The measures of heights (in inches) of a class of students are shown. 60, 60,54, 62, 62, 57,58, 65, 54,67, 63,57, 62, 54, 72, 66, 54, 69, 55, 61 Find the mean, median, mode, range, and standard deviation of the heights.b. A new student who is 7 feet tall joins your class. How would you expect this student’s height to affect the measures in part (a)?

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Let's solve, using Trigonometry ~

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \frac{54}{72} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \frac{3}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 37 \degree[/tex]

Answer:

[tex]\displaystyle 36,9[/tex]

Step-by-step explanation:

[tex]\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]

OR

[tex]\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

Answer:

150ft^2

Step-by-step explanation:

FINDING THE LENGTHS

50 = x + 5 + x + x + 5 + x

50 = 4x + 10

50 - 10 = 4x

40 = 4x

40/4 = x

10ft = x

AMOUNT OF FLOORING

area = l x b

= (10 + 5) x 10

= 15 x 10

= 150ft^2

The BAC of the female is an illustration of proportion

BAC is calculated using:

BAC = Alcohol consumed/(Body Weight * R)

The weight is given as:

Body weight = 140 lb

Convert to kg

Body weight = 63.5 kg

For female

R = 0.55

So, we have:

BAC = Alcohol/(63.5 * 0.55)

BAC = Alcohol/34.925

BAC = 0.029Alcohol

The weight or volume of the alcohol consumed is given.

So, we represent it with w.

BAC = 0.029w

Hence, the BAC after consuming the three drinks is 0.029w

We have:

BAC1 = 0.029w

Time (t) = 3 hours

The BAC after 3 hours is

BAC = BAC1 * (t - 0.015)

So, we have:

BAC = 0.029w * (3 - 0.015)

Evaluate the product

BAC = 0.087w

Hence, the BAC three hours after consuming the drinks is 0.087 w

Read more about BAC at:

https://brainly.com/question/1781657

Answer:

$1,350

Step-by-step explanation:

Simple interest formula

I = Prt

where:

Given:

⇒ Total interest earned = 1000 × 0.1 × 5 = $500

If you have to pay 30% income tax on the interest earned annually, then you will keep 70% of your earned interest.

⇒ 70% of $500 = 0.7 × $500 = $350

Account balance = principal + interest earned after tax

                             = $1,000 + $350

                             = $1,350

Answer:

2(x - 2)

Step-by-step explanation:

- 4(x + 1) + 6x ← distribute parenthesis by - 4

= - 4x - 4 + 6x ← collect like terms

= 2x - 4 ← factor out 2 from each term

= 2(x - 2)

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

Let's simplify this expression.

The first step is to use the distributive property, which states:-

[tex]\bigstar{\boxed{a(b+c)}[/tex]

Simplify:-

[tex]\bigstar{\boxed{-4(x+1)}[/tex]

[tex]\longmapsto\sf{-4x-4}[/tex]

Add 6x:-

[tex]\longmapsto\sf{-4x+6x-4}[/tex]

Combine Like Terms:-

[tex]\longmapsto\sf{2x-4}[/tex]

Now, we should write our answer in factored form, so we factor 2 out:-

[tex]\longmapsto\sf{2(x-2)}[/tex]

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

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

The probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

For two events A and B, by chain rule, we have:

[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]

where P(A|B) is probability of occurrence of A given that B already occurred.

For this case, the table given is:

Entries                          4-wheel drive        No 4-wheel drive        Total

Third Row Seats                  18                                12                        30

No Third Row Seats             7                                28                        35

Total                                     25                               40                        65

Let we take

A = event that a randomly selected car has no-4 wheel drive

B = event that a randomly selected car has third row seats

The total ways a car can be selected = 65 = n(S)

Total ways A can happen = n(A) = 40 (from the table).

