The measurement of the height of 600 students of a college is normally distributed with a mean of
175 centimeters and a standard deviation of 5 centimeters.


What percent of students are between 170 centimeters and 180 centimeters in height?


16

34

68

81.5

Answer:

Two solutions were found :

6x^2-x1=0

x = -1/3 = -0.333

x = 1/2 = 0.500

The solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

6x² - x - 1 = 0

Here a = 6, b = -1, c = -1

[tex]\rm x = \dfrac{-(-1) \pm\sqrt{(-1)^2-4(6)(-1)}}{2(6)}[/tex]

[tex]\rm x = \dfrac{1 \pm\sqrt{25}}{12}[/tex]

[tex]\rm x = \dfrac{1 \pm 5}{12}[/tex]

x = 6/12 = 1/2 or

x = -4/12 = -1/3

Thus, the solution of the equation 6x² - x - 1 = 0 are x = 1/2 and x = -1/3 after using the quadratic formula.

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Answer:

Option A

Step-by-step explanation:

In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars.

So total number of cars = 6 + 7 + 3

                                       = 16

Now a train is to be made by 9 cars, out of 16 cars.

So number of ways the train can be made up will be =[tex]^{n}P_{r}[/tex]

where n = 16 and r = 9

so number of ways =[tex]^{16}P_{9}[/tex]

Option A is the answer.

Considering the definition of permutation, you use 16P9 to find the number of ways the train could be made up. (Option A).

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

[tex]mPn=\frac{m!}{(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

In a train yard there are 6 flat cars, 7 box-cars and 3 livestock cars. So total number of cars is 6 + 7 + 3= 16.

A train is made up of 9 cars, out of 16 cars.

To obtain the total of ways in which 16 elements can be placed in 9 positions, you use the permutation 16P9.

Finally, you use 16P9 to find the number of ways the train could be made up. (Option A).

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Answer:

The interest rate was 15%

Step-by-step explanation:

The simple interest formula is the easiest and most straightforward to use since it doesn't involve using logs or natual logs or Euler's number.  It is

I = Prt

Filling in using our info gives us 300 = 1000(r)(2)

and 300 = 2000r

Divide both sides by 2000 and you get r = .15.  Multiply by 100 to get the percentage.

Answer:

BF = 30

Step-by-step explanation:

Since B and F are midpoints then BF is parallel to CE and half it's size

BF = 0.5 × CE = 0.5 × 60 = 30

Answer:

10 pounds

Step-by-step explanation:

You forgot the inequality sing, but since Antoine can't spend more than $18.20, I am positive that the sign is [tex]\leq[/tex] (Antony can spend $18.20 or less than $18.20).

Therefore, our inequality is: [tex]1.30x+5.20\leq 18.20[/tex]

where [tex]x[/tex] is the pounds of oranges

Let's solve step-by-step to find how many pounds of oranges he can buy

Step 1. Subtract 5.20 fro both sides of the inequality

[tex]1.30x+5.20-5.20\leq 18.20-5.20[/tex]

[tex]1.30x\leq 13[/tex]

Step 2. Divide both sides of the inequality by 1.30

[tex]\frac{1.30x}{1.30} \leq \frac{13}{1.30}[/tex]

[tex]x\leq 10[/tex]

We can conclude that Antony can buy 10 pounds of oranges.

Answer:

52 ft

Step-by-step explanation:

For each chord, the product of segment lengths is a constant. We can find that constant as the product of the segment lengths of the bisected chord:

(24 ft)·(24 ft) = 576 ft^2

Then the missing segment length (DX) of the diameter chord is ...

DX·(36 ft) = 576 ft^2

DX = (576 ft^2)/(36 ft) = 16 ft

So, the total length of the diameter chord is ...

DX +XL = 16 ft + 36 ft

DL = 52 ft

_____

We know DL is a diameter because the perpendicular bisector of any chord intersects the center of the circle.

Answer:

[tex]\begin{array}{cccc}&\text{Prefer Pizza}&\text{Do not Prefer Pizza}&\text{Total}\\\text{Prefer Punch}&23&29&52\\\text{Do not Prefer Punch}&66&7&73\\\text{Total}&89&36&125\end{array}[/tex]

Step-by-step explanation:

There are 125 members.

89 of them preferred pizza and 23 of 89 preferred punch, so 89-23=66 preferred only pizza.

52 members preferred punch, 23 of them preferred both pizza and punch, so 52-23=29 preferred only punch.

Now,

66 members preferred only pizza,

23 members preferred both,

29 members preferred only punch,

125-66-23-29=7 members did not prefer both

The two-way table is

[tex]\begin{array}{cccc}&\text{Prefer Pizza}&\text{Do not Prefer Pizza}&\text{Total}\\\text{Prefer Punch}&23&29&52\\\text{Do not Prefer Punch}&66&7&73\\\text{Total}&89&36&125\end{array}[/tex]

Final answer:

To complete the two-way table, we calculate preferences for pizza only, punch only, both, and neither by using the given numbers. For example, 'Pizza Only' is found by subtracting those who prefer both pizza and punch from the total that prefers pizza.

