Given the normally distributed random variable X with mean 18 and variance 6.25, find (a) P(16 < X < 22). (b) the value of k1 such that P(X < k1) = 0.2946 (c) the value of k2 such that P(X > k2) = 0.8186 (d) the two cut-off values that contain the middle 90% of the normal curve area

The value of the test statistics is , χ² = 15.3902

The value of P is less than 0.005 and the conclusion which we can draw from this is that  the health insurance coverage is depending on the size of the business in point a.

The percentages of employees without health insurance based on company size for small , medium and large companies is ,

We established our null hypothesis and alternate hypothesis as

H0: The availability of health insurance for employees is unrelated to the size of the business

H1 :The availability of employee health insurance is depending on the size of the business.

2) The alpha level for significance is set at 0.05.

3) The H0 test statistic is

O is the measured frequency, and E is the anticipated frequency, so that 2 = (O - E)2/E

This has a chi-square distribution that is around (3-1) (2-1)= 2 d.f.

We reject the null hypothesis that employee health insurance coverage is NOT independent of the size of the company because the calculated 2 = 15.3902 falls in the critical area 2 5.99.

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The percentage of the darts hit the bullseye will be 14%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A sum of 50 individuals plays darts. Every player is given 3 darts to attempt to stir things up around town. Assuming 21 of the darts hit the bullseye.

The total number of dart is calculated as,

Total dart = 50 x 3

Total dart = 150

The percentage is given as,

P = (21 / 150) x 100

P = 0.14 x 100

P = 14%

The percentage of the darts hit the bullseye will be 14%.

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The equation that shows the relationship between x and y is y = 2x. Option D is the correct option.

What is relationship between two variables?

A correlation exists between the two variables in question. A correlation coefficient is a metric that quantifies the strength of a relationship or level of correlation. A correlation coefficient is a measure of the strength and direction of a relationship expressed numerically.

The general equation of a line that passes origin is y = mx.

Find some point on the line:

The points that lie on the line are (1,2) , (2, 4), (3,6) etc.

Since the points lie on the line, thus they will be satisfy the equation of line.

Putting x = 1 and y = 2 in y = mx:

2 = m × 1

m = 2

Putting m = 2 in y = mx:

y = 2x

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Answer:

y = -x + 5

Step-by-step explanation:

2x+2y=10 slope intercept equation

2x+2y=10

subtract 2x from both sides:

2y = 10 - 2x

rearrange right side:

2y = - 2x + 10

divide all terms by 2:

y = -x + 5

Answer:

Step-by-step explanation:

5 over 2

Answer:

  (b)  y=(x+1)²−9

Step-by-step explanation:

You want the vertex form equation of the graphed parabola, which opens upward and has its vertex at (-1, -9).

The vertex form equation for a parabola with vertex (h, k) is ...

  y = (x -h)² +k

The vertex of the parabola shown is (h, k) = (-1, -9). Using these values in the equation gives ...

  y = (x +1)² -9

__

Additional comment

The equation may include a scale factor that multiplies the square. Here, the curve rises 1 unit for 1 unit either side of the vertex, so the scale factor is 1. (The rise at ±1 from the vertex is the scale factor.)

Steps: (1) read the vertex coordinates from the graph; (2) put those coordinates in the vertex form equation; (3) check to see that the vertical scale factor is 1.

The best approximation to the solution of the system of equations is (2, 3)

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

Equation 1 is 5 x plus 2 y equals 16.

Equation 2 is x plus 3 y equals 12.

Rewrite the equations properly

So, we have the following representation

5x + 2y = 16

x + 3y = 12

Make x the subject in the second equation

So, we have

x = 12 - 3y

Substitute x =12 - 3y in the equation 5x + 2y = 16

So, we have

5(12 - 3y) + 2y = 16

Open the brakects

This gives

60 - 15y + 2y = 16

Evaluate the like terms

-13y = -44

Divide both sides by -13

y = 3.39

Substitute y = 3.39 in x = 12 - 3y

x = 12 - 3 * 3.39

Evaluate

x = 1.83

Approximate the solutions

x = 2 and y = 3

Hence, the solution is (2, 3)

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Answer:

Step-by-step explanation:

The vertex form of a quadratic function is given by the equation f(x) = a(x - h)² + k, where (h, k) is the coordinates of the vertex of the parabola, and a is a constant coefficient.

To find the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7, we can first use the formula for the x-coordinate of the vertex of a quadratic function, which is given by h = -b / 2a. In this case, the quadratic function is f(x) = x² + 8x + 7, so b = 8 and a = 1. Plugging these values into the formula, we get:

h = -8 / 2(1) = -4

Therefore, the value of h is -4.

Next, we can use the formula for the y-coordinate of the vertex of a quadratic function, which is given by k = f(h) = a(h - h)² + k. In this case, we know that the value of h is -4, and we can plug this value into the original quadratic function to get the value of k:

k = f(-4) = (-4)² + 8(-4) + 7 = 16 - 32 + 7 = -9

Therefore, the value of k is -9.

Finally, we can use the equation f(x) = a(x - h)² + k to find the value of a. Since we know that the coordinates of the vertex are (-4, -9) and the equation of the quadratic function is f(x) = x² + 8x + 7, we can plug these values into the equation to solve for a:

f(x) = a(x - h)² + k

x² + 8x + 7 = a(x - (-4))² + (-9)

We can then distribute the squared term and simplify the equation to get:

x² + 8x + 7 = a(x² - 8x + 16) + (-9)

x² + 8x + 7 = a(x²) - 8a(x) + 16a + (-9)

We can then collect like terms to get:

x² + 8x + 7 = a(x²) - 8ax + 16a - 9

Comparing the coefficients of the x², x, and constant terms on both sides of the equation, we can see that a = 1.

Therefore, the values of a, h, and k for the given quadratic function f(x) = x² + 8x + 7 are a = 1, h = -4, and k = -9.

Using Pythagoras theorem, the length of AE in the square  2√2 unit

To find the length of side AE, we have to use use the dimension of BD given.

In the figure given, the length of all sides are equal to one another. This implies that the sides are equidistant to one another.

In a given square, all the sides are equal to one another, but the length of the diagonal is the square root of the sum of two sides

This can be further explained as

BD = AC

Using Pythagoras theorem

BD² = AD² + BA²

4² = x² + x²

16 = 2x²

x² = 8

x = √8

x = 2√2

However, we need to find the length of AE

AE is half the length size of AD

AE = 2√2 / 2

AE = √2

The distance AE = √2

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Student 4 used the least amount of paint for the art project

Given:

Student 1 used seventeen twentieths => 17/20

Student 2 used 1 and one-fourth => 1 1/4 = 5/4

Student 3 used 65% = 65/100

Student 4 used 0.20 = 20/100

Since the amount of paint used for the art project has been expressed in fractions. Find the LCM:

17/20, 5/4, 65/100, 20/100

The  LCM of 20, 4 and 100 is 100

Student 1: 17/20 = 85/100

Student 2: 5/4 = 125/100

Student 3: 65/100

Student 4: 20/100

Thus, student 4 used the least amount of paint

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Answer: Student 4 (d)

Step-by-step explanation:

Brainliest?

A vertex is a point where two or more curves, lines, or edges meet.

In geometry, vertex generally refers to an intersection point or a corner where lines, curves or edges meet. As a consequence of this definition, the point where two lines meet to form an angle called an included angle are considered vertices. Hence, the corners of triangle, polygons and polyhedral are vertices. For example, the lines of square or rectangle intersect at four corners which are called its vertices (which is the plural of vertex). Similarly, the vertex of curve(s) is where they intersect with each other or with its line of symmetry.

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The number of tiles in the bag of 10 that are yellow in colour are; 5 tiles

We are given;

Total number of tiles in bag = 10 tiles

Now, we are told that in the bag, the tiles are either blue, green, red, or yellow.

Now, after selecting a tile, we are told that it is put back and as such we have after 100 selections that we have 24 blue tiles, 12 green tiles and 12 red tiles. Thus;

Number that will be yellow = 100 - 24 - 12 - 12 = 52 yellow tiles

Thus, it means that the probability of selecting a yellow tile is;

52/100

Thus, number of tiles out of the 10 in the bag that are yellow =

(52/100) * 10 = 5.2

Approximately 5 yellow tiles

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Complete question is;

How many yellow tiles are most likely in the bag? Enter the answer in the box. A tile is randomly selected from a bag that contains 10 tiles. The tiles are either blue, green, red, or yellow. After the color is recorded, the tile is placed back in the bag. A tile is pulled 100 times, of which 24 are blue tiles, 12 are green tiles, and 12 are red tiles.​

If f{g(x)} = g(x) and g{f(x)} = f(x)

That means they cannot be inverse functions of one another.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that f(3) = 2 and g(-2) = 6.

From the expression, f⁻¹(2) = 3 and g⁻¹(6) = -2

So now we take the composition,

f{g(-2)} = f (6) = y (let)

Then f⁻¹(y) = 6 = g (-2) , which is given.

Now, f{g(-2)} = g (-2).

And similarly g{f(3)} = g (2) = k (let)

g⁻¹(k) = 2 = f (3)

Now, g{f(3)} = f (3)

Therefore, if f{g(x)} = g(x) and g{f(x)} = f(x)

That means they cannot be inverse functions of one another.

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The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Here,

1. Statement: AB=CD,BC=AD

Reason: By definition of parallelogram.

