Evaluate the expression 2x (3+1)+2

The product is 2993317.888 and the answer in scientific notation is 2.993317888 x 10⁶

In mathematics, a product is the result of the multiplication of numbers or expressions e.g product of 5 and 6 is 5 x 6 = 30.

Scientific notation is a way of writing very large numbers or very small numbers in a simpler form.

Therefore,  the product of 5.3 x 1012 and 5.12 x 109 will be:

(5.3 x 1012) x (5.12 x 109) = 5363.6 x 558.08 = 2993317.888

To express 2993317.888  in scientific notation, we will move the position of the decimal point to the back of the first number(2) and take note of the number of steps we take to get to there. The  number of steps will then be  used as the power of 10:

2993317.888 = 2.993317888 x 10⁶

Therefore, the product of the numbers is 2993317.888 and the final answer in scientific notation is 2.993317888 x 10⁶

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Answer:

\(\huge\boxed{\text{The answer for part b) is 96}}\)

Step-by-step explanation:

Right away, because the scale factor of the dilation is 1/2, which is less than 1, the new surface area should be less than the original.  Simply multiply each side length by 1/2, then recalculate for surface area to get 4*4*6, or 96.

Hope it helps :) and let me know if you want me to elaborate.

The options that represent solutions to the given inequality are:

The inequality is:

\(y > 2 + 9x\)

Item a:

x = 7, hence, the solution is:

\(y > 2 + 9(7)\)

\(y > 67\)

67 > 65, hence it is a solution.

Item b:

x = 8, hence, the solution is:

\(y > 2 + 9(8)\)

\(y > 74\)

74 = 74, hence it is not a solution.

Item c:

x = 5, hence, the solution is:

\(y > 2 + 9(5)\)

\(y > 47\)

49 > 47, hence it is a solution.

Item d:

x = 4, hence, the solution is:

\(y > 2 + 9(4)\)

\(y > 38\)

37 < 38, hence it is not a solution.

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Answer:

0.00128

Step-by-step explanation:

4

3125

is already in the simplest form. It can be written as 0.00128 in decimal form (rounded to 6 decimal places).

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 4 and 3125 is 1

Divide both the numerator and denominator by the GCD

4 ÷ 1

3125 ÷ 1

Reduced fraction:  

4

3125

Therefore, 4/3125 simplified to lowest terms is 4/3125.

74% and 40% are parameters because they represent characteristics of the population of Americans who had yet to retire, which the Gallup poll aims to estimate through their sample data.

a) The population of interest is Americans who had yet to retire.

b) The sample that was collected consists of 1,000 or more adults living in the United States, aged 18 and older, who were interviewed through telephone.

c) The value 74% is a parameter. A parameter is a numerical measurement that describes a characteristic of a population. In this case, the percentage (74%) represents the proportion of all Americans who had yet to retire (the population) who look to retirement accounts as major funding sources when they retire. The Gallup poll aims to estimate this parameter based on the responses of the sample.

d) The value 40% is also a parameter. Similar to the explanation in part c, it represents the proportion of all Americans who had yet to retire (the population) who look to stocks or stock market mutual fund investments as major funding sources when they retire. The Gallup poll aims to estimate this parameter based on the responses of the sample.

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The fate of the 22 checked bags can be considered the Bernoulli trials.

A Bernoulli trial is a random experiment with two possible outcomes, often referred to as a "success" or "failure." In the context of the lost luggage problem, success would be a checked bag that is not misplaced, and failure would be a checked bag that is misplaced.

For a set of trials to be considered Bernoulli trials, the following conditions must be met:

In this case, the fate of the 22 checked bags can be considered Bernoulli trials if the following conditions are met:

Therefore, the fate of the 22 checked bags can be considered Bernoulli trials.

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The y-intercept of (f - g)(x) has the coordinates given as follows:

D. (0, −9).

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For function f(x), we have that when x increases by 2, y increases by 10, hence the slope m is given as follows:

m = 10/2

m = 5.

Hence:

f(x) = 5x + b

When x = -6, f(x) = -36, hence the intercept b is given as follows:

-36 = -30 + b

b = -6.

Hence:

f(x) = 5x - 6.

For function g(x), we have that when x increases by 2, y decays by 4, hence the slope m is given as follows:

m = -4/2

m = -2.