Explanation:

The student's question is about completing a two-way table with the given data about food preference for an event. According to the information provided, out of 125 members surveyed, 89 preferred pizza, and out of those, 23 also preferred punch. There were 52 members in total who preferred punch. To fill in the two-way table:

Pizza and Punch: This is given directly as 23.

Pizza Only: To find this, subtract those who like both from those who like pizza, 89 - 23 = 66.

Punch Only: Subtract those who like both from the total that like punch, 52 - 23 = 29.

Neither Pizza Nor Punch: Subtract the totals of pizza lovers and punch lovers from the surveyed members, 125 - 89 - (52 - 23) = 125 - 89 - 29 = 7.

Answer: if the iguana is five feet it would be 60 inches

Answer:

Step-by-step explanation:

A parallel plane will have the same normal vector (the coefficients of x, y, z), so will differ only in the constant. Changing the constant from 9 to anything else gives the equation of a parallel plane.

A perpendicular plane will have a normal vector that is perpendicular to the normal vector of the given plane. That is, the dot-product of the normal vectors will be zero. There are an infinite number of possible solutions. One of them is ...

  5x -3y = 0

Its normal vector is <5, -3, 0> and the dot-product of that with the normal vector of the given plane is ...

  <5, -3, 0> · <3, 5, -1> = (5)(3) +(-3)(5) +(0)(-1) = 15 -15 +0 = 0

Any plane whose coefficients a, b, c satisfy 3a+5b-c = 0 will be a normal plane.

Answer:

a(n) = 3*3^(n-1).

Step-by-step explanation:

The first term of this sequence is 3.  The next one is 3 times 3, or 9; the next is 3 times 9, or 27; and so on.  So the common ratio is 3.

The formula for the nth term is thus a(n) = 3*3^(n-1).

Answer:

the perimeter is 46.6 feet

Step-by-step explanation:

The length of Chen’s office is 15.5 feet and the width is 7.8 fee

length =15.5

width = 7.8

Use the formula [tex]P = 2l + 2w[/tex]

where 'l' is the length and 'w' is the perimeter

Plug in the values of length and width in the perimeter formula

[tex]P = 2l + 2w[/tex]

[tex]P = 2(15.5) + 2(7.8)=46.6[/tex]

So the perimeter is 46.6 feet

The perimeter of the office is 46.6 feet

The office is in the shape of a rectangle

A rectangle is a 2-dimensional quadrilateral.

Characteristics of a rectangle

The perimeter of a rectangle = 2(length + width)

2length + 2width

2(15.5) + 2(7.8)

31 + 15.6 = 46.6 feet

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the equation should be 7+2x=t

x=the number if items he gets

t=total

The equation that represent the given situation should be  7+2x=t

Alex goes to a movie on Saturday for $7. While there, he pays $2 for each item he buys at the concession stand.

7+2x=t

here x be the number

And, t means the total

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Answer: the scatter plot you just sent me the answer would be 5

Answer:

b

Step-by-step explanation:

Answer:

  those angles are congruent

Step-by-step explanation:

ABCD is a rhombus. The diagonals of a rhombus are angle bisectors. The two angles that result from bisecting angle C are congruent.

Answer:

They are the same.

Step-by-step explanation:

Answer:

1) The probability of getting an even number when rolling a six-sided number cube is 0.5. Choice A

2) 80%. Choice C

Step-by-step explanation:

1)

We are required to determine the probability of getting an even number when rolling a six-sided number cube. The six-sided number cube has the following numbers written on its faces;

1, 2, 3, 4, 5, 6

The numbers; 2, 4, and 6 are even

The probability of getting an even number;

= ( number of faces with even numbers)/ (total number of faces)

= 3/6

0.5

2)

We are required to determine the probability of choosing a letter that is not a vowel after placing the letters for the word smart in a bag.

The non-vowels in the word smart are; s, m, r, and t. There are 4 non-vowels out of a total of 5 letters. The required probability is thus;

(4/5)*100 = 80%

Answer:

73

292

173

Step-by-step explanation:

x = first number

4x = second number

100 + x = third number

x + 4x + 100 + x = 538

6x + 100 = 538

6x + 100 - 100 = 538 - 100

6x = 438

6x/6 = 438/6

x = 73

Check:

73 + 4(73) + 100 + 73 = 538

73 + 292 + 173 = 538

538 = 538

Answer:

The numbers are 73, 173 and 292.

Step-by-step explanation:

If the numbers are x, y and z we have:

y = 4x

z = x + 100

x + y + z = 538

Substituting for y in the last equation:

x + 4x + z = 538

5x + z = 538.............(1)

From the second equation:

z - x = 100................(2)

Equation (1) - (2) gives:

6x = 438

x = 73

Therefore y = 4x) = 4(73) = 292

and z = x + 100 = 73 + 100 = 173.

The standard of deviation is 4.

The mean is 10

20 minutes - 10 ( the mean) = 10 minutes longer than the mean.

10 minutes longer / 4 minutes ( deviation) = 2.5 standard deviations.

2.5 on the Z-table = 0.9938

The probability of being more than 20 minutes = 1 - 0.9938 = 0.0062 (0.62%)

The answer is the third one.

The first two are easy, you can see that the radius of S is 4 and the radius of T is 5-4=1.

The point of intersection is where the two circles touch each other, and is is (4, 1), because you have to put the x value first.

The equation of the tangent line is just y=4, because it is a straight vertical line.

Answer:

All real numbers

Step-by-step explanation:

They ask us to find the domain of (fg)

f(x) = x+2

g(x) = ( 1 / x + 2 )

Multiplying these two equations, we get:

y = 1. And this equation is a straight line passing through 1 on the y-axis.

This means, the domain is all the real numbers.

Answer:

Domain is all real number except  [tex]-2[/tex]

Step-by-step explanation:

[tex]f(x)= x+2[/tex] and [tex]g(x)= \frac{1}{x+2}[/tex]

now we find fg

[tex]fg= f(x) * g(x)[/tex]

Replace f(x) and g(x)

[tex]f(x) * g(x)= (x+2)*\frac{1}{x+2}[/tex]

[tex]f(x) * g(x)=\frac{x+2}{x+2}[/tex]

We have x+2 at the top and bottom. cancel it out

So we have hole at x+2

set the denominator =0 and solve for x

[tex]x+2=0[/tex]

Subtract 2 on both sides

[tex]x=-2[/tex]

the value of x cannot be [tex]-2[/tex]

Domain is all real number except  [tex]-2[/tex]

Answer:

False

Step-by-step explanation:

SA=2πrh+2πr²

SA = 2 · (3.14) · 3.6 · 9.7 + 2 · (3.14) · 3.6²

SA = 6.28 · 34.92 + 6.28 · 12.96

SA = 219.30 + 81.39

SA = 300.69

For this case we have that by definition, the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

A: It's the radio

h: It's the height

Substituting according to the data we have:

[tex]SA = 2 \pi * 3.6 * 9.7 + 2 \pi * (3.6) ^ 2\\SA = 219.2976 + 81.3888\\SA = 300.6864 \ units ^ 2[/tex]

If we round up we have:

[tex]SA = 300.69 \ units ^ 2[/tex]

Answer:

False

Answer:

the min is 53 the max is 90 median is 65 first  quartile  is 60 and the third quartile is 82

Step-by-step explanation:

The correct answers are: Minimum: 53, First quartile: 60, Median: 65, Third quartile: 82, Maximum: 90.

To read a box plot, we look at the five-number summary: the minimum, first quartile, median, third quartile, and maximum.

The box plot shows the middle 50% of the data, which is the interquartile range (IQR). The IQR is represented by the box, with the median represented by the line inside the box.

The whiskers extend from the box to the minimum and maximum values, respectively.

In this box plot, the minimum value is 53 and the maximum value is 90. The IQR is 65 - 60 = 5, which means that the middle 50% of the data is within 5 points of the median. The median is 65, so the first quartile is 60 and the third quartile is 82.

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Step-by-step answer:

The normal probability curve is symmetrical about the mean.  

This means that for an event that is normally distributed, there is a 50% probability that it falls below the mean, and a 50% probability that it falls above.

From the given information, the mean is 20" and we need the probability that a given infant is longer than 20", namely the mean.

Therefore by the definition of the normal probability curve, there is a 50% probability that the length falls above 20".

This can be verified by referencing a normal probability table with Z=0, meaning at the mean, the probability is equal to 0.5 for Z<0, and therefore 0.5 for Z>0.

Z=(X-mean) / Standard deviation

When Z>0, X (measurement) is greater than the mean

When Z<0, X is less than the mean.

Answer:

0.5, half therefore 50%

Answer:

Option A. Ahmed wins the chess game

Step-by-step explanation:

we know that

The probability of Ahmed winning the chess games is 45%

45%=045/100=0.45

The probability of Ahmen winning the checkers games is 0.36

Compare the probability

0.45> 0.36

so

Is more likely that  Ahmed wins the chess game

Answer:

A

Step-by-step explanation:

Answer:

The answer is 4.

Step-by-step explanation:

I believe that, if I'm correct, 2 students are equal to 1%. 2 x 35 = 70. 2 x 33 = 66. 70 - 66 = 4 more students. I hope this is correct.

