Lelt on together, the cold and hot water faucets of a certain bathtub take 7 minutes to fill the tub. If it takes the hot water faucet 17 minutes to fill the tub by
itself, how long will it take the cold water faucet to fill the tub on its own?

a) The length of the hypotenuse AB is 15.

b) The angle ∠A is approximately 53 degrees.

c) The angle ∠C is 90 degrees.

d) The angle ∠B is approximately 37 degrees.

a) To find the length of the hypotenuse AB, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. In this case, we have:

AB² = AC² + CB²

AB² = 12² + 9²

AB² = 144 + 81

AB² = 225

AB = √225

AB = 15

Therefore, the length of the hypotenuse AB is 15.

b) To find the angle ∠A, we can use trigonometry. The sine of an angle is the ratio of the opposite side to the hypotenuse. In this case, we have:

sin(∠A) = AC/AB

sin(∠A) = 12/15

sin(∠A) = 0.8

Taking the inverse sine of 0.8, we get:

∠A = sin⁻¹(0.8)

∠A ≈ 53

Therefore, the angle ∠A is approximately 53 degrees.

c) Since angle ∠C is the right angle, its measure is 90 degrees.

d) To find the angle ∠B, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:

∠B = 180 - ∠A - ∠C

∠B = 180 - 53 - 90

∠B ≈ 37

Therefore, the angle ∠B is approximately 37 degrees.

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It will take 12 seconds until Hudson and Knox have run the same number of feet.

Let's denote the time it takes until Hudson and Knox have run the same number of feet as "t" (in seconds).

The distance Hudson runs can be calculated by multiplying his speed (8.8 feet/second) by the time "t". Thus, the distance Hudson covers is 8.8t feet.

Knox, on the other hand, had a head start of 30 feet. So the distance Knox covers can be calculated by multiplying his speed (6.3 feet/second) by the time "t" and adding the head start of 30 feet. Thus, the distance Knox covers is 6.3t + 30 feet.

To find the time when both runners have covered the same distance, we set their distances equal to each other:

8.8t = 6.3t + 30

Simplifying the equation:

2.5t = 30

Dividing both sides by 2.5:

t = 30 / 2.5

t = 12

Therefore, it will take 12 seconds until Hudson and Knox have run the same number of feet.

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When analyzing the pairwise confidence intervals following an ANOVA test with Fisher, Tukey, or Bonferroni methods, significant differences between two treatments are determined based on certain criteria.

After conducting an ANOVA test to compare multiple treatments, further analysis can be performed using pairwise confidence intervals.   The Fisher, Tukey, and Bonferroni methods are commonly used for this purpose.    These methods help identify significant differences between two treatments by comparing the confidence intervals associated with their means.   The criteria for determining significance may vary depending on the method used. However, in general, significant differences are typically observed when the confidence intervals do not overlap or when the difference between the upper and lower bounds of the intervals exceeds a certain threshold. These methods provide a statistical framework to assess the magnitude of differences between treatments and determine if they are statistically significant, aiding in the interpretation of the ANOVA results.

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Answer:

B=27 degree angle

Answer

The blue one, the purple one, and the green one that's in the bottom right hand corner

Step-by-step explanation:

The rectangle and Parallelogram has pair of parallel sides.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions

Rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

and a parallelogram is a simple quadrilateral with two pairs of parallel sides.

In the given figures, The rectangle which is in blue color has pair of parallel lines and Parallelogram which are pink and in green color at corner has pair of straight lines.

Hence, the rectangle and Parallelogram has pair of parallel sides.

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Answer:

The statement is 6 in the negative direction

5 + (-4) = 1

Step-by-step explanation:

The requried value of ∂y/∂x at the point (1,3) is 7/2, which is option E.

We are given the curve in the xy-plane as:

f(x)g(y) = 24 + x + y

Substituting the point (1,3) in the above equation, we get:

f(1)g(3) = 24 + 1 + 3

f(1)g(3) = 28 ----- (1)

Now, we are also given the values of f(1), f'(1), g(3), and g'(3):

f(1) = 4

f'(1) = -2

g(3) = 7

g'(3) = 1

We need to find the value of ∂y/∂x at the point (1,3).

Using the product rule of differentiation, we can differentiate both sides of equation (1) with respect to x:

g(3) f'(1) + f(1) g'(3) ∂y/∂x = 0

Substituting the given values, we get:

7(-2) + 4(1) ∂y/∂x = 0

-14 + 4 ∂y/∂x = 0

∂y/∂x = 14/4

∂y/∂x = 7/2

Therefore, the value of ∂y/∂x at the point (1,3) is 7/2, which is option E.

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Answer:

vfgtfrdcfvgbhnjuytrfdecv

Step-by-step explanation:cvhnjuytgfrvgbhjuhyt

Answer:

I can say 5764 x 10^7  bc its 57640000

Step-by-step explanation:

yea that

Answer:

Step-by-step explanation:

1-1=0

Answer:You will have 0 moms.

Step-by-step explanation:

First you take 1 away from 1.

After that you get your answer of 0.

Natural numbers are strictly only plain numbers like no percents or integers, such as 1, 2, 3, 4, 5, 6 etc. Natural numbers are whole numbers and positive, so 0 would not be considered natural since it is not positive or negative

Rational numbers are numbers like 1, -100, .33, -10000, 2.4, etc it can be ALMOST anything, rational numbers fit every category but one IRRATIONAL

Irrational numbers are numbers like pie (3.145.......) it goes on forever and ever if the number never stops and repeats its called a repeating decimal, (HUGE TIP, IF YOU CAN MAKE IT A FRACTION IS IS ALMOST ALWAYS RATIONAL)

Answer:

$7

because theres 4 quarters in a mile so one mile would equal to $2  bc

0.50 x 4 = $2

and you have to go 2 miles so

$2 + $2 = $4

then you add the the cost of the taxi so

$4+ $3

= $7

0.03 x 0.6

= (3 x 6) / 1000

= 18 / 1000

0.018

it is blurry so take it again

Answer:

1/6

Step-by-step explanation:

the probability of rolling a 2 is 1/6

per annum, namely compound interest with an APR of 5%.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$15000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}\)

\(A=15000\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=15000(1.05)^3\implies A=17364.375 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{the interest earned is simply}}{17364.375 - 15000}\implies 2364.375\)

Answer:

the answer is 252

Step-by-step explanation:

7 x 8 x 9

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

     2

An electronic store uses a 35% markup on cost; thus the cost of the television is $404.88.


The cost of the television that sells for $600 can be determined by using the cost-plus pricing method. This pricing method involves adding a markup to the cost price to determine the selling price. To calculate the cost of the television, we can start by dividing the selling price by (100% + 35% markup percentage) since the markup percentage is 35%. 100% represents the cost of the item. This gives us the cost of the television, as shown below:  

Cost Price = Selling Price ÷ (100% + Markup Percentage)  

Cost Price = 600 ÷ 1.35  

Cost Price = $444.44  

Therefore, the cost of the television is $404.88 when rounded up to the nearest penny.

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Answer:

Simplifying

9x + 7 = 5x + -3

Reorder the terms:

7 + 9x = 5x + -3

Reorder the terms:

7 + 9x = -3 + 5x

Solving

7 + 9x = -3 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

7 + 9x + -5x = -3 + 5x + -5x

Combine like terms: 9x + -5x = 4x

7 + 4x = -3 + 5x + -5x

Combine like terms: 5x + -5x = 0

7 + 4x = -3 + 0

7 + 4x = -3

Add '-7' to each side of the equation.

7 + -7 + 4x = -3 + -7

Combine like terms: 7 + -7 = 0

0 + 4x = -3 + -7

4x = -3 + -7

Combine like terms: -3 + -7 = -10

4x = -10

Divide each side by '4'.

x = -2.5

Simplifying

x = -2.5

make me brainiest plz!!!

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

-43 - 9x = -7 - 15x - 18

-43 - 9x = -15x - 25

15x -9x = 43 -25

6x = 18

x = 3

Answer:

\(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

Step-by-step explanation:

The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9

\(\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]\)

To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.

\(A^{-1}\) = (1 / determinant of A) x Adjoint of A

the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2

Adjoint of A = \(\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]\)

\(A^{-1}\)= \(\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]\) = \(\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]\)

Answer:

The image does not have four right angles because translations preserve angle measures.

The angular area of the HST's field of view is 25 square degrees.

The field of view is the extent of the sky that the Hubble Space Telescope (HST) can observe at a given time. It is usually measured in degrees.

To calculate the angular area, we can use the formula for the area of a circle:

Area = π * (angular size/2)^2

Where π is a mathematical constant approximately equal to 3.14, and the angular size is in degrees.

Let's say the angular size of the HST's field of view is 10 degrees.

First, we divide the angular size by 2:

10 degrees / 2 = 5 degrees

Next, we square the result:

5 degrees * 5 degrees = 25 square degrees

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Answer:

Slope intercept form y=mx+b use that

Step-by-step explanation:

it works and you'll get the right answer

To estimate the conditional probabilities for the given terms, you need to know the joint probabilities for each combination of the events. However, without any context or specific data, it is impossible to provide accurate estimates.

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome. It is calculated by multiplying the probability of the preceding event by the renewed probability of the succeeding, or conditional, event. The probability of occurrence of any event A when another event B in relation to A has already occurred is known as conditional probability. It is depicted by P(A|B). Please provide more information or context to help me provide a better answer.

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Answer:

8.7m

Step-by-step explanation:

Use the Pythagorean theorem, a^2 + b^2 = c^2

a and b are the sides going either horizontally or vertically, it doesn't matter which is which as long as it's only between those 2.

c is the diagonal side, also called the hypotenuse.

so plug in:

a^2 + b^2 = c^2

5^2 + b^2 = 10^2

25 + b^2 = 100

subtract 25 from both sides

b^2 = 75

square root both sides

\(\sqrt{b^2} = \sqrt{75}\)

b = 8.66, round it up and it's 8.7

Answer:

a. 1142.5 m

b. 57.13 m/s

Step-by-step explanation:

a here we shall use the trigonometry to solve.

since the plane si moving it is covering some distance, we use the angle of elevation and the height from the ground to calculate the distance covered.

we use tan a = opposite/adjacent

tan 35 = 800/X

Xtan 35° = 800

X = 1142.5 m

b. speed = distance covered/ time taken

= 1142.5/20

= 57.125 m/s

= 57.13m/s

yes you are correct because when you plug 8 into the equation you get (8+3(8))/4