I need help on these anybody?

the difference of two squares, you will use the formula. answers are (x + y)(x - y), (x + 4)(x - 4), (a + 5)(a - 5), (x + 11)(x - 11), (15 + a)(15 - a), (20 + y)(20 - y), (30 + z)(30 - z), (2x + 7)(2x - 7), (4x + 5)(4x - 5), 8(3x + 4)(3x - 4), (8 + a)(8 - a),8(3x + 4)(3x - 4), (5a + 4)(5a - 4), 9(a + 9)(a - 9), (7a + 2)(7a - 2), (10x + 3)(10x - 3), (8x + 5)(8x - 5),4(6x + 5)(6x - 5), 25(x + y)(x - y)

what is formula ?

A formula is a mathematical equation or expression that is used to solve a specific problem or perform a specific calculation. Formulas are often used in mathematics, physics, chemistry, engineering, and other fields to express a relationship between different variables or quantities.

In the given question,

Sure! To solve by finding the difference of two squares, you will use the formula:

a² - b² = (a + b)(a - b)

Using this formula, we can simplify the expressions given:

x² - y² = (x + y)(x - y)

=>  (x + y)(x - y) =0

=>  (x + y)=0    , (x - y)=0

=> x = -y   ,x = y

x² - 16 = (x + 4)(x - 4)

=>  (x + 4)(x - 4) =0

=>  (x + 4)=0    , (x - 4)=0

=> x = -4   ,x = 4

a² - b² = (a + b)(a - b)

a² - 25 = (a + 5)(a - 5)

x² - 121 = (x + 11)(x - 11)

225 - a² = (15 + a)(15 - a)

400 - y² = (20 + y)(20 - y)

900 - z² = (30 + z)(30 - z)

4x² - 49 = (2x + 7)(2x - 7)

16x² - 25 = (4x + 5)(4x - 5)

36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)

64 - a² = (8 + a)(8 - a)

36x² - 64 = (6x + 8)(6x - 8) = 8(3x + 4)(3x - 4)

25a² - 16 = (5a + 4)(5a - 4)

9a² - 81 = 9(a + 9)(a - 9)

49a² - 4 = (7a + 2)(7a - 2)

100x² - 9 = (10x + 3)(10x - 3)

64x² - 25 = (8x + 5)(8x - 5)

144x² - 100 = 4(6x + 5)(6x - 5)

25x² - 25y² = 25(x + y)(x - y)

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Answer:

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

2. x^2 - 16 = (x+4)(x-4)

3. a^2 - b^2 = (a+b)(a-b)

4. a^2 - 25 = (a+5)(a-5)

5. x^2 - 121 = (x+11)(x-11)

6. 225 - a^2 = (15+a)(15-a)

7. 400 - y^2 = (20+y)(20-y)

8. 900 - z^2 = (30+z)(30-z)

9. 4x^2 - 49 = (2x+7)(2x-7)

10. 16x^2 - 25 = (4x+5)(4x-5)

11. 36x^2 - 64 = 4(3x+4)(3x-4) or (6x+8)(6x-8)

12. 64 - a^2 = (8+a)(8-a)

13. 36x^2 - 64 = (6x+8)(6x-8) or 4(3x+4)(3x-4)

14. 25a^2 - 16 = (5a+4)(5a-4)

15. 9a^2 - 81 = 9(a+3)(a-3)

16. 49a^2 - 4 = (7a+2)(7a-2)

17. 100x^2 - 9 = (10x+3)(10x-3)

18. 64x^2 - 25 = (8x+5)(8x-5)

19. 144x^2 - 100 = 4(6x+5)(6x-5) or (12x+5)(12x-5)

20. 25x^2 - 25y^2 = 25(x+y)(x-y)

Step-by-step explanation:

:)

Required area of the rhombus is 173 cm².

What is rhombus?

A rhombus is a parallelogram with four equal sides. It is also called a diamond or a lozenge. In a rhombus, opposite angles are equal, and the diagonals bisect each other at right angles. Since all sides of a rhombus are equal, its opposite sides are parallel, and its opposite angles are congruent. The area of a rhombus can be calculated by multiplying the length of one of its diagonals by the length of the other diagonal and dividing the result by 2.

