There are 30 stuffed animals in a gift gallery.
Seven more stuffed animals added to the collection.
Find the total number of animals.

There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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Answer:

78

Step-by-step explanation:

Given:

h + 9g

Required:

Evaluate when g = 8 and h = 6

Solution:

Plug in the values of the variables into the expression

Thus,

6 + 9(8)

= 6 + 72

= 78

To verify the zeros of the function f(x) = -x^3 - 7x^2 - 7x + 15 at x = -5, -3, and 1, we need to substitute these values into the function and check if the result is zero.

1. For x = -5: f(-5) = -(-5)^3 - 7(-5)^2 - 7(-5) + 15 = 0
2. For x = -3: f(-3) = -(-3)^3 - 7(-3)^2 - 7(-3) + 15 = 0
3. For x = 1: f(1) = -(1)^3 - 7(1)^2 - 7(1) + 15 = 0

As f(x) evaluates to zero for all three values, we can confirm that -5, -3, and 1 are indeed the zeros of the function.

To describe the end behavior of the function, we can look at the leading term, which is -x^3. Since the exponent is odd and the coefficient is negative, the end behavior is as follows:

- As x approaches positive infinity, f(x) approaches negative infinity
- As x approaches negative infinity, f(x) approaches positive infinity

This means that the graph of the function starts in the top left quadrant (when x is very negative) and ends in the bottom right quadrant (when x is very positive).

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The dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

In three dimensional space prism is a polyhedron where two ends are similar.

Given that volume of rectangular prism is 168 cubic centimeters.

And the wooden block is 2x cm tall, (x-4) cm wide and (x-3) cm long.

And also given that a wooden block in a set of building blocks is a rectangular prism.

That means,

Volume of wooden block = Volume of rectangular prism = 168 cm³

Volume of wooden block ;

length × width × height = 168 cm³

Substituting given values in above expression,

2x (x-3) (x-4) = 168 cm³

2x (x²-7x + 12) = 168 cm³

2x³ - 14x²+ 24x = 168 cm³

Simplifying the above equation;

2x³ - 14x²+ 24x- 168 = 0

x³ - 7x²+ 12x- 84 = 0

The factor of above cubic equation is x = 7.

Now the 2x = 14 , x-3 = 4, x-4 = 3.

Therefore the dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.

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Answer:

variable would be best modeled as discrete

Step-by-step explanation:

Since there are finite students and finite backpacks, so the weights will also be finite and hence countable, so the variable would be best modeled as discrete

The amount of space that a particular substance or object holds usually within a container.

Answer:

  8%

Step-by-step explanation:

You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.

The fraction of the total number that had whipped cream is ...

  2/(2+23) = 2/25

The percentage is found by multiplying the fraction by 100%:

  2/25 × 100% = 8%

8% of the milkshakes had whipped cream.

By solving a linear equation we will see that the value of x is 10.

Remember that for any triangle, the sum of all internal angles is always equal to 180°.

Here only look at triangle BCD, we know that:

m∠DBC = m∠ABC = 3x

m∠BCD = m∠ACB + m∠ABD = 2x + 65°

m∠ADC = 65°

Now we can write the linear equation as:

3x + 2x + 65° + 65° = 180°

5x + 130° = 180°

5x = 180° - 130°

5x = 50°

x = 50°/5 = 10°

The value of x is 10.

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Answer:

I am not 100% confident, but I think that she is 11.

Step-by-step explanation:

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

\((x - 5)^2=5x+11\)

To find Zeba's age now, solve the equation for x.

Expand the brackets:

\(\implies x^2-10x+25=5x+11\)

Subtract 5x from both sides:

\(\implies x^2-10x+25-5x=5x+11-5x\)

\(\implies x^2-15x+25=11\)

Subtract 11 from both sides:

\(\implies x^2-15x+25-11=11-11\)

\(\implies x^2-15x+14=0\)

Factor the found quadratic

To factor a quadratic in the form \(ax^2+bx+c\), find two numbers that multiply to \(ac\) and sum to \(b\), then rewrite \(b\) as the sum of these two numbers:

\(\implies x^2-14x-x+14=0\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-14)-1(x-14)=0\)

Factor out the common term (x - 14):

\(\implies (x-1)(x-14)=0\)

Apply the zero product property:

\(\implies (x-1)=0 \implies x=1\)

\(\implies (x-14)=0 \implies x=14\)

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

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Answer:

− 3 w 2 + 9 w + 1

The scores that need to be examined in order to determine the median value of n = 24 are the 12th and 13th values.

