(4x3+2x+6)+(2x3−x2+2

The experimental probability of drawing a heart is given as follows:

0.30.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of outcomes is given as follows:

6 + 4 + 7 + 3 = 20.

Out of these 20 trials, 6 resulted in a heart, hence the experimental probability of drawing a heart is given as follows:

p = 6/20

p = 0.3

p = 30%.

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Explanation

By definition.

so

Let

hence

I hope this helps you

Answer:

4,343.475

Step-by-step explanation:

I just multiplied what she earned and how much she is going to make

Answer:

X=2, please mark me brainliest

Step-by-step explanation:

−5(4x−2)=−2(3+6x)

(−5)(4x)+(−5)(−2)=(−2)(3)+(−2)(6x)(Distribute)

−20x+10=−6+−12x

−20x+10=−12x−6

Step 2: Add 12x to both sides.

−20x+10+12x=−12x−6+12x

−8x+10=−6

Step 3: Subtract 10 from both sides.

−8x+10−10=−6−10

−8x=−16

Step 4: Divide both sides by -8.

−8x

−8

=

−16

−8

x=2

Answer:

150:200

Step-by-step explanation:

You can simplify it too. 3:4

The height in meters of a lava rock that falls for 5 seconds will be 122.5 meters.

The missing function is y = 1/2 gt².

A function is a remark, tenet, or regulation that establishes a relationship between the two parameters.

The height of lava fountains spewed from volcanoes cannot be measured directly.

Instead, their height in meters can be found using the equation is given as

y = 1/2 gt²

where y represents the height, g is 9.8, and t represents the falling time of the lava rocks.

Then the equation will be

y = 1/2 × 9.8 × t²

y = 4.9t²

Then the height in meters of a lava rock that falls for 5 seconds will be

y = 4.9 x 5²

y = 122.5 meters

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To construct a box plot for the given data, we need to find the five key statistics: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

These values will determine the positions of the five movable parts of the box plot. To construct the box plot, we start by ordering the data in ascending order: 45, 45, 46, 47, 49, 55, 59, 61, 70, 70, 79, 79. The minimum value is 45, and the maximum value is 79. The median is the middle value of the dataset, which in this case is the average of the two middle values: (55 + 59) / 2 = 57. The first quartile (Q1) is the median of the lower half of the dataset, which is the average of the two middle values in that half: (45 + 46) / 2 = 45.5. The third quartile (Q3) is the median of the upper half of the dataset, which is the average of the two middle values in that half: (70 + 70) / 2 = 70.

Now that we have the five key statistics, we can construct the box plot. The plot consists of a number line where we place the movable parts: minimum (45), Q1 (45.5), median (57), Q3 (70), and maximum (79). The box is created by drawing lines connecting Q1 and Q3, and a line is drawn through the box at the median. The whiskers extend from the box to the minimum and maximum values. Any outliers, which are data points outside the range of 1.5 times the interquartile range (Q3 - Q1), can be represented as individual points or asterisks. In this case, there are no outliers.

In summary, the box plot for the given data will have the following positions for the movable parts: minimum (45), Q1 (45.5), median (57), Q3 (70), and maximum (79).

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Answer:

\(10a - 41\)

Step-by-step explanation:

We can represent the area of the shaded section with the equation:

\(A_\text{shaded} = A_\text{rect} - A_\text{square}\)

First, we can solve for the area of the large enclosing rectangle:

\(A_\text{rect} = l \cdot w\)

↓ plugging in the given side lengths

\(A_\text{rect} = (a+4)(a-4)\)

↓ applying the difference of squares formula ... \((a + b)(a - b) = a^2 - b^2\)

\(A_\text{rect} = a^2 - 16\)

Next, we can find the area of the non-shaded square.

\(A_\text{square} = l^2\)

↓ plugging in the given side length

\(A_\text{square} = (a-5)^2\)

↓ applying the binomial square formula ... \((a - b)^2 = a^2 - 2b + b^2\)

\(A_\text{square} = a^2 - 10a + 25\)

Finally, we can plug these areas into the equation for the area of the shaded section.

