Rusty’s pizza has two family deals each Wednesday. The first family deal is $14.50 constant fee (which includes pizza and potato wedges) and $1.75 per beverage. The second family deal is a $10 constant fee and $2.50 per beverage. At how many beverages, b, will the family deals cost the same amount?

Answer:

0.50x=0.40x+3

0.50x-0.40x=3

0.1x=3

————-

0.1

x=30

Answer:

the answer is 56

Step-by-step explanation:

first off you need to add every number up which adds to be 336,

then you divide by the number of pieces in the data which in this case is 6,

366 divided by 6 is 56

I HOPE THIS HELPED!

The solutions of the equation  x² + 2x + 10 = - 3x + 4 are  x=-2 and x=-3

The given equation is x² + 2x + 10 = - 3x + 4.

Take all the terms to the left side

x² + 2x + 10+3x-4=0

Combine the like terms

x²+5x+6=0

x²+2x+3x+6=0

Take out the factors

x(x+2)+3(x+2)=0

(x+3)(x+2)=0

x=-2 and x=-3

Hence, x=-2 and x=-3 are the solutions of the equation  x² + 2x + 10 = - 3x + 4.

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Antonia could use a spreadsheet or database software to quickly process the data she collects about the runners.

A spreadsheet provides a tabular format that allows Antonia to organize and analyze the data efficiently. She can create columns for different variables like runner ID, name, age, gender, race time, etc. and input the data accordingly.

Spreadsheets offer functionalities like sorting, filtering, and mathematical operations that enable Antonia to perform calculations, generate statistics, and visualize the data through charts or graphs.

Alternatively, a database software like Microsoft Access or MySQL can be used to store and manage the runner data. Databases offer a structured approach to handle large amounts of data, allowing Antonia to create tables, define relationships, and write queries to extract specific information from the data set.

Both spreadsheet and database software provide tools to handle and process data efficiently, enabling Antonia to analyze the information she collects about the runners in a quick and organized manner.

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Answer: x=m-y/n

Step-by-step explanation:

The expression with x as the subject is x = mn - y.

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.

We have,

m = (x + y) / n

x as the subject means we have to solve for x.

Now,

m = (x + y) / n

Multiply both sides by n.

mn = x + y

Subtract y on both sides.

mn - y = x

x = mn - y

Thus,

x = mn - y.

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Answer:

70

Step-by-step explanation:

Answer:

31.5

Step-by-step explanation:

5*6=30

30+5=35

35*0.3=31.5

Answer:

1.32

Step-by-step explanation:

total area = 33

33/5 1/2 = 6 .         X=6

5 1/2 x 1/2 = 2.75 .       6 x 1/2 = 3

2.75 x 3 = 8.25

new area = 8.25

8.25 x .13 = 1.32

\(\huge\text{Hey there!}\)

\(\mathsf{3p + 5(2q + p) + 3p - 6q}\\\mathsf{= 3p + 5(2q) + 5(p) + 3p - 6q}}\\\mathsf{= 3p + 10q + 5p + 3p - 6q}\\\large\textbf{COMBINE the LIKE TERMS}\\\mathsf{= (3p + 5p + 3p) + (10q - 6q)}\\\mathsf{= 3p + 5p + 3p \bold{+} 10q - 6q}\\\mathsf{= 8p + 3p + 4q}\\\mathsf{= 11p + 4q}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{11p + 4q}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

(a^4+b^4)/(a^2b^2)

Step-by-step explanation:

The logical equivalence (p ∨ ~q) ∧ (~p ∨ ~q) ≡ ~q.

1. Start with the given expression: (p ∨ ~q) ∧ (~p ∨ ~q).
2. Apply the distributive law: (p ∧ ~p) ∨ (~q ∧ ~q).
3. Apply the law of contradiction: False ∨ (~q ∧ ~q).
4. Simplify: ~q ∧ ~q.
5. Apply the law of idempotence: ~q.

In this derivation, we used the distributive law to expand the expression and then applied the law of contradiction to simplify it further. Finally, we used the law of idempotence to arrive at the final expression ~q, which proves the logical equivalence.

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Answer:

To find the image of point D after the translation (x,y) --> (x + 13.5, y - 8.5), we need to add 13.5 to the x-coordinate of D and subtract 8.5 from the y-coordinate of D.

Therefore, the image of point D after the translation is:

D' = (32.5 + 13.5, -23 - 8.5)

= (46, -31.5)

So the answer is D. (46, -31.5).

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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Answer:

Step-by-step explanation:4

Answer:

x > 8

Step-by-step explanation:

-6x + 18 < 2 - 4x

-2x + 18 < 2

-2x < -16

x > 8

The binomial expansion of (1 + i)^2n can be written as ∑(n choose k)(i^k)(1^(n-k)), where (n choose k) represents the binomial coefficient of n and k. And that's the binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).

Using the identity cos(npi/2) = 0 when n is odd and cos(npi/2) = (-1)^n/2 when n is even, we can simplify the expression to:
(1 + i)^2n * 2^n * cos(npi/2) = ∑(n choose k)(i^k)(1^(n-k)) * 2^n * cos(npi/2)
When n is odd, cos(npi/2) = 0, so the expression simplifies to:
∑(n choose 2k)(i^(2k))(1^(n-2k)) * 2^n
When n is even, cos(npi/2) = (-1)^n/2, so the expression simplifies to:
∑(n choose 2k)(i^(2k))(1^(n-2k)) * 2^n * (-1)^(n/2)
Therefore, the binomial expansion of (1 + i)^2n * 2^n * cos(npi/2) can be written as either of these simplified forms, depending on whether n is odd or even.

The binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).
Step 1: Apply the binomial theorem to the term (1+i)^2n.
The binomial theorem states that (a+b)^n = Σ [n! / (k!(n-k)!) * a^k * b^(n-k)], where the sum runs from k=0 to k=n.
In this case, a=1 and b=i. Applying the theorem:
(1+i)^2n = Σ [2n! / (k!(2n-k)!) * 1^k * i^(2n-k)]
Step 2: Simplify the expression for the binomial expansion.
For the complex number i, we have i^2 = -1, i^3 = -i, and i^4 = 1. Using this pattern, we can rewrite the i^(2n-k) term in the expansion:
(1+i)^2n = Σ [2n! / (k!(2n-k)!) * 1^k * (-1)^((2n-k)/2) * i^(k % 4)], for even k values.
Step 3: Multiply the binomial expansion by 2^n * cos(nπ/2).
Now, we just need to multiply our expansion by the given factors:
(1+i)^2n * 2^n * cos(nπ/2) = Σ [2n! / (k!(2n-k)!) * 1^k * (-1)^((2n-k)/2) * i^(k % 4) * 2^n * cos(nπ/2)], for even k values.
And that's the binomial expansion of (1+i)^2n * 2^n * cos(nπ/2).

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The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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The shortest distance between airports A and B that can be covered by an airplane flying from airport A at a heading of 300 (N 60 W) is =  401 miles.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, is a trigonometric formula that simply establishes a relationship between the length of a triangle and the cosine of one of its angles. The length of the third side of a triangle can be calculated if we know the lengths of the first two sides and the angle between them.

An aircraft takes off from airport A with a heading of 300 (N 60 W). The aircraft changes its direction to 350 (N 10 W) after flying 320 miles, and after flying an additional 112 miles, it reaches airport B.

Below is an attachment with the problem's image. The two sides in this image are 112 miles and 320 miles apart, and the angle between them is 130 degrees. As a result, x has the value

So, by putting the values we get:

\(x=\sqrt{112^{2}+130^{2}-2(112)(130) \cos 130^{\circ}}\)

x = 401 miles.

Therefore, the shortest distance between airports A and B that can be covered by an airplane flying from airport A at a heading of 300 (N 60 W) is 401 miles.

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To calculate the total amount accrued when you deposit the money in an account that earns compound interest you have to use the following formula

A: amount accrued

P: principal amount

t: time, years

r: interest rate, expresed as a decimal value

n: number of coumpound periods

For this exericse

The principal amount is P=$1000

The time is t= 9 years

The interest rate is 9%/100=0.09

The compounding periods are 12/year (the interest is compounded monthly) so for the 9 year time period is 9*12=108

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Answer:

because there is no number is greater than 4 and less than 1

Answer:

Step-by-step explanation:

Some of the expressions that can be derived that have the values of 12 are:

i. 2a = 2 x 6

      = 12

ii. 3b = 3 x 4

        = 12

iii. (b  + c) x a = (4 - 2) x 6

                = 2 x 6

                = 12

iv. 2b + \(c^{2}\) = (2 x 4) + (-2 x -2)

                = 8 + 4

                = 12

v. \(b^{2}\) -  \(c^{2}\) = (4 x 4) - (-2 x -2)

             = 16 - 4

             = 12

vi. \(c^{4}\) - b = (-2 x -2 x -2 x -2) + 4

             = 16 - 4

             = 12

If x = M/10^t, where M is an integer not divisible by 10, then x has a terminating decimal representation.

To prove this, let's consider the fraction x = M/10^t, where M is an integer not divisible by 10 and t is a positive integer.

The decimal representation of x is obtained by dividing M by 10^t. Since M is not divisible by 10, it means that the prime factorization of M does not contain any factors of 2 or 5.

We can express 10^t as 2^t * 5^t. Since the prime factorization of M does not include any factors of 2 or 5, when we divide M by 10^t, all the factors of 2 and 5 will cancel out in the denominator.

For example, let's consider x = 37/10^3:

x = 37/(2^3 * 5^3)

x = 37/(8 * 125)

x = 37/1000

Here, we can see that all the factors of 2 and 5 have canceled out in the denominator. Therefore, the decimal representation of x will terminate, as there are no recurring digits.

If x = M/10^t, where M is an integer not divisible by 10, then x will have a terminating decimal representation. This is because the prime factorization of M does not contain any factors of 2 or 5, resulting in the cancellation of these factors in the denominator when dividing by 10^t. As a result, there are no recurring digits, and the decimal representation of x will terminate.

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Answer:

1.) 14.09 m/s

2.) 6.9 m/s

Step-by-step explanation:

Given that the boat is pointing North and can typically move at a speed of 12.8 m/s in calm waters. The boat travels through water where there is a 5.9 m/s current flowing to the East.

The speed of the boat relative to a stationary observer on land will be achieved by using pythagorean theorem

V^2 = 12.8^2 + 5.9^2

V^2 = 198.65

Square root both sides

V = 14.09 m/s

2.) If the boat turns to face directly West.

Since the boat can move at speed 12.8 m/s in a calm water, the speed of the boat if it face west will be

12.8 - 5.9 = 6.9 m/s

Therefore, the boat is moving relative to land at 6.9m/s

Answer:

4300 x 5/100 = 215

215 x 7 = 1 505

4300 + 1505 = 5 805

Answer:

.27 or 27/100

Step-by-step explanation:

each tenth is equal to 10 one hundredths

Answer:

yes

Step-by-step explanation:

Substitute x = 2 and y = 5 into the left side of the equations and if equal to the right side then they are a solution.

x + 2y = 2 + 2(5) = 2 + 10 = 12 ← True

3x + 6y = 3(2) + 6(5) = 6 + 30 = 36 ← True

Thus x = 2, y = 5 is a solution to both equations

Answer:

i dont understand your question

Step-by-step explanation:

They function by balancing their budgets through a combination of these revenue streams, along with careful budgeting and expenditure management.

Comparing a state without an income tax to one with an income tax, the key differences lie in the tax burden placed on residents and businesses. In the absence of an income tax, individuals in the state without income tax enjoy the benefit of not having a portion of their businesses may find it more attractive to operate in such states due to lower tax obligations. However, these states often compensate for the lack of income tax by imposing higher sales or property taxes.

States without a state income tax, such as Texas, Florida, and Nevada, function by generating revenue from various alternative sources. Sales tax is a major contributor, with higher rates or broader coverage compared to states with an income tax.

Property taxes also play a significant role, as these states tend to rely on this form of taxation to fund local services and public education. Additionally, fees on specific services, licenses, or permits can contribute to the state's revenue stream.

Comparing such a state to one with an income tax, the key differences lie in the tax structure and the burden placed on residents and businesses. In states without an income tax, individuals benefit from not having a portion of their earnings withheld, resulting in potentially higher take-home pay. This can be appealing for professionals and high-income earners. For businesses, the absence of an income tax can make the state a more attractive location for investment and expansion.

However, the lack of an income tax in these states often means higher reliance on sales or property taxes, which can impact residents differently. Sales tax tends to be regressive, affecting lower-income individuals more significantly. Property taxes may be higher to compensate for the revenue lost from the absence of an income tax.

Additionally, the absence of an income tax can result in a greater dependence on other revenue sources, making the state's budget more susceptible to fluctuations in the economy.

Overall, states without a state income tax employ alternative revenue sources and careful budgeting to function. While they offer certain advantages, such as higher take-home pay and potential business incentives, they also impose higher sales or property taxes, potentially impacting residents differently and requiring careful management of their budgetary needs.

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Answer:

1.3

Step-by-step explanation: