The elephants at the Hancock Zoo are fed 4 9/10 barrels of corn each day. The buffalo are fed 1/6 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?

Write your answer as a fraction or as a whole or mixed number.

PLEASE PLEASE PLEASE HELP

The length of the longer leg of this 30-60-90 triangle is 6.93 units.

In a 30-60-90 triangle, the length of the shorter leg is opposite to the 30-degree angle. The longer leg is opposite to the 60-degree angle, and the hypotenuse is opposite to the 90-degree angle.

The ratio of the sides in a 30-60-90 triangle is always the same. The length of the shorter leg is half of the length of the hypotenuse. The longer leg is the square root of three times the length of the shorter leg.

Let's use this information to solve a problem. Suppose you have a 30-60-90 triangle with a shorter leg of length 4 units. We can use the ratio to find the length of the longer leg.

The length of the hypotenuse is twice the length of the shorter leg, which is 2 times 4 units = 8 units.

The longer leg is the square root of three times the length of the shorter leg, which is the square root of three times 4 units = 6.93 units.

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Therefore, the simplified form of the given expression is 7/36.

In mathematics, an expression is a combination of numbers, variables, and operators that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve one or more operations or functions. Expressions are an important concept in mathematics and are used in a wide range of applications, from simple arithmetic calculations to advanced mathematical modeling and analysis.

Here,

To simplify this expression, we can multiply the numerators of the fractions and multiply the denominators of the fractions, and then simplify the resulting fraction:

7/8 x 1/3 x 2/3 = (7 x 1 x 2)/(8 x 3 x 3)

= 14/72

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

14/72 = (2 x 7)/(2 x 36)

= 7/36

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Answer:

2.25 feet, 45 inches, and 6 yards

Step-by-step explanation:

first, convert all to the same unit of measurement

I will use inches

45 inches = 45 inches

6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches

Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.

Now let's look at the complete conversion

45 inches

6 yards = 216 inches

2.25 feet = 27 inches

looking at the inches we can see that 27 is the least then 45 then 216 therefore

2.25 feet < 45 inches <  6 yards so the order is

2.25 feet, 45 inches, and 6 yards

Answer:

(x+2)^2+(y-5)^2=81

Step-by-step explanation:

standard form equation is (x-h)^2+(y-k)^2=r^2

so, input the values:

(x+2)^2+(y-5)^2=9^2

simplify:

(x+2)^2+(y-5)^2=81

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

1. Range of Surveyed Students: 1,650 to 1,800 students.

2. Range of Students in Orange County: 39,364 to 42,972 students

To determine the range of surveyed students that agreed with the statement, we need to calculate the minimum and maximum percentages based on the margin of error. Given that 86% of students agreed with the statement and the margin of error is ±3.7%, we can find the range as follows:

Minimum percentage: 86% - 3.7% = 82.3%

Maximum percentage: 86% + 3.7% = 89.7%

Now, we'll apply these percentages to the total number of surveyed students (2,006):

Minimum number of students: 0.823 x 2,006 ≈ 1,650 students

Maximum number of students: 0.897 x 2,006 ≈ 1,800 students

Range of Surveyed Students: 1,650 to 1,800 students

b. To determine the range of grade 10-12 students in OCPS who would likely agree with the statement, we'll apply the same minimum and maximum percentages found earlier (82.3% and 89.7%) to the total number of grade 10-12 students in Orange County Public Schools (47,851):

Minimum number of students: 0.823 * 47,851 = 39,364 students

Maximum number of students: 0.897 * 47,851 = 42,972 students

Range of Students in Orange County: 39,364 to 42,972 students

The above answer is based on the information below provided in the picture;

A research survey of 2,006 public and private school students in the United States (grades 10-12) between April 12 and June 12, 2016 asked students if they agreed with the statement, "If I make a mistake, I try to figure out where I went wrong." The survey found that 86% students agreed with the statement. The margin of error for the survey is +3.7%.

a. Determine the range of surveyed students that agreed with the statement.

