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2 years ago

How many 4-digits number can be formed out of 0,1,2,3,5,7 and 8. If:

Mathematics

1 answer:

Bad White [126]2 years ago

5 0

Answer:

Below in bold.

Step-by-step explanation:

No repetition.

There are a total of 7 numbers.

For the number to be even it must end in 0, 2 or 8.

The other 3 numbers will be the number of permutations of 3 from the 6 other numbers.

Number of 4 digit numbers ending in 0

= 6P3 = 6! / 6-3!

= 120.

Now the number could also end in 2 or 8,

so there are 3*120 = 360 4-digit even numbers (no repetition).

With repetition.

There are 3 * 7^3 = 1029 with repetition.

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Answer quick please I dont really get this

Triss [41]

Answer:

f(9) = 24

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = 4(x - 3)

f(9) is x = 9

Step 2: Evaluate

Substitute in x: f(9) = 4(9 - 3)
Subtract: f(9) = 4(6)
Multiply: f(9) = 24

4 0

3 years ago

If log7=a and log… help me solve ths math problem on picture

tatiyna

$\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}$

Let's solve ~

$\qquad \sf \dashrightarrow \: log_{4}(39.2)$

$\qquad \sf \dashrightarrow \: log_{4}( {2}^{3} \times {7}^{2} \times 10 {}^{ - 1} )$

$\qquad \sf \dashrightarrow \: log_{4}( {2}^{3} ) + log_{4}( {7}^{2} ) + log_{4}(10 {}^{ - 1} )$

$\qquad \sf \dashrightarrow \: log_{ {2}^{2} }( {2}^{3} ) + log_{ {2}^{2} }( {7}^{2} ) + log_{ {2}^{2} }(10 {}^{ - 1} )$

$\qquad \sf \dashrightarrow \: \frac{3}{2} log_{2}(2) + \frac{2}{2} log_{2}(7) - \frac{1}{2} log_{2}(10)$

$\qquad \sf \dashrightarrow \: \frac{3}{2} + a - \frac{b}{2}$

That's the required result ~

also you can take it's LCM and write it as :

$\qquad \sf \dashrightarrow \: \dfrac{2a - b + 3}{2}$

3 0

2 years ago

Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal place

Katyanochek1 [597]

Answer:

a. 0.2898

b. 0.0218

c. 0.1210

d. 0.1515

e. This is because the population is normally distributed.

Step-by-step explanation:

Assume that SAT scores are normally distributed with mean 1518 and standard deviation 325. Round your answers to 4 decimal places

We are using the z score formula when random samples

This is given as:

z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is the random number of samples

a.If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.

For x = 1500, n = 100

z = 1500 - 1518/325/√100

z = -18/325/10

z = -18/32.5

z = -0.55385

Probability value from Z-Table:

P(x<1500) = 0.28984

Approximately = 0.2898

b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600

For x = 1600, n = 64

= z = 1600 - 1518/325/√64.

z= 1600 - 1518 /325/8

z = 2.01846

Probability value from Z-Table:

P(x<1600) = 0.97823

P(x>1600) = 1 - P(x<1600) = 0.021772

Approximately = 0.0218

c. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575

For x = 1550, n = 25

z = 1550 - 1518/325/√25

z = 1550 - 1518/325/5

z = 1550 - 1518/65

= 0.49231

Probability value from Z-Table:

P(x = 1550) = 0.68875

For x = 1575 , n = 25

z = 1575 - 1518/325/√25

z = 1575 - 1518/325/5

z = 1575 - 1518/65

z = 0.87692

Probability value from Z-Table:

P(x=1575) = 0.80974

The probability that they have a mean between 1550 and 1575

P(x = 1575) - P(x = 1550)

= 0.80974 - 0.68875

= 0.12099

Approximately = 0.1210

d. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480

For x = 1440, n = 16

z = 1440 - 1518/325/√16

= -0.96

Probability value from Z-Table:

P(x = 1440) = 0.16853

For x = 1480, n = 16

z = 1480 - 1518/325/√16

=-0.46769

Probability value from Z-Table:

P(x = 1480) = 0.32

The probability that they have a mean between 1440 and 1480

P(x = 1480) - P(x = 1440)

= 0.32 - 0.16853

= 0.15147

Approximately = 0.1515

e. In part c and part d, why can the central limit theorem be used even though the sample size does not exceed 30?

The central theorem can be used even though the sample size does not exceed 30 because the population is normally distributed.

6 0

3 years ago

Which expressions represent rational numbers? select all the apply. startroot 100 endroot startroot 100 endroot 13.5 startroot 8

zlopas [31]

The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.

<h3>What is a rational number?</h3>

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

1. √100 × √100

→ √100 × √100

→ 10 × 10 = 100

This is a rational number.

2. 13.5 + √81

→ 13.5 + √81

→ 13.5 + 9 = 22.5

This is a rational number.

3. √9 + √729

→ √9 + √729

→ 3 + 27 = 30

This is a rational number.

4. √64+ √353

→ √64 + √353

→ 8 + √353

This is an irrational number.

5. 1/3 + √216

→ 1/3 + √216

This is an irrational number.

6. 1/5 + 2.5

→ 1/5 + 2.5

→ 0.2 + 2.5 = 2.7

This is a rational number.

More about the rational number link is given below.

brainly.com/question/9466779

7 0

3 years ago

Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose

gavmur [86]

Answer:

Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

Step-by-step explanation:

We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.

If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.

Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.

SO, Margin of error formula is given by;

Margin of error = $Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }$

where, $\alpha$ = significance level = 10%

$\sigma$ = standard deviation = 2.0

n = number of families

Now, in the z table the critical value of x at 5% ( $\frac{0.10}{2} = 0.05$ ) level of significance is 1.645.

SO, Margin of error = $Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }$

0.5 = $1.645 \times \frac{2}{\sqrt{n} }$

$\sqrt{n} =\frac{2\times 1.645 }{0.5}$

$\sqrt{n} =6.58$

n = $6.58^{2}$

= 43.3 ≈ 43

Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.

4 0

3 years ago