Hence:

g(x) = -2x + b

When x = -6, y = 15, hence the intercept b is given as follows:

15 = 12 + b

b = 3.

Hence:

g(x) = -2x + 3.

The subtraction function is given as follows:

(f - g)(x) = 5x - 6 + 2x - 3

(f - g)(x) = 7x - 9

Hence the coordinates of the intercept are given as follows:

D. (0, −9).

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To approximate the area between the graph of the function g(x) = 4sin(x) and the x-axis over the interval [0, ], using 6 rectangles, we can use the left and right endpoints method.

To find the approximations of the area between the graph of the function g(x) = 4 sin(x) and the x-axis over the interval [0, π] using left and right endpoints with 6 rectangles, we divide the interval into 6 equal subintervals.

For the left endpoint approximation, we evaluate the function at the left endpoint of each subinterval and multiply it by the width of the subinterval. Then, we sum up these areas.

For the right endpoint approximation, we evaluate the function at the right endpoint of each subinterval and multiply it by the width of the subinterval. Again, we sum up these areas.

Calculating these approximations, the left endpoint approximation is approximately X.XXXX and the right endpoint approximation is approximately X.XXXX (rounded to four decimal places).

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The value of the interval where each function is continuous is,

⇒ (- ∞ , 1} - {1/2, 3}

We have to given that;

Function is,

⇒ f (x) = √ - (x + 1) / (2x² - 7x + 3)

Now, We know that;

Function is not defined at denominator = 0.

Hence,

2x² - 7x + 3

2x² - 6x - x + 3

2x(x - 3) -1 (x - 3)

(x - 3) (2x - 1)

So, Function is not defined at x = 3,and x = 1/2.

And,

- (x + 1) ≥ 0

x + 1 ≤ 0

x ≤ 1

Thus, The value of the interval where each function is continuous is,

⇒ (- ∞ , 1} - {1/2, 3}

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Answer:

Umm, maybe ask your parents? Or maybe just save the money for college.

LOL

On the interval [0.2, 4], the absolute maximum value of f(x)  is 3.75, and the absolute minimum value is -4.8.

To obtain the absolute maximum and minimum values of the function f(x) = x - 1/x on the interval [0.2, 4], we need to evaluate the function at the critical points and the endpoints of the interval.

We need to obtain where the derivative of f(x) is equal to zero or undefined.

The derivative of f(x):

f'(x) = 1 - (-1/x^2) = 1 + 1/x^2

To obtain the critical points, we set f'(x) = 0:

1 + 1/x^2 = 0

1/x^2 = -1

x^2 = -1 (This equation has no real solutions)

There are no critical points in the interval [0.2, 4]

Evaluate the function at the endpoints of the interval [0.2, 4].

f(0.2) = 0.2 - 1/0.2 = 0.2 - 5 = -4.8

f(4) = 4 - 1/4 = 4 - 0.25 = 3.75

Comparing the values obtained above to determine the absolute maximum and minimum:

∴ The absolute maximum value is 3.75, which occurs at x = 4,

The absolute minimum value is -4.8, which occurs at x = 0.2.

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If I throw a ball with an Initial velocity Vi=10 m/s with an angle Theta of 60 degrees above the Horizontal axis x, then the velocity Vx and Vy are; C. Vx= 5 m/s Vy=8.66 m/s

The formula to find the velocity of an object thrown at an angle is;

Horizontal velocity component; Vx = v_i*cosθ

Vertical velocity component; Vy = v_i*sinθ

where;

v_i is initial velocity

θ is angle at which object is thrown.

Now, we are given that;

Initial velocity; v_i = 10 m/s

Angle of throw; θ = 60°

Thus;

V_x = 10 * cos 60

V_x = 10 * 0.5

V_x = 5 m/s

V_y = 10 * sin 60

V_y = 10 * 0.8660

V_y = 8.66 m/s

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Answer:

yes its a polynomial espero te sirva

The probability that the engine over heats and leaks is 0.0096

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

Engine leaks oil AND overheats,

hence P(Engine overheats) = P(Engine overheats) X P(Engine leaks oil) = 0.12 X 0.08 = 0.0096

Hence the probability of leaking of engine due to over heating is 0.0096

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Answer:

b) 12.6 inches

Step-by-step explanation:

tangent is the ratio of the side opposite over adjacent, so if we let x= length of the opposite side, 1.40=x/9, x=12.6 inches

b) 12.6 inches

Hope it helps!!

The 98% confidence interval for the mean temperature (in degrees Fahrenheit) is approximately (-0.175, 30.035).

To calculate the 98% confidence interval for the mean temperature, we can use the following formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)

Given that the sample temperatures are:

19.5, 0, 46.7, 33.4, 2, 15.2, 15.3, 1.5, 13.7, 2.7

Let's calculate the confidence interval step by step:

Step 1: Calculate the sample mean.

Sample Mean = (19.5 + 0 + 46.7 + 33.4 + 2 + 15.2 + 15.3 + 1.5 + 13.7 + 2.7) / 10

= 149.3 / 10

= 14.93

Step 2: Calculate the standard deviation of the sample.

To calculate the standard deviation, we need to calculate the sum of squared differences from the sample mean.

Squared Differences: (19.5 - 14.93)^2, (0 - 14.93)^2, (46.7 - 14.93)^2, (33.4 - 14.93)^2, (2 - 14.93)^2, (15.2 - 14.93)^2, (15.3 - 14.93)^2, (1.5 - 14.93)^2, (13.7 - 14.93)^2, (2.7 - 14.93)^2

Sum of Squared Differences = (19.5 - 14.93)^2 + (0 - 14.93)^2 + (46.7 - 14.93)^2 + (33.4 - 14.93)^2 + (2 - 14.93)^2 + (15.2 - 14.93)^2 + (15.3 - 14.93)^2 + (1.5 - 14.93)^2 + (13.7 - 14.93)^2 + (2.7 - 14.93)^2

= 16.1349 + 222.4249 + 874.1029 + 341.9329 + 159.5049 + 0.7129 + 0.1369 + 167.9929 + 14.0929 + 152.5529

= 1950.6359

Sample Standard Deviation = √(Sum of Squared Differences / (Sample Size - 1))

= √(1950.6359 / (10 - 1))

≈ √(216.73732)

≈ 14.720 (rounded to three decimal places)

Step 3: Calculate the critical value corresponding to the desired confidence level.

Since we want a 98% confidence interval, we need to find the critical value that corresponds to a 1% tail on each side (α = 0.01).

Using a t-table or calculator with the given sample size (n = 10) and degrees of freedom (n - 1 = 9), the critical value for a 1% tail is approximately 3.250.

Step 4: Calculate the standard error.

Standard Error = Sample Standard Deviation / √(Sample Size)

= 14.720 / √(10)

≈ 4.651 (rounded to three decimal places)

Step 5: Calculate the confidence interval.

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)

= 14.93 ± (3.250) * (4.651)

= 14.93 ± 15.105

≈ ( -0.175, 30.035 )

Therefore, the 98% confidence interval for the mean temperature (in degrees Fahrenheit) is approximately (-0.175, 30.035).

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Answer:

Step-by-step explanation:

4+(7-5)2= 8 I guess

Answer:

Missing side length = 45

Step-by-step explanation:

In this problem, we're trying to find the longest side, or hypotenuse, of the triangle. Luckily, there's a formula to find this!

The Pythagorean Theorem is a formula that allows us to find any of the three sides of a right triangle using the lengths of the other two sides.

The formula is, a² + b² = c², where a and b are the side lengths of the two sides that make the right angle and c is the length of the side across from the right angle, the hypotenuse.

To use the formula, we just have to plug in the lengths of the two sides we know and then solve for the third variable. When we're looking for the hypotenuse length, we'll plug in the values for a and b, then solve for c. The a and b values are completely interchangeable, so it won't matter which side length you plugin for which. You just have to make sure that c is going to be the hypotenuse length.

Let's go ahead and plug in our known values for the equation. We're given the two side lengths 27 and 36, which will be our a and b values. Remember, they're interchangeable!

27² + 36² = c²          Next, we can square the a and b numbers.

729 + 1296 = c²       Now add them together.

2025 = c²                 And finally, square root both sides of the equation.

\(\sqrt{2025}= \sqrt{c^2}\)

45 = c

So, the length of the hypotenuse for this triangle is 45. Now, you can use this formula to solve for any of the three sides of a right triangle when given the other two side lengths.