Range of Surveyed Students .......................................................

b. In 2022, there were 47,851 students in grades 10-12 in Orange County Public Schools (OCPS). Determine the range of grade 10-12 students in OCPS who would likely agree with the statement, "If I make a mistake, I try to figure out where I went wrong."

Range of Students in Orange County ..................................

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For given data, Carrie threw the ball highest = 35ft and ball stayed in the air longest = 3s for Carrie as well.

Any object that is fired into the air and travels in that direction is referred to as a projectile. Gravitation, however, is another force that an object experiences after the first force that pushes it.

Three distinct individuals, Alberto, Ben, and Carrie, each toss a ball straight up into the air.

Following equation may be used to explain Alberto's throw.

[tex]H = -16t^2 + 32t + 4[/tex]

Now , to find the maximum height, we solve for first derivative w.r.t.t,

[tex]-32t + 32 = 0[/tex]

[tex]32t=32\\t = 1s[/tex]

Using t=1, we can find maximum height as

[tex]H =-16(1)^2 + 32(1) + 4\\\\H=(-16)+32+4[/tex]

[tex]H= 20[/tex] ft

Thus, when Alberto threw ball, maximum height attained= 20 ft and total time duration ball was in air = 1s.

From the given table( refer to attached image),

Fom given table,

we can drive the function for maximum height as,

[tex]H=at^2+bt+c[/tex]

now, putting values of t, to get values of H,

from table, for t=0,H=6

6=[tex]a(0)+b(0)+c[/tex]

[tex]c=6[/tex]

[tex]H=at^2+bt+6[/tex]

for t=1,H=14

[tex]14=a(1)^2+b.1+6\\\\8=a+b............(1)[/tex]

similarly,for t=2,H=14

[tex]14=a(2)^2+b.2+6\\\\8=4a+2b........(2)[/tex]

solving equation 1 and 2,

a=(-4) and b=12

∴[tex]H=-4t^2+12t+6[/tex]

we know, [tex]t=\frac{-b}{2a}\\\\t=\frac{-12}{-8}=3/2=1.5s[/tex]

When Ben threw ball, the maximum height ball attained was 14 ft and total time duration for which ball was in air was 1.5 seconds.

From the given graph(refer to attached image),When Carrie threw the ball Maximum Height attained = 35ft and Time duration ball was afloat is 3s

Thus,When Carrie threw the ball attained Maximum Height 35ft  and ball stayed in the air longest.

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Complete Question: A ball is thrown straight up into the air by three different people, Alberto, Ben and Carrie. Below are different representations of their throws. Alberto’s throw can be described by the equation height=−16(time)^2+32(time)+4 Ben's throw can be described by the following table(refer to attached image).Who threw the ball highest and for whom the ball was in air for the longest?

The amount of juice that can be poured into 6 cups with a diameter of 4.4 inches and a height of 7 inches is 638.30 cubic inches (rounded to the nearest hundredth).

Solution:We can use the formula to find the volume of a cylinder,V = πr²hwhere V is the volume of the cylinder, r is the radius of the base, h is the height of the cylinder, and π is the mathematical constant approximately equal to 3.14.To begin solving this problem, we must first find the radius of the base of the cylinder.

Since the diameter of each cup is given as 4.4 inches, the radius is half of this, or 2.2 inches.Now we can use the formula for the volume of a cylinder, with r = 2.2 inches and h = 7 inches.V = πr²hV = 3.14(2.2)²(7)V ≈ 106.38 cubic inches

This is the volume of juice that can be poured into a single cup. To find the total volume of juice that can be poured into 6 cups, we multiply this by 6.6(106.38) ≈ 638.30 cubic inches

Therefore, the answer is 638.30 cubic inches.