2. Statement: AC=AC

Reason: Reflexive property of equality.

The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.

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The correct option is D .

This is a parabola with domain all real numbers D .

The number of tickets that will be sold is 5560.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets sold will be = 94520/17 = 5560.

Hence, the number of tickets that will be sold is 5560.

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Answer:

somone in my class is literally a new York rat

Step-by-step explanation:

45 people used credit card on that particular day , this could be found out using simplified multiplication.

What is proportion?

A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.

A proportion is Associate in Nursing equation within which 2 ratios ar set up to one another.

Main body:

We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.

To find the number of people, who used credit card, we will find 75% of 60.

The number of people who used credit card = (75 / 100 )* 60

The number of people who used credit card = 0.75 *60

The number of people who used credit card = 45

Therefore, 45 people used credit card on that particular day.

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Answer:

[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]

Step-by-step explanation:

There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.

There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.

The only option that satisfies this is Option 1.

The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.

The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.

Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.

Hence , the graph of the function is plotted

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Answer:

-36

Step-by-step explanation:

-3[tex]a^{2}[/tex]b  Substitute -2 for a and 3 for b

-3[tex](-2)^{2}[/tex](3)

-3(4)(3)

-36

Answer:

= -36

Step-by-step explanation:

-3a²b

if:

a = -2

b = 3

Then:

= -3*-2²*3

= -3(-2*-2) * 3

= -3*4*3

= -36

Answer:

9 x (x - 2) and (2 x - 3) (2 x + 3)

Step-by-step explanation:

Factor the following:

9 x^2 - 18 x

Factor 9 x out of 9 x^2 - 18 x:

Answer: 9 x (x - 2)

Factor the following:

4 x^2 - 9

4 x^2 - 9 = (2 x)^2 - 3^2:

(2 x)^2 - 3^2

Factor the difference of two squares. (2 x)^2 - 3^2 = (2 x - 3) (2 x + 3):

Answer: (2 x - 3) (2 x + 3)

If the decision of enrolling in the course in independent events, the probability of not enroll in chemistry is 0.55

The chances of enroll in physics = 10%

The chances of the not enroll in physics but enroll in chemistry = 45%

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Given that her decision of enrolling in a course is independent of enrolling in other courses

The probability of not enroll in chemistry = 1 - The probability of enroll in chemistry

Substitute the value in the equation

The probability of not enroll in chemistry = 1 - 0.45

= 0.55

Therefore, the probability of not enroll in chemistry is 0.55

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Internal validity refers to the accuracy of the evaluation in attributing the changes identified to the program and not to other factors, such as demographic differences between the participants and the control group.

To ensure internal validity, one must compare the participants and the control groups on demographic characteristics in order to show that the differences found in the evaluation are due to program differences and not to demographic differences. This is done by conducting a statistical comparison of the two groups and calculating the probability that any differences found between them are due to the program and not to some other factor. This is done by computing the probability that the two groups are the same, given the observed mean differences, and then evaluating the results to determine if the differences are statistically significant. For example, if the two groups have different means, the probability of them being the same is calculated, and if this probability is low, then the difference is likely to be due to the program and not to some other factor. This type of statistical analysis speaks to the internal validity of the evaluation.  

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Answer:

x = 13

x = 1

Step-by-step explanation:

The (x – 7)2 = 36 gives the value of x as 25.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

(x – 7)2 = 36

Now, dividing both side by 2

(x – 7)2/2 = 36 /2

(x – 7) = 18

Now, add 7 both side

x- 7+ 7= 18 + 7

x = 25

Hence, the value of x is 25.

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Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

Given that,

A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.

We have to determine the camper's hiking speed.

We know that,

Let x represent the increasing rate and 10x represent the driving rate.

Time equation is

80/10x+4/x=3

Simplify

8/x+4/x=3

12/x=3

x=12/3=4

Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

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The solution for the variable is that the variable should be greater than 9.375

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: the inequality 58x+170 > 42x+320. The unknown variable is x

In word problem, we can write:

When a variable x is multiplied by 58 and then 170 is added. The result is greater than variable x multiplied by 42 with 320 added

Solution for the unknown

58x+170 > 42x+320

58x-42x > 320-170

16x > 150

x > 150/16

x > 9.375

Thus, the solution for the unknown is that the unknown should be greater than 9.375

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Answer:

Given:

Sum of edge lengths = TSA of cube

there are 12 edges in a cube

[tex]12n = 6 {n}^{2} \\ 6 {n}^{2} - 12n = 0 \\ 6n(n - 2) = 0 \\ 6n = 0 \\ n = 0 \\ n - 2 = 0 \\ n = 2[/tex]

n ≠ 0 (since length can't be 0)

therefore n=2