Complete the fraction to make a true inequality, and explain your reasoning


4 × < 4
3




I know this because the fraction I made

The probability that the randomly selected student  will chose running  can be written as  12/57.

The concept used is the probability which is the likelyhood of an event to take place.

Total number of students was given as  57

Total number of boys  that was given was  26

Total number of girls  can be written as 57-26=31`

Number of Girls that chose football  can be written as 15

Number of boys that chose football  can be wriitten as  9

Number of students that chose Tennis can be written as  18

Now, number of students that chose running will be;

Number of students that chose running = 57 - (24 + 18) = 15

Therefopre, probability that a randomly selected student chose running = 15/57

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Answer: 40 minus 8 divided by -4 + 6 x -7 = 0

Step-by-step explanation: i literally just used a calculator -_-

If the function f(x)= 2x – 3 and g(x) = 3/2x + 1 then g(4) < f(4) is a true statement?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

A function can also be said to be a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Functions are generally represented as f(x).

Let , f(x) = [tex]x^{3\\}[/tex].

It is said as f of x is equal to x cube.

Functions can also be represented by g(), t(),… etc.

For g(4) < f(4);

g(4) = 3/2(4) + 1

g(4) = 3/9

f(4) = 2(4) - 3

f(4) = 8 - 3

f(4) = 5

Therefore; g(4) < f(4)

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90 minutes

Step-by-step explanation:

1/2 an hour = 30 minutes

1/4 an hour = 15 minutes

45+15=60

60+30=90

The equation of the line that passes through the point (4, -2) and has a slope of 5/4, in point-slope form is: y + 2 = 5/4(x - 4).

If we are given a point (a, b), that a line goes through and we also know the slope (m) of the line, the equation of the line can be written as y - b = m(x - a) in point-slope form

Given that the line has the following:

A point (a, b) = (4, -2)

The slope of the line (m) = 5/4

To write the equation of the line, substitute m = 5/4, a = 4, and b = -2 into y - b = m(x - a):

y - (-2) = 5/4(x - 4)

y + 2 = 5/4(x - 4)

The answer is: y + 2 = 5/4(x - 4).

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Answer:

1.d

2.a

3.e

4.g

5.f

6.c

7.b

Step-by-step explanation:

did it already

Sleep hours per night is independent.

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The analysis will be conducted using the Chisquare statistic:

The supposition

H0: The amount of sleep each night is independent

H1: The amount of sleep each night is not independent

χ² = (observed - Expected) (observed - Expected)2 / Predicted

to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:

The evaluation statistic is 4.0061.

Row - 1 * The degree of freedom (column - 1)

Degree of freedom is equal to (4-1)*(2-1)=3*1=3.

Pvalue is 0.261.

Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %

> 6 _____38 36_ 74 _ 14.8

6 to 6.9 61 58 _ 119 23.8

7 to 7.9 __76 74 150 30

8 or higher 65 92 157 31.4

_______240 260 500 100

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The maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is  0 ≤ x ≤ 5 is 5^b.

Generally, To find the maximum value of a function on a given interval, it is generally helpful to find the critical points (points, where the derivative is equal to zero or the function, is undefined) and the endpoints of the interval, and then evaluate the function at these points to find the maximum value.

The d/dx f(x) is given by:

f'(x) = ax^(a-1)(5-x)^b - bx^a(5-x)^(b-1)

Setting this equal to zero and solving for x, we find that the critical points are x = 0, x = 5, and x = (5b)/(a+b).

We can then evaluate the function at these points to find the maximum value. At x = 0, f(x) = 0^a*(5-0)^b = 5^b.

At x = 5, f(x) = 5^a*(5-5)^b = 0.

At x = (5b)/(a+b),

f(x) = [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

Since a and b are positive, the maximum value must occur at either x = 0 or

x = (5b)/(a+b).

To determine which of these points gives the larger value of f(x), we can compare the values of

5^b and [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

The expression [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b is equal to [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b.