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The table for the function f(x) = 2ˣ should be completed as follows;

x         -4      -3     -2    -1    0

f(x)      1/16   1/8    1/4   1/2  1

As x approaches negative infinity, f(x) decreases.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the negative power rule to the function based on each of the x-values, we have the following:

f(x) = 2⁰ = 1

f(x) = 2⁻¹ = 1/2

f(x) = 2⁻² = 1/2² = 1/4

f(x) = 2⁻³ = 1/2³ = 1/8

f(x) = 2⁻⁴ = 1/2⁴ = 1/16

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Situation (A) "$400 deposited in a savings account earning 3% yearly compound interest" would yield us the highest amount in the account.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.  

The interest you earn on interest is known as compound interest.

Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

You will wind up with $110.25 at the conclusion of the second year.

So, we know that anytime compound interest will make us more money than simple interest so options (C) and (D) would be wrong.

So, in option (B) we deposit $200 which is compounded for 2 years at 5%.

In option (A) we deposit $400 which is compounded at the rate of 3% and time is not given so we will assume that it will keep compounding for years and hence it will make us the most amount of money.

Therefore, situation (A) "$400 deposited in a savings account earning 3% yearly compound interest" would yield us the highest amount in the account.

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Answer:

the answer is...

Step-by-step explanation:

6d^2 + 10d + 21

The gross death rate is 8.38%.

What is a Rate?

A rate is a measure of the frequency of an event or occurrence in relation to a specific population or time period. Rates are often expressed in terms of units per time or per population, such as cases per 100,000 people or births per year.

The gross death rate is the number of deaths in a given time period divided by the total population or, in this case, the total number of discharges.

To calculate the gross death rate for City Hospital in June, we need to subtract the eight deaths that occurred within 48 hours of admission from the total number of deaths:

Total deaths = 49 - 8 = 41

Then, we divide the total number of deaths (41) by the total number of discharges (489) and multiply by 100 to get the rate per 100 discharges:

Gross death rate = (41 ÷ 489) x 100 = 8.38%

Therefore, the gross death rate for City Hospital in June is 8.38%.

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Answer:The discount would be 25%.

Step-by-Step explanation:

1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.

2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.

3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.

Discount given=25%=21.72

the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:

x = 1 + 3 cosθ

y = -4 + 3 sinθ

( x -1)^2 = (r cosθ)^2

x - 1 = r cosθ

= 3 cosθ

x = 1 + 3 cosθ

y + 4 = 3 sinθ

= y = -4 + 3 sinθ

There, the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:

the sets of parametric equation that represents (x-1)²+(y+ 4)² = 9 is:

x = 1 + 3 cosθ

y = -4 + 3 sinθ

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The question is incomplete, see missing part in the attached image.

The amount of the sales tax is 0.26

Now, The sales tax is 4%.

The cost of lunch is 6. 50.

=> 4% of 6.50

4/ 100 × 6.50

0.04 × 6.50

=> 0.26

Hence, The amount of the sales tax is 0.26

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The approximate area of the sketch for the new lamp is : A = 70

We have,

A trapezium is one pair of parallel sides and one pair of non-parallel sides.

from the diagram we can extract the necessary information needed to find the area of the trapezium.

for the first trapezium (lamp shade)

a = 4 in

b = 6 in

h = 6 in

A1 = a+b/2 * h

   = 5 * 6 = 30

For the area of the second trapezium (lamp base)

a = 4 in

b = 6 in

h = 4 in

A2  =a+b/2  * h

      = 5 * 4 = 20

For the area of the third trapezium (lamp base)

a = 6 in

b = 4 in

h = 4 in

A3 = a+b/2  * h

     =  5 * 4 = 20

The total Area of the trapezium (lamp)

A =  A1 +  A2  + A3

A = 30 + 20 + 20

A = 70

In conclusion, The approximate area of the sketch for the new lamp is :

A = 70

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The simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

To solve the given expression, we can start by simplifying it using trigonometric identities.

Given expression: tanx / (1 + secx) + (1 + secx) / tanx

Step 1: Simplify denominators

We can rewrite secx as 1/cosx, and tanx as sinx/cosx. Using these identities, we get:

tanx / (1 + 1/cosx) + (1 + 1/cosx) / (sinx/cosx)

Step 2: Find the least common denominator (LCD)

The LCD is cosx, as it is the common denominator for both fractions.

