Angie was planning a party and wanted to get the best deal on a venue. Venue A charges a fee of $50 plus $25 per hour. Venue B charges a fee of $10 plus $35 per hour. Using systems of equations, answer the following questions. Show all your work.

A. Write a system of equations that represent the situation above. (Be sure to identify the variables.)

B. When will the Venues' cost the same amount? Explain how you found your solution.

C. Which Venue is cheaper for a party that will only be 2 hours?

Answer:

The answer is 6.5

Step-by-step explanation:

It was a long process, but overall if you look at how long the segment x looks, it has to be less than half of the segment that is 30 units long so the only one that makes sense is 6.5

If A and B are independent, then the correct statements are P(A and B) = 0.12 and P(A or B) = 0.58.

Let's evaluate each statement:

P(B/A) = 0.4:

This statement is incorrect. If events A and B are independent, the occurrence of event A does not affect the probability of event B.

Therefore, P(B/A) would still be equal to the probability of B, which is 0.4 in this case.

P(A and B) = 0.12:

This statement is correct. The probability of the intersection of independent events A and B is calculated by multiplying their individual probabilities. In this case, P(A and B) = P(A) * P(B) = 0.3 * 0.4 = 0.12.

P(A/B) = 0.3:

This statement is incorrect. If events A and B are independent, the occurrence of event B does not affect the probability of event A. Therefore, P(A/B) would still be equal to the probability of A, which is 0.3 in this case.

P(A or B) = 0.58:

This statement is incorrect. To calculate the probability of the union of two events, we need to consider whether the events are mutually exclusive or not.

If events A and B are independent, but not mutually exclusive, we can calculate P(A or B) as P(A) + P(B) - P(A and B). In this case, P(A or B) = 0.3 + 0.4 - 0.12 = 0.58.

Therefore, the correct statements are:

The statements regarding P(B/A) = 0.4 and P(A/B) = 0.3 are incorrect in the context of independent events A and B.

Learn more about probability and independent events

brainly.com/question/3742321

#SPJ11

Answer:

\(\sf x^3 -2x+2\)

a = 1, b = 0, c = -2, d = 2

Explanation:

using distributive method:

expand:

group terms:

final form:

comparing with  \(\sf ax^3 + bx^2 + cx + d\)  ||   our input: \(\sf x^3 +0x^2 -2x+2\)

we can determine that: a = 1, b = 0, c = -2, d = 2

Answer:

a = 1

b = 0

c = -2

d = 2

Step-by-step explanation:

Given polynomial:

\(\sf= (2x-1)(x^2-2)-x(x^2-x-2)\\\\Distributing \\\\= 2x(x^2-2)-1(x^2-2)-x^3+x^2+2x\\\\= 2x^3-4x-x^2+2-x^3+x^2+2x\\\\Combining \ like \ terms\\\\= 2x^3-x^3-x^2+x^2-4x+2x+2\\\\= x^3-2x +2\\\\Comparing \ it \ with \ \bold{ax^3+bx^2+cx+d}, \ we \ get:\\\\a = 1\\\\b = 0\\\\c = -2\\\\d = 2\\\\\rule[225]{225}{2}\)

Hope this helped!

we remove the parenthesis and add the number that have the same exponent

Answer:

see explanation

Step-by-step explanation:

1 vertex form

2 factored form

3 standard form

Answer:

1. neither

2. factored form

3. standard form

Step-by-step explanation:

Vertex form of a quadratic equation:  \(y=a(x-h)^2+k\)

Standard form of a quadratic equation:  \(y=ax^2+bx+c\)

Factored form of a quadratic equation: \(y=a(x+d)(x+e)\)

\(\textsf{1.}\quad(x-1)^2+6\)

This is in vertex form, so as this is not an option → neither

\(\textsf{2.}\quad(2x-3)(x+4)\)

This is in factored form

\(\textsf{3.}\quad3x^2-5x+7\)

This is in standard form

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

To more on Progression:
https://brainly.com/question/30442577
#SPJ8

Answer:

103.75 score

Step-by-step explanation:

10 % scored higher than the mean?

 50% is the mean %   so we need to look for the z score corresponding to 60 %    from z-score table   this is z-score of   .25

.25 standard deviations (which is 15)   above 100 =

    .25  * 15       +   100 = 103.75   score

The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.

You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

Now according to the question,

Possible letter combinations

Choose any letter and make it a repeat letter = 26 ways

But, there are ⁴C₂ = 6 spots available for the identical letters.

And there are (25)×(24) other methods for selecting the other two letters.

The total amount of "words" equals ⁴C₂ × 26 × 25 × 24 = 93600.

Furthermore, because the numerals cannot be repeated = 10 × 9 = 90

So, the total number of choices = 93600 × 90 = 8,424,000

Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.

To know more about the combination, here

https://brainly.com/question/11732255

#SPJ4

==========================================

Work Shown

45 girls : 15 boys

45/15 girls : 15/15 boys .... divide both parts by 15

3 girls : 1 boy

This tells us there are three times as many girls as there are boys.

We write this as the ratio 3 : 1. The order of the terms is important. We cannot say 1:3 since that would imply there are more boys than girls, but it's the other way around.

The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.

The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.

The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.

What is experimental probability?

The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Given that two coins flip together. The outcomes of a coin is {H,T}.

The outcomes after flipping of two coins are

{HH, HT, TH, TT}

The total number of outcomes is 4.

The number of outcomes to get two tails is 1.

The probability of getting two tails is 1/4 = 0.25 = 25%.

The number of outcomes to get two heads is 1.

The probability of getting two heads is 1/4 = 0.25 = 25%.

The number of outcomes to get one head and one tail is 2

The probability of getting one head and one tail is 2/4 = 0.50 = 50%.

The theoretical probabilities will change for every experiment.

To learn more about probability, click on the below link:

https://brainly.com/question/16052744

#SPJ1

In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels

The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.

LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.

Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.

To know more about dependent variable refer here:

https://brainly.com/question/1479694?#

#SPJ11

The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and and the common multiple of 16 and 40 could be 2 .

What is prime factor ?

prime factor can be defined as the number which is divisible by that number and the number should be prime.

The prime factor tree for 16 as follows

16 = 2*8 = 2* 2 * 4 = 2*2*2*2

                16

            2         8

                     2    4

                         2     2

The prime factor tree for 40 as follows

40 = 2*20 = 2*2*10 = 2*2*2*5

                40

           2            20

                      2        10

                              2      5

Hence, The prime factor trees for 16 and 40 could be 2,2,2,2 and 2,2,2,5 respectively and the common multiple of 16 and 40 could be 2 .

To learn more about prime factor from the given link.

https://brainly.com/question/29775157

#SPJ1

Answer:

triangle 4 is coming under asa criterion

The number of years that the glory days of the cowboy period lasted was about 2 decades.

The glory days of the cowboy times is typically deemed as the span between the conclusion of the Civil War in 1865 to around the dawn of the1900s. During these years, cowboys played an indispensable role in boosting and improving the American West peculiarly in the cattle industry.

With bravery and courage, they would drive a herd of cattle across wide expanses frequently grappling with harsh conditions and situations of peril. The genesis of industrialization phased out the cowboy era with train networks expediting the transportation of both bovine species and freight with efficiency.

Find out more on cowboys at https://brainly.com/question/21524558

#SPJ1

Answer:

2nd Bullet point / (B)

Step-by-step explanation:

divide by b on both sides

For 7 tests, the probability is approximately 0.066. For 18 tests, the probability is approximately 0.184. To achieve a probability of at least 0.9, the number of tests required would be 22.

The probability of committing a type I error (rejecting a true null hypothesis) in a single hypothesis test at a significance level of 0.01 is 0.01. However, when performing multiple tests, the probability of at least one type I error increases.

(a) To find the probability of committing at least one type I error for 7 tests, we need to calculate the complementary probability of not committing any type I error in all 7 tests.

The probability of not committing a type I error in a single test is 1 - 0.01 = 0.99. Since the tests are independent, the probability of not committing a type I error in all 7 tests is 0.99⁷ ≈ 0.934.

Therefore, the probability of committing at least one type I error is approximately 1 - 0.934 ≈ 0.066.

Similarly, for 18 tests, the probability of not committing a type I error in all 18 tests is 0.99^18 ≈ 0.818. Thus, the probability of committing at least one type I error is approximately 1 - 0.818 ≈ 0.184.

(b) To determine the number of tests needed for a probability of at least 0.9, we need to solve the equation 1 - (1 - 0.01)ᵇ ≥ 0.9.

Rearranging the equation, we have (1 - 0.01)ᵇ ≤ 0.1. Taking the logarithm of both sides, we get b * log(0.99) ≤ log(0.1). Solving for b, we find m ≥ log(0.1) / log(0.99).

Using a calculator, we find b ≥ 21.85. Since m represents the number of tests, we round up to the next whole number, resulting in b = 22. Therefore, it would take at least 22 tests to achieve a probability of at least 0.9 of committing at least one type I error.

Learn more about probability:

brainly.com/question/32117953

#SPJ11

Answer:

Yes

Step-by-step explanation:

y>3x+6 creates this graph:

Where (-5,-8) is in the shaded area

Answer:

24 cm

Step-by-step explanation:

Perimeter of equilateral triangle = 12 cm

Therefore, measure of one side of equilateral triangle = 12/3 = 4 cm

Perimeter of hexagon = 6 * measure of one side of equilateral triangle

= 6 * 4 = 24 cm

Answer:

y = −4x^2 + 4x − 3

Step-by-step explanation:

1) The first iteration, n, turns out to be (x1, y1) = ( , ).

2) If the second iteration, n, is (x2, y2) = ( , ).

To find the values of (x1, y1) and (x2, y2), we need additional information or the specific steps of the gradient method applied in MATLAB. The gradient method is an optimization algorithm that iteratively updates the variables based on the gradient of the function. Each iteration involves calculating the gradient, multiplying it by the learning rate (λ), and updating the variables by subtracting the result.

3) After s many iterations (and perhaps changing the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt, yopt) = ( , ).

To determine the values of (xopt, yopt), the number of iterations (s) and the specific algorithm steps or convergence criteria need to be provided. The gradient method aims to reach the minimum of the function by iteratively updating the variables until convergence is achieved.

4) The value of the minimum, once the convergence is reached, will be determined by evaluating the function at the point (xopt, yopt). The specific value of the minimum is missing and needs to be provided.

Learn more about gradient method here:

brainly.com/question/28016665

#SPJ11

the complete question is:

Matlab The Gradient Method Was Used To Find The Minimum Value Of The Function North F(X,Y)=(X^2+Y^2−12x−10y+71)^2 Iterations Start At The Point (X0,Y0)=(2,2.6) And Λ=0.002 Is Used. (The Number Λ Is Also Known As The Size Or Step Or Learning Rate.) 1)The First Iteration N Turns Out To Be (X1,Y1)=( , ) 2)If The Second Iteration N Is (X2,Y2)=( ,

Matlab

The gradient method was used to find the minimum value of the function north

f(x,y)=(x^2+y^2−12x−10y+71)^2 Iterations start at the point (x0,y0)=(2,2.6) and λ=0.002 is used. (The number λ is also known as the size or step or learning rate.)

1)The first iteration n turns out to be (x1,y1)=( , )

2)If the second iteration n is (x2,y2)=( , )

3)After s of many iterations (and perhaps change the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt,yopt)=( , );

4)Being this minimum=

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

More can be learned about linear functions at https://brainly.com/question/15602982

#SPJ1

Answer:

w1= -1.4, w2= 3

Step-by-step explanation:

I will assume that "x" is a w since there is no x within the question

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w

1

=−1.4,w

2

=3

Evaluate

5×∣4w−1∣=5w+40

Simplify

5∣4w−1∣=5w+40

Rewrite the expression

5∣4w−1∣−5w−40=0

Separate the equation into 2 possible cases

5(4w−1)−5w−40=0,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,4w−1≥0

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

5(−(4w−1))−5w−40=0,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,4w−1<0

Evaluate

w=3,w≥

4

1

w=−

5

7

,w<

4

1

Find the intersection

w=3

w=−

5

7

,w<

4

1

Find the intersection

w=3 w=− 57

Solution

w

1

=−

5

7

,w

2

=3

Alternative Form

w 1=−1.4,w 2

=3

the answer

155

324

5/9 (87/3(1/12)= 155/324

Answer:

66.66%

Step-by-step explanation:

The first model is the one you should use here as 24 and 18 are multiples of 3, this means that there is eight students in each group

That means that 18/24 is equal to 2/3 so the percentage of students that like to dance is 66.66%

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of option (C) the variability around the regression line

The standard error of the estimate in a regression-based forecast is a measure of the variability of the actual data points around the predicted values of the regression line.

It tells us how much the actual data points are likely to deviate from the predicted values, and provides a measure of the accuracy of the forecast. It is not related to the time required to derive the forecast equation, the maximum error of the forecast, or the time period for which the forecast is valid.

Therefore, the correct option is (C) The variability around the regression line.

Learn more about regression-based forecast here

brainly.com/question/14803765

#SPJ4

The give question is incomplete, the complete question is:

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of:

A. the time required to derive the forecast equation.

B. the maximum error of the forecast.

C. the variability around the regression line.

D. the time period for which the forecast is valid.

Answer: 30

Step-by-step explanation:

     A LCD, or least common denominator, is the lowest common multiple of both denominators.

     Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...

     Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...

    We can see the LCD of 3/5 and 5/6 is:

           30

Read more about least common denominators here:

https://brainly.com/question/17498894

The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal.  In this case, the problem is asking us to determine the LCD or least common denominator of two numbers.  We are provided with two fractions that we will use to help determine our solution.  However, before solving for the LCD let us first define what LCD means.

Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.

Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.

Permutations

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

We have a total of 21 students to choose from. There are four positions to be filled.

The total number of ways to fill the positions out of the 21 students can be calculated by using the permutation formula:

Where n is the total number of elements in the set and r is the number of elements selected. In our case, n=21 and r = 4, thus:

Applying the properties of the factorial function:

Simplifying:

There are 143,640 possible ways to choose for the 4 positions

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

Let the lengths of a triangle be 6x , 7x and 10x.

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \boxed{ \text{Sum \: of \: all \: sides \: of \: triangle = Perimeter \: of \: a \: triangle}}}\)

⟹ \( \sf{6x + 7x + 10 = 92}\)

Solve for x

⟹ \( \sf{23x = 92}\)

⟹ \( \sf{ \frac{23x}{23} = \frac{92}{23}} \)

⟹ \( \sf{x = 4}\) cm

Now , Replacing the value of x :

⟼ \( \sf{6x = 6 \times4 = 24}\) cm

⟼ \( \sf{7x = 7 \times 4 = 28}\) cm

⟼ \( \sf{10x = 10 \times 4 = 40}\) cm

Hence , the sides of the triangle are 24 cm , 28 cm and 40 cm.

Hope I helped ! ♡

Have a wonderful day / night ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