A math test has 12 multiplication problems and 24 division problems.

What is the ratio value of multiplication problems to division problems?

Answer as a fraction in simplest form.

the assumption being that h(t) is the height of the rock in "t" seconds, so by the time the rock hits the ground h(t) = 0, namely it has reached 0 height because, well, is on the ground :)

[tex]h(t)=36t^2 - 64\implies 0=36t^2 - 64\implies 64=36t^2\implies \cfrac{64}{36}=t^2 \\\\\\ \sqrt{\cfrac{64}{36}}=t\implies \sqrt{\cfrac{16}{9}}=t\implies \cfrac{4}{3}=t\implies 1.\overline{33}=t[/tex]

If Kashif and Ali invested equal sums in the two different banks at 9 % and 10% , then in 6 years Ali will have $0.0945 more than Kashif .

We use the formula for compound interest, to calculate the amount that each person will have after 6 years  ;

Amount after 6 years for Kashif is :

⇒ A = P(1 + r/n[tex])^{nt}[/tex]

where A = (amount after 6 years) ; P = (initial investment)

r = interest rate = 9%  ; n = 1 ; t = time period (6 years) ;

So, A = P(1 + 0.09/1)⁶  ⇒ P(1.09)⁶  ;

Amount after 6 years for Ali is :

⇒ A = P(1 + 0.10/1)⁶ = P(1.10)⁶  ;

So , difference in the amounts that Kashif has compared to Ali after 6 years is  ⇒ P(1.09)⁶ - P(1.10)⁶  ;

Simplifying this expression, we get:

⇒ P(1.09⁶ - 1.10⁶)  ;

≈ -$0.0945     ;

Since the value is negative, it means that after 6 years, Ali will have more money than Kashif and difference between their amounts is approximately $0.0945    .

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The probability of getting two odd numbers or two even numbers is 50%, since there are an equal number of odd and even numbers.

There are 6 possible outcomes when rolling two dice:

(1,1), (1,2), (2,1), (2,2), (1,3), (3,1).

The probability of getting two odd numbers is

2/6, or 1/3.

The probability of getting two even numbers is also

2/6, or 1/3.

Therefore, the probability of getting either two odd numbers or two even numbers is 2/3.

The probability of getting two odd numbers or two even numbers is 50%. This is because there are an equal number of odd and even numbers, so each outcome is equally likely. This means that the probability of getting two odd numbers or two even numbers is the same as the probability of getting one odd number and one even number. In both cases, the probability is 50%, since each outcome is equally likely. Therefore, the probability of getting two odd numbers or two even numbers is 50% as there are an equal number of odd and even numbers. This is because all possible outcomes are equally likely, and there are an equal number of odd and even numbers, so the probability of getting either two odd numbers or two even numbers is the same.

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Answer:

x=12

Step-by-step explanation:

Since b would equal E

We can make an equation.

x^2 -5x = 84

So that can be solved down to

x^2 -5x -84= 0

(x-12)(x+7)=0

x=12

x=-7

Now we see which one equals 84.

(12)^2 -5(12)=84

-7^2-5(-7)=14

therefore 12 is the correct answer and -7 does not work.

The volume of the triangular prism is 433.013cm^3.

Triangular prism formulas

volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length. area = length * (a + b + c) + (2 * base_area) , where a, b, c are sides of the triangle and base_area is the triangular base area.

We are given that;

Base area of prism = 10cm

Breadth of prism= 10cm

Height of prism = 10cm

Now,

To find the volume of triangular prism

Volume = base area × length of the prism

=10x43.3013cm

=433.013

Therefore, the volume of prism will be 433.013cm^3

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Answer:

Step-by-step explanation:

a

n

​

=ar

n−1

a

3

​

=ar

2

=24...(1)

a

6

​

=ar

5

=192...(2)

dividing (2)  by (1)  we get

ar

2

ar

5

​

=

24

192

​

r

3

=8⇒r=2

From (1)

ar

2

=24

a=

2

2

24

​

=6

∴a

10

​

=(6)(2)

10−1

=3072

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved lateral surface. The volume of a cylinder is the amount of space contained within the cylinder. It can be calculated using the formula:

Volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively. Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock =[tex]\mathrm{ \pi r_c^2h_c}[/tex]

Volume of Ptolemy's clock = [tex]\mathrm{\pi r_p^2h_p}[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock. We are given that after 2 hours of draining, both clocks have the same water height. Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

[tex]\pi r_c^2h_c / 4 = \pi r_p^2h_p / 5[/tex]

[tex]h_c / h_p = (r_p / r_c)^2 \times (5 / 4)[/tex]

We are not given the values of the radii, but we can see that the ratio of heights depends only on the ratio of the radii squared. Therefore, we don't need to know the actual sizes of the clocks, only the ratio of their radii. Let's call this ratio x:

[tex]x^2 = (h_c / h_p) \times(4 / 5)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]\pi r_c^2(h_c - 2h_c/4) = \pi r_p^2(h_p - 2h_p/5)[/tex]

[tex]\pi r_c^2h_c/2 =\pi r_p^2h_p/5*3[/tex]

[tex]r_c^2h_c/2 = r_p^2h_p/15[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]\mathrm{h_c - (3/4)h_c = (1/4)h_c}[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]\mathrm{ h_p - (3/5)h_p = (2/5)h_p}[/tex]

([tex]h_p[/tex]  / (2/5)[tex]h_p[/tex] ) = ((1/4)[tex]h_c / h_c[/tex])

([tex]h_p[/tex]  / (2/5)) = 1/4

[tex]h_p[/tex] = 2/5 * 1/4

[tex]h_p[/tex] = 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

[tex]h_p / h_c[/tex]= 1/10 / (1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

[tex]h_c / (2/5)h_p[/tex] = (1/4) / (2/5)(1/10) = (1/4) / (1/20) = 5/4

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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The point (-1, 2) lies on the line 3x = 2x - 1.

The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.

So the line passes through the point (-1, y) for any value of y.

To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.

a) (0, -1)

3(0) = 2(0) - 1

0 = -1

This point does not lie on the line.

b) (-1, 2)

3(-1) = 2(-1) - 1

-3 = -3

This point does lie on the line.

c) (1, -4)

3(1) = 2(1) - 1

3 = 1

This point does not lie on the line.

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Answer: b (b²+b+4)

Step-by-step explanation:
b²=bb
b³=b²b
=b²b+bb+4b
=b(b²+b+4)

The equation with infinitely many solutions is given as follows:

7(2W + 3) = 14W + 21.

The system of equations for this problem is defined as follows:

7(2W + 3) = 14W + 20.

Applying the distributive property to the left side, we will have that:

14W + 21 = 14W + 20.

The two lines have the same slope but different intercepts, hence the system contains zero solutions.

To contain an infinite number of solutions, they must have the same slope and the same intercept, then the equation is given as follows:

7(2W + 3) = 14W + 21.

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Step-by-step explanation:

=

[tex]7(2w + 3) = 14w \\ 14w + 21 = 14w \\ 14w - 14w = - 21 \\ 0 = - 21 \\ = - 21[/tex]

Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.

To choose 20 items at the grocery store, Caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. Since he wants all 3 cheeses, he only needs to choose 17 more items.

The number of ways he can choose these 17 items from the remaining vegetables, fruits, and breads is given by the combination: C(5+8+7, 17) = C(20, 17) = 1140.

This formula means that there are 20 items to choose from, and Caleb wants to choose 17. The order doesn't matter, so we use a combination.

Therefore, Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.

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The solution is Option E.

The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , -4 )

Let the second point be Q ( 7 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = 10 / 10 = 1

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 6 = 1 ( x - 7 )

y - 6 = x - 7

y = x - 1   be equation (1)

Now , the point of intersection of lines is at ( 3 , 2 )

Substitute the value of x and y in the equation , we get

when x = 3 , y = 2

2 = 3 - 1

2 = 2

Hence , the solution to the equation is ( 3 , 2 )

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There are 56 servings in a 28 pound bag of dog food.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Each day Fei yen's dog eat dog food = 8 ounces

Fei yen bought a 28 pound bag of dog food.

And we know that 1 pound = 16 ounces

Then ,the food in ounces

= 28 x 16

= 448 ounces

Now, the number of 8 ounces servings are in a 28 pound bag of dog food

= 448 / 8

= 56

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Answer:

17.3 feet

Step-by-step explanation:

We can use the tangent function to evaluate the height of the building.

The definition of the tangent function is

[tex]\tan x=\frac{O}{A}[/tex]

Where

[tex]A[/tex] is the side adjacent to the angle

[tex]O[/tex] is the side opposite to the angle

In this example we are given values of the adjacent side and the angle.

Knowing that we can evaluate the side opposite to the angle.

Numerical Evaluation

We are given

[tex]x=68\\A=7[/tex]

Substituting these values into the equation for the tangent function yields[tex]\tan 68=\frac{O}{7}[/tex]

Lets solve for [tex]O[/tex].

Multiply both sides by [tex]7[/tex].

[tex]O=7*\tan 68[/tex]

Evaluate [tex]\tan 68[/tex].

[tex]O=7*2.47508685[/tex]

[tex]O=17.325608[/tex]

Rounding to the nearest tenth gives us

[tex]O=17.3[/tex]

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40%=

5

2

​

5

2

​

⋅40=16 cars at 8000 each =128,000 in sales

40−16=

​

24 cars at 9000 each

​

=216,000 in sales

Total sales: 128,000+216,000=344,000

Total expense: 6500⋅40=260,000

Total profit: 344,000−260,000=84,000

Answer:

$84000

Step-by-step explanation:

40% of the cars would be 16 cars that are sold for $8000 each.

16×$8000=$128000

The remaining 60% of cars would be 24 cars to be sold at $9000 each.

24×$9000=$216000

The total profit = the sum - the amount he paid for all cars.

total profit = ($128000+$216000) - (40×$6500)

total profit = $344000 - $260000

total profit = $84000

The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.

The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.

The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.

What is experimental probability?

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Given that two coins flip together. The outcomes of a coin is {H,T}.

The outcomes after flipping of two coins are

{HH, HT, TH, TT}

The total number of outcomes is 4.

The number of outcomes to get two tails is 1.

The probability of getting two tails is 1/4 = 0.25 = 25%.

The number of outcomes to get two heads is 1.

The probability of getting two heads is 1/4 = 0.25 = 25%.

The number of outcomes to get one head and one tail is 2

The probability of getting one head and one tail is 2/4 = 0.50 = 50%.

The theoretical probabilities will change for every experiment.

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Answer:

85

Step-by-step explanation:

The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85

The product of 486 as a product of it's prime factor is 2¹×3⁵

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Expressing a number as a product of it's prime factors simply means that we are going to use only prime numbers as factors.

for example expressing 12 as a product of it's factor means 2²× 3 i.e 4 × 3 will give 12

Similar expressing 486 as a product of it's prime factors;

486/2 = 243

243/3 = 81

81/3 = 27

27/3 = 9

9/3 = 3

3/3 = 1

therefore 486 = 2¹× 3⁵

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The perimeter of the updated blueprint would be = 62units.

The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.

To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;

= 10+4+2+4+2+4+10+2+2+8+2+2

= 62 units.

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Answer:

According to Kepler's third law, what is the orbital period of this asteroid in terms of Earth years? A certain asteroid is approximately 50 AU from the Sun.

We can say in this triangle by Pythagorean theorem A2 = B2 + C2 => AC = sqrt115 after answering the provided question.

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Pythagorean theorem applies here, in this triangle

[tex]A^2 = B^2 + C^2[/tex]

[tex]AC = \sqrt{14^2 - 9^2}[/tex]

[tex]AC = \sqrt{196 - 81}[/tex]

[tex]AC = \sqrt{115}[/tex]

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8 is (6x^2-7x-5)/(2x + 1)

The given expression is a fraction in the form of[tex](n^2 + 2n + 5)/n[/tex], which is an element of the set Omega ([tex]n^2[/tex]). This expression is true.

The given expression is a fraction in the form[tex](n^2 + 2n + 5)/n[/tex], which belongs to the set Omega[tex](n^2).[/tex] This statement is valid, as the fraction is simply a simplified form of a polynomial, which is an element of the Omega set. The numerator of the fraction is [tex]n^2 + 2n + 5[/tex], which is a quadratic equation in n. The denominator is n, which is a linear equation in n. As the numerator and denominator are both polynomials of n, the fraction is an element of the Omega set. Therefore, the statement is true.

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The sector area of the sector defined by the minor arc CB is given as follows:

7.5 cm².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

We have that the radius is half the diameter, hence it's measure is given as follows:

r = 3 cm.

The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.

CB + 84º = 180º.

CB = 96º.

An entire circle has an angle of 360º, hence the area of the sector is given as follows:

A = 96/360 x π x 3²

A = 7.5 cm².

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The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.

[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]

[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]

[tex]3.8\sqrt{2}x^{5+3+9}[/tex]

[tex]3.8\sqrt{2}x^{17}[/tex]

[tex]24\sqrt{2}x^{17}[/tex]

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Answer:

J(t) = 230,600(1.009)^t

Step-by-step explanation:

J(t) = 230,600(1 + 0.009)^t, or

J(t) = 230,600(1.009)^t                                                                                                                                                                                                              If this is Wrong ill do. it again!!

The linear equation that gives the dollar value V of the product in terms of the year t is V = - $5600t + $344,000.

V(t) is a function of t that expresses the value in the year 2000+t.  

We know that the decrease is $5600 per year.

So,

V(t) = -$5600t + c  

where c is the constant.

V(15) =  -$5600 (15) + c = $260,000     [t = 15]

Hence, we can say that -  

c = $260,000 + $5600 (15)

c= $260,000 + $84,000

c= $344,000

Now we got the value of c. We can write the equation as follows -

V = - $5600t + $344,000

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Answer:

16

Step-by-step explanation:

20/5 = 12/3 = x/4

x/4 = 4

x = (4)(4) = 16

Answer:16

Step-by-step explanation:multiply 4 by 4

If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:

9 x 9 x 9 x 9 x 9 = 59,049

In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:

Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.

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The total cost of the skateboard is $76.07.

The first step is to determine the price of the skateboard after the 12% discount. A discount reduces the price of an item.

Price after discount = price before discount x (1 - percent discount)

$79.86 x (1 - 12/100)

$79.86 x (1 - 0.12)

$79.86 x 0.88

= $70.28

Price after the sales tax = (1 + sales tax) x price after discount

= (1 + 8.25/100) x $70.28

(1 + 0.0825) x $70.28

1.0825 x $70.28 = $76.07

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