Step 3: Combine the fractions

Using the LCD, we can combine the fractions:

[(tanx * cosx) + (1 + 1/cosx)(cosx)] / cosx

Step 4: Simplify the numerator

Multiplying through by cosx to simplify the numerator, we get:

[tanx * cosx + (cosx + 1)] / cosx

Step 5: Combine like terms

Combining like terms in the numerator, we get:

[tanx * cosx + cosx + 1] / cosx

Step 6: Factor out cosx

We can factor out cosx from the numerator:

cosx * (tanx + 1) + 1 / cosx

So, the simplified form of the given expression is:

(cosx * (tanx + 1) + 1) / cosx

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QUESTION IS - simplify . tanx/1+secx  +  1+secx/tan x

The perimeter of rectangle JKLM which has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2) On the coordinate plane is 30 units.

By applying the Pythagorean distance formula we calculate the length of each side of the rectangle as,

Distance, d = √{(x₁ - x₂)² + (y₁ - y₂)²}  (units)

where  (x₁, y₁ ) and ( x₂, y₂) are the coordinates of both the end of a side of the rectangle.

The coordinates of the rectangle JKLM are given as J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2).

Thus,

| JK | = √{(-2 - 6)² + (2 +4)²} = 10 units

| JM | = √{( -2 +5)² + (2 +2)²} = 5 units

| KL | =√{(6-3 )² + (-4+8 )²} = 5 units

| LM | = √{(3+5)² + (-8+2)²} = 10 units

Therefore,  JK and LM are sides opposite to each other (and let it be length) and JM and Kl are the other pair (and let it be the breadth) in the rectangle.

Thus, perimeter of a rectangle can be found with the formula,

Perimeter of JKLM = 2( length + breadth) in units

= 2(10+ 5) units

= 30 units

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y=-3x + 10 is neither of these.

y − 5 = − 1/3(x + 2) is  perpendicular to p

y = 1/3x is neither of these.

-3x + y = 1 is parallel to p

What are parallel lines?

Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel.

The line p passes through the points (2,2) and (-1,1).

The slope of the line is m = (-1-2) /(1-2)= 3.

Now compare the y=-3x + 10 with y = mx +c:

m₁ = -3, c=10

The slope of the line y=-3x + 10 is -3.

The product m and m₁ is  3 ×(-3) = -9

y=-3x + 10 is neither of these.

Rewrite the equation y − 5 = − 1/3(x + 2)

y = (− 1/3)x - (2/3) + 5

Now compare they = (− 1/3)x - (2/3) + 5 with y = mx +c:

m₂ = − 1/3, c=10

The product m and m₂ is  3 ×( − 1/3) = -1

Thus y − 5 = − 1/3(x + 2) is perpendicular to p.

Now compare the y=1/3x  with y = mx +c:

m₃ = 1/3, c=0

The slope of the line  y=1/3x + 10 is 1/3.

m₃≠m and mm₃ ≠ -1 , thus  y=1/3x is neither of these.

Rewrite the equation -3x + y = 1

y= 3x +1

Now compare the y= 3x +1 with y = mx +c:

m₄ =3, c=1

Since m₄ = m. thus -3x + y = 1 is parallel to p.

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When calculating a confidence interval, the level of confidence chosen determines the range of values within which the true population parameter is expected to fall.

A 95% confidence interval means that if we repeatedly sample from the population and construct confidence intervals, 95% of those intervals will contain the true population parameter.

On the other hand, a 99% confidence interval means that if we repeatedly sample from the population and construct confidence intervals, 99% of those intervals will contain the true population parameter.

The margin of error, which is the amount by which the interval may vary due to sampling error, is directly affected by the level of confidence chosen.

As the level of confidence increases, the margin of error also increases. Therefore, when a 99% confidence interval is calculated instead of a 95% confidence interval with n being the same, the margin of error will be wider.