Since a and b are positive, [(5b)/(a+b)]^a and [(a+b-5b)/(a+b)]^b are both greater than or equal to 1, so the expression [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b is greater than or equal to 1.

Therefore, the maximum value of f(x) is 5^b, which occurs at x = 0.

Thus, the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 5^b.

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the trigonometric function of all the given question is obtained.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

Given: Cos θ = (3/5), Find: Csc θ = 5/4

Given: Sin θ = (5/6), Find: Cot θ = 11/5

Given: tan θ = (3/4), Find: Cot θ= 4/3

Given: Sec θ = (7/2), Find: Cos θ= 2/7

Given: Sin θ = (2/3), Find: Cosec θ=3/2

Given: Sin θ = (2/3), Find: Cos θ=5/3

Given: Tan θ = (6/4), Find: Sin θ=6/7.21

Given: Tan θ = (7/5), Find: Cos θ=5/8.6

Given: Tan θ = (7/5), Find: Sec θ= 8.6/5

Hence the above trigonometric function of all the given question is obtained.

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90% confidence interval is 82.11 < μ < 93.89

"Information available from the question"

The complete question is this:

The managers of a company are worried about the morale of their employees. In order to determine whether a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.

Due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88 points. What is the 90% confidence interval?

Now, According to the question:

We have :

The confidence level = 0.90

The significance level, [tex]\alpha[/tex] = 0.10

The sample mean, x = 88

The population standard deviation, σ = 24

The sample size, n = 45

Critical value of z using the z - distribution table:

z(critical) = [tex]z_\alpha[/tex] /2

               =  [tex]z_0_._0_5[/tex]

               = ±1.645

90% confidence interval:

μ = x ± z. σ/[tex]\sqrt{n}[/tex]

μ = 88 ± 1.645 x 24 / [tex]\sqrt{45}[/tex]

μ = 88 ± 5.89

82.11 < μ < 93.89

Hence, 90% confidence interval is 82.11 < μ < 93.89

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Answer:

24

Step-by-step explanation:

4+5+6+4+5=24

simple

no big deal

Answer:

Previous meter reading: 2090

Charge per unit: 12p per unit

Step-by-step explanation:

Answer:

£43.26

Step-by-step explanation:

Given readings:

Calculate the number of units used:

[tex]\begin{aligned} \textsf{Number of units used} &= \textsf{Present meter reading} - \textsf{Previous meter reading}\\&= \sf 2410 - 2090\\&= \sf 320\; units \end{aligned}[/tex]

Given charges:

Calculate the cost excluding VAT:

[tex]\begin{aligned}\textsf{Cost (exc. VAT)}&=\textsf{(\# of units $\times$ charge per unit)}+\textsf{(\# of days $\times$ service charge per day)}\\ & = \sf 320 \times \£0.12 + 14 \times \£0.20\\&= \sf \£38.4+\£2.8\\&= \sf \£41.20\end{aligned}[/tex]

To find the total cost including VAT at 5%, multiply the cost (exc. VAT) by 1.05:

[tex]\begin{aligned}\textsf{Cost (inc. VAT at 5\%)}&= \sf \£41.20 \times 1.05\\&= \sf \£43.26\end{aligned}[/tex]

The z-score for the time spent on advertisement as calculated is 1.666 .

According to a television station, there is 15  minutes on average of advertising every hour of broadcast time, with a standard deviation of 1.2 minutes.

i.e.

mean = 15

SD =1.2

Per hour's worth of advertising is represented by the random variable x.

z = x - mean / SD

Since x=17 , we have

z = ( 17 - 15 ) / 1.2

  = 2 / 1.2

  = 1.666

Consequently, this amount of advertising time has a z-score of -1.666.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

A standard normal table is a mathematical table for the values of, displaying the values of the cumulative distribution function of the normal distribution. It is also known as the unit normal table or the z-score table. The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.

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Answer:

1. Given

2. Subtraction P.O.E

3. Addition P.O.E

4. Division P.O.E

5. Symmetric P.O.E

Step-by-step explanation:

P.O.E stands for Property of Equality

Answer: 45

Step-by-step explanation:

The PE ratio will be equal to $22. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jangles Co. earned $1.80 per share. Assuming a closing price of $40. The PE ratio will be calculated as,

Earning per share = $1.80

The price of the share = $40

PE ratio = Price of the share ÷ Earning per share

PE ratio = $40/$1.8-

PE ratio = $22.

Therefore, the PE ratio will be equal to $22. The correct option is B.

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Answer: 48

Step-by-step explanation:

[tex]\displaystyle\\\frac{32(150\%)}{100\%} =\\\\\frac{4800}{100}= \\\\48[/tex]

Answer:

48

Step-by-step explanation:

150% = 150/100 = 1.5

Then:

32 * 1.5 = 48

The probability of winning or loosing the game is x/559

The term probability is known as  the occurrence of a random event and it can be written between zero to one.

Here we need to find how much would you expect to win or lose, if you played this game 559 times.

While we looking into the given question, we have known that there is no proper number of time that the coin has tossed so let us consider x be the amount of time the coin has been tossed.

AS we know that the formula to find the probability is written as

P(E) = n(E)/n(S)

here the value of n(S) is 559 and the value of n(E) is x.

So, the probability is written as,

=> P = x/559

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The dimensions of a rectangle are 19m.

Here we have to find the dimensions of a rectangle.

Data given:

Perimeter = 76m

The formula for the perimeter of the rectangle:

perimeter = 2( length + breadth)

So,

76 = 2 ( l+b)

l + b = 38

l = 38 -b

The formula for the area of the rectangle:

Area = length × breadth

A =( 38-b)×b

  = 38b - b²

At maximum point:

dA/ dw = 38 - 2b

38 - 2b = 0

b = 19

Therefore the dimension is 19m.

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The appropriate conclusion at the 5% significance level is b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

[tex]\bar{x_1}[/tex] = pounds per batch distributor A = 23

[tex]\bar{x_2}[/tex] = pounds per batch distributor B = 18

[tex]\sigma_{1}[/tex] = standard deviation distributor A = 4

[tex]\sigma_{2}[/tex] = standard deviation distributor B = 5

n = sample size = 4

α = significance level = 5% = 0.05

Test statistic is using z test to find the z value from two population, after that we can search p-value and then comparing the p-value with significance level.

If p-value is lower than significance level, the null hypothesis (H0) is accepted. But, if p-value is higher than significance level, the H0 is rejected.

Calculate test statistic by this formula,

Z = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1 + \sigma^2_2}{n}}}[/tex]

= [tex]\frac{23-18}{\sqrt{\frac{4^2 + 5^2}{4}}}[/tex]

= [tex]\frac{5}{\sqrt{\frac{16 + 25}{4}}}[/tex]

= 1.56

Using z table for 1.56, we get 0.9406. Since is right tailed test. So, p value is

p-value = 1 - 0.9406

= 0.0594

Then, p-value is 0.0594 is higher than significance level 0.05. So, H0 is rejected.

Thus, the conclusion is reject H0, we cannot conclude the mean amount of fertilizer per batch distributor A is greater than distributor B.

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Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.

Here,

This mathematical sequence can be written as follows:

A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or

where:

First term: a

d stands for common variation.

It is stated that the arithmetic sequence formula is

a = a + (n-1)d

where

First term: a

n = the number of terms

d stands for common variation.

Common Difference

In mathematical terminology, the common difference is the difference between two words.

2, 5, 8, 11, and more problems

Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.

d = 5 - 2 d = 8 - 5 d = 11-8

d = 3.

Each of them differs by 3 points.

The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.

Issues 2, 4, 6, 8, and 10 exist.

Answer:

d = -4 - 2 = -6

d = 6 - (-4) = 10

It does not contain arithmetic sequences because there is no common difference.

