In a class of 25 students, 13 have a brother and 9 have a sister. There are 7 students who do not have any siblings. What is the probability that a student chosen randomly from the class has a brother and a sister?

Answer:

g(x) = 5|(x - 2) - 2| - 2

Step-by-step explanation:

To shift 5 units right :

⇒ f(x) = 5|(x - 2) - 2| - 7

⇒ Applied rule : a units right → f(x) = (x - a)

To shift 5 units up :

⇒ g(x) = 5|(x - 2) - 2| - 7 + 5

⇒ g(x) = 5|(x - 2) - 2| - 2

Answer:

[tex]g(x)=5|x-4|-2[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

Parent function:

[tex]f(x)=5|x-2|-7[/tex]

Translate 2 units right:

[tex]\begin{aligned}\implies f(x-2)& =5|x-2-2|-7\\ & =5|x-4|-7 \end{aligned}[/tex]

Then translate 5 units up:

[tex]\begin{aligned}\implies f(x-2)+5& =5|x-4|-7+5\\ & =5|x-4|-2 \end{aligned}[/tex]

Therefore:

[tex]\implies g(x)=5|x-4|-2[/tex]

Answer:

618 391 .87

Step-by-step explanation:

5 years 6 months = 22 quarters

8% = .08      .08/4 = .02 interest per period

400 000 ( 1 + .02)^22 = 618 391.87

Answer:

the answer is 27

Step-by-step explanation:

because 45 divided by 5 equals 9

and 9 times 3 equals 27

Step-by-step explanation:

Consider the LHS, after the 5th step, consider the RHS

[tex]2 \csc(2x) = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \frac{1}{ \sin(2x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex]2 \times \frac{1}{2 \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \frac{1}{ \sin(x) \cos(x) } = \csc {}^{2} (x) \tan(x) [/tex]

[tex] \csc(x) \sec(x) = \csc {}^{2} (x) \tan(x) [/tex]

Consider the RHS

[tex] \csc(x) \sec(x) =( 1 + \cot {}^{2} (x) ( \tan(x)) [/tex]

[tex] \csc(x) \sec(x) = \tan(x) + \cot(x) [/tex]

[tex] \csc(x) \sec(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } [/tex]

[tex] \csc(x) \sec(x) = \frac{1}{ \sin(x) \cos(x) } [/tex]

[tex] \csc(x) \sec(x) = \csc(x) \sec(x) [/tex]

Answer:

We need to find 74% of 84 (that's the amount that was sold// If you would have been asked for the amount left, it would be (100%-74%), but here it's easier since it's already given to us)

Now, let's write the percentage as a fraction

74/100 of 84

**Trick, for percentages, anytime you see a "of" replace it with a multiplication symbol

74/100 x 84

Now, it's just a simple multiplication

(74x84)/100

*You can use a calculator and find your answer

It would give you 62.16 and you will need to round it to a whole number, so 62 gallons

*If you can't use a calculator, simplify the fraction as much as you can and try to approximate

Step-by-step explanation:

~62

Answer:

b = 40

Step-by-step explanation:

Solve system of equations.

1) w = y

2) c + b = 90

3) y + c = 180

Since we want to solve for b, second equation would be a good starting point.

c + b = 90

b = 90 - c

But what is c?

Let's make c the subject in 3rd equation.

y + c = 180

c = 180 - y

Insert c back in second equation.

b = 90 - c

b = 90 - (180 - y)

b = 90 - 180 + y

b = -90 + y

All we need now is y. Notice that in the first equation w equals y and w is 130°, which means y is also 130°. Substitute again.

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40

---

This is how it looks like if you solve it in one go (same procedure as above but in one place).

c + b = 90

b = 90 - c

b = 90 - (180 - y)

b = -90 + y

b = -90 + w

b = -90 + 130

b = 40

Answer:

x = 2

Answer is explained in image itself.

Answer:

y = 4 * sec x - 1

Step-by-step explanation:

From looking at the graph we can safely determine it's either CSC x or SEC x.

It SEC x because at the origin of it is exactly the same. Now we determine whether it has a vertical/horizontal stretch/shrink and translation shift.

Seeing it is a vertical stretch by 4 and translation 1 down.

I am not sure how to explain it in the more correct way. I have graphed it just to confirm if it is similar to your graph.

Answer:

A. 9.9%

Step-by-step explanation:

[tex] {e}^{14r} = 4[/tex]

[tex] ln(4) = 14r[/tex]

[tex]r = \frac{ ln(4) }{14} = .099 = 9.9\%[/tex]

Answer:

c=-9x^2-15x

Step-by-step explanation:

Answer:

c = 6.25

Step-by-step explanation:

For this to occur, the discriminant of the quadratic formula must = 0

b^2 - 4ac = 0

15^2 - 4(9)(c) = 0

36c = 225

c = 6.25

Answer:

12n + 16

Step-by-step explanation:

2 (6n + 8)

= (2*6n) + (2*8) [distributive property]

= 12n + 16

Hope it helps ⚜

Answer:

12n + 16

Step-by-step explanation:

Distributive Property

Distributing the terms

The measure of the unknown angle in the full circle is calculated as: 310 degrees.

