choose the correct order

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.

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 :)

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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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?

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

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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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...

------------

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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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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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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Answer:

As addition: -13+(-7)=-20

Answer:

34

Step-by-step explanation:

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

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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The distance around the triangle is equivalent to 13x/12.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are the sides of triangle as x/2, x/3, x/4

The distance around the triangle is equivalent to perimeter of triangle. We can write perimeter as -

P = x/2 + x/3 + x/4

P = (6x + 4x + 3x)/12

P = 13x/12

Therefore, the distance around the triangle is equivalent to 13x/12.

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Final answer: 3[tex]b^{2}[/tex] + 8b + 2

12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)

An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.

Given by the question.

3b (b+4) - 4 (b-5)

= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.

= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.

Final answer: 3[tex]b^{2}[/tex]+ 8b + 20

12(3y + 6)

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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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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:

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.

The figure that is a dilation of figure E is the figure F

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The graph represents the given parameter

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point E must pass through the same point on the shape

From the figure, the line passes through the same point on figure E and F

Hence, figure F is a dilation of figure

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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.

Answer:

x^3 + 64 + 11x - 20bxy - 80by

(if I am wrong, apologies)

Answer:

x^2+4x-5

Step-by-step explanation:

x^3+8x^2+11x-20/x+4=x^2+4x-5

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:

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

Step-by-step explanation:

The domain is the list of possible inputs

Answer:

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

Given is a parallelogram

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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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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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:

3.87

Step-by-step explanation:

b =

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