In a class of 40 students, 2
5
of the total number of students like to study English and 3
5
of the

total students like to study Mathematics.
a) How many students like to study English?
b)How many students like to study Mathematics?

Answer:

b. 2.333

Step-by-step explanation:

Test if the mean transaction time exceeds 60 seconds.

At the null hypothesis, we test if the mean transaction time is of 60 seconds, that is:

[tex]H_0: \mu = 60[/tex]

At the alternate hypothesis, we test if it exceeds, that is:

[tex]H_1: \mu > 60[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

60 is tested at the null hypothesis:

This means that [tex]\mu = 60[/tex]

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds.

This means that [tex]n = 16, X = 67, s = 12[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{67 - 60}{\frac{12}{\sqrt{16}}}[/tex]

[tex]t = \frac{7}{3}[/tex]

[tex]t = 2.333[/tex]

Thus, the correct answer is given by option b.

Answer:

3x4 +x3+ 15x2+30x-14

Step-by-step explanation:

Explanation:

P(T = 1) is the notation that means "The probability of getting exactly one tail". The table shows 3/8 in the bottom row, under the "1" in the top row. So that's why P(T = 1) = 3/8

Or it might make more sense to say P(one tail) = 3/8 so we don't have too many equal signs going on.

Answer:

[tex] 1 \dfrac{13}{15} [/tex]

Step-by-step explanation:

[tex] 2 \dfrac{1}{5} - \dfrac{1}{3} = [/tex]

[tex] = \dfrac{11}{5} - \dfrac{1}{3} [/tex]

[tex] = \dfrac{33}{15} - \dfrac{5}{15} [/tex]

[tex] = \dfrac{28}{15} [/tex]

[tex] = 1 \dfrac{13}{15} [/tex]

Answer:

A cuboid has a total of 6 rectangular sides. If you calculate the area of each of the 6 rectangular sides and add them up, you will get the surface area of the cuboid.

Surface Area of a Rectangle = Width x Height

Answer:

x is 37.,.,.,.,.,.,.,.,.,.,.,.,.,.,.,.

Answer:

x = 37

Step-by-step explanation:

Interior angles of a square is 90 each.

∠JKL = 90°

Given ∠JKL = 3x - 21

Therefore, 3x - 21 = 90

                    3x = 90 + 21

                    3x = 111

                      x =  37

Answer:

$3.53 per lb of salami

Step-by-step explanation:

0.75 lb of salami for $2.65

The price per of salami will be :

0.75 lb = $2.65

1 lb = x

Using cross multiplication :

0.75 * x = $2.65 * 1

0.75x = $2.65

Divide both sides by 0.75

0.75x / 0.75 = $2.65 / 0.75

x = $3.533

This means that :

The price per unit of salami is $3.53

Answer:

0.75 lb of salami for $2.65 is $3.53 per lb of salami.

Answer:

[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                                    [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                       [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

y = (2x - 5)²(5 - x)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Given:

The data set is:

87, 84, 85, 85, 86, 90, 79, 82, 78, 76

To find:

The mode of the given data set.

Solution:

We have,

87, 84, 85, 85, 86, 90, 79, 82, 78, 76

Arrange the data values in the ascending order.

76, 78, 79, 82, 84, 85, 85, 86, 87, 90

We know that the mode of date set is the most frequency value of the data set.

From the above data set it is clear that the number 85 has the highest frequency 2.

Therefore, the mode of the data set is 85.

Answer:

45

hope this helps

Answer:

45

Step-by-step explanation:

9x5=45

Answer:

A and A.

Step-by-step explanation:

Got it correct on edge 2022.

Answer:

Table C

Step-by-step explanation:

Given

[tex]1\ package = 6\ balls[/tex]

Required

Which table is correct

We have:

[tex]1\ package = 6\ balls[/tex]

For 7 packages, it will be:

[tex]7\ packages = 42\ balls[/tex] --- i.e. 6  * 7

For 8:

[tex]8\ packages = 48\ balls[/tex] --- i.e. 8 * 7

For p packages

[tex]f(p) = 6p[/tex]

Using the above formula, we can conclude that table (C) is correct

Answer:

acute triangle

Step-by-step explanation:

First find the other angle

The sum of the angles is 180

x+65+60  = 180

x + 125 = 180

x = 180-125

x = 55

All three angles are different so all three side lengths are different

All the angles are less than 90 so all the angles are acute

This is an acute scalene triangle

Answer:

im is 55 so the only correct option is c

Step-by-step explanation:

hope this helps! have a great day!!