\(A_\text{shaded} = A_\text{rect} - A_\text{square}\)

↓ plugging in the areas we solved for

\(A_\text{shaded} = \left[\dfrac{}{}a^2 - 16\dfrac{}{}\right] - \left[\dfrac{}{}a^2 - 10a + 25\dfrac{}{}\right]\)

↓ distributing the negative to the subterms within the second term

\(A_\text{shaded} = \left[\dfrac{}{}a^2 - 16\dfrac{}{}\right] + \left[\dfrac{}{}-a^2 + 10a - 25\dfrac{}{}\right]\)

↓ applying the associative property

\(A_\text{shaded} = a^2 - 16 -a^2 + 10a - 25\)

↓ grouping like terms

\(A_\text{shaded} = (a^2 -a^2) + 10a + (- 16 - 25)\)

↓ combining like terms

\(\boxed{A_\text{shaded} = 10a - 41}\)

Answer:

$34.38

Step-by-step explanation:

Y: A random variable that indicates the amount of money that the seller will receive.

p=2,50$

if  x=0  →  y=0.2,50=0$

if  x=5  →  y=5.2,50  = 12,5  $

if  x=10  →  y=10.2,50= 25$

if  x=15  →  y=15.2,50=  37,5$

if  x=20  →  y=20.2,50=  50  $

if  x=25  →  y=25.2,50=  62,5$

Y=  { 0$ ; 12,5$ ; 25$ ; 37,5$ ; 50$ ; 62,5$ }

E(Y)=  ∑Y.P(Y)

=  0.P(0)+12,5.P(12,5)+  25.P(25)+  37,5.P(37,5)+  50.P(50)+  62,5.P(62,5)

=  0.0,01+  12,5.0,15+  25.0,25+  37,5.0,3+  50.0,25+  62,5.0,04

= 0 + 1,875 + 6,25 + 11,25 + 12,5 + 2,5

= 34,38$ expected value of the amount of money the seller receives.

Answer:

x=1 and y=−5

Step-by-step explanation:

Problem:

Solve y=−5x;y=x−6

Steps:

I will solve your system by substitution.

y=−5x;y=x−6

Step: Solve y=−5x for y:

Step: Substitute −5x for y in y=x−6:

y=x−6

−5x=x−6

−5x+−x=x−6+−x (Add -x to both sides)

−6x=−6

−6x/−6=−6/−6 (Divide both sides by -6)

x = 1

Step: Substitute 1 for x in y=−5x:

y=−5x

y=(−5)(1)

y=−5(Simplify both sides of the equation)

Answer:

x=1 and y=−5

Thank you,

Eddie

Answer:

Its 3 bro

Step-by-step explanation:

my guy A is just B scaled 3 times, every number on B times 3 equals their counterpart in A

The arithmetic sequence that has the given features is presented as follows:

\(a_n = 2 + 3(n - 1)\)

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and called common difference d.

The nth term of an arithmetic sequence is obtained by the following rule:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term of the sequence.

The sum of the first n terms is presented as follows:

\(S_n = \frac{n(a_1 + a_n)}{2}\)

The sum of the first nine terms is of 126, hence:

\(S_9 = 126\)

\(\frac{9(a_1 + a_9)}{2} = 126\)

\(4.5(a_1 + a_9) = 126\)

The ninth term is written as follows:

\(a_9 = a_1 + 8d\)

Hence:

\(4.5(a_1 + a_1 + 8d) = 126\)

\(9a_1 + 36d = 126\)

\(a_1 + 4d = 14\)

The sum of the second nine terms is of 369, hence:

\(S_{18} = 126 + 369\)

\(S_{18} = 495\)

Then:

\(\frac{18(a_1 + a_{18})}{2} = 495\)

\(a_{1} + a_{18} = 55\)

The 18th term is:

\(a_{18} = a_1 + 17d\)

Hence:

\(2a_1 + 17d = 55\)

From the first equation, it is found that:

\(a_1 = 14 - 4d\)

Hence the common difference is obtained as follows:

2(14 - 4d) + 17d = 55

28 - 8d + 17d = 55

9d = 27

d = 3.

Hence the first term is of:

\(a_1 = 14 - 4(3) = 2\)

Thus the definition of the sequence is:

\(a_n = 2 + 3(n - 1)\)

The problem asks for the definition of the arithmetic sequence.

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Answer:

the difference of 2 times d minus 3= 6

4 added to the difference of d minus 3= 4

the difference of d minus 3 divided by 2= 0

the quotient of 12 divided by the difference of 3 times d minus 3= 2

Step-by-step explanation:

2 times 3 equals 6. 3 minus 3 equals 0. 6-0=6

d minus 3 equals 0. 4+0 equals 4

3 minus d equals 0. 0 divided by two is 0

3 times d= 9. minus 3 = 6. 12 divided by 6 = 2

hope this helps! (:

Answer:

The answer is 8.3 W + 17.4

If you click on the image it will show you how to solve the equation and I hope this helps you.

Answer:

Step-by-step explanation:

Hello :)

We know that :

30g of cornflakes ⇒ 2.5g of fat

320g of cornflakes ⇒ xg of fat

x = 320 * 2.5 ÷ 30 ≈ 26.7 g of flat

Have a nice day!

The probability of z being less than 0.25 as 0.5987 based on population proportion.

To use the normal approximation, we first need to check if the conditions are met. For this, we need to check if np and n(1-p) are both greater than or equal to 10.

np = 98 x 0.56 = 54.88

n(1-p) = 98 x 0.44 = 43.12

Since both np and n(1-p) are greater than 10, we can use the normal approximation.

Next, we need to find the mean and standard deviation of the sampling distribution of proportion.

Mean = np = 54.88

Standard deviation = sqrt(np(1-p)) = sqrt(98 x 0.56 x 0.44) = 4.43

Now we can standardize the variable X and find the probability:

z = (X - mean) / standard deviation = (56 - 54.88) / 4.43 = 0.25

Using a standard normal table or calculator, we can find the probability of z being less than 0.25 as 0.5987.

Therefore, P(X < 56) = P(Z < 0.25) = 0.5987.

Note that we rounded the mean and standard deviation to two decimal places, but you should keep the full values in your calculations to minimize rounding errors.

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Answer:

1.5cm

Step-by-step explanation:

I TOOK THE TEST

Answer:

2.814 * 10^14

Step-by-step explanation:

For exponential growth:

A = A0*e^kt

A = final amount ; A0 = initial amount ; t = time

Since bacterium doubles ever half hour ;

In 1 hour number of bacterium will be 2² = 4

Hence

Final amount after 1 hour

4 = 1*e^k*1

4 =e^k

Take In of both sides

In(4) = k

Number of bacterium in 24 hours

A = 1*e^In4 * 24

A = e^24In4

A = e^33.271064

A = 281474976710656

A = 2.814 * 10^14

Answer: (5,4)

4 + 6 / 2 = 5

10 + (-2) / 2 = 4

Answer:

cant help sry

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

80-45=35

Answer:

\(\frac{1}{2x-3}\)

Step-by-step explanation:

(\(\frac{f}{g}\) )(x)

= \(\frac{f(x)}{g(x)}\)

= \(\frac{x+1}{2x^2-x-3}\) ( factorise the denominator )

= \(\frac{x+1}{(2x-3)(x+1)}\) ← cancel the common factor (x + 1) on numerator/ denominator

= \(\frac{1}{2x-3}\)

Answer:

tan x

Step-by-step explanation:

Using the trigonometric identities

secx = \(\frac{1}{cosx}\) , cosecx = \(\frac{1}{sinx}\) , then

\(\frac{secx}{cosecx}\)

= \(\frac{\frac{1}{cosx} }{\frac{1}{sinx} }\)

= \(\frac{1}{cosx}\) × sinx

= \(\frac{sinx}{cosx}\)

= tan x

Answer:

197

Step-by-step explanation:

to solve Hypotenuse:

a^2+b^2=c^2

Plug in:

28^2+195^2=c^2

Solve:

784+38025=c^2

38809=c^2

sqrt 38809=sqrt c^2

c=191

I hope it helps!!!

