1004.8 into 3 significant figures

the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

Given the probabilities, you can use Bayes' theorem to calculate the probability that it will rain on the following day, given that it rained tomorrow. Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B)

Where: P(A|B) is the likelihood that event A will occur assuming event B has already happened. P(B|A) is the probability of event B given that event A has occurred. The prior probability of event A is P(A). The prior probability of event B is P(B).

In this case, let A be the event that it rains on the following day and B be the event that it rains tomorrow.

So, P(A|B) = P(B|A) * P(A) / P(B) = 0.9 * 0.3 / P(B)

To calculate P(B), you can use the total probability theorem:

P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) = 0.9 * 0.3 + 0.08 * 0.7 = 0.327

Now, you can substitute the values into the formula for P(A|B) to get:

P(A|B) = 0.9 * 0.3 / 0.327 = 0.75

So, the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.

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Answer:

x = 40.5

Step-by-step explanation:

SQ is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is

[tex]\frac{PS}{RS}[/tex] = [tex]\frac{PQ}{RQ}[/tex] ( substitute values )

[tex]\frac{20}{18}[/tex] = [tex]\frac{45}{x}[/tex] ( cross- multiply )

20x = 18 × 45 = 810 ( divide both sides by 20 )

x = 40.5

Answer:

give the diagram please

The function operation (f-g)(x) in the functions f(x) = 2√3x and g(x) = -4√3x is 6√3x and  the value of (f-g)(12) is 36.

A function is simply a relationship that maps one input to one output.

Given that;

First, set up the function;

(f - g)(x) = f(x) - g(x)

Replace the function designators with the actual function.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 2√3x - (-4√3x)

(f - g)(x) = 2√3x + 4√3x

(f - g)(x) = 6√3x

Now, we evaluate when x = 12.

(f - g)(x) = 6√3x

Replace x with 12

(f - g)( 12 ) = 6√3(12)

(f - g)( 12 ) = 6√36

(f - g)( 12 ) = 6 × 6

(f - g)( 12 ) = 36

Therefore, the function operation (f-g)(x) is 6√3x and (f-g)(12) is 36.

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The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.

The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by

Here we have

The pair of points (11, 8), (- 13, 11)  

By the given formula,

Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]

The slope from (11, 8) to (- 13, 11) can be calculated as follows

Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8

Therefore,

The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.    

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Answer:

Equation of perpendicular line:

[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]

Step-by-step explanation:

Generalized lope-intercept form of a line is y = mx + b    [1]

where

m = slope

b = y-intercept

Equation of the given line is y = 2x - 1           [2]

We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)

Answer:

6x^2 + 17x + 12

Step-by-step explanation:

(3x + 4)(2x + 3) - Distribute

6x^2 + 9x + 8x + 12

6x^2 + 17x + 12

The missing length of the triangle is the hypotenuse which is given by 12.08

Pythagorean theorem states that the sum of the square of the opposite and adjacent sides of a triangle is equal to the square of the hypotenuse.

a² + b² = c²

c = √a² + b²

a = 11

b = 5

c = √a² + b²

= √11² + 5²

= √121 + 25

= √146

c = 12.08304597359

Approximately,

c = 12.08

Consequently, the hypotenuse of the triangle is approximately 12.08

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Answer:

B. x=3

Step-by-step explanation:

3x+4y=12

9x-4y=24

Add 9x and 3x

Subtract -4y from 4y which will cancel out

Add 12 and 24

12x=36

divide both sides by 12

x=3

The amount of money Jamar will make in his 18th year working at this job is = $107,500

A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis.

here, we have,

Calculation of yearly salary outcome

The amount of money Jamar made in his first year= $48,000

The salary rise per year = $3,500

The amount of money he will make for the extra 17 years is

= 17 × $3,500

= $59,500

Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500

= $107,500

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The sine of Z is 0.834.

Assume that "α" is the angle in a right triangle XYZ. The sine formula is then given as Sin = Opposite side/ Hypotenuse.

