The average age of the children at a campout is shown in the box plot below. Which statement is true about the box plot? The youngest age is 7. It is skewed right. More of the children were close to 12 years old than 6 years old. Half of the children were between 6 and 9 years old.

Techechtium-99m has a half-life of 6 hours. It will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.

To determine how many hours it will take for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg, we can use the concept of half-life.

Techechtium-99m has a half-life of 6 hours, which means that after every 6 hours, half of the initial amount will decay.

So, to find the number of half-lives required to reach 62.5 mg, we can divide the initial amount by the remaining amount:

1000mg / 62.5mg = 16.

Since each half-life is 6 hours, we can multiply the number of half-lives by 6 to find the total number of hours:

16 x 6 = 96.

Therefore, it will take 96 hours for 62.5 mg of Techechtium-99m to remain from an initial amount of 1000mg.

Answer:

The correct option is 4.

Step-by-step explanation:

In triangle ABC and XYC,

[tex]\angle BAC=\angle YXC=60^{\circ}[/tex]                   (Given)

[tex]\angle BCA=\angle YCX[/tex]                                    (Reflexive Property)

By AA rule of similarity,

[tex]\triangle ABC\sim \triangle XYC[/tex]

The corresponding sides of similar triangles are proportional.

Since triangle ABC and XYC, therefore

[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]

[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]

[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]

[tex]\frac{10}{AC}=\frac{7}{11}[/tex]

Therefore option 4 is correct.

Answer:

[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.

Step-by-step explanation:

A polynomial of degree two is called quadratic function,

Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),

Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,

⇒  [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,

[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,

⇒  [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,

[tex]f(x) = -3x+2[/tex] has degree 1,

⇒  [tex]f(x) = -3x+2[/tex] is not a quadratic function,

[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,

⇒  [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,

Answer:

The resulting price is $99.36.

Step-by-step explanation:

Original cost of the item = $100

The decrease percentage is 8% or 0.08

So, the reduced price becomes :

[tex]100-(0.08\times100)=92[/tex] dollars

Now again the reduced price is increased by 8%.

So, multiplying the reduced price by 8% and adding it again we get;

[tex]92+(0.08\times92)[/tex] =$99.36

So, the resulting price is $99.36.

The solution is Option A.

The factorized form of the polynomial equation A = x³ + 4x² - x - 4 is given by B = ( x + 1 ) ( x - 1 ) ( x + 4 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the factorized equation be represented as = B

Now , let the equation be A

The value of A is given by A = x³ + 4x² - x - 4

On simplifying the equation , we get

A = x³ + 4x² - x - 4

Taking x² as the common term in the first two terms of the equation ,

A = x² ( x + 4 ) - x - 4

The equation can be further simplified as

A = x² ( x + 4 ) - ( x + 4 )

Taking ( x + 4 ) as the common term in the first two terms of the equation ,

A = ( x² - 1 ) ( x + 4 )

Now , ( x² - 1 ) can be simplified as ( x + 1 ) ( x - 1 )

So , the value of B is

B = ( x + 1 ) ( x - 1 ) ( x + 4 )

Therefore , the value of B is ( x + 1 ) ( x - 1 ) ( x + 4 )

Hence , the factorized equation is ( x + 1 ) ( x - 1 ) ( x + 4 )

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Answer:

14 5/8

Step-by-step explanation:

multiply each number by it's frequency  the product is the total value  .

Answer: Ellen's house is farther away by 898 feet.

Step-by-step explanation:

Given: The distance between Haley's house and Ellen's house = 1.41 miles

We know that 1 mile = 5,280 feet

Then, [tex]1.41\text{ miles}=1.41\times5,280\text{ feet}=7,444.8\text{ feet}[/tex]

The distance between Haley's house and Dirk's house = 6,547 feet

Clearly, 6,547<7,444.8

And [tex]7444.8-6547= 897.8\approx898[/tex]

Therefore, Ellen's house is farther away by 898 feet.

Answer:

[tex](30\sqrt{3}-21\sqrt{6})[/tex]

Step-by-step explanation:

We have to find the product of the expressions.

[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]

= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)

= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]

= [tex]15\sqrt{12}-21\sqrt{6}[/tex]

= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]

= [tex]30\sqrt{3}-21\sqrt{6}[/tex]

= [tex](30\sqrt{3}-21\sqrt{6})[/tex]

Answer:

the answer is d:)

Step-by-step explanation:

i took the quiz on edge and got 100:D

[tex] |\Omega|=360\\
|A|=120\\\\
P(A)=\dfrac{120}{360}=\dfrac{1}{3}\approx33\% [/tex]

To find x-values where a function's tangent line is horizontal, find the derivative, set it to zero, and solve for x considering any function's restriction.

To find all the values of x where the tangent line is horizontal, we need to understand that these are the points where the derivative of the function is zero. This is because the derivative of a function at a point gives us the slope of the tangent line at that point. And, for a line to be horizontal, its slope needs to be zero.

So, to find these values:

The solutions will give you the x-values where the tangent line is horizontal. Do note that you need to be aware of the domain and any restrictions of the original function to have valid solutions.

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Answer:

The correct answer is 68.5°

The calculated result of the angle FDE is 68.5°. Whenever two chords cut across a circle, the resulting angle is equivalent to half of the sum of the measurements of the arc the angle intersects and that which the angle vertical to the first angle intercepts.

m<FDE = 1/2( Arc BC + Arc 76)

m<FDE = 1/2 (61° + 76°)

m<FDE = 137/2 = 68.5°

Give Brainliest if you please

Your answer should be C.

[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]

Answer:  The magnitude of the vector u is √12 units.

Step-by-step explanation:  Given that the dot product of a vector u with itself is 12.

We are to find the magnitude of the vector u.

Let <a, b> represents the vector u.

That is, u = <a, b>

Then, according to the given information, we have

[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]

Thus, the magnitude of the vector u is √12 units.

The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).

The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:

x^2 - 64 = (x - 8)(x + 8)

This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.

Answer:

44

Step-by-step explanation:

1:4

4+1=5

55/5=11

11*4=44

the answer is 44