An archaeologist found a fossil whose length is489.44 in.
Consult the conversion table to calculate the length of the fossil infeet.
Round your answer to the nearest tenth.

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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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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The distance you live from the library, would be 6. 4 miles.

Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.

Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.

The equation is:

0. 5 x = 3. 2

x = 3. 2 / 0. 5

x = 6. 4 miles

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If f(x)= √(x−1) and g(x)=12x+5, then the value of (f∘g)(2) is 2√7.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the value of (f∘g)(2), we first need to evaluate g(2), and then use the result as the input for f.

So,

g(2) = 12(2) + 5 = 24 + 5 = 29

Now, we use the value g(2) = 29 as the input for f:

f(g(2)) = f(29)

Since f(x) = √(x-1), we have:

f(29) = √(29-1) = √28 = 2√7

Therefore, the value of (f∘g)(2) is 2√7.

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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:

the answer os 53

Step-by-step explanation:

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!

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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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!

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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Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

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%

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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Answer:I need part A to answer

Step-by-step explanation:

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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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.

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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An equation that could represent P(x) include the following: A. P(x) = (x + 1)(x - 2)²

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 1 at x = -1;

x = 2 ⇒ x - 2 = 0.

(x - 2)²

x = -1 ⇒ x + 1 = 0.

(x + 1)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 2)²(x + 1)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 4), we have;

4 = a(0 - 2)²(0 + 1)

4 = a4

a = 4/4.

a = 1

Therefore, the required polynomial function is given by:

p(x) = (x - 2)²(x + 1)

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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:

[tex]\$1342.64[/tex]

Step-by-step explanation:

We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:

[tex]A = P\cdot e^{rt}[/tex]

This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]

We can now solve for [tex]A[/tex].

↓ simplifying [tex]e[/tex]'s exponent

[tex]A = \$900 \cdot e^{0.4}[/tex]

↓ plugging into a calculator

[tex]A \approx \$1342.64222788[/tex]

↓ rounding to the nearest cent

[tex]\boxed{A \approx \$1342.64}[/tex]

Answer:

Step-by-step explanation:

B. 40.63

Answer:

Step-by-step explanation:

B. 40.63

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:

Answer is obstacle by giving up yours

Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.

To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.

To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.

So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.

Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.

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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.

a. The proportion of students have scores less than 380 is 11.51%.

b. The proportion of students have scores greater than 639 is 8.23%.

1. Using the z-score formula:

We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.

Using a standard normal distribution table, we find that:

2. Similarly, a score of 639 corresponds to a z-score of 1.39.

Using a standard normal distribution table, we find that:

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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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Answer:

-78, -5/6, -0.2001, 20%

Step-by-step explanation:

The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.

-5/6 = -0.8333...

-0.2001

20% = 0.2

-78

-78 is the smallest by far

-0.8333... is the next smallest

-0.2 is next

and 0.2 is the largest