Answer:

B. Quincy's claim is correct.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

[tex]M = z\frac{s}{\sqrt{n}}[/tex]

In which z is related to the confidence level, s is the standard error and n is the size of the sample.

From this interval, we have that the margin of error and the sample size are inversely proportional, that is, if we increase the sample size, the margin of error decreases, and so does the width of the confidence interval.

Peggy claims that the width of the confidence interval will increase if a sample size of 30 is used, all other things remaining the same.

Peggy is wrong, as the increase of the sample size results on the decrease of the margin of error, and a decrease of the width.

Quincy claims that the width of the confidence interval will decrease if a sample size of 30 is used.

Margin of error decreases, and so does the width of the interval, thus, Quincy's claim is correct, and the correct answer is given by option b.

Answer:

98

Step-by-step explanation:

x(o) + 1(o)  = 180(o)

∠2° = ∠x°

∠1° = ∠3°

Answer:

angle 2 is 82 also and angle 3 and 4 is 180 - 82 = 98

Sample variance = 228.408

Standard deviation = 15.113

The well formatted frequency table has been attached to this response.

To calculate the sample variance and standard deviation of the given grouped data, follow these steps:

i. Find the midpoint (m) of the class interval.

This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e

For class 0 - 9, we have

m = (0 + 9) / 2 = 4.5

For class 10 - 19, we have

m = (10 + 19) / 2 = 14.5

For class 20 - 29, we have

m = (20 + 29) / 2 = 24.5

For class 30 - 39, we have

m = (30 + 39) / 2 = 34.5

For class 40 - 49, we have

m = (40 + 49) / 2 = 44.5

This is shown in the third column of the attached table.

ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e

For class 0 - 9, we have

frequency (f) = 13

midpoint (m) = 4.5

=> f x m = 13 x 4.5 = 58.5

For class 10 - 19, we have

frequency (f) = 7

midpoint (m) = 14.5

=> f x m = 7 x 14.5 = 101.5

For class 20 - 29, we have

frequency (f) = 10

midpoint (m) = 24.5

=> f x m = 10 x 24.5 = 245

For class 30 - 39, we have

frequency (f) = 9

midpoint (m) = 34.5

=> f x m = 9 x 34.5 = 310.5

For class 40 - 49, we have

frequency (f) = 11

midpoint (m) = 44.5

=> f x m = 11 x 44.5 = 489.5

This is shown in the fourth column of the attached table.

iii. Calculate the mean (x) of the distribution i.e

This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e

x = ∑(f x m) ÷ ∑f

Where;

∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205

∑f = 13 + 7 + 10 + 9 + 11 = 50

=> x = 1205 ÷ 50

=> x = 24.1

Therefore, the mean is 24.1

This is shown on the fifth column of the attached table.

iv. Calculate the deviation of the midpoints from the mean.

This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint

For class 0 - 9, we have

midpoint (m) = 4.5

=> m - x = 4.5 - 24.1 = -19.6

For class 10 - 19, we have

midpoint (m) = 14.5

=> m - x = 14.5 - 24.1 = -9.6

For class 20 - 29, we have

midpoint (m) = 24.5

=> m - x = 24.5 - 24.1 = 0.4

For class 30 - 39, we have

midpoint (m) = 34.5

=> m - x = 34.5 - 24.1 = 10.4

For class 40 - 49, we have

midpoint (m) = 44.5

=> m - x = 44.5 - 24.1 = 20.4

This is shown on the sixth column of the attached table.

v. Find the square of each of the results in (iv) above.

This is done by finding (m-x)²

For class 0 - 9, we have

=> (m - x)² = (-19.6)² = 384.16

For class 10 - 19, we have

=> (m - x)² = (-9.6)² = 92.16

For class 20 - 29, we have

=> (m - x)² = (0.4)² = 0.16

For class 30 - 39, we have

=> (m - x)² = (10.4)² = 108.16

For class 40 - 49, we have

=> (m - x)² = (20.4)² = 416.16

This is shown on the seventh column of the attached table.

vi. Multiply each of the results in (v) above by their corresponding frequencies.

This is done by finding f(m-x)²

For class 0 - 9, we have

=> f(m - x)² = 13 x 384.16 =  4994.08

For class 10 - 19, we have

=> f(m - x)² = 7 x 92.16 = 645.12

For class 20 - 29, we have

=> f(m - x)² = 10 x 0.16 = 1.6

For class 30 - 39, we have

=> f(m - x)² = 9 x 108.16 = 973.44

For class 40 - 49, we have

=> f(m - x)² = 11 x 416.16 = 4577.76

This is shown on the eighth column of the attached table.

vi. Calculate the sample variance.

Variance σ², is calculated by using the following relation;

σ² = ∑f(m-x)² ÷ (∑f - 1)

This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.

∑f(m-x)² = sum of the results in (vi)

∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192

∑f - 1 = 50 - 1 = 49         {Remember that ∑f was calculated in (iii) above}

∴ σ² = 11192 ÷ 49 = 228.408

Therefore, the variance is 228.408

vii. Calculate the standard deviation

Standard deviation σ, is calculated by using the following relation;

σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]

This is done by taking the square root of the variance calculated above.

σ = [tex]\sqrt{228.408}[/tex]

σ = 15.113

Therefore, the standard deviation is 15.113

Answer:

y

Step-by-step explanation:

In function notation, f(x) is another way of saying y. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

Tables, symbols, and graphs can all be used to represent functions. Every one of these interpretations has benefits. Tables provide the functional values of certain inputs in an explicit manner. How to compute direct proportionality is succinctly stated in symbolic representation.

The function is represented as,

y = f(x)

In function notation, f(x) is another way of saying y. Then the correct option is A.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Respuesta:

3215360 cm³

Explicación paso a paso:

Dado que :

Radio = 160/2 = 80 cm

Altura, h = 160 cm

Volumen de un cilindro = πr²h

Volumen del cilindro = π * 80² * 160

Volumen = 3215360 cm³

Answer:

Mary's friend Larry is taller by 15cm.

Step-by-step explanation:

First look for the bigger number.

Then subtract the smaller number from the bigger number.

[tex]h(-3) - h( - 2) = - \frac{5}{ 8} \\ \\ [/tex]

Step-by-step explanation:

[tex]\boxed{h(x) = \frac{2 {x}^{2} - x + 1}{3x - 2}}[/tex]

[tex]h(2) = \frac{2 {(2)}^{2} - (2) + 1}{3(2) - 2} [/tex]

[tex]h(2) = \frac{2 {(4)} - 2 + 1}{6 - 2} [/tex]

[tex]h(2) = \frac{ 8 - 1}{4} [/tex]

[tex]h(2) = \frac{7}{4}[/tex]

[tex]h( - 3) = \frac{2 {( - 3)}^{2} - ( - 3) + 1}{3( - 3) - 2} \\ h( - 3) = \frac{2 (9) + 3 + 1}{ - 9- 2} \\ h( - 3) = \frac{18 + 4}{ - 11} \\ h( - 3) = \frac{22}{ - 11} \\ h(-3) = -2[/tex]

[tex]h( - 2) = \frac{2 {( - 2)}^{2} - ( - 2) + 1}{3( - 2) - 2} \\ h( - 2) = \frac{2 (4) + 2+ 1}{- 6 - 2} \\ h( - 2) = \frac{8 + 3}{- 8} \\ h( - 2) = \frac{11}{- 8} [/tex]

[tex]h(3) - h( - 2) = -2 - \frac{11}{- 8} \\ h(3) - h( - 2) =-2 + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-2}{1}+ \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16}{8} + \frac{11}{ 8} \\ h(3) - h( - 2) = \frac{-16+11}{8} \\ h(3) - h( - 2) = \frac{-5}{8} \\ - \frac{5}{ 8} [/tex]

Answer:

Subtract x x from both sides of the equation. 8y=20−x 8 y = 20 - x. Divide each term by 8 8 and simplify.

Solve for x 2x-4y=4. 2x−4y=4 2 x - 4 y = 4. Add 4y 4 y to both sides of the equation. 2x=4+4y 2 x = 4 + 4 y. Divide each term by 2 2 and simplify.

Answer:

100/8 = 12.5 (s)

Step-by-step explanation:

hmm bro

Answer:

[tex]{ \boxed{ \tt{formular : { \bf{ \green{time = \frac{distance}{speed} }}}}}} \\ time = \frac{100}{8} \\ { \boxed{time = 12.5 \: seconds}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]

Answer:

I think it's approximately 44°

You gave no options but the simplest way to solve this is to set it equal to all of the answers to see if it is correct.

Answer:

c I think that's the right answer