Emma is buying a gift for her mother's birthday. She purchases flowers and a gift certificate that cost a total of $68, not including tax. If the cost of the gift certificate is $14 more than 2 times the cost of the flowers, what is the cost of the flowers? Set up a system of equations, then solve using a matrix.

The center of mass is (2,1) since m1 has a mass of 10 and is located at (4,2). The center of mass is the average of the locations of the masses, weighted by the masses.

We can calculate the center of mass of these two spheres by using the formula c = (m1*L1 + m2*L2) / (m1 + m2). m1 is the mass of the first sphere, and L1 is the location of the first sphere. In this case, m1 is 10, and L1 is (4,2). We assume that m2 is 0 and L2 is (0,0). Plugging these values into the formula, we get c = (10*(4,2) + 0*(0,0)) / (10 + 0), which is (2,1).  This is because the center of mass is the average of the locations of the masses, weighted by the masses. In this case, the only mass is 10, and it is located at (4,2). Therefore, the center of mass is simply (4,2) since it is the only mass that contributes to the calculation.

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The complete question: find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1 = 10, L1 = ( 4,2)

The inequality that best represent the expression is x ≥ 12

A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

The sign for greater than is >

The sign for less than <

The sign for greater than or equal to is ≥

The sign for less than or equal to is ≤

There must be at least 4 people in the group. This means that a group member must greater or equal to 4. There are 3 groups.

Represent the value of the number of friends by x

then, x/3 ≥ 4

therefore x ≥ 12

this means that the number of friends must be greater or equal to 12

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A binomial setting is one in which there are a fixed number of trials, the outcome in each trial is either a success or a failure, the probability of success or failure is known, and the probability doesn't change from trial to trial.

A binomial setting is one in which we know the number of repetitions (n=20), the outcome of each trial can be considered either a success or a failure (p=0.4, q=1-p=0.6), and the probability of success or failure of any trial does not change from trial to trial (p=0.4, q=1-p=0.6).

For example, if we toss a coin 20 times, and we know the probability of success (head) is 0.4 and the probability of failure (tail) is 0.6, then this is a binomial setting. We can calculate the probability of getting exactly 10 heads in 20 tosses using the binomial formula: P(X=10) = (20C10) * (0.4^10) * (0.6^10) = 0.1775.

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After solving the given equation we know that students worked for 17 hours a week.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, the given equation is:

g=−0.0007h+0.018h+3.02

Now, we know that g is 2.72, so we can calculate for h as follows:

2.72=−0.0007h+0.018h+3.02

2.72 = -0.0173h + 3.02

- 0.3 = -0.0173h

h = -0.3/-0.0173

h = 17.34

Rounding off: 17 hours

Therefore, after solving the given equation we know that students worked for 17 hours a week.

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Standard Deviation, σ: 3.152

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given, Data set: 8, 7, 10, 10, 17, 13, 7, 10

variance:

σ² = Σ(xi - μ)²/N

σ²=  ((8 - 10.25)² + … + (10 - 10.25)²)/8

σ²= 79.5/8

σ²  =9.9375

σ = √9.9375

σ = 3.1523

The sampling mean most likely follows a normal distribution. In this case, the standard error of the mean can be calculated using the following equation:

σ =  σ/√N

σ = 1.114

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The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:

Perimeter of the square = 4a unit

The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,

4(x + 2) = 40

Simplify the equation, then we have

4(x + 2) = 40

(x + 2) = 10

x = 10 - 2

x = 8

The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.

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The complete question is given below.

Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).

Answer:

So, there are 5,280 feet in a mile, so you will want to find out how many times 5, 280 will go into 23,760. To do this, you will divide.

23,760/5,280 = 4.5

There are 4.5 or 4 1/2 miles in 23,760 feet!

Step-by-step explanation:

Hope it helps! =D

The missing numbers are -80 and -20.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

There is a number line in the question.

In a number line, numbers are arranged in equal intervals.

The constant interval here = -40 - -60 = 20

x - -100 = 20

x + 100 = 20

x = 20 - 100

x = -80

First missing number is -80.

y - -40 = 20

y + 40 = 20

y = 20 - 40

y = -20

Hence the numbers missing are -80 and -20.

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The Correlation Coefficient -0.12 shows that The taller the baby, the lighter the baby.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.

Given:

Correlation Coefficient = -0.12

As, The range of a correlation coefficient ranges from -1 to 1.

When the number is closer to -1 or closer to 1, there is a substantial association, and when the number is closer to 0, there is no link.

The correlation coefficient in this instance is -0.12, indicating a marginally negative correlation. The negative sign indicates that when one component changes, the other decreases, making a baby that is taller and lighter.

Hence, The taller the baby, the lighter the baby.

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Answer:

1/2

Step-by-step explanation:

Triangle XYZ has endpoints (0,0) (0,8) and (4,6)

Triangle X'Y'Z' has endpoints (0,0) (0,4) and (2,3)

As you can see, all the coordinates from Triangle XYZ are halved to get the coordinates of Triangle X'Y'Z', so the scale factor is 1/2.

The equation that matches the hanger diagram is 2x=5

From the question, we have the following parameters that can be used in our computation:

The hanger diagram added as an attachment

From the diagram, we hav

Left = x + x

Right = 1 + 1 + 1 + 1 + 1

This gives

Left = 2x

Right = 5

So, we have

2x = 5

hence, the equation is 2x = 5

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Answer:

c (72)

Step-by-step explanation:

since there are four wheels to every bike, you just have to multiply the number of bikes to the amount of wheels per bike. given this, 18 * 4=72.

a) 0.04550 has four significant figures.

b) 5.0003 has four significant figures.

c) 1.000 x [tex]10^5[/tex] has four significant figures.

d) 0.00002 has one significant figure.

e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.

f) 7 has one significant figure.

Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.

Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.

For example, in the given number 5.006, there is four significant number,

since all zeros between integers are always significant.

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Answer:

An agency that occurs when a principal and an agent categorically agree to enter into an agency agreement with each other is known as which of the following?

These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear function is given below.

y = 2x – 6

The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.

As when the put the given points in the equation , than it satisfies the given condition.

Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.

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Answer:hie

hie

Step-by-step explanation:hie

A solution of the first order IVP consisting of this differential equation is   y = [tex]\frac{1}{x^2-5}[/tex] and the domain of y considered as a function over the reals is (-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

We have to find the domain of y considered as a function over the reals.

The differential equation is  y' + 2x[tex]y^2[/tex] = 0

The solution of the given differential equation is y = 1/([tex]x^2[/tex] + c)......(1)

The given initial value; y(-3) = 1/4

Replace the initial value in the first-order DE solution provided. To obtain the equation for y, locate the constant c and then re-substitute 'c'.

Now put x = -3 and y(-3) = 1/4 in equation 1

[tex]\frac{1}{4}=\frac{1}{(-3)^2+c}[/tex]

[tex]\frac{1}{4}=\frac{1}{9+c}[/tex]

9+c = 4

Subtract 9 on both side, we get

c = -5

Now substitute the value of c again in equation 1

y = [tex]\frac{1}{x^2-5}[/tex]

To find the domain of y we can write it as

y = [tex]\frac{1}{(x)^2-(\sqrt{5})^2}[/tex]

Now the simplified form is

y = [tex]\frac{1}{(x-\sqrt{5})(x+\sqrt{5})}[/tex]

Now the domain of y over R is

(-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).

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The complete question is:

y = 1/([tex]x^2[/tex] + c) is a one parameter family of solutions of the first order DE y' + 2x[tex]y^2[/tex] = 0. Find a solution of the first order IVP consisting of this differential equation and the given initial condition.

y(-3) = 1/4

Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)

Answer:

Option 3. Look at my screenshot so you can see the circled one

Step-by-step explanation:

The reasoning behind this is slope is rise over run (rise/run)
Graph 3 goes down 3 so -3 and runs 1 over so (-3/1)
This is simplified as -3.

I hope this helps you out :D

The equivalent expression for 1/2(2a - 6b+ 8) will be a - 3b + 4

Expressions that are equivalent do the same thing even though they have different appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are substituted for the variable and both expressions yield the same result, you can also tell if two expressions are equivalent.

This will be:

1/2(2a - 6b+ 8)

= a - 3b + 4

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Complete question

Distribute to create an equivalent expression with the fewest symbols possible 1/2(2a - 6b+ 8) =

Answer: 602.88 square feet

Equation for surface area of cylinder:

A = 2πrh+2πr^2

r = 6, because radius is half of the diameter

h = 10

A = 2(3.14)(6)(10) + 2(3.14)(6)^2

A = 376.8 + 226.08

A = 602.88 square feet

The solution to the equation is i , -i , 4i , -4i

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

x⁴ + 17x² + 16 = 0   be equation (1)

On simplifying the equation , we get

Substitute the value of x² = u

u² + 17u + 16 = 0

The roots of the quadratic equations are

u = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

u = [ -17 ± √ ( 289 - 4 ( 1 ) ( 16 ) ) ] / 2

On further simplification , we get

u = [ -17 ± √ ( 289 - 64 ) ] / 2

u = ( -17 ± √ 225 ) / 2

u = ( -17 ± 15 ) / 2

The two values of u are

u = ( -17 - 15 ) / 2

u = -16

And , u = ( -17 + 15 ) / 2

u = -1

Substitute the value of x² = u , we get

x² = -16

Taking square roots on both sides of the equation , we get

x = ± √ ( -16 )

x = ± 4i

And ,

x² = -1

x = ± i

So , the values of x are i , -i , -4i and 4i

Hence , the equations are solved

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The average salary for college graduates is 53% higher than that of high school graduates.

Mathematically, percentage increase can be calculated by using this mathematical expression:

Percentage increase = [Final value - Initial value]/Initial value × 100

Substituting the given parameters into the percentage increase formula, we have the following;

Percentage increase = [62,047 - 40,626]/40,626 × 100

Percentage increase = 21,421/40,626 × 100

Percentage increase = 0.527 × 100

Percentage increase = 52.7 ≈ 53%.

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21.931% of Nicole's monthly pay goes to rent.

percent = (638/2900) x 100

percent = 0.21931 x 100

percent = 21.931%

The general form of exponential formula is y = a * b^x, the  population of the city in 2018 6.058454 million.(c) the population of the city be 8 million19.38548963 years.

In this problem, a = 5.21 million and b = 1 + 2.86%/100 = 1.0286.

In 2012, the population was 5.89 million.

In 2018, the population will be 5.89 * 1.0286 ^ (2018 - 2012) = 5.89 * 1.0286 ^ 6 = 6.058454 million.

To find when the population will be 9 million, your equation becomes:

9 = 5.21 * 1.0286 ^ x divide both sides of this formula by 5.21 to get:

9/5.21 = 1.0286 ^ x take the log of both sides of the equation to get:

log(9/5.21) = log(1.0286^x) since log(1.0286^x) = x * log(1.0286), the equation becomes:

log(9/5.21) = x * log(1.0286)

Divide both sides of this equation by log(1.0286) to get:

log(9/5.21) / log(1.0286) = x

Solve for x to get:

x = 19.38548963.

Confirm by replace x in the original equation to get:

9 = 5.21 * 1.0286 ^ 19.38548963 becomes 9 = 9.

This confirms the value of x is good.

The population will grow to 9 million in 19.38548963 years.

To find when the population will double, the equation becomes:

2 = 1 * 1.0286 ^ x

Simplify to get:

2 = 1.0286 ^ x

Take the log of both sides of this equation to get:

log(2) = log(1.0286 ^ x)

Since log(1.0286 ^ x) = x * log(1.0286), this equation becomes:

log(2) = x * log(1.0286)

solve for x to get:

x = log(2) / log(1.0286) = 24.5808602.

to confirm this is true, replace x in the original equation to get:

2 = 1.0286 ^ 24.5808602 which becomes 2 = 2.

This confirms the value of x is true.

The population will double in 24.5808602 years.

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Work Shown:

A = P*(1+r*t)

A = 5000*(1+0.12*30/12)

A = 6500

The amount $6500 is what you pay back

Divided over 30 months gives 6500/30 = 216.67 dollars per month.

Side note: The value t is in years, so 30 months = 30/12 years.

Answer:

$10,224.30

Step-by-step explanation:

The approximate length of the pendulum is 2 feet.

Two or more expressions with an Equal sign is called as Equation.

Given that period (T) of a pendulum is related to the length (L) of the pendulum and

acceleration due to gravity (g) by the formula T=2π√L/g.

g=32 ft/s2

t=1 sec

We need to find L

1=2×3.14√L/32

32=6.28√L

32/6.28=√L

5.09=√L

Square on both sides

L=25.9 inches

L=2 feet because 12 inches = 1ft.

Hence, the approximate length of the pendulum is 2 feet.

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Answer: To determine how many months it will take for an initial investment of Rs1000 to grow to Rs1200 at a 10% interest rate, we can use the formula:

Time = (ln(final value / initial value)) / (ln(1 + interest rate))

where ln is the natural logarithm function.

Plugging in the given values:

Time = (ln(1200/1000)) / (ln(1 + 0.10))

Time = (ln(1.2)) / (ln(1.10))

Time = 0.18232 / 0.09531

Time = 1.913 months

It will take approximately 1.913 months for an investment of Rs1000 to grow to Rs1200 at a 10% interest rate.

Step-by-step explanation:

The height in meters is 19.75 meters

The rocket hit the ground after 8.06 sec

The maximum height in seconds is 81 meters

we would have to use 0.5 as the value for t in the formula

h(t) = -5t² + 40t + 1

h(0.5) = -5(0.5)² + 40(0.5) + 1

= -1.25 + 20 +1

= 19.75

To find when the rocket hit the ground, we need to find when the height of the rocket is equal to 0. So we will set h(t) = 0 and solve for t:

-5t² + 40t + 1 = 0

by using Quadratic equation formula we get t = (-b ± √(b²-4ac))/2a

we solve this using the calculator

so t1 = (40 + 40.6)/10 = 80.6/10 = 8.06 sec

Since the time of the rocket hit the ground should be positive, so the rocket hit the ground after 8.06 seconds after launch.

To find the rocket's maximum height, we need to find the vertex of the parabola. The vertex of the parabola can be found by using the formula x = -b/2a,

where x is time and a, b, c are from equation.

so, x = -b/2a

= -40/2*-5

= -40/ -10

= 4 sec

and by using the above formula of x, we get the

h(4) = -5(4)² + 40(4) + 1

= -80 + 160 + 1

= 81 meters

Therefore, the rocket's maximum height is 81 meters.

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