which is Bart's. So, Jay lives in house 4 and Davina lives in house 5, on the other side of Jay from Lamar.

Davina lives in house 5, so has the most DVDs.

__

Since Freda gave p DVDs to Jay, she has 17-p. Lamar has p-2, Bart has p+4, Tara has 4p-13, and Davina has the most at 3(p-2).

We want Davina to have the most DVDs, so there are some inequalities that must be true:

  3(p-2) > 4p-13   ⇒   p < 7

  3(p-2) > p +4   ⇒   p > 5

The only value of p satisfying both of these requirements is p = 6.

_____

Tara lives in house 1 and has 11 DVDs.

Bart lives in house 2 and has 10 DVDs.

Lamar lives in house 3 and has 4 DVDs.

Jay lives in house 4 and has 6 DVDs.

Davina lives in house 5 and has 12 DVDs. (the most)

Freda lives in house 6 and has 11 DVDs.

Answer: its 4. Look at the graph, x is horizontal and y is vertical (first go sideways then go up.) if coordinates are x,y then first go sideways when looking for x. they give you x. 7. then we go up. the graph intersects 7 at 4, therefore the coords are 7, 4 and your y coordinate is 4.

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

Answer:

The mean of the sampling distribution(SRS 49) of the sample mean is 420 and the standard deviation is 3.

The mean of the sampling distribution(SRS 576) of the sample mean is 420 and the standard deviation is 0.875.

By the Central Limit Theorem, the sample size does not influence the sample mean, but it does decrease the standard deviation of the sample

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Population

mean = 420, standard deviation = 21.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{49}} = 3[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 3.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{576}} = 0.875[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 0.875.

Increasing the sample size from 49 to 576 in a simple random sample from a population with a mean of 420 and a standard deviation of 21 keeps the mean of the sampling distribution the same but decreases the standard deviation.

When taking a simple random sample (SRS) from a population where the mean (μ) is 420 and the standard deviation (σ) is 21, and using a sample size (n) of 49, the sampling distribution of the sample mean will have:

When the sample size increases to 576, the sampling distribution of the sample mean will still have a mean of 420, but the standard deviation will decrease because it is inversely proportional to the square root of the sample size. The new standard deviation will be 21/√576 = 21/24 = 0.875.

The effect of increasing the sample size is that while the mean of the sampling distribution remains the same, the standard deviation decreases, leading to a more narrow distribution. This indicates that there is less variability in the sample means, and they will be closer to the population mean, which is in accordance with the Central Limit Theorem.

Answer:

7

3.5

Step-by-step explanation:

Answer:

The radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\)[/tex].

Explanation:

The radius [tex](\(r\))[/tex] of a circle is half of its diameter ([tex]\(d\)[/tex]), and the diameter ([tex]\(d\)[/tex]) is twice the radius ([tex]\(r\)[/tex]). So, we can find the radius and diameter of the circle with a given radius of 7 cm.

Given:

Radius ([tex]\(r\)[/tex]) = 7 cm

To find the diameter ([tex]\(d\)[/tex]), we use the relationship:

[tex]\[d = 2r\][/tex]

Substituting the given value of the radius:

[tex]\[d = 2 \times 7\][/tex]

[tex]\[d = 14\][/tex]

So, the diameter of the circle is [tex]\(14 \, \text{cm}\)[/tex].

Therefore, the radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\).[/tex]

Question:

What is the diameter of a circle whose radius is 7 cm?