Here given,the rhombus with a base of 20 centimeters and a height of 17.3 centimeters.

So, the area of the given rhombus is

[tex] \frac{1}{2} \times base \times \: height \\ = \frac{1}{2} \times 20 \times 17.3 \\ = 173[/tex]

So, Area = 173 cm²

Therefore, the area of the given rhombus is 173 cm².

Hence, the correct option is C.

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The probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.

Probability is a branch of mathematics that deals with the study of uncertainty and randomness. It is used to describe the likelihood or chance of a particular event occurring. Probability is expressed as a number between 0 and 1, where 0 indicates an event is impossible, and 1 indicates that the event is certain to occur.

The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes. For example, if you roll a six-sided die, the probability of rolling a four is 1/6, because there is one way to roll a four out of six possible outcomes.

When the first marble is drawn, there are a total of 30 + 20 + 10 = 60 marbles in the box. If the first marble is red, then there are 29 red marbles left out of a total of 59. If the first marble is not red, then there are still 30 red marbles left out of a total of 59.

So, the probability that the first marble is red is:

P(Red on first draw) = 30/60 = 1/2

And the probability that the second marble is red, given that the first marble was red, is:

P(Red on second draw given first marble is red) = 29/59

The probability that the second marble is red, given that the first marble was not red, is:

P(Red on second draw given first marble is not red) = 30/59

To find the probability that both marbles are red, we need to multiply the probability of getting a red marble on the first draw by the probability of getting a red marble on the second draw given that the first marble was red:

P(Both marbles are red) = P(Red on first draw) × P(Red on second draw given first marble is red)

= (1/2) × (29/59)

= 0.245

Therefore, the probability that both marbles are red is approximately 0.245, rounded to 3 significant digits.

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Let's start by simplifying both sides of the equation:

−4(3x + 2) = x + 2(x − 1)

−12x − 8 = x + 2x − 2 (distributing the negative 4)

−12x − 8 = 3x - 2 (combining like terms)

Now we can add 12x to both sides and add 2 to both sides:

−12x − 8 + 12x + 2 = 3x - 2 + 12x + 2

−6x = 0

Finally, we can divide both sides by -6 to isolate x:

x = 0

Now we can check which of the given equations is equivalent to this solution:

A. −12x + 2 = 3x − 1 (substituting x = 0 gives 2 = -1, which is false)

B. −12x − 8 = 2x − 2 (substituting x = 0 gives -8 = -2, which is false)

C. −8 = 15x − 2 (substituting x = 0 gives -8 = -2, which is false)

D. −15x = −10 (substituting x = 0 gives 0 = 0, which is true)

So the answer is D.

Answer:

Step-by-step explanation:

First, let's solve the equation -4(3x + 2) = x + 2(x − 1):-

→ [tex]\boxed{\bf {x=-\frac{2}{5}\;\;or\:\:x=-0.4}}[/tex]

________________________

A. -12x + 2 = 3x - 1

The sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

B. -12x - 8 = 2x - 2

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

C. −8 = 15x − 2

Sides are equal therefore, this equation is True and is equivalent to −4(3x + 2) = x + 2(x − 1).

________________________

D. -15x = -10

Sides are not equal therefore, this equation is false and not equivalent to −4(3x + 2) = x + 2(x − 1).

Hence, C. -8 = 15x - 2 is the only equation equivalent to -4(3x + 2) = x + 2(x - 1).

______________________

Hope this helps!

Answer:

it is 10 and 40 i think

Answer:

slope = -3

Step-by-step explanation:

The function f(x) = -3x + 125 is a linear function in slope-intercept form y = mx + b.  The slope, m, is -3.  This means that for every increase of 1°C, 3 less fish are caught.  

(a)the volume will reach 275000 shares in a week at two different times.

(b)the volume will reach 400,000 shares in a week at two different times.

(a) 275,000 shares in a week (V=2750),  solve the equation:

the part of the quadratic formula underneath the square root symbol.

[tex]250t - 5t^2 = 2750\\5t^2 - 250t + 2750 = 0[/tex]

by quadratic formula,

t = [250 ± ([tex]\sqrt{250^2 - 4(5)(2750))}[/tex]]/(2(5))

t = [250 ± [tex]\sqrt{187500}[/tex]]/10

t = [250 ± [tex]50\sqrt{3}[/tex]]/10

[tex]t = 25 ± 5\sqrt{3}[/tex]

Since both solutions are real, the volume will reach 275000 shares in a week at two different times.

(b)  400,000 shares in a week,  solve the equation:

[tex]250t - 5t^2 = 4000\\5t^2 - 250t + 4000 = 0[/tex]

by discriminant formula, we have:

[tex]b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500[/tex]

the discriminant is positive but not equal to zero, the quadratic equation has two real roots. Therefore, the volume will reach 400,000 shares in a week at two different times.

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The function that determines the number of triangles in any given level of the pyramid is given as n = n ×(n + 1) / 2 where 'n' represents the level of the pyramid.

It is a rule that assigns to each input value a unique output value, based on a specific set of operations or calculations. Functions are commonly represented using function notation, such as f(x) or g(y), where the input variable (x or y) is substituted into an expression to obtain the corresponding output value.

A pyramid is a geometric shape that has a polygonal base and triangular faces that meet at a common vertex. The polygonal base can be any shape, such as a square, rectangle, triangle, or polygon, and the number of triangular faces depends on the number of sides of the base. Pyramids are named according to the shape of their base, such as a square pyramid, rectangular pyramid, triangular pyramid, or pentagonal pyramid.

Args:

level (int): The level of the pyramid.

Returns:

int: The number of triangles in the given level.

if level ≤ 0:

return 0

else:

Each level of the pyramid has one large triangle at the top

and additional smaller triangles underneath it, forming a pattern

of 1 + 2 + 3 + ... triangles, where each term is the level number.

The number of triangles in a given level can be calculated as the

sum of the first 'level' numbers using the formula (n × (n + 1)) / 2.

num of triangles = (level × (level + 1)) // 2

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Answer:

33.46cm²

Step-by-step explanation:

big rectangle minus little rectangle

(9.3x4.2)-(3.5x(9.3-4.8-2.9))

39.06-(3.5x1.6)

39.06-5.6

33.46

Answer:

A) 77°

B) 77°

C) 103°

Step-by-step explanation:

A) Vertical angles are congruent

B) Alternate exterior angles are congruent.

C) Angles B and C are supplemental.  They add to 180°

Helping in the name of Jesus.

The final figure is congruent to the original figure because a reflection over the y-axis is an isometric transformation.

A translation is a rigid transformation that moves an object without rotating or reflecting it.

In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection.

1) Given the original coordinates of A, B, and C:

A(7, 5), B(2, 9), C(1, 3)

To translate the triangle 4 units to the left and 8 units up, we add -4 to the x-coordinates and +8 to the y-coordinates:

New coordinates for A:

x-coordinate: 7 - 4 = 3

y-coordinate: 5 + 8 = 13

Therefore, A after translation is A(3, 13).

2) To reflect A over the y-axis, we use the rule for reflecting a point over the y-axis, which is to keep the y-coordinate unchanged and change the sign of the x-coordinate:

New coordinates for A after reflection:

x-coordinate: -3

y-coordinate: 13

Therefore, A after reflection is A(-3, 13).

3) The rule for reflecting a point (x,y) over the y-axis is:

(x, y) -> (-x, y)

This means that we take the original x-coordinate, change its sign, and keep the y-coordinate the same.

4) The coordinates for A after reflection are (-3, 13).

5) Yes, the final figure after translation and reflection is congruent to the original figure. This is because both translation and reflection are rigid transformations, which means they preserve distances and angles, and therefore, they preserve the shape and size of the original figure. Translation preserves the orientation of the figure, and reflection preserves the orientation and reverses the handedness. Therefore, the new figure is congruent to the original figure.

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Therefore, the number of minutes of talk time used each month is 581.

In terms of time measurement, a minute is a unit of time equal to 60 seconds. It is one-sixtieth of an hour and one-third of an hour. The word "minute" comes from the Latin word "minutes," meaning "small" or "minute."

Minutes are commonly used in everyday life to measure short durations of time, such as the length of a phone call or the time it takes to boil an egg. They are also used in scientific fields to measure very small-time intervals, such as in nuclear physics or astronomy. Additionally, minutes are often used in meetings and official proceedings to record the details of what was discussed and decided.

Let's first calculate the cost of 500 minutes of talk time, which is $23.70.

To get email access, it costs 10% of the price for 500 minutes of talk time, which is 0.1 x $23.70 = $2.37.

So the total cost per month is $23.70 + $2.37 = $26.07 for 500 minutes of talk time and email access.

For each additional minute over 500, it costs $0.07. Let's say you use x minutes of talk time per month, where x is greater than 500.

Then the cost for talk time would be[tex]$23.70 + ($0.07)(x - 500).[/tex]

The total cost per month, including email access, would be [tex]$2.37 + $23.70 + ($0.07)(x - 500) = $26.07 + ($0.07)(x - 500).[/tex]

Since the bill is the same each month for 8 months, the total cost for 8 months is[tex]$26.07(8) + ($0.07)(x - 500)(8) = $208.56 + ($0.07)(x - 500)(8) = $253.92.[/tex]

Simplifying, we get:

[tex]($0.07)(x - 500)(8) = $253.92 - $208.56[/tex]

[tex]($0.07)(x - 500)(8) = $45.36[/tex]

Dividing both sides by 0.56:

[tex](x - 500)(8) = 648[/tex]

[tex]x - 500 = 81[/tex]

[tex]x = 581[/tex]

Therefore, the number of minutes of talk time used each month is 581.

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The total number of pages that each student will read aloud is 2.5 pages.

There are 18 students in Ms. Avila's reading class. Ms. Avila will assign an equal number of pages for each student to read aloud from a book that contains a total of 45 pages.

Therefore, the total number of pages each student will read aloud can be calculated as follows:

We have 18 student in the class that want s to read 45 pages of book equally.

Hence,

number of pages each student will read aloud = 45 / 18 = 2.5 pages

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There is not enough Evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

To test the claim that more than 20% of users of a pain medication will develop nausea, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) would be that the proportion of users who develop nausea is less than or equal to 0.20, while the alternative hypothesis (Ha) would be that the proportion is greater than 0.20.

To conduct the test, we can use the binomial distribution since we are looking at the number of successes (subjects who develop nausea) out of a fixed number of trials (total number of subjects). We can calculate the expected number of successes under the null hypothesis by multiplying the total number of subjects (239) by the assumed proportion (0.20). This gives an expected number of 47.8 subjects who would develop nausea.

We can then use a one-sample z-test to compare the observed proportion of subjects who developed nausea (52/239 = 0.218) to the expected proportion under the null hypothesis (0.20). The test statistic is calculated as (0.218 - 0.20) / sqrt(0.20 * 0.80 / 239), which is approximately 1.08.

With a significance level of 0.05 and one-sided test, the critical value for the z-statistic is 1.645. Since the calculated test statistic (1.08) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the claim that more than 20% of users of the pain medication will develop nausea.

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The total area of the figure is 272.64 yd2. Hence, the answer is option (A) 272.64 yd².

It is a trapezoid with base sides of a length of 21.3 yards and 14.9 yards, a height of 12.8 yards, and a portion of the top from the perpendicular side to a right vertex of 6.4 yards. We can use the formula for the area of a trapezoid, which is A = (b1 + b2)h/2, where b1 and b2 are the base sides, and h is the height. We have b1 = 21.3 yards, b2 = 14.9 yards, and h = 12.8 yards. To find the missing length, we can use the fact that the sum of the lengths of the two portions of the top is equal to the length of the top, which is (b1 - b2) = 6.4 + 14.9 = 21.3. Solving for b2, we get b2 = 21.3 - 6.4 = 14.9. Substituting the values in the formula, we get A = (21.3 + 14.9) x 12.8 / 2 = 272.64 yd².

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The amount of water wasted in a year is 36,960 gallons and the additional cost on the water bill due to the leaky faucet is $381.31.

(a). We know that the faucet leaks 9 oz of water per minute. There are 60 minutes in an hour and 24 hours in a day, so the total number of minutes in a day is

60 x 24 = 1440

The number of ounces of water wasted in a day is

1440 x 9 = 12,960.

To find out how many ounces of water is wasted in a year, we multiply the number of ounces wasted in a day by the number of days in a year is

12,960 x 365 = 4,734,240 oz.

To convert the number of ounces wasted in a year to gallons, we divide by the number of ounces in a gallon is

4,734,240 ÷ 128 = 36,960

(b). Water costs ​$10.31 per 1000​ gal, so to find the cost per gallon

$10.31 ÷ 1000 = $0.01031 per gallon.

To calculate the additional cost on the water bill, we multiply the number of gallons wasted in a year by the cost per gallon is

36,960 x $0.01031 = $381.31.

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The transformations that turn y = cos(x) into the graph of y = cos(5(x + 3)) - 2 is a horizontal translation of -3 units, followed by a horizontal compression by a factor of 5, and finally a vertical translation of -2 units.

To transform the graph of y = cos(x) into the graph of y = cos(5(x + 3)) - 2, we can use the following sequence of transformations:

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Answer:24x5^29

Step-by-step explanation:

(5^2 -1) x5^29

(25-1)x5^29

24x5^29

Answer:

log10(0. 01)=−2

Please mark brainliest!

Answer:

It is A. dont ask i did that on paper

(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

(a) The linear cost function C(x) can be calculated by summing the fixed costs and the variable costs. In this case, the fixed cost is $400 for the table at the art fair, and the variable cost is $7 per pair of earrings. Therefore, the linear cost function C(x) can be expressed as:

C(x) = 400 + 7x

where x represents the number of pairs of earrings produced.

(b) The average cost function C(x) is calculated by dividing the total cost (C(x)) by the number of units produced (x). So, the average cost function C(x) can be expressed as:

C(x) = (400 + 7x)/x

(c) To find C(5), we substitute x = 5 into the average cost function C(x):

C(5) = (400 + 7(5))/5 = 435/5 = $87

This means that when 5 pairs of earrings are produced, the average cost per pair of earrings is $87.

(d) To find C(50), we substitute x = 50 into the average cost function C(x):

C(50) = (400 + 7(50))/50 = 850/50 = $17

This means that when 50 pairs of earrings are produced, the average cost per pair of earrings is $17.

(e) The horizontal asymptote of C(x) is determined by the behavior of the average cost function as x approaches infinity. In this case, since the average cost function is given by C(x) = (400 + 7x)/x, the horizontal asymptote is y = 7. This means that as the number of pairs of earrings produced (x) increases indefinitely, the average cost per pair of earrings approaches $7. In practical terms, this indicates that the artist's cost of producing one additional pair of earrings (marginal cost) remains constant at $7 as production levels increase, which could suggest economies of scale, where the artist may be able to produce earrings at a lower cost per pair as production volume increases. However, this may also depend on other factors such as demand, pricing strategy, and efficiency of production processes.

So, the horizontal asymptote at y = 7 indicates the long-term cost trend for the artist's earrings production. Overall, the artist should carefully consider the production volume and associated costs to optimize their profit margins. It's also worth noting that this analysis assumes that the cost function remains linear and does not account for potential nonlinearities in the artist's cost structure. Real-world cost functions may be more complex and require further analysis. Additionally, the artist should also consider other factors such as market demand, pricing, and competition when making production decisions. Consulting with a financial or business advisor may also be beneficial for making informed decisions. Always remember to consider the specific context and assumptions when interpreting mathematical models in real-world situations. It's important to thoroughly analyze all relevant factors before making any business decisions. Safety Disclaimer: Remember to always consult with a qualified professional for financial and business advice. This response is for informational purposes only and should not be taken as financial or business advice. The accuracy and applicability of this information to your specific situation should be verified by a qualified professional.

Therefore,(a) C(x) = 400 + 7x, (b) C(x) = (400 + 7x)/x, C(5) = $87 (average cost per pair when 5 pairs produced), C(50) = $17 (average cost per pair when 50 pairs produced), horizontal asymptote at y = 7 (indicating long-term cost trend).

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Answer:

9/2 π

Step-by-step explanation:

Area of semicircle = πr²/2

The degree of the polynomial is 9.

What is polynomial in maths?

In mathematics, a polynomial is an expression composed of variables (also called indeterminates) and coefficients, and involves only addition, subtraction, multiplication, and non-negative integer powers of the variables. An example of a single indefinite x-polynomial is x2 − 4x + 7.

                                     Polynomials can be classified by the number of terms with nonzero coefficients, so a 1st polynomial is called a monomial and a 2nd polynomial is called a monomial. Binomials, tripartite polynomials are called trinomials. The term "quaternomial" is sometimes used for a fourth-order polynomial.  

Determine the degree of  y = 10x⁹ - 18x⁸ + 12x⁶

                  Degree = 9

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Answer: Since cos(theta) = 2/3 and theta is in quadrant IV, we know that sin(theta) is negative. We can use the Pythagorean identity to find the value of sin(theta):

sin^2(theta) + cos^2(theta) = 1

Substituting cos(theta) = 2/3, we get:

sin^2(theta) + (2/3)^2 = 1

Simplifying, we get:

sin^2(theta) = 1 - (2/3)^2 = 1 - 4/9 = 5/9

Since sin(theta) is negative in quadrant IV, we have:

sin(theta) = -sqrt(5/9) = -sqrt(5)/3

Therefore, sin(theta) = -sqrt(5)/3.

Step-by-step explanation:

Answer:

The recursive formula for the sequence 100, 95, 90, 85 is: a(n) = a(n-1) - 5 where a(1) = 100.

The probability that they will win the World Cup is 17.01%. This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

It is used to estimate the chance of winning, the chance of drawing a particular card, or the chance of rolling a particular number. It is a measure of the potential for a certain outcome to happen.

P(win WC| lost 1st game) = P (win WC ∩ lost 1st game) / P (lost 1st game)

P (win WC ∩ lost 1st game) = P (win WC) * P (lost 1st game| win WC)

= 0.63 * 0.27

= 0.1701

P (lost 1st game) = P (lost 1st game| win WC) + P (lost 1st game| lose WC)

= 0.27 + 0.73

= 1

Therefore, the probability that your team will win the World Cup is

0.1701 / 1 = 17.01%.

This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

This is because the team that wins the championship usually wins the first game of the series 67% of the time, so if your team did not win the first game, their chances of winning the championship decreased. Therefore, the probability that they will win the World Cup is 17.01%.

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Answer:

4 cups=2 pint

3 cups=1.5 pint

5 cups=2.5 pints

Step-by-step explanation:

Because there are 2 cups in each pint, we can divide the number of cups by two to get the number of pints.

4/2=2

3/2=1.5

5/2=2.5

Let me know if you have any questions!

If you earn a $65,000 salary, you would owe approximately $5,772.50 in FICA taxes.

As a self-employed individual on a $65,000 salary, you would owe $9,945.00 in FICA taxes.

The measure of angle ABD is 45 degrees.

What is angle?

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The two rays are also referred to as the sides of the angle.

Angles are measured in degrees, with a full circle being 360 degrees. Angles can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), and reflex (greater than 180 degrees and less than 360 degrees).

In the given diagram, we can see that angle ABD and angle BDC are complementary angles, which means they add up to 90 degrees.

We are asked to find the measure of angle ABD. To do this, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the measure of angle BCD as follows:

angle BCD = 180 - angle BDC - angle CBD

Since angle BDC and angle CBD are both 45 degrees, we have:

angle BCD = 180 - 45 - 45 = 90 degrees

Now, since angle ABD and angle BCD are both complementary to angle BDC, we have:

angle ABD = angle BDC = 45 degrees

Therefore, the measure of angle ABD is 45 degrees.

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