Which postulate proves the two
triangles are congruent?
A HL
B SAS
C ASA
D nOne

Answer:

D)

Step-by-step explanation:

a)The 95% to 5% split for 160 coin tosses is approximately 44.34% to 55.66%.

b)The probability of detecting a 60% coin is approximately 0.0436 or 4.36%.

c)The probability of detecting a 70% coin is approximately 0.0527 or 5.27%.

a) The 95% to 5% split refers to the range of outcomes that would be considered statistically significant. In the case of a coin toss, we can determine this split using binomial distribution. The formula to calculate the range is as follows:

p ± z\(\times \sqrt((p \times (1 - p)) / n)\)

Where:

p = probability of success (0.5 for a fair coin)

z = z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)

n = number of trials (160 coin tosses)

Calculating the split:

Lower bound = 0.5 - 1.96 * sqrt((0.5 * (1 - 0.5)) / 160)

Upper bound = 0.5 + 1.96 * sqrt((0.5 * (1 - 0.5)) / 160)

Lower bound ≈ 0.4434

Upper bound ≈ 0.5566

Therefore, the 95% to 5% split for 160 coin tosses is approximately 44.34% to 55.66%.

b) To determine the probability of detecting a 60% coin, we can use the binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) = probability of getting exactly k successes

C(n, k) = number of combinations of n items taken k at a time

p = probability of success (0.6 in this case)

n = number of trials (160 coin tosses)

k = number of successful outcomes (96 for 60% of 160)

Calculating the probability:

P(X = 96) = C(160, 96) * 0.6^96 * (1 - 0.6)^(160 - 96)

The calculation involves a large number of terms and may be better suited for a statistical software or calculator. Using software, the probability is approximately 0.0436.

Therefore, the probability of detecting a 60% coin is approximately 0.0436 or 4.36%.

c) Similarly, to determine the probability of detecting a 70% coin, we can use the same binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) = probability of getting exactly k successes

C(n, k) = number of combinations of n items taken k at a time

p = probability of success (0.7 in this case)

n = number of trials (160 coin tosses)

k = number of successful outcomes (112 for 70% of 160)

Calculating the probability:

P(X = 112) = C(160, 112) * 0.7^112 * (1 - 0.7)^(160 - 112)

Again, the calculation involves a large number of terms. Using software, the probability is approximately 0.0527.

Therefore, the probability of detecting a 70% coin is approximately 0.0527 or 5.27%.

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By combinations, there are 210 10 bit strings which contains exactly 4 ones.

To find out how many 10-bit strings there are that contain exactly 4 ones, we can use the binomial coefficient formula.

The binomial coefficient formula is given by `C(n, k) = n! / (k! * (n-k)!)`,

where,

n is the total number of items, and k is the number of items

we want to choose from n. In this case, we want to choose 4 ones from 10 bits, so n = 10 and k = 4. Therefore, the number of 10-bit strings that contain exactly 4 ones is:

`C(10, 4) = 10! / (4! * (10-4)!) = 210`.

Hence, there are 210 10-bit strings that contain exactly 4 ones.

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Answer:

282.6 in³

Step-by-step explanation:

Volume = area circle * height

Area circle = πr²

Area circle = 3.14 * 9 = 28.26

28.26 * 10 = 282.6 in³

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

OPtion B)

Step-by-step explanation:

Answer: Choice C)

y < (-1/5)x + 1

The boundary line is y = (-1/5)x+1 as it goes through the points shown. The boundary line is dashed or dotted, meaning that points on this boundary line are not in the solution set. So we will not have an "or equal to" as part of the inequality sign. More specifically, the inequality sign is "less than" because we shade below the boundary line. So that's how we end up with y < (-1/5)x+1.

Answer:

3/8

Step-by-step explanation:

So, Leena eats 1/8 of the bread first.

Now, she gave 1/6 of the bread to EACH of her 3 friends.

So you will need to do 1/6*3, which is 3/6=1/2.

Now you want to do 1/8+1/2 = 1/8+4/8 = 5/8.

This means 5/8 of the bread is gone.

Now you will need to do 1-5/8 = 8/8-5/8=3/8.

Therefore, 3/8 of the bread is left.

I hope this helps!

If the average of vehicles is 35.7 mpg then

(a) the variable is found to be "average miles per gallon .

(b) The variable is quantitative .

In the question ,

we are studying about the average miles per gallon (mpg) for new hybrid small cars .

by consumer reports the random sample of such vehicles gave an average of 35.7 mpg .

Part (a)

here the variable is "average miles per gallon(mpg) " , because it varies with the different cars .

Part(b) ;

This variable is Quantitative , because here we are studying about the term "how much" that means : average miles per gallon .

Therefore , the variable is "average miles per gallon" and is quantitative .

The given question is incomplete , the complete question is

The average miles per gallon (mpg) for all new hybrid small cars , Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg.

(a) Identify the variable.

(b) Is the variable quantitative or qualitative ?

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Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer:

9+10 is 19 i-

Step-by-step explanation:

Answer:

256.695 feet

Step-by-step explanation:

We Know

Circumference of circle = d x 3.14

d = 81.75 feet

What was the circumference of the cookie in feet to the thousandths?

We Take

81.75 x 3.14 = 256.695 feet

So, the circumference of the cookie is 256.695 feet.

Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

\(y+6=4(x-0.3)\)

The y-intercept is when x=0, so substituting in x=0,

\(y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2\)

So, the y-intercept is (0, -7.2).

Answer:

write down the equations for each, add them then do some manipulation to get the pencil and erasors on one side

If a hypothesis test is significant at level α = 0.05, then the P-value is less than or equal to 0.05 or P-value ≤ 0.05.

The P-value is a measure of the strength of the evidence against the null hypothesis. It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level α, it means that the observed evidence is unlikely to have occurred by chance under the null hypothesis, and we can reject the null hypothesis in favor of the alternative hypothesis.

For example, if the P-value of a hypothesis test is 0.03, it means that there is a 3% chance of obtaining the observed test statistic (or a more extreme one) if the null hypothesis is true. Since this is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Hence, if a hypothesis test is significant at level α = 0.05, then P-value ≤ 0.05.

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Answer:

126 miles

Step-by-step explanation:

28.95*4=115.8

150-115.8=34.2

34.2/0.27=126

Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F

and 014≤ 640 ≤ 2TT outward normal is

(r = 18) = √x² + y²+z2)

= F = ૪ 3

flux = [[Finds

. Rsing dodo = 83

(from put value of n

13 sind do do 23

2 TT, TT sing do do

R 11 R [["e. / sind dado (r= 171 = radius of ephare)

Π 2T ए [e" [" sind do do= ["- Casp" "do 0

[-(-1-1) do 2TT = 2x (2-0) 2 = do flux

flux = [[F·ñ-ds S = 4π

The flux is 411 and it depends on radius 'R'

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Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

To calculate the distance traveled, we can multiply the speed by the time traveled.

Speed = 1000 miles per hour

Time = 7.5 * 10⁵ hours

Distance = Speed * Time

Distance = 1000 miles/hour * 7.5 * 10⁵ hours

To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:

Distance = 1000 * 7.5 * 10⁵ miles

Distance = 7.5 * 10⁸ miles

Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

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Answer:

He should sell 0.988$ per fruit.

Step-by-step explanation:

I. When 15% is rotten so find the remain of good fruits.

       15/100 = x/60

       15 * 60 = 100x

           900/100 = x

             x = 9

Good fruit = total - rotten

                 = 60 - 9

So good fruit is 51

II. Find profit of 80% on cost, when cost is 28$

           80/100 = x/28

            2,240 = x100

                   x = 22.4

Profit cost = 28 + 22.4

So profit cost is 50.4$

III. Find selling price per fruit, when good fruit is 51 and profit cost is 50.4

          50.4/51 = 0.988

So selling price per fruit is 0.988$

You can ask me for anything.

Answer:

Step-by-step explanation:

Given the expression simplified by Pablo as \((2^{-4})^{-2}\)

On simplification we have;

According to one of the law of indices \((a^{m})^{n} = a^{mn}\)

Applying this law to the question will give;

\((2^{-4})^{-2}\\=2^{-4*-2} \\\= 2^{8}\)

Based on the calculation above, the exponent of 2 is 8 which means that Pablo should have found 8 as the exponent, not –8.

Answer:

C. He should have found 8 as the exponent, not –8.

Step-by-step explanation:

Answer:

difference of 10 min

Step-by-step explanation:

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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The derivative of the function \(y=5 \tan ^{-1}\left(x-\sqrt{1+x^2}\right)\) is \(\frac{d y}{d x}=\frac{5}{2\left(1+x^2\right)}\).

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.

Use the chain rule to differentiate the given function.

\(\frac{d y}{d x}=5 * \frac{1}{1+\left(x-\sqrt{1+x^2}\right)^2} * \frac{d}{d x}\left(x-\sqrt{1+x^2}\right)\)

\(=\frac{5}{1+\left(x^2-2 x \sqrt{1+x^2}+\left(\sqrt{1+x^2}\right)^2\right)} *\left(1-\frac{x}{\sqrt{1+x^2}}\right)\)

Simplify the above expression.

\(\frac{dy}{dx} =\frac{5}{1+x^2-2 x \sqrt{1+x^2}+1+x^2} *\left(\frac{\sqrt{1+x^2}-x}{\sqrt{1+x^2}}\right)\)

Combine like terms.

\(\frac{dy}{dx} =\frac{5}{2+2 x^2-2 x \sqrt{1+x^2}} *\left(\frac{\sqrt{1+x^2}-x}{\sqrt{1+x^2}}\right)\)

Further, simplifying the above expression.

\(\frac{dy}{dx} =\frac{5}{2\left(1+x^2-x \sqrt{1+x^2}\right)} *\left(\frac{\sqrt{1+x^2}-x}{\sqrt{1+x^2}} \cdot \frac{\sqrt{1+x^2}+x}{\sqrt{1+x^2}+x}\right).\)

\(=\frac{5}{2\left(1+x^2-x \sqrt{1+x^2}\right)} *\left(\frac{1+x^2-x^2}{1+x^2+x \sqrt{1+x^2}}\right)\)

\(\begin{aligned}& =\frac{5}{2\left[\left(1+x^2\right)^2-\left(x \sqrt{1+x^2}\right)^2\right]} \\& =\frac{5}{2\left[\left(1+2 x^2+x^4\right)-\left(x^2\left(1+x^2\right)\right]\right.} \\& =\frac{5}{2\left[1+2 x^2+x^4-\left(x^2+x^4\right)\right]} \\& =\frac{5}{2\left[1+2 x^2+x^4-x^2-x^4\right]} \\& =\frac{5}{2\left[1+x^2\right]}\end{aligned}\)

Therefore, the derivative of the given function is \(\frac{d y}{d x}=\frac{5}{2\left(1+x^2\right)}\).

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Answer: 96 cups

Step-by-step explanation: A gallon  holds 128 ounces there were 6 gallons used to make the punch. 128x6= 768 ounces

A cup holds 8 ounces so you would do 768/8 and that would give you 96 cups

Based on the data provided, we can calculate the slope and y-intercept of the line that fits the data points.

First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). We can use the first two data points for this calculation:

m = (27 - 32) / (10 - 5) = (-5) / 5 = -1

Now, let's find the y-intercept (b) using the formula: y = mx + b. We can use the first data point (5, 32) and the slope we found:

32 = -1 * 5 + b
32 = -5 + b
b = 37

Therefore, the correct slope is -1, and the y-intercept is 37.

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Answer:

1.5

2.1/5

Step-by-step explanation:

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^