Determine whether each ratio or rate is proportional. Explain your reasoning and write the proportion : Question #1) 24 points in 4 games; 48 points in 10 gamesQuestion #2) 15 songs for $5; 45 songs for $15

Direction: Find the value of each variable in a parallelogram.

\(\begin{gathered}\quad\quad\begin{gathered}\begin{array}{cc}\rm 1.) Finding \: the \: value \: of \: x \\ 8x - 3 = 2x + 9 \\ 8x - 2x = 9 + 3 & \\ 6x = 12 \\ \boxed{\pmb{x = 12}} \\ \\ \rm Finding \: the \: value \: of \: y \\ 3y - 5 = y + 5 & \\ 3y - y = 10 \\ 2y = 10 & \\ \boxed{\pmb{y = 5}} \end{array}\end{gathered}\end{gathered}\)

\(\begin{gathered}\quad\begin{gathered}\begin{array}{cc} \rm 2.) Finding \: the \: value \: of \: x \\ (2x + 10) \degree + (5x - 5) \degree = 180 \degree \\ 7x = 180 \degree - 10 \degree + 5 \degree \\ 7x = 180 \degree - 5 \degree \\ 7x = 175 \degree \\ \rm x = \frac{175}{7} \\ \rm \boxed{\pmb{x = 25 \degree}} & \rm \\ \\ \rm Finding \: the \: value \: of \: y \\ (5x - 5) \degree + y = 180 \degree \\ y = 180 \degree - (5x - 5) \degree \\ y = 180 \degree - 120 \degree \\ \boxed{\pmb{y = 60 \degree}}\end{array}\end{gathered}\end{gathered} \)

\(\begin{gathered}\quad\quad\begin{gathered}\begin{array}{cc} \rm 3.) Finding \: the \: value \: of \: x \\ 3x - 1 = 2x + 3 \\ 3x - 2x = 3 + 1 \\ x = 3 + 1 \\ \boxed{\pmb{x = 4}} \\ \rm \\ \rm Finding \: the \: value \: of \: y \\ 6y + 11 = 53 \\ 6y = 53 - 11 \\ 6y = 42 & \\ y = \frac{42}{6} \\ \boxed{\pmb{y = 7}} \end{array}\end{gathered}\end{gathered} \)

Answer:

294 in.²

Step-by-step explanation:

I believe this figure is a rectangular prism.

------------------------------------------------------------------------------------

Explain:

To find the surface area of a rectangular prism, use this formula:

\(SA=2lw+2lh+2wh\)

              or

\(SA=2(lw+lh+wh)\)

\(l-length\)

\(w-width\)

\(h-height\)

A phrase I use to help remember this formula is:

LISA WILSON LOST HER WITCH HAT TWICE (2)

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Solve:

The length of this rectangular prism is 9 in.

This width is 10 in.

The height is 3 in.

Now, I will plug the numbers into the first formula.

\(SA=(2*9*10)+(2*9*3)+(2*10*3)=294 in.^2\)

------------------------------------------------------------------------------------

Conclude:

I, therefore, believe the area of this rectangular prism is 294 in.²

Answer:

7

Step-by-step explanation:
add 7 to 3x

Then: 4x-3x=1x which gives:

1x=7

7/1=7

Answer:

The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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Answer:

22

Step-by-step explanation:

√(x+3) –4 = 1

√(x+3) = 1 +4

√(x+3) = 5

x + 3 = 5²

x = 25 –3

x = 22

Answer:125

Step-by-step explanation:

the drawing (fountains) was 10 inches apart, but real life was 400. 400/10 = 40. this means that the real life distance is 40x the distance of the drawing.

therefore, multiply 3.125 by 40 as well. you get 125.

Answer: 125 ft

Step-by-step explanation:

Let x be the real remove between the two shows.

At that point, we are able set up the extent:

10 inches / 400 feet = 3.125 inches / x

To illuminate for x, able to cross-multiply and disentangle:

10 inches * x = 400 feet * 3.125 inches

10x = 1250

x = 125 feet

It takes time of near about 35 year.

Given that,

Storage capability of computers has been doubling every 5 years

The date of 1st computer made = 1980

computer could store 5 megabytes,

Now,

We can use the following calculation to determine how long it took computers to store 100 megabytes:

Therefore,

Log₂ (final amount / beginning amount)

=  Log₂ (100 / 0.5)

= log₂ (200)

= 7.64 is the number of doublings.

If each doubling takes five years, then it would take computers just over seven doublings or almost 35 years to store 100 megabytes.

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Hello :

    3/8 = x/(15 + x)

⇔ 3(15 + x)/8 = x

⇔ (45 + 3x)/8 = x

⇔ 45 + 3x = 8x

⇔ 8x - 3x = 45

⇔ 5x = 45

⇔ x = 45/5

⇔ x = 9

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

Answer:

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

Step-by-step explanation:

Mutually exclusive:

If two events are mutually exclusive, if one events happen, the other cannot happen, and vice-versa.

Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4}

A die has the following outcomes: 1,2,3,4,5,6

Even numbers: 2,4,6

Greater than 4: 5, 6

6 is an outcome of both events A and B, so they are not mutually exclusive.

Picking a card; A= {Selecting a 7}, B={Selecting a Heart}

Cards numbered from 1 to 13, each number with 4 types. So we can have a card of hearts numbered 7, which means that these events are not mutually exclusive.

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

If you get no heads, the probability of at least 1 head is 0.

If you get at least 1 head, the probability of no heads is 0.

This means that this is the answer, that is, these events are mutually exclusive.

Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

(3,1) or (1,3) has a sum of 4 and a 3 on one die, which means that these events are not mutually exclusive.

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.

We are given the following measures:

\(\sf\:m\angle AB = 56 \\\)

\(\sf\:m\angle BC = 59 \\\)

\(\sf\:m\angle CD = 63 \\\)

\(\sf\:m\angle DE = 63 \\\)

\(\sf\:m\angle EF = 31 \\\)

To find the measure of the geometry-big circle, we add up these measures:

\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)

Substituting the given values:

\(\sf\:56 + 59 + 63 + 63 + 31 \\\)

Simplifying the expression:

\(\sf\:272 \\\)

Therefore, the measure of the geometry-big circle is 272.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

A. y=-2x+1

Step-by-step explanation:

rise over run rise(up or down) 2 run(right or left) 1

Answer:

\(35degrees\)

Given:

Required:

Find whether the series is arithmetic or geometric.

Explanation:

(1) The given terms are

Find the common difference of the following terms.

The common difference is the same between each term so the given sequence is arithmetic.

(2)The given terms are

Find the common difference as:

Since the common difference is not the same between each term so the given sequence is not arithmetic.

Now find the common ratio as:

Since the common ratio is not the same between each term so the given sequence is not geometric.

Thus the given sequence is neither arithmetic nor geometric.

(3)The given terms are

Find the common difference as:

Since the common difference is not the same between each term so the given sequence is not arithmetic.

Now find the common ratio as:

Since the common ratio is not the same between each term so the given sequence is not geometric.

Thus the given sequence is neither arithmetic nor geometric.

(4) The given sequence is:

Thus the terms of the sequence are 5,7,10,14,19.

\(3(4 - 2x) = - 2x\)

\(12 - 6x = - 2x\)

\(12 = - 2x + 6x \\ 12 = 4x \\ \frac{12}{4} = x \\ 3 = x\)

\(3(4 - 2x) = - 2x \\ 3(4 - 2(3)) = - 2(3) \\ 3(4 - 6) = - 6 \\ 3( - 2) = - 6 \\ - 6 = - 6 \: \: \green{ \checkmark}\)

The equation is true when x = 3. Therefore the answer is D. 3

\( \large \boxed{x = 3} \: \: \sf{or} \: \: \large \boxed{ \sf{D \: \: choice}}\)

Answer:

solution

Step-by-step explanation:

3 (4-2x)= -2x

12-6x= -2x

12= -2x+6x

12= 4x

12÷4= x

3= x

D

Answer:

12

Step-by-step explanation:

Arranging in ascending order -> 9, 10, 12, 12, 13, 15, 16

n = 7

Median = value of ((n + 1) / 2) th term

             = value of (7+1) / 2 th term

             = value of 4 th term

             = 12

Hope it helps :)

The range of the graphed function in this problem is given as follows:

[-9, 9].

The values of y in this function are between -9 and 9, inclusive, hence the range of the function is given as follows:

[-9, 9].

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Answer:first: x,y second: -x,y third:-x,-y fourth: x,-y, you can use this as a guide since it already tells you where to put it, the slop isn’t basically the change in y values between the same two points, this could get you through since I can’t point it out when my files can’t load. Sorry

Step-by-step explanation:

As per the given statement, the inequality will be equal to y<2/3x+2.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

here, we have,

As per the data provided in the question,

The statement is,

y is less than 2/3 times of x, that is = y<(2/3)x and,

then it is plus two is added to the equation,

y<(2/3)x+2

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Answer:

The actual distance is of 21.76 kilometers.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

The scale on a map is given as 1 : 320,000

This means that each unit on the map represents 320,000 units of distance.

Distance between the top of the two mountains on the map is 6.8cm

Then

1 cm - 320,000 cm

6.8 cm - x

Applying cross multiplication:

\(x = 6.8*320000 = 2176000\)

Distance in kilometers

To convert from centimeters to kilometers, we divide by 100000. So

2176000/100000 = 21.76

The actual distance is of 21.76 kilometers.

Answer:

A''(3, 2), B''(-1, 4), C''(2, 0)

Step-by-step explanation:

For the first step, negate the y coordinate.

For the second step, add 4 to the x coordinate and 5 to the y coordinate.

\(A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)\)

The sign of F on the interval -4<x<1 is 0

We know that in mathematics,  a function from a set X to a set Y assigns to each element of X exactly one element of Y.

The given function is

f(x)=(x-2)(x+4)(x+5)(x-1)(x-9)

The Interval is given as -4<x<1

Substituting the values of x in the function we have

f(x)=(-5-2)(-4+4)(1+5)(2-1)(9-9)

This implies that

f(x)=(0)(0)(6)(1)(0)

Multiplying the brackets to have

f(x)=0

In conclusion, the sign of F on the interval -4<x<1 is 0

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Answer:

b = 3.8

Step-by-step explanation:

- b/0.1 +2.9= -35.1

Subtract 2.9 from each side

- b/0.1 +2.9-2.9= -35.1-2.9

-b/.1 = -38

Multiply each side by -.1

-b/.1 * (-.1) = -38 *(-.1)

b = 3.8