Matthew plays soccer for h hours per day for five days in a row. Over the weekend, he played in a soccer tournament for a total of 6.5 hours. Which expression represents the number of hours Matthew played soccer in a full week?
5 + h + 6.5
5h + 6.5
StartFraction h over 5 EndFraction + 6.5
11.5h

We know that the equation of a line is y=mx+c y = m x + c where m is the slope of the line and c is the y-intercept.

Answer:

y=2x+-5 or y=2x-5

Explanation:

The slope-intercept form of a linear equation is:

y

=

m

x

+

b

Where is the slope the y-intercept value.

(A) The probability of obtaining 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes is approximately 0.246 * 0.190 * 0.282 ≈ 0.013.

(B) The probability of selecting exactly 1 individual with blue eyes and 1 individual with green eyes is given by (3 choose 1) * (1 choose 1) * (6 choose 8) / (10 choose 2) ≈ 0.429.

(C) The probability that at least 7 of the 10 people have brown eyes is 0.452.

(a) The probability of selecting 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes out of a sample of 10 people can be calculated using the binomial probability formula. Here, the probability of success (i.e., an individual having brown eyes) is 0.51, and the probability of failure (i.e., an individual not having brown eyes) is 0.49. The probability of obtaining 5 individuals with brown eyes is given by (10 choose 5) * 0.51^5 * 0.49^5 ≈ 0.246. Similarly, the probability of obtaining 3 individuals with blue eyes is (10 choose 3) * 0.32^3 * 0.68^7 ≈ 0.190, and the probability of obtaining 2 individuals with green eyes is (10 choose 2) * 0.17^2 * 0.83^8 ≈ 0.282. Therefore, the probability of obtaining 5 individuals with brown eyes, 3 individuals with blue eyes, and 2 individuals with green eyes is approximately 0.246 * 0.190 * 0.282 ≈ 0.013.

(b) To calculate the probability of exactly one person in the sample having blue eyes and exactly one person having green eyes, we can use the hypergeometric distribution. Here, we have a population of N = 10 individuals, of which n1 = 3 have blue eyes and n2 = 1 have green eyes. We need to select 2 individuals from the population who have blue and green eyes, respectively, and the remaining 8 individuals can have any eye color. Therefore, the probability of selecting exactly 1 individual with blue eyes and 1 individual with green eyes is given by (3 choose 1) * (1 choose 1) * (6 choose 8) / (10 choose 2) ≈ 0.429.

(c) To calculate the probability that at least 7 of the 10 people have brown eyes, we can use the binomial probability formula again. Here, we need to calculate the sum of probabilities for selecting 7, 8, 9, or 10 individuals with brown eyes. Therefore, the probability of selecting at least 7 individuals with brown eyes is given by the sum of the probabilities for selecting 7, 8, 9, or 10 individuals with brown eyes. This is approximately equal to (10 choose 7) * 0.51^7 * 0.49^3 + (10 choose 8) * 0.51^8 * 0.49^2 + (10 choose 9) * 0.51^9 * 0.49^1 + (10 choose 10) * 0.51^10 * 0.49^0 ≈ 0.452.

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Answer:

\((a \times 220) - 398 = 8\)

For the given frequency distribution the individual scores in the entire  set are 12, to get the answer we just add up the frequencies of each class interval in the table .

For example the first class interval, the frequency is 5, so 5 individual scores fall in this range. then added up the frequencies for all the class intervals to get a total of 1. It is important to understand the concept of frequency distribution for any type of data. Frequency distribution is the way of organizing data into groups or classes according to the number of times each value occurs.

It is used to gain a better understanding of the data, and it can help identify patterns such as an increase or decrease in values. Knowing the frequency of each class interval in a frequency distribution can help us determine the total number of individual scores in the entire set.

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The executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

Let x be the number of days the executive stayed in London, y be the number of days he stayed in Paris, and z be the number of days he stayed in Rome.

