A regular pyramid has a height of 12 centimeters and a square base. if the volume of the pyramid is 256 cubic centimeters, how many centimeters are in the length of one side of its base

there are 13 diamonds per deck

26 black cards

4 aces

 so a 13/52 chance for a diamond

 a 26/52, reduced to 1/2 chance for a black card

 and a 4/52 chance for an ace

13/52 x 1/2 x 4/52 = 52/5408 = 1/104 probability

Final answer:

After using the compound interest formula with an initial deposit of $25,000, an annual interest rate of 11%, and a time period of 16 years, the balance rounds to $120,034.10, which does not match any of the provided answer choices.

Explanation:

To find out how much is in the account when the child turns 16 years old, we can use the formula for compound interest: an = a1(1 + r)n, where a1 is the original amount deposited, r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested. In this case, a1 is $25,000, r is 0.11 (11%), and n is 16.

Using the formula, we calculate the account balance as follows:

Account Balance = 25,000(1 + 0.11)16

Account Balance = 25,000(1.11)16

Account Balance = 25,000(4.801364)

Account Balance = $119,999.10

However, this result is not in the given answer choices, so let's ensure we are rounding to the nearest cent:

Account Balance = $120,034.09 (before rounding)

Account Balance = $120,034.10 (after rounding to the nearest cent)

None of the answer choices matches this amount, so it is possible there has been a mistake in the provided choices or in our calculations. We should double-check the interest rate, time period, and the formula used.

Answer:

D) c - 2 = 25 + c + 10√c

Step-by-step explanation:

The given equation is sqrt(c-2) - sqrt(c) = 5

Taking square on both sides, we get

Here we used ( a+ b)^2 = a^2 + b^2 + 2ab formula.

c - 2 = 5^2 + (√c)^2 + 2(5)√c

c - 2 = 25 + c +10√c

Hope this helps!! Have a great day!! ❤

The correct equation resulting from isolating a radical term and squaring both sides of the original equation is D) [tex]\( c-2 = 25-c+10\sqrt{c} \)[/tex].

To arrive at this result, let's start with the original equation and isolate one of the radical terms:

[tex]\[ \sqrt{c-2} - \sqrt{c} = 5 \][/tex]

Now, isolate the radical on one side:

[tex]\[ \sqrt{c-2} = 5 + \sqrt{c} \][/tex]

Next, square both sides to eliminate the radical:

[tex]\[ (\sqrt{c-2})^2 = (5 + \sqrt{c})^2 \] \[ c-2 = 25 + 2 \cdot 5 \cdot \sqrt{c} + (\sqrt{c})^2 \] \[ c-2 = 25 + 10\sqrt{c} + c \][/tex]

Now, we want to isolate the term with the radical on one side and the rest on the other side:

[tex]\[ c-2 = 25 + 10\sqrt{c} + c \][/tex]

Subtract c from both sides to get:

[tex]\[ c-2-c = 25 + 10\sqrt{c} \] \[ -2 = 25 + 10\sqrt{c} \][/tex]

Finally, add 2 to both sides to isolate the radical term:

[tex]\[ -2 + 2 = 25 + 10\sqrt{c} + 2 \] \[ 0 = 25 + 10\sqrt{c} - 2 \] \[ c-2 = 25 - c + 10\sqrt{c} \][/tex]

This matches option D, confirming that the correct equation is:

[tex]\[ c-2 = 25-c+10\sqrt{c} \][/tex]

The value of dimensions of rectangle are 5 and 7.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangular table top has a perimeter of 24 inches and an area of 35 square inches.

Let the dimensions of rectangle are;

Length = L

Width = W

So, We can formulate;

⇒ 2 ( L + W ) = 24

⇒ L + W = 12   ..(i)

And,

⇒ L × W = 35

⇒ L = 35 / W  ... (ii)

Substitute the value from (ii) in (i), we get;

⇒ L + W = 12

⇒ 35/W + W = 12

⇒ 35 + W² = 12W

⇒ W² - 12W + 35 = 0

⇒ W² - (7W + 5W) + 35 = 0

⇒ W² - 7W - 5W + 35 = 0

⇒ W (W - 7) - 5 (W - 7) = 0

⇒ (W - 5) (W - 7) = 0

⇒ W = 5

And, W = 7

And, We get;

⇒ L = 35 / W

Put W = 5;

⇒ L = 35 / 5

⇒ L = 7

And,

⇒ L = 35 / W

Put W = 7;

⇒ L = 35 / 7

⇒ L = 5

Thus, The possible values of dimensions are;

⇒ 5 and 7.

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Answer:

Option: B is correct.

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Step-by-step solution:

Clearly from the graph we could see that the graph of the function touches x=2.

that means that x=2 is a root of the function

Also when the graph touches the point of x-axis and does not pass that point than that zero is the repeated zero of the function.

That means that x=2 is a repeated zero of the function f(x).

Hence,

The factorization of the polynomial graphed below is:

f(x)=(x-2)(x-2)

Hence, option B is correct.

( Also in first option:

A) x(x+2)

x=0 must also be an zero but in the graph we could see that x=0 is not a solution.

Hence option A is false.

C)

x(x-2)

again as in option: A x=0 must be a solution.

Hence, option C is false.

D)

(x+2)(x+2)

x=-2 must be a solution but the graph does not touches x=-2.

Hence, option D is incorrect )

Answer:

8 half-lives of polonium-210 occur in 1104 days.

0.1174 g of polonium-210 will remain in the sample after 1104 days.

Step-by-step explanation:

Initial mass of the polonium-210 = 30 g

Half life of the sample, = [tex]t_{\frac{1}{2}}=138 days[/tex]

Formula used :

[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]

where,

[tex]N_o[/tex] = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope

[tex]\lambda[/tex] = rate constant

[tex]\lambda =\frac{0.693}{138 days}=0.005021 day^{-1}[/tex]

time ,t = 1104 dyas

[tex]N=N_o\times e^{-(\lambda )\times t}[/tex]

Now put all the given values in this formula, we get

[tex]N=30g\times e^{-0.005021 day^{-1}\times 1104 days}[/tex]

[tex]N=0.1174 g[/tex]

Number of half-lives:

[tex]N=\frac{N_o}{2^n}[/tex]

n =  Number of half lives elapsed

[tex]0.1174 g=\frac{30 g}{2^n}[/tex]

[tex]n = 7.99\approx 8[/tex]

8 half-lives of polonium-210 occur in 1104 days.

0.1174 g of polonium-210 will remain in the sample after 1104 days.

the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar

 doing that I estimate $23.00

Answer is C

Answer: Option 'C' is correct.

The perimeter will be 10 times the original .

Step-by-step explanation:

Since we have given that

Length of the rectangle = 6 cm

Breadth of the rectangle = 3 cm

As we know the formula for "Perimeter of rectangle "

[tex]\text{Perimeter of original rectangle }=2(Length+ Breadth)\\\\\text{Preimeter of rectangle }=2(6+3)\\\\\text{Perimeter of rectangle }=18\ cm[/tex]

According to question, each side is increased by a factor of 10

so, Perimeter of new rectangle is given by

[tex]10\times 2\times (6+3)\\\\=180\ cm[/tex]

Hence, Option 'C' is correct.

So, the perimeter will be 10 times the original .

Answer:

$1,056,000 ≤ x ≤ $1,344,000

Step-by-step explanation:

took test

Answer:

x = −3, 3, −4

Step-by-step explanation:

Answer:

-_- Answer is -3

Step-by-step explanation:

Doing the instruction vidio.

The length of longest side of the triangle is 20 ft .

The perimeter of a triangle is defined as the total length of its boundary.

The basic formula used to calculate the perimeter of a triangle is:

Perimeter = sum of the three sides

According to the question

The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5 .

Let  common constant factor within ratio = x

Therefore,

Sides of triangle = x , 2x , 5x

and the perimeter of the triangle = 32 ft  

i.e

according to the formula of perimeter of a triangle:

Perimeter = sum of the three sides  

Now,

Substituting the value in formula

[tex]32 = x + 2x + 5x[/tex]

[tex]32 = 8x[/tex]

[tex]x = 4[/tex]  

The sides of triangle is  : 4 ft  , 2*4 , 5*4

                                       : 4 ft   , 8 ft  , 20 ft    

Hence, the length of longest side of the triangle is 20 ft

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When [tex]\(x = 6\)[/tex], the expression [tex]\(4x - 7\)[/tex] simplifies to 17 following the order of operations.

To evaluate the expression [tex]\(4x - 7\)[/tex] when [tex]\(x = 6\)[/tex], substitute the value of [tex]\(x\)[/tex] into the expression and simplify using the order of operations.

[tex]\[4x - 7\][/tex]

Replace [tex]\(x\)[/tex] with 6:

[tex]\[4(6) - 7\][/tex]

Following the order of operations (PEMDAS), perform the multiplication first:

[tex]\[24 - 7\][/tex]

Now, perform the subtraction:

[tex]\[17\][/tex]

Thus, when \(x = 6\), the value of [tex]\(4x - 7\)[/tex] is 17.

In this expression, the variable [tex]\(x\)[/tex] is multiplied by 4, and then 7 is subtracted from the result. By substituting the value of [tex]\(x\)[/tex], which is 6 in this case, and simplifying according to the order of operations, we obtain the final result of 17.

To find the number, we set up the equation 7 - 1/(3x) = 1/(2x) and solve for x.

To find the number, we need to set up an equation based on the given information.

Let's assume the number is 'x'.

According to the problem, the reciprocal of three times the number is subtracted from 7 and is equal to the reciprocal of twice the number. We can write this as:

7 - 1/(3x) = 1/(2x)

To solve this equation, we can multiply both sides by the common denominator, which is 6x. This will eliminate the fractions.

6x * 7 - 6x * 1/(3x) = 6x * 1/(2x)

42x - 2 = 3

Subtracting 2 from both sides, we get:

42x = 1

Dividing both sides by 42, we find:

x = 1/42

Therefore, the number is 1/42.

To solve this problem, let us first assign some variables. Let us say that:

x = pigs

y = chickens

z = ducks

From the problem statement, we can formulate the following equations:

1. y + z = 30                                         ---> only chicken and ducks have feathers

2. 4 x + 2 y + 2 z = 120                      ---> pig has 4 feet, while chicken and duck has 2 each

3. 2 x + 2 y + 2 z = 90                        ---> each animal has 2 eyes only

Rewriting equation 1 in terms of y:

y = 30 – z

Plugging this in equation 2:

4 x + 2 (30 – z) + 2 z = 120

4 x + 60 – 2z + 2z = 120

4 x = 120 – 60

4 x = 60

x = 15

From the given choices, only one choice has 15 pigs. Therefore the answers are:

She has 15 pigs, 12 chickens, and 18 ducks.

The transformation of the function f(x) to g(x) is a horizontal stretch.

The parent function f(x) is given by:

             [tex]f(x)=\sqrt{x}[/tex]

and the transformed function g(x) is given by:

              [tex]g(x)=\sqrt{0.5x}[/tex]

Now we know that the transformation of the type:

       f(x) → f(bx)

is a horizontal stretch if 0<b<1

and is a horizontal shrink if b>1

Here we have:

[tex]b=\dfrac{1}{2}=0.5[/tex]

i.e.

[tex]0<b<1[/tex]

This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.

Using trigonometry, it can be determined that the beam will clear the wires when it stands up straight. The beam's length remains constant and by finding the height of the beam at different angles, we can confirm that it will not hit the wires.

The problem can be solved using trigonometry. Firstly, you need to find out the length of the beam when it makes an 40° angle with the ground. The length of the beam would be 8 ft / sin(40°) around 12.61 ft. Now, when the beam makes a 60° angle with the ground, the top of the beam will be sin(60°) * 12.61 ft = 10.92 ft off the ground. Because the wires are 2 ft above that (at 8 ft + 2 ft = 10 ft), the beam will clear the wires as it stands up straight.

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By applying trigonometry principles, it is determined that the beam will not clear the wires when it is lifted to stand up straight as the top of the beam at 60° angle is lower than the bottom of the wires.

To answer whether the beam will clear the wires when it is lifted, we need to apply basic trigonometry principles. First, we determine the height of the beam when it is at a 40° angle with the ground, and we know the top is 8 ft above the ground. We can use the tangent of the angle to relate this height to the length of the beam, which remains constant as the beam is raised.

So we have tan(40°) = 8ft/beam_length. Solving for beam_length, we get beam_length = 8ft/tan(40°) ≈ 9.442ft.

Next, when the beam makes a 60° angle with the ground, it is not fully raised and the wires are 2ft above the beam's top. The length of the beam when it's at this angle is beam_length = 2ft + height_at_60°. We can use the tangent function again to find this height, which gives us tan(60°) = height_at_60°/beam_length.

Solving for height_at_60°, we get height_at_60° = beam_length * tan(60°), substituting beam_length from earlier, height_at_60° = 9.442ft * tan(60°) ≈ 16.34ft.

As the bottom 2 ft of the wires are not cleared by the 16.34 ft high beam, the conclusion is that the beam will not clear the wires when it is being erected up straight.

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