an instructor gives a course grade of b to students who have total score on exams and homeworks between 800 and 900, where the maximum possible is 1000. if the total scores have approximately a normal distribution with mean 830 and standard deviation 50, about what proportion of the students receive a b?

The fewest possible number of green marbles in the bag is 5.

As per the stated question.

Since there is a 35% possibility of obtaining a red, the same percentage must apply to getting a white.

35+35=70%

You have a 100% probability of selecting a marble,

70+30=100

The probability that you will select a blue or green stone must thus be 30%.

And if there are B blue marbles, then there will be 5 green marbles.

B+5B=30%

6B=30%

Blue=5%

Green = 30-5=25%

Thus, the ratio becomes.

Red: White: Green : blue

35  : 35     :       25:    5

Dive each by 5.

7    : 7      :      5   :   1

Thus, the fewest possible number of green marbles in the bag is 5.

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The complete question is-

A bag contains red marbles, white marbles, green marbles, and blue marbles. There are an equal number of red marbles and white marbles, and five times as many green marbles as blue marbles. There is a 35% chance of selecting a red marble first. What is the fewest possible number of green marbles in the bag?

The total length of the sari Divya make is 6 yards, so option A is correct.

Four sides, four corners, and four right angles (90°) make up the enclosed 2-D shape known as a rectangle. A rectangle has opposite sides that are parallel and equal. A rectangle has length and width because it is a two-dimensional form. The length of a rectangle is its longer side; its breadth is its shorter side.

Given:

The length of saris Divya can make = 6 yards,

As the graph is showing,  to make a sari Divya required 6 yards of fabric,

Therefore, the total length of the sari Divya make is 6 yards.

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0.001828 (option b) is the probability that the hand contains 4 jacks .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Number of ways to pick the four jacks = 4C4

Number of ways to pick the other 8 cards from 48= 48C8

Number of ways to pick a hand of 12 from the full deck = 52C12

P(4 J's and 8 others)= [4C4*48C8]/52C12 = 377348994/2.06379...x10^11

=0.001828...

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This is the same as the probability of picking 8 cards that are not

jacks in a hand of 12 cards or 48C8/52C12.

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Step-by-step explanation:

1. in a parallelogram the opposite angles are equal.

so,

3x - 7 = x + 73

and

angle DAB = angle DCB = z - 3

3x - 7 = x + 73

2x - 7 = 73

2x = 80

x = 40

angle ADC = angle ABC = x + 73 = 40 + 73 = 113°

to get to z we need also to remember, as a quadrilateral shape the sum of all inner angles of a parallelogram is 360°.

so,

2×113 + 2×(z - 3) = 360

226 + 2z - 6 = 360

220 + 2z = 360

2z = 140

z = 70

angle DAB = angle DCB = z - 3 = 70 - 3 = 67°

Answer:

Step-by-step explanation:

By definition of a parallelogram, we know that the opposite angles are equal.

Thus, x+73=3x-7.

We can further use algebra and subtract by 3x and 73 on both sides.

We now have -2x=-80.

If we divide both sides by -2, then we get x=40.

We can plug x=40 back into 3x-7 and x+73, and we get 113 for both angles, which of course makes sense because they should be equal.

By definition of a parallelogram, we know that the angles of a parallelogram add up to 360, and that angle DAB = angle BCD = z-3.

This means that 113+113+z-3+z-3=360.

Combining like terms, we get 220+2z=360.

We can use algebra again, and subtract both sides by 220, getting 2z=140.

Dividing both sides by 2, we get z=70.

Because angle DAB=z-3, and z=70, we can plug in 70 for z, producing the result of angle DAB=67.

No, to construct a confidence interval, the population should be is approximately normal.

The information about distribution of population is important in order to find out the sampling distribution. When we want to construct confidence interval, the accuracy of results depend on three conditions.

1. The data needs to be randomly selected.

2. The sampling distribution needs to be normally distributed

3. The observations must be independent.

So one of the conditions is to ensure that the population is normally distributed.

We know from the central limit theorem, the sampling distribution is approximately normal as long as the expected number of successes and failures are equal or greater than 10

np ≥ 10

n(1 - p) ≥ 10

When the population follows normal distribution then a small number of samples will be adequate, on the other hand, if the population is skewed then we need a greater sample size to ensure normal sampling distribution.  

Therefore, the population is approximately normal before constructing a confidence interval.

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Answer:

The parent graph has been dilated by a scale factor of 100 and has been moved to the right by 5 units

Step-by-step explanation:

The change made to f(x) = 1/x to f(x) = 100/x is a dilation by a scale factor of 100(the function has been multiplied by 100) .

The transformation of function f(x) = 100/x to f(x) = 100/x-5 is moving o the right 5 units (whenever a constant, let's call it "c", is being subtracted from the x when graphing, it means the graph has moved "c" units to the right, and vice versa--if "c" was added to x, then the graph would be moved "c" units to the left.).

TL;DR: f(x-c) means c units to the right, f(x+c) means c units to the left. f(x)*c means a dilation of c units.

If sara takes two random sweets. The probability that the two sweets will not be the same is :111/190.

Probability of getting two of each sweet:

P( Liquorice) = (12/20)×(11/19)

P (Liquorice) =132/380

P (mints) =(5/20)×(4/19)

P (mints)  =20/380

P (Humbugs) =(3/20)×(2/19)

P (Humbugs) =6/380

Probability that two sweets will be the same

P(same) =132/380+20/380+6/380

P(same) =158/380

Hence,

Probability that two sweets will not be the same

P(not same) = 1- (158/380)

P(not same) =380 -158 /380

P(not same) = 222 /380

P(not same) =111 /190

Therefore the probability is 111/190.

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Answer:

Step-by-step explanation:

Equation are true:

C.

(3⁴)·(3⁵) = 3⁽⁴⁺⁵⁾ = 3⁹

D.

[tex]( 8^6 = \frac{1}{8^{-6}} )[/tex]

Answer:

C and D

Step-by-step explanation:

Steps for C:

Step 1: Combine exponent terms on left side
[tex]4+5=9[/tex]

Leave the base the same.

[tex]3^9=3^9[/tex]

[tex]True[/tex]

Steps for D:

Step 1: Simplify left side

[tex]\frac{1}{8^{-6} }=\frac{1/1}{262144} =262144[/tex]

Step 2: Simplify right side

[tex]8^6=262144[/tex]

[tex]262144=262144[/tex]

[tex]True[/tex]

Hope this helps :)

Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36

Two systems of equations are equivalent if they have the same solution(s)

In a simpler term, two equations are equivalent if they have the same solution.

Therefore, let's simplify the equation to find the equivalent solutions.

[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]

let's open the brackets of the right side of the equation.

[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]

[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]

[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]

Therefore, let's cross multiply

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36

Therefore, the equivalent equation are as follows:

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Answer:

34

Step-by-step explanation:

Absolute value means the distance from 0. So the absolute value of 34 is just 34.

The expressions for the length, width, and height are 18 - 2x, 12 - 2x, and x while the volume function is V = (12 - 2x)(18 - 2x)x

From the question, we have the following parameters:

Dimension of sheet = 8 inches by 12 inches

Also from the question, we understand that:

He cuts equal squares from each corner.

The cut-out length from the sheet would represent the height of the box

Represent this cut-out length with x

So, we have

Height = x

The width and the length are then represented as

Width = Initial width - 2x

Length = Initial length - 2x

So, we have

Width = 12 - 2x

Length = 18 - 2x

The volume of a box is the product of its dimensions

In this case, we have

Width = 12 - 2x

Length = 18 - 2x

Height = x

So, we have

Volume = Width * Length * Height

Substitute the known values in the above equation So, we have the following equation

V = (12 - 2x)(18 - 2x)x

So, the volume function is V = (12 - 2x)(18 - 2x)x

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The equation can be given as X+20 = 60

Wyatt needs to save $40 to buy the new game.

What is an equation?

An equation is an expression which has an equality symbol in it.

We are given that, Wyatt is saving up money for a new game. It costs $60,

including tax.

He has already saved $20. At least how much more money, X, does he need to save

Hence the equation can be given as

X + 20 = 60

On solving the equation X = 40

Hence Wyatt needs to save $40 to buy the new game

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Answer:

range

Step-by-step explanation:

The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

Given,

The width of bolts of fabric is normally distributed with mean 951 mm (millimeters) and standard deviation 10 mm.

Z = X - 951/10 ≈ N(0.1)

P(942 ≤ X ≤ 959)

P(942 - 951/10 ≤ X - 951/10 ≤ 959- 951/10)

P( -0.9 ≤ Z ≤ 0.8)

P(Z ≤ 0.8) - P(Z ≤ -0.9)

∅(0.8) - (1 - ∅(0.9))

∅(0.8) + ∅(0.9) - 1

0.788 + 0.859 - 1

0.647

The probability that a randomly chosen bolt has a width between 942 and 959 mm is 0.647.