Answer:

x = 45

Step-by-step explanation:

Forming the equation,

→ (x)² = (36)² + (27)²

Now the value of x will be,

→ (x)² = (36)² + (27)²

→ x² = 1296 + 729

→ x² = 2025

→ x = √2025

→ [ x = 45 ]

Hence, the value of x is 45.

Answer:

If the circle is inside the square the area of the square is 144

Step-by-step explanation:

The diameter of a circle is equal to the side length of a square.

So \(d = 2r\)  the diameter of the circle is 2(6)=12

so one side length of the equals 12

Area of square = \(s^{2}\)    \(12^{2} = 144\)

Also can I plz get brainiest?

Answer: -0.07142857142

I looked the question up on google ;)

by dividing both sides by 1.5.

To solve the problem, we need to first determine the total amount of time Ricky spends in his classes. We know that each class is 1.5 hours long, so if he takes c classes, then he will spend a total of 1.5c hours on class time. In addition, we know that he spends 6.5 hours on homework. Therefore, the total amount of time Ricky spends on his classes and homework is:

Total time = Class time + Homework time

Total time = 1.5c + 6.5

We also know that Ricky has 23 hours per week to dedicate to his classes and homework. Therefore, we can set up the following equation:

Total time = 23

Substituting the expression for a total time from the first equation, we get:

1.5c + 6.5 = 23

Now we can solve for c:

1.5c = 23 - 6.5

1.5c = 16.5

c = 11

Therefore, Ricky takes 11 classes.

The equation that models the question is b) 23=6.5+1.5c. This equation correctly represents the total time Ricky spends on his classes and homework (23 hours), as well as the time he spends on homework (6.5 hours) and the time he spends in class (1.5c hours).

by dividing both sides by 1.5.

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\(\\ \bull\sf\longmapsto 250\times 35\%\)

\(\\ \bull\sf\longmapsto 250\times \dfrac{35}{100}\)

\(\\ \bull\sf\longmapsto 5\times \dfrac{35}{2}\)

\(\\ \bull\sf\longmapsto \dfrac{175}{2}\)

\(\\ \bull\sf\longmapsto 87.5\)

\(\bf \large \implies \: \frac{35}{100} \: \times \: 250 \\ \)

\(\bf \large \implies \: \frac{35}{10 \cancel0} \: \times \: 25 \cancel0\)

\(\bf \large \implies \: \frac { \cancel{35} \: \: ^{3.5} }{ \cancel{10}} \: \times \: 25\)

\(\bf \large \implies \: 3.5 \: \times \: 25\)

\(\bf \large \implies \: 87.5\)

Answer:

Question 1: The total cost before tax is $47.99

Question 2: cant help ya there, not that smart sorry..

Step-by-step explanation:

Answer:

I'm just answering this for the points haha

a) The chance that both servers fail is 0.05% (or 0.0005). b) The chance that exactly one of the servers fails is 5.9%. c) The chance that at least one of the servers fails is 5.95%. d) The assumption that the two servers fail independently may not be entirely realistic in all scenarios.

To find the probabilities in this scenario, we can use the probabilities of the main server and backup server failing, assuming they fail independently.

Let's denote:

P(M) = Probability of the main server failing = 0.01 (1%)

P(B) = Probability of the backup server failing = 0.05 (5%)

a) To find the chance that both servers fail, we need to calculate the probability of the intersection (AND) of the events:

P(both servers fail) = P(M) * P(B) = 0.01 * 0.05 = 0.0005 (0.05%)

b) To find the chance that exactly one of the servers fails, we can calculate the probability of the union (OR) of the mutually exclusive events:

P(exactly one server fails) = P(M) * (1 - P(B)) + (1 - P(M)) * P(B)

= 0.01 * (1 - 0.05) + (1 - 0.01) * 0.05

= 0.01 * 0.95 + 0.99 * 0.05

= 0.0095 + 0.0495

= 0.059 (5.9%)

c) To find the chance that at least one of the servers fails, we can calculate the probability of the complement (NOT) of both servers being operational:

P(at least one server fails) = 1 - P(both servers work)

= 1 - (1 - P(M)) * (1 - P(B))

= 1 - (1 - 0.01) * (1 - 0.05)

= 1 - 0.99 * 0.95

= 1 - 0.9405

= 0.0595 (5.95%)

d) The assumption that the two servers fail independently might not be entirely realistic in all scenarios. Factors such as shared infrastructure, common vulnerabilities, or external factors can introduce dependencies between the failure probabilities of the servers. If there are dependencies or shared factors that could cause correlated failures, the assumption of independence becomes less realistic.

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Answer:

56

Step-by-step explanation:

A fraction consists of two numbers and a fraction bar:

14/25

The number above the bar is the numerator: 14

The number below the bar is the denominator: 25

Divide the numerator by the denominator to get fraction's value:

Val = 14 ÷ 25

Hoped it helped

Answer:

Step-by-step explanation:

I would start with the form

y = mx + b

and then convert to standard form.  Using the given point and the given y-intercept, find the slope from

-3 = 7m + 2 ⇒ m = -5/7

y = (-5/7)x + 2  

7y = - 5x + 14

5x + 7y = 14 (standard form)

The equation in standard form of the line is 5x + 7y = 14

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, a line is passing through (7, -3) and has a y intercept of 2

The general equation of a line is y = mx + b

Using the given point and the given y-intercept, find the slope from

-3 = 7m + 2

m = -5/7

y = (-5/7)x + 2  

7y = - 5x + 14

Converting into standard form;

5x + 7y = 14

Hence, the equation in standard form of the line is 5x + 7y = 14

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Result:

1. Based on the properties, the most precise name for figure is A. parallelogram

2. From the properties, the most precise name for the figure is B. rhombus.

We can determine the precise name of the figure calculating the slopes of AB, BC, CD, and DA using the slope formula and/or the distance formula:

1. Using the slope formula:

AB = (0 - (-6))/(2 - (-5)) = 2

BC = (9 - 0)/(11 - 2) = 9/9 = 1

CD = (3 - 9)/(4 - 11) = -6/-7 = 6/7

DA = (-6 - (-5))/( -5 -(-5)) = 0

Calculate the lengths of the sides using distance formula:

AB = \(\sqrt((2 - (-5))^2 + (0 - (-6))^2)\) = \(\sqrt(7^2 + 6^2)\) = \(\sqrt{85}\)

f BC = \(\sqrt((11 - 2)^2 + (9 - 0)^2)\) = \(\sqrt(9^2 + 9^2)\) = 9√2)

CD = \(\sqrt((4 - 11)^2 + (3 - 9)^2)\) = sqrt\(\sqrt(7^2 + 6^2)\) = √85

DA = \(\sqrt((-5 - 4)^2 + (-6 - (-9))^2)\) = \(\sqrt(9^2 + 3^2)\) = 3√10

The slopes of AB and CD are equal (2 and 6/7, respectively), and the slopes of BC and DA are equal (1 and 0, respectively).

Therefore, opposite sides are parallel that is a parallelogram.

2. First, we can calculate the slopes of AB, BC, CD, and DA using the slope formula:

AB = (1 - (-4))/(-7 - (-9)) = 5/2

BC = (5 - 1)/(1 - (-7)) = 4/4 = 1

CD = (0 - 5)/(-1 - 1) = -5/-2 = 5/2

DA = (-4 - 0)/(-9 - (-1)) = 4/8 = 1/2

Next, using the distance formula, we calculate the lengths of the sides:

AB = \(\sqrt((-7 - (-9))^2 + (1 - (-4))^2)\) = \(\sqrt(2^2 + 5^2)\) = \(\sqrt29\)

BC = \(\sqrt{(1 - (-7))^2 + (5 - 1)^2}\) = \(\sqrt(8^2 + 4^2)\) = 4\(\sqrt17\)

CD = \(\sqrt((-1 - 1)^2 + (0 - 5)^2)\) = \(\sqrt(2^2 + 5^2)\) = \(\sqrt29\)

DA = \(\sqrt((-9 - (-1))^2 + (-4 - 0)^2)\) = \(\sqrt(8^2 + 4^2)\) = \(\sqrt80\))

The slopes of AB and CD are equal (5/2 and 5/2, respectively), and the slopes of BC and DA are equal (1 and 1/2, respectively). meaning the opposite sides are parallel.

AB and CD have the same length (\(\sqrt(29)\)), and BC and DA have the same (4\(\sqrt(17}\)), which means it's a rhombus.

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Answer:

hey i think it is -2,-6

Step-by-step explanation: