Ten of 16 students in Nyack's class are girls. His teacher selected two helpers by randomly drawing names. He drew a boys name first and then a girls names. Nyack thinks that the probability of this happening is 15/64. Is he correct? If not, Explain his error.

Answer:

  5/12

Step-by-step explanation:

The fraction that is girls is the ratio of girls to the total of boys and girls:

  girls/(boys+girls) = 5/(7+5) = 5/12

Answer:

  C.  (-2, -8)

Step-by-step explanation:

The function reduces to ...

  f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2

At x=-2, the function would evaluate to ...

  f(-2) = -2 -6 = -8

but cannot, because there is a hole in the function definition at that point.

There is a hole at (-2, -8).

The greatest number of students that could be in each row is 12, which is the greatest common divisor of 36 and 120. The color guard will have 3 rows, and the high school marching band will have 10 rows.

To determine the greatest number of students that could be in each row and the number of rows each group will have, we need to find the greatest common divisor (GCD) of the two numbers representing the members in each group, 36 and 120. The greatest common divisor is the largest number that divides both numbers without leaving a remainder. Calculate this by listing the factors of each number or using the Euclidean algorithm.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The greatest common divisor is the largest factor both numbers share, which is 12. Therefore, the greatest number of students per row is 12.

Now, to find the number of rows for each group, divide the total number of members in each group by the number of students per row:

So, there will be 3 rows of color guard members and 10 rows of marching band members.

Answer:

(140, 37)

Step-by-step explanation:

If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same.  The number of miles will also be the same at this cost.  That means we need cost functions for each.  x is the number of miles that is driven, our independent variable.  If A-1 charges .10 per mile, the expression is .1x.  If the flat fee is 23, regardless of how many miles you drive, you can expect to pay

y = .1x + 23

If EZ charges .05 per mile, the expression is .05x.  If the flat fee is 30, regardless of how many miles you drive, you can expect to pay

y = .05x + 30

If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.

.1x + 23 = .05x + 30 and

.05x = 7 so

x = 140 miles.

In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.

y = .1(140) + 23

y = 14 + 23

y = 37

The coordinate pair is (140 miles, $37)

This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.

Answer:

¼ yd

Step-by-step explanation:

2/5 - 3/20

1. Find the lowest common denominator of the two fractions.

The LCD of 5 and 20 is 20.

2. Give the fractions the same LCD

2/5 - 3/20 = 8/20 - 3/20

3. Subtract the numerators

Keep the same denominator.

8/20 - 3/20 = 5/20

4. Simplify the fraction

5/20 = ¼  

The beetle crawled ¼ yd further than the spider.

Answer:

  b.  x^2 +2cx +bc+ac-ab = 0

Step-by-step explanation:

It's a matter of what I would describe as tedious algebra. You have to multiply by the least common denominator, then simplify to standard form.

After multiplying the equation by (x+a)(x+b)(x+c) and subtracting the right side, you have ...

  (x +b)(x +c) +(x +a)(x +c) -(x +a)(x +b) = 0

Expanding each factor pair gives ...

  (x² +(b+c)x +bc) +(x² +(a+c)x +ac) -(x² +(a+b)x +ab) = 0

Collecting terms gives ...

  x²(1 +1 -1) +x(b+c +a+c -a -b) +(bc +ac -ab) = 0

  x² +2cx +bc +ac -ab = 0 . . . . . matches selection B

Answer:

  1050 g < weight ≤ 1150 g

Step-by-step explanation:

Let w represent the weight of the package in grams. The the number of 100-gram increments after the first 250 grams is given by ...

  ⌈(w-250)/100⌉ . . . . . . . where ⌈ ⌉ signifies the ceiling function

and the charges for a package exceeding 250 grams will be ...

  0.65 + 0.10⌈(w -250)/100⌉ = 1.55

  0.10⌈(w -250)/100⌉ = 0.90 . . . . . . . . subtract 0.65

  ⌈(w -250)/100⌉ = 9 . . . . . . . . . . . . . . . divide by 0.10

  8 < (w-250)/100 ≤ 9 . . . . . . . . . . . . . . meaning of ceiling function

  800 < w -250 ≤ 900 . . . . . . . . . . . . . multiply by 100

  1050 < w ≤ 1150 . . . . . . . . . . . . . . . . . add 250

The weight in grams could be greater than 1050 and at most 1150 for a charge of $1.55.

Answer:

Option D RX=4 units

Step-by-step explanation:

we know that

In the right triangle RTS

The cosine of angle TRS is equal to

cos(TRS)=RT/RS

substitute

cos(TRS)=6/9 -----> equation A

In the right triangle RTX

The cosine of angle TRX is equal to

cos(TRX)=RX/RT

substitute

cos(TRX)=RX/6 -----> equation B

∠TRS=∠TRX -----> is the same angle

Match equation A and equation B

6/9=RX/6

RX=6*6/9=4 units

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

========================================

We have:

[tex]f(x)=3x+6\to m_f=3[/tex]

From the table:

[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]

[tex]m_f=m_g=3[/tex]

Answer:

1st one

Step-by-step explanation:

Answer: [tex]\dfrac{3}{10}[/tex]

Step-by-step explanation:

Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.

