There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c
where T represents the temperature in degrees Fahrenheit and
c represents the number of times the cricket chirps in one minute. What is the meaning of the c-value when T=65?

A) The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
B) The expected temperature in degrees Fahrenheit if the cricket has chirped 0 times per minute.
C)The expected temperature in degrees Fahrenheit if the cricket has chirped 65 times per minute.
D) The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F

The following properties of equality are used to solve the given equation:

division property, multiplication property, addition property, Subtraction Property, distributive property

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Equation:

2((2/5) x+8)=4(14-(1/5)x)

1. The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal .

2((2/5) x+8)/2=4(14-(1/5)x)/2

(2/5) x+8=2(14-(1/5)x)

2. multiplying a quantity by the sum of two or more terms is the same as adding together the products of the original quantity and each term

(2/5) x+8=28-(2/5) x

3. when the same quantity is added to both sides of an equation, it produces an equivalent equation

(2/5) x +(2/5) x+8=(2/5) x+28-(2/5) x = 28

4. The Subtraction Property of Equality states that an equal value subtracted or removed from two equal items will result in a new equal amount

(4x)/5+8-8=28-8=20

5. The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

*5(4x)/5= 20*5

4x=100

6.  The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal .

4x/4=100/4

x=25

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The standard form equation for a line passing through the point (6, -1) and parallel to the line denoted by 8x + 3y = 15 is 8x + 3y = 45.

The standard form equation

ax + by = c

Here a, b, and c are constants and therefore use the slope-intercept form.

y = mx + c .... (1)

where m is the slope, b = y-intercept

8x + 3y = 15

3y = -8x + 15

y = -8 / 3 x + 5

Slope (m) = - 8 / 3

It passes through a line that has points (6, -1)

Let's find b by putting the value of m = - 8/3, x = 6, and y = -1 in equation (1).

-1 = - 8 / 3 (6) + c

-1 = -48 / 3 + c

-1  = -16 + c

c = -1 + 16

c = 15

Therefore,

y = - 8 / 3 x + 15

8 / 3 x  + y = 15

=> 8x + 3y = 45

8x + 3y = 45 is the standard form of the line that passes through (6,-1) and is parallel to the line represented by 8x + 3y= 15.

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The events A and B are independent events

The sections on the dice are given as

S = {1, 2, 3, 4, 5, 6}

These sections mean that:

n(3) = 1 and n(4) = 1

Recall that:

A be the event that the number rolled is a 3 or a 4.

So, we have

P(A) = P(3) + P(4)

This gives

P(A) = 1/6 + 1/6 = 1/3

Also, we have

Coin = {Head, Tail}

Where

B be the event that a head is flipped.

This means that

P(B) = 1/2

The occurrence of an event in event A does not hinder the occurrence of another occurrence in event B

This means that the events are independent event

i.e. they do not depend on each other

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Answer:

1. Corresponding angles

2. Alternate Interior angles

Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk. which is the correct answer would be an option (C).

Distance is defined as the product of speed and time.

The function shows Mr. Baker's distance (d), in meters, from the check-in counter while he has been standing on the moving sidewalk for s seconds. d = 2s + 20.

Here He travels at a speed of two meters per second while standing on the moving sidewalk, and he walked 20 meters to get there.

Thus, Mr. Baker moves 2 meters per second while standing on the moving sidewalk, and he walked 20 meters to get to the moving sidewalk.

Hence, the correct answer would be option (C).

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The Solution to the trigonometry expression is 1/2

Trigonometry expression

A trigonometric expression is one that contains a trigonometric function with a variable. It can also be in terms of the sine and cosine functions.

cos75°cos15° + sin75°sin15°

Using the relation  Cos (θ) = Sin( 90° - θ)

Sin (θ) = cos (90° - θ)

Sin ( 2θ) = 2 sin θ cos θ

So:

cos75° cos15° + sin75° sin15° = Sin 15° cos 15°  +  Sin 15°  cos 15°

Sin 15° = 1/2

Therefore, the expression cos75°cos15° + sin75°sin15° = 1/2.