The total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option, fourth is correct.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

From the diagram, we can see the total 35% students preferred apples.

Total number of students = 200

The number of students who preferred apples than cherries = 200×35%

= 200(35/100)

= 2(35)

= 70

Thus, the total number of students who preferred apples than cherries are 70 if the two hundred students were surveyed about their favorite fruit option fourth is correct.

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Answer:

(x, y) = (-1, 4), (2, -1), (5, -6)

Step-by-step explanation:

You can choose any value you like for either x or y, then solve for the other value. I like to plot points with integer coefficients, so I would look for sets of those.

The nature of this equation is that it will have integer solutions with x-values spaced 3 apart and y-values spaced 5 apart. (The spacing of each corresponds to the coefficient of the other.) So, the trick is to find an x-value that gives an integer solution for y. (You will need to try at most 3 consecutive integers.)

Solving the equation for y, we get ...

y = -5/3x +7/3

Right away, we know that x=0 will not give an integer solution for y. Nor does x=1. The third consecutive integer that is easy to try is x = -1, so ...

y = (-5/3)(-1) +7/3 = (5+7)/3 = 4 . . . . an integer value for y

Our first point is then (x, y) = (-1, 4).

Since the slope is negative, we know that increasing x will decrease y. Thus we can simply add (3, -5) to any point to get another point on the line.

Two more points on the line are ...

(-1, 4) +(3, -5) = (2, -1)

(2, -1) +(3, -5) = (5, -6)

Three integer-valued points on this line are (-1, 4), (2, -1), (5, -6).

the answer for this question is twelve

Answer:

Step-by-step explanation:

For 2 triangles to be similar, they have to have congruent angle measures with corresponding sides that exist in proportion to one another.  #14 shows a triangle with 2 angle measures given.  We can find the third angle in that triangle to be 65.  The one on the right in #14 shows a triangle with 66 degrees in the position corresponding to 65 on the left.  Those are not similar (we know nothing about the side lengths so we have no choice but to work with the angles).

#15 shows 2 triangles that are "attached" by angle M in the center.  Those 2 angles meet to create vertical angles, and vertical angles are congruent, so angle HMG and angle KMJ are congruent.  If both triangles have 2 angles that are corresponding and congruent, then the third angles in both will also be guaranteed to be congruent.  So those 2 triangles are similar by AA

It A because the two mirror each other so you can simplify them to (3x−5)^2.

Answer:

(A) [tex](3x-5)(3x-5)[/tex]

Step-by-step explanation:

Perfect-square trinomials have this form:

[tex]a^2x^2 \± 2ab + b^2[/tex]

And can be expressed as a squared binomial:

[tex](ax \± b)^2[/tex]

Which is the same as: [tex](ax+b)(ax+b)[/tex] or  [tex](ax-b)(ax-b)[/tex]

You can observe that [tex](3x-5)(3x-5)[/tex] (Shown in the option A) matches with the form [tex](ax-b)(ax-b)[/tex], therefore, it will result in a perfect square trinomimal.

You can verify this by applyin Distributive property. Then:

[tex](3x-5)(3x-5)=\\=3^2x^2+(3x)(-5)+(3x)(-5)+5^2\\=9x^2-15x-15x+25\\=9x^2-30x+25[/tex]

The result is a perfect square trinomial.

Answer:

The simplest form is 2(3x - 7)/x(x³ + 4)

Step-by-step explanation:

* Lets revise how can divide fraction by fraction

- To simplify (a/b)/(c/d), change it to (a/b) ÷ (c/d)

∵ a/b ÷ c/d

- To solve it change the division sign to multiplication sign and

 reciprocal the fraction after the sign

∴ a/b × d/c = ad/bc

* Now lets solve the problem

∵ [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{2}}{2}+\frac{2}{x}}[/tex]

- Lets take the denominator and simplify by make it a single

 fraction, let the denominator of it 2x and change

 the numerator

∴ [tex]\frac{x^{2}}{2}+\frac{2}{x}=\frac{x(x^{2})+2(2)}{(2)(x)}=\frac{x^{3}+4}{2x}[/tex]

∴ The fraction = [tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}[/tex]

* Now lets change it by (up ÷ down)

∴ [tex]\frac{3x-7}{x^{2}}[/tex] ÷ [tex]\frac{x^{3}+4}{2x}[/tex]

- Change the division sign to multiplication sign and reciprocal

 the fraction after the sign

∴ [tex]\frac{3x-7}{x^{2}}[/tex] × [tex]\frac{2x}{x^{3}+4}[/tex]

∴ [tex]\frac{(2x)(3x-7)}{(x^{2})(x^{3}+4)}[/tex]

- We can simplify x up with x down

∴ [tex]\frac{2(3x-7)}{x(x^{3}+4)}[/tex]

* The simplest form is 2(3x - 7)/x(x³ + 4)