Challenge: -6, -10, -14, -18,...

Answer:

d = -10 - (-6) = -4

d= -14 - (-10) = -4

d= -18 - (-14) = -4

There is a -4 difference between them all.

The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.

Issues 40, 42, 44, 46,...

Answer:

d = 42 - 40 = 2

d = 44 - 42 = 2

d = 46 - 44 = 2

All of them differ by 2 points.

The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.

Issues: 1.2, 1.8, 2.4,...

Answer:

d = 1.8 - 1.2 = 0.6

d = 2.4 - 1.8 = 0.6

They are all separated by 0.6.

1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.

Issues 1, 5, and 9,13

Answer:

d = 5 - 1 = 4

d = 9 - 5 = 4

d = 13 - 9 = 4

They are all divided by 4 in common.

The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

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Answer: x=3

Step-by-step explanation:

[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]

Divide both parts of the equation by 4:

[tex]x=3[/tex]

As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday

Probability:

In statistics, probability refers the possible and favorable outcome of the particular event.

Given,

Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.

Here we know that the writers of the same genre may not speak on consecutive nights.

And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday

So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.

Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.

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Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.

Two or more expressions with an Equal sign is called as Equation.

Given,

Distance = Rate x Time

Let Kala's swimming speed = X

4 km =   (X-2)×Time

12 km = (X+2) × Time

4/x-2 = 12/x+2

Apply cross multiplication

4(x+2)=12(x-2)

4x+8=12x-24

Take all variables on one side

4x-12x=-24-8

-8x=-32

Divide both sides by 8

x=4

Kala swims 4 km/hour

With the current he swims 6 km/hour

Hence, Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.

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Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .

Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;

Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute

We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;

Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute

Amount of water in Container A in one minute = (4/3) - (1/3)

= 1

Similarly;

Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;

Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute

We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;

Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute

Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6

Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6

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Complete question is;

two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain

The option a "The chi-square test for independence" is correct.

In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.

The given options are

A) The chi-square test for independence

B) Pearson product moment test

C) The chi-square test for homogeneity

D) Goodness-of-fit test

E) Welch’s t test

As we know that;

When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.

So, the chi-square test for independence is correct answer.

Option (B) and (E) are two-sample tests.

(C) involves two attributes.

(D) Doesn't check association.

Hence all these are incorrect.

So the option a "The chi-square test for independence" is correct.

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Answer:

option 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 10 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex]

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{1}{6}[/tex] and (a, b ) = (5, - 8 ) , then

y - (- 8) = - [tex]\frac{1}{6}[/tex] (x - 5 ) , that is

y + 8 = - [tex]\frac{1}{6}[/tex] (x - 5) ← equation of perpendicular line

Using the t-distribution, it is found that the 95% confidence interval for the mean peak power after training is (301.2, 328.8).

We have the standard deviation for the sample, thus, the t-distribution is used.

The sample mean is 315.

The sample standard deviation is s = 16.

The sample size is n = 7.

The interval is:

mean ± t s/√n

To build the interval, we need to find the critical value, which looking at the t-table for a 95% confidence interval with 8 - 1 = 7 df is t = 2.4469.

Then, replacing the values:

315 - 2.4469 16/√8 = 301.2

315 + 2.4469 16/√8 = 328.8

The 95% confidence interval for the mean peak power after training is (301.2, 328.8).

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R possess Symmetric property.

Let S be the set of all polynomials of degree at most 3.

s(x) = ax³ + bx² + cx + d

we know that polynomial is a mathematical expression of one or more algebraic terms each of which consist of a constant multiplied by one or more variables raised to a non negative power.  

The reflexive property states that every element of the set is related to itself.

The symmetric property is defined as if one element in a set is related to the other, then we can say that the second element is also related to the first element.

The transitive property states that if a, b, c are three quantities, and if a is related to b and b is related to c then a and c are related  to each other.

So here we observe that R will posses symmetric property.

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