The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?

Answer:

bbbb

Step-by-step explanation:

Answer:

8(r+2)

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

You have to divide 1 and 25 and your answer will be 0.04 :)

To determine whether the given series converges or diverges, we use the Alternating Series Test.

This is because the series consists of alternating positive and negative terms whose magnitudes are decreasing. That is:

Σ (-1)"e-n 72=0= 1 - 1/ e^72 + 1/e^144 - 1/e^216 + ...

The sequence {1/e^n} is decreasing and converges to 0 as n → ∞.

Therefore, the series is alternating, decreasing, and converges to 0. Thus, the Alternating Series Test states that the given series converges. Now, we have to determine whether it is absolutely convergent or conditionally convergent. The series is not absolutely convergent because the series of absolute values of terms, Σ |(-1)"e-n| from n = 0 to ∞, is the harmonic series, which diverges. Hence, the series Σ (-1)"e-n 72=0 is conditionally convergent.

To decide whether the given series is convergent or divergent, we use the Alternating Series Test.

This is because the series consists of alternating positive and negative terms whose magnitudes are decreasing.

That is:Σ (-1)"e-n 72=0= 1 - 1/ e^72 + 1/e^144 - 1/e^216 + ...

The sequence {1/e^n} is decreasing and converges to 0 as n → ∞.

Therefore, the series is alternating, decreasing, and converges to 0. Thus, the Alternating Series Test states that the given series converges.Now, we have to determine whether it is absolutely convergent or conditionally convergent. The series is not absolutely convergent because the series of absolute values of terms, Σ |(-1)"e-n| from n = 0 to ∞, is the harmonic series, which diverges.

Hence, the series Σ (-1)"e-n 72=0 is conditionally convergent.

The given series Σ (-1)"e-n 72=0 is convergent, and it is conditionally convergent.

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Answer:

If the graph of a function f is known, it is easy to determine if the function is 1 -to- 1 . ... If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 . A function f has an inverse f−1 (read f inverse) if and only if the function is 1 -to- 1 .

Step-by-step explanation:

Plz Give brainliest

Answer:

(8/3, ∝)

Step-by-step explanation:

Definition

The Mean Value Theorem states that for a continuous and differentiable function \(f(x)\) on the closed interval [a,b], there exists a number c from the open interval (a,b) such that \(\bold{f'(c)=\frac{f(b)-f(a)}{b-a}}\)

Note:

A closed interval interval includes the end points. Thus if a number x is in the closed interval [a, b] then it is equivalent to stating a ≤ x ≤ b.

An open interval does not include the end points so if x is in the open interval (a, b) then a < x < b

This distinction is important

The function is \(y = f(x)=\ln\left(3x-8\right)\)

Let's calculate the first derivative of this function using substitution and the chain rule

Let

\(u(x) = 3x-8\\\\\frac{du}{dx} = \frac{d}{dx}(3x-8) = \frac{d}{dx}(3x) - \frac{d}{dx}8 = 3 - 0 =3\\\\\)

Substituting in the original function f(x), we get

\(y = ln(u)\\\\dy/du = \frac{1}{u}\)

Using the chain rule

\(\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}\)

We get

\(\frac{dy}{dx}=\frac{1}{u}3=\frac{1}{3x-8}3=\frac{3}{3x-8}\)

This has a real value for all values of x except for x = 8/3 because at x = 8/3, 3x - 8 = 0 and division by zero is undefined

Now \(ln(x)\) is defined only for values of x > 0. That means 3x-8 > 0 ==> 3x > 8 or x > 8/3

There is no upper limit on the value of x for ln(x) since ln(x) as x approaches ∝ ln(x) approaches  ∝ and  as x approaches ∝ 3/(3x-8) approaches 0

So the interval over which the mean theorem applies is the open interval (8/3, ∝)

At x = 8/3 the first derivative does not exist

Graphing these functions can give you a better visual representation

Answer:

57

Step-by-step explanation:

57 rad×180/pie

ans:57.296 round to 10th

equals 57

The value of the angle 1 radian to a degree is 57.25.

The standard unit of angular measurement used in many branches of mathematics is the radian, indicated by the symbol rad. It is the unit of angle in the International System of Units. Previously, the unit was a SI supplementary unit.

The one radian is equal to the 180 divided by π. So the value of one radian in degree will be calculated as,

1 Radian = 180 / π

1 Radian = 57.25°

Therefore, the value of the one radian in degree is equal to 57.25.

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The measure of angle 14 is 83° in the parallel line t and s and transversal n.

Parallel lines are a pair of lines in a two-dimensional plane that never intersect or cross each other, regardless of how far they are extended in either direction. Parallel lines have the same slope, which determines their steepness or inclination, and they maintain the same slope throughout their length.

A transversal is a line that intersects two or more other lines in a plane at distinct points. Specifically, if two or more lines in a plane are intersected by a third line, that third line is called a transversal. The lines being intersected are referred to as the "transversed lines".

According to the given information:

Given the parallel lines are t and s, the transversal are line m and n

the given angles are ∠2 = 97° and ∠6 = 83°

In the parallel lines t and s , line n is transversal

By the property that "corresponding angles are equal"

we can say that ∠5 =∠13, ∠7 =∠15, ∠6= ∠14, ∠8=∠16

given ∠6 = 83°, We know that ∠6= ∠14

∠14 = 83°       (Corresponding angles are equal)

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Answer:

I will win the war again like the last one .....

Step-by-step explanation:

if you would just maintain your natural curiosity and imaginative qualities, geometry would be the easiest of all math disciplines, because you can always "see" the things you are working with and on, almost "touch" them.

a few things you should burn into your brain though, and keep them there for the rest of your life :

Pythagoras in right-angled triangles : come on !

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90° angle). a and b are the legs of the triangle enclosing the 90° angle.

AND : the sum of all angles in a triangle is always (ALWAYS !) 180°.

so,

in the first case

x² = 6² + 6² = 36 + 36 = 72

x = sqrt(72) = sqrt(9×4×2) = 3×2×sqrt(2) = 6×sqrt(2)

FYI this is 8.485281374...

in the second case we have to use also trigonometry, a little bit (not just geometry).

first the angle at the bottom right corner is

180 - 90 - 60 = 30° (again, because the sum of all angles is 180°).

so, 8×sqrt(3) = sin(30) × x

because the basic sine and cosine values are only for the standard circle with radius = 1. for any larger (or smaller) circle these values have to be scaled up by the actual radius, which is in our case here x.

sin(30) = 0.5

so, we get

8×sqrt(3) = x/2

16×sqrt(3) = x

FYI - that is 27.71281292...

Answer:

2xz + 2yz + xy    See Below

Step-by-step explanation:

In this room, you would have one pair of walls that have the same area and a second pair of walls that would have the same area.

The first pair would be the long wall (x) times the height (z).

The second pair would be the broad wall (y) times the height (z)

So you really have just two equations:

x times z = area of one wall

x times z = area of the opposite wall

y times z = area of the other wall

y times z = area of the opposite wall

Total wall area = (x times z) + (x times z) + (y times z) + (y times z)   OR

Total wall area = 2(x times z) + 2(y times z) OR

Total wall area = 2xz + 2yz

The ceiling would be the long wall (x) times the broad wall (y)

Ceiling area = x times y  OR   xy

Total area of all 4 walls and ceiling:

2xz + 2yz + xy

The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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The conversion of 5 c to pints, represented as pt will give 2.5 pt.

The conversion rate of 1 pint to cup is at the rate of 1 pint to 2 cups. So when we have 5 cups for conversion to pints, we will have to multiply 5 cups by 1 pint and then divide the result by 2.

When this is done, the resulting figure will be 2.5 pt. In the same vein, the conversion of 2.5 pt to cup will give 5 cups. So, for the number 8 question above, we can arrive at 2.5 pt as the answer for the conversion of 5 cups to pints.

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The calculated expectation of X is 0.1

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

P{X = -1}=0.2, P{X = 0} = 0.5, P{X = 1}=0.3

The expectation of X is calculated as

E(x) = ∑xp(x)

So, we have

E(x) = -1 * 0.2 + 0 * 0.5 + 1 * 0.3

Evaluate

E(x) = 0.1

Hence, the expectation of X is 0.1

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On solving the inequality we get -6>5 which is not possible; hence there is NO SOLUTION possible for s.

We solve the given inequality for s as follows

2(4s-3) ≥ 5+8s

⇒8s - 6≥ 5 +8s

⇒ -6 > 5               (on subtracting 8s from both sides)

the last statement shows that variables cancel out from both sides of the inequality and we get -6>5 which is not possible. Because -6>5 is not possible or false, hence no value of s will be able to satisfy the given inequality. Thus the answer for s is NO SOLUTION.

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Answer:

The simplified expression is: 2(2y^3-25y-10)/y

Step-by-step explanation:

Answer:

y2-y

Simplify ———————

y2 - 25

2.1 Pull out like factors :

y2 - y = y • (y - 1)

2.2 Factoring: y2 - 25

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Check : 25 is the square of 5

Check : y2 is the square of y1

Factorization is : (y + 5) • (y - 5)

Final result

4y

—————

y + 5

Step-by-step explanation:

hope it helps

(a) In the equilibrium bidding strategy, bidders bid below their cost. The difference between a contractor's quote and their cost represents their strategic behavior in the auction.

By bidding below their cost, contractors try to increase their chances of winning the auction and securing the project.

This strategy allows them to potentially earn a higher profit if they win the auction and their cost turns out to be lower than their bid.

(b) The probability of contractor A winning when she submits a quote equal to b and contractor B submits a quote according to the equilibrium bidding function β(⋅) can be calculated as follows:

P(A wins) = P(A's bid ≤ B's bid)

Since the contractors' costs are independently drawn from a Uniform [0,1] distribution, the probability can be expressed as:

P(A wins) = P(A's cost + A's bid ≤ B's cost + B's bid)

Given that A's bid is b and B's bid is β∗(B's cost), the probability becomes:

P(A wins) = P(A's cost + b ≤ B's cost + β∗(B's cost))

(c) Contractor A's expected payoff when she has a cost of completing the project equal to c and submits a quote equal to b, while her rival bids according to the equilibrium strategy βx(⋅), can be calculated as follows:

Payoff(A) = P(A wins) × (b - c)

Using the probability expression from part (b), the expected payoff can be written as:

Payoff(A) = P(A's cost + b ≤ B's cost + βx(B's cost) × (b - c)

(d) To show that the bidding strategy βx(c) = 2/(1+c) is a (symmetric) Bayesian Nash Equilibrium, we need to verify two conditions:

(i) the strategy is optimal for a contractor given the strategies of other bidders, and

(ii) no bidder has an incentive to deviate from the equilibrium strategy.

(i) Optimality: Given the bidding strategy βx(c) = 2/(1+c), a bidder's expected payoff is maximized when they follow this strategy. This can be shown by calculating the expected payoff for a bidder who anticipates a cost of completing the project as c and submits a quote equal to βx(c). The expected payoff is maximized when the bidder follows the equilibrium strategy.

(ii) No incentive to deviate: Suppose a bidder deviates from the equilibrium strategy and chooses a different bidding strategy. In this case, the bidder's expected payoff would be lower than or equal to the expected payoff obtained by following the equilibrium strategy. Therefore, no bidder has an incentive to deviate from the equilibrium strategy, indicating that βx(c) = 2/(1+c) is a Bayesian Nash Equilibrium.

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The perimeter of the given square region is 28 cm if 1 cm square tiles form a rectangular region with a perimeter of 30 cm.

Let's start by setting up some equations based on the given information. Let x and y be the dimensions of the rectangular region in terms of the number of tiles. Then we have

Perimeter of the rectangular region: 2x + 2y = 30

Area of the rectangular region: xy

Number of tiles used: xy

Since the same number of tiles can also form a square, we know that the area of the square is also xy. Let s be the length of a side of the square in terms of the number of tiles. Then we have

Area of the square: s²

Number of tiles used: s²

Setting the expressions for the number of tiles used equal to each other, we get

xy = s²

Solving for y in terms of x using the perimeter equation, we get

y = 15 - x²

Substituting this into the expression for xy, we get

x(15 - x) = s²

Expanding and rearranging, we get

x² - 15x + s² = 0

This is a quadratic equation in x, and we can solve for x using the quadratic formula

x = (15 ± √(225 - 4s²)) / 2

Since x and y must be positive, we can only take the positive root. We also know that x must be an integer (since it represents the number of tiles in a dimension), so we can restrict our attention to integer values of s that make 225 - 4s² a perfect square. The possible values of s are 1, 2, 3, 4, 5, 6, 7, and 8.

For each value of s, we can compute x using the formula above. For example, when s = 1, we get

x = (15 + √221) / 2 ≈ 8.02

This is not an integer, so s = 1 does not work. Continuing in this way, we find that the only value of s that gives an integer value of x is s = 5, which gives

x = (15 + √65) / 2 ≈ 7.38

Rounding to the nearest integer, we get x = 7 and y = 8. Plugging these values back into the perimeter equation, we find that the perimeter of the rectangular region is 30 cm, as required. The side length of the square is also 7 cm (since it has the same area as the rectangular region), so the perimeter of the square is 4 × 7 = 28 cm. Therefore, the answer is 28 cm.

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Answer:

he needs 10 c

Step-by-step explanation:

Jorge needs 10 large c because 6 large salads need 10 tomatoes

Answer:

C

Step-by-step explanation:

-2x+6 \(\geq\)-4

     -6   -6

-2x \(\geq\)-10

divide both sides by -2

-2/2=-1

-10/2=-5

-5*-1=5

x\(\geq\)5

x is greater than 5 so the number should be larger than 5 or equal to 5.

Answer: an acute angle so it bout 55

Step-by-step explanation:

Answer:

Ordered Pair An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Step-by-step explanation:

i hope this helped! :)

Answer:

An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.

Step-by-step explanation:

Answer:

28 and 29

Step-by-step explanation:

the equation is x÷7≤4

26÷7= 3.7 ≠ x÷7≤4

27÷7= 3.8 ≠ x÷7≤4

28÷7=4

29÷7= 4.14=x÷7≤4

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

The width is 24 inches and the length is 120 inches.

Step-by-step explanation:

Let x represent the width of the carpet

The length can be represented by x + 96

Create an equation:

x + x + x + 96 + x + 96 = 288

Add like terms and solve for x:

4x + 192 = 288

4x = 96

x = 24

So, the width is 24 inches. Plug this into x + 96 to find the length:

x + 96

24 + 96

= 120

So, the width is 24 inches and the length is 120 inches.

Answer:

answer is 4 goals per hour

Step-by-step explanation:

12 Divided by 3 is 4

Answer:

4 goals per hour.

Step-by-step explanation:

0.0945 (approx)  is the probability that exactly 12 of them are strikes.

p(x=12)

nC12(p)12 (q) (n-12)

22C12 (0.431)12 (0.569)(22-12)

=646646(0.431)12 (0.569)10

=0.094518

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula.

probability = number of paths to success—a total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

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