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option D, y=x^2-2x+1 , 2x-y=2 represents system of equations .

Given:

points (1,0) and (3,4)

line equation is y - y1 = m(x-x1)

y - 0 = 4-0/3-1(x - 1)

y = 2(x-1)

y = 2x - 2

2x - y =2.

The vertex of the given upward parabola is in the first quadrant so the coefficient of [tex]x^{2}[/tex]  must have positive values.

so y = [tex]x^{2} -2x+1[/tex]

Therefore option D y=x^2-2x+1 , 2x-y=2 is correct.

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Answer:

A and C

Step-by-step explanation:

For every x value, there should be at most 1 y value.

B and D violate that constraint.

Answer:

a) y = 0

Step-by-step explanation:

Given equation,

→ 3y - 7(y + 5) = y - 35

Now the value of y will be,

→ 3y - 7(y + 5) = y - 35

→ 3y - 7y - 35 = y - 35

→ -4y - y = -35 + 35

→ -5y = 0

→ y = 0/-5

→ [ y = 0 ]

Hence, the value of y is 0.

The equation of the relation x and y is y = 4x  - 4

The relation follows a linear pattern. Therefore, the relationship is linear.

A linear relationship can be represented in different form such as slope intercept form and point slope form.

Let's represent the equation in slope intercept form.

y = mx + b

where

Therefore,

m = 4 - 0 / 2 - 1

m = 4 / 1

m = 4

Therefore, let's find the y-intercept using (1, 0)

y = 4x + b

0 = 4(1) + b

b = -4

Therefore, the equation is y = 4x - 4

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Answer:

Step-by-step explanation:

This problem is solved using the Pythagorean theorem  (a2+b2=c2).  In this formula a and b are the legs of the right triangle while c is the hypotenuse.

Using the labels of our triangle we have:

o2+a2=h2

\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}

h2=100ft2+289ft2

h=389ft2−−−−−√

So with this information you can see that the correct answer is 19.7ft

The quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

The given graph is a parabola where the mouth is open upwards. So from here we can clearly say that the coefficient of [tex]x^{2}[/tex] will be positive.

The vertex of the parabola  is given as (2 , -5) in the graph.

So let us put value of x in the inequations given to us.

first option is

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

y ≤ 2*[tex]2^{2}[/tex] - 8*2 + 3

y ≤ 8 - 16 + 3

y ≤ -5

Therefore the quadratic inequality that will represent the parabola will be

y ≤ 2[tex]x^{2}[/tex] - 8x + 3

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Answer:

see explanation

Step-by-step explanation:

m + 20 and 100 are vertically opposite angles and are congruent , then

m + 20 = 100 ( subtract 20 from both sides )

m = 80

The angles are vertically opposite angles and value of m is 80°

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given two angles which are Vertically opposite to each others,

We know Vertically opposite angles are equal to each other, so,

m + 20° = 100°

m = 100° - 20°

m = 80°

Hence, the value of m is 80°

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The solution to the system of inequalities is -6 < x [tex]\leq[/tex] -3

Inequality shows the relationship between two values in an algebraic expression that are not equal. Inequality signs can indicate that one variable of the two sides of the inequality is greater than, greater than or equal to, less than, or less than or equal to another value.

The system of linear equations,

x + 4 > -2 or -4x [tex]\geq[/tex] 12

from first inequality,

x + 4 > -2

making x stand alone,

x > -2 -4

x > -6

from second inequality,

-4x  [tex]\geq[/tex] 12

divide both sides bu -4

x [tex]\leq[/tex] 12/-4

x  [tex]\leq[/tex] -3

The combined inequality is -6 < x [tex]\leq[/tex] -3

In conclusion, -6 < x [tex]\leq[/tex] -3 is the solution for the set of inequalities.

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Answer:

Domain: {-2, 0, 3, 5}

Step-by-step explanation:

The domain is the list of possible inputs

Answer:

3.87

Step-by-step explanation:

b =

[tex] \sqrt{8 ^{2} -7 ^{2}} [/tex]

Answer:

1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)

Step-by-step explanation:

The angles congruent to <5 are:

<1 by corresponding angles.

<3 by alternate interior angles.

<7 by vertical angles.

<5 by the theorem: congruence of angles is reflexive.

Answer:

0.000065 km

Step-by-step explanation:

To get from cm to km you need to divide 6.5 by 0.000001 which equals 0.000065km

Answer:

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

Given is a parallelogram

Answer:

24,278

Step-by-step explanation: