Air is escaping from a balloon at the rate of R(t)=60/1+t^2 cubic feet per minute, where t is measured in minutes. How much air, in cubic feet, escapes during the first minute​

It is JG! You must rotate the second triangle so both triangles are at the same angle. Then, look at the lines and find the corresponding line segment on the other triangle.

let's recall something about a right-triangle.

it has a 90° angle, and the longest side, the hypotenuse, from the pythagorean theorem, is c² = a² + b², or namely c = √( a² + b²).

so, let's take a peek at the two smaller sides, 60 and 11, can we get the longest side from it using the pythagorean theorem?

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{61}\\ a=\stackrel{adjacent}{60}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ 61=\sqrt{60^2+11^2}\implies 61=\sqrt{3600+121} \\\\\\ 61=\sqrt{3721}\implies 61=61~~\stackrel{\textit{yeap, it is}}{\checkmark}[/tex]

The given lengths of 60ft, 61ft, and 11ft can form a right triangle. This has been confirmed by applying the Pythagorean theorem, which gives equal results for both sides of the equation.

In the field of Mathematics, the formation of a right triangle with given side lengths can be verified using the Pythagorean theorem. The theorem states: If a triangle is a right triangle, then the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, as represented by this formula: a² + b² = c².

Applying this theorem to your question, we can use the three lengths you've provided: 60ft, 61ft, and 11ft. Let's assign the longest length (considered as the hypotenuse in a right triangle) as 'c', which is 61ft in this case. The other sides 'a' and 'b' would be 60ft and 11ft.

Here's how the theorem fits: 60² + 11² = 61².

Calculating the squares gives us 3600 + 121 = 3721 for the left-hand side, and 3721 for the right-hand side as well. Since the results are equal, the given lengths can indeed form a right triangle according to the Pythagorean theorem.

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Answer:

advance tickets cost $20 each & same-day tickets cost $35 each

Step-by-step explanation:

Let cost of advanced ticket be x and cost of same-day ticket be y. Now we can write 2 equations and solve them simultaneously.

"The combined cost of one advance ticket and one same-day ticket is $55":

[tex]x+y=55[/tex]

and

"...40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $1325":

[tex]40x+15y=1325[/tex]

We solve for x in the first equation to get x = 55 - y and substitute this into 2nd equation and solve for y:

[tex]40(55-y)+15y=1325\\2200-40y+15y=1325\\-25y=1325-2200\\-25y=-875\\y=\frac{-875}{-25}=35[/tex]

Now plugging in y = 35 into the first equation, we can solve for x:

[tex]x+y=55\\x+35=55\\x=55-35\\x=20[/tex]

Hence, advance tickets cost $20 each & same-day tickets cost $35 each

Answer:

x < 61

Step-by-step explanation:

Given

x + 12 < 73

Isolate x on the left side by subtracting 12 from both sides

x < 63 ← is the solution

Answer:

A and B

Step-by-step explanation:

Parallel lines are lines which have the same slope. Perpendicular lines have negative reciprocal slopes.

For the options:

A. Both equations have 7/5 as the slope. They are parallel.

B. The slopes are 1 and -1. These are perpendicular.

C. The slopes are 9/2 and are parallel.

D. The slopes are 7/3 and -3/7. They are perpendicular.

The solution is A and B.

Answer:

3/8

Step-by-step explanation:

1/2 of a yard is 4/8 of a yard, so you can subtract 7-4 to get 3/8 of a yard.

ANSWER

[tex]8 {cm}^{2} [/tex]

EXPLANATION

First let us determine the scale factor of the enlargement

[tex]k = \frac{image \: length}{corresponding \: object \: length} [/tex]

[tex]k = \frac{8}{1.6} [/tex]

[tex]k = 5[/tex]

This implies that that, the corresponding length of the smaller rectangle is

[tex]l = \frac{25}{5} = 5cm[/tex]

The area of the smaller rectangle is

[tex] = 5 \times 1.6 = 8 {cm}^{2} [/tex]

When she adds to the original four sections by coloring three more, it represents the total colored sections.

Answer:

A. 4/8+3/8

E. 1/8+1/8+1/8+1/8+1/8+1/8+1/8

Step-by-step explanation:

Select the two correct answers:

A. 4/8+3/8

B. 4+3

C. 8/4+8/3

D. 1/8+3

E. 1/8+1/8+1/8+1/8+1/8+1/8+1/8

Answer: C. The y-intercept means the concentration will remain 30% if no solution is added.  <-- on edgen2020

Explanation: The first person who answered is correct! I'm attaching a screenshot of my quiz with this- Good luck everyone! :)

Answer:

C. The y-intercept means the concentration will remain 30% if no solution is added.  

Step-by-step explanation:

edge2022

Answer:6.2 and 6.5

Step-by-step explanation:

First, make a plotline from least to greatest and organize your list of numbers from least to Greatest.

Next, go through your list of organized numbers and add a dot to that number on the plotline. Repeat until done with list of numbers.

Then, go through your plotline and find the number(s) with the most dots and you have your mode.

Definition of mode: The number which appears most often in a set of numbers.

Answer provided in the image attached.

Answer:

first...you have to split the net into three rectangles and two triangles

picture inserted

Step-by-step explanation:

step 1

triangular base area

1/2 bh = 1/2 (44 in)(64 in)

= 1/2 (2,816 sq in)

= 1,408 sq in.

2 x 1,408 sq in = 2,816 sq in.

step 2

end rectangle area

lw = (68 in)(69 in)

= 4,692 sq in

2 x 4,692 sq in = 9,384 sq in

Now find the area of the middle rectangle

lw - (69 in) (44 in) = 3,039 sq in.

then add all the areas together

2,816 + 9,384 + 3,036 = 15,236 sq in

The fabric that is required to make the tent should be B. 15,236 sq in.

triangular base area

1/2 bh = 1/2 (44 in)(64 in)

= 1/2 (2,816 sq in)

= 1,408 sq in.

Now

2 (1,408 sq in) = 2,816 sq in.

Now

end rectangle area

lw = (68 in)(69 in)

= 4,692 sq in

So,

2  (4,692 sq in) = 9,384 sq in

Now determine the area of the middle rectangle

So,

lw - (69 in) (44 in) = 3,039 sq in.

So, the fabric required is

= 2,816 + 9,384 + 3,036

= 15,236 sq in

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Answer:

Step-by-step explanation:

2x = 27

He could be thinking of any number between 3.1451 and 3.1459

Answer:

Thursday

Step-by-step explanation:

Since the forecast being  completely accurate would be 0, you would have to choose the closest number to 0, and if you look -2 or Thursday is the closest number the 0,

Answer:

B

Step-by-step explanation:

Answer:

Option 2 -  [tex]-6x^3+x^2-\sqrt5[/tex]

Step-by-step explanation:

To find : Which algebraic expression is a polynomial?

Solution :

Polynomial is defined is the expression consisting of several terms with variable and constant.

Polynomial is always positive not a negative exponential.

Option 1 - [tex]4x^2-3x+\frac{2}{x}[/tex]

This is not a polynomial because it has a negative exponent.

Option 2 - [tex]-6x^3+x^2-\sqrt5[/tex]

This is a polynomial by definition.

Option 3 - [tex]8x^2+\sqrt x[/tex]

This is not a polynomial as  [tex]\sqrt x[/tex] is not considerable.

Option 4 - [tex]-2x^4+\frac{3}{2x}[/tex]

This is not a polynomial because it has a negative exponent.

Therefore, Option 2 is correct.

Answer:

d = b/c.

Step-by-step explanation:

Just divide both sides by c:

b = cd

b / c = cd/ c

b/c = d.

Answer:

[tex] d = \frac { b } { c } [/tex]

Step-by-step explanation:

We are given the following equation and we are to solve it for d:

[tex] b = c d [/tex]

Since we are asked to solve this equation for d and it contains all variables, it means that we need to make the variable 'd' the subject of the equation by keeping all other variables at the other side of the equation.

[tex] b = c d [/tex]

[tex]d=\frac{b}{c}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]S=45m+15[/tex]

Step-by-step explanation:

we have

E------>the number of sit-ups

m---->  the time in minutes

S----> the number of sit-ups after drinking the sports drink

[tex]E=15m+5[/tex] ----> equation A

[tex]S=3E[/tex] ----> equation B

substitute the equation A in the equation B

[tex]S=3(15m+5)[/tex]

[tex]S=45m+15[/tex]

Answer: Its the Second one!

Step-by-step explanation: Ur welcome <3

10% × 23.8 =

(10 ÷ 100) × 23.8 =

(10 × 23.8) ÷ 100 =

238 ÷ 100 =

2.38

Proof

2.38 ÷ 23.8 =

0.1 =

0.1 × 100/100 =

0.1 × 100% =

(0.1 × 100)% =

10%

Answer:

238

Step-by-step explanation:

Question: Find 10% of 238.  

Answer: 10% of 238 is 23.8.

Explanation

STEP 1: 1% of 238 = 238100=2.38

STEP 2: 10% of 238 = 10⋅2.38=23.8

Explanation 2:

STEP 1: Write 10% as a decimal number: 10%=10100=0.1

STEP 2: Multiply 0.1 by 238: 0.1⋅238=23.8

Result

Question: The number 238 is 10% of what number?

Answer: The number 238 is 10% of 2380.

Explanation

STEP 1: Write 10% as a decimal number:

10=10100=0.1

STEP 2: Divide 238 by 0.1:

2380.1=2380

Interest (I) = Principal (P) X Rate (R) X Time (T)

They tend to use 'Exact Interest' in which Interest calculated using a 365-day year. Time that counts exact number of days in the month that the borrower has the loan

Hope this helps :)

Answer:

Interest (I) = Principal (P) X Rate (R) X Time (T)

Hope this helps you:)

5INGH

Step-by-step explanation:

D is the answer............

Answer:

5/13

Step-by-step explanation:

Since the triangles are similar, the cos F = cos C

Cos C = adjacent side/ hypotenuse

Cos C = 5/13

Cos F = 5/13

Answer:

The correct answer is,

| -8|

| 4 |

Step-by-step explanation:

It is given two matrices,

1)Let Matrix A =   5  -2

                          -6    2

2) Matrix B =       -1

                          -1

Matrix A is 2 x 2 matrix and matrix B is 2 x 1 matrix

To find the product of two matrices

A x B =    5  -2       x      -1     =   -10+2      =   -8

             -6    2              -1             6 -2            4

Therefore the correct answer is

| -8|

| 4 |

Mean (μ) ≈ 53.84, Standard deviation (σ) ≈ 16.51.

To solve this problem, we can use the properties of the normal distribution and the given information about the percentage of students scoring certain marks.

Let's denote the mean as μ and the standard deviation as σ. We know that in a normal distribution:

1. 10% of the students score more than 75 marks.

2. 20% of the students score less than 40 marks.

To find the values of μ and σ, we'll utilize the standard normal distribution table (Z-table), which provides the cumulative probabilities for a standard normal distribution (mean = 0, standard deviation = 1). Then we'll apply the z-score formula to convert these values to the corresponding marks in our distribution.

Let [tex]\( Z_{75} \)[/tex] be the z-score corresponding to 75 marks, and [tex]\( Z_{40} \)[/tex]  be the z-score corresponding to 40 marks.

From the standard normal distribution table:

1. The z-score corresponding to the 90th percentile (10% above) is approximately [tex]\( Z_{75} = 1.28 \)[/tex] .

2. The z-score corresponding to the 20th percentile (20% below) is approximately [tex]\( Z_{40} = -0.84 \)[/tex].

The z-score formula is:

[tex]\[ Z = \frac{{X - \mu}}{\sigma} \][/tex]

where:

- [tex]\( X \)[/tex] is the raw score (marks)

- [tex]\( \mu \)[/tex] is the mean

- [tex]\( \sigma \)[/tex] is the standard deviation

Using the z-score formula, we can write two equations based on the given percentiles:

1. For 75 marks:

[tex]\[ 1.28 = \frac{{75 - \mu}}{\sigma} \][/tex]

2. For 40 marks:

[tex]\[ -0.84 = \frac{{40 - \mu}}{\sigma} \][/tex]

Now, we have two equations with two unknowns [tex](\( \mu \) and \( \sigma \))[/tex], we can solve them simultaneously to find the values of [tex]\( \mu \) and \( \sigma \)[/tex].

From equation 1:

[tex]\[ 1.28\sigma = 75 - \mu \][/tex]

[tex]\[ \mu = 75 - 1.28\sigma \][/tex]

From equation 2:

[tex]\[ -0.84\sigma = 40 - \mu \][/tex]

[tex]\[ \mu = 40 + 0.84\sigma \][/tex]

Now, equating the expressions for [tex]\( \mu \)[/tex] :

[tex]\[ 75 - 1.28\sigma = 40 + 0.84\sigma \][/tex]

Solving for [tex]\( \sigma \)[/tex] :

[tex]\[ 1.28\sigma + 0.84\sigma = 75 - 40 \][/tex]

[tex]\[ 2.12\sigma = 35 \][/tex]

[tex]\[ \sigma[/tex] ≈ [tex]\frac{35}{2.12}[/tex]

[tex]\[ \sigma[/tex] ≈ [tex]16.51[/tex]

Now that we have [tex]\( \sigma \)[/tex], we can find [tex]\( \mu \)[/tex] using one of the equations for [tex]\( \mu \)[/tex]:

[tex]\[ \mu = 75 - 1.28 \times 16.51 \][/tex]

[tex]\[ \mu[/tex] ≈ [tex]75 - 21.16[/tex]

[tex]\[ \mu \approx 53.84 \][/tex]

So, the values of [tex]\( \mu \) and \( \sigma \)[/tex] are approximately 53.84 and 16.51, respectively.

The center of the circle is the x and y in the equation.

To find the center you need to solve for x and Y when the equations inside parenthesis are set to zero.

(x-6)=0

x = 6

(y+3)=0

y = -3

The center of the circle is (6,-3)

Answer:

15 inches

Step-by-step explanation:

Suppose length of original square is L inches.

Now, to form a new square the length increases by 2.5 inches

So, new length=L+2.5 inches

Given that, perimeter of new square =70 inches.

Formula:-

        Perimeter=4*length of square

Therefore 70=4*(L+2.5)

                   70 =4 L+10

                   4 L=60

                  L=15 inches

Answer:

The original length of each side was 15 inches.

Step-by-step explanation:

In this case we have to have clear that the perimeter of square consists in the addition of the length of each one of its four sides, this is:

[tex]perimeter=a+a+a+a[/tex]

The new square has a perimeter of 70, and we have to find the original length of each side, the equation will be:

[tex]70=a+2.5+a+2.5+a+2.5+a+2.5[/tex]

[tex]70=4a+10[/tex]

We have to clear a:

[tex]a=\frac{70-10}{4} \\a=\frac{60}{4} \\a=15[/tex]

The original length of each side was 15 inches.

Answer:

The answer is 17 1/6  you didnt notice the little line above the six you techniclly just convert the decimal to a fraction i had this on my lesson it tricked me to

Step-by-step explanation:

Answer:

Option C is correct

[tex]3x^3-4x^2-10[/tex]

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Find the difference of the following:

[tex](3x^3-2x^2+4)-(2x^2+14)[/tex]

Remove the parenthesis we get;

[tex]3x^3-2x^2+4-2x^2-14[/tex]

Combine like terms;

[tex]3x^3-4x^2-10[/tex]

Therefore, the difference of [tex](3x^3-2x^2+4)-(2x^2+14)[/tex] is, [tex]3x^3-4x^2-10[/tex]

Answer:

The answer is c, 24 units.

Answer:

c

Step-by-step explanation:

The correct option is c. $336.36. The previous day's closing price of  stock was:c. $336.36.

To determine the closing price of stock the previous day, we need to use the information provided in the table. The table shows the net change (Chg) in the stock price and the current closing price (Close). The net change is the difference between the current closing price and the previous day's closing price.

From the table:

- Current closing price (Close): $342.64

- Net change (Chg): $6.28

Since the net change represents the increase in the stock price from the previous day to the current day, we can calculate the previous day's closing price by subtracting the net change from the current closing price.

[tex]\[\text{Previous day's closing price} = \text{Current closing price} - \text{Net change}\][/tex]

[tex]\[\text{Previous day's closing price} = 342.64 - 6.28 = 336.36\][/tex]

Therefore, the previous day's closing price of stock was:

c. $336.36