Using the Pythagorean theorem, we can find the length of side Y:

Y² = X² + Z²

Y² = 7² + ( √(21) )²

Y² = 49 + 21

Y² = 70

Y = √(70)

Now we can use the definition of sine:

sin(Z) = opposite/hypotenuse

sin(Z) = X / Y

sin(Z) = 7 / √(70)

sin(Z) = (7 / 10) √(70)

So the sine of Z is (7 / 10) √(70), or approximately 0.834.

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The total number of new cars made by a factory from 1,254 tires as each car required four tires is equal to 314 ( round off to nearest whole number ).

Total number of tires in the factory is equal to 1,254

Number of tires required by each new car is equal to 4 tires.

The total number of new car made by a factory is equal to :

4 tires = 1 new car

⇒ 1 tire = ( 1 / 4 ) new car

⇒ 1,254 tires = 1,254 ×  ( 1 / 4 ) new car

⇒ 1,254 tires = ( 1,254 / 4 ) new cars

⇒ 1,254 tires =  313.5 new cars

But number of new cars cannot be in the decimals or fraction.

Round off to the nearest whole number .

⇒ 1,254 tires =  314 new cars ( nearest whole number )

Therefore the total number of new cars made by a factory is equal to 314 new cars.

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The length of segment AC is equal to 9.

Since B is between A and C, we can use the fact that AB + BC = AC. Similarly, since C is between B and D, we can use the fact to state the lengths of the following segments that: CD + BC = BD.

Substituting the given values, we get:

AB + BC = AC

CD + BC = BD

We are given segments BD = 7 and BC = 3, so we can substitute these values:

CD + 3 = 7

Solving for CD, we get:

CD = 7 - 3

CD = 4

Now we can use the fact that AD = AC + CD to solve for the length of segment AC:

AD = AC + CD

13 = AC + 4

AC = 9

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The ordered pairs that are solution to the system are (15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

From the question, we have the following parameters that can be used in our computation:

2x + 3y>10

y≥ -3x + 2

Represent properly

2x + 3y > 10

y ≥ -3x + 2

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the coordinates in the shaded area are

(15, -1) (0,4) (10, 30) (5, 5) (1, 10)​

None of the options represent the shaded area (see attachment)

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4214.7 is the balance in the account after 2 months .

What does compound and simple interest mean?

A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.

                                Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.

P = $4200

R = 2.1% = 2.1/100 = 0.021  =

     T = 2 month = 2/12 = 1/6

    I = PRT

     = 4200 * 0.021 * 1/6 = 14.7

 Amount = P + I = 4200 + 14.7  = 4214.7

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The probability of a person dying of renal failure if neither of their parents had renal failure is 0.056 or about 5.6%.

To solve this problem, we can use Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find the probability of a person dying of renal failure given that neither of their parents had renal failure. Let's define the following events:

R: death due to renal failure

P: at least one parent with renal failure

NP: neither parent has renal failure

We are given the following information:

Total deaths = 1000

Deaths due to renal failure (R) = 321

People with at least one parent with renal failure (P) = 460

Deaths due to renal failure among people with at least one parent with renal failure = 115

Using this information, we can calculate the probabilities as follows:

P(R) = 321/1000

P(P) = 460/1000

P(R|P) = 115/460

To find the probability of a person dying of renal failure given that neither of their parents had renal failure (i.e., P(R|NP)), we need to use Bayes' theorem. We can start by finding the probability of neither parent having renal failure (i.e., P(NP)):

P(NP) = 1 - P(P) = 1 - 0.46 = 0.54

Next, we can use the law of total probability to find the probability of dying of renal failure among people with neither parent having renal failure:

P(R|NP) = P(R) * P(NP|R) / P(NP)

We can find P(NP|R) using the formula:

P(NP|R) = P(NP ∩ R) / P(R)

To find P(NP ∩ R), we can use the formula:

P(NP ∩ R) = P(R|NP) * P(NP)

Substituting the values, we get:

P(R|NP) = P(R) * P(NP|R) / P(NP)

= 321/1000 * (1 - 115/460) / 0.54

= 0.056

This calculation shows how conditional probabilities can be calculated using Bayes' theorem and the law of total probability.

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The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches

Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :

= 1 / 3 x

The equation would then be :

x - 1 / 3 x - 10 - 5 = 35 + 1 / 2

x - 1 / 3 x - 10 - 5 = 35 . 5

The length of the original fabric is:

2 / 3x  = 35. 5 + 10 + 5

x = 50. 5 ÷ 2 / 3

x = 50. 5 x 3 / 2

x = 75 .75 inches

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0.3 as a fraction would be 3/10

33.3 would be 333/10

To check it so 3 ÷ 10 and 333 ÷ 10

It will give you the decimal again.

You're welcome.

Answer: the answer is 33.3 is 33 3/10  and 0.3 is 3/10

Step-by-step explanation:

you welcome (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

The altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

What is the altitude?

The height of an object or point in relation to sea level or ground level.

Part A:

To create a table for the given equation, we substitute the given values of x in the equation and calculate the corresponding values of y:

x y = -128x + 3,840

0 3,840

5 3,200

8 2,624

10 2,304

30 0

Part B:

To find the altitude after 5 minutes, we substitute x = 5 in the given equation:

y = -128(5) + 3,840

y = 3,200

So the altitude of the airplane after 5 minutes of descending is 3,200 feet.

To find the altitude after 30 minutes, we substitute x = 30 in the given equation:

y = -128(30) + 3,840

y = 0

The altitude of the airplane is decreasing as time (x) increases, as given by the negative slope (-128) of the equation.

At 5 minutes, the airplane has descended to an altitude of 3,200 feet, which is still relatively high.

At 30 minutes, the altitude has decreased to 0, which means the airplane has landed on the ground.

Hence, the altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.

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The average rate of change is 2.The rate of change of the function is its gradient or slope.

To get the average rate of change, divide the change in y-values by the change in x-values.Knowing the average rate of change is necessary to detect changes in observable metrics like average speed or average velocity.

It displays the typical rate of change of the function for each unit during that time. It is determined using the slope of the line connecting the ends of the interval in the function graph.

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The area of the composite figure is equal to 99 mm² square milimetresmetres.

The composite figure can be observed to be made up of two horizontal rectangle, and a vertical rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the bigger horizontal rectangle = 11 mm × 3 mm

area of the bigger horizontal rectangle = 33 mm²

area of the smaller horizontal rectangle = 5 mm × 2 mm

area of the smaller horizontal rectangle = 10 mm

area of the vertical rectangle = 14 mm × 4 mm

area of the vertical rectangle = 56 mm²

total area of the composite figure = 33 mm² + 10 mm² + 56 mm²

total area of the composite figure = 99 mm²

Therefore, the area of the composite figure is equal to 99 mm² square milimetres.

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The standard deviation is used more frequently then the variance because  standard deviation is more stable and less sensitive to outliers.

The Standard Deviation and Variance are defined as two closely related measures of the spread or dispersion of a set of data.

The Variance is defined as average of squared differences from mean, while Standard Deviation is square root of variance.

The reason why the standard deviation is used more frequently than  variance is because the standard deviation is expressed in same units as the original data, whereas  the variance is expressed in squared units.

For Example, if we measure  heights of a group of people in inches, the standard deviation will be expressed in inches, whereas variance will be expressed in square inches.

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Answer:

Step-by-step explanation:

is this in deltamath or bigideas? lol

(31.19-1.67)/24=x

"/" means divide.

It will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.

What is Approximation?
Approximation is the act of estimating or finding a value that is close to the true or exact value, but not necessarily identical to it. In other words, an approximation is a rough calculation or an educated guess that is used when the exact value is not known or is too difficult to calculate. Approximations are commonly used in mathematics, science, engineering, and many other fields where exact values are often difficult to obtain or not required. The level of accuracy of an approximation depends on the method used and the degree of precision needed for the particular situation.

Let's use the information given to find the rate of temperature increase per minute.

Between the first two data points, the temperature increased by 3 degrees in 1 minute. Between the next two data points, the temperature increased by (112.5 - 3) = 109.5 degrees in (5 - 1) = 4 minutes. So the rate of temperature increase is (109.5/4) = 27.375 degrees per minute.

To find out how long it will take the oven to reach 375 degrees, we can use the formula:

time = (final temperature - initial temperature) / rate of temperature increase

In this case, the initial temperature is 3 degrees and the final temperature is 375 degrees. Substituting these values and the rate of temperature increase we calculated earlier, we get:

time = (375 - 3) / 27.375 = 12.96 minutes (rounded to two decimal places)

So it will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.

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The given proof follows the symmetric property of angle congruence. Therefore, option C is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that,

       Statements            Reasons

1. ∠ABC≅∠DEF           1. Given

2. m∠ABC=m∠DEF     2. Definition of congruent angles

3. m∠DEF=m∠ABC     3. Symmetric property of equality

4. ∠DEF≅∠ABC          4. Definition of congruent angles

The symmetric property says that if one geometric shape is congruent to another, than the second shape is also congruent to the first. The symmetric property of congruence says that for any angles A and B, if ∠A≅∠B then ∠B≅∠A.

Therefore, option C is the correct answer.

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The area of the trapezoid KELP is approximately 2285.47 square units.

What is a trapezoid?

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The formula to find the area of a trapezoid is -

A = (1/2) × h × (b1 + b2)

where -

A is the area of the trapezoid.

h is the height of the trapezoid.

b1 and b2 are the lengths of the parallel bases of the trapezoid.

Using the given values, we can substitute them into the formula and solve for the area -

A = (1/2) × h × (b1 + b2)

A = (1/2) × 52.6 × (47.8 + 39.1)

A = 2285.47

Therefore, the area value is 2285.47 square units.

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No, if the figures on the left side of the area model were changed to 20, 10, and 5, the product would retain the same.

Area model multiplication is what?

The area model approach is based on the straightforward equation that may be used to calculate the area of a rectangle: LxW=A. As this anchor chart from Primary Punch illustrates, students typically begin by learning basic arrays for one-digit multiplication. When we multiply each digit of one number by each digit of another number while maintaining the place value of each digit, the resulting numbers are called partial products.

According to the supplied query,

30 and 5 on the left side of the area model are altered to 20,10, and 5 

Thus, after multiplying partial products, we obtain:

First row = 20×100+20×20+8×20

               = 2000+400+160 = 2560

Second row = 10×100+10×20+10×8

                     = 1000+200+80 = 1280

Third row = 5×100+5×20+5×8

                = 500+100+40 = 640

Adding all the rows we get,

2560+1280+640 = 4480

The item we receive when the dimensions are 30 and 5 is the same as this. In each instance, the area product stays the same.

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Kim saved $9 by using the coupon.

How to find Original price?

The MSRP (i.e., Manufacturer's Suggested Retail Price) set the original price, which is the cost. In the majority of cases, the original price would have been less expensive than the current price, though this is not always the case. Finding an item's original price and knowing the price after a discount are both made possible by original price.

Original price = Sales price/(100%-Discount%)

To find out how much money Kim saved, we need to first find out how much the birdhouse cost after the coupon was applied.

The coupon took 25% off the original price, so the birdhouse cost 100% - 25% = 75% of its original price.

So, the new price of the birdhouse would be:

36 * 75% = $27

Kim saved 36 - 27 = $9 by using the coupon.

Therefore, Kim saved $9 using the coupon.

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The value of the expression is the same as the second option: !a || (b & !c).

Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.

The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:

!(a & !(b & !c)) = !a || (b & !c)

Therefore, the value of the expression is the same as the second option: !a || (b & !c).

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