On the 6th grade math test, twelve students had a score of 80 points. Eight students had a score of 88 points.

What was the class average?

well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t[/tex]

Answer:

8

Step-by-step explanation:

To find the average of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers in the set.

So, to find the average of the set of numbers 7, 6, 12, 5, 7, 6, 13, you would first add up all the numbers:

7 + 6 + 12 + 5 + 7 + 6 + 13 = 56

Then you would divide the sum by the total number of numbers in the set, which is 7:

56 / 7 = 8

Therefore, the average of the set of numbers 7, 6, 12, 5, 7, 6, 13 is 8.

Answer:

the answer you are looking for would be 8

Answer:7 units

Step-by-step explanation:

Answer:

There are no boxes bro so how can I answer you . I gonna get better to see your boxes but I can't see i think there is a attachment you forget to take with quest .Because this quest is not looking like Mathematics it's like English Grammar.If you didn't like my answer you will say anything you want . But in my decision you my bestfriend. I help others to give answers so I am trying my best.

-Thank You By MrIshaan

The value of coordinates of fourth vertex of rectangle is, (0, 3)

We have to given that;

A rectangle is made up from points (-2,-1), (4,-1), (4,3),

Since, Midpoints of the points are same both diagonal.

Hence, Let the fourth vertex = \(x, y)

Midpoint of point (- 2, - 1) and (4, 3) is,

(- 2 + 4) / 2,. (- 1 + 3) / 2

(2, 1)

Midpoint of (x, y) and (4, - 1) is,

(x + 4)/2, (y - 1)/2

Which is same as (2, 1).

Hence, We can compare as;

(x + 4) / 2 = 2

x + 4 = 4

x = 0

y - 1 / 2 = 1

y - 1 = 2

y = 3

Thus, The value of coordinates of fourth vertex of rectangle is, (0, 3)

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Complete question is,

If a rectangle is made up from points (-2,-1), (4,-1), (4,3),

Then, The value of fourth coordinate is?

The volume of the hemisphere as given in the task content to the nearest tenth is; 718.4 mm³.

It follows from the task content that the volume of the hemisphere as represented in the attached image is to be determined.

Since the volume of the hemisphere is given by;

V = 2/3πr³

where radius = diameter/2 = 14/2 = 7.

Consequently, the volume, V is;

V = 2/3 × π × 7³

V = 718.4 mm³.

Ultimately, the volume is; 718.4 mm³.

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Answer:

28(17) + π(7^2)

= 476 + 49π square meters

= 629.94 square meters

Darrion ran a total distance of 38 3/4 miles in 10 days.

We have,

To find the total distance Darrion ran in 10 days, we need to add up the distance he ran in the first five days and the distance he ran in the next five days.

Distance ran in the first five days

= 3 1/2 miles per day x 5 days

= 17 1/2 miles

Distance ran in the next five days

= 4 1/4 miles per day x 5 days

= 21(1/4) miles

Total distance Darrion ran in 10 days

= Distance ran in the first five days + Distance ran in the next five days

= 17 1/2 miles + 21 1/4 miles

= 38 3/4 miles

Therefore,

Darrion ran a total distance of 38 3/4 miles in 10 days.

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The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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Answer:

(1/2)(4)(3)(2) = 12 cubic yards

The correct answer is A.

The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.

In the given question, 2,560 rounded to the nearest ten would be,

2,560 rounded up to 2,560 + 10 = 2,570.

Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

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The probability of drawing two green marbles in a row is 4/9.

Given that, a box has 1 red marble, 1 blue marble, and 4 green marbles.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Number of favorable outcomes = 4

Total number of outcomes = 6

Probability of drawing 1st green marble = 4/6

= 2/3

Probability of drawing 2nd green marble = 4/6

= 2/3

Probability of drawing two marbles = 2/3 × 2/3

= 4/9

Therefore, the probability of drawing two green marbles in a row is 4/9.

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Answer:7.02

Step-by-step explanation: cause im right

The correct sentences in the passage are option A, option B, and option E.

Let's check all the options, then we have

Any two squares are either similar or congruent. The statement is true.

If two lines are parallel, they never intersect. The statement is true.

