A sight-seeing boat travels at an average speed of 21 miles per hour in the calm water of a large lake. The same boat is also used for sight-seeing in a nearby river. In the river, the boat travels 2.6 miles downstream (with the current) in the same amount of time it takes to travel 2 miles upstream (against the current). Find the current of the river.

Answer:

8.0 × 10^-3 ÷ 4.0 × 10^4

= 2.0 × 10^-3-4

= 2.0 × 10^-7

or 0.0000002

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Answer:

-25x-45y, because if we have got + and -, so we will write minus.

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

Now, the boat goes Upstream 48 miles, so Downstream must be travelling the same 48 miles back.

\({\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&48&b-c&3\\ Downstream&48&b+c&2 \end{array}\hspace{5em} \begin{cases} 48=(b-c)(3)\\\\ 48=(b+c)(2) \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 1st equation}}{48=(b-c)3}\implies \cfrac{48}{3}=b-c\implies 16=b-c\implies \boxed{16+c=b} \\\\\\ \stackrel{\textit{using the 2nd equation}}{48=(b+c)2}\implies \cfrac{48}{2}=b+c\implies 24=b+c\implies \stackrel{\textit{substituting}}{24=(16+c)+c} \\\\\\ 24=16+2c\implies 8=2c\implies \cfrac{8}{4}=c\implies \boxed{2=c}~\hfill~\stackrel{ 16~~ + ~~2 }{\boxed{b=18}}\)

The research explores the various factors that may influence the learning choices of first-year undergraduates, such as the family and educational background of the student, their socioeconomic status and the availability of resources, among others.

Factor is a mathematical quantity which is multiplied with another quantity to give a product. Factors can also be defined as the numbers that divide a given number exactly. Factors are used in everyday life to calculate many different types of problems, such as compound interest, speed, distance and time, and more. Factors are also used in statistics and probability to determine the likelihood of certain events occurring.

The paper will also examine the various types of postgraduate courses that are available to undergraduates, including those offered by universities and other institutions, such as professional courses or distance learning programmes.

The research adopts a qualitative approach, and will use semi-structured interviews with first-year undergraduates to gain an understanding of their learning choices, and the factors that influence them. Interviews will be conducted with students in different disciplines, in order to gain an insight into how the different disciplines shape students' learning preferences. The research will also use questionnaires to obtain data on the socioeconomic background, family background and educational background of students.

In addition, the research will use documentary analysis of university prospectuses and websites, and information from other sources, such as employers and professional bodies, to gain