(x,y) (7,11) (8,13) (9,15) (10,17) Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer:

It will take them 3.43 hours.

Step-by-step explanation:

Let T denote the total cookies that need to be cocked. Observe that:

Then, by 1) and 2), if they work together would we able to make

[tex]\frac{T}{6}+\frac{T}{8}=\frac{8T+6T}{48}=\frac{14}{48}T=\frac{7}{24}T[/tex]

cookies per hour.

Therefore, in order to finish the T cookies they will need [tex]\frac{24}{7}\approx3.43 hours[/tex]

Answer:

896 apples

Step-by-step explanation:

We need to order this data to solve the problem. "X" will be the total number of apples he collected.

"He gave the first guard half of his apples and 1 apple more". Mathematically:

[tex]Guard 1 = \frac{X}{2}+1\\[/tex]

"To the second guard, he gave half his remaining apples and 1 more". Mathematically:

[tex]Guard2 = \frac{X}{4}+1[/tex]

"He did the same to each of the remaining five guards". Mathematically:

[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":

[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]

Solving this equation results in X = 896 apples.

Answer:

55 children's tickets

Step-by-step explanation:

Let the number of adult tickets sold  = a

Let the number of children tickets sold = c

As per the statement "The adult tickets were sold four times as many as children's tickets".the equation will be

a = 4c ----- (1)

As per second statement "the prices of the tickets for adults and children are $10 and $5 respectively."

The total price of the adult tickets = 10a

the total price of the children tickets = 5c

total tickets were sold for = $2,475

So the equation will be

10a + 5c = 2,475 ------(2)

Now substitute the the value of a from equation (1) to equation (2).

10(4c) + 5c = 2,475

40c + 5 c = 2,475

45c = 2,475

c = [tex]\frac{2475}{45}[/tex]

c = 55

The number of children's tickets 55.

Final answer:

To find the number of children's tickets sold in a spaghetti dinner event with given total sales and ticket prices, set up and solve the relevant equations step by step.

Explanation:

Given:

Total ticket sales for a spaghetti dinner = $2475

Adult ticket price = $10

Children's ticket price = $5

Number of adult tickets sold = 4 times the number of children's tickets sold

To find: Number of children's tickets sold

Step-by-Step Solution:

Let the number of children's tickets sold be x

Number of adult tickets sold = 4x

Write the equation: 5x + 10(4x) = 2475

Solve for x to find the number of children's tickets sold

x = 55

Answer:

q.1 quarter mile

q.2 half mile

:)

addition!

Step-by-step explanation:

Answer:

Self-fulfilling prophecy

Step-by-step explanation:

According to my research on studies conducted by various psychologists, I can say that based on the information provided within the question this is an example of a Self-fulfilling prophecy. This is defined as a phenomenon of when an individual believes something will happen a certain way, and that event ends up happening only because the individual changed their behaviors and actions causing it to happen. Which is what Jenna did with her statistics class.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

Self-fulfilling prophecy

Step-by-step explanation:

A  self-fulfilling prophecy is the social and psychological phenomenon that, when exposed to a personal belief,  a person will change its conduct or behaviour in order to confirm or make real that particular belief in order to   avoid cognitive dissonance or the fact of being wrong.

Jenna believes she is bad in statistics. But that belief, which is not really or necessarily true, makes her change her behaviour and not study or abandon her effort to become better at statistics, which at the same time makes her perform badly in statistics in the future. This reinforcing loop maintains the belief and prophecy going in time.

Answer:  it is B.) 7,000,000

Step-by-step explanation:

Answer:

9 (option D)

Step-by-step explanation:

Hi Dlynjen! How are you?

Well, as maybe you know a quadratic function is a polynomial of degree 2, that is, the highest exponent in the variable is 2 (formula: y = ax^2 + bx + c). The graph of a quadratic function is a parabola (it has a U-shape).

The vertex of a parabola is the highest or lowest point of the curve (depending on whether the U opens up or down). In this case the parabola opens up because the exercise mentions the vertex is the point (x = 0, y = 1) and then for the other values of “x” (1, 2, 3, etc.) the values of “y” are higher (1, 4, 9, etc.), that's why the vertex is the lowest point in this case.

The exercise asks you to calculate the slope (or average rate of change) of the curve between x = 5 and x = 6, all you know so far is that as the curve opens up it is assumed that the slope will be positive but to calculate the slope must apply the following formula:

M = (y2 - y1) / (x2 -x1)

But we only know x1 = 5, x2 = 6, y1 = 16 (value of the table that corresponds to x1 = 5) and we must first know how much y2 is worth (for x2 = 6). For this we must know what is the quadratic function (formula) that gives rise to our parable.

If we analyze the table, we see that for each value of “x”, the value of “y” is equal to the square of (x-1), that is, if we take x = 3 as an example, the value of Y = (3 -1) ^ 2 = (2) ^ 2 = 4. And so with all the values. Having obtained this formula we can now calculate the value of “y” for x2 = 6:

Y2 = (6-1) ^ 2 = (5) ^ 2 = 25

Finally, we calculate the average exchange rate with the previous formula, knowing x1 = 5, x2 = 6, y1 = 16 and y2 = 25:

m = (y2 - y1) / (x2 -x1)  

m = (25-16) / (6-1)  

m = (9) / (1)  

m = 9

I hope I've been helpful!

Regards!

Analyzing the data, the following values were

Mean = 21.84

Median = 15.8=

Standard deviation = 18.97

Coefficient of skewness = 0.955

a. To find the mean, median, and standard deviation, you can use the following formulas:

Mean = sum of all values / number of values

Median = middle value when the values are arranged in ascending order

Standard deviation = square root of [(sum of squared differences from the mean) / (number of values - 1)]

Mean = (4.2 + 6.3 + 7.5 + ... + 83.6) / 15 = 21.84

Median = 15.8 (the 8th value when arranged in ascending order)

Standard deviation = √([(4.2 - 21.84)² + (6.3 - 21.84)² + ... + (83.6 - 21.84)²] / 14) = 18.97

b. To find the coefficient of skewness using Pearson's method, you can use the following formula:

Coefficient of skewness = (3 * (mean - median)) / standard deviation

Coefficient of skewness = (3 * (21.84 - 15.8)) / 18.97 = 0.955

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Step-by-step explanation:

By the problem we know that our events are:

[tex]A=[/tex]A batch is formed from two different lots.

[tex]B=[/tex]A batch requires additional processing.

So, according to that:

a) [tex]P(A)=3%=0.03[/tex]

Because P(A) and [tex]P(A^{'} )[/tex] are complementary events

b) [tex]P(A^{'} )=1-P(A)=1-0.03=0.97=97%[/tex]

Because of the problem, we know that:

c) [tex]P(B/A)=0.4=40%[/tex]

and,

d) [tex]P(B/A^{'} )=0.05=5%[/tex]

From the formula

e) P(A ∩ B)= P(A)*P(B/A)=[tex](0.03)*(0.4)=0.012[/tex]

f) P(A ∩ B')=P(A)-P(A ∩ B)=[tex]0.03-0.012=0.018[/tex]

And, finally

g) P(B)=P(B/A)*P(A)+P(B/A')*P(A')=[tex](0.4)*(0.03)+(0.05)(0.97)=0.0605[/tex]

(a)Probability of P(A) = 0.03  (b)Probability ofP(A')  = 0.97.(c) Probability of P(B|A) = 0.40 (d) Probability of P(B|A') = 0.05 (e) Probability of P(A ∩ B) = 0.012. (f)Probability of P(A ∩ B') =  0.03 - 0.012 = 0.018. (g) Probability ofP(B) = 0.0605.

Let's determine the various probabilities step-by-step for the given scenario.

       Given: P(A) = 0.03 (3% of all batches).

        P(A') = 1 - P(A) = 1 - 0.03 = 0.97.

       Given: P(B|A) = 0.40 (40% of such batches).

        Given: P(B|A') = 0.05 (5% of such batches).

        P(A ∩ B) = P(B|A) * P(A) = 0.40 * 0.03 = 0.012.