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The perimeter of the right triangle would be 66.6 cm.

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 is a right triangle with side 19 centimeters and side 20 centimeters.

Using the Pythagoras theorem, we get -

h² = (19 x 19) + (20 x 20)

h² =  761

h = 27.6 cm

The perimeter will be -

P = [h] + [p] + [b]

P = 27.6 + 19 + 20

P = 66.6 centimeters

Therefore, the perimeter of the right triangle would be 66.6 cm.

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Answer:

[tex]\frac{14}{9}[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

To prove both triangle similar ratio of their sides must be equal

AC/GI = BC/HI

Therefore last option is correct .

The difference between congruence and similarity can be examined mathematically. These two words are defined by  shape, proportion, and angle.

Congruent shapes have the same dimensions and overlap when stacked. Two congruent objects have the same size and shape, but different orientations and placements in  space. This doesn't change the fact that they are the same as they have the same physical properties, angles and dimensions.

Similarity means similar but not identical. A shape can be mathematically equivalent in its base form as follows: B. Circles, but different sizes.

to prove both triangle similar ratio of their sides must be equal

AC/GI = BC/HI

Therefore last option is correct .

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The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of the cuboid = length × height × width.

As per the given cylinder,

The radius of the base of the cylinder = 3

Height = 7

Base area = π(radius)²

Base area = π(3)²

Base area = 9π

The volume of the cylinder = Base area × Height

Volume = 9π × 7 = 198.

Hence "The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198".

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The confidence is 66%. We are 66% confident that the mean score for the students is in the given interval

Given: standard deviation(s) = 16, number of sample(n) = 110, margin of error(E) = 1.471

E = z x s /√n where z is z-score

1.47 = (z x 16)/√110

z = (1.471x√110)/16 = 0.96

Use the z-score to check the value of p in the table for Area under normal curve (image attached) to determine:

p(-0.96 < z< -0.96)

The value shows that about 66.3% of area under the curve is between -0.96 and 0.96

Therefore, confidence level is 66%. So we are 66% confident that the mean score for all students taking the exam is in the interval

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[tex]\cfrac{3}{5}\times\cfrac{3}{5}\times\cfrac{3}{5}\implies \cfrac{3\times 3\times 3}{5\times 5\times 5}\implies \cfrac{27}{125}[/tex]

Answer:27/125

Step-by-step explanation:

Multiply the tops 3x3x3=27

Multiply the bottoms 5x5x5=125

Answer:

Applying the product rule of exponents, (a²c)³ = .

What is the Product Rule of Exponents?

When multiplying two numbers with the same base, their powers/exponents would be added.

For example, .

Given:

(a²c)³

Therefore:

(a²c)³ = (a²c)(a²c)(a²c)

(a²c)³ =

(a²c)³ =

Therefore, applying the product rule of exponents, (a²c)³ = .

Step-by-step explanation:

The sum of the given expression is (8z³ + 4z² - 8).

Given, an expression

(-2z² + 4) + (8z³ + 6z² - 12)

Now, we have to find the sum of the given expression,

On simplifying, we get

= (-2z² + 4)+(8z³ + 6z² - 12)

=  -2z² + 4 + 8z³ + 6z² - 12

= 8z³ - 2z² + 6z² - 12 + 4

= 8z³ + 4z² - 8

So, (8z³ + 4z² - 8) is the sum of the given expression.

Hence, the sum of the given expression is (8z³ + 4z² - 8).

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Answer:

A, B

Step-by-step explanation:

East and west are opposite directions along the same line. If one is positive, the other one is negative.

Up and down are also opposite directions on the same line.

Answer: A, B

Answer:

16

Step-by-step explanation:

Let the number be x.

[tex]\frac{3}{4}x = 12[/tex]

∴ x = 12 ÷ [tex]\frac{3}{4}[/tex]

     = 16

Step-by-step explanation:

1/6, 5,26/5,5.277,5.28

The Area of the parallelogram is 27.57 cm² .

If the length of the parallelogram with sides a and b , and the angle between the sides a and b is θ , then

Area of Parallelogram = a × b × Sin(θ)

In the question ,

it is given that

the length of the parallelogram is 4cm and 7 cm , and the angle between is 100° .

By substituting the values in the formula for Area of parallelogram

we get ,

Area = 4 × 7 × Sin(100°)

= 4 × 7 × 0.9848              ....because Sin(100°) = 0.9848  

= 27.57 cm²

Therefore , The Area of the parallelogram is 27.57 cm² .

The given question is incomplete , the complete question is

If the length of the sides of parallelogram is 4 cm and 7 cm and the angle between them is 100° , Work out the Area of the parallelogram ? Give your answer to 2 significant figures. ​

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The y-intercept of a function is the value of y when x = 0, which is represented as the value of b in the slope-intercept equation y = mx + b. b is the y-intercept.

If an equation of graph that represents a function is given in slope-intercept form as y = mx + b, the value of b in the function is the value of the y-intercept of the y-intercept.

The y-intercept of the function is the same as the value of y when the value of x is 0, or the point where the line of the function intercepts the y-axis on a given graph that represents the function.

For example, if we are given the equation of a graph that represents a function as, y = 3x + 4, the y-intercept of the function would be 4.

In summary, the y-intercept of the function is the value of b in the equation of the function that is expressed as y = mx + b in slope-intercept form.

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Answer:

option D and E

Step-by-step explanation:

a) What is the slope of the line parallel to it?

Parallel lines will never intersect, meaning they have equivalent slopes, so the answer to this part is -(6/5).

b) What is the slope of the line perpendicular to it?

Perpendicular lines will intersect, creating a 90-degree angle, meaning all values in the graphs have been flipped. Thus, the slope of any perpendicular line is the negative reciprocal of the given slope (-1/x). The negative reciprocal of -(6/5) is 5/6, so that is the answer.

The probability that exactly two dog bite victims will arrive is 0.099.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

Based on the information, the probability that exactly two dog bite victims will arrive will be:

P(x = 2) = e^(-06) (0.6)2 / 2!

= (0.549) × (0.36) / 2

= 0.099

The probability is 0.099.

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Answer:

100 + 40

Step-by-step explanation:

to get from 100 to 140 you have to add 40 to 100

The x-intercept of the line is x = -2,and the y-intercept of the line is y = -6.

From the question, we are to determine the x-intercept and y-intercept of the line.

The x-intercept of a line is the point where y = 0

and

The y-intercept of a line is the point where x = 0

The equation for the line is

6x + 2y = -12

To determine the x-intercept, substitute y = 0 in the equation

6x + 2y = -12

6x + 2(0) = -12

6x + 0 = -12

6x = -12

Divide both sides by 6

6x/6 = -12/6

x = -2

Hence, the x-intercept is x = -2

To determine the y-intercept, substitute x = 0 in the equation

6x + 2y = -12

6(0) + 2y = -12

0 + 2y = -12

2y = -12

Divide both sides by 2

2y/2 = -12/2

y = -6

Hence, the y-intercept is y = -6

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Answer:

8

Step-by-step explanation:

2 rows with 4 oranges each -> 2*4 = 8

Answer: I gotcha. This is the RIGHT ANSWER!

Answer: The mass of the nitrous oxide gas produced is 0.011 kg.

Step-by-step explanation:

To calculate the mass of the gas, we use the formula:

We are given:

Specific density of the gas =

Mass of the gas = ? kg

Volume of the gas = (Conversion Factor:  )

Putting values in above equation, we get:

Therefore , the mass of the nitrous oxide gas produced is 0.011 kg.

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The system of equations that could be used to find the cost of postcards and stamps include:

p = 4s

2p + 4s =3

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let postcard = p

Let stamps = s

Two postcards and four stamps cost $3. This will be illustrated as:

2p + 4s = 3

A postcard cost 4 times as much as a stamp. This will be:

p = 4s

The equations can be used to find the costs.

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