In a right triangle, given legs of lengths 5 and 12, find the length of the hypotenuse.

a) The probability of eating at a restaurant with unsanitary conditions is 3/7. If you plan to eat at 10 different restaurants, the probability of eating at exactly 3 restaurants with unsanitary conditions is given by the binomial probability formula:

P(X = 3) = (10 choose 3) * (3/7)^3 * (4/7)^7 = 120 * (0.42857)^3 * (0.57143)^7 = 0.1437

So, the likelihood of eating at three restaurants with unsanitary conditions is 14.37%.

b) The probability of eating at 4 or 5 restaurants with unsanitary conditions can be found by summing the binomial probabilities for each case:

P(X = 4) = (10 choose 4) * (3/7)^4 * (4/7)^6 = 210 * (0.42857)^4 * (0.57143)^6 = 0.1735

P(X = 5) = (10 choose 5) * (3/7)^5 * (4/7)^5 = 252 * (0.42857)^5 * (0.57143)^5 = 0.1428

P(X = 4 or X = 5) = P(X = 4) + P(X = 5) = 0.1735 + 0.1428 = 0.3163

So, the likelihood of eating at 4 or 5 restaurants with unsanitary conditions is 31.63%.

c) The probability of eating in at least one restaurant with unsanitary conditions can be found by subtracting the probability of eating in no restaurants with unsanitary conditions from 1. The probability of eating in no restaurants with unsanitary conditions is given by the binomial probability formula:

P(X = 0) = (10 choose 0) * (3/7)^0 * (4/7)^10 = 1 * (1) * (0.57143)^10 = 0.0139

P(X >= 1) = 1 - P(X = 0) = 1 - 0.0139 = 0.9861

So, the probability of eating in at least one restaurant with unsanitary conditions is 98.61%.

d) The most likely number is 3, as it has the highest probability of occuring.

e) The data is not very variable around the most likely number, as the probability of the other numbers is relatively low.

f) Yes, this is a binomial distribution as the experiment has only two possible outcomes, "success" (eating at a restaurant with unsanitary conditions) or "failure" (eating at a restaurant with sanitary conditions) and the number of trials is fixed (10)

g) No, the likelihood of success is not always 50% in a binomial distribution. The probability of success is given by the proportion of successful trials in the population, which in this case is 3/7.

The exact distance from home plate to second base on a baseball diamond is √16,200 feet. To convert this distance to decimal form, we must first understand the concept of a square root and how it relates to the distance formula.

A square root is a mathematical operation that represents the value whose square is equal to a given value. In this case, the square root of 16,200 is equal to the distance from home plate to second base.

To find the decimal form of the square root of 16,200, we can use a calculator or we can use the long division method. With a calculator, we simply input √16,200, which will give us the result of 126.84955592153876

To round to the nearest hundredth we look at the hundredths digit (8) if it's 5 or above we round up otherwise we round down so 126.84955592153876 rounded to the nearest hundredth is 126.85

The distance from home plate to second base on a baseball diamond is 126.85 feet in decimal form.

It's worth noting that the distance from home plate to second base is a critical aspect of the game and it's really important for the catcher to make a quick and accurate throw to second base.

Answer: c lower your mortgage interest rate

Step-by-step explanation

The higher your credit score, the less risk you represent for a lender.

My dad taught me this.

On observing the provided question, we can say that the the provided equation f(x) =  is the basic cubic function.f(x) = 8100

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

basic cubic function is =  f(x) = x^2

x =  90

f(x) = 8100

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On solving the provided question, we can say that It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.

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x = 5

7x+8=43

First, we want to separate the variable, so we subtract 8 from both sides:
7x=35

Then we divide both sides by 7 to get x all by itself:

x=5

This is because 35/7=5

Answer:

The equation 10x2+28x-6 can be simplified using a few steps. Firstly, the greatest common factor (GCF) needs to be identified. The GCF of this equation is 2, which can be identified by factoring out the coefficient of the first term, 10. After factoring out 2, the equation becomes -3 + -14x + 5x2.

The next step is to factor the remaining polynomial. This can be done by multiplying the coefficient of the first term by the constant and then finding two factors whose sum equals the coefficient of the middle term. In this case, the multiplication of the coefficient of the first term (5) and the constant (-3) gives -15. Then, two factors of -15 whose sum adds up to -14 must be found. These factors are -15 and 1. Therefore, the equation can be rewritten as 5x2 - 15x + 1x - 3.

Afterwards, the four terms in the equation can be added up in pairs, pulling out like factors. This results in (5x+1)(x-3), which is the desired factorization. Finally, the expression can be written as 2(x-3)(5x+1). Thus, the GCF of 10x2+28x-6 is 2.

Step-by-step explanation:

Answer:

2 is the answer .

if u r not sure u can try doing it yourself

the answer will be the same as I told

Answer:

3,10,8,5,4,1,7,2,9,6

Step-by-step explanation:

In step 2 the addition property of equality was applied. Thus, the correct option is A.