This means that the range of values within which the true population parameter is expected to fall will be larger with a 99% confidence interval, making the interval less precise but more conservative.

It is important to note that choosing a higher level of confidence comes at the cost of a wider margin of error, which may not always be practical or necessary depending on the research question and context.

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The number of heart cakes that were sold at the cake sale was 28

According to the question,

Cost of circular-shaped cake = $7

Cost of heart shaped cake = $5

Total sale = $238

Let the number of circular cakes shaped be x

Since the number of heart cakes was sold twice as many as the circular cake, the number of heart cakes will be 2x

Cost of x circular-shaped cake = $7 * x

Cost of 2x heart shaped cake = $5 * 2x

Total sale = Cost of x circular cake + Cost of 2x heart cake

Thus, we get the following equation,

238 = 7x + 10x

238 = 17x

x = 14

Thus, the number of heart cakes sold was 2x that is 28.

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The hypotenuse is c and the other leg is b.

Given is a right triangle we need to label the sides,

The sides are =

PR = a

PQ = c

QR = b

Here, a and b are the legs and c is the hypotenuse of the given right triangle.

Hence the hypotenuse is c and the other leg is b.

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the total amount of water lost between 9 and 11 am is 5 liters.

To find out how much water is lost between 9 and 11 am, we need to calculate the total amount of water that leaks out during that time period.

First, we need to find the number of hours between 7 am and 9 am, which is 2 hours. Similarly, the number of hours between 7 am and 11 am is 4 hours.

Next, we can use the given rate of water leakage to calculate the amount of water lost during each of these time periods:

Amount of water lost between 7 am and 9 am:

2.5 liters/hour × 2 hours = 5 liters

Amount of water lost between 7 am and 11 am:

2.5 liters/hour × 4 hours = 10 liters

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The correct statement about the numbers is,

⇒ The number is even or less than 12.

We have to given that;

A number is selected at random from the set (2, 3, 4.... 10).

Hence, We can check all the options as;

⇒ 10 is divisible by 5

Hence, A is incorrect.

⇒ Since, 2 = 2

Hence, B is incorrect.

⇒ Since, Every numbers are less than 12 and some numbers are even.

Hence, The correct statement about the numbers is,

⇒ The number is even or less than 12.

Thus, The correct statement about the numbers is,

⇒ The number is even or less than 12.

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The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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Answer:

Therefore, the answer to how much is in the checking account is $677.

Step-by-step explanation:

The amount in the checking account after all the transactions would be $677.

Here's the breakdown of the transactions:

Starting balance: $910

Bill payment: -$185

Withdrawal for lunch: -$30

Purchase of pants: -$43

Purchase of gift card: -$15

Refund for pants: +$43

Total = $910 - $185 - $30 - $43 - $15 + $43 = $677

Mark Twain's quote about breaking down overwhelming tasks into manageable pieces is a valuable lesson for high school students, particularly when it comes to writing. (option d)

In the context of writing, this quote can be particularly helpful. Writing a story or essay can seem like a daunting task, but if you break it down into smaller pieces, it becomes much more manageable. This is where the process of outlining comes in. An outline is essentially a roadmap of your writing, breaking it down into smaller components that you can tackle one at a time.

In mathematical terms, you can think of this process as a series of equations. Each equation represents a small, manageable piece of the overall problem.

By breaking down the problem into smaller equations, you can solve each one individually, which ultimately leads to solving the larger problem. This is similar to how breaking down a writing project into smaller pieces can help you write a well-structured and coherent piece.

Hence the correct option is (d).

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Answer:

A correct option is option (b).

Given,

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

Now, calculate the angles.

Again,

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Step-by-step explanation:

Answer: The sum of the exterior angles of any polygon is 360 degrees.

The measure of one exterior angle of a regular polygon with n sides is given by the formula:

360/n

For a polygon with 26 sides, the measure of one exterior angle is:

360/26 = 13.8 degrees (rounded to one decimal place)

Step-by-step explanation: