If your original biconditional statement is true, would the contrapositive be true? Give an example to illustrate your reasoning. ＇

Based on the given trapeziums, each problem's answers are:

Let's discuss each problem we have:

1. The given trapezium is an isosceles trapezium, hence:

J = K = 7x  + 2

M = L = 25x - 14

Since trapezium is a part of parallelogram, then:

∠J + ∠K + ∠L + ∠M = 360°

2∠J + 2∠M = 360°

2(7x + 2) + 2(25x - 14) = 360°

14x + 4 + 50x - 28 = 360°

64x - 24 = 360°

64x = 384

x = 6

∠J = ∠K = 7x + 2

∠J = ∠K = 7(6) + 2 = 44°

∠M = ∠L = 25x - 14

∠M = ∠L = 25(6) - 14 = 136°

2. Since EFGH is an isosceles trapezoid, then:

EH = FG

4x - 27 = x + 9

3x = 36

x = 13

EG = FH

3y + 19 = 11y - 21

40 = 8y

y = 5

3. It was given that:

PQ = 27

SR = 39

WX?

WX is the mig segment, where:

Mid segment = (base + top) / 2

WX = (PQ + SR) /2

WX = (27 + 39) / 2

WX = 66/2

WX = 33

4. It was given that:

MN = 22

DC = 29

AB ?

MN is mid segment

MN = (AB + DC) / 2

22 = (AB + 29) / 2

44 = AB + 29

AB = 15

5. JK = 3x + 11

NP = 45

ML = 10x - 12

NP is mid segmet

NP = (JK + ML) / 2

45 = [(3x + 11) + (10x - 12)] / 2

90 = (3x + 11) + (10x - 12)

90 = 13x - 1

13x = 91

x = 7

ML = 10x - 12

ML = 10(7) - 12

ML = 58

6. BC = 19

GH = 9x - 3

FE = 5x + 1

GH is mid segment

GH = (BC + FE) / 2

(9x - 3) = (19 + (5x + 1)) / 2

18x - 6 = 19 + (5x + 1)

18x - 6 = 20 + 5x

13x = 26

x = 2

GH = 9x - 3

GH = 9(2) - 3

GH = 15

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Step-by-step explanation:

To solve this problem, we'll use the exponential growth formula:

P(t) = P0 * e^(rt)

Where P(t) is the population after t years, P0 is the initial population (1543), r is the growth rate (0.038), and t is the number of years (5.2).

P(5.2) = 1543 * e^(0.038 * 5.2)

Using a calculator or natural logarithm rules:

P(5.2) = 1543 * e^0.199

P(5.2) = 1543 * 1.22

P(5.2) = 1887.46

So the population will be approximately 1887.46 after 5.2 years.

Answer:

42

Step-by-step explanation:

If angle one equals 42, then angle 3 should too since they are the same angle.

hope it helps...

"The A minor scale uses the white notes on the keyboard from A to A, but with G# instead of G." is True Option A

Generally, The tonic of a minor scale, which is the first note of the scale, is located a minor third above the root note of the scale. A minor scale is a sort of musical scale that consists of seven notes.

The A minor scale is a 7-note, the diatonic scale made up of the notes A, B, C, D, E, F, & G. It's the only minor scale that doesn't contain any sharps or flats.

A Natural Minor is A, B, C, D, E, F, G, A. Notice that the A Natural Minor Scale has no notes with accidentals. Let's build a G# Natural Minor Scale. Our starting note will be G#.

Therefore, Option A is true

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Answer:

12 root 3

Step-by-step explanation:

first, you can say that QRP is similar to PRS

with the ratios, you can say that

[tex]\frac{QR}{PR} = \frac{PR}{RS}\\[/tex]

by substituting values, you have

[tex]\frac{6}{PR} = \frac{PR}{18}\\[/tex]

[tex]PR^2=108[/tex]

[tex]PR=6\sqrt{3}[/tex]

using pythagorean theorem, you can determine that

[tex]PS^2=(6\sqrt{3})^2+18^2[/tex]

[tex]PS^2=432[/tex]

[tex]PS=\sqrt{432}=12\sqrt{3}[/tex]

Answer:

12√3

Step-by-step explanation:

cos∠RSP = 18/PS

cos∠PSQ = PS/24

∠RSP=∠PSQ     (the angle at S)

18/PS = PS/24

(PS)² = (18)(24) = 432

PS = √432 = 12√3

Answer:

A rate is two variables that relies on each other so a example would be a projectile and a cannon, in relation the cannon goes no where while the projectile is flying through the air

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Two triangles = one square

Since there are 4 squares, then there are 8 triangles

We see one triangle is shaded.

We also see one square is shaded, which means 2 triangles are shaded.

2 + 1 = 3 triangles shaded. Since there are a total of 8 triangles, then the fraction would be 3/8

Answer: 30

Step-by-step explanation:

Vertical angles are congruent.

[tex]x+30=2x \implies x=30[/tex]

Answer:

1. consistent independent
2. consistent dependent
3. inconsistent

Step-by-step explanation:

1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} \neq b_{1} :b_{2}[/tex]

2. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} = c_{1} : c_{2}[/tex]

1. when we take the ratios of the two equations,
[tex]a_{1} : a_{2} = b_{1} :b_{2} \neq c{1} : c_{2}[/tex]

Step-by-step explanation:

4x + y = 8

x + 3y = 8

consistent independent

both equations are lines with different slope.

so, they intersect at one point.

that is the solution.

-4x + 6y = -2

2x - 3y = 1

consistent dependent

both equations are actually identical lines.

multiply the second equation by -2.

and you see the equality.

that means every point is a solution.

there are infinitely many solutions.

5x - 2y = 4

5x - 2y = 6

inconsistent

both equations are lines with identical slopes.

but with different y-intercepts.

they are parallel and never intersect.

there is no solution.

there is no (x, y) that their sum has 2

different results.

The required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

Limit, which can be defined as every nearby value of a variable for a function that exists, is called limits

Here,
According to the question,
[tex]y = \lim_{x \to \ a} 1/[x-a]^n[/tex]

Put a = 2 and n = 7
[tex]y = \lim_{x \to \ 2} 1/[x-2]^7[/tex]

As n = 7 is odd, from the theorem,
y = -∞, as 7 is an odd number.

Thus, the required solution is as follows,
(A) The value of the limit is -∞, as 7 is an odd number.
(b) Graf of the function has been shown.

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Answer:

4x² + 4x + 9 = 0 , has no real solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the solutions can be determined using the discriminant.

Δ = b² - 4ac

• if b² - 4ac > 0 , then real solutions

• if b² - 4ac = 0 , then real and equal solutions

• if b² - 4ac < 0 , then no real solutions

4x² + 4x + 9 = 0 ← in standard form

with a = 4, b = 4 , c = 9

b² - 4ac

= 4² - (4 × 4 × 9)

= 16 - 144

= - 128 ← no real solutions

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

- 4x² + 56x - 196 = 0 ← in standard form

with a = - 4 , b = 56 , c = - 196

b² - 4ac

= 56² - (4 × - 4 × - 196)

= 3136 - 3136

= 0 ← has real solutions

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

- 5x² - 10x + 10 = 0 ← in standard form

with a = - 5 , b = - 10 , c = 10

b² - 4ac

= (- 10)² - (4 × - 5 × 10)

= 100 - (- 200)

= 100 + 200

= 300 ← has real solutions

The value of function f ' (2) is, 7/4.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

We have to given that;

The function is,

⇒ f (x) = 7/x

Now, We an solve as;

⇒ f ' (2) = lim h → 0 ( f (2 + h) -  f (2) / h )

⇒ f ' (2) = lim h → 0 ( 7 / (2 + h) - 7/2 / h )

⇒ f ' (2) = lim h → 0 ( 7/h (2 - 2 - h) / (2 + h)×2)

⇒ f ' (2) = lim h → 0 ( 7/h ( - h ) / 2 (2 + h) )

⇒ f ' (2) = lim h → 0 ( - 7 / 2 (2+ h))

⇒ f ' (2) = - 7/4

Thus, The value of function f ' (2) is, 7/4.

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Answer:    a = 2    f(x) = x^5

Step-by-step explanation:

The length of DE is  25. So correct option is (4).

In geometry, the term "parallel" refers to two lines that are equidistant from each other over their entire length and will never intersect, no matter how far they are extended. In other words, two parallel lines are parallel if they lie in the same plane and maintain the same distance between them at all times.