When the same amount is added to both sides of an equation, according to the addition property of equality, the equation remains the same. An equation that reads as A = B still holds true if a number x is added to both sides. The equation is A + x = B + x in mathematics.

When the same amount is added to both sides of an equation, the equation remains true, which is known as the addition property of equality. One of the basic characteristics of equality in mathematics, it is also very significant. The division, multiplication, and addition properties of equality are the additional characteristics.

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Full question:-

Select the correct answer. The given equation has been solved in the table. (see attachment)

A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error.

A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

However, the official definition goes a little bit beyond. The range of values in a confidence interval that lie below and above the sample statistic is known as the margin of error.

The confidence interval is a tool for displaying the level of uncertainty surrounding a certain statistic (i.e. from a poll or survey).

According to our question-

Because the sample proportions' range is 0.97-0.73 = 0.24

Calculate the standard deviation:

Range = 6* (s-bar)

= 0.24

s-bar = 0.04

S/Sqrt (100) then equals 0.04

and s = 0.4

S.D = 0.04 + 0.04

= 0.08

Hence, A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.

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The value of y is 6 and the length of RS and ST are 28, 26 respectively.

What is a line ?

line is a straight one dimensional figure having no thickness is called as the line.

Given , number lines

RS = 4y+4

ST = 3y+8

RT = 54

From the given figure ,

RS+ST = RT

4y+4+3y+8 = 54

7y+12 = 54

7y = 54-12

7y = 42

y =42/7

y = 6

The RS = 4y+4 = 4*6+4 = 28

ST = 3y+8 = 3*6+8 = 26

Hence, The value of y is 6 and the length of RS and ST are 28, 26 respectively.

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Answer:150

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

since half of 100 is 50, 2 classes will have 50 minutes. If you add 100+50 you get 150. So therefore ur answer is 150!

1. The complete table is shown below.

2. The graph is attached below.

3. the function h(x) is an odd function.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

m(x)=[tex]x^4[/tex]

and, h(x)= [tex]1/4 (x-6)^4[/tex]

So, the -6' in the h(x) there is Horizontal transformation on right side by 6 units, i.e., (x, y)--->(x +6, y)

and, 1/4 in h(x) shows there is Vertical stretch in h(x).

So, (x,  y)--->(x, y/4)

Now, Points on m(x)    points on h(x)

            (x, y)                      (x+6, y/4)

            (-2, 16)                   (4, 4)      

            (-1, 1)                      (5, 1/4)      

            (0, 0)                     (6, 4)      

            (2, 16)                    (8, 4)      

2. The graph is attached below.

3. Replace h(x) by h(-x) we get

h(-x) = [tex]1/4 (x-6)^4[/tex]

h(-x) = [tex]1/4 (-x-6)^4[/tex] will give an odd function.

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one of the most common forms of the equation of lines called slope-intercept form along with derivation.

The linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:

(y – y1) = m(x – x1)

Here, (x1, y1) = (0, c)

Substituting these values, we get;

y – c = m(x – 0)

y – c = mx

y = mx + c

Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c

Slope Intercept Form Formula

As derived above, the equation of the line in slope-intercept form is given by:

y = mx + c

Here,

(x, y) = Every point on the line

m = Slope of the line

c = y-intercept of the line

Usually, x and y have to be kept as the variables while using the above formula

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Answer:

e

Step-by-step explanation:

The rate of change for the interval between –6 and –3 on the x-axis is; 2

To find the rate of change  for the interval between –6 and –3 on the x-axis, we will first identify the ordered pairs at those two points. The ordered pairs from the graph would be (3, -2) and (6, 4).

Using the slope formula with those two points, we can find the rate of change as;

slope; m = (y₂ - y₁)/(x₂ - x₁)

m = (4 + 2)/(6 - 3)

m = 6/3

m = 2

This value of m represents the rate of change

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-2 is the answer i cant exaplin it bc i jsut guessed and got it right

Using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Basic arithmetic operations or calculations, such as addition, subtraction, multiplication, and division, are covered in Fundamentals of Mathematics and are concepts we learn in primary school.

Students will eventually study fundamental ideas like algebra, geometry, factors, ratios, etc. in upper classes.

So, we have that:

Crispy Flakes have 0.23 grams of sodium per cup.

Corn Puffers have 0.28 grams of sodium per cup.

Energy Doodles have 0.26 grams of sodium per cup.

Now, brands that have less than 1/4 gram of sodium per cup:

100 * 1/4 = 25

Then, 1/4 of 1.00 = 0.25

0.23 > 0.25

Therefore, using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.

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The value of b in the Line JK passes through points J(–4, –5) and K(–6, 3) is

b = –21

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 slope, m of the linear function is calculated using the points J(–4, –5) and K(–6, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 + 5) / (-6 + 4)

m = (8) / (-2)

m = -4

equation passing through point K(–6, 3)

(y - y₁) = m'  (x - x₁)

y - 3 = -4(x + 6)

y - 3 = -4x - 24

y = -4x - 24 + 3

y = -4x - 21

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The x-intercept is the point where the graph of a line intersects the x-axis. The y-intercept is the point where the graph of a line intersects the y-axis.

Given data :

y = ( 2 / π )²

y = 2² / π²

y = 4 / π²

Here i attached the graph of x interception

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The point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center [tex](0,1)[/tex] is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.

The equation of a circle with center (h, k) and radius r is:

[tex](x - h)^2 + (y - k)^2 = r^2.[/tex]

The equation of the line is given as [tex]y = x + 1[/tex].

Given the center of the circle is (0,1) and the radius is 4, the equation of the circle is [tex](x-0)^2 + (y-1)^2 = 4^2[/tex]

This can be simplified as [tex]x^2 + y^2 - 2y + 1 = 0[/tex]

Now we can substitute [tex]y = x + 1[/tex] in the circle equation:

[tex]x^2 + (x+1)^2 - 2(x+1) + 1 = 0\\x^2 + x^2 + 2x + 1 + 2x + 1 = 0\\2x^2 + 4x = -2\\x^2 + 2x = -1\\(x+1)^2 = 0\\x = -1[/tex]

Now that we have the value of x, we can substitute it in the equation [tex]y = x + 1[/tex]  to find the corresponding y value:

[tex]y = -1 + 1\\y = 0[/tex]

So, the point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center (0,1) is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.

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Answer:

y = [tex]\frac{8}{p+q+4}[/tex]

Step-by-step explanation:

py + qy = - 4y + 8 ( add 4y to both sides )

py + qy + 4y = 8 ← factor out y from each term on the left side

y(p + q + 4) = 8 ← divide both sides by p + q + 4

y = [tex]\frac{8}{p+q+4}[/tex]

Answer:

Step-by-step explanation: Umm multiply 80 by 2 and divied 78 after add 10

The sets of numbers that could represent three sides of a triangle is given as follows:

{12, 18, 29}.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence the set in this problem is given as follows:

{12, 18, 29}.

The larger measure is of:

29.

The sum of the two smaller measures is given as follows:

12 + 18 = 30.

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Answer:

d

Step-by-step explanation:

I think the a answer is d

It would take 28.6 years for the value of the account to reach $390.

The equation reads A(t) = Ao (2) Where

A(t) = 3902, Ao = 230, and t =?, k = 7 years

Hence, 3902 = 230 × (2)

^t/7

We divide 230 on both sides (3902/230 = 230) (2)

^t/7/230

16.965217391 = (2) (2)

^t/7

Calculate the ln of both sides:

16.965217391 = ln (2)t/7

ln 16.965217391 = t/7 ln (2) (2)

In 16.965217391/ln 2 = t/7

t = 4.0874628413× 7

t = 28.612239889 years

Approximately = 28.6 years

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T-test for independent groups analyzes the difference between the means of two independent samples. Hence, option B is the correct answer.

B. T-test for independent groups is the test that analyzes the difference between the means of two independent samples. This test assumes that the two samples are drawn from populations that have normal distributions and that the variances of the two populations are equal. The T-test for independent groups compares the means of the two samples and determines if there is a statistically significant difference between them. This test is also known as a two-sample T-test or independent T-test.

The other options A and C are not the correct ones.

A. Correlated T-Test is used when comparing means of dependent samples, it's also known as a dependent t-test

C. Sign test is a non-parametric test that is used to compare two dependent samples.

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The domain and the range of the graphed relation are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

As the graph contains open circles at both the ends of the domain, the domain is composed by an open interval.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

The graph assumes a minimum value of -6, hence the lower bound is closed, however the upper bound at y = 4 is open, as the only point the graph reaches y = 4 is on the open circle.

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Answer:

Yes

Step-by-step explanation:

Let's calculate the resistance of one inch for our wire and compare it with the maximum:

20250 / 25 = 810 Ohm

810 < 840 ? Yes!

Yes, this is within the acceptable limit. Wire can be used.

Answer:

375 mL

Step-by-step explanation:

Let x = Amount of fluid patient receives in 3 hours

Fluid drip rate: 1000 mL --------- 8hr

                                x        --------- 3 hr

Cross multiplication is applied:

(x).(8 hr) = (1000 mL).(3hr)

x = [(1000mL).(3 hr)]/ (8 hr)

x = 375 mL

Answer:

Step-by-step explanation:

L = 4 in real life = 4*30 =120 miles

W=6 in real life =6*30=180 miles

actual area = 120*180 = 21600sq miles

to fit into a 6sq in paper it'll need to shrink to 2x3 inches, 1/2 of what it was before, so the scale becomes 1" for every 60miles.