Which piecewise function is shown on the graph?

A.) The length of the missing part of the triangle would be given as follows;

a = 4

b = 3

To calculate the missing part of the triangle, the sine formula should be used such as follows;

x /SinX = b/sinB

where;

x= 5

X = 90

b = ?

B = 37°

That is;

5/sin90 = b/sin37

make b the subject of formula;

b = 5× 0.601815023/1

= 3

a² = C²- b²

= 25-9

= 16

a = √16 = 4

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The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

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The values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.

The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.

We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):

μ[tex]= 7000/16,780 = 0.4168[/tex]

We can use μ as the value of λ in the Poisson distribution since they are equal.

To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:

P(x=3) = (e^(-λ) * λ^x) / x!

where x = 3.

Substituting the values we have:

[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]

Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:

[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]

[tex]P(x=3) ≈ 0.000305[/tex]

Therefore, the values we used in the Poisson probability formula are:

μ = λ = 0.4168

x = 3

e ≈ 2.718

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It can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.

Therefore, X= 2.7532; T = 0.1203; P = 0.4524.

H0: ‘The mean class GPAs for a given course’ is equal to 2.75.

H1: ‘The mean class GPAs for a given course’ exceeds 2.75.

Our 'sample size' n = 50 and we calculate the ‘sample mean and sd’ with 'Excel', through its respective code ‘AVERAGE()’.

The resultant ‘sample mean’ xbar equals to 2.7532, while implementing the code ‘STDEV.S()’ gives us the ‘sample sd’ s being 0.188164.

The ‘hypothesized mean’ μ0 is again fixed at 2.75. Given that the ‘population sd is unknown’, we are obliged to perform a ‘t-test’ in order to receive our data.

Evaluating this test statistic provides us with-

T = (xbar-μ0)/(s/√n)

= (2.7532-2.75)/(0.188164/√50)

= 0.0032/0.0266

= 0.1203

Also, taking into account the 'degrees of freedom', which is (n-1), we figure out that it sums up to 49.

After conjuring a 'students t distribution', we get a P-value of 0.4524. Hereby, as the ‘P-value surpasses the significant level of 0.05’, the ‘null hypothesis fails to be dismissed’.

Consequently, it can be concluded that there exists ‘insufficient evidence’ depicting that the ‘new mean GPA is more than 2.75’.

Therefore, X= 2.7532; T = 0.1203; P = 0.4524.

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The two figures that have the same number of cubes are given.

We have,

The number of cubes in each figure drawn = 5 cubes

We can also find the area of each figure,

Consider each cube has a side of 2 cm

Figure 1:

Two rectangles.

So,

Area = 6 x 2 + 4 x 2 = 12 + 8 = 20 square units

Figure 2:

Area = 10 x 2 = 20 square units.

Thus,

The two figures that have the same number of cubes are given.

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Okay, let's break this down step-by-step:

U = {x | x < 20, x is a natural number}

A = {x | 3 < x < 15}

B = {x | 1 < x < 15}

C = {x | x is an odd number, x is a natural number}

(a) A n B' (using De Morgan's law: A n B' = A' U B')

= {x | x ≥ 15 or x ≥ 3}

= {16, 17, 18, 19}

(b) B C' U A

= B U (C' U A)

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} U {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

(c) (A' n C ')

= (A' C') (by De Morgan's law)

= {x | x > 15 and x is even, x is a natural number}

= {16, 18}

The Venn diagram would be:

U A B C

_____|_____|_____|_____

| | | |

| | | |

| | ___|_____|___

| | | |

| | | 16, 17, 18, 19

| | | |

| | |_____|_____|___

| | | | |

| | | ___|_____|___

| | | | 16, 18

| | | |_____|_____|___

Does this make sense? Let me know if you have any other questions!

a) P(psychology student)  = 1/3. b) P(psychology or anthropology student)  = 5/6. c) P(not sociology student)= 5/6

(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:

P(psychology student) = 4/(6+2+4) = 4/12 = 1/3

(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:

P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6

(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:

P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6

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Step-by-step explanation:

We can use the binomial distribution to compute the probability that exactly 91 out of 153 registered voters will vote in the presidential election, assuming that the probability that any given registered voter will vote in the presidential election is 59%.

