49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Group of answer choices

Answer:

D, 49.42

Step-by-step explanation:

ΔVFT=180-90-43=47

formula

a/sin A = b/sin B/ = c/sin C

So,

FV/sin90=53/sin47

FV=72.4684

FT=√(72.4684)^2-(53)^2

FT=49.4234

Ans:D

The length FT in the given right-angle triangle is 49.42.

So option D is the correct answer.

We are given a right-angle triangle and to find the length of any side we can use Pythagoras theorem or trigonometric identities.

In the triangle, we see that TV = 53 and ∠ FVT = 43°

We will find the length FT by using Pythagoras theorem or trigonometric identities.

What are trigonometric functions?

There are some commonly used trigonometric identities:

SinФ = Perpendicular / hypotenuse

Cos Ф = Base / hypotenuse

Tan Ф =  Perpendicular / Base

We will use Tan Ф =  Perpendicular / Base to find the length FT.

Because we need to use trigonometric identities that have TV and FT.

Tan Ф = FT / TV

Tan 43° = FT / 53

FT = Tan 43° x 53

FT = 0.932515 X 53

FT = 49.42

Thus we got FT = 49.42 using the tan function.

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This question is incomplete, here is the complete question:

Specifications for a part for a DVD player state that the part should weigh between 25.2 and 26.2 ounces. The process that produces the parts has a mean of 25.7 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A

a) What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places.

b) Within what values will 95.44 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)

Answer:

a) What percentage of parts will not meet the weight specs = 4.56%

b) values within which 95.44 percent of sample means of this process falls are;

UCL = 25.88 ounces

LCL = 25.52 ounces

Step-by-step explanation:

Given that;

Mean u = 25.7 ounces

Std deviation = 0.25 ounces

a)

Z-score (Upper) = (X- u) / s = (26.2 - 25.7) / 0.25 = 2

Z-score (Lower) = ( 25.2-25.7 ) / 0.25 = -2

using the T - table

For Z = 2.0

the area in the tail of the curve to the right of the mean (upper) = 0.4772

therefore;

Number of defective = 0.5000 - 0.4772 = 0.0228

These are errors on one side of normal distribution.

To get the total error, we say

Total error = 2 × 0.0228

Total error = 0.0456 ≈ 4.56% ( 2 decimal place )

b)

given that;

n = 8,

standard deviation = 0.25 ounce

Standard deviation of X = Std deviation / √n

= 0.25 /√8 = 0.088

Now for 95.44% of confidence interval, Z = 2

UCL = Mean + Z × Standard deviation of X

= 25.7 + 2 × 0.088

= 25.88 ounces

LCL = Mean - Z × Standard deviation of X

= 25.7 - 2 × 0.088

= 25.52 ounces

Answer:

x = -70

Step-by-step explanation:

x/10 = -7

Multiply each side by 10

x/10*10 = -7*10

x = -70

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▹ Answer

80

▹ Step-by-Step Explanation

(2²)³ + (2³)² ÷ 4

Rewrite:

2⁶ + 2⁶ ÷ 2²

Divide:

2⁶ + 2⁴

Factor:

(2² + 1) * 2⁴

Evaluate:

(4 + 1) * 2⁴

Calculate:

5 * 16

= 80

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

3.25 US Quarts

Step-by-step explanation:

Step-by-step explanation:

The inequality shows by line is

i) 1<=x<=6

OR,

x is an positive integer.

Answer:

The two numbers are 1 and 2.

Step-by-step explanation:

Let the two numbers be a and b.

One number is twice another, so let's let b=2a.

Their reciprocals are 3/2. Thus:

[tex]\frac{1}{a}+\frac{1}{b} =\frac{3}{2}[/tex]

Substitute and solve for a:

[tex]\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\[/tex]

Combine the fractions by forming a common denominator by multiplying the left term by 2:

[tex]\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}[/tex]

Combine and cross-multiply:

[tex]3/2a=3/2\\6a=6\\a=1\\b=2(1)=2[/tex]

Thus, the two numbers are 1 and 2.

Answer:

D. 800,000

Step-by-step explanation:

It is D because you find the hundred thousand place which is the 8, the you go to the number next door which is 3, if the 3 is 5 or greater the 8 will become a 9 or if it is not then it will stay the same. And everything to the left stays the same, everything to the right turns into zeros.

Answer:

x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

6x - 10 = 4(x+3)

6x - 10 = 4*x + 4*3

6x - 10 = 4x + 12

6x - 4x = 12 + 10

2x = 22

x = 22/2

x = 11

check:

6*11 - 10 = 4(11+3)

66 - 10 = 4*14 = 56

Answer:

Step-by-step explanation:

2x2=4 4x1=4

Answer:

7units²

Step-by-step explanation:

I cut the shape into smaller shapes, found the area of each smaller shape, then added those areas together to find the total area for the whole shape :)

Answer:

which side are you looking for, SOHCAHTOA

OPPOSITE

tan50.34=x÷180

x=180×1.2062(tan50.34)

x=2117.116

Answer:

[tex]Cost = 338500[/tex]

Step-by-step explanation:

Given

Startup = $116000

Cost per item = $25

Equation: 25q + 116000

Required

Determine the cost of producing 8900 items

The question implies that q = 8900

To solve further, we have to substitute 8900 for q in the given equation

Equation = 25q + 116000 becomes

[tex]Cost = 25 * 8900 + 116000[/tex]

[tex]Cost = 222500 + 116000[/tex]

[tex]Cost = 338500[/tex]

Hence, the cost of producing 8900 items is $338500

Answer =  A.  Aella

Step-by-step explanation: Add 60, 25, and 95 degrees because that will equal 180 which is what the triangle equals.

Answer:

16.50 gallons per minute

Step-by-step explanation:

Because this is a proportional function, we can set up the equation y = kx, where k is the constant of proportionality. By plugging in one point (and this point can be any point provided by the table), we can use the equality k = y/x to find the proportionality constant. If we plug in the information at 1 minute, we get 16.50/1 = 16.5

The constant of proportionality is same for all the rows that is 16.50 gallons per minute.

WE can calculate the Constant of proportionality as;

Constant of proportionality = no of gallons of water per 1 minute.

we have 16.50 gallons of water per 1 minute and 24.75 gallons of water in 1.5 minutes.

In 1 minute, we will have,

24.75 ÷ 1.5 = 16.50 gallons

Similarly,

33 gallons in 2 minutes. In 1 minute, we will have,

33 ÷ 2 = 16.50 gallons.

We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, that is 16.50.

Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as:

w = 16.50t

Hence, the constant of proportionality, 16.50, is same for all rows.

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Answer: ABCD is a parallelogram.

Step-by-step explanation:

First we plot these point on a graph as given in attachment.

From the attachment we can observe that AD || BC || x-axis .

also, AB ||CD, that will make ABCD a parallelogram ,  but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".

Mid point of AC= [tex](\dfrac{-5+4}{2},\dfrac{2+5}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Mid point of BD= [tex](\dfrac{-3+2}{2},\dfrac{5+2}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]

Thus, Mid point of AC=Mid point of BD

i.e. diagonals bisect each other.

That means ABCD is a parallelogram.

Answer: ABCD is a parallelogram.

Step-by-step explanation:

First, we plot these points on a graph as given in the attachment. From the attachment, we can observe that AD || BC || x-axis. Also, AB ||CD, which will make ABCD a parallelogram, but to confirm, we check the parallelogram property "diagonals bisect each other," i.e., "Midpoint of both diagonals is equal."

The midpoint of AC=. The midpoint of BD=. Thus, the Midpoint of AC=Mid point of BD diagonals bisects each other. That means ABCD is a parallelogram.

Answer:

  a) position 22

  b) 26

  c) shuffle 25

Step-by-step explanation:

Assuming the shuffling occurs so that the bottom card of the top half of the deck (card 26) becomes the bottom card (card 52), while the top card of the bottom half (card 27) becomes the top card (card 1), the sequence of card 1 positions with successive shuffles is ...

  {2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1}

That is, after the first shuffle, card 1 is at position 2; after the second shuffle, it is at position 4; and so on.

(a) Hence the position of card 1 after the 7th shuffle is 22.

__

(b) The top card is in position 52 after 26 shuffles.

__

(c) The top card is in position 26 after 25 shuffles; the bottom card is in position 27 after 25 shuffles. That is when they first touch. (They touch again after 51 shuffles.)

Answer:

y=1/3x

Step-by-step explanation:

change in y/ change in x

2-0/6-0= 2/6=1/3

since its a positive slope, it’s 1/3

Answer:

E. [tex]y=\frac{1}{3}x[/tex]

Step-by-step explanation:

Take the two points shown:

[tex](0,0)(6,2)[/tex]

Use these to make an equation in slope-intercept form:

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

m is the slope and b is the y-intercept (where x is equal to 0).

Use the slope formula:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert coordinate points:

[tex](0_{x1},0_{y1})\\\\(6_{x2},2_{y2})\\\\\frac{2-0}{6-0}[/tex]

Simplify:

[tex]\frac{2-0}{6-0} =\frac{2}{6} =\frac{1}{3}[/tex]

The slope is [tex]\frac{1}{3}[/tex]. Insert this into the equation:

[tex]y=\frac{1}{3}x+b[/tex]

Now find the y-intercept. Take one of the coordinate points and insert:

[tex](6_{x},2_{y})\\\\2=\frac{1}{3}(6)+b[/tex]

Solve for b. Simplify multiplication:

[tex]\frac{1}{3}*\frac{6}{1}=\frac{6}{3}=2\\\\ 2=2+b[/tex]

Use reverse operations to isolate the variable:

[tex]2-2=2-2+b\\\\0=b[/tex]

The y-intercept is equal to 0. Insert this into the equation:

[tex]y=\frac{1}{3}x+0[/tex]

or

[tex]y=\frac{1}{3}x[/tex]

:Done

Answer:

x = 11 or 3

Step-by-step explanation:

f(x) = (1/2)(x- 7)² – 8​

to find the zeros, we equate f(x) = 0

f(x) = 0

(1/2)(x- 7)² – 8​ = 0      (add 8 to both sides)

(1/2)(x- 7)² = 8     (multiply both sides by 2)

(x- 7)² = (8)(2)

(x- 7)² = 16

x-7 = ±√16

x-7 = ±4

hence,

x - 7 = 4

x = 4 + 7

x = 11

or

x - 7 = -4

x = -4 +7

x = 3

Answer:

x = 11 or 3

Step-by-step explanation:

I confirmed the answer in grandpoint.

Answer:

9-x^2

Step-by-step explanation:

The difference of means subtracting. the first number is 9 and the second is x^2, so you get 9-x^2

Answer:

  C)  Reflection about the origin

Step-by-step explanation:

DE points to the right and slightly down. D'E' points to the left and slightly up. The segments are parallel, not perpendicular, so represent a rotation of 180°, not 90°. If the figure were subject only to translation, these segments would point in the same direction.

The transformation is a reflection about the origin (C). (This is equivalent to a rotation of 180°.)

Answer:

42.7 mm

Step-by-step explanation:

To the nearest tenth of a mm, 42.67 mm would be 42.7 mm.

After estimate of this value rounded to the nearest tenth of a millimeter,

⇒ 42.67 ≈ 42.7

We have to given that,

According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters.

Hence, After estimate of this value rounded to the nearest tenth of a millimeter, we get;

⇒ 42.67

As, 7 is grater than 5, so we can add 1 to the tenth place.

⇒ 42.67 ≈ 42.7

Therefore, After estimate of this value rounded to the nearest tenth of a millimeter,

⇒ 42.67 ≈ 42.7

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Answer:

C

Step-by-step explanation:

The set of data will only become more narrow when the standard deviation is decreased, so D isn't correct. The data isn't going to shift directions unless there's a translation, so A and B are both out. That leaves us with C. The opposite of answer D.

Answer:

C. It produces a wider range of probable values

Step-by-step explanation:

The set of data that we have cannot shift in directions unless there is a translation, so therefore, A and B are both out. The set of data would become smaller when the standard deviation is decreases so therefore, D isn't correct. So, that leaves us with only one answer.

C. It produces a wider range of probably values.

Answer:

52 units^2

Step-by-step explanation:

It's unclear what the leg lengths and the width are.  I must assume that the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units.  You were given an illustration for this problem and should have shared it or described the trapezoid in words.  Please do this if the answer given below does not agree with any of your answer choices.

If the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units, then the area is

      12 units + 14 units

A = ---------------------------- * 4 units = 52 units^2

                    2

Answer:

Step-by-step explanation:

Since the base of the pyramid PABCD is a rectangle, the shape in question is a rectangular based pyramid. Volume of a rectangular based pyramid is expressed as V = 1/3 * Base Area * Height of the pyramid.

Given a rectangle ABCD with AB = 8 and BC = 4, the area of the rectangle will be equivalent to the base area of the pyramid.

Base Area = Length * Breadth

Base Area = AB * BC

Base Area = 8*4 = 32

If [tex]\overline{PA}\perp \overline{AD}\ and \ \overline{PA}\perp \overline{AB}[/tex], and PB = 17, then the height of the pyramid is PB = 17.

Volume of the pyramid = 1/3 * 32 * 17

Volume of the pyramid = 1/3 * 544

Volume of the rectangular based pyramid = 181.33

Answer:

Step-by-step explanation:

Given

2^x [(x+1)³ -1] = 2^x - (x+1)³ + 1

Lep p = 2^x, and q = (x+1)³ - 1

Then the original equation becomes

pq = p - q

p - q - pq = 0

p(1 - q) - q = 0

p = q/(1 - q)

2^x = [(x+1)³ - 1]/[-(x+1)³]

2^x = [1 - (x+1)³]/[(x+1)³]

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

Answer:

Below

Step-by-step explanation:

First let's find the equation of the doted line.

Notice that the line is crossing these points:

● (0,1)

● (1,2)

The equation of the line has the following form:

● y = ax+c

C is the y-intercept wich is given by the output of 0.

Notice that the output of 0 is 1.

● y = ax+1

● a = rise / run = (2-1)/(1-0) = 1

So y = x + 1

■■■■■■■■■■■■■■■■■■■■■■■■■■

Notice that the line divide the plan into 2 areas.

● y > x+1 => x+1-y < 0

● y < x+1 => x+1 -y > 0

To khwo wich one that represent the shaded area take a point and replace x and y by its coordinates

● (-1,2)

● -1+1-2 = 0-2 = -2

It is a negative value so the inequality is

● y > x+1

Answer:

The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.

Answer:

The frequency distribution does not appear to be normal.

Step-by-step explanation:

The data provided is as follows:

S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}

It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.

The frequency distribution table is as follows:

Class Interval  Count

 0.00 - 0.19            21

 0.20 - 0.39             6

 0.40 - 0.59             2

 0.60 - 0.79             0

 0.80 - 0.99             0

  1.00 - 1 . 19             0

  1.20 - 1. 39             1

The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.

Thus, the frequency distribution does not appear to be normal.

Answer:  The next term is -12.

Step-by-step explanation:

16,9,2,-5  

Looking at these numbers to go from 16 to 9 you will add -7 or subtract 7 . The same way you subtract 7 from 9 to get 2  and subtract 7 from 2 to get -5.

So to determine the next term subtract 7 from -7   or add -7.

-5 - 7 = -12

0r  -5 + -7 = -12  

[tex] &#128075 [/tex] Hello ! ☺️

Step-by-step explanation:

•Find the next term of the sequence.

Let us find the interval between two successive terms:

16 - 9= 7

-7 is therefore the common différence of this sequence. (d)

Find the next term :

-5 + (-7)= -12

[tex]\boxed{\color{gold}{N = -12}} [/tex]

[tex]<marquee direction="left" scrollamount="2" height="100" width="150">&#x1F498;Mynea04</marquee>[/tex]

Answer:

500

Step-by-step explanation: