700 million times 400=

Answer:

1

Step-by-step explanation:

the greatest common factor is 1

The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Learn more about binomial probability here:

https://brainly.com/question/12474772

#SPJ4

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

for such more question on measure of angle

https://brainly.com/question/25716982

#SPJ8

Landry paid $18,040 for the vehicle, and the amount of sales tax that Landry had to pay is $1,397.90, thus the total amount of Landry's bill is $19,437.90 the correct option is (d).

The price Landry paid for the vehicle is \(\frac{4}{5}\) of the sticker price, which means he paid is:

= \(\frac{4}{5}\) x $22,550

= $18,040

To find the amount of sales tax, we need to multiply the price of the vehicle by the tax rate, which is 7.75% or 0.0775 as a decimal:

$18,040 x 0.0775 = $1,397.90

To find the total amount of Landry's bill, we add the price of the vehicle and the sales tax is:

$18,040 + $1,397.90

= $19,437.90

Therefore, Landry's bill was $19,437.90

To learn more about tax follow the link:

https://brainly.com/question/13136037

#SPJ1

The complete question is:

Landry purchased a vehicle for 4/5 of the sticker price of $22,550. He had to pay 7.75% sales tax. What was the amount of Landry's bill?

a. $16,641.90

b. $18,040.00

c. $18,214.76

d. $19,437.90

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

To know more about continuous here

https://brainly.com/question/30089268

#SPJ1

Answer:

x=405

28.7

x=450

Step-by-step explanation:

Answer:

Let me know if you can see this SS

Step-by-step explanation:

It has the answers

  In a two way frequency table,

"To get the relative frequency divide all frequencies by total frequency"

      Therefore, relative frequency table for the given table will be,

                                                  Lunch order

                              Sandwich                   Pasta                     Total

Volleyball              \(\frac{19}{70}\times 100=27\)            \(\frac{15}{70}\times 100=21\)          \(\frac{34}{70}\times 100=49\)

Swimming             \(\frac{26}{70}\times 100=37\)            \(\frac{10}{70}\times 100=14\)          \(\frac{36}{70}\times 100=51\)

Total                      \(\frac{45}{70}\times 100=64\)            \(\frac{25}{70}\times 100=36\)          \(\frac{70}{70}\times 100=100\)

Learn more,

https://brainly.com/question/12134864

Answer:

It is (x - 3)³ - 9x(3 - x)

Step-by-step explanation:

Express 27 in terms of cubes, 27 = 3³:

\( = {x}^{3} - {3}^{3} \)

From trinomial expansion:

\( {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ \)

open first two brackets to get a quadratic equation:

\( {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)\)

expand further:

\( {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}\)

take y to be 3, then substitute:

\(( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)\)

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

learn more on equation here: https://brainly.com/question/29135995

#SPJ1

Corresponding angle postulate

Corresponding angles:

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position.

Here we need to prove ∠3 ≅ ∠7

From the properties of the two parallel line cut by the transversal line, these angle is corresponding angles.

i.e., ∠3 ≅ ∠7 (by the properties of the corresponding angles)

To know more about a parallel line cut by a transversal line refer to the link given below:

https://brainly.com/question/2497532

#SPJ1

Answer:

A. 1.4 pounds

Step-by-step explanation:
She divided 5.6/4 so in each jar there would be 1.4 pounds.
You can check your work by multiplying 1.4 to 4 and you'll get 5.6.

Start with the base of the tree, which is at (C, 4). Next, use the tool to place the tree at (D, 2). Make sure to show all construction lines! Now, continue moving up the drawing, using the tool to place the tree at (E, 6). Again, make sure to show all construction lines! Finally, place the tree at (F, 8). Make sure to connect the dots between the different points!

Probabilities are used to determine the chances of an event.

The probability of obtaining a z value of less than 1.68 is 0.95352

The probability is represented as:

\(\mathbf{P(z < 1.68)}\)

To do this, we make use of the z-score of probabilities table and/or calculator.

Using the calculator, we enter 1.68 as the z-score.

The result is:

\(\mathbf{P(z < 1.68) = 0.95352}\)

This means that:

The probability of obtaining a z value of less than 1.68 is 0.95352

Read more about standard normal distribution at:

https://brainly.com/question/11876263

Answer:

\(x = A cos\theta\)

Step-by-step explanation:

Given

Resultant Vector = A

Required

Determine the x component of vector A

To answer this question, I'll make use of the attachment

In the attachment, the relationship between A and the x component is as follows (using Pythagoras theorem):

\(cos\theta = \frac{x}{A}\)

Multiply both sides by A

\(A * cos\theta = \frac{x}{A} * A\)

\(A * cos\theta = x\)

\(A cos\theta = x\)

Reorder the equation

\(x = A cos\theta\)

Hence, the x component of A is: \(Acos\theta\)

Answer: -27

Step-by-step explanation:

Answer:

SA=160

Step-by-step explanation:

surface area of cuboid=2lw+2wh+2hl

=2(12)(4)+2(4)(2)+2(2)(12)

=96+16+48

=160

MARK ME BRAINLIEST THANKS MY ANSWER PLEASE

We get the cost of the system and cost of the games  as $126 and $378 respectively.

Given, the price of the video game and several games are sold for $504.

The cost of the game is 3 times as much as the cost of the system.

we need to determine the cost of the system and the cost of the game = ?

Let x = the cost of the games.

Let y = the cost of the system.

therefore, x+y=504

and y = 3x

substitute the value of y.

⇒ x + y = 504

⇒ x + 3x = 504

combine like terms.

⇒ 4x = 504

Divide both sides by 4.

⇒ x = 504/4

⇒ x = 126

The cost of the system is $126.

Use y = 3x substituting 126 for x.

g = 3(126)

g = 378

The cost of the games is $378.

Hence we get the cost of the system and cost of the games as $126 and $378 respectively.

Learn more about Linear equations here:

brainly.com/question/4074386

#SPJ1

Answer:

The actual answer is 9.25

Step-by-step explanation:

The mistake is in Step 4, as 4 × 2 = 8, not 6

Answer:

Step-by-step explanation:

\( \frac{x - 1}{x + 5} \times \frac{x + 1}{x - 5} \)

To multiply the fraction, multiply the numerators and denominators separately

\( \frac{(x - 1) \times (x + 1)}{(x + 5) \times (x - 5)} \)

Using \( {a}^{2} - {b}^{2} = (a - b)(a + b)\) simplify the product

\( = \frac{ {x}^{2} - 1 }{ {x}^{2} - 25 } \)

Hope this helps..

Best regards!!

Answer:

a. A two way table is presented as follows;

\(\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}\)

ii) The percentage of students in the study that have myopia are approximately 24.867%

iii) The percentage of children living in Australia with myopia are approximately 3.2258%

The percentage of children living in Singapore with myopia are approximately 29.14%

b. Children in Australia spend more time reading, writing and also outdoors than children in Singapore

c. The study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children

The study does not suggests that more time spent outdoors is associated with a greater risk of myopia

d. The advantage is to reduce associated variables the generate more accurate findings or result

Step-by-step explanation:

a. A two way table is presented as follows;

\(\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}\)

ii) The percentage of students in the study that have myopia are;

(4 + 183)/(124 + 628) × 100 ≈ 24.867%

iii) The percentage of children living in Australia with myopia is given as follows;

4/124 × 100 ≈ 3.2258%

The percentage of children living in Singapore with myopia is given as follows;

183/628 × 100 ≈ 29.14%

b. The data for the time spent reading and writing is presented as follows;

                    Number of children  \({}\)  Mean     Standard deviation

Australia        109       \({}\)                      20.8        13.9

Singapore \({}\)    611                               17.8          8.8

The data for the time spent outdoors is presented as follows;

                    Number of children  \({}\)  Mean     Standard deviation

Australia        102       \({}\)                       13.75        1.02

Singapore \({}\)    586                               3.05        0.12

From the data, more children in Australia spend more time reading and writing and also outdoors than children in Singapore

c. From the data, more children spend their time reading and writing in Australia and are also less likely to develop myopia than children in Singapore

Therefore, the study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children

Similarly, the study does not suggests that more time spent outdoors is associated with a greater risk of myopia

d. The advantage of collecting data from children with the same ethnicity compared with selecting random samples of children from each location regardless of ethnicity is to reduce the variables or influential factors that may alter the impact on the test and the results

Answer:

let's hope for the best ....XD

Answer:

ummmm....iam sorry I tried but failed ,umm...I think he got your answer see from there!! sorry!!

Answer:

1/7

Step-by-step explanation:

Given series :-

To find :-

From the Series , the common ratio will be ,

⇝ CR = -2/25 ÷ 1/5

⇝ CR = -2/25 × 5

⇝ CR = -2/5

Using formula of GP :-

⇝ S_∞ = a /1 - r , -1 < r < 1

⇝ S = 1/5 ÷ ( 1 - (-2/5))

⇝ S = 1/5 ÷ ( 1 +2/5)

⇝ S = 1/5 ÷ 5/7

⇝ S= 1/7

Answer:

180

Step-by-step explanation:

The area of a parallelogram is given by the formula A = b × h, where b is the base and h is the height. In this case, the base is 10 and the height is 18. Therefore, the area is:

A=10×18

A=180

The area of the parallelogram is 180 square units

Answer:

C

Step-by-step explanation:

have trust

We know that

• The entrance fee is $15.

• There are charged $1.50 per pound.

The equation to model this situation is

For y = 24, let's solve for x.

Answer:

The median of the data is 3

Step-by-step explanation:

\(-\frac{5}{4}\) or \(-1.25\).

1. Express as a fraction or fractions.

\(-\frac{8}{\frac{64}{10} }\)

2. Use the properties of fractions to convert.

Used property: \(\frac{a}{\frac{b}{c} } =a*\frac{c}{b}\)

\(-\frac{8}{\frac{64}{10} } =-8*\frac{10}{64}\)

3. Solve the fraction product.

\(-8*\frac{10}{64}=-\frac{8*10}{64} =-\frac{80}{64}\)

3. Simplify.

\(-\frac{80/16}{64/16}=-\frac{5}{4} =-1.25\)

4. Espress the result.

\(-\frac{5}{4}\) or \(-1.25\).

The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

Learn more about percentages, here:

https://brainly.com/question/29306119

#SPJ1

Answer:

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Step-by-step explanation:

To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.

The volume of a cylinder is given by the formula:

V = πr^2h

Where:

V is the volume,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

V = π(56^2)(4,000)

V ≈ 3.14159 * 56^2 * 4,000

Calculating the volume:

V ≈ 9,839,916,800 cubic feet

The surface area of the lateral (curved) part of a cylinder is given by the formula:

A = 2πrh

Where:

A is the surface area,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

A = 2π(56)(4,000)

A ≈ 2 * 3.14159 * 56 * 4,000

Calculating the surface area:

A ≈ 1,000,530.9 square feet

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.