i need help on this question

Answer:

[tex]log 9! = a-1[/tex]

Step-by-step explanation:

[tex](log10! = a) = (10^{a} = 10!)\\\\\\10! = 10 * 9 * 8 * 7 ...\\\\10^a = 10 * 9 * 8 * 7 ...\\\\10^a = 10 * 9!\\\\\frac{10^a}{10^1} = 9!\\\\10^{a-1} = 9!\\\\log9! = a-1[/tex]

The expression for log 9! in terms of a is [tex]log9! = a - 1[/tex].

Given that,

Based on the above information, the calculation is as follows:

[tex](log10! = a) = (10^{a} = 10!)\\\\10! = 10\times 9\times 8\times 7\\\\10^{a} = = 10\times 9\times 8\times 7\\\\10^{a} = 10\times 9!\\\\\frac{10^{a}}{10^{1}} = 9!\\\\10^{a - 1} = 9!\\\\log9! = a - 1[/tex]

Learn more: brainly.com/question/16911495

Answer:

57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes 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, we have that [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.9, n = 144[/tex]

So

[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{144}} = 0.025[/tex]

What is the probability that the proportion of people who will order coffee with their meal is within 2% of the population mean?

This is the pvalue of Z when X = 0.9 + 0.02 = 0.92 subtracted by the pvalue of Z when X = 0.9 - 0.02 = 0.88. So

X = 0.92

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.92 - 0.9}{0.025}[/tex]

[tex]Z = 0.8[/tex]

[tex]Z = 0.8[/tex] has a pvalue of 0.7881

X = 0.88

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.88 - 0.9}{0.025}[/tex]

[tex]Z = -0.8[/tex]

[tex]Z = -0.8[/tex] has a pvalue of 0.2119

0.7881 - 0.2119 = 0.5762

57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.

Answer:

1, -3

Step-by-step explanation:

I'm pretty sure it's that one because it doesn't fit with the others.

This question is incomplete because it lacks the attached diagram.

Find attached to this answer the appropriate diagram

Answer:

500 square centimeters

Step-by-step explanation:

From the question above, we are told that the top and bottom of the triangular prism is open.

Hence, the area of the piece of the cardboard is = Lateral Surface Area of the triangular prism

The formula for Lateral Surface Area of a Triangular Prism = Perimeter of the Triangular prism × Height of the Triangular prism.

Perimeter of the Triangular prism = Side a + Side b + Side c

Where Side a = 9cm

Side b = 9cm

Side c = 7 cm

Perimeter of the Triangular prism = 9cm + 9cm + 7cm

= 25cm

Height of the Triangular prism = 20cm

The Lateral Surface Area of the Triangular prism = 25cm × 20cm

= 500cm² or 500 square centimeters.

Since we are told that Lateral Surface Area = Area of the cardboard,

The Area of the cardboard = 500 cm² or 500 square centimeters.

Answer:

20 ft

Step-by-step explanation:

Given;

Length of flagpole shadow = 30 ft

Sign post height = 4 ft

Length of sign post shadow = 6 ft

Since the two objects are close to each other (the same location)

The height and shadow length of the two objects follows the same ratio, just like similar triangles;

Using the Ratio or similar triangles Formula;

height of flagpole/flagpole shadow length = height of sign post/ sign post shadow length

Substituting the values;

h/30 = 4/6

h = 4/6 × 30 = 20 ft

Flagpole height = 20 ft

Answer:

None of input and output table work for the rule.

Step-by-step explanation:

Start with the numbers given at A, B,C.

According to the rule you need to multiply by 666 to get the output.

A 000 * 666 = 0 (=NOT the output)

B 111 * 666 = 73926 (=NOT the output)

C 222 * 666 = 147852 (=NOT the output)

None of input and output table work for the rule.

Answer:

c

Step-by-step explanation:

khan academy

Answer:

(x-3)^2 = 4

Step-by-step explanation:

2 (x-3)^2 + 6 = 14

Subtract 6 from each side

2 (x-3)^2  = 8

Divide each side by 2

2/2 (x-3)^2 + 6 = 8/2

(x-3)^2 = 4

Answer:

rwrrwrwrr

Step-by-step explanation:

wrrwrrw

Answer: D

Step-by-step explanation:

every time x increases by 1 y increases by 5

hope this helps :3

Answer:

Step-by-step explanation:

7/12

no. of not prime number/ total no. of number

Answer:

where is the picture so i can help you

Answer:

6 friends (4 pay € 1.75 and 2 pay € 1)

Step-by-step explanation:

We have to:

x = friends

y = payment

x * y = 9

y = 9 / x

It follows from the problem:

(x-2) * (y + 0.25) = 9 - 2

(x-2) * (9 / x + 0.25) = 7

x * 9 / x + 0.25 * x - 2 * 9 / x - 2 * 0.25 = 7

9 + 0.25 * x - 18 / x - 0.5 = 7

multiply by 100

100 * 0.25 * x - 100 * 18 / x + 100 * (9 - 0.5 - 7) = 0

25 * x - 1800 / x + 150 = 0

multiply by x

25 * x ^ 2 + 150 * x - 1800 = 0

we factor:

(x - 6) * (x + 12) = 0

x = 6

x = -12

The positive value is taken: x = 6

Each one had to pay = 9/6 = € 1.5

But as two pay € 1, 4 will pay € 0.25 more: 1.5 +0.25 = € 1.75

Thus :

(4 * 1.75) +2 (1) = € 9

Therefore, they are 6 friends (4 pay € 1.75 and 2 pay € 1)

Answer:

6

Step-by-step explanation:

In order to get r by itself, you would want to multiply both sides by 6 to cancel out the denominator. From this, you get r=5.

Hope this helps :)

Answer:

1397.54248594

Step-by-step explanation:

I am glad you asked!First we need to write square root for our equation.Then we need to do 125[tex]^[/tex]^3.We then need to put all this together.We get square root 125[tex]^[/tex]^3.It equals 1397.54248594.

The solution of expression is,

⇒ 1404.9

We have to give that,

An expression is,

''square root of 125 to the power of 3''

Now, It can be written as,

⇒ ( √125 )³

⇒ [tex]125^{3/2}[/tex]

⇒ (11.2)³

⇒ 11.2 × 11.2 × 11.2

⇒ 1404.9

To learn more about the Number system visit:

https://brainly.com/question/17200227

#SPJ6

Answer:

D

Step-by-step explanation:

[tex]8x^3+12x=\\4(2x^3+3x)=\\4x(2x^2+3)[/tex]

Therefore, the correct answer is D. Hope this helps!

Answer:

(4x+1)^2

Step-by-step explanation:

Anything times itself is itself squared

Answer:

8x+2

Step-by-step explanation:

(4x+1) (4x+1)

= 8x + 2

Answer:

Step-by-step explanation:

X^2 + 7x + 7x + 49 = x*(x+7) + 7*(x+7) = (x+7)(x+7) = (x+7)^2

Answer:

The simplest form should be (x + 7)^2 (squared)

Step-by-step explanation:

This is a Perfect Square Trinomial. If the A and C values are both perfect squares then you can take the square root of them and that would become the factored version. Hope this helps! Please mark Brainliest! :)

Answer:

a) 1/800 or 0.00125

b) i) 0.0013

ii) 0.001

c) 60%

Step-by-step explanation:

T = [tan(2×30)+1][2cos(30)-1] ÷ (y²-x²)

T = (tan60 + 1)(2cos30 - 1) ÷ (41² - 9²)

T = (sqrt(3) + 1)(sqrt(3) - 1) ÷ 1600

T = (3-1)/1600

T = 2/1600

T = 1/800

T = 0.00125

Error: 0.002 - 0.00125

0.00075

%error

0.00075/0.00125 × 100

60%

Answer:

55.71 ft.

Step-by-step explanation:

hope this helps have a good day!

Answer: 784π mm²

Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle which is shown below.

Area = πr²

Notice that here, we're given the diameter instead of the radius.

Remember that the radius is equal to half of the diameter. So the radius of this circle will be equal to half 56 millimeters or 28 millimeters.

