Use the frequency distribution to construct a histogram. Using a loose interpretation of the requirements for a normal​ distribution, does the histogram appear to depict data that have a normal​ distribution? Why or why​ not?

Answer:

[tex]{ \bf{(a).}} \\ { \tt{ {n}^{th} = a + (n - 1)d }} \\ { \tt{ {n}^{th} = 6 + (n - 1) \times - 4 }} \\ {n}^{th} = 10 - 4n \\ \\ { \bf{(b).}} \\ { \tt{ {n}^{th} = - 8 + (n- 1) \times - 7 }} \\ { \tt{ {n}^{th} = -1 - 7n}}[/tex]

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Answer:

The x-intercept is the value of the variable x when the value of the function is equal to zero

so

In the table we have

(-1, 0)(−1,0) is a x-intercept, because

For x=-1x=−1 the value of the function is equal to zero

(-6, 0)(−6,0) is a x-intercept, because

For x=-6x=−6 the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

(-1, 0)(−1,0)

(-6, 0)(−6,0)

Answer:

theres the graph

Step-by-step explanation:

Answer:

Yea you are right.

Step-by-step explanation:

Step-by-step explanation:

everything can be found in the picture

Answer:

5 × (x + 27) ≥ 6 × (x + 26).

Step-by-step explanation:

The solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

For this case, let the number in consideration be 'x', then according to the condition specified, we get:

Also, we get:

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 as:

[tex]5(x+27) \geq 6(x+26)[/tex]

Expanding and taking x on one side:

[tex]5x+135 \geq 6x+156\\135-156 \geq x \\\\x \leq -21[/tex]

Thus, the considered statement is true for all the numbers which is smaller or equal to -21. Symbolically, the solution set is: (-∞, -21]

The square bracket shows that the -21 is included in the interval. And the interval  (-∞, -21] is  set of all real numbers smaller or equal to -21.

Thus, the solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]

Learn more about inequalities here:

https://brainly.com/question/27425770

Answer:

[tex]y=-2x+8[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]y=-2x+1[/tex]

The given line has a slope of -2. Because parallel lines always have equal slopes, we know that the line parallel to this would also have a slope of -2. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-2x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-2x+b[/tex]

Plug in the given point (2,4) to solve for b

[tex]4=-2(2)+b\\4=-4+b[/tex]

Add 4 to both sides to isolate b

[tex]4+4=-4+b+4\\8=b[/tex]

Therefore, the y-intercept of the line is 8. Plug this back into [tex]y=-2x+b[/tex]:

[tex]y=-2x+8[/tex]

I hope this helps!

Answer:

The total number of ways to give the answer of the question is 16777216.

Step-by-step explanation:

Total number of questions = 24

The number of possibilities so that the answer is given is only 2. It is either true or false.

So, the total number of ways to complete the test is

[tex]2^{24} = 16777216[/tex]

Answer:

Option (3)

Step-by-step explanation:

Base function in the graph is 'f' and the transformed form of the function 'f' is function 'g'.

Since, the base function 'f' is reflected across the x-axis,

h(x) = -f(x)

Followed by the translation by 3 units downwards,

g(x) = h(x) - 3

      = -f(x) - 3

Therefore, function in the form of g(x) = -f(x) - 3 will be the answer.

Option (3) is the correct option.

[tex]f'(4) = 43[/tex]

Explanation:

Given: [tex]f(x)=5x^2 + 3x + 3[/tex]

[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]

Note that

[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]

[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]

[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]

Substituting the above equation into the expression for f'(x), we can then write f'(x) as

[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]

[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]

[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]

Therefore,

[tex]f'(4) = 10(4) + 3 = 43[/tex]

Answer:

64 cm^3

Step-by-step explanation:

answer for question no 5

length , breadth and height of the cube are always equal .So

here length = 4 cm

volume of a cube = l^3

=4^3

=64 m^2

Answer:

add a picture so i can see .

Step-by-step explanation:

Answer: (X-12)(x+4)

The middle number is -8 and the last number is -48.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -8

Multiply together to get -48

Can you think of the two numbers?

Try 4 and -12:

4+-12 = -8

4*-12 = -48

Fill in the blanks in

(x+_)(x+_)

with 4 and -12 to get...