Since AB is parallel to DE and BD is perpendicular to both AB and DE, by alternate interior angles, we have:

angle BDA = angle DEC

Since BD is 7 and BC is 15, we have:

triangle BCD is a 7-15-17 right triangle (the Pythagorean theorem)

So, angle BDA = angle DEC = 90 - arctan(7/15) = arctan(15/7).

Also, since AB is parallel to DE, and BD is perpendicular to both AB and DE, we have:

angle ABD = angle CDE

So, by the vertical angles theorem, we have:

angle ABD = angle CDE = 90 degrees - arctan(15/7) = arctan(7/15)

Then, by the Pythagorean theorem, the length of DE can be found as:

[tex](DE)^{2}[/tex] = [tex](AB)^{2}[/tex] + [tex](BD)^{2}[/tex] = [tex]21^{2}[/tex] + [tex]7^{2}[/tex] = 441 + 49 = 490

So, DE = [tex]\sqrt{490}[/tex] = 2[tex]\sqrt{122}[/tex] = 2 * 11 = 22

Therefore, the length of DE is (4) 25.

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If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.

The simple interest is the interest system that does not compute interest on accumulated interest.

Unlike simple interest, compound interest charges interest on accumulated interest.

Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.

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Answer: Option A will have the least amount of interest because simple interest generates earnings from principal only.

Step-by-step explanation: because it says it’s right on the computer;p

The rule for the function is P(t) = 170 + 680t

Let's call Julia's final position after t hours as P.

If she drove at a constant speed v (in miles per hour), then the distance traveled can be given as:

P - P0 = vt

Given that she was 170 miles east from Denver after driving for a quarter of an hour (0.25 hours), we can write the first equation:

170 = v * 0.25

v = 680

This means that her speed was 680 miles per hour.

Using this speed, we can write the second equation:

P = 680 * t

100 = 680 * t

t = 100 / 680 = 0.147

Combining the two equations, we can find the function that gives Julia's position east from Denver after t hours as:

P(t) = P0 + v * t ----- P0 = 170 i.e. her initial position

P(t) = 170 + 680 * t

So, the rule for the function P(t) is:

P(t) = 170 + 680t

P^-1(16) is the inverse of the function P(t) at the value 16.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

To find its value, we can use the equation of the function P(t):

P(t) = 170 + 680 * t

16 = 170 + 680 * t

-154 = 680 * t

t = -154 / 680

Time cannot be negative.

So, it does not exist

P^-1(-141) is the inverse of the function P(t) at the value -141.

In other words, it gives us the time t after which Julia is 16 miles east from Denver.

So, we have

-141 = 170 + 680 * t

-311 = 680 * t

t = -311 / 680

Time cannot be negative.

So, it does not exist

We simply make t the subject in P(t)

So, we have

P^-1(t) = (t - 170) / 680

The graph is attached

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Answer: 1 3 4

Step-by-step explanation:

Answer:

"w" (and any subsequent words) was ignored because we limit queries to 32 words.

w = 0.33 so, w lies before A, B, and C.

Option A is the correct answer.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

We have,

Average weight.

w = Sum of all the weight / 3

w = (0.5 + 0.3 + 0.2) / 3

w = 1/3

w = 0.33

Now,

A = 3, B = 6, and C = 7 on the number line.

0.33 lies before A, B, C

Thus,

w lies before A.

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Answer:The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

Step-by-step explanation:

The statement "The bank has the best decors and paintings in their branch" should not be one of Macky's reasons for choosing a bank. While the appearance of a bank branch may be important to some customers, it is not a primary factor in choosing a bank account. Macky should focus on more important factors such as interest rates, fees, customer service, and overall financial stability of the bank.

Answer:

im confused are you asking a question or telling us about something?

Step-by-step explanation:

4

Ws

a) The probability that the player makes exactly 3 of the 5 shots = 0.3087

b) The probability that the player makes exactly 4 of the 5 shots = 0.36015

c) The probability that the player makes all 5 shots = 0.16807

d) The probability that the player makes 3 or 4 of the shots = 0.66885

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability be represented as P

The total number of trials n = 5

The probability of getting a success p = 0.70

The probability of getting a failure q = 0.30

Now , the equation will be

a)

The probability that the player makes exactly 3 of the 5 shots = A

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 3

Substituting the values in the equation , we get

A = ⁵C₃ ( 0.70 )³ ( 0.30 )²

A = 10 ( 0.343 ) ( 0.09 )

A = 0.3087

So , probability that the player makes exactly 3 of the 5 shots is 0.3087

b)

The probability that the player makes exactly 4 of the 5 shots = B

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 4

Substituting the values in the equation , we get

B = ⁵C₄ ( 0.70 )⁴ ( 0.30 )¹

B = 5 ( 0.2401 ) ( 0.3 )

B = 0.36015

So , probability that the player makes exactly 4 of the 5 shots is 0.36015

c)

The probability that the player makes all 5 shots = C

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ  

n = 5

x = 5

Substituting the values in the equation , we get

C = ⁵C₅ ( 0.70 )⁵ ( 0.30 )⁰

C = 0.16807

So , probability that the player makes all 5 shots is 0.16807

d)

The probability that the player makes 3 or 4 of the shots = D

D = A + B

D = 0.3087 + 0.36015

D = 0.66885

Hence , the probability is solved

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Answer:

12

Step-by-step explanation:

The answer for your question is 12

Answer:

=12

Step-by-step explanation:

1(4×3)/3+ 8=

1(12)/3+8=

12/3 + 8=

4 + 8 = 12

I hope I help you in this ans and tq.

The percentage of the employees at the water slides are temporary​ is 88%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.

To find the percentage of the employees that are temporary

66/75 x 100/1

=88%

Hence, 88% is the percentage of the employees at the water slides are temporary​

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The algebraic expression for "the square of the difference of 10 and j less than the product of ten cubed" is  (10 - j)² < 10³.

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

The statement "the square of the difference of 10 and j less than the product of ten cubed" can be written as follow:

Step 1: Square the difference of 10 and j: (10 - j)²

Step 2: less than the product of ten cubed: (10 - j)² < 10³

Therefore, the algebraic expression is (10 - j)² < 10³

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The given statement exists true. A segment from the vertex of a triangle that is parallel to the other side.

The total of the lengths of any two segments must be greater than the length of the third segment in order to create a triangle. Any two sides of a triangle's lengths added together must be longer than the third side.

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is seen in the above figure.

A segment from the vertex of a triangle that is parallel to the other side. This section could be found on the triangle, inside it, or outside it.

There are three medians for every triangle, just as there are three altitudes, angle bisectors, and perpendicular bisectors. The lines that connect a triangle's vertices to the middles of its two opposite sides are known as the medians. The centroid of the triangle is the location where the three medians intersect.

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True. Since all the three combinations of segments when added the sum is greater than the third side the given segments can form a triangle.

According to the Triangle Inequality Theorem, a triangle's two side lengths added together are always greater than its third side. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.

Given that the length of the three segments is:

AC = 9 units

CB = 4 units

BA = 11 units

According to the Triangle Inequality Theorem the sum of two sides of a triangle is always greater than third side. If this is true for all three combinations, then the triangle can be formed.

For the given segments:

AC + CB > BA

9 + 4 > 11

13 > 11 True

4 + 11> 9

True

9 + 11 > 4

Since all the three combinations when added the sum is greater than the third side the given segments can form a triangle.

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The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The cost of the new Star Wars after a coupon for 25% off and a 6% tax will be given as,

⇒ $82 x (1 - 0.25) x (1 + 0.06)

⇒ $82 x 0.75 x 1.06

⇒ $65.19

The total cost after shipping will be given as,

Total cost = $65.19 + $7

Total cost = $72.19

The total cost of Mr.Bhavsar's order after the coupon for 25% off, a 6% tax, and $7 shipping will be $72.19.

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The value of DC is of 80, hence the statement is false.

Similar triangles share these two features listed as follows:

The similar triangles for this problem are given as follows:

AOB and COD.

Hence the proportional relationship established between the side lengths is given as follows:

OA/OC = OB/OD = 1/4 = AB/DC.

Taking the last two terms, considering that AB = 20 cm, the length of DC is given as follows:

DC = 4 x AB

DC = 4 x 20 cm

DC = 80 cm.

Hence the statement is false, as the length is of 80 cm and not of 120 cm.

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