So plugging into the formula, we have (π)(28 mm)².

A common mistake is to plug 56 millimeters into the formula but remember that we must plug in the radius and not the diameter.

Multiplying, (28 mm)² is equal to (28 mm)(28 mm) or 784 mm².

So we have 784π mm².

So the area of the circle is 784π mm².

Answer:

x=4

Step-by-step explanation:

4(3x+5)=6(x+8)-x

Distribute

12x +20 = 6x +48 -x

Combine like terms

12x+20 = 5x+48

Subtract 5x from each side

12x-5x +20 = 5x-5x+48

7x +20 = 48

Subtract 20 from each side

7x+20-20 = 48-20

7x = 28

Divide each side by 7

7x/7 = 28/7

x = 4

Answer:

4x^2−4x+7

Step-by-step explanation:

Let's simplify step-by-step.

4x^2−10x+9+6x−2

=4x^2+−10x+9+6x+−2

Combine Like Terms:

=4x^2+−10x+9+6x+−2

=(4x^2)+(−10x+6x)+(9+−2)

=4x^2+−4x+7

Answer:

=4x^2−4x+7

Answer:

A

Step-by-step explanation:

Answer:

The amount of frozen fruit used to make smoothies is equal to the total number of frozen fruits minus the remainder of fruits after making smoothies.

Step-by-step explanation:

Let

Total number of frozen fruits = F

Let the amount of frozen fruits used for making smoothies = S

The remaining frozen fruits = R

Then

F - S = R

To get the amount of frozen fruits used to make smoothies, we make S the subject of the formula.

-S = R - F

S = F - R

That is, the amount of frozen fruit used to make smoothies is equal to the total number of frozen fruits minus the remainder of fruits after making smoothies.

Answer:

1. Area of rectangular rug is [tex]110 ft^{2}[/tex]

2. Area of triangular room is [tex]330ft^{2}[/tex]

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, rectangle and triangle.

step one

let us start by solving for the area of the rectangular rug

given data

Area A =  ?

Length l =  11 ft

Width w=  10 ft

we know that the area of a rectangle is expressed as

[tex]Area=Length * Width[/tex]

substituting our given data we have

[tex]Area= 11*10\\Area= 110 ft^{2}[/tex]

step two

let us  solve for the area of the triangular room

given data

Area A =  ?

base b =  30 ft

height  h=  22 ft

we know that the area of a triangle is expressed as

[tex]Area= \frac{1}{2} *base* height\\[/tex]

substituting our given data we have

[tex]Area= \frac{1}{2} * 30* 22\\Area=\frac{660}{2} \\Area= 330 ft^{2}[/tex]

Answer:

That means that the roller coaster can be 800 feet or taller

which means greater than or equal to

r≥800

Step-by-step explanation:

Answer:

y is greater than or equal to 800 feet

Step-by-step explanation:

It says it is at least 800 feet, so it has to be higher than 800

Answer:

B) x=16

Step-by-step explanation:

The 3 is the base, the expression in the parenthesis is the argument and the 4 is the exponent

We also know that [tex]base^{exponent}[/tex] = argument

so therefore the new equation is [tex]3^{4}[/tex] = 5x+1

3 to the fourth power is 81

so 81=5x+1

then solve algebraically

Answer:

The type of triangle is this triangle is the acute isosceles triangle

Step-by-step explanation:

They are all less than 90 degrees and two of the sides are the same and two of the angles are the same

Answer:

The type of triangle is this triangle is the acute isosceles triangle

Step-by-step explanation:

bro get smart stop cheating

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation

Juan has just completed a 15 kilometer race in 20 minutes.  What was his average speed in kilometers per hour?

Solution

First, 15 kilometers is a distance, so

       d  =  15

Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute.  We need to convert 20 minutes to hours.  Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took

t  =  20 minutes / 60 minutes per hour =  1/3 hours

Now we can use the d=rt equation:

15  =  (r)(1/3)

If we multiply both sides

(3)(5)  =  (r)(1/3)(3)  or  r  =  45

Juan's average speed was 45 kilometers per hour.