The angle measure of a full circle equals 360 degrees.

The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.

The unknown angle = 360 - 50 = 310 degrees.

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Answer:

So our unknown width is X and the unknown length is X + 3.  We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:

2 X + 2 (X+3) = 24

Now solve for X

2 X + 2 X + 6 = 24

4 X + 6 = 24

4 X = 18

X = 4.5 - this is the width

X + 3 = 4.5 + 3 = 7.5 - this is the length

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

If the lines are parallel, then this means that by the corresponding angles theorem, the two angles marked in the image are congruent.

If we consider the right triangle, then by the exterior angle theorem, [tex]4x+90=11x-8 \longrightarrow x=14[/tex].

So, if [tex]x=14[/tex], then the indicated angle measures [tex]56^{\circ}[/tex], and since vertical angles are congruent, [tex]9y+2=56 \longrightarrow \boxed{y=6}[/tex]

Answer:

60 miles per hour.

Step-by-step explanation:

speed = distance / time

= 750 / 12.5

= 60 miles per hour.

Answer:

By multiplying both side with the inverse of the coefficient of x

Step-by-step explanation:

coefficient of x = -6/4

inverse of coeefficient =-4/6.

multiply both sides.

x = 12(-4/6) = -8

Answer:

Bias compare results implement treatments

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.5 x 4.5 x 4.5 = 30.375

30.375  ÷ 3 = 10.125

10.125= volume of the triangle

3 x 4.5 x 4.5 = 60.75

60.75 = volume of rectangle

60.75 + 10.125 = 70.875

70.875 = total volume

Answer:

y = -3x - 3

Step-by-step explanation:

The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis

Step-by-step explanation:

we can easily count this, as the diagonal lines are squares truly in half. so, 2 such cut squares are in total 1 full square.

there is one central rectangle of 4×6 squares = 24.

then in the upper left corner there is a small 2×2 square = 4.

and then we have in the bottom left 2 and the bottom right also 2 small triangles (4 in total) with each having 1 full square and 2 half-squares (2 squares in total) as area.

so, 4×2 = 8 squares.

so, the whole area is

24 + 4 + 8 = 36

The angle of elevation is = 70° and the distance the airplane travelled in the air is = 17,557ft

tan x° = opposite/adjacent

where opposite = 16,500 feet

adjacent = 6,000 ft

tan x° = 16,500 / 6,000

tan x° = 2.75

X = arctan ( 2.75)

X = 70°

C² = a² + b²

C² = 16,500² + 6,000²

C² = 272250000 + 36000000

C² = 308250000

C= √308250000

C= 17,557ft

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Answer:

9.

Step-by-step explanation:

1) the condition 'One x-intercept of y = x2 – 6x + c is 3' means, that x=3 and y=0;

2) it is possible to substitute the values x=3 and y=0 into the given equation and to calculate 'c':

0=9-18+c; ⇒ c=9.

The percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.

In a density curve,

Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,

t=30-16

t=14 min

Thus, the percentage of the time will Oliver get a written warning is,

p=(14/30)*100

p=46.7 %

Thus, the percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

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Answer:

46.7%

Step-by-step explanation:

Answer: 70

Step-by-step explanation:

By the corresponding angles theorem, [tex]4x-50=2x+30 \longrightarrow x=40[/tex]

This means that [tex]2x+30=110[/tex].

Now, if we notice the linear pair, this means that [tex]y=\boxed{70}[/tex]

Answer:

640; 581 R 90; 90

Step-by-step explanation:

you can round 110 to 100

64000/100 is simply 640

then you do the real math

the quotient is 581 r 90

this means the remainder is 90

Answer:

x²-8x-84

Using quadratic Formular -b±√b²-4ac/2a

--8±/8²-4×1×-84 /2×1

8±/64+336/2

8±/400/2

8±20/2

8+20/2, 8-20/2

28/2, -12/2

14,-6

Answer: A. No; the graph fails the vertical line test.

The vertical line test is a tool used to determine if we have a function. If we can draw a single straight vertical line through more than one point on the red curve, then the graph is said to have failed the vertical line test. Consequently, this leads to the relation not being a function.

For this circle graph, we can draw a vertical line through more than one point, which is why we don't have a function here.

Put another way, there are inputs (x) that produce more than one output (y), so that's why we don't have a function.

By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.

As planes ABCD and BCLK are perpendicular to each other, the triangles AKL and AKC are right angled. The required angles can be found by using the following trigonometric relationships:

[tex]\angle AKL = 90^{\circ}[/tex] (As line segments AK and KL are perpendicular to each other)

[tex]\angle AKC = \tan^{-1} \left(\frac{AC}{KC} \right) = \tan^{-1} \left(\frac{\sqrt{2}\cdot a}{\sqrt{5} \cdot a} \right) = \tan^{-1} \sqrt{\frac{2}{5} }[/tex] (as line segments AC and KC are perpendicular to each other)

[tex]\angle AKC \approx 32.312^{\circ}[/tex]

By concepts of trigonometry and of perpendicularity, the angles AKL and AKC from respective right triangles have measures of 90° and 32.3°, respectively.

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