What is the measure of (arc) BC?

A. 55

B. 110

C. 48

D. 96

Answer:

x = −3, 3, −4

Step-by-step explanation:

Answer:

A. r^n=a

B. a^1/n=r

Step-by-step explanation:

ape x

The true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

The equation is given as:

[tex]\sqrt[n]a = r[/tex]

Take the power of n on both sides of the equation

[tex](\sqrt[n]a)^n = r^n[/tex]

This gives

a = r^n

Rewrite as:

r^n = a

Also, we have:

[tex]\sqrt[n]a = r[/tex]

Apply the law of indices

a^1/n = r

Hence, the true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r

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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

If all three guesses for the number of jelly beans 98, 137, and 164 were off by 12, 27, and 39 the correct guess for the number of jelly beans is 125.

The number of jelly beans was 125.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. 

Example:

2x + 3 is an expression

2x  - 3 = 4 is an expression

We have,

Three guesses for the number of jelly beans:

98, 137, and 164.

These three guesses were all wrong.

The three guesses were off by:

12, 27, and 39.

The correct guess is 125 because,

98 + 27 = 125

137 - 12 = 125

164 - 39 = 125

Thus,

The number of jelly beans was 125.

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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

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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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.

Answer:

Step-by-step explanation:

From the figure, it can be seen that CD is the perpendicular bisector of AB and also, we have:

(A) CD is the Perpendicular bisector of AB.

(B) If AB=10, then [tex]EB=\frac{AB}{2}=\frac{10}{2}=5[/tex]

(C) [tex]AE=\frac{1}{2}(AB)[/tex]

(D) E is the mid point of AB.

(E) [tex]{\angle}BED=90^{\circ}[/tex] (Because ED is  perpendicular to AB)

Answer:

-_- Answer is -3

Step-by-step explanation:

Doing the instruction vidio.

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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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

Answer:  The equivalent expression in degrees is 60°.

Step-by-step explanation:  We are given to find the equivalent of the following expression in degrees.

[tex]E=\dfrac{\pi}{3}~\textup{radians}.[/tex]

We will be using the UNITARY method the solve the given problem.

We know that

[tex]\pi~\textup{radians}=180^\circ\\\\\\\Rightarrow 1~\textup{radian}=\left(\dfrac{180}{\pi}\right)^\circ\\\\\\\Rightarrow \dfrac{\pi}{3}~\textup{radians}=\left(\dfrac{\pi}{3}\times\dfrac{180}{\pi}\right)^\circ=60^\circ.[/tex]

Thus, the equivalent expression in degrees is 60°.

Final answer:

Levers are classified based on the positions of the fulcrum, input force, and output force. First-class levers have the fulcrum in the middle, second-class levers have the load in the middle, and third-class levers have the effort in the middle. The Mechanical Advantage of a lever indicates how much the lever amplifies the input force.

Explanation:

The three classes of levers are differentiated by the positions of the fulcrum, input force, and output force. A first-class lever has the fulcrum placed between the input force and the output force. Examples would include a seesaw and a crowbar. A second-class lever has the output force between the input force and the fulcrum, with examples being a wheelbarrow and a nutcracker. Lastly, a third-class lever has the input force between the output force and the fulcrum, as seen in a pair of tweezers or a human arm when lifting a weight.

The Mechanical Advantage (MA) is a calculation that shows how much a lever amplifies the input force. It is given by the ratio of the distance from the fulcrum to the input force (effort arm) and the distance from the fulcrum to the output force (resistance arm). Levers are simple machines that utilize torque and the physical distances from their pivot point to achieve an output force that is greater or faster or travels a further distance than the input force.

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.

The measure of the angle opposite to the shortest side is, 29.25°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The legs of a right triangle measure 14 and 25.

Now, We know that;

⇒ tan θ = Perpendicular / Base

⇒ tan θ = 14 / 25

⇒ θ = tan ⁻¹ (14/25)

⇒ θ = 29.25°

Thus, The measure of the angle opposite to the shortest side is, 29.25°

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