        P(A ∩ B') = P(A) - P(A ∩ B) = 0.03 - 0.012 = 0.018.

       P(B) = P(B|A) * P(A) + P(B|A') * P(A') = (0.40 * 0.03) + (0.05 * 0.97) =    0.012 + 0.0485 = 0.0605.

Answer:

1st car is 6mph 2nd car is 100mph

Step-by-step explanation:

ans to first car is in the question

and just subtract total travelled distance of car 1 after 2.5 hours. then subtrct it from the total distance and with the remaining distance solve for speed of other car which is distance over time.

The speed of the slower car is 52 mph, and the speed of the faster car is 52 mph + 6 mph, which equals 58 mph. This was calculated using the relationship between speed, distance, and time.

Let's denote the speed of the slower car as v miles per hour (mph), which means the faster car will have a speed of (v + 6) mph. Since they are travelling in opposite directions, their speeds add up when determining how far apart they will be over a period of time.

Combined speed = v + (v + 6) = 2v + 6 mph

After 2.5 hours, they are 275 miles apart. Using the formula for distance, which is Distance = Speed ×Time, we have:

Distance = (2v + 6) × 2.5

275 miles = (2v + 6) × 2.5

Solving for v, we divide both sides by 2.5:

110 = 2v + 6

Now, subtract 6 from both sides:

104 = 2v

Finally, divide by 2 to find the speed of the slower car:

v = 52 mph

Therefore, the speed of the slower car is 52 mph, and the faster car is 52 mph + 6 mph, which equals 58 mph.

Answer:

The answer to your question is: 3.7 hours

Step-by-step explanation:

Kam can make 72 cookies/ 3 hours

Madison can make 120 cookies/4 hours

Time to make 200 cookies together = ?

First, calculate the number of cookies make per hour

Kam            72 ---------------- 3

                   x   ----------------  1 hour

  x = 72/3 = 24 cookies/h

Madison

             120 -------------   4 hours

               x ---------------      1 hour

x = 120 / 4 = 30 cookies

Now we write and equation where "t" will be time

         24t + 30t = 200      and solve it

         54t = 200

        t = 200/54

        t = 3.7 hours

The time taken by both of them will be 3.7 hours.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The given problem can be solved as follows,

The number of cookies made by Kam in 1 hour = 72/3 = 24.

The number of cookies made by Madison in 1 hour = 120/4 = 30.

The total number of cookies made by them in one hour = 30 + 24 = 54.

The time taken to make 200 cookies is the ratio of 200 and 54 as given below,

Time taken by both to make 200 cookies = 200/54 = 3.7 hours.

Hence, Kam and Madison would take 3.7 hours to make the cookies together.

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Answer:

  y = 8x + 3

Step-by-step explanation:

The slope-intercept form of the equation of a line is ...

  y = mx + b

Putting 8 where m is, and 3 where b is, we get ...

  y = 8x + 3

_____

Yes, it's really that simple.

The equation of the line with a slope of 8 and a y-intercept of 3 is y = 8x + 3. This is found by substituting the given values into the slope-intercept formula, which is y = mx + b.

In Mathematics, the slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept of the line. So, for the question, since the given slope, m = 8, and the y-intercept, b = 3, you can substitute these values into the formula to get the equation of the line. This results in the equation y = 8x + 3.

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Answer:

Either B or D.

Step-by-step explanation:

I consider both options valid. It all depends on how the employer is keeping track of time, ie if the pay "ticks" every 60 minutes, or an employee is allowed to clock in half hours.

Will I be able to work 30 and a half hour for example? If I'm allowed to, D.

If I have to work multiple of 60 minutes, B.

Answer:

The answer is D

Step-by-step explanation:

Answer:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

Step-by-step explanation:

The scenario that is most likely to be shown in the graph is:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

We can see that the initial calories are 50 as shown in the graph.

When x=0 the value on the y-axis is 50.

And this value is increasing by 100 units.

Answer:

The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.

Choice D.

Step-by-step explanation:

Answer:

Actual Perimeter = 100 km

        Actual Area = 625 km²

Step-by-step explanation:

A scale drawing of a square has a side length of 5 millimeters.

The drawing has a scale of 1 mm : 5 km (which represents 1 mm is equal to 5 km)

We need to find the actual measurement of 5 mm square on scale.

                1 mm = 5 km

               5 mm = 5 × 5 km

                          = 25 km

The actual length of the side of square is 25 km

Now, we find the perimeter and area of the square.

                                 = 4 × 25

                                = 100 km

                                        = 25 × 25

                                        = 625 km²

Hence, The actual perimeter is 100 km and area of the square is 625 km²

Answer:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Step-by-step explanation:

We will have a partial funcion to define an expression for the monthly phone charge, because we have a condition that changes the monthly cost.

For months under 130 minutes, there will not be any additional charge other that tha base monthly cost, so the expression for the months under 130 minutes will be the monthly fee.

For months over 130 we will have the same information than above, but we have to add a fee for every minute over 130 minutes. To find the amaunt of minutes over 30 minutes we will just subtract 130 to the amount of minutes used: (m-130). Then we will multiply that number times the cos of each minute over 130 minutes: 9*(m-130). Finally we will add the basic phone fee: 15.99 + (0.09*(m-130)).

Now we set the conditions and use the correct notation for a partial function and we get:

[tex]p=\left \{ {{15.99,m[tex]\leq[/tex]130} \atop {15.99+0.09*(m-130),m>130}} \right.[/tex]

Answer:

The answer to your question is:

a) ∠FGH = 34°

b) ∠HGI = 34°

c) ∠FGI = 68°

Step-by-step explanation:

We know that GH bisects ∠FGI

a) Find ∠FGH

∠ FGH = 5x - 6

∠ HGI = 6x -14

                      ∠ FGH = ∠ HGI

                     5x - 6   =  6x - 14

                    5x - 6x = -14 + 6

                          -1x = - 8

                            x = 8

∠ FGH = 5(8) - 6

            = 40 - 6

            = 34°          

b) m∠HGI = 6(8) -14

                = 48 - 14

                =  34°          

c) m∠FHI =  ∠ FGH + ∠ HGI

                = 34 + 34

               = 68°    

Answer: 20 times

Step-by-step explanation:

1 hour = 60 minutes.

Duration of the song = 3 minutes each time = 3minutes/time

So, the number of times the song can be played in an hour=

= 60minutes÷3minutes/time = 20 times

So, you can play that song in an hour for 20 times.

Answer: 20 times

[tex]\textit{\textbf{Spymore}}[/tex]  

Final answer:

A 3-minute song can play 20 times in an hour by simply dividing the 60 minutes in an hour by the length of the song, which is 3 minutes.

Explanation:

A 3-minute song can play 20 times in an hour. Here's a step-by-step breakdown of the math:

Understand that there are 60 minutes in an hour.

Divide the total minutes in an hour (60) by the length of the song (3 minutes).

The result is the number of times the song can be played in one hour, which is 20 times.

The question seems to diverge from the provided information about the collection of songs with varying lengths. However, for the direct question asked, we do not need those details.

Answer:

Transformation is the altering of shapes using different operations.

Step-by-step explanation:

The different operations of transformation are translation, reflection, and rotation.

Step-by-step explanation: A transformation is when we change the position or size of a given figure.

In part a, notice that we can flip the triangle on the left over the following line to the position of the triangle on the right. When we flip a figure over a line to create a mirror image, the new image is called a reflection. Therefore, the transformation shown in part a is called a reflection.

In part b, notice that we can turn the triangle on the top to the position of the triangle on the bottom. When we turn a figure to a new position, it's called a rotation. Therefore, the transformation in part b is a rotation.

In part c, notice that we can slide the triangle on the left to the position of the triangle on the right. When we slide a figure to a new position, it's called a translation. Therefore, the transformation in part c is a translation.

In part d, notice that the triangle on the left has been reduced in size to form the triangle on the right. When we reduce or increase the dimensions of a figure while maintaining its shape, the new image is called a dilation. Therefore, the transformation in part d is a dilation.

Answer:

This is cluster sampling.

Step-by-step explanation:

American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.

This is a type of cluster sampling.

This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.

Answer:

5x - y = 27

Step-by-step explanation:

Slope is the direction of line and it is calculated as,

[tex]Slope = \frac{y-y_{1}}{x-x_{1}} [/tex]

where (x₁, y₁) is any two points on the line.

Here, we have given that

Slope = 5  and (x₁, y₁) = (5, -2)

∴  [tex]5 = \frac{y-(-2)}{x-5} [/tex]

⇒ 5(x - 5) = y + 2

⇒ 5x - 25 = y + 2

⇒ 5x - y = 27

Hence, the equation of a line is: 5x - y = 27

Answer:

The answer to your question is: $ 3.92 / kg

Step-by-step explanation:

Data

Lean ground beef cost = $1.78

price of 1 kg = ?

Equivalence  1 kg = 2.2 lbs

Process (rule of three)

                                 $1.78  -------------------   1 pounds

                                    x      -------------------    2.2 pounds

                       x = 2.2(1.78) / 1 = $ 3.92 / kg

The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;

⇒ 4x² + 8x - 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (6x – 5 + 4x²) + (2x - 2)

Now, Solve the expression is solve as,

⇒ (6x – 5 + 4x²) + (2x - 2)

⇒ 6x – 5 + 4x² + 2x - 2

⇒ 4x² + 6x + 2x - 5 - 2

Solve common terms,

⇒ 4x² + 8x - 7

Therefore,

The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;

⇒ 4x² + 8x - 7

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Answer:

Han used a convenience nonrandom sampling approach

Step-by-step explanation:

The convenience nonrandom sampling approach consists in collecting a sample just because it is convenient. This means that the subjects are easy to select.

Han did precisely this, he went to the teacher's lounge and surveyed the faculty present there. He did not put any further effort like, for example, wait for more teachers to have a larger sample or make sure the ratio between female and male teachers was the same.

Answer:

134.375 - 12.5 - 6 = 115.875

The area of the rug that can be seen after covering love seat and entertainment center is 115.875 square feet.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

Given that,

The length of rug in living room = 12¹/₂ feet = 25 /2 feet.

And the width of rug = 10 ³/₄ feet= 43 /4 feet.

The area of the rug = width x length = 25/2 x 43 / 4 = 1075 / 8 = 134.375 square feet.

Also given that,

A love seat having area =  12¹/₂ square feet.

And area of entertainment center = 6 square feet

Area covered by love seat and entertainment center = 12.5 + 6 = 18.5 square feet

The remaining area that can be seen = 134.375 - 18.5 = 115.875 square feet.

The required area is 115.875 square feet.

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the answer is b)  5/3    1/3

                           x       y

Explanation:

All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.

The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.

The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.

Answer:13

Step-by-step explanation: Six down to zero. Then zero up to seven.

Answer: There are 151,200 ways the members can be appointed.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 10

Number of remaining spots available = 6

Here, rank matters.

so, we will use "Fundamental theorem of counting or by Permutation":

So, Number of different ways the members can be selected is given by

[tex]^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200[/tex]

Hence, there are 151,200 ways the members can be appointed.

The number of different ways the president can appoint the members of the cabinet given that order matters and there are 10 eligible candidates for the remaining 6 positions is 151,200.

The question is asking for the number of different ways the six remaining cabinet positions can be filled, given that there are ten eligible candidates and rank matters. This scenario is an example of a permutation problem in combinatorics, a subfield of mathematics. A permutation is an arrangement of objects in a specific order. If rank matters, this means that the order in which the candidates are chosen for the cabinet positions is important. In this case, the formula for permutations is applicable. The formula for permutation when there are 'n' items available (10 eligible candidates) and 'r' items are chosen (6 positions) is given by nPr = n! / (n-r)!. Substituting these values, we have 10P6 = 10! / (10-6)!. After performing the calculation, we find there are 151,200 different ways in which the president can appoint the members of the cabinet.

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