The price of stock A at 9 a.m. was 12.67. Since then, the price had been increasing at the rate of $
0.06

Answer:

2/9

Step-by-step explanation:

Coin

A coin has 1 side heads and 1 side tails.

total number of possible outcomes = 2

desired outcome: heads

number of desired outcomes = 1

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(heads) = 1/2

Spinner

The spinner has 9 sections of equal size.

possible outcomes: the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9

total number of possible outcomes = 9

desired outcome: even number

number of desired outcomes = 4

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(even number) = 4/9

Combined probability

The coin and spinner are independent events. The overall probability of independent events is the product of the individual probabilities.

p(heads then even) = 1/2 × 4/9 = 4/18 = 2/9

Answer: 2/9

Answer:

695,512

Step-by-step explanation:

no explanation just x

The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.

Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.

Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.

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Answer:

There are 14 blue marbles in the bag.

Step-by-step explanation:

Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.

First, we need to find the total number of parts in the ratio. That's 12+5+2=19.

Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:

2/19 (x + x + 112 + blue) = blue

Simplifying this equation, we get:

2x + 224 = 17blue

Now we can solve for blue:

blue = (2x + 224)/17

We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:

blue = (2(3) + 224)/17 = 14

Therefore, there are 14 blue marbles in the bag.

The rule used by the merchant is a function because it establishes a relationship between the cost of an item and its selling price

A function is simply described as a mathematical rule, law or expression that shows the relationship between two variables.

These two variables are known as;

From the information given, we have that;

Function assigns a unique selling price for every cost input

Input: cost

Output: selling price = cost + 10% of cost Formula: SP = C + 0.1C.

By following this rule, consistent selling prices can be determined efficiently based on cos

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Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer:

There are 40 tables.

Step-by-step explanation:

Since we know that there are 9 times as many chairs, then there are tables, all we have to do is divide the number of chairs by 9, and we get the answer 40.

Answer:

x = 5

Step-by-step explanation:

3x + 7 = 22 <-- Subtract 7 on both sides

3x = 15 <-- Divide both sides by 3 to isolate x

x = 5

The value of x is:

x = 5

Work/explanation:

The objective of this problem is to solve 3x + 7 = 22 by isolating x.

I begin by subtracting 7 from each side:

3x = 22 - 7

3x = 15

Next, I divide each side by 3:

x = 5

Hence, the value of x is 5.

Part A: Approximately 50% of newborn babies weigh more than 3000 grams. Part B: Approximately 84.13% of newborn babies weigh more than 2000 grams. Part C: Approximately 84.13% of newborn babies weigh less than 4000 grams. Part D: Approximately 68% of newborn babies weigh between 2000 and 4000 grams. Part E: The range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.

1: Calculate the Z-scores for the given weights using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For Part A:

Z = (3000 - 3000) / 500 = 0

Using the Z-table, we find that the percentage of babies weighing more than 3000 grams is approximately 50%.

For Part B:

Z = (2000 - 3000) / 500 = -2

Using the Z-table, we find that the percentage of babies weighing more than 2000 grams is approximately 97.72%. Since we want the percentage of babies weighing more than 2000 grams, we subtract this value from 100% to get approximately 2.28%.

For Part C:

Z = (4000 - 3000) / 500 = 2

Using the Z-table, we find that the percentage of babies weighing less than 4000 grams is approximately 97.72%.

For Part D:

To find the percentage of babies weighing between 2000 and 4000 grams, we subtract the percentage of babies weighing more than 2000 grams from the percentage of babies weighing less than 4000 grams.

Approximately 97.72% - 2.28% = 95.44%

For Part E:

Since the Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, we need to find the weights that correspond to the boundaries of this range.

The lower boundary would be the mean minus one standard deviation: 3000 - 500 = 2500 grams.

The upper boundary would be the mean plus one standard deviation: 3000 + 500 = 3500 grams.

Therefore, the range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.

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The approximate revenue obtained from selling the 7th unit of this product is $24,387.93.

To find the revenue from selling the 7th unit, we first need to determine the price at which the 7th unit will be sold. We can do this by substituting x = 7 in the given price function:

p(7) = 9000e^(-0.1*7) = 9000e^(-0.7) = 3483.99

Therefore, the price at which the 7th unit will be sold is approximately $3,483.99.

Now we can calculate the revenue obtained from the sale of the 7th unit as the product of the price and the quantity:

Revenue = 7 * 3483.99 = $24,387.93

Thus, the approximate revenue obtained from selling the 7th unit of this product is $24,387.93.

It is important to note that the given price function is an example of an exponential decay function, which is often used to model situations where the demand for a product decreases as the price increases. In this case, the function shows that as the price increases, the quantity demanded decreases at an accelerating rate (-0.1 is the rate of decay). The revenue function can be derived as the product of the price and the quantity, and the revenue can be maximized by finding the price that will result in the highest quantity of units sold. However, in this problem, we were given the quantity and asked to find the revenue, so we simply used the price function to determine the price of the 7th unit and multiplied it by 7 to find the revenue.

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Answer:

∠ 1 = 110° , ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is

6x + 20 + 4x + 10 = 180

10x + 30 = 180 ( subtract 30 from both sides )

10x = 150 ( divide both sides by 10 )

x = 15

Then

∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°

∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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The equation that shows the Pythagorean identity is true for θ = 270° and is in the form sin²θ + cos²θ = 1 is option  B. 0² + (-1)² = 1

The Pythagorean identity is a fundamental trigonometric identity that relates the sine and cosine functions. It states that for any angle θ, the sum of the squares of the sine and cosine of that angle is equal to 1: sin²θ + cos²θ = 1.

We are given θ = 270° and we need to select the equation that satisfies the Pythagorean identity in the given form.

Let's evaluate each option:

A. 0² + 1² = 1

In this case, sin²θ = 0² = 0 and cos²θ = 1² = 1. Adding them together, we get 0 + 1 = 1, which satisfies the Pythagorean identity.

B. 0² + (−1)² = 1

Here, sin²θ = 0² = 0 and cos²θ = (−1)² = 1. Adding them, we have 0 + 1 = 1, which satisfies the Pythagorean identity.

C. (−1)² + 0² - 1

In this equation, sin²θ = (−1)² = 1 and co

s²θ = 0² = 0. However, the equation does not satisfy the Pythagorean identity because 1 + 0 - 1 ≠ 1.

D. 1² + 0² = 1

For this option, sin²θ = 1² = 1 and cos²θ = 0² = 0. Adding them together, we get 1 + 0 = 1, which satisfies the Pythagorean identity.

Based on our evaluation, options A and B both satisfy the Pythagorean identity for θ = 270°. Therefore, either A or B can be selected as the correct equation.The correct answer is  b.

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The Question was Incomplete, Find the full content below :

Which equation shows that the Pythagorean identity is true for θ = 270°?

Select the equation that is in the form sin²θ+ cos²θ = 1.

A. 0² + 1² = 1

B. 0² + (−1)² = 1

C. (-1)² + 0² - 1

D. 1² + 0² = 1

Answer:

  A.  p(t) = 16 -5t +2t²

Step-by-step explanation:

You want the interpolating polynomial for points (1, 13), (2, 14), and (3, 19).

The given system of equations can be solved by your favorite method to find ...

The interpolating polynomial is p(t) = 16 -5t +2t².

__

Additional comment

The points and the polynomial are graphed in the second attachment.

<95141404393>

The interpolating polynomial  is (a) p(t) = 13 - 2.5t +1.5t²

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

Points =  (1, 13), (2, 14), and (3, 19).

Using the general form of the quadratic formula, we have

a + b + c = 12

4a + 2b + c = 14

9a + 3b + c = 19

Subtract the equations to eliminate c

So, we have

3a + b = 2

5a + b = 5

Subtract the equations to eliminate b

So, we have

2a = 3

So, we have

a = 1.5

Next, we have

3a + b = 2

3(1.5) + b = 2

Evaluate

b = -2.5

Lastly, we have

4a + 2b + c = 14

4(1.5) + 2(-2.5) + c = 14

Evaluate

c = 13

So, the equation is p(t) = 13 - 2.5t +1.5t²

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Answer:

Θ = 23.9°

Step-by-step explanation:

Use inverse tangent in a calculator.

tan Θ = 23/52

tan Θ = 0.4423

tan^-1 0.4423 = 23.9°

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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a) The force in the coupling between the first carriage and the locomotive can be found by analyzing the net force acting on the train. It is determined to be 100 N.

b) The force in the coupling between the first carriage and the locomotive is a tension force.

a) To find the force in the coupling between the first carriage and the locomotive, we need to analyze the forces acting on the train.

The forces acting on the train are:

The driving force applied by the locomotive: 700 N

The resistance force of each carriage: 400 N (assuming equal resistance forces for both carriages)

The force in the coupling between the first carriage and the locomotive (unknown)

Since the train comes to rest, the net force acting on the train must be zero. We can set up the equation for the net force as:

Net force = Driving force - Resistance force - Force in coupling = 0

Substituting the given values:

700 N - 2(400 N) - Force in coupling = 0

Simplifying the equation:

700 N - 800 N - Force in coupling = 0

-100 N - Force in coupling = 0

Therefore, the force in the coupling between the first carriage and the locomotive is 100 N (opposite in direction to the driving force).

b) The force in the coupling between the first carriage and the locomotive is a tension force. Tension forces act along a string, cable, or any stretched connection. In this case, the coupling acts as a connection between the locomotive and the first carriage, so the force in the coupling is a tension force.

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The answer is 3.99 metric tons.

To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.

The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.

The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.

To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.

Rounding this value to two decimal places, we get 3.99 metric tons.

Therefore, the answer is 3.99 metric tons.

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The inverse of the equation is determined as [tex]y = \log_{6}(-3x)[/tex].

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

[tex]-3x = 6^y[/tex]

Take the logarithm of both sides of the equation with base -6:

[tex]\log_{6}(-3x) = y[/tex]

Finally, replace y with x to obtain the inverse equation as follows;

[tex]y = \log_{6}(-3x)[/tex]

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The expression to estimate the number of containers of salsa needed is: 48 × 3 × 9. none of the option is correct.

To estimate how many containers of salsa are needed for all the tables in one day, we need to consider the total number of tables and the number of salsa containers required for each table.

Given that there are 48 tables and each table has 3 different types of salsa, we can estimate the total number of containers needed by multiplying the number of tables by the number of salsa types.

However, we also need to account for the fact that there are 9 different sets of customers throughout the day. Each set of customers will use all the tables, so we need to multiply the estimated number of containers by the number of sets of customers to get an accurate estimation for the day.

Let's analyze the options provided:

A) 50 × 9: This option assumes there are 50 tables, which is incorrect based on the given information.

B) 16 × 3 × 9: This option assumes there are 16 tables, which is incorrect based on the given information.

C) 50 × 3 × 10: This option assumes there are 50 tables and 10 different sets of customers. Although the number of tables is incorrect, this option accounts for the number of salsa types and the number of sets of customers. However, it does not accurately represent the given scenario.

D) 40 × 5 × 5: This option assumes there are 40 tables and 5 different sets of customers. It also considers the number of salsa types. However, it does not accurately represent the given scenario as the number of tables is incorrect.

None of the options provided accurately represent the given scenario. The correct expression to estimate the number of containers of salsa needed for all the tables in one day would be:48 × 3 × 9

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Jolly Goods Limited may not be able to accept the order for 2,000 ornaments due to the limited capacity of the finishing department. While the cutting and assembling departments have the capacity to fulfill the order by working at 100% capacity, the finishing department cannot complete the required work within the given deadline. The company as a whole is operating at 85% of capacity, which suggests that the finishing department is already working close to its maximum capacity.

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Answer:

X=68m

Step-by-step explanation:

X²=40²+55²

X²=1600+3025

X²=4625

X=(4625)½

X=68m.

The measure of angle LOP is given as follows:

m < LOP = 52º.

The segment OP bisects the angle O of the rhombus into two smaller angles, which are NOP and LOP.

.

A bisection means that the larger angle is divided into two smaller angles of equal measure.

The measure of angle NOP is given as follows:

m < NOP = 52º.

Hence the measure of angle LOP is given as follows:

m < LOP = 52º.

The final sentence is to find the measure of angle LOP.

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Answer: (-5, -7)

Step-by-step explanation: To find the intersection of two functions, you need to set them equal to each other and solve for x.

In this case, we have:

2x + 3 = -4x - 27

Adding 4x to both sides, we get:

6x + 3 = -27

Subtracting 3 from both sides, we get:

6x = -30

Dividing both sides by 6, we get:

x = -5

Now that we have the value of x, we can find the corresponding value of y by plugging it into either of the original equations. Let's use f(x) = 2x + 3:

f(-5) = 2(-5) + 3 = -7

Therefore, the intersection of the two functions is (-5, -7).

Answer: Its going down by odd numbers

Step-by-step explanation:

5-2=3, 2-(-3)= 5, then it would go on 7, 9, 11, 13...

Answer:

The difference between the numbers does not follow a common pattern; hence, the sequence is not arithmetic.

Step-by-step explanation:

Let's take the 1st two digits, 5 and 2

The difference between the numbers, 5-2 = 3

Following this pattern,

2-(-3) = 5

-3-(-10) = 7 and,

-10-(-19) = 9.

We can see that the differences are 3, 5, 7 and 9 and therefore we can prove that there is no common difference between the numbers.

Hence the sequence does not follow an arithmetic pattern as there is no common difference

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The factoring of the polynomials gives;

1) Option C

2) Option A

3) Option B

4) Option C

5) Option A

6) Option B

7) Option C

8) Option C

9) Option B

10) Option B

1) 9x - 9

9(x - 1)

2) [tex]3x^2 - 9x[/tex]

3x(x - 3)

3) [tex]36x^2 - 1[/tex]

By the difference of two squares;

(6x + 1) ( 6x - 1)

4) [tex]x^2 - 4[/tex]

By the difference of two squares;

(x + 2) (x - 2)

5)

[tex]x^2 + 12x + 36\\x^2 + 6x + 6x + 36[/tex]

x(x + 6) + 6(x + 6)

(x + 6) (x + 6)

[tex](x + 6)^2[/tex]

6)

[tex]25x^2 - 20x + 4\\5x^2 + 2(5x) -2 + (-2)^2\\(5x - 2)^2[/tex]

7) [tex]x^2 - 3x - 54[/tex]

(x + 6) (x - 9)

8) [tex]2x^2 + 9x + 18 x+ 81\\ 2x^2 + 18 x + 9x + 81[/tex]

2x(x + 9) + 9 (x + 9)

(2x + 9) (x + 9)

9)

[tex]9y^2 + 18y + 8\\9y^2 + 12y + 6y + 8[/tex]

3y(3y + 4) + 2y(3y +4)

(3y + 2) (3y + 4)

10)

[tex]20z^2 - 3z - 9\\20z^2 - 15z + 12z - 9[/tex]

5z(4z - 3) + 3(4z - 3)

(5z - 3) (4z + 3)

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Answer:

y = x^2 + 6x +7

y=-x+1

Step-by-step explanation:

To answer this question, we need to find the equation for the line and for the parabola. So, let's do just that!

Line:

The line has a slope of -1 and and y-intercept of 1. This means that the equation for the line is y=-x+1.

Parabola:

To find the vertex form of a parabola, we must first find the vertex form of a parabola. The vertex form of a parabola is y=a(x-h)^2+k, where the vertex is (h,k). Since the vertex of the parabola is (-3,-2), h=-3 and k=-2. Let's plug these values into the vertex form of a parabola.

y=a(x-h)^2+k

y=a(x-(-3))^2+(-2)

y=a(x+3)^2-2

We're not done yet, though, as we still need to find the value of a. To do this, we will take one of the points on the parabola and plug it into the equation. I will be using the point (-1,2).

y=a(x+3)^2-2     [Plug in x and y values]

2=a((-1)+3)^2-2     [Simplify]

2=a(2)^2-2     [Simplify]

2=4a-2     [Add 2 to both sides]

4=4a     [Divide both sides by 4]

a=1

Now, we know that the equation of our parabola in vertex form is y=(x+3)^2-2. This isn't what the problem is asking for, though. Instead, they want the standard form of the parabola. To do this, we will need to expand y=(x+3)^2-2.

y=(x+3)^2-2

y=x^2 + 6x + 9 -2

y = x^2 + 6x +7

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Answer:

[tex]\huge\boxed{\sf 44\ boys}[/tex]

Step-by-step explanation:

= Length × Width

Length = 32 m

Width = 11 m

Area of school room:

= Length × Width

= 32 × 11

= 352 m²

= 352 / 8

[tex]\rule[225]{225}{2}[/tex]

The given pair of equations is y = 4x + 2 and y = x + 5, and we are to determine which of the given graphs represents their solution. The first equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing this with the given equation, we see that its slope is 4 and y-intercept is 2.

The second equation is also in slope-intercept form, y = mx + b. Comparing it with the given equation, we see that its slope is 1 and y-intercept is 5.Since we have two lines, we need to find their point of intersection. Substituting y = 4x + 2 into y = x + 5, we have4x + 2 = x + 5Simplifying the equation, we get3x = 3, which gives x = 1.

Substituting this value of x into either of the equations, say y = 4x + 2, we have y = 4(1) + 2 = 6. Hence, the point of intersection is (1, 6). Now, let's examine the given graphs and see which one has (1, 6) as a point of intersection:

Graph 1: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 1 is not the solution.

Graph 2: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 2 is not the solution.

Graph 3: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2.

Hence, these two lines cannot intersect at (1, 6). Graph 3 is not the solution.Graph 4: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 4 is not the solution.

Therefore, none of the given graphs represents the solution to the pair of equations.

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