10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x + y = 8
-x - 3y = -12
3y + 12
-3y + 12
3y - 12
-3y - 12

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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Answer and Explanation:

B, because a rectangle has 2 pairs.

Theoretically, D could also be correct, but not in every scenario; all rectangles are parallelograms, but not all parallelograms are rectangles.

Answer: no 25 is a perfect square

Step-by-step explanation:

The account balance at the end of the month is $283.61

What distinguishes withdrawals from deposits?

The deposits into the bank would increase the balance, hence, they have positive sign whereas the withdrawals would decrease the balance since their sign is negative, in other words, we can determine the account balance at the end of the month by adding deposits to beginning balance and deducting all withdrawals

ending balance=beginning balance+ deposits-withdrawals

beginning balance=$80.83

total deposits=$107.51+$102.07+$110.57

total deposits=$320.15

total withdrawals=-$99.71-$17.66

total withdrawals=-$117.37

ending balance=$80.83+$320.15-$117.37

ending balance=$283.61

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Answer:

The number of quarts of apple juice in a case of 24 bottles is 18.75.

Step-by-step explanation:

This question is solved by proportions, using rules of three.

Amount of ounces:

1 bottle - 25 ounces

24 bottles - x ounces

Applying cross multiplication:

\(x = 25*24 = 600\)

600 ounces to quarts:

Each ounce has 0.03125 quarts.

1 ounce - 0.03125 quarts

600 ounces - x quarts:

\(x = 600*0.03125 = 18.75\)

The number of quarts of apple juice in a case of 24 bottles is 18.75.

Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

Answer:

410.77

Step-by-step explanation:

Hope this helps

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

125cm cubed

Step-by-step explanation:

First, the formula for volume is l x h x w, so we have to multiply 5 x 5 x 5 which equals 125.

Hope this helps!

Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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Answer:

The relevance of the background is to give more insight into a topic you are researching. It can provide clarifying information to your reader.

Hope this helped and have a great day,

Ginny

Step-by-step explanation:

Answer:

y = x - 2

Step-by-step explanation:

slope: 1

y-int. = -2

equation: y = x - 2

The radius of convergence is a-R a+R = 6+12 =18 and 6-12 = -6 for the |6x 12/<78 and diverges if |6x 12| 78.

The set of actual numbers x wherein the collection converges is the c program language period of convergence. If there exists a actual wide variety R such that the collection converges for |x−a|R, then R is the radius of convergence.

The radius of convergence is 1/2 of of the duration of the c program language period of convergence. If the radius of convergence is R then the c program languageperiod of convergence will consist of the open c program languageperiod: (a − R, a + R). To discover the radius of convergence, R, you operate the Ratio Test.

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Answer: it went up 25%

Step-by-step explanation: if it would have went up 50%, that would be $20, meaning it would be $60. It is 25% and it is half of 50% and half of $20 is $10 equaling $50

A $40 autographed and framed poster of the Spice Girls goes up in price to $50. What is the percent of increase in the price?

=

25% increase

The numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total (-7, 7), (-5, 5), (-3, 3), (-1, 1).

To arrange the numbers -7, -5, -3, 3, -1, and 1 into three pairs with the same total, we need to find a combination of pairs that will give us the same sum for each pair.

Let's start by examining the numbers:

-7, -5, -3, 3, -1, 1

To find pairs with the same total, we can start by pairing the numbers with their additive inverses (numbers that sum to zero). In this case, -7 and 7, -5 and 5, -3 and 3 can be paired up. This leaves us with -1 and 1.

We have three pairs now: (-7, 7), (-5, 5), (-3, 3). However, we still have -1 and 1 remaining. To make the sum of the pairs equal, we can pair -1 with 7 and 1 with -5.

The three pairs with the same total are:

(-7, 7), (-5, 5), (-3, 3), (-1, 1).

Each pair sums up to zero, resulting in the same total for each pair. For example, (-7 + 7 = 0), (-5 + 5 = 0), and so on.

Therefore, the numbers -7, -5, -3, 3, -1, and 1 can be arranged into three pairs with the same total:

(-7, 7), (-5, 5), (-3, 3), (-1, 1).

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Answer:

A

Step-by-step explanation:

The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = \(πr^2\)

A ≈ 3.14 × \((2^2)\)

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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The total cost of all the items he wants to buy with the applied discount and before tax is $9.9.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Bashir has a loyalty card good for a 10% discount at his local hardware store.

So, Each good he buys at (100 - 10)% = 90% of the value before tax.

He wants to buy some items that cost $11  before the discount and tax.

Therefore the amount he has to pay is,

= (90/100)×11.

= $9.9

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