(x+4)(x-12)

Answer:

(x+4)(x−12)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { (x - 12)(x + 4 )}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{2} - 8x - 48[/tex]

[tex] = {x}^{2} + 4x - 12x - 48[/tex]

Taking [tex]x[/tex] as common from first two terms and [tex]12[/tex] from last two terms, we have

[tex] = x \: (x + 4) - 12 \: (x + 4)[/tex]

Taking the factor [tex](x+4)[/tex] as common,

[tex] = (x - 12)(x + 4)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

5x / (x - 4)

Step-by-step explanation:

(x + 1)/(x - 4) • 5x/(x + 1)

Method 1:

Cancel out x + 1

Leaving 5x/(x - 4)

Method 2:

(x + 1)/(x - 4) • 5x/(x + 1)

Multiply numerator and denominator separately

= 5x(x + 1) / (x - 4)(x + 1)

Cancel out (x + 1) in the numerator and (x + 1) in the denominator

= 5x / (x - 4)

Therefore,

(x + 1)/(x - 4) • 5x/(x + 1) = 5x / (x - 4)

Answer:

5.7

Step-by-step explanation:

We can use a proportion to solve the problem:

24 : 100 = 1.37 : x

x = (100 * 1.37)/24 = 137/24 = 5.7

Answer:

0.1111

Step-by-step explanation:

From the given information;

Number of staffs in the actuary = 80

Out of the 80, 10 are students.

i.e.

P(student actuary) = 10/80 = 0.125

number of weeks in a year = 52

off time per year = 10/52 = 0.1923

P(at work || student actuary) = (50 -10/52)

= 42/52

= 0.8077

P(non student actuary) = (80 -10)/80

= 70 / 80

= 0.875

For a non-student, they are only eligible to 4 weeks off in a year

i.e.

P(at work | non student) = (52-4)/52

= 48/52

= 0.9231

∴

P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)

P(at work) =  (0.125 × 0.8077) + ( 0.875 × 0.9231)

P(at work) = 0.1009625 + 0.8077125

P(at work) = 0.90868

Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)

P(he is a student) = (0.125 × 0.8077) ÷ 0.90868

P(he is a student) = 0.1009625 ÷ 0.90868

P(he is a student) = 0.1111

Answer:

[tex]\sigma = 12.5[/tex] ---- sample standard deviation

[tex]\sigma^2 = 157.2[/tex] ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

[tex]x_1 = \frac{56 + 64}{2} = 60[/tex]

[tex]x_2 = \frac{65 + 73}{2} = 69[/tex]

And so on

So, the table becomes:

[tex]\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}[/tex]

Calculate the mean

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}[/tex]

[tex]\bar x = \frac{4191}{55}[/tex]

[tex]\bar x = 76.2[/tex]

The variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}[/tex]

[tex]\sigma^2 = \frac{8488.8}{54}[/tex]

[tex]\sigma^2 = 157.2[/tex]

The sample standard deviation is:

[tex]\sigma = \sqrt{\sigma^2[/tex]

[tex]\sigma = \sqrt{157.2[/tex]

[tex]\sigma = 12.5[/tex]

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

[tex]\sigma^2 = 157.2[/tex]

Answer:

a) The mean is of [tex]\mu = 0.16[/tex]

b) The standard deviation is of [tex]s = 0.008[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Question a:

Exactly 16% of all applications were from minority members

This means [tex]p = 0.16[/tex], and thus, the mean is of [tex]\mu = p = 0.16[/tex]

b. Find the standard deviation of p.

2100 open positions, thus [tex]n = 2100[/tex].

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.16*0.84}{2100}}[/tex]

[tex]s = 0.008[/tex]

The standard deviation is of [tex]s = 0.008[/tex]

Answer:

The total number of registered doctors was 167,722.

Step-by-step explanation:

Total number of doctors:

The total number of doctors is given by x.

31.6% of all registered doctors were female. 53,000 female doctors.

This means that:

[tex]0.316x = 53000[/tex]

What was the total number of registered doctors?

We have to solve the above equation for x. So

[tex]x = \frac{53000}{0.316}[/tex]

[tex]x = 167722[/tex]

The total number of registered doctors was 167,722.

Answer:

Step-by-step explanation:

Answer:

6.667

Step-by-step explanation:

I just did the calculations

Answer:

787.50

Step-by-step explanation:

interest=3500*7.5*3/100

interest=35*7.5*3

interest=787.50

Step-by-step explanation:

I am not critically certain but the ways you have jotted down your enquiry..

13 × (4×11)

13 × 44

=572 - 44= 528

528+13 =541

541 ×13=7033

Answer:

Y is -1.

Step-by-step explanation:

If you substitute the values, you find that that's the correct answer.

Answer:

50"

В

A

mC

m B

mA

Step-by-step explanation:

Answer:

the answer will be table -1

Step-by-step explanation:

Answer:

324 yds ^2

Step-by-step explanation:

If length=l and width=w, you could write an equation to find the length and width. Then use that to find the area. L=4w. There are two of each side in the rectangle. 4w+4w+w+w=10w. 10w=90. w=9. 4w=36. L=36. 36*9=324yds^2