In order to determine the median value of n = 24, you would need to examine the 12th and 13th scores. This is because the median value is the middle number of a sequence of values, so when there is an even number of values, the median is the average of the two numbers in the middle. So in the case of n = 24, there are two values in the middle, the 12th and 13th numbers. To find the median, you would need to add the two values together and divide the result by two. This will give you the median value of the sequence. If there were an odd number of values instead of an even number, then the median would be the middle number rather than the average of two numbers.

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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Answer:

11.17

120-8.30 an then ÷10

Answer:

120 - (10b) = $8.30

Step-by-step explanation:

Answer:

%41.8 or 0.418

Step-by-step explanation:

I didn't know how you wanted the answer so there.

To get the answer you divide 627 by 1500 to get 0.418 then multiply that by 100 to get your percent.

hope this helps. . .

have a good day. UwU

Answer:

41.8%

Step-by-step explanation:

(627/1500) * 100 = 41.8

While calculating percentage for such questions, the total always is the denominator, while 'to be found percentage number' is the numerator.

Hope it helps!

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:10X^2 +7

Step-by-step explanation:

There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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Answer:

Your other answers all look good - I think the word in the blank is producer, which means an organism that makes its own food. Green plants do so through photosynthesis.

Answer:

producer

Step-by-step explanation:

Because it makes sense

The amount of inventory that Baryla can hold is **$16.1 million**.

The inventory turnover ratio is calculated as sales / inventory. To maintain an inventory turnover ratio of at least 5.6, Baryla's inventory must be no more than $90 million / 5.6 = $16.1 million.

Calculation:

```

sales = $90 million

gross profit margin = 35%

inventory turnover ratio = 5.6

inventory = sales / inventory turnover ratio = $90 million / 5.6 = $16.1 million

```

**b. Currently, some of Baryla's inventory includes $1.5 million of outdated and damaged goods that simply remain in inventory and are not salable. What inventory turnover ratio must the good inventory maintain in order to achieve an overall turnover ratio of at least 5.6 (including the unsalable items)?**

The good inventory must maintain an inventory turnover ratio of **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

The overall inventory turnover ratio is 5.6, and the unsalable inventory is $1.5 million. This means that the good inventory is $90 million - $1.5 million = $88.5 million.

The good inventory must maintain an inventory turnover ratio of $88.5 million / 5.6 = **9.4 times** in order to achieve an overall turnover ratio of at least 5.6.

overall inventory turnover ratio = 5.6

unsalable inventory = $1.5 million

good inventory = $90 million - $1.5 million = $88.5 million

good inventory turnover ratio = $88.5 million / 5.6 = 9.4 times

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Answer:

29.5735296 cc = 1 oz

The pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

A pentagonal prism is a prism that has two pentagonal bases like top and bottom and five rectangular sides.

Given that, the volume of a pentagonal prism is 360 in³, with a height of 3 inches,

We need to find the area of the base,

We know that, the volume of a pentagonal prism is =

V = 1/4 √(5(5+2√5)·a²h

Where a is the base edge and h is the height,

360 = 1/4·3 √(5(5+2√5)·a²

1/4·√(5(5+2√5)·a² = 120

Since, the base of a pentagonal prism is a pentagon, and the area of a pentagon = 1/4 √(5(5+2√5)·a²

And we have,

1/4 √(5(5+2√5)·a² = 120

Therefore, the base area is 120 in²

Hence, the pentagonal prism with volume 360 in³ and height of 3 inches have a base area of 120 in²

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9514 1404 393

Answer:

  (2x +y)(2x -y +6)

Step-by-step explanation:

The shaded area is the difference of the areas of the outer square and the inner square. In turn, those areas are the square of the edge dimension of the square. So, the shaded area is the difference of squares:

  area = (2x +3)² -(y -3)²

The difference of squares is a "special product" in that it has a factored form that is worth remembering.

  a² -b² = (a -b)(a +b)

Using this form for our area, we have ...

  area = ((2x +3) -(y -3))((2x +3) +(y -3))

  area = (2x -y +6)(2x +y)

Answer:

1. (2.2, -1.35) and (2.2, -1.4)

2. y = 8x - 7

3. infinite number of solutions

4. (2.2,-1.4) (2.2,-1.35)

5. 6

6. (1.33,1)

Step-by-step explanation:

The area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

To find the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ), we need to determine the limits of integration for θ.

First, let's find the values of θ where the circle and the vertical line intersect:

r = 4cos(θ)

sec(θ) = 4cos(θ)

To simplify the equation, let's convert sec(θ) to its reciprocal form:

1/cos(θ) = 4cos(θ)

Multiplying both sides by cos(θ), we get:

1 = 4\(cos^2\)(θ)

Rearranging the equation, we have:

4\(cos^2\)(θ) - 1 = 0

Using the identity \(cos^2\)(θ) - \(sin^2\)(θ) = 1, we can rewrite the equation as:

\(cos^2\)(θ) - \(sin^2\)(θ) = 1/4

Applying the double-angle formula for cosine, we get:

cos(2θ) = 1/4

Taking the inverse cosine of both sides, we have:

2θ = ± \(\cos^{-1}\left(\frac{1}{4}\right)\)

Solving for θ, we get two values:

θ = ± (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Since we are interested in the region to the right of the vertical line, we'll consider the positive value of θ:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Now, we can find the area by evaluating the integral:

A = ∫[θ, π/2] 1/2 (\(r^2\)) dθ

Substituting the equations for r, we have:

\(A = \int_{\theta}^{\frac{\pi}{2}} \frac{1}{2} (4\cos^2(\theta)) \, d\theta\)

Simplifying further:

\(A = \int_{\theta}^{\frac{\pi}{2}} 8\cos^2(\theta) \, d\theta\)

Using the double-angle formula for cosine, we have:

A = ∫[θ, π/2] 4(1 + cos(2θ)) dθ

Integrating term by term, we get:

A = [4θ + 2sin(2θ)] evaluated from θ to π/2

Now, Substituting the limits of integration, we get:

A = [4(π/2) + 2sin(2(π/2))] - [4θ + 2sin(2θ)] evaluated from θ to π/2

Simplifying:

A = 2π + 2sin(π) - (4θ + 2sin(2θ))

Since sin(π) = 0, we can simplify further:

A = 2π - (4θ + 2sin(2θ))

Now, we need to substitute the value of θ, which we found earlier:

θ = (1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)

Substituting this value, we have:

A = 2π - (4(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(2(1/2) \(\cos^{-1}\left(\frac{1}{4}\right)\)))

Simplifying:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2sin(\(\cos^{-1}\left(\frac{1}{4}\right)\)))

Since cos(\(\cos^{-1}\left(x\right)\)) = x, we have:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(1 - (1/4)^2)))

Simplifying further:

A = 2π - (2 \(\cos^{-1}\left(\frac{1}{4}\right)\) + 2(√(15/16)))

A = 2π - 2 \(\cos^{-1}\left(\frac{1}{4}\right)\) - √15

So, the area of the region inside the circle r = 4cos(θ) and to the right of the vertical line r = sec(θ) is \(2\pi - 2\cos^{-1}\left(\frac{1}{4}\right) - \sqrt{15}\).

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The expression that simplifies to 2/15 is 4/30.

Option C is the correct answer.

We have,

To find the expression that simplifies to 2/15, we need to simplify each option and see which one equals 2/15.

Let's simplify each option:

A) 4/17: This expression cannot be simplified further. It does not equal 2/15.

B) 6/19: This expression cannot be simplified further. It does not equal 2/15.

C) 4/30: We can simplify this expression by dividing both the numerator and denominator by their greatest common divisor, which is 2. Simplifying gives us 2/15, so option C equals 2/15.

D) 12/60: We can also simplify this expression by dividing both the numerator and denominator by their greatest common divisor, which is 12. Simplifying gives us 1/5, not 2/15.

Therefore,

The expression that simplifies to 2/15 is 4/30.

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The complete question:

Which expression simplifies to 2/15 ??

A 4/17

B 6/19

C 4/30

D 12/60

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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If f(x) is an antiderivative of x^2/1 x^5, such that f(1)=0 then :

f(4) = 15/32

We can use the fundamental theorem of calculus to solve this problem. According to the theorem, if f(x) is an antiderivative of x^n, then ∫[a,b] x^n dx = f(b) - f(a).

In this case, f(x) is an antiderivative of x^2/1 x^5. We can simplify this expression to x^-3 and apply the theorem.

∫[1,4] x^-3 dx = f(4) - f(1)

Using the power rule of integration, we have:

∫[1,4] x^-3 dx = [-x^-2/2] from 1 to 4
= [-1/32] - [-1/2]
= 15/32

Therefore, f(4) - f(1) = 15/32. We know that f(1) = 0, so we can simplify:

f(4) - 0 = 15/32
f(4) = 15/32

Therefore, f(4) = 15/32.

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