Similarly, n(B) = 30

P(A) = n(A)/n(S) = 40/65

P(B) = n(B)/n(S) = 30/65

P(A∩B) = n(A∩B)/n(S) = 12/65

As by chain rule, we have:

P(A∩B) = P(A)P(B|A) = P(B)P(A|B)

We need P( A randomly selected car has three seats given that the selected car is with no 4-wheel drive)

which is symbolically P( B | A)

Thus, we use: P(A∩B) = P(A)P(B|A)

or

[tex]12/65 = (30/65)(P(B|A))\\\dfrac{12/65}{30/65} = P(B|A)\\\\P(B|A) = \dfrac{12}{30} = \dfrac{2}{5} = 0.4[/tex]

Thus, the probability that a randomly selected car with no 4-wheel drive has third-row seats is given by: Option B: 0.4

Learn more about probability here:

brainly.com/question/1210781

Answer:

b.  0.4

Step-by-step explanation:

took the test

The value of n will the terminal side fall on the y-axis at n=3

The terminal side of an angle fall along the positive portion of the y-axis,

If it can written in the form of [tex](90^0)a[/tex]

Where a = positive odd integer,

We hyave given the given angle is,

[tex](870n)^0,[/tex]

The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side

Now for n=3

[tex](870(3))^0=2610^0[/tex]

The  angle will be 2610°

Its terminal side fall along the positive portion of the y-axis,

[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )

Therefore  for n = 3,  the terminal side of the angle (870n)° falls along the positive portion of the y-axis,

For n = 4,

Our angle will be 3480°

Its terminal side fall along the positive portion of the y-axis,

[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]

Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis

Next is for n = 5,

Our angle will be 4350°

Its terminal side fall along the positive portion of the y-axis,

[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]

Thus, for n = 5,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,

For n = 6,

Our angle will be 5220°

Its terminal side fall along the positive portion of the y-axis,

[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]

Thus, for n = 6,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.

Therefore,the value of n will the terminal side fall on the y-axis at n=3.

To learn more about the terminal side visit:

https://brainly.com/question/24680641

Answer:

a

Step-by-step explanation:

x=3 on edge

[tex]\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}[/tex]

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because all the orher ones are wrong and not correct.

Answer:

between 222 and 223 days

Step-by-step explanation:

This relation includes the point (0, 2).

A proportional relation must include the point (0, 0).

This is not proportional, but it may be linear.

Points: (0, 2), (2, 20)

y = mx + b

20 = (20 - 2)/(2 - 0) × 2 + b

20 = 18/2 × 2 + b

b = 2

y = 18x + 2

When 4000 people know, y = 4000.

y = 18x + 2

4000 = 18x + 2

3998 = 18x

x = 3998/18

x = 222.111...

Answer: between 222 and 223 days

[tex]5^{7/3} = 42.75[/tex] (approximately)

using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem

so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75

Answer:

C

Step-by-step explanation:

Remark

The way to solve the problem is to figure out how many cubic feet would be present if the window was not there and then calculate the volume of the window and subtract it. That is the general method used to obtain the answer to the question you have asked.

Volume Original Shape

Each side of the figure is one side of a square.

So the volume of the square face is 6 by 6 or 6*6 = 36 (no window)

The window is 2*2 which is 4.

The volume of the original shape is 36 - 4 = 32

Volume new shape

Each side of the figure is 12 by 12 = 144    With no window

The size of the window is 4 by 4 =   16   With the window (Subtract)

The size of the modified figure is    128

Answer and discussion

The question is a bit ambiguous. I think the question means that the wall has gone from 32 to 128 cubic feet.  So you need Subtract to find the difference..

Answer: 128 - 32 = 96 which is C.

Answer:

Step-by-step explanation:

[tex]y=ab^x\\x=0,y=4\\4=ab^0\\4=a(1)\\a=4\\y=4b^x\\x=2,y=256\\256=4b^2\\b^2=\frac{256}{4} =64\\b=\pm8\\y=4(8)^x\\or\\y=4(-8)^x[/tex]

Step-by-step explanation:

Consider this polynomial,

[tex]8 {x}^{2} + 2x - 3[/tex]

First, I do the AC memethod. To find my two numbers,

That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C

And that will also add to 2, my middle term.

So using that

[tex]8 \times - 3 = - 24[/tex]

So let find factors of-24:

Factors can be positve or negative

The factors of 24 are : 1,2,3,4,6 8,12,24.

So which one of these add up to 2.

[tex]6 + ( - 4) = 2[/tex]

and

[tex]6 \times - 4 = - 24[/tex]

So six and negative four is our numbers.

Now, let set up our binomials

Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.

Disclaimer: The placement of these numbers doesn't matter.

So we have

[tex]8 {x}^{2} + 6x - 4x - 3[/tex]

Step 2: Group the first two terms and last two terms

[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]

Factors the first group by finding the GCF.

x is the greatest common variable, and 2 is the gcf so we have

[tex]2x(4x + 3) + ( - 4x - 3)[/tex]

Next, factor the next group by -1.

[tex]2x(4x + 3) - 1(4x + 3)[/tex]

Combine the outside factors.

[tex](2x - 1)(4x + 3)[/tex]

So those are the factors.

Answer:

y=-2x-1

Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.

Answer:

There are 33 nuts in the bag, to 21 dried fruits.

Total number of dried fruits is 21, while the total number of nuts is 33.

Step-by-step explanation:

Answer:

12%, 0.12, 5/17, or as a ratio: 5:17

Step-by-step explanation:

To find the percentage:

Take the 40 students who prefer cheese and divide it by 340:

0.11764705882 rounded would be 0.12.

Convert 0.12 into 12% of students prefer cheese pizza.

To find the decimal, to the same exact thing I did up there, but, don't turn it into a percent, just leave it as 0.12.

To find the fraction, turn it into:

40/340

Then simplify it:

5/17 prefer cheese pizza.

For ratio, do the same as fraction, but, instead of the slash mark, turn it into a colon like this: 5:17.

:)

[11]

Equation: 180° - 75°

Measure: 105°

      A straight line has an angle measurement of 180°. Since we have GFB, 75°, we can find EFB this way.

[12]

Equation: 90° - 40°

Measure: 50°

      The little box in the angle shows that it is equal to 90°. Since they give us HGB, 40°, we can solve for EFB using this information.

Answer:

x = -3

Step-by-step explanation:

A vertical line has an equation of the form

x = a

where a is the x-coordinate of every point on the line.

Every point on the line has x-coordinate -3, so the equation is

x = -3

Answer:

B 24 million years old

Step-by-step explanation:

i did this quiz a long time ago tho so it might be B or D

Answer:

64 cm^3

Step-by-step explanation:

V = lwh

V = 4 x 4 x 4

V = 64 cm^3

Hope this helps!

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]

[tex] \mathsf \pink{v = {4}^{3} }[/tex]

[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]

Answer: 1.56

Step-by-step explanation:

Add all the cost together, the subtract the ten dollars.

2.18 + 2.28+ 3.98 = 8.44

10.00 - 8.44 = 1.56

Answer:

(a) 8000 times 5 times 2 = 800

Answer:

234 mm^2

Step-by-step explanation:

These questions are tricky but to make them easier, try to break down the shape into smaller regular shapes and work them out.

I would divide this shape into 2 rectangles and one triangle

Area of small bottom rectangle: 4 x 11 = 44mm^2

Area of rectangle in the middle: 14 x 8 = 112mm^2

Area of triangle: 12 x 13/2 = 78mm^2

Add all the areas together = 44+112+78 = 234mm^2

Step-by-step explanation:

area of triangles

1/2*9*8= 36

area of.rectangle

8*9= 72

36+72=108 square inches

Answer:

[tex]4[/tex]

Step-by-step explanation:

[tex]\ln e^4= 4\ln e = 4 \log_e e = 4 \times 1 = 4[/tex]

Answer:

B

Step-by-step explanation:

No these triangles are not congruent.

Left triangle

Shortest side = 6 cm

Longest side = 13 cm

3rd side = unknown but < 13

Right triangle

Shortest side = 6 cm

Longest side = unknown but > 13

3rd side = 13 cm

Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.

We do not know if any of the angles are congruent.  If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.

Answer:

Scale factor = 3

Step-by-step explanation:

A - B = 1-3

3 - 1 = 2

A' - B' = 3-9

9 - 3 = 6

6 / 2 = 3