We can set up the following equations to represent the given information:

180x + 230y + 160z = 2660 (hotel bills)

110x + 120y + 90z = 1520 (meal expenses)

x = y + z (he spent as many days in London as he did in Paris and Rome combined)

We can rearrange the third equation to get y + z - x = 0 and substitute it into the first two equations to eliminate x:

180x + 230y + 160z = 2660

110x + 120y + 90z = 1520

-180y - 180z + 180x = 0

Adding the first and third equations gives us:

360x + 50y - 20z = 2660

Adding the second and third equations gives us: 290x - 60y - 90z = 1520

We can now solve for x by multiplying the first equation by 3 and the second equation by 5 and subtracting them:

1080x + 150y - 60z = 7980

-1450x + 300y + 450z = 7600

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

1630x - 150y - 510z = 380

Solving for x gives us:

x = (150y + 510z + 380) / 1630

Substituting this back into the third equation gives us:

y + z - (150y + 510z + 380) / 1630 = 0

Multiplying by 1630 and rearranging gives us:

1480y + 490z = 380

We can now solve for y by multiplying the first equation by 490 and the second equation by 50 and subtracting them:

490(360x + 50y - 20z) = 490(2660)

50(290x - 60y - 90z) = 50(1520)

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

19600x + 24500y - 9800z = 1303400

-14500x + 3000y + 4500z = 76000 --------------------------------------------------

4100x - 21500y - 14300z = 1227400

Solving for y gives us:

y = (4100x + 14300z - 1227400) / 21500

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480(4100x + 14300z - 1227400) / 21500 + 490z = 380

Multiplying by 21500 and rearranging gives us:

606800x + 2054200z - 1817320000 = 0

Solving for z gives us:

z = (1817320000 - 606800x) / 2054200

Substituting this back into the equation x = y + z gives us:

x = y + (1817320000 - 606800x) / 2054200

Multiplying by 2054200 and rearranging gives us: 606800x^2 - 2054200xy - 2054200x + 1817320000y + 3707618640000 = 0

Using the quadratic formula, we can find the value of x:

x = (2054200y + 2054200 ± √[(2054200y + 2054200)^2 - 4(606800)(1817320000y + 3707618640000)]) / (2*606800)

Plugging in the value of y from earlier gives us:

x = (2054200(4100x + 14300z - 1227400) / 21500 + 2054200 ± √[(2054200(4100x + 14300z - 1227400) / 21500 + 2054200)^2 - 4(606800)(1817320000(4100x + 14300z - 1227400) / 21500 + 3707618640000)]) / (2*606800)

Simplifying and solving for x gives us:

x = 10

Substituting this back into the equation x = y + z gives us:

10 = y + z

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480y + 490(10 - y) = 380

Solving for y gives us:

y = 6

Substituting this back into the equation 10 = y + z gives us: 10 = 6 + z

Solving for z gives us:

z = 4

Therefore, the executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

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Answer:

C. -12-(-15) =3

Step-by-step explanation:

you subtract the two numbers to get the distance.

Answer:

C).

Step-by-step explanation:

In A and B  they  are making generalisations . Their deductions are not valid.

Binary 000 100 010 001 000 . 111 110

Base 6 0 4 2 1 0 . 5 4

Hence, 111.1 F in hexadecimal is equivalent to 04210.54 in base 6.

a.) EBA.C to base 6 number

The hexadecimal number EBA.C can be converted to base 6 number by first converting it to binary and then to base 6. To convert a hexadecimal number to binary, each digit is replaced by its 4-bit binary equivalent:

Hexadecimal E B A . C
Binary 1110 1011 1010 . 1100

Next, we group the binary digits into groups of three (starting from the right) and then replace each group of three with its corresponding base 6 digit:

Binary 111 010 111 010 . 100Base 6 3 2 3 2 . 4

Hence, EBA.C in hexadecimal is equivalent to 3232.4 in base 6.

b.) 111.1 F to base 6 number

The hexadecimal number 111.1 F can be converted to base 6 number by first converting it to binary and then to base 6. To convert a hexadecimal number to binary, each digit is replaced by its 4-bit binary equivalent:

Hexadecimal 1 1 1 . 1 F
Binary 0001 0001 0001 . 0001 1111

Next, we group the binary digits into groups of three (starting from the right) and then replace each group of three with its corresponding base 6 digit:

Binary 000 100 010 001 000 . 111 110

Base 6 0 4 2 1 0 . 5 4

Hence, 111.1 F in hexadecimal is equivalent to 04210.54 in base 6.

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The οption that represents the reasonable range for s is: s greater-than-or-equal-to 4.

The function is a relationship or expression involving one or more variables.

We are given that the function s(V) = -∛V describes the side length, in units, of a cube with a volume of V cubic units.

To find a reasonable range for s, we can set a minimum volume of 64 cubic centimetres and sο lve for s:

s³ = V

s³ = 64

s = ∛64

s = 4

So, the minimum value for s is 4 centimeters.

Therefore, the reasonable range for s, the side length of Jason's cube, would be s ≥ 4 centimeters.

Hence, the option that represents the reasonable range for s is:

s greater-than-or-equal-to 4.

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Step-by-step explanation:

b) average velocity : ∆x/∆t = 100/9.8 ≈ 10.204 m/s

c) ∆x = v.∆t = 10.204 × 3 = 30.612 m

d) ∆t = ∆x/v = 80/10.204 = 7.84 s

The car's residual is given by k=0.0091 if a car is weighing 2684 pounds and average fuel efficiency of 24.6 miles per gallon.

Efficiency is frequently measured as the ratio of usable output to total input, which may be stated mathematically as r=P/C, where P is the quantity of useful output ("product") created divided by the amount C ("cost") of resources consumed.

The state or trait of being efficient, or of being able to complete something with the least amount of time and effort; performance proficiency completion of or ability to perform a task with the least amount of time and effort: The assembly line boosted industry efficiency.

Given,

Weight of the car=2684 pounds

Average fuel efficiency y=24.6 miles

Car's residual, k=?

We know that,

k=y/w

k=24.6/2684

k=0.0091

Therefore, the car's residual is given by k=0.0091

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Answer:

-249.6

Step-by-step explanation:

Convert 2/5 to 0.4. Then subtract 0.4 and 250 to get -249.6

Hope this helped! :)

Answer:

6:1:3

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

there are 3 numbers on the dice less than six and 3 of six is 1/2

Answer:

try hard

Step-by-step explanation:

Answer:

The common continuous interval will be (0,∞).

Step-by-step explanation:

Given that,

The numerator = 12+√x

The denominator = √12+x

We know that,

For the numerator,

Any function under square root should be greater than and equal to the zero.

\(x\geq 0\)

So, the continuous interval is (0, ∞)

For the denominator,

\(\sqrt{12+x}>0\)

\(12+x>0\)

\(x>-12\)

The interval for the continuous and non zero function is,

(-12, ∞)

We need to calculate the continuous interval

Using given quotient

\(\dfrac{12+\sqrt{x}}{\sqrt{12+x}}\)

The continuous interval of numerator and  denominator are (0, ∞) and (-12, ∞).

Hence, The common continuous interval will be (0,∞).

Answer:

134

Step-by-step explanation:

q+ p+ 4q + 8p

5q +9p

125+9

134

helps if not then I'm sorry

Answer:

Domain: [-4,4]

Range: [-4,6]

Step-by-step explanation:

To domain pertains to the x-coordinates, while the range pertains to the y-coordinates.

Looking at the graph, we can see that the farthest point to the left is (-4,3) and the farthest point to the right is (4,6). Now, we know that the domain is [-4,4].

Looking at the graph, we can see the highest point is (4,6) and the lowest point is (0,-4). Now, we know the range is [-4,6].

Now, we know that the domain is [-4,4] and the range is [-4,6].

Answer:

$20,300.88

Step-by-step explanation:

First Year : 75,000x(1-23%)

Second Year: 75,000x(1-23%)x(1-23%)

=75,000x(1-23%)^2

Third Year : 75,000x(1-23%)x(1-23%)x(1-23%)

=75,000x(1-23%)^3

x Year : 75,000x(1-23%)^x              (Analogical Reasoning)

Hence : Fifth year:75,000x(1-23%)^5 = 75000x(0.77)^5

23%=0.23 1-23%=1-0.23=0.77

Therefore Fifth Year: 75000x(0.77)^5=$20300.88

The approximation provides a second-order accurate estimate of the derivative f'(x) using the function values f(x), f(x + h), and f(x + 2h).

To derive a second-order accurate, one-sided difference approximation to f'(x) using Taylor series, we can start by expanding the function f(x + h) and f(x + 2h) in their Taylor series expansions around x.

Using Taylor series expansion for f(x + h), we have:

f(x + h) = f(x) + f'(x)h + f''(x)(h²)/2 + O(h³)

Using Taylor series expansion for f(x + 2h), we have:

f(x + 2h) = f(x) + 2hf'(x) + 2h²f''(x) + O(h³)

Now, let's construct a one-sided difference approximation for f'(x) using these expansions.

Taking the difference between f(x + h) and f(x), we get:

f(x + h) - f(x) = f'(x)h + f''(x)(h²)/2 + O(h³)

Similarly, taking the difference between f(x + 2h) and f(x + h), we get:

f(x + 2h) - f(x + h) = f'(x)h + f''(x)h² + O(h³)

We can rearrange the first equation to solve for f'(x):

f'(x) = (f(x + h) - f(x))/h - f''(x)(h/2) + O(h²)

Substituting the second equation into the above expression, we have:

f'(x) = (f(x + h) - f(x))/h - (f(x + 2h) - f(x + h))/(2h) + O(h²)

Simplifying the expression, we get the second-order accurate, one-sided difference approximation to f'(x):

f'(x) ≈ (3f(x + h) - 4f(x) + f(x + 2h))/(2h)

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Adding the score of each round, Connor's current score is of -11 points.

To find the sum of two negative numbers, we keep the signal and add numbers.

For each round, Connor's scores are given as follows:

The combined score is the sum of each score, hence:

C = -5 + (-6) = -5 - 6 = -(5 + 6) = -11.

Connor's current score is of -11 points.

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Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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If side JM = 30 and side LM = 8, the length of side KM is equal to 15.49 units.

In this exercise, we would assign the variable x to the length of side KM. Based on the information provided about triangle JKM and triangle KML, we can logically deduce the following parameters;

Side JL = [(30 + 8) × x]/2

Side JL = 38x/2

Side JL = 19x.

Since point M is the perpendicular bisector of both triangle JKM and triangle KML, the length of side KM can be calculated as follows;

19x = √[(30² + x²)(x² + 8²)]/2

38x = √[(30² + x²)(x² + 8²)]

By taking the square of both sides, we have:

38²x² = (900 + x²)(x² + 64)

38²x² = 900x² + 57,600 + x⁴ + 64x²

38²x² = 964x² + 57,600 + x⁴

(x² - 240)² = 0

x² = 240

x = √240

x = 15.49 units.

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Answer:

The area of a triangle =55x^3+15x^2-25

1/2×length×width=55x^3+15x^2-25

5x/2×width=55x^3+15x^2-25

width=[55x^3+15x^2-25]×2/5x

width=22x²+6x-10/x is your answer

When a triangle is translated, the resulting triangle will be congruent to the original triangle.

The congruency statement is ABCD = ZYXW

Given

Quadrilateral ABCD is translated up and to the right and then is rotated 180 degrees about point Q to form quadrilateral XYZW.

Quadrilateral ABCD is translated up and to the right and then rotated about point Q.

When a triangle is translated, the resulting triangle will be congruent to the original triangle.

From the complete question, corresponding points are:

Point A and point Z

Point B and point Y

Point C and point X

Point D and point W

This means that:

Points A and Z are corresponding.

Points B and Y are corresponding.

Points C and X are corresponding.

Points D and W are corresponding.

Hence, the congruency statement is ABCD = ZYXW

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Answer:

B

Step-by-step explanation:

Answer:

10 times greater

Step-by-step explanation:

When you write these as numbers, you get:

800,000,000 (8 hundred million place)

80,000,000 (8 ten million place)

Then divide the greater number by the less number:

800,000,000/800,000,00

make this easier by eliminating 0's:

800,000,000/80,000,000

80/8

10

10 times greater is your answer

Hope this helps!

Answer:

C

Step-by-step explanation:

Longest practice is 2 1/2 hours long

Shortest is 1 1/4 hours long

For difference, subtract 1 1/4 from 2 1/2

Convert mixed to improper fractions

(2*2+1)/2 - (1*4+1)/4

5/2 - 5/4

10/4 - 5/4 = 5/4

Change back to mixed fraction

1 1/4