The factors of 15 = [tex]1,\ 3,\ 5[/tex]

Then ,the probability of obtaining a factor of 15 is given by :-

[tex]P(A)=\dfrac{3}{5}[/tex]

The probability of getting a tail :-

[tex]P(B)=\dfrac{1}{2}[/tex]

Since both the events are independent , thus

The probability of obtaining a factor of 15 and a tail is given by :-

[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]

Hence, the required probability : [tex]\dfrac{3}{10}[/tex]

Answer:

  one real root: n ≈ 2.38450287889

Step-by-step explanation:

My favorite solution method for higher-degree polynomials is to use a graphing calculator.

Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).

You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.

__

Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...

  y = (n +2.692)² + 6.591

Hence, the complex roots will be near -2.692±i√6.591.

_____

There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...

  n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889

Answer:

  C.  y = Ae^(-(x-b)²/c)

Step-by-step explanation:

A is a model of exponential growth.

B is a model of exponential decay.

D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.

The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.

The model that the graph represent is C that is y = Ae^(-(x-b)²/c).

A is an exponential growth model.

B is an exponential decay model.

D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.

The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.

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Answer:

(s-6)/r

option D

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.

Now we are also given that (r,s) is on our line which means s=c(r)+6.

We need to solve this for c to put c in terms of r and s as desired.

s=cr+6

Subtract 6 on both sides:

s-6=cr

Divide both sides by r:

(s-6)/r=c

The slope in terms of r and s is:

(s-6)/r.

Answer:

Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.

This in real becomes :

[tex]0.15\times46=6.90[/tex] dollars

But, Tess  says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20

So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of [tex]4.6+2.3=6.9[/tex] dollars which is the real amount.

Answer:

Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.

This in real becomes :

dollars

But, Tess  says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20

So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of  dollars which is the real amount.

Step-by-step explanation:

trust me

Answer:

The determinant is 15.

Step-by-step explanation:

You need to calculate the determinant of the given matrix.

1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):

[tex]\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right][/tex]

2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):

[tex]\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right][/tex]

3. Expand along the row 2: (See attached picture).

We get that the answer is 15. The determinant is 15.

Answer:

The answer is 15

Step-by-step explanation:

This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).

11x11 rectangle = 165cm^2 area.

2 circles of 2cm radius = 2*4pi = 8pi = 25.13

165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)

Answer:

139.9

Step-by-step explanation:

First find the area of the circles.

A = pi*r^2

So pi*2^2

2^2 = 4

4*pi = 12.57

Then divide 12.57 by 2 because its only half a circle.

12.57/2 = 6.285

Then multiply 6.285 by 4 since there are 4 half circles.

6.285*4 = 25.14

Now find the area of the square.

A = lw

A= 15*11

A = 165

Now subtract 165 and 25.14.

165 - 25.14 = 139.86

Now round 139.86 to the nearest tenth

So 139.9

Answer:

6

Step-by-step explanation:

The 8 is the leading coefficient, the -7 is the linear term, and the 6 is the constant.

Answer:

the constant term is 6.

Second option is correct.

Step-by-step explanation:

The quadratic function is [tex]f(x)=8x^2-7x+6[/tex]

The general form of a quadratic function is [tex]y=ax^2+bx+c[/tex]

Here c is the constant term and a can't be zero.

On comparing the given equation with the general form, we get

a = 8

b = -7

c = 6

Therefore, the constant term is 6.

Second option is correct.

[tex](5ab)^{\tfrac{3}{2}}=\sqrt{(5ab)^3}=\sqrt{125a^2b^3}[/tex]

Answer:

True

Step-by-step explanation:

The binomial distribution that has a probability of success equal to .20, would be left skewed for sample size of 20.

The given statement "The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20" is false.

The statement is incorrect. The binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would not necessarily be left-skewed. The shape of the binomial distribution depends on the values of the probability of success and the sample size.

In general, for a binomial distribution with a small probability of success (such as 0.20) and a large sample size (such as 20), the distribution tends to approximate a normal distribution. As the sample size increases, the binomial distribution becomes more symmetric and bell-shaped.

Therefore, it is not accurate to claim that the binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would be left-skewed.

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Answer:

Step-by-step explanation:

Income less expenses

Answer:

15

Step-by-step explanation:

i got it right pls mark brainliest

Answer:

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = Bh . . . . . where B is the base area and h is the height

The volume of a pyramid or cone is given by ...

  V = (1/3)Bh . . . . . where B is the base area and h is the height

The area of a square of side length s is ...

  A = s²

The area of a circle of radius r is ...

  A = πr²

___

Using these formulas, the volumes of these objects are ...

  cylinder: (9π in²)(10 in) = 90π in³

  square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³

  cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid

Answer:

12.5

Step-by-step explanation:

How many households is 463 households

Answer:

C

Step-by-step explanation:

Just got it right.

Answer:

[tex]P (X = 140) = 0[/tex]

Step-by-step explanation:

We know that the heron wingspan follow a normal distribution with an mean of 125 cm.

In this case we seek to find

[tex]P (X = 140)[/tex]

If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.

Then by definition of continuous random variable we have to:

[tex]P (X = a) = 0[/tex] where a is a constant.

That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.

Finally we can conclude that

[tex]P (X = 140) = 0[/tex]

To find the proportion of herons with a wingspan of exactly 140cm, calculate the z-score using the given mean and standard deviation. Use the z-score to find the area under the normal curve and determine the proportion. The resulting area is approximately 0.8944 or 89.44%.

To find the proportion of herons with a wingspan of exactly 140cm, we need to calculate the z-score for 140cm using the formula:

z = (x - μ) / σ

where x is the value being analyzed, μ is the mean, and σ is the standard deviation. Plugging in the values:

z = (140 - 125) / 12 = 1.25

To find the proportion, we can use the z-table or calculator to find the area under the normal curve to the left of z = 1.25. The resulting area is approximately 0.8944 or 89.44%.

Answer:

downtown workers

Step-by-step explanation:

The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.

Thus, option "downtown workers" is correct.

The population of the survey would be the city residents.

The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.

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Answer:

[tex]f: (0,1) \to \mathbb{R}[/tex]

[tex]f(x) = \sin(1/x)[/tex]

Step-by-step explanation:

f is continuous because is the composition of two continuous functions:

[tex]g(x) = \sin(x)[/tex] (it is continuous in the real numbers)

[tex]h(x) = 1/x[/tex] (it is continuous in the domain (0,1))

It is bounded because [tex]-1 \leq \sin(\theta) \leq 1[/tex]

And it is not uniformly continuous because we can take [tex]\varepsilon = 1[/tex] in the definition. Let [tex] \delta > 0[/tex] we will prove that there exist a pair [tex]x,y\in \mathbb{R}[/tex] such that [tex]|x-y|< \delta[/tex] and [tex]|f(x) -f(y)|> \varepsilon = 1[/tex].

Now, by the archimedean property we know that there exists a natural number N such that

[tex] \frac{1}{N} < 2\pi \delta[/tex]

[tex]\Rightarrow \frac{1}{2\pi N} < \delta[/tex].

Let's take [tex]x = \frac{1}{2\pi N + \pi/2}[/tex] and [tex]y = \frac{1}{2\pi N + 3\pi/2}[/tex]. We can see that

[tex]|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}<\frac{1}{2\pi N} <\delta[/tex]

And also:

[tex]|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon[/tex]

And we conclude the proof.

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

f(x) = -3 sin (x-pi) +2

Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value

sin has a maximum of 1

f (min) = -3(1) +2 = -1

g(x) has a minimum at x =3  

g(minimum) = -1

h(x) = (x+7)^2 -1

        The smallest a squared value can be is zero

     = 0 -1

h(min) =-1

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

Just did this :)

Answer:

its answer is -x^3+x^2+3x-1

Step-by-step explanation:

f(x) +g(x)

= 8-4x-x^3+x^2+7x-9

= -x^3+x^2+3x-1

Answer:

The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Step-by-step explanation:

The given functions are

[tex]f(x)=8-4x-x^3[/tex]

[tex]g(x)=x^2+7x-9[/tex]

We have to find the value of f(x)+g(x).

[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]

[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]

On combining like terms we get

[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]

On simplification we get

[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]

Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Answer:

The dimensions of enclosed area are 200 and 400/3 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 800 feet of fencing

- We will but it around a rectangular field

- We will divided the field into 2 identical smaller rectangular plots

 by placing a fence parallel to one of the field's shorter sides

- Assume that the long side of the rectangular field is a and the

 shorter side is b

∵ The length of the fence is the perimeter of the field

∵ We will fence 2 longer sides and 3 shorter sides

∴ 2a + 3b = 800

- Lets find b in terms of a

∵ 2a + 3b = 800 ⇒ subtract 2a from both sides

∴ 3b = 800 - 2a ⇒ divide both sides by 3

∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)

- Lets find the area of the field

∵ The area of the rectangle = length × width

∴ A = a × b

∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]

- To find the dimensions of maximum area differentiate the area with

  respect to a and equate it by 0

∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]

∵ [tex]\frac{dA}{da}=0[/tex]

∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides

∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3

∴ 800 = 4a ⇒ divide both sides by 4

∴ 200 = a

- Substitute the value of a in equation (1)

∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]

* The dimensions of enclosed area are 200 and 400/3 feet

Answer:

Is there supposed to be a photo

Step-by-step explanation: