A tearm scores 96 in 2

matches. Find the rates of scores per match

Answer:

y=3x-7

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

Consider the coordinates of T(- 3, 3 ) → T' (3, - 1 )

- 3 → 3 is 6 units right in the positive  x-direction

3 → - 1 is 4 units down in the negative y- direction

Then translation rule is

(x, y ) → (x + 6, y - 4 )

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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Answer:

A ∪ B = [3, 9)

Step-by-step explanation:

Set X is 3, and all number greater than 3 up, but not including, 5.

Set Y is all numbers from 4 to 9, but not including 4 or 9.

The union of the sets is all numbers from 3 up to 9, including 3 but not including 9.
A ∪ B = [3, 9)

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

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Answer:

r = 7

Step-by-step explanation:

Given

3r - 5 = 16 ( add 5 to both sides )

3r = 21 ( divide both sides by 3 )

r = 7

Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

The probability of each outcome in the sample space is B. 1/20.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

For given example, the total number of students:n(S) = 5. The probability of selecting one student would be: P(A) = 1/5.

Now, there are 4 students.n(S) = 4

So, probability of selecting second student from remaining 4.P(B) = 1/4

Hence, the probability of each outcome in the sample space would be:

1/5 × 1/4

= 1/20

Therefore, the probability of each outcome in the sample space is 1/20.

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The probability of getting 5 green seeds and 1 white seed in a single pod is 0.25 or 25%.

In bush beans, green seed color is dominant to white seed color. If a heterozygous plant with green seeds (Gg) self-fertilizes, we can use the principles of Mendelian genetics to determine the probability of obtaining 6 seeds in a single pod with 5 green and 1 white seed.

When the plant self-fertilizes, each seed in the pod receives one allele from the mother plant (G) and one allele from the father plant (g). Since the plant is heterozygous (Gg), there are two possible combinations of alleles that can result in a white seed: Gg or gg. The probability of getting a white seed is equal to the probability of inheriting the gg combination.

To calculate the probability, we can use a Punnett square. When a heterozygous plant self-fertilizes, the Punnett square shows that there is a 25% chance (1 out of 4 possible combinations) of obtaining a white seed (gg). Therefore, the probability of getting 5 green seeds and 1 white seed in a single pod is 0.25 or 25%.

It is important to note that this probability assumes that the inheritance of seed color follows Mendelian genetics and that there are no other factors influencing the expression of seed color in bush beans.

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Let the areas of the three rugs be a, b, and c. Then according to the given information, a + b + c = 2200Also, area of overlap of the rugs (covered by exactly two layers of rug) = 24m²Hence, (a + b + c) – 2(area covered by two layers of rug) = area covered by three layers of rug (2200 – 2 × 24)m² = 2152m².

Therefore, area covered by three layers of rug is 2152m². Three rugs have a combined area of 2200m^2 . By overlapping the rugs to cover a floor area of 140m^2 , the area which is covered by exactly two layers of rug is 24m^2 . What area of floor is covered by three layers of rug Three rugs have a combined area of 2200m^2 . By overlapping the rugs to cover a floor area of 140m^2 , the area which is covered by exactly two layers of rug is 24m^2 .

What area of floor is covered by three layers of rug. Let the areas of the three rugs be a, b, and c. Then according to the given information, a + b + c = 2200Also, area of overlap of the rugs (covered by exactly two layers of rug) = 24m²Hence, (a + b + c) – 2(area covered by two layers of rug) = area covered by three layers of rug (2200 – 2 × 24)m² = 2152m².

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When evaluating the integral ∫ tan³x sec⁵x dx you should substitute u = sec x.

option C.

The integral of the function ∫ tan³x sec⁵x dx is determined by applying substitution method as follows;

Let u = sec x

du/dx = sec x tan x

We will substitute the value of u and solve for the integral.

∫ tan³x sec⁵x dx = ∫ tan³x (sec x)⁵ (du / (sec x tan x))

∫ tan³x sec⁵x dx = ∫ tan³x sec⁴x du

u = sec x,  so sec⁴x =  u⁴

∫ tan³x sec⁵x dx = ∫ tan³x u⁴ du

So we can conclude that, when evaluating the integral ∫ tan³x sec⁵x dx you should substitute u = sec x

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Answer:

P=21

Step-by-step explanation:

The solution to the equation P - 18 = 3 for P is P = 21

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

P - 18 = 3

Add 18 to both sides of the equation

so, we have the following representation

18 + P - 18 = 3 + 18

Evaluate the like terms on the right hand side

This gives

18 + P - 18 = 21

Evaluate the like terms on the left hand side

This gives

P = 21

Hence. the solution is 21

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Answer:

D. k(x)=x²+7

Step-by-step explanation:

f(x)=x² + 5

y=mx+c

since it is not moved horizontally the x and slope(m) will remain the same but the 2 will be added to the intercept(c) which is 5 to become seven

Step-by-step explanation:

the answer is in the above image

Answer:

61°

Step-by-step explanation:

(x+18)°=(4x-15)°alternate angles, because BC is parallel to AD

x°+18°=4x°-15°

18°+15°=4x°-x°

33°=3x°

33°/3°=3x°/3°

11=x

angle ABD

90°-(x+18)°. the sides of a rectangle meet at 90°

90°-(11+18)°

90°-(29)°

90°-29°

61°

the correct answer is 8

Answer:

X ≥ 59.50

Step-by-step explanation:

So to begin, your equation would need to solve for x. X has to be greater than or equal to the minimum amount each player needs to raise for the uniforms. To find how much money they need to raise subtract $224.36 from $759.84 to get $535.48. Divided $535.48 by 9 players to see the minimum amount they each need to contribute. You should get $59.50 roughly. So each player would need to raise greater than or equal to $59.50.

Hope this helps!

Answer:

Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.

Step-by-step explanation:

The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.

Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.

Now let's examine the given answer choices:

A. .4,4,5,5,6,6

B. .4,10,4,11,4,12

C. 8,9,8,10,8,11

D. 10,10,10,11,10,12

Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.

Therefore, based on the given scatter plot, the set of numbers that matches the points is C.

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Answer:

48 minutes

Answer:

48

The value of the integral\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\)  = 2(x²) ln(x²)² - 2(x²) ln(x²) + 2(x²) + C, where C is the constant of integration.

To evaluate the integral ∫₀^(e⁵) (ln²(x²)/x) dx, we can use a substitution. Let's set u = x², then du = 2x dx. Rearranging, we have dx = du/(2x). Substituting these into the integral, we get:

\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\) dx = ∫₀^(e⁵) (ln²(u)/(2x)) du/(2x)

= 1/4 ∫₀^(e⁵) (ln²(u)/u) du

Now, let's focus on the integral ∫₀^(e^5) (ln²(u)/u) du. We can integrate this by parts twice. The formula for integration by parts is ∫u dv = uv - ∫v du.

Let's choose:

u = ln²(u)    -->   du = 2ln(u) / u du

dv = du/u     -->   v = ln(u)

Using integration by parts, we have:

\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\) = ln²(u) * ln(u) - ∫2ln(u) * ln(u) du

Let's integrate the remaining term:

∫2ln(u) * ln(u) du = 2 ∫ln²(u) du

We can use integration by parts again:

u = ln(u)    -->   du = (1/u) du

dv = ln(u)   -->   v = u ln(u) - u

Applying integration by parts, we have:

2 ∫ln²(u) du = 2 (ln(u) * (u ln(u) - u) - ∫(u ln(u) - u) (1/u) du)

= 2 (ln(u) * (u ln(u) - u) - ∫(ln(u) - 1) du)

= 2 (ln(u) * (u ln(u) - u) - u ln(u) + u) + C

= 2u ln(u)² - 2u ln(u) + 2u + C

Now, substituting back u = x², we have:

\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\)= 2(x²) ln(x²)² - 2(x²) ln(x²) + 2(x²) + C

Therefore, the value of the integral ∫₀^(e⁵) (ln²(x²)/x) dx is:\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\) = 2(x²) ln(x²)² - 2(x²) ln(x²) + 2(x²) + C, where C is the constant of integration.

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Incomplete question:

Evaluate the following integral.

\(\int\limits^{e^{5}}_0 {ln^{2}(x^{2})/x} \, dx\)

The length of the Mural is 28 feet

Area of mural which is a rectangle= length x height

which gives 224 = length x 8

which gives length= 224/8

and gence lentgh of mural = 28 feet

The probability that an emotional health index score is less than 80.2 given that it is already less than 81 is approximately 0.141

Let A be the event that the emotional health index score is less than 80.2, and let B be the event that the emotional health index score is less than 81. Then we want to find P(A|B), the probability of A given that B has occurred.

We can use Bayes' theorem to find this probability:

P(A|B) = P(B|A) × P(A) / P(B)

where P(B|A) is the probability of B given that A has occurred, P(A) is the probability of A, and P(B) is the probability of B.

From the given data, we know that the emotional health index scores are normally distributed with a mean of 82.6 and a standard deviation of 6.8. Therefore, we can find the probabilities of A and B using the normal distribution:

P(A) = P(X < 80.2) = 0.019

P(B) = P(X < 81) = 0.135

where X is a normally distributed random variable with mean 82.6 and standard deviation 6.8.

To find P(B|A), we need to find the probability that the score is less than 81 given that it is less than 80.2. This probability can be found using the conditional probability formula:

P(B|A) = P(A and B) / P(A)

We can assume that the scores are distributed normally with the given mean and standard deviation. Then, we can use the standard normal distribution to find the probabilities:

P(X < 80.2) = (80.2 - 82.6) / 6.8 = -0.353

P(X < 81) = (81 - 82.6) / 6.8 = -0.235

The probability of A and B can be found by finding the probability of A and multiplying it by the conditional probability of B given A:

P(A and B) = P(X < 80.2 and X < 81)

= P(X < 80.2)

= 0.019

Therefore,

P(B|A) = P(A and B) / P(A)

= 0.019 / 0.019

= 1

Now we can use Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) × P(A) / P(B)

= 1 × 0.019 / 0.135

= 0.141

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The given question is incomplete, the complete question is:

what is the probability that an emotional health index scores is less than 80.2 given that it is already less than 81?

Answer:

these are what I ythink the answers are

1) C

2)A

For 1. the answer is B

Answer: A =a2

Step-by-step explanation:

The difference between the experimental probability of getting three heads and its theoretical probability is 11/40.

To find the difference between the experimental probability and the theoretical probability of getting three heads when tossing three coins simultaneously, we need to calculate both probabilities and subtract them.

The theoretical probability is determined by considering all possible outcomes and their likelihood.

When tossing three coins, there are 2³ = 8 possible outcomes since each coin can land either heads or tails.

Out of these 8 outcomes, only one outcome results in three heads.

The theoretical probability of getting three heads is therefore 1/8.

The experimental probability is determined by conducting the actual experiment and recording the observed outcomes.

The experiment was carried out 100 times, and three heads occurred 40 times.

The experimental probability of getting three heads is therefore 40/100 or 2/5.

To find the difference between the experimental probability and the theoretical probability, we subtract the theoretical probability from the experimental probability:

Experimental probability - Theoretical probability = 2/5 - 1/8

To simplify this fraction, we need to find a common denominator:

2/5 - 1/8 = (16/40) - (5/40)

= 11/40

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Answer:

false

Step-by-step explanation:

Because the length of the sides are not the same

Taylor series for x^3tan^-1x^2 at x0 = 0 can be found by using the power series operations. The Taylor series for x^3tan^-1x^2 at x0 = 0 is:

x^3tan^-1x^2 = x^3(x^2 - (x^2)^3/3 + (x^2)^5/5 - ...)

To find the Taylor series, we need to express the function as a sum of terms with powers of (x - x0). We can start by using the power series for tan^-1x:

tan^-1x = x - x^3/3 + x^5/5 - ...

Then, we substitute x^2 for x and multiply by x^3 to get:

x^3tan^-1x^2 = x^3(x^2 - (x^2)^3/3 + (x^2)^5/5 - ...)

This gives us the Taylor series for x^3tan^-1x^2 at x0 = 0.

We can simplify the expression by expanding the powers of x:

x^3tan^-1x^2 = x^5 - x^7/3 + x^9/5 - ...

This means that the function can be approximated by the sum of these terms, which become more accurate as we include more terms. The Taylor series can be useful for approximating functions and making calculations easier, especially when using computers to perform calculations.

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The correct statement regarding whether the triangle is equilateral is given as follows:

No, AB is not congruent to AC.​

An equilateral triangle is a triangle in which all the side lengths have the same measure.

Given the coordinates of the side lengths, we use the formula for the distance between two points to obtain the side lengths.

For example, the length AB is given as follows:

AB = sqrt([8 - 1]² + [-9 - 0]²)

AB = sqrt(130).

The length AC is given as follows:

AC = sqrt([1 - 9]² + [-9 - 8]²)

AC = sqrt(353).

AB is different of AC, hence the triangle is not equilateral.

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