Rich bought 5 cupcakes and one pie. He knows his total bill and knows the pie was $6.89, but he wants to find the price of the cupcakes. How can he determine the price of each cupcake?

To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.

To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.

Here we start with the original equation:

K - X = V - W

First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:

K = X + V - W

Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides

X = K - V + W

So, the solution to the equation when solved for the letter 'x' is X = K - V + W.

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the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.

To find the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex], we need to compute the sum of the expression 17n - 15 for n ranging from 1 to 13.

Using the formula for the sum of an arithmetic series, we can express this sum as:

[tex]\[ \sum_{n=1}^{13} (17n - 15) = \sum_{n=1}^{13} 17n - \sum_{n=1}^{13} 15 \][/tex]

We know that the sum of the first \(n\) natural numbers can be expressed as [tex]\( \sum_{n=1}^{N} n = \frac{N(N+1)}{2} \).[/tex]

So, the sum of [tex]\(17n\) from \(n=1\) to \(n=13\)[/tex] is:

[tex]\[ \sum_{n=1}^{13} 17n = 17 \sum_{n=1}^{13} n = 17 \cdot \frac{13 \cdot (13 + 1)}{2} \][/tex]

[tex]\[ = 17 \cdot \frac{13 \cdot 14}{2} = 17 \cdot 91 = 1547 \][/tex]

And the sum of 15, 13 times (since there are 13 terms) is[tex]\(15 \cdot 13 = 195\).[/tex]

Now, we can find the value of the given expression:

[tex]\[ \sum_{n=1}^{13} (17n - 15) = 1547 - 195 = 1352 \][/tex]

So, the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.

To solve the equation b + c = 10/a for a, isolate a on one side of the equation by multiplying both sides by a, distribute a to both terms inside the parentheses, and then solve for a by dividing both sides by (b + c).

To solve the equation b + c = 10/a for a, we need to isolate a on one side of the equation. We can start by multiplying both sides of the equation by a to get rid of the denominator:

a(b + c) = 10

Next, we can distribute a to both terms inside the parentheses:

ab + ac = 10

Finally, we can solve for a by dividing both sides of the equation by (b + c):

a = 10 / (b + c)

Answer:

The mean will shift to the left.

Step-by-step explanation:

Answer:

Option: B

There are three times as many participants in the 40-59 age group than in the 0-19 age group.

Step-by-step explanation:

From the histogram we have following observations:

Number of people in the age group  0-19= 20

Number of people in the age group 20-39=40

Number of people in the age group 40-59=60

Number of people in the age group 60-79=50

Hence, from the data we could say that  there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).

Hence, option B is correct.

Answer:

Option D. 2.51 is correct.

Step-by-step explanation:

Magnitude of first earthquake = 8.6

Let intensity of first earthquake be x

[tex]Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)[/tex]

Magnitude of second earthquake = 8.2

Let intensity of second earthquake be y

[tex]Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)[/tex]

Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)

[tex]\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51[/tex]

Hence the required factor is 2.51

Therefore, Option D. 2.51 is correct.

Answer:

2.51

Step-by-step explanation:

Two translation rigid transformations are required to transform shape 1 to shape 2

The rigid transformation that can be performed on shape 2 to show that shape 2 is congruent to shape 1 is the option

Reasons:

The coordinates of the three points on shape 1 are; (2, 12), (4, 14), (6, 14)

The coordinates of the three points shape 2 are; (8, 4), (10, 6), (12, 6)

The difference in the coordinates are;

Difference in x-coordinate are;

Point 1 = 8 - 2 = 6

Point 2 = 10 - 6 = 6

Point 3 = 12 - 6 = 6

Therefore;

To get the x-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of -6 units or 6 units left

Difference in y-coordinate are;

Point 1 = 4 - 12 = -8

Point 2 = 6 - 14 = -8

Point 3 = 6 - 14 = -8

Therefore;

To get the y-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of 8 units or 8 units up

The composite transformation is therefore;

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Answer:

Option A

Step-by-step explanation:

Whenever we want to arrange a number of objects or letters or numbers n then we must check whether

i) repitition is allowed

If repitition is allowed then total number of ways = n!

ii) repitition not allowed.

In this case again we have to check whether order matters or not.

If order matters then no of ways nPn.  

Here n =5

We find that nPn = 5!

Thus both are correct.

Hence option A

Answer:

C) 2

Step-by-step explanation:

I took the quiz and got a 100%.

Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.

To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.

To set up the proportion, we have:

We can write the proportion as:

h1/s1 = h2/s2

Substituting the known values into the proportion gives us:

60/10 = x/25

Now we solve for x:

x = (60/10) * 25

x = 6 * 25

x = 150

Therefore, the height of the second building is 150 feet.

The sequence alternates between adding 2 and multiplying by -4. Starting with 6, the sequence progresses by these operations to reach 120. Following this pattern, the next term after 120 is a) 122 by adding 2.

The student has asked to make a conjecture about the next item in the sequence 6, 8, -32, -30, 120. To determine the pattern, let's look at the differences between each pair of numbers.

From 6 to 8, we add 2.

From 8 to -32, we multiply 8 by -4.

From -32 to -30, we add 2.

From -30 to 120, we multiply -30 by -4.

It appears that the sequence alternates between adding 2 and multiplying by -4. Following this pattern, after 120 the next operation should be adding 2.

Therefore, the next number in the sequence would be 120 + 2 = 122. Hence, the answer is option a. 122.

Answer:

E. HH, C. AA

Step-by-step explanation:

Got these from the quiz

To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.

Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.

First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.

Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.