The average adult male has a height of 70 inches, with a standard deviation of 3 inches. What percentage of adult males have a height between 65 and 75 inches?

The length of side AB after the dilation is 2 units.

Given that, ΔABC is dilated by a factor of 1/4.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.

The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.

From the given figure, AB=8 units, BC=6 units and AC=10 units.

Let the x be the length of side AB after the dilation.

Now, using scale factor formula 1/4 = x ÷ 8

⇒x=2 units

Therefore, the length of side AB after the dilation is 2 units.

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(-5 , 0) is the point we got after slope-intercept form of equation .

What exactly does slope intercept mean?

Equation from the value given table -

1)      y = 3x + 15

2)      y = 5x + 25

3)      y = 7x + 35

4)      y = 9x + 45

5)      y = 10x + 50

graph attached of all equation .

(-5 , 0) is the point .

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The measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The figure is given in the picture:

From the property of interior angles:

x + 85 = 180

x = 95 degrees

6z - 85 + 85  = 180

z = 180/6

z = 30 degrees

Thus, the measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.

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Answer:

its {A} Hope gets some of a full chocolate bar

Step-by-step explanation:

she gets 7/8 of a chocolate bar the next day she gets 6/12       7+6=13 so she gets a full chocolate bar

(a) We have 13 possibilities that a five-card hand will contain four of a kind.

(b) We have 12 possibilities that a five-card hand will contain a full house.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.

Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)

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Answer:

c the last 1

Step-by-step explanation:

bc y where the line ends on y is more than 30 and only 1 line is 5 so 35

Answer:

I think its the last one but it could also be the first

Amy can make 29 meatballs from the remaining beef.

What are mathematics operations?

Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs

We have to subtract 3/8 from 4

= 4 - 3/8

= 29/8

There are 29/8 pounds of ground beef left

Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;

= 29/8 ÷ 1/8

= 29

Hence Amy can make 29 meatballs

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The final value of n is -7 for linear equation 3(n - 9) - 2(n + 4) = 6n.

3(n - 9) - 2(n + 4) = 6n

6n = 3n - 27 - 2n - 8

-6n + n - 35 = 0

-5n = 35

5n = -35

n = -7

Given equation is 3(n-9)-2(n+4)=6n.

Open the brackets for multiplication, 3n - 27 - 2n - 8 = 6n.

After shifting the variables to the left-hand side and constant to the right-hand side, 5n = -35.

As the value of the constant in the above step is negative the final constant value will be also negative, n = -7.

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The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.

what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.

Let y be the weight of the airplane and x be the amount of fuel

And we know that the general form of a linear

function is

(1) And given that the slope of the line is

y = mx + c

m = 5.9

Then (1) becomes

y = 5.9x + c

And given that for x = 53 , y = 2212.7

Then from (2), we have

2212.7 = 5.9 (53) + c

⇒ 2212.7 = 312.7 + c

c = 2212.7 - 312.7

c = 1900

Thus, (2) becomes

y = 5.9x + 1900

Then for x=22, from (3) y = 118 + 2100

= w = 2218

The weight of the plane with 20 gallons in its fuel tank is 2218 pounds

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x^2+ y^2-2x-2y = 0 has center (1,1) and radius sqrt 2 and the circle x^2+y^2 =1 has center (0,0) and radius 1

the unit circle has center

(1,1)  , ( 0,0)

and the unit circle has radius

1 , sqrt 2

for this the equation of the circle is

x^2 + y^2 = 1

if we take center as (0,0) then radius become 1

therefore equation of circle becomes x^2 +y^2 =1

similarly if we take center ( 1,1 ) and radius sqrt 2

then (x -1 )^2 + ( y-1 )^2 =2

x^2 +y^2 -2x- 2y +2 =2

this implies x^2 +y^2 -2x -2y =0

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The value of solution of expression is,

⇒ (3⁵)

We have to given that;

The expression is,

⇒ (3³ × 3⁴) ÷ 3²

Now, We can simplify by rule of exponent as;

⇒ (3³ × 3⁴) ÷ 3²

⇒ (3³ ⁺ ⁴) ÷ 3²

⇒ (3⁷) ÷ 3²

⇒ (3⁷⁻²)

⇒ (3⁵)

Thus, The value of solution of expression is,

⇒ (3⁵)

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The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.

By expressing the given linear equation in slope-intercept form; it follows that we have;

x + y = 6

y = -x + 6

Hence, the slope of the equation by comparison with; y = mx + c is; -1.

Therefore, the slope of the required equation is same as the two lines are said to be parallel.

Therefore, the required equation from point-slope form of an equation is;

( y - 8) = -1 ( x - (-4))

y - 8 = -x - 4

x + y = -4 +8

x + y = 4.

Ultimately, the required equation is; x + y = 4.

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Given: The base function

To Determine: The transformation that would give the function G(x)

Solution

Let us plot the graph of the base function and the new function as shown below

It can be observed that there exist a reflection across the x-axis, also a vertical stetch by a factor of 4

Hence, the correct answer is a vertical stretch by a factor of 4, followed by a reflection across the x-axis, OPTION A

Answer:

Assuming that this is referring to simple interest, your answer is C) 1,750.

Step-by-step explanation:

[tex]5000[/tex] x [tex]0.05[/tex] = [tex]250[/tex]

[tex]250[/tex] x [tex]7[/tex] = [tex]1750[/tex]

The value of t after solving 2b+2.50t = 40 is t = (40-2b)/2.50.

According to the question,

We have the following expression:

2b+2.50t = 40

Now, in order to find the value of t, we will move other variables and numbers from the left hand side to the right hand side.

First, moving 2b from the left hand side to the right hand side will result in the change of the sign from plus to minus:

2.50t = 40-2b

Now, 2.50 is in multiplication on the left hand side. So, it will be in the division on the right hand side.

t = (40-2b)/2.50

Hence, the value of t after solving the given expression is t = (40-2b)/2.50.

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y=4x+64

Explanation:

Two lines are perpendicular if the product of their slopes is -1.

Step 1: Find the slope of the line a

Line a passes through the points (1,-3) and (9,-5)

The slope of line a = -1/4

Step 2: Determine the slope of line b.

Let the slope of line b = k

Since the product of the two slopes is -1:

The slope of line b = 4

Step 3: Find the equation of line b.

Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.

Using the slope-point form of the equation of a line:

Substitute the given values

The equation of line b is y=4x+64.

Answer:

[tex]y = -\dfrac{1}{2}x + \dfrac{13}{2} \;\; \text{or}\\\\y = -0.5x + 6.5\\\\[/tex]

Step-by-step explanation:

The slope-intercept form of a straight line is

y = mx + b

where m = slope and b = y-intercept

A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through

Given
Line 1:  y = 2x - 6
Slope m = 2

Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5

So the equation would be y = (-1/2)x + b

We can solve for b given the info that the line passes through (5,4)

Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b

4 = -5/2 + b

4 + 5/2 = b

8/2 + 5/2 = b

13/2 = b

or b = 13/2

So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2

or
y = -0.5x + 6.5

"An empty set is included in set N" is the translation of the mathematical sentence.

A set is defined as a collection of well-defined objects, numbers or things. In set theory, we use different symbols to represent statements.

To translate Ø⊆N, we need to know the meaning of the symbols we have:

Ø means empty set (A set that does not contain anything).

⊆ means subset (is included in)

N means set N

So we can translate  Ø⊆N as:

An empty set is included in set N or

Therefore, the mathematical sentence Ø⊆N can be translated as "an empty set is included in set N"

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Hellow what grade of math is this?

The result of the expression 36 ÷ (4+2) is 6

The expression is  

36 ÷ (4+2)

To solve this expression, we have to apply the arithmetic operations in the given expression

An arithmetic operation is the operation specified by combining number or variable with one arithmetic operator. The basic arithmetic operations are addition, subtraction, division and multiplication.

First do the arithmetic operations in the bracket

Add 4 and 2 in the expression

36 ÷ (4+2) = 36 ÷ 6

Divide the number 36 by 6 in the expression

36 ÷ 6 = 6

Hence, the result of the expression 36 ÷ (4+2) is 6

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Answer: 6+1=7

Step-by-step explanation:

Answer:

f(x) = ax^2 + bx + c

I) f(1) = a + b + c = -2

II) f(2) = 4a + 2b + c = -2

III) f(3) = 9a + 3b + c = -4

II - I

IV) 3a + b = 0

III - I

V) 8a + 2b = -2

V - 2IV

2a = -2 --> a = -1

3(-1) + b = 0 --> b = 3

(-1) + (3) + c = -2 --> c = -4

f(x) = -x^2 + 3x - 4

Answer:

60

Step-by-step explanation:

0.2x = 12

x=60

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We may be thinking about either of these choices depending on whether we are talking about immigration or emigration.

[tex]\frac{d P}{d t}=r_g \pm r[/tex]

This is further explained below.

Generally, The rates of births and deaths will be represented accordingly by the superscripts [tex]r_b[/tex] and [tex]r_d[/tex].

The model transforms into the following when subjected to the circumstances outlined in the problem:

[tex]\frac{d P}{d t}=r_b P-r_d P^2[/tex]

In conclusion, You need to submit model 1 in order to get more information.

In the event that the proportionality assumptions about birth and death be loosened up, the model that is necessary for issue 1 would become the following:

[tex]\frac{d P}{d t}=r_g \pm r[/tex]

Depending on whether we are discussing immigration or emigration, we may be contemplating either of these options.

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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. Then the probability that the sample is more than 8.42 is 0.0029 or 0.29%.

Using the normal distribution and the central limit theorem,

The mean is μ = 8.5

The standard deviation is σ = 0.22 .

A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362

The probability that the sample average is more than 8.40 is the p-value of Z when X = 8.4, hence:

Z = X - μ/σ

Z = 8.4 - 8.5/0.0362

Z = 2.76

Z = -2.76 has a p-value 0.0029

0.0029 = 0.29% probability that the sample average is more than 8.40.

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Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.

Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.

Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.

Converse of the statements will be as If two lines are parallel, then they have equal slopes.

Conditional statement will be; If two lines have same slopes, then the lines are parallel.

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