In a play-school with 500 students, the number of boys is 20 more than five-sevenths of the number of girls. Let’s find the number of boys and girls in the play-school.

If we assume x to be the number of girls in the play-school, the number of boys can be expressed as:

Answer:

The probability that at least two of the customers exceed their limit is 0.2642.

Step-by-step explanation:

We are given that Past records indicate that the probability of customers exceeding their credit limit is 0.05.

On a given day, 20 customers place orders.

Let X = the number of customers who exceed their credit limit

The above situation can be represented through binomial distribution;

\(P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......\)

where, n = number of trials (samples) taken = 20 customers

            r = number of success = at least two

            p = probability of success which in our question is the probability 

                  of customers exceeding their credit limit, i.e; 0.05.

So, X ~ Binom(n = 20, p = 0.05)

Now, the probability that at least two of the customers exceed their limit is given by = P(X \(\geq\) 2)

        P(X \(\geq\) 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

=  \(1- \binom{20}{0}\times 0.05^{0} \times (1-0.05)^{20-0}- \binom{20}{1}\times 0.05^{1} \times (1-0.05)^{20-1}\)

=  \(1- (1 \times 1 \times 0.95^{20})- (20 \times 0.05^{1} \times 0.95^{19})\)

=  0.2642

the slope for this line is 2

The slope or gradient of a line is a number  that describe both the direction and the steepness of the line. the steepness of a line is defined as the slope (or gradient). The slope is the ratio of vertical distance to the horizontal distance between any two points on a line. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2.

So, A.T.Q:-

  The formula of slopet intercept is  Y2 -Y1 /X2-X1

  From the question:

              slope = -1-1/0-1

              slope = 2

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Step-by-step explanation:

=41/5kg/630 g

=21/5kg/630g

=21/5×1000 g/630g

=4200g/630g

=20/3

Answer:

\( \large \sf \blue{Find \: the \: H.C.F \: of : }\)

\( \sf \purple{➪ \: 84 \: and \: 156}\)

\( \large\sf \red{Simplify: - }\)

\( \sf\: 4 \frac{1}{5}kg : 630g\)

-,- -,- xD xD

Answer:

880 feet; 0.166666666 miles or ⅙ of a mile

Step-by-step explanation:

First convert miles to feet so 1 mile is 5280 feet.

Now divide it by 2 because we're working with half a mile per 3 minutes.

Now we know that Kelly can run 2640 feet every 3 minutes. Divide that by three to get her pace for every minute and we know that she runs 880feet per minute. In miles that would be 0.166 or ⅙ of a mile

Step-by-step explanation:

the ratio is

1/2 mile per 3 minutes

= 1/2 / 3

now, we need to keep the value of that ratio unchanged but still transform the ratio (= a fraction) so that we get as ultimate denominator 1 instead of 3 (how far did he run in 1 minute).

what do we need to do to transform 3 to 1 ?

we need to divide by 3.

and because we have to keep the ratio value, we have to devide also the numerator by 3 :

1/2 / 3 × 1/3 / 1/3 = (1/2 × 1/3) / (3 × 1/3) = 1/6 / 1

so, we can read from the result directly :

when running with the same pace (ratio) for 1 minute, he will run 1/6 mile.

Answer:

a. Domain : All Real Numbers

b. Range: y≥ -1

c. The x-intercepts are (0,0) and (-4,0)

d. The y-intercept is (0,0).

e. f(2)=3

   f(-2)=-1

Step-by-step explanation:

If this has helped you please mark as brainliest

Answer:

Table 1

The first table

Step-by-step explanation:

Answer:

the first table (A

Step-by-step explanation:

the inputs dont repeat

Answer:

7%

Step-by-step explanation:

30.80%=0.308

0.308/440=0.0007%

0.0007 is the same as 7%

Explanation

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal)

it means

let

AB=2x+12

CD=34

Now, replace

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

\(x^2 + 10x -24 = 0 \: \\ is \: equivalent \: to \: ( x + 2) {}^{2} + 10x - 36=0\)

Step-by-step explanation:

\(x^2 + 10x -24 = 0 \\ x^2 + 12x - 2x -24 = 0 \\x(x + 12) - 2(x + 12) = 0 \\ (x - 2)(x + 12) = 0\)

The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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Answer:

y = -2x + 5

Step-by-step explanation:

Points on the path: (0, 5) and (1, 3)

Slope:

m=(y2-y1)/(x2-x1)

m=(3-5)/(1-0)

m= (-2)/1

m= -2

Slope-intercept:

y - y1 = m(x - x1)

y - 5 = -2(x - 0)

y - 5 = -2x

y = -2x + 5

Answer:

3 is incorrect

Step-by-step explanation:

ab is too long so if it were multiplied twice itd be no where near ac

Tanya will then have 286 cookies after baking 12 more batches.

A linear equation's slope-intercept form is y = mx + b. The variables in the equation are x as well as y. The integers m and b represent the the line's slope (m) and the value of y when x is 0 respectively (b). Because (0,y) is the point when the line crosses the y-axis, the value of y when x is 0 is known as the y-intercept.

A linear equation with one variable is one with only one variable. It has the formula Ax + B = 0, where A and B can be any two real numbers as well as x is an unknown variable with a single solution. 9x + 78 = 18, for example, is a one-variable linear equation.

y = 70 + 18(x)

x = 12 batches.

substituting the value in the equation:

y = 70 + 18(x)

y = 70 + 18(12)

   = 70 + 216

y  = 286.

Tanya will then have 286 cookies after baking 12 more batches.

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Answer:

  1

Step-by-step explanation:

You want to know the value of i^4.

The fourth power of i, √(-1), can be found the same way the value of any fourth power can be found: carry out the multiplication.

  i^4 = i·i·i·i = -1·i·i = -i·i = -(-1) = 1

The fourth power of i is 1.

__

Additional comment

As you can see from the evaluation process, ...

  i¹ = i

  i² = -1 . . . . . definition of i

  i³ = -i

  i⁴ = 1

The sequence repeats for higher powers.

Answer and Step-by-step explanation:

This requires the use of the Sine trig function to solve for x.

The Sine trig function is as follows:

sin(θ) = \(\frac{Opposite Side}{Hypotenuse}\)

Plug in the values and solve for x.

sin(60) = \(\frac{x}{24\sqrt{3}}\)

Multiply each side by \(24\sqrt{3}\)

\(24\sqrt{3} (sin(60)) = x\\\\\\\\36 = x\)

36 is equal to x.

#teamtrees #PAW (Plant And Water)

Using the iterative formula the values are calculated to be

x₁ = 2

x₂ = 0.742

x₃ = -0.721

x₄ = 2.247i - 3

The given formula is

Xₙ₊₁ = √7xₙ - 3

the values are solved by substitution as shown below

x₂ = √(7 * 2) - 3 = √14 - 3 = 0.742

x₃ = √(7 * 0.742) - 3 = √14 - 3 = -0.721

x₄ = √(7 * -0.721) - 3 = 2.247i - 3

the values in 3 dp are x₂ = 0.742, x₃ = -0.72, and x₄ = 2.247i - 3

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The two relationships that describe a function in the table are A: Name as a function of hair color, and D: Eye color as a function of hair color.

A function is a relationship between two sets of values in which each element of the first set corresponds to exactly one element of the second set. In this table, for each hair color there is only one associated name, so the relationship between name and hair color is a function. Similarly, for each hair color there is only one associated eye color, so the relationship between eye color and hair color is also a function.

Note that the other relationships listed in the question (B, C, E and F) are not functions because they do not have a one-to-one correspondence between the two sets of values. For example, in the relationship between eye color and name, multiple people (Juan and Keshia) have the same eye color (brown), so this relationship does not describe a function.

Therefore, options A and D are the correct answer.

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The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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Answer:

a)2.2360

b)4.123

c)3.641

d)8.654

Answer:

either b or d hopes this helps bud

The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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Answer:

-30,10

Step-by-step explanation:

How to get 60 to -30 : 60 divided by -30 is -2

How to get -20 to 10: -20 divided by 10 is -2

The solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

To solve the simultaneous equations:

Begin by rearranging the second equation to solve for one variable in terms of the other. In this case, we'll solve for y:

5x + 2y = 6

2y = 6 - 5x

y = (6 - 5x)/2

Substitute the expression for y in terms of x into the first equation:

\(2x^2 + y^2 = 12\)

\(2x^2 + ((6 - 5x)/2)^2 = 12\)

Simplify the equation by expanding and combining like terms:

\(2x^2 + (6 - 5x)^2/4 = 12\)

\(2x^2 + (36 - 60x + 25x^2)/4 = 12\)

Multiply through by 4 to eliminate the fraction:

\(8x^2 + 36 - 60x + 25x^2 = 48\)

Rearrange the equation to form a quadratic equation:

\(33x^2 - 60x - 12 = 0\)

Solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula here:

\(x = (-b ± √(b^2 - 4ac)) / (2a)\)

Plugging in the values from the quadratic equation, we have:

\(x = (-(-60) ± √((-60)^2 - 4 * 33 * -12)) / (2 * 33)\)

x = (60 ± √(3600 + 1584)) / 66

x = (60 ± √5184) / 66

x = (60 ± 72) / 66

Calculate the values of x:

For x = (60 + 72) / 66: x ≈ 2.18

For x = (60 - 72) / 66: x ≈ -0.18

Substitute the x values back into the second equation to find the corresponding y values:

For x ≈ 2.18:

5(2.18) + 2y = 6

10.9 + 2y = 6

2y = 6 - 10.9

2y ≈ -4.9

y ≈ -2.45

For x ≈ -0.18:

5(-0.18) + 2y = 6

-0.9 + 2y = 6

2y = 6 + 0.9

2y ≈ 6.9

y ≈ 3.45

Therefore, the solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

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Answer:

I don't know i just came to get the 20 points THX

Step-by-step explanation:

You should ask your teacher