The probability mass function of the binomial distribution is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

- n is the number of trials (in this case, the number of registered voters)

- k is the number of successes (in this case, the number of registered voters who will vote in the election)

- p is the probability of success on any individual trial (in this case, the probability that a given registered voter will vote in the election)

Using this formula, we can calculate:

P(exactly 91 out of 153 voters will vote) = (153 choose 91) * 0.59^91 * (1 - 0.59)^(153 - 91)

= 0.037

Therefore, the probability that exactly 91 out of 153 registered voters will vote in the presidential election is approximately 0.037, or about 3.7%.

Answer:

A: (2x + 7)(5x + 9) = 10x^2 + 53x + 63

B: second-degree (quadratic) polynomial

C: The product of two polynomials is a polynomial.

Part A: we simply need to multiply this out using the distributive property:

Area = 2x5x + 2x9 + 75x + 79

= 10x² + 18x + 35x + 63

= 10x² + 53x + 63 (4 points)

Part B:A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)

Part C:In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)

Part A:

The area of a rectangle is given by the product of its length and width. Therefore, for a rectangle with sides measuring (2x + 7) units and (5x + 9) units, the area can be represented as:

Area = (2x + 7)(5x + 9)

Now, we simply need to multiply this out using the distributive property:

Area = 2x5x + 2x9 + 75x + 79

= 10x² + 18x + 35x + 63

= 10x² + 53x + 63 (4 points)

Part B:

The degree of a polynomial is the highest power of x in the polynomial. Here, the highest power of x is 2 (in the term 10x²), so the degree of this polynomial is 2.

A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)

Part C:

The closure property of an operation (like addition, multiplication, etc.) on a set says that applying the operation to any elements in the set always results in an element that is also in the set.

In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)

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Answer:

  162 square units

Step-by-step explanation:

You want the surface area of the trapezoidal prism.

The triangle at the top of each base is a right triangle with leg 3 units and hypotenuse 5 units. This tells you it is a 3-4-5 right triangle and the width of the prism is 4 units.

The area of each trapezoidal base is ...

  A = 1/2(b1 +b2)h = 1/2(3 +6)(4) = 18 . . . . . square units

The lateral area is the product of the height of the prism (7) and the perimeter of the base. The vertical edges of the base are 3 and 6, the horizontal edge is 4 (see above), and the slant edge is shown as 5. This means the perimeter is 3+6+4+5 = 18 units.

The lateral area of the prism is ...

  LA = Ph = (18)(7) = 126 . . . . . square units

The total surface area of the prism is the sum of the areas of the two bases and the lateral area:

  2(18) +126 = 162 . . . . . . square units

The surface area of the composite solid is 162 square units.

__

Additional comment

If you have forgotten about the 3-4-5 right triangle, you can find the missing side length using the Pythagorean theorem.

  a² +b² = c²

  3² +b² = 5²

  b² = 25 -9 = 16

  b = √16 = 4 . . . . . . the missing triangle side is 4 units long

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1) Percent of time that customers at the old store bought milk shakes is: 20%

2) Percent of time that customers at the new store bought milk shakes is:

26%

3) Percent of total sales that were ice cream is: 78%

4) Percent of new store sales of both shops is: 35%

We are given the following parameters:

Number of Servings of Icecream in Old store = 52100

Number of milk shakes in old store = 13400

Number of Servings of Icecream in New store = 25800

Number of milk shakes in new store = 9200

1) Percent of time that customers at the old store bought milk shakes is:

Percentage = [13400/(52100 + 13400)] * 100%

≈ 20%

2) Percent of time that customers at the new store bought milk shakes is:

Percentage = [9200/(25800 + 9200)] * 100%

≈ 26%

3) Percent of total sales that were ice cream:

Percentage = [(52100 + 25800)/(52100 + 25800 + 13400 + 9200)] * 100%

≈ 78%

4) Percent of new store sales of both shops is:

Percentage = (25800 + 9200)/(52100 + 25800 + 13400 + 9200)] * 100%

≈ 35%

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Answer:

1:4

Step-by-step explanation:

30% of (B - A) = 18% of (A + B)

0.3(B - A) = 0.18(A + B) (converting percentages to decimals)

0.3B - 0.3A = 0.18A + 0.18B (distributing on both sides)

0.3B - 0.18B = 0.18A + 0.3A (grouping like terms)

0.12B = 0.48A

Simplifying further gives:

B/A = 0.48/0.12 = 4/1

Therefore, the ratio of A:B is 1:4.

Let's start by simplifying the given equation:

30% of (B-A) = 18% of (A+B)

0.3(B-A) = 0.18(A+B)

0.3B - 0.3A = 0.18A + 0.18B

0.12B = 0.48A

B = 4A

Now we know that B is 4 times A.

To find the ratio A:B, we can express B in terms of A:

B = 4A

A:B = A/4A = 1/4

Therefore, the ratio A:B is 1:4.

Answer:I need part A to answer

Step-by-step explanation:

The equation of the transformed function is y = -f(x + 6)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x

On simplifying , we get

Reflecting over the x-axis: To reflect a function over the x-axis, we multiply the function by -1. This changes the sign of the y-coordinate of each point on the graph of the function. So, the function after reflection over the x-axis would be y = -f(x).

Translating 6 units left: To translate a function 6 units to the left, we replace x with (x + 6). This shifts the graph of the function horizontally to the left by 6 units. So, the function after translation 6 units left would be y = -f(x + 6)

Hence , the function is y = -f(x + 6)

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The proportion of cans that are scrapped is approximately 0.0241.

We know that the fill volume of cans follows a normal distribution with a mean of 367 ml and a standard deviation of 3 ml. Let's define X as the fill volume of a single can. Then we can write:

X ~ N(367, 3)

We want to find the proportion of cans that are scrapped, i.e., the proportion of cans with a fill volume less than 358 ml or greater than 373 ml. Let's call this proportion p:

p = P(X < 358 or X > 373)

To solve this problem, we can use the standard normal distribution and the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution. We can standardize the values 358 and 373 using this formula:

z1 = (358 - 367) / 3 = -3

z2 = (373 - 367) / 3 = 2

Now we can find the probabilities of the two events separately using the standard normal distribution table or a calculator:

P(X < 358) = P(z < -3) ≈ 0.0013

P(X > 373) = P(z > 2) ≈ 0.0228

The probability of either event happening is the sum of the probabilities:

P(X < 358 or X > 373) = P(X < 358) + P(X > 373) ≈ 0.0241

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Answer:

Step-by-step explanation:

B. 40.63

Answer:

Step-by-step explanation:

B. 40.63

multiply each shapes by length x width

Step-by-step explanation:

an example:

5x3 is 15

then do that for all of the shapes in this photo then add all of your answer together to get you're area

hope this helps

Using the Pythagorean's theorem we can see that the length of the ramp is 6.32ft

We know that the ramp is a right triangle whose legs are 2 ft and 6 ft. Remember that by Pythagorean's theorem we know that the square of the hypotenuse is equal to the sum of the squares of the legs.

Then the length of the ramp L will be:

L² = (2ft)² + (6ft)²

L = √((2ft)² + (6ft)²)

L = 6.32ft

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Answer:

the answer os 53

Step-by-step explanation:

a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.

b)  If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.

The credit card balance refers to the difference between the beginning balance, payments, and interests.

a) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = 15%

= $225 ($1,500 x 15%)

Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)

Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)

b) Current balance on a credit card = $1,500

Interest rate = 15.99%

Minimum payment = $75

Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)

Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)

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The percent of the raisins that Victoria she keep for herself is 70%

Based on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.

Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:

= (1 - 3/10) × 100

= 70%

Therefore, the percent of the raisins that Victoria she keep for herself is J 70%

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Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.

About what percent of the raisins did she keep for herself?

F 30%

G 33%

H 66%

J 70%

Answer:     <ABC =  <GHI     transitive property

Step-by-step explanation:

<ABC =  <GHI     transitive property

this is because if you have <B=<E and <H=<E   then <B=<H

thisis a tranisitive property

The system of equations that can be used to determine q and n is:

25q + 5n = 355

q = 2n - 5

We have,

Let's use q to represent the number of quarters and n to represent the number of nickels.

The value of q quarters is 25q cents, and the value of n nickels is 5n cents.

The total value of Mariano's coins is 3.55, or 355 cents.

We can write the first equation based on these values:

25q + 5n = 355

The second sentence tells us that the total number of coins is 5 less than twice the number of nickels.

Since each nickel is one coin, the number of quarters must be two less than the total number of coins.

We can write the second equation based on this information:

q = 2n - 5

Therefore,

The system of equations that can be used to determine q and n is:

25q + 5n = 355

q = 2n - 5

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If Lily took a survey of 80 students of 7th grade and 150 students of 8th grade, then there are 64 "7th" grade students, and 90 "8th" grade students who like music.

First we find the the number of students who like music in "7th-grade".

Number of 7th grader students that are being surveyed = 80,

Percent of 7th graders who like country music = 80%,

So, Number of 7th graders who like country music are

⇒ 80% of 80 = 0.8 × 80 = 64

So, 64 out of the 80 students in 7th grade like country music.

For 8th graders;

Number of "8th-grader" students that are being surveyed = 150,

Percent of 8th graders who like country-music = 60%,

So, Number of 8th graders who like country music

⇒ 60% of 150 = 0.6 × 150 = 90,

Therefore, 90 out of the 150 students in 8th grade like country music.

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The given question is incomplete, the complete question is

Lily took a survey of 80 students on 7th grade and 150 students in 8th grade she found that 80% of the 7th graders like country music while only 60% of the 8th graders like it. Find the number of students from each grade who like music.

Answer:

a discount rate of 5%

Step-by-step explanation:

The formula to calculate the present value of a perpetuity is:

PV = PMT / r

Where PV is the present value, PMT is the constant payment, and r is the discount rate.

In this case, the PMT is $25,000 and the PV is -$500,000 (negative because it represents a cash outflow). So we can rearrange the formula to solve for r:

r = PMT / PV

r = $25,000 / -$500,000

r = -0.05 or -5%

Therefore, at a discount rate of 5%, the policy would be a fair deal.

To calculate this in Excel, you can use the following formula in a cell:

=r(-25000/500000)

This will give you a result of -0.05, or -5%, which represents the fair discount rate.

Hope this helps!

The triangle presented in the diagram drawn is known as equilateral triangle.

A triangle with angle 60 degrees is known as equilateral triangle because the sum of angles in a triangle is 180 degrees.

So if the total angles in a triangles is 180 degrees, and two known angles are 60 degrees, then the remaining side will be 60 degrees.

In an equilateral triangle, each of the interior angle measures 60 degrees.

Thus, the triangle presented in the diagram drawn is known as equilateral triangle.

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Answer:

Answer is obstacle by giving up yours

Answer:

First, we need to calculate Michael's daily interest rate:

0.1199 / 365 = 0.0003282

Then, we can calculate his daily finance charge:

327.50 x 0.0003282 = 0.1075

To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:

0.1075 x 30 = 3.225

So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).

The number of solutions to the system of equations is n = 0

Given data ,

Let the first equation be represented as A

-6x - 4y = -4   be equation (1)

Let the second equation be represented as B

3x + 2y = 6   be equation (2)

Now , on simplifying , we get

-6x - 4y = -4

Multiply by -1 on both sides , we get

6x + 4y = 4

Divide by 2 on both sides , we get

3x + 2y = 2   be equation (3)

Now , the equation (2) and ( 3) are similar but the constant term is different

The slope of the first equation is -3/2 and the slope of the second equation is also -3/2. Since the slopes are the same, the two lines are parallel to each other.

When two lines are parallel, they never intersect, which means there are no common solutions for the system of equations

Hence , the equations are solved

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