While Marsha, Jan, and Cindy individually have transitive preferences over three goods, it is possible that the group's preferences might not be transitive when deciding on the "fruit of the month."

This scenario arises due to the aggregation of individual preferences and the potential conflicts that can emerge during the voting process.

When individuals vote on their preferred fruit of the month, the group's preference is determined by aggregating individual preferences. However, the aggregation process can lead to inconsistencies in transitivity. For example, let's assume Marsha prefers oranges to apples, Jan prefers apples to pears, and Cindy prefers pears to oranges.

Individually, their preferences are transitive. However, when their preferences are aggregated, conflicts arise. If the group votes between oranges and apples, Marsha's preference would favor oranges, Jan's preference would favor apples, and the group might choose apples as the fruit of the month. Similarly, if the group votes between apples and pears, Jan's preference would favor apples, Cindy's preference would favor pears, and the group might choose pears.

Now, if the group votes between oranges and pears, Marsha's preference would favor oranges, Cindy's preference would favor pears, but there is no unanimous preference between apples and pears. In this case, the group's preference would not be transitive because oranges are preferred to apples, apples are preferred to pears, but oranges are not preferred to pears.

This example demonstrates that the aggregation of individual preferences in a voting process can lead to situations where the group's preferences are not transitive.

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The difference between Georgina's total stock earnings and her real return is $119.70. he difference between Georgina's total stock earnings and her real return is $119.70.

What is the difference?

The term "difference" refers to the amount by which one quantity is greater or less than another.

The difference between Georgina's total stock earnings and her real return can be calculated as follows:

Difference = Total stock earnings - Real return

Difference = $395.50 - $275.80

Difference = $119.70

Hence, the difference between Georgina's total stock earnings and her real return is $119.70.

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We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)  .

The definition of the average value of a continuous function f(x) can be expanded to include the infinitely long interval [a,∞] as follows:

\(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)

Let's assume that f(x) is any continuous function. Assume that the integral \(\int\limits^i_0 {f(x)} \, dx\)   is divergent and that f(x)≥0 in the range [a,∞].

Show that, if this limit exists, \(f_{ave} = \lim_{x \to \infty} f(x)\) .

Hence, We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)  .

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The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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The least possible number of adult men in the town is 100.

Given that in a certain town, 2/3 of the adult men are married to 3/5 of the adult women. Also, we have to assume that all marriages are monogamous (no one is married to more than one other person). Thus, we have to determine the least possible number of adult men in the town. Let us solve this question using the following steps: Let the total number of adult men in the town be x. Since 2/3 of adult men are married, the number of married men in the town = 2/3x. Also, the remaining number of unmarried men = x - 2/3x = 1/3x.According to the question, 3/5 of adult women are married to 2/3 of adult men.

Thus, we have to assume that there are 2/3x married men and 3/5 of women are married. Therefore, the number of married women in the town = 3/5 × total number of women Number of women = Total number of men × 3/2 (since, 3/5 of women are married to 2/3 of men)Number of women = x × 3/2 × 3/5 = 9/10x∴ Number of married women in the town = 3/5 × 9/10x = 27/50x Since all marriages are monogamous, the number of married men and women in the town should be equal. 2/3x = 27/50x2/3 * 50 = 27/50 * x(2/3 * 50)/(27/50) = x=100 Therefore, the least possible number of adult men in the town is 100.

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Answer:

D

Step-by-step explanation:

the measure of a secant- tangent angle is half the difference of the intercepted arcs, then

\(\frac{1}{2}\) (154 - (12x + 2) ) = 6x + 4 ( multiply both sides by 2 to clear the fraction )

154 - 12x - 2 = 12x + 8 , that is

152 - 12x = 12x + 8 ( subtract 12x from both sides )

152 - 24x = 8 ( subtract 152 from both sides )

- 24x = - 144 ( divide both sides by - 24 )

x = 6