If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.

The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.

A line can be drawn through any two distinct points. The statement is true.

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The distribution that is positively skewed would be the Box plot in Option C.

When discussing distributions, a positive skew refers to the tail being lengthier on the right side as opposed to the left. As such, more extreme values are located on the right-hand portion of said distribution.

To put it another way, there is a predominance of data clustering toward the left with only a handful of instances where extreme values are found further along the right-hand scale. This scenario would prompt an observer to note how the mean outstrips the median.

The box plot in option C has most of the data towards the left side which is the positive side so this is positively skewed.

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The probability that the Jones family had at least 4 girls is 0.5625 and the probability that the Jones family had at most 3 girls is 0.65625.

We can use the binomial probability formula to solve this problem. Let X be the number of girls in the Jones family, then X follows a binomial distribution with parameters n = 6 and p = 0.5.

The probability of having k girls in a family of 6 children is given by:

P(X = k) = (6 choose k) * [tex]0.5^{k}[/tex] * [tex]0.5^{6-k}[/tex]

where (6 choose k) is the binomial coefficient.

To find the probability of having at least 4 girls, we need to calculate the probability of having 4, 5, or 6 girls and add them up:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6)

= (6 choose 4) * [tex]0.5^{4}[/tex] * [tex]0.5^{2}[/tex] + (6 choose 5) * [tex]0.5^{0.5}[/tex] * [tex]0.5^{1}[/tex] + (6 choose 6) * [tex]0.5^{6}[/tex] * [tex]0.5^{0}[/tex]

= 0.234375 + 0.3125 + 0.015625

= 0.5625

Therefore, the probability that the Jones family had at least 4 girls is 0.5625 or 56.25%.

To find the probability of having at most 3 girls, we need to calculate the probability of having 0, 1, 2, or 3 girls and add them up:

P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (6 choose 0) * [tex]0.5^{0}[/tex] * [tex]0.5^{6}[/tex] + (6 choose 1) * [tex]0.5^{1}[/tex] * [tex]0.5^{5}[/tex] + (6 choose 2) * [tex]0.5^{2}[/tex] * [tex]0.5^{4}[/tex] + (6 choose 3) * [tex]0.5^{3}[/tex] * [tex]0.5^{3}[/tex]

= 0.015625 + 0.09375 + 0.234375 + 0.3125

= 0.65625

Therefore, the probability that the Jones family had at most 3 girls is 0.65625 or 65.625%.

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1. The area of the smaller rectangle is approximately 96 in².

2. The length of the hypotenuse of the smaller triangle is 32 units.

If the scale factor of two similar rectangles is 4/7, then the ratio of their areas is (4/7)^2 = 16/49. This means that the area of the smaller rectangle is (16/49) times the area of the larger rectangle.

Let A be the area of the smaller rectangle. Then we have:

A = (16/49) * 294 in²

A = 96 in² (rounded to the nearest whole number)

Therefore, the area of the smaller rectangle is approximately 96 in².

2.  4/9, which simplifies to 2/3.

This means that the length of the hypotenuse of the smaller triangle is (2/3) times the length of the hypotenuse of the larger triangle.

Let x be the length of the hypotenuse of the smaller triangle. Then we have:

(2/3) * 48 = x

x = 32 units

Therefore, the length of the hypotenuse of the smaller triangle is 32 units.

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The standard error of the mean δ  for a sample of size n is calculated as:

δ = σ / √(n)

where σ is the population standard deviation and n is the sample size.

For a sample of size 8 taken from a normally-distributed population with a mean of 32 and a standard deviation of 7, the δ is:

δ  = 7 / √(8) ≈ 2.475

The 99.7% confidence interval for the sample mean is given by:

x ± 3 Substituting the values, we get:

32 ± 3(2.475)

where x is the sample mean.

Substituting the values, we get:

32 ± 3(2.475)

which simplifies to:

[24.575, 39.425]

Therefore, about 99.7% of the sample means taken from this population will fall within the interval [24.575, 39.425].

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The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,

The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters

Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

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The line a and line d are perpendicular to each other.

Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another.

Perpendicular lines cross one another in a specific way.  The intersection of perpendicular lines forms 90 degree angles.

Constructing lines a and d:

After constructing the two lines; line a and line intersect or meet each other at 90 degrees to the horizontal.

Thus, we can conclude that the line a and line d are perpendicular to each other.

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Answer:line a and line d are perpendicular

saw the answers

Answer:

C

Step-by-step explanation:

8 x 10^4 = 80,000

3 x 10^3 =   3,000

1  x  10 ^2 =    100

2 x 10^1 =         20

add it up

83,120

C is correct

Answer:

the missing value is y = 48.

Step-by-step explanation:

In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:

y / 18 = 8 / 3

To solve for y, we can cross-multiply:

y = 18 * 8 / 3

y = 48

Therefore, the missing value is y = 48.

Answer: 97

Step-by-step explanation:

Average: All the numbers added divided by the number of numbers

Start adding the smallest grade in her notes: 87+96+81+89+81= 434/5= 86.8

Keep adding 1 to the last grade until you find a number that gives us an average of 90.

87+96+81+89+97+ 450

Then divide it by the amount of grades

450/5= 90

Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.

-1 is the value of the slope.

To find the slope of a line that is perpendicular to the line x - y = 0, we need to find the slope of the given line first.

To do this, we can rearrange the equation x - y = 0 to solve for y:

x - y = 0

y = x

So the given line has a slope of 1 since the coefficient of x is 1.

Since a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of 1:

the slope of the perpendicular line = -1/1

the slope of the perpendicular line = -1

Therefore, the slope of a line that is perpendicular to the line x - y = 0 is -1.

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The percent of data within the following interval from 28 to 82 is 99.73%

From the question, we have the following parameters that can be used in our computation:

Mean = 55

Standard deviation = 9

Scores = from 28 to 82

So, we have

z = (28 - 55)/9 = -3

z = (82 - 55)/9 = 4

This means that it is between a z-score of -3 and a z-score of 3

This is represented as

Probability = (-3 < z < 3)

Using a graphing calculator, we have

Probability =  0.9973

Express as percentage

Probability =  99.73%

Hence, the probability is 99.73%

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The solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

The given equation is 1/(x-3) + 1/(x+5) = 1/3

Take LCM on left hand side

(x+5)+(x-3)/(x-3)(x+5)= 1/3

2x+2/(x-3)(x+5) = 1/3

2(x+1)/(x-3)(x+5) = 1/3

6(x+1)=(x-3)(x+5)

6x+6 = x²+5x-3x-15

6x+6 = x²+2x-15

x²+2x-6x-15-6=0

x²-4x-21=0

x² -7x+3x-21=0

x(x-7)+3(x-7)

(x+3)(x-7)

The solutions are x=-3, x=7

Hence, the solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

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The probability that event A or B takes place is P ( A ∪ B ) = 4/13

Given data ,

Let the probability of event A happening P ( A ) = 1/13

Let the probability of event B happening P ( B ) = 3/13

And , the probability of event A and B happening P ( A ∩ B ) = 0

So , from the probability rule ,

The probability that event A or B takes place is P ( A ∪ B ) and

P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

On simplifying , we get

P ( A ∪ B ) = 1/13 + 3/13 - 0

P ( A ∪ B ) = 4/13

Hence , the probability is 4/13

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The number name of 97600305 in international system of numeration Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

The number 97600305 can be written with commas as,

Place the commas after hundred.

That is after 305.

Read as three hundred five.

then place the commas after thousands.

Place the comma after 600.

Read as six hundred thousands.

and place the comma after million.

that is after 97.

Read as Ninety-Seven Million.

Combine all and write in the international system of numeration,

The number 97600305 is read as,

Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

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The given question is incomplete, I answer the question in general according to my knowledge:

Write the number name for the numeral 97600305 by inserting commas and write the number name in international system of numeration.

1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:

If something weighs more than 2000 pounds, then it weighs more than Jill’s car.

Sally weighs more than 2000 pounds.

Therefore, Sally weighs more than Jill's car.

2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Sally weighs more than Jill's car.

Therefore, Sally is too heavy for the bridge.

The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.

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