In Exercises 1 and 2, complete the proof.
1. Given PQ=RS
Prove PR=QS
2. Given ∠1 is a complement of ∠2.
∠2≅∠3

Prove ∠1 is a complement of ∠ 3
In Exercises 3-6, name the property that the statement illustrates.
3. If PQ≅ ST and ST≅UV, then PQ≅UV

Answer:.

Step-by-step explanation:

The percentage of data within 1 population standard deviation of the mean, to the nearest percent is; 71%

The mean of a data sample is defined as the average of that data sample. The formula for the mean is;

μ= ∑x/n

Thus;

μ = (58 + 58 + 50 + 64 + 59 + 62 + 58)/7

μ = 409/7

μ =  58.429

The standard deviation is defined as a measure of how dispersed the data is in relation to the mean. It is gotten from the formula;

σ = √[Σ(xi - μ)²/N]

Solving this with a standard deviation calculator gives;

σ = 4.065

Thus, 1 standard deviation from the mean is;

58.429 ± 1(4.065)

= (54.364, 62.494)

The values that fall in this range from the given data set are;

58, 58, 59, 62, 58

They are 5 in number out of 7 and so the percentage = (5/7) * 100%

= 71.43%

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Answer:

88 cm²

Step-by-step explanation:

Area of trapezium = [tex]\frac{1}{2}[/tex](a + b)h

12 * 2 = 24

68 -24 = 44

44 is (a + b) as they are the sum of the parallel sides of the trapezium.

h (altitude) = 4

[tex]\frac{1}{2}[/tex](44)(4) = 88 cm²

Answer:

88 cm², hope it helps.

Percentage of the time will he record a base hit is 18.

To find the percentage of times that Professor Conner recorded a base hit, you need to divide the number of times he recorded a base hit by the total number of at bats, and then multiply by 100%.

In this case, the percentage of times that Professor Conner recorded a base hit would be

= (2 base hits / 11 at bats) * 100%

= 18.2%.

After Rounding off to nearest whole number it becomes 18%.

What is a Base Hit?

A fair ball hit in such a way that the hitter can reach a base safely without a fielding error by the other side.

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Percentage of the time will he record a base hit is 18.

To find the percentage of times that Professor Conner recorded a base hit, you need to divide the number of times he recorded a base hit by the total number of at bats, and then multiply by 100%.

In this case, the percentage of times that Professor Conner recorded a base hit would be

= (2 base hits / 11 at bats) * 100%

= 18.2%.

After Rounding off to nearest whole number it becomes 18%.

A fair ball hit in such a way that the hitter can reach a base safely without a fielding error by the other side.

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A linear function gives us the following:

a) At 0 seconds, there are 300 liters of water in the aquarium.

b) The amount of water is losing volume at a rate of 60 liters per minute as time goes on.

Given,

Linear function;-

Modeling a linear function involves:

y = ax + b

That where:

The y-intercept in this problem is 300, hence 300 liters of water are present in the tank at 0 seconds.

The quantity drops by 60 liters each minute, so:

Water is losing volume at a rate of 60 liters per minute as time goes on.

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The two values of x that are roots of the polynomial are:

x = -5 + i√11/2

x = -5 - i√11/2

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

x² + 5x + 9 = 0

It is in the form of ax² + bx + c

a = 1

b = 5
c = 9

Using the determinant.

x = -b ± √(b² - 4ac) / 2a

x = -5 ± √(25 - 36) / 2

x = -5 ± √-11 / 2

x = -5 ± i√11/2

Where i = √-1

Thus,

The roots of the polynomial are:

x = -5 + i√11/2 and x = -5 - i√11/2

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The distances travelled in each hour for both part are given as 5760 m and 5.76 km respectively.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given problem can be solved by ratio method as follows,

(A)  The average walking rate is 1.6 m/s

The speed in meter per hour is calculated as,

1 second = 1/3600 hour

Take the ratio of 1.6 and 1/3600 as follows,

1.6 ÷ 1/3600

= 3600 × 1.6

= 5760

(B) The average walking rate is 1.6 m/s

It implies that 1.6 m in 1 second.

Now, 1 m = 1/1000 km

=> 1.6 m = 1.6/1000 km

And, 1 second = 1/3600 hour

Thus, the distance travelled in kilometer per hour can be evaluated by taking the ratio as follows,

1.6/1000 ÷  1/3600

= (3600 × 1.6)/1000

= 5.76

Hence, the distances travelled per hour in meter and kilometer are given as 5760 m and 5.76 km respectively.

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The product of two given numbers 37 and 4 using distributive property is 148.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Given that, 37×4.

Using distributive property, we can find the product of two given numbers

That is 37×4

= (30+7)4

= 30×4+7×4

= 120+28

= 148

Therefore, the product of two given numbers using distributive property is 148.

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Answer:

a. annually

Step-by-step explanation:

anually means yearly, semi anual means twice a year

In 2401  meters will sound travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line. Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Given

Speed = 343 m

Time = 7 seconds

For distance,

Distance = Time × Speed

Distance = 343 × 7

Distance = 2401

In 2401 meters sound will travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.

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The solution to the inequality -9k + 7 ≥ 16 and 5 - k ≤ 13 is -8 ≤ k ≤ -1

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

-9k+7>=16 and 5-k<=13

Rewrite the above inequality expressions

So, we have the following representation

-9k + 7 ≥ 16 and 5 - k ≤ 13

Evaluate the like terms in the above inequality expressions

So, we have the following representation

-9k  ≥ 9 and - k ≤ 8

Divide both sides of the above inequality expressions by the coefficient of x

So, we have the following representation

k ≤ -1 and k ≥ -8

When  the solution is merged, we have

-8 ≤ k ≤ -1

Hence, the solution is -8 ≤ k ≤ -1

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Complete question

Solve for k in -9k+7>=16 and 5-k<=13

The expression that shows the change in the​ stock's value is -159 * 14

From the question, we have the following parameters that can be used in our computation:

Rate of decrement = $159

Duration = 14 months

Using the above as a guide, we have the following:

The expression that shows the change in the​ stock's value is

Expression = Rate of decrement * Duration

Substitute the known values in the above equation, so, we have the following representation

Expression = -159 * 14

Evaluate the products

Expression = -2226

Hence, the required expression is -159 * 14

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Answer:

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

Substitute g(x) into x of f and evaluate:

First spot: 9 choices (0-9)

Second spot: 9 choices (0-9)

Third spot: 9 choices (0-9)

.

.

.

Ninth spot: 9 choices (0-9)

There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.

Explination:

9^9 = 387420489 possible social security numbers

The value of cos60° is 1/2.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

We know,

For a 30-60-90 triangle, the sides opposite to 30° is a, the side opposite to 60° is √3a and the side opposite to 90° is 2a.

Therefore,

If a = 1,

The sides are  where,

perpendicular = 1

Base = √3

Hypotenuse = 2

We know cosΦ = Base/ Hypotenuse

But in the case of cos60°,  we have to take base as 1 and hypotenuse as 2, that is the angle has to be at base.

Base = 1

Hypotenuse = 2

Therefore,

cos60° = Base/ Hypotenuse

cos60° = 1/2

Therefore, the cos60° = 1/2.

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Answer:

The slope of a line perpendicular to the line y=1/3x-2 is the negative reciprocal of the slope of that line. The slope of the line y=1/3x-2 is 1/3, so the slope of a line perpendicular to it is -3.

Answer:

first and fourth statements are true

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , so

2x + 1 + x + x + 15 = 180 , that is

4x + 16 = 180 ( subtract 16 from both sides ) ← True

4x = 164 ( divide both sides by 4 )

x = 41 ≠ 49

then

∠ A = 2x + 1 = 2(41) + 1 = 82 + 1 = 83° ≠ 99°

∠ C = x + 15 = 41 + 15 = 56° ← True

Answer:

a.) Constant Rate of Change - yes

b.) origin - yes

c.) Change in y / Change in x - yes

d.) rise/run - yes

e.) inverse - Not apply

What is the difference between rate of change and slope coefficient?

The terms rate of change, gradient, slope coefficient, and rise over run are all equivalent to the slope in a proportional relationship. The slope of a line describes the rate at which a variable changes in relation to another variable. Rate of change is the same concept, but it is more general and can be applied to any relationship, not just linear. Gradient is another term for the slope of a line, which is the change in one variable compared to the change in another variable. Slope coefficient is a mathematical term for the slope of a line, which is the ratio of the vertical change to the horizontal change. Rise over run is another term for the slope of a line, which describes the rate of change by measuring the vertical change (rise) over the horizontal change (run). All of these terms describe the same concept, which is the rate of change in a proportional relationship.

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Answer:

1.727 x 10^4

Step-by-step explanation:

2.26 x 10^4 = 22 600

5.33 x 10³ = 5330

22 600 - 5330 = 17 270

17 270 = 1.727 x 10^4

For each $23.457" borrowed, you would pay about  a year $8,586 in interest, as in the case of a credit card with an APR of 5%.

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Answer:

y=f+3.5x

Step-by-step explanation:

Let the total bill be y

and let the number of movies be x

let the flat fee be f

given that he pays $3.5 per movie

and his total bill is  $54

The expression is given bellow for his total bill

y=f+3.5x

For 5 movies his total bill is $54

54=f+3.5(5)

54=f+17.5

54-17.5=f

f=36.5

Therefore the flat fee is $36.5

slpoe is -1/2 and y-intercept is 2

Answer:

[tex] \huge{ \boxed{m = \frac{3}{2} }}[/tex]

Step-by-step explanation:

[tex] - 15x + 10y = 50[/tex]

Equation of a line is given by

[tex] \bold{y = mx + c}[/tex]

where

m is the slope

c is the y intercept

To find the slope, we must first rewrite the equation in the given form y = mx + c and compare both equations.

[tex] - 15x + 10 y = 50 \\ \\ 10y = 15x + 50 \\ \\ \frac{10y}{10} = \frac{15}{10} x + \frac{50}{10} \\ \\ y = \frac{3}{2} x + 5[/tex]

Comparing it with the general equation y=mx + c,

[tex]m = \frac{3}{2} \\ [/tex]

The diameter of the plate. show all work. will be 9.24 inches. The diameter is double of the hypotenuse.

What is the diameter?

A diameter is a line that travels through the center of an object and intersects the circumference at opposing ends. It measures twice as long as the object's radius.

The radius of the circle becomes the hypotenuse when a right triangle is formed by joining the edge of the knife to the center of the circle and the center of the knife to the center of the circle.

With the help of the trigonometric function, the value of the hypotenuse is found as;

sin60 = 8/h

h = 4.62 inches

The diameter of the plate is double the hypotenuse in the given figure;

D = 2 X h

D = 2 X 4.6

D = 9.8

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changing the default admin password  will achieve the security level.

What is a router  ?

An networking device called a router is used to forward data packets between computer networks. On the worldwide Internet and between networks, routers handle traffic directing. Data packets are the unit of data delivered via a network, such as an email or a web page. An internetwork (such as the Internet) is made up of networks, and a packet is normally passed from one router to another router over those networks until it reaches its destination node.

Default admin password can be known for many people and they can use the internet.

So, changing the default admin password will achieve the security level.

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The kiddie pool can hold 128 pints of water which is equivalent to 16 gallons.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 gallon is equal to 8 pints.

So, To obtain the number of pints in 16 gallons of water we have to multiply the total no.of gallons with a unitary pint value of 1 gallon which is,

= (16×8) pints.

= 128 pints.

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Answer: 128 pints

Step-by-step explanation:

1 gallon is 8 pints, 8 multiplied by 16 equals 128

The probability of getting an even number or a 1 is 11/20

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given that there are 20 cards numbers 1,2... 20.

A card is randomly drawn.

We have to find the probability of drawing either 1 or even card.

P(drawing even card) = no of even cards/total cards = 10/20= 0.5

P(drawing one) = no of 1's/total cards = 1/20 = 0.05

P(drawing both one and even card) = 0 (since impossible)

Hence P(drawing even or one) =0.5+0.05-0

=0.55

= 11/20

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Answer:

7

Step-by-step explanation:

A'B' should be equal to AB, as AB corresponds to A'B' in the second image attached. Since AB = 7, A'B' will also equal to 7.

Answer:

Answer A

Step-by-step explanation:

7 units