Please try to prove that the slope of the normal line of y=mx+bis -1/m

The probability that Jordan will win in three or fewer matches if they play 5 matches using binomial probability distribution is; 0.95636

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula for binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring

x = the number of expected successful outcomes

n = the number of trials you perform

nCx = the number of different combinations for x items you test in n trials

We are given probability that Jordan wins the match as 1/3. Thus;

p = 1/3 = 0.333

Thus, probability that Jordan will win in three or fewer matches if they play 5 matches is;

P(X ≤ 3) = P(0) + P(1) + P(2) + P(3)

From online binomial probability calculator, we have;

P(X ≤ 3) = 0.95636

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The conversion of 230.2 g to metric ton is given by 0.0002302 metric tons.

Grams (g) and metric ton (MT) are the SI units of mass. Scientist measure various things with different units. The following are measures and their units;

Convert metric ton to grams:

1 metric ton = 1,000,000 grams

230.2 g = 230.2 ÷ 1,000,000

= 0.0002302 metric tons

Therefore, it can be said that 230.2 g is equivalent to 0.0002302 metric tons

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The value of the given limits [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

Because the value of that function at that point doesn't define.

a)

[tex]\lim_{x \to \infty} 1/x^2[/tex] by substitute limit 1/∞² = 0

b)

[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] here (x² - 4)/(x - 2) = (x - 2)(x + 2)/(x - 2) = (x + 2)

Putting x = 2 will give the limit as 2 + 2 = 4.

c)

[tex]\lim_{x \to \pi} sinx\\[/tex] herer put x to π so sinπ = 0.

c)

[tex]\lim_{x \to \55} e[/tex] here no variable thus e will be the answer.

Hence "The value of [tex]\lim_{x \to \infty} 1/x^2[/tex] is 0,[tex]\lim_{x \to \22} \frac{(x^2-4)}_(x-2)}[/tex] is 4  ,[tex]\lim_{x \to \pi} sinx\\[/tex] is 0 and [tex]\lim_{x \to \55} e[/tex] is e".

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The measure of the missing length of the triangle is 16 units.

According to the question,

We have the following information:

We have a figure of right-angled triangle where two sides are given.

In order to find the third side of this triangle, we will use the Pythagoras theorem.

So, we have the following expression:

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]

[tex](20)^{2} = AB^{2} + (12)^{2}[/tex]

400 = [tex]AB^{2}[/tex] + 144

Subtracting 144 from both sides of the equation:

[tex]AB^{2}[/tex] = 400-144

[tex]AB^{2}[/tex] = 256

We know that the square root of 256 is 16 or in other words, the square of 16 is 256.

AB = 16 units

Hence, the measure of the missing length of the triangle is 16 units.

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement that could be true for g is: D. g(-13) = 20.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

From the information provided, the domain and range of this function g(x) in interval notation is given by:

Function g(0) = 2 is false because it was stated that g(0) = -2. Also, g(-4) = -11 is outside the scope of the given range for this function.

Furthermore, function g(7) = -1 is not within the domain for the given function. However, g(-13) = 20 is within the domain for the given function and produces an output that is within the scope of the given range for this function.

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[tex]\stackrel{\textit{\LARGE arithmetic mean}}{\cfrac{14+7+10+5}{\underset{\textit{number of data elements}}{4}}\implies \cfrac{36}{4}\implies \text{\LARGE 9}}[/tex]

Answer:

the mean is 9 .

Step-by-step explanation:

i did this & got it correct .

Answer:

-9

Step-by-step explanation:

From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

The answer in blocks will be (-3) and (-6)

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

Given,

In the question:

Fill in the blanks to complete the equation that describes the diagram.

Now, According to the question:

From the scores on the diagram we can tell that the arrow first stand on the point -3 and then on the point -6.

If we add -6 to -3 the product will be:

(-3) + (-6) = -9

What is Number line ?

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Hence, The answer in blocks will be (-3) and (-6)

If we add -6 to -3 the product will be:

(-3) + (-6) = -9.

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Answer:

A and C = 13 and D and E = 24

Step-by-step explanation:

The given exponential function is increasing so it will be growth and the percentage increase is 97%.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given function,

y = 7000(1.97)^x

As x increase the 1.97^x will be increased thus, y will be increased so it will be growth.

Suppose x = 0

y = 7000

Suppose x = 1

y = 1.97 x 7000

% increase = (1.97 x 7000 - 7000)/7000

% increase = 97 %

Hence "The given exponential function is increasing so it will be growth and the percentage increase is 97%".

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The amount of raisins that Ben will mix if he wants to make a larger batch is 21 ounces of raisins

The amount is determined by comparing the trial mix used

Initially, 8 ounces of peanuts, 6 ounces of raisins, and 10 ounces of chocolate candies. This has a ratio of

peanut : raisins : chocolate

8 : 6 : 10

If 8 ounces of peanuts was used with 6 ounces of raisins, 28 ounces of peanuts wall be mixed with ? raisins

8 peanuts  = 6 raisins

28 peanuts = ? raisins

? = 28 * 6 / 8

? = 21 ounces of raisins

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The markup amount of the purchase is $1114

From the question, we have the following parameters that can be used in our computation:

Discount = 30%

Selling price = $780

The markup amount is calculated using the following equation

Selling price = Markup amount * (1 - discount)

Make the markup the subject

Markup = Selling price/(1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Markup = 780/(1 - 30%)

Evaluate

Markup = 1114

Hence, the markup is $1114

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Answer:

  True

Step-by-step explanation:

You want to know if My-Lien has enough room in a truck with a capacity of 3.385 tons to move 3 5/16 tons of gravel.

The empty space can be found by subtracting the load from the capacity of the truck. The attached calculator output shows there is room for an addition 0.0725 tons.

My-Lien will have enough room to move the gravel.

__

Alternate solution

You can convert 3 5/16 to a decimal: 3.3125. Clearly, this amount is less than 3.3850.

The solutions to the trigonometric equation sin(2x) = sin(x) on the first quadrant is given as follows:

The trigonometric equation in this problem is defined as follows:

sin(2x) = sin(x).

To verify the solutions, we replace each possible solution into each side of the equation, and verify if they are equal, as follows:

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Answer:

Step-by-step explanation:

12x-20

Answer:

Answer: 4 ∙ 3x - 4 ∙ 5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The distance between the lines stays constant, and they never intersect. In other words, you can translate (move) either line by that constant distance, in some direction, to get the other line. It's just like how when you change the y-intercept but keep the slope the same, you get parallel lines.

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a) The claim is given as follows:

[tex]\mu < 122[/tex]

b) The null and the alternative hypothesis are given as follows:

The claim in this problem is given as follows:

The mean systolic blood pressure of all healthy adults is less than 122 mm Hg.

Symbolically, the claim is given as follows:

[tex]\mu < 122[/tex].

As:

At the null hypothesis, it is tested if there is not enough evidence to conclude that the claim is true, that is, not enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_0: \mu \geq 122[/tex].

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, enough evidence to conclude that the mean systolic blood pressure of all healthy adults is less than 122 mm Hg, hence:

[tex]H_1: \mu < 122[/tex].

The questions are given by the image at the end of the answer.

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The value of 198.02 percent of £83.02 is £164.40

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

The value will be illustrated thus:

198.02% × £83.02

= 1.9802 × £83.02

= £164.3962

= £164.40

The value is £164.40.

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Answer: 32 km

Step-by-step explanation:

Set the unknown value as x and use proportions to find the answer:

[tex]\frac{72}{90} =\frac{x}{40} \\\\90x=72*40\\\\x=\frac{72*40}{90} =32[/tex]

Proved that ΔXYW ≅ ΔZYW

Consider the two triangles triangle XYW and triangle ZYW

According to SAS congruent rule if 2 sides and one angle of the one triangle is equal to the 2 sides and one angles of the another triangle, then both the triangles are congruent

The length of the side XY = The length of the side ZY

The line YW bisect the angle XYZ

Then the measure of angle XYW = The measure of angle ZYW

The length of the YW is common

Therefore the 2 sides and one angle of the triangle XYW is equal to the 2 sides and one angle of the triangle ZYW

Then the  triangles XYW and triangle ZYW are congruent

Hence, proved that ΔXYW ≅ ΔZYW

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The balance of the account at the end of 21 years, given the deposit amount and the interest rate is $10, 351. 41

The balance on the account at the end of 21 years is the future value of the amount in the account today. This means that this balance can be found by the formula:
= Amount deposited x ( 1 + rate) ^ number of years

The balance on the Credit union client's account after 21 years is therefore:
= 2, 500 x ( 1 + 7%) ²¹

= $10, 351. 41

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The quadratic function of the given graph is y = (x + 3)² + 8.

Quadratic function:

Basically, the standard form of the quadratic function is written as,

f(x) = a(x - h)² + k,

And a not equal to zero.

Here if a is positive, the graph opens upward, and if a is negative, then it opens downward. And the line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Given,

Here we have the graph and we have to find the quadratic function of the graph.

While we looking in to the given graph,

We have identified then the graph is opening the upward direction, So, the value of a is positive.

Now, we have to find the value of a which is 1.

And the vertex of the graph is (-3, 8).

So, the standard form of the quadratic function of the graph is written as,

=> y = (x + 3)² + 8.

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The Median and the modal sales is 45 and 49 respectively.

A median simply means the middle number when the number are arranged in ascending order. The mode is the number that appears most.

Since the number of sales of cars sold from January to November are 28, 20, 49, 29, 38, 40, 45, 49, 50, 55 and 60, this will be arranged as:

20, 28, 29, 38, 40, 45, 49, 49, 50, 55, 60

Therefore, the middle number is 45 and mode is 49.

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The slope is 3. The line is going up 3 and right 1. If it were the other way around, up 1 and right 3, that would be a slope of 1/3.

But the slope is 3.

Answer:

She can make 12 cups of sugar for 18 pies

Step-by-step explanation:because 6x3=18 so you multiply  4x3 to get 12, she need 12 cups of sugar for 18 pies or 18 pies with 6 cups of sugar

Tell me if it is wrong in the comment

Thank you.

The unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

Given that, Brand A has a box of 42 forks for $2.17. Brand B has a box of 48 forks for $3.97.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The cost of each fork of brand A

= 2.17/42

= $0.0517

The cost of each fork of brand B

= 3.97/48

= $0.0828

Therefore, the unit price for brand A is $0.0517 and the unit price for brand B is $0.0828. Based on the unit price Brand A is better to buy.

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Answer:

f(3)=13

Step-by-step explanation:

f(x)=5x-2

f(3)=5(3)-2

 =15-2

 =13