There are 24 children in a kindergarten class. Three quarters of them can already write the whole alphabet. How many children can write the alphabet?

Answer:

y=-3x

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

let 'n' = the number

n/3 + 10 = 2

n/3 +10 - 10 = 2 - 10

n/3 = -8

n = -24

Answer:

x= -24

Step-by-step explanation:

let the number be x

x/3 +10=2

Multiply through by 3

3 * x/3 + 3 *10 = 2*3

x + 30 = 6

x= 6 - 30

x= -24

note * = multiplication sign

Step-by-step explanation:

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PAGAL KUTTA

Answer:

The equation of the horizontal line passing through  (4, 9) will be:

\(y=9\)

Please also check the attached line graph.

Step-by-step explanation:

We know that the equation of a horizontal line is always the kind of equation such as:

\(y=k\)

Thus, the equation of the horizontal line passing through  (4, 9) will be:

\(y=9\)

Please also check the attached line graph.

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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Answer:

• mean = 61

• mode = 50

• median = 57.5

Step-by-step explanation:

• The mean is calculated by adding all the values together, and dividing the result by the number of values.

∴ mean =  \(\frac{60 + 50 + 50 + 70 + 40 + 80 + 65 + 55 + 50 + 90}{10}\)

⇒ mean = \(\frac{610}{10}\)

⇒ mean = 61

• The mode of a set of values is the value that is the most common (has highest frequency) among them.

50 is the most common value.

∴ mode = 50

• The median is the middle-value of a set of ordered values.

∴ We have to first rearrange the set:

⇒  40, 50, 50, 50, 55, 60, 65, 70, 80, 90

Now we need to find the middlemost value:

Since we have 10 values, which is an even number, we have to use the formula:

median = \(\frac{(n/2)^{th} \space\ term \space\ + \space\ [(n/2) + 1]^{th} \space\ term }{2}\)

where n is the number of values.

∴ median =  \(\frac{(10/2)^{th} \space\ term \space\ + \space\ [(10/2) + 1]^{th} \space\ term }{2}\)

⇒ median =  \(\frac{5^{th} \space\ term \space\ + \space\ 6^{th} \space\ term }{2}\)

The 5th and 6th terms in our ordered series are 55 and 60 respectively.

∴ median = \(\frac{55 + 60}{2}\)

⇒ median = 57.5

Points are (0,0) and (2,8).

What is the gradient?

The vector field f's value at a point p in the vector calculus is the "direction and rate of fastest increase" for a scalar-valued differentiable function f with many variables.

Here, we have

Given: y = 4x

The number in front of the x is the gradient (slope). This number represents the amount of up or down for a given amount of long.

If the number in front of the x (coefficient) is positive the 'slope' goes up. If the coefficient is negative it means the 'slope' is down.

Now, substitute any value you chose into x, multiply it by 4 and you have your value for y

Let x = 0,

y = 4(0) = 0

So this can be our first point on the graph.

(x₁, y₁) ⇒ (0,0)

Let x = 2

y = 4(2) = 8

So this can be our second point on the graph.

(x₂, y₂) ⇒ (2,8)

Now, we draw a line through them extending it to the edges of the axis.

Hence, Points are (0,0) and (2,8).

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During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer:

-10/16

Step-by-step explanation:

-7z3=-10 and 7-(-9)=16

Answer:

\(\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.\)

Step-by-step explanation:

\(\frac{2}{3} \ of \ a \ right \ angle \ = \frac{2}{3} \times 90^{\circ} = 60^{ \circ}\\\\A \ whole \ wheel \ is \ = 360^ {\circ}\\\\\)

Now to find what part of 360 is 60 :

\(Let \ it \ be \ x\\\\x \times 360 = 60 \\\\x = \frac{60}{360} = \frac{1}{6}\)

Therefore ,

          \(\frac{2}{3} \ part \ of \ right \ angle \ is \ \frac{1}{6} \ part \ of \ a \ whole \ wheel.\)

Answer:

Step-by-step explanation:

use SOH CAH TOA to remember sin cos and tan functions

Sin = oppostive/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent

22. cos(x) = b/c
24. sin(x) = 2/2sqrt(17) = 1/sqrt(17)
26. tan(x) = 2/8 = 1/4

28. cos(y) = 2/2sqrt(17) = 1/sqrt(17)
30. sin(30)
in a 30 60 90 triangle, the side opposite 30 is 1, the side opposite 60 is sqrt(3), the side opposite 90 is 2.
sin(30) = opposite/hypotenuse = 1/2/1 = 1/2
32.
in a 45 45 90 triangle, the side opposite 45 is 1, the side opposite 45 is 1, the side opposite 90 is sqrt2.

sin = opposite/hypotenuse = 1/sqrt(2)
34. cos(30) = sqrt(3)/2

36. tan(31) = AC/9 --> AC = 9tan(31) = 5.408

Answer:

22.  \(\dfrac{b}{c}\)

24.  \(\dfrac{\sqrt{17} }{17}\)

26.  \(\dfrac14\)

28.  \(\dfrac{\sqrt{17} }{17}\)

30.  \(\dfrac12\)

32.  \(\dfrac{\sqrt{2} }{2}\)

34.  \(\dfrac{\sqrt{3} }{2}\)

36. AC = 5.41 (nearest hundredth)

Step-by-step explanation:

Using trig ratios:

\(sin(\theta)=\dfrac{O}{H}\\\\\\cos(\theta)=\dfrac{A}{H}\\\\\\tan(\theta)=\dfrac{O}{A}\)

where \(\theta\) is the angle, O is the side opposite the angle, A is the side adjacent the angle, H is the hypotenuse of a right angle

22. \(cos(x)=\dfrac{b}{c}\)

24.  \(sin(x)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\)

26. \(tan(x)=\dfrac{2}{8}=\dfrac14\)

28. \(cos(y)=\dfrac{2}{2\sqrt{17} }=\dfrac{\sqrt{17} }{17}\dfrac{}{}\)

30. \(sin(30)=\dfrac12\)

32. \(sin(45)=\dfrac{\sqrt{2} }{2}\)

34. \(cos(30)=\dfrac{\sqrt{3} }{2}\)

36. \(tan(31)=\dfrac{AC}{9}\)

\(\implies AC=9tan(31)=5.41\) (nearest hundredth)

Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

Answer:

isosceles triangle

Step-by-step explanation:

first by using corresponding angle theorem:

<A=<C

<A=50°

then by using exterior angle theorem:

<A+<C=<B(the outer angle)

50°+<C=<B,<B=180°-80°(angle B lies in a staight line)

<B=100°

50°+<C=100°

<C=50°

The cost of a 25-minute rental will be $92.00.

To find the amount a 25-minute rental would cost, we need to first determine the rate per minute and the flat fee. We can do this by setting up the following system of equations:

30 minutes x rate + flat fee = $110.50

40 minutes x rate + flat fee = $145

To solve this system of equations, we can multiply the first equation by 2 and subtract the second equation from it to eliminate the rate:

(30 minutes x 2) x rate + flat fee x 2 = 2 x $110.50

80 minutes x rate + flat fee x 2 = 2 x $110.50

Subtracting the second equation from the first equation, we get:

flat fee x 2 - flat fee x 2 = 2 x $110.50 - 2 x $145

flat fee x 2 - flat fee x 2 = -$34.50

Since the left side of the equation is equal to zero, we can divide both sides by 2 to solve for the flat fee:

flat fee - flat fee = -$34.50 / 2

flat fee - flat fee = -$17.25

Since the left side of the equation is also equal to zero, the flat fee must be zero.

We can now use either of the original equations to solve for the rate per minute. Using the first equation, we get:

30 minutes x rate + flat fee = $110.50

30 minutes x rate = $110.50

rate = $3.68

We can now use this rate to find the cost of a 25-minute rental:

25 minutes x $3.68 + flat fee = $92.00 (Since the flat fee is zero)

Thus, a rental of 25 minutes costs $92.00.

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Answer:

4. 1), 2), 4) are true

5. x = 7

Step-by-step explanation:

In question 4.

1), 2), and 4) are true

Triangles ABD and CBD are congruent by AAS. Then by CPCTC, 1) and 4) are true. 2) is true by definition of altitude and all right angles are congruent.

5.

Your drawing is good.

Since IF is a median, then IE = IG = (1/2)GE

IE = (1/2)GE

x + 6 = (1/2)(3x + 5)

2x + 12 = 3x + 5

-x = -7

x = 7

Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

Multiplying by (-1)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

This polynomial has roots  such that , given by the following formulas

In this question:

So

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.The height of the coin, after t seconds, is given by the following equation:

Answer:

Step-by-step explanation:

the dot would either (1,4) or (4,1)

a squared+ b squared= c squared

the length of the sides are 3

3 squared + 3 squared= c squared

9+9 =c squared

18= c squared

square root of 18 rounded to the nearest tenth is 4.2

Step-by-step explanation:

\(smallest \: 7-digit = 1000000 \\ \\ largest \: 4 - digit \: number = 9999 \\ \\ sum = (1000000 + 9999) \\ \\ sum = \: 1009999 \\ \\ hope \: it \: is \: helpful \: to \: you \: (◕ᴗ◕✿)\)

The percent of the total calories in each brownie that comes from fat is 26.9%

We know that the total amount of calories in each brownie is 420 calories, so that number represents our 100%, then we can write the relation:

420 cal = 100%

Now, the fat has 113 calories, this is a percentage X that we want to find, so we can write:

113 cal = X

We have the two relations:

113 cal = X

420 cal = 100%

If we take the quotient we get:

(113 cal/420 cal) = X/100%

Solving for X.

(113 cal/420 cal)*100% = X = 26.9%

So, the percent of the total calories in each brownie that comes from fat is 26.9%.

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Answer: Area: 460.48 ft^2         Perimeter: 90.12 ft

Step-by-step explanation:

The area is 1/2 * 3.14 * (16 / 2)^2 (area of semicircle)

+ 10 * 12 / 2 (area of triangle)

+ 20 * 15 (area of rectangle)

= 460.48

The perimeter is 1/2 * 16 * 3.14 (perimeter of semicircle)

+ 10 (perimeter of triangle)

+ 20 + 15 + 20 (perimeter of rectangle)

= 90.12

Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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Answer:

5

Step-by-step explanation:

this is because there is totally 6 side and there is 5 character for the probability

Answer:

1.3x10^-6

trust me it's right

Step-by-step explanation:

A cube has equal sides ....

volume = s  x  s  x  s  = 343 cm^3

                  then s^3 = 343

                                s = 7 cm

then the perimeter of one side would be 7 + 7 + 7 + 7 = 28 cm

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

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