PLEASE HELP!!!

A lead pellet has a volume of 1.2x10⁻² mL and a density of 11.3 g/mL. What is the mass of the lead pellet?

Ratios 18:3 and 6:1 are equivalent because they represent the same relationship between two quantities. This can be seen by simplifying the first ratio to 6:1, which is the same as the second ratio.

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Ratios are equivalent if they represent the same relationship between two or more quantities. In the ratios 18:3 and 6:1, both ratios represent the same relationship between two quantities.

To see why, we can simplify the first ratio by dividing both the numerator and denominator by 3:

18 ÷ 3 = 6

3 ÷ 3 = 1

The simplified ratio is now 6:1, which is equivalent to the second ratio.

This means that for every 18 units of the first quantity, there are 3 units of the second quantity, and for every 6 units of the first quantity, there is 1 unit of the second quantity. The relationship between the quantities is the same in both ratios, so they are equivalent.

Therefore, ratios 18:3 and 6:1 are equivalent because they represent the same relationship between two quantities. This can be seen by simplifying the first ratio to 6:1, which is the same as the second ratio.

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Answer:

\( \boxed{\sf (c) \ 9a - 8 {a}^{2}} \)

Step-by-step explanation:

\( \sf Simplify \: the \: following: \\ \sf \implies 3a - 2a \times 4a + 6a \\ \\ \sf - 2a \times 4a = - 2 {a}^{2} \times 4 : \\ \sf \implies \boxed{ \sf - 2 {a}^{2} \times 4} + 3a + 6a \\ \\ \sf - 2 \times 4 = - 8 : \\ \sf \implies \boxed{ \sf- 8} {a}^{2} + 3a + 6a \\ \\ \sf 3a + 6a = 9a : \\ \sf \implies 9a - 8 {a}^{2} \)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The final expression of the expression 3a - (2a x 4a) + 6a is

9a - 8a².
Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example:

2 + 3x + 4y = 7 is an expression.

3x + 5 + 3 is an expression.

4x = 6 is an expression.

We have,

3a - (2a x 4a) + 6a

3a - 8a² + 6a

Combine like terms.

9a - 8a²

We can also write,

-8a² + 9a

There is no common factor or like terms to simplify further.

So,

9a - 8a²

Thus,

The final expression of the expression 3a - (2a x 4a) + 6a is

9a - 8a².
Option C is the correct answer.

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement which is most likely true for g is that: A. g(-13) = 20.

In Mathematics, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Based on the information provided in this scenario, the domain and range of this function g(x) in interval notation are as follows:

Function g(0) = 2 is false because it was stated that g(0) = -2. Also, g(-4) = -11 is outside the scope of the given range for this function.

Furthermore, function g(7) = -1 is not within the domain for the given function. However, we can logically deduce that g(-13) = 20 is within the domain for the given function and it would produce an output that is within the scope of the given range for this function.

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two buses leave towns miles apart at the same time and travel toward each other. then the Rate of first bus = 72 mph and Rate of second bus  = 62 mph

let first bust travels at x mph

then,  2nd but will travel at ( x - 10) mph

distance travelled by first bus in 2 hours = 2x

distance travelled by 2nd but in 2 hours = 2( x- 10) = 2x - 20

distance between the two is 268 miles

so we can write

2x + 2x - 20 = 268

4x = 288

x = 288 / 4 = 72 mph

rate of first bus = 72 mph

and second bus = 72 - 10 = 62 mph

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Answer:

Choice 2 and 4

Step-by-step explanation:

3x-1>2

+1 +1

3x>3

x>1

8-4x<4

-8 -8

-4x<-4

x>1

Answer:

The factored form of 4m³ – 28m² – 120m is 4m(m – 10)(m + 3). The zeroes of the function would be m = 0, m = –3, and m = 10.

Step-by-step explanation:

I'll give this a shot.

4m³ – 28m² – 120m = 0 — The original expression

4m³ – 28m² – 120m — Did that 0 have any purpose? I just deleted it.

4(m³ – 7m² – 30m) — There's a common factor in here, 4. Let's pull that aside.

4m(m² – 7m – 30) — Actually, there's two common factors. The second one is m! Let's pull that out too!

To factor an expression, you have to break apart the middle term, so to speak. That's only possible if you can find two numbers whose product equals that of the outside terms and whose sum equals the middle term. Here, I'm just dealing with numbers and putting that variable aside.

–30 = 10 × –3

–30 = –10 × 3

–30 = –2 × 15

–30 = 2 × –15 — To solve for any potential factors, let's find all the numbers integers that multiply to –30

Now let's see which one adds up to –7!

15 – 2 = 13 — it's not this one

2 – 15 = –13 — nor this one

10 – 3 = 7 — we're pretty close! Let's switch that negative

3 – 10 = –7 — here we go! Here's our numbers!

4m[(m² – 10m) + (3m – 30)] — now we break apart the middle term. This is all multiplied by 4m, so that still encases everything with brackets.

4m[m(m – 10) + 3(m – 10)] — Factoring the two expressions

4m(m + 3)(m – 10) — simplifying to find our answer! Ta-da!

Answer:

\(\boxed{202}\)

Step-by-step explanation:

\((101.5)^2-(100.5)^2\)

\(= 10302.25 - 100.5^2\)

\(= 10302.25 - 10100.25\)

\(= 202\)

Hope this helped you!

202

Hi there !

(101.5)² – (100.5)² =

use formula a² - b² = (a - b )(a + b)

= (101.5 - 100.5)(101.5 + 100.5)

= 1×202

= 202

Good luck !

The dimension of the max garden is 125*125 and the max area is 15625 square feet.

Let the length and width of the garden be L and B.

Now, let the barn is along the width. So, now the width became = B-50

So the perimeter = 2(L+B-50)

Now to fence the garden we need 400 feet material.

So, 2(L+B-50) = 400

L+B-50 = 200

B = 250-L .........(i)

So the area of the total garden is given by,

A = LB = L(250-L) \(=250L-L^2\)

So now differentiating the area with respect to length,

dA/dL = 250-2L

\(\frac{d^2A}{dL^2}=\) -2

Now, dA/dL = 0 gives,

250-2L = 0

2L = 250

L= 125

At L = 125, \(\frac{d^2A}{dL^2}=-2 < 0\)

Max A = \(250\times125-125^2=15625\) square feet

So area is maximum when L = 125 feet.

Then the width = B = 250-125 = 125 feet.

Hence the dimension of the max garden is 125*125 and the max area is 15625 square feet.

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Distance between the points (-3, 5, -7) and (2, -4, 6) is 5√11 units.

What is cartesian coordinate points?

The Cartesian coordinates of a point in three dimensions are the triple (x, y, z). The three numbers or coordinates give the signed distance from the origin along the x, y, and z axes respectively.

Solution:

Given, x1 = -3     ,  x2 = 2

           y1 = 5      ,  y2 = -4

           z1 = -7     ,  z2 = 6

The formula for finding the distance between two points on 3D graph is given below

Distance =√((x2-x1)²+(y2-y1)²+(z2-z1)²)

⇒Distance =√{(2-(-3))²+(-4-5)²+(6-(-7))²}

⇒Distance =√{(2+3)²+(-9)²+(6+7)²}

⇒Distance =√{5²+81+13²}

⇒Distance =√(25+81+169)

⇒Distance =√275

⇒Distance =5√11

Thus, the distance between (-3, 5, -7) and (2, -4, 6) is 5√11.

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According to the given information the distance between the points 16.58 units.

the algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective dimensions (see coordinate system). The distance formulae for locations in rectangular coordinates in two- and two half Euclidean space are based upon that Pythagorean theorem.

We can determine an object's actual size by learning how far it is from us. The area that an object occupies in the sky may be measured. The distance to an object is then necessary to calculate its real size. An thing appears smaller the farther it is away.

The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂)

\(\begin{equation}d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}\end\)

x₁, y₁, z₁ = -3, 5, -7

x₂, y₂, z₂ = 2, -4, 6

\(\begin{equation}d=\sqrt{\left(2+3\right)^2+\left(-4-5\right)^2+\left(6+7\right)^2}\\\begin{equation}d=\sqrt{\left(5\right)^2+\left(-9\right)^2+\left(13\right)^2}\\\begin{equation}d=\sqrt{25+81+169}\\\begin{equation}d=\sqrt{275}\\\)

= 16.58 units

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Answer: Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

Step-by-step explanation:

Let's use "x" to represent the amount of money Jerod took to the mall.

After he spends $8.50 on a snack, he will have x - 8.50 dollars left.

Since he wants to keep a minimum of $10.00 in his pocket at all times, we can set up an inequality:

\(\sf:\implies x - 8.50 \geqslant 10.00\)

To solve for x, we can add 8.50 to both sides of the inequality:

\(\sf:\implies x \geqslant 18.50\)

Therefore, Jerod took at least $18.50 to the mall to ensure that he had at least $10.00 left after buying a snack.

Greetings! ZenZebra at your service, hope it helps! <33

Answer:

x = 8

Step-by-step explanation:

Subtract 2x from both sides

5x +7−2x=2x+31−2x

3x+7=31

Subtract 7 from both sides

3x+7−7=31−7

3x=24

Divide both sides by 3

3x/3 = 24/3

x = 8

Hope this helps!

Answer:

x=8

Step-by-step explanation:

5x-2x=7-31

3x=24 then divide 3 divided by 24=8

The distribution used to obtain the critical value in this situation is the Student's t-distribution.

Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.

The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.

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The one-space dimensional heat equation is a mathematical representation of how temperature changes in a one-dimensional system over time. The function represents the temperature at a given point in space and time. The equation includes two partial derivatives, which describe how temperature changes with respect to space and time.

It is important to note that this equation only works for one-dimensional objects, which do not exist in nature. However, it can still be used as an approximation for certain real-world scenarios. The boundary conditions for this equation specify the temperature at the boundaries of the system. The first boundary condition, (0), indicates that there is no heat flux entering or leaving the system at the boundary. The second boundary condition, (t,0), indicates that the temperature of the system is 2000 for all time at the boundary. These boundary conditions are crucial for solving the heat equation and obtaining a solution for the temperature function. It is important to understand the function, boundary conditions, and limitations of the one-space dimensional heat equation when working with temperature changes in a one-dimensional system.

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Answer:

5

Step-by-step explanation:

Answer:

2(x - 1) + 3

Step-by-step explanation:

Two times the difference of x and one = 2(x - 1)

Three more than = + 3

Answer:

75 dollars.

Step-by-step explanation:

Each person costs 25 dollars and p=3 we just put this into a equation.

25 × 3 = 75

C = 75

Answer:

7.44

Step-by-step explanation:

?

Given a line L¹ in R³, which is the span of the basis 18 -9 0, a basis for L² is given by the set of orthogonal-vectors:(1, 2, 0)T (0, 0, 1)T

We have to find a basis for the orthogonal complement of the line, which is denoted by L².

The orthogonal complement of L¹ is a subspace of R³ consisting of all the vectors that are orthogonal to the line.

Thus, any vector in L² is orthogonal to the vector(s) in L¹.

To find a basis for L², we can use the following method:

Find the dot product of the vector(s) in L¹ with an arbitrary vector (x, y, z)T, which represents a vector in L².

Setting this dot product equal to zero will give us the equations that the coordinates of (x, y, z)T must satisfy to be in L².

Solve these equations to find a basis for L².Using this method, let (x, y, z)T be a vector in L², and (18, -9, 0)T be a vector in L¹.

Then, the dot product of these two vectors is:

18x - 9y + 0z = 0.

Simplifying this equation, we get:

2x - y = 0

y = 2x

Thus, any vector in L² has coordinates (x, 2x, z)T, where x and z are arbitrary.

Therefore, a basis for L² is given by the set of orthogonal vectors:

(1, 2, 0)T (0, 0, 1)T

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The fox population predicted to be in the year 2022 is 53,110 foxes.

The change in population for a specific location over time is known as population growth. The formula to calculate population growth is given as \(P = P_0(1+r)^t\) where P is the population at time t, r is the growth rate, and P₀ is the initial population.

The time period is calculated from the initial and final years,  

t = 2022 - 2012 = 10 years.

Given the initial population is 24,600 and the rate is 8% = 0.08.

Then, the predicted population in the year 2022 is calculated as,

\(\begin{aligned}P&=24,600(1+0.08)^{10}\\&=53,109.55\\&\approx53,110\end{aligned}\)

The answer is 53,110 foxes.

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The area of the given trapezoidal site is 250,000 sq. ft.

The area of the trapezoidal with the dimensions of both bases and the height is given by the formula,

Area = 1/2 × height × (base1 + base2)

Units: square units

The given trapezoidal site has a base of 150 feet, i.e., base1 = 150 ft; a height of 2000 ft, i.e., height = 2000 ft and a parallel base of 100 feet, i.e., base2 = 100 ft.

Then, the area of the trapezoidal is

= 1/2 × 2000 × (150 + 100)

= 1/2 × 2000 × 250

= 250,000 sq. ft

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Answer:

  90°

  it is half the measure of the semicircular arc AC

Step-by-step explanation:

You want the measure of angle ABC inscribed in a semicircle.

An inscribed angle has half the measure of the arc it subtends. Angle ABC subtends a semicircle, an arc of 180°, so its measure is 180°/2 = 90°.

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The solution for the inequality in this problem is problem is given as follows:

v ≤ 81.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality is given as follows:

5v/9 ≤ 45.

v ≤ 45 x 9/5

v ≤ 9 x 9

v ≤ 81.

Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.

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Answer:

4 packages of AA batteries

6 packages of AAA batteries.

Step-by-step explanation:

Let the number of packages of AA batteries bought be x

Let

the number of packages of AAA batteries bought be Y

He Brought 10 packages of AA and AAA

thus,

x+y = 10   equation 1

Given

The AA batteries are sold in packages of 6, it means one packet contains 6 batteries

Thus,

Total number of AA  batteries in x packages = 6x

The AAA batteries are sold in packages of 8, it means one packet contains 8 batteries

Thus,

Total number of AAA  batteries in y packages = 8y

Given total no. of batteries is 72

thus    

6x + 8y = 72   equation 2

x+y = 10

y = 10-x ---using this in equation 2

6x + 8(10 - x)  = 72  

=> 6x + 80 - 8x = 72

=> -2x = 72-80 = -8

=> x = -8/-2 = 4

y = 10 -x = 10 -4 = 6

y = 6

Thus,

he bought 4 packages of AA batteries

6 packages of AAA batteries.

Answer:

-75

Step-by-step explanation:

-123 + 48

-*+ = -

123-48

75

But as the bigger number i.e 123 has a negative sign before so the answer will be in negative

i.e -75

Answer:

3/5

can also be written as 3:5

Step-by-step explanation:

Use:

squares/circles

Fill in the given info.

6/10

simplify (reduce the fraction)

6/10 = 3/5

3/5 is the ratio in simplest form.

Answer:

See below.

Step-by-step explanation:

Anthony                                                              Ciara

Week (x)    Process     Total dollars    Week (x)    Process  Total dollars

                                             (y)                                                      (y)

0                50+20•0        50                     0            10+30•0          10

1                 50 + 20•1       70                      1             10+30•1           40

2                 50 + 20•2      90                    2             10+30•2          70

3                 50 + 20•3      110                    3             10+30•3        100

4                 50 + 20•4      130                   4             10+30•4        130

5                 50 + 20•5      150                   5             10+30•5        160  

8                 50 + 20•8      210                   8             10+30•8        250

10                50 + 20•10    250                 10            10+30•10        310

Working together, they can complete the task in 4 hours and 48 minutes.

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

Tracy needs 8 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/8 hours = 1/8 task per hour.

This means that she can complete 1/8 of the task per hour.

Dave needs 12 hours to complete the task, then his ratio is:

1 task/12 hours = 1/12 task per hour.

This means that he can complete 1/12 of the task in one hour.

If they work together, then the ratios can be added:

R = \(\frac{1}{8}\) +  \(\frac{1}{12}\)

  = \(\frac{3+2}{24}\)

  = \(\frac{5}{24}\)

So, working together, in one hour they can complete  \(\frac{5}{24}\) of the task, now we can find the number of hours needed to complete the task as:

\(\frac{5}{24}\)×\(x\)= 1 task

x = \(\frac{24}{5}\) hours = 4.8 hours

knowing that an hour is 60 minutes, then 0.8 of an hour is 60*0.8 = 48 minutes.

Then x = 4 hours and 48 minutes.

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Answer:

Universal set is a set which contains all values

Union of Sets : The joining of two or more sets  .

Step-by-step explanation:

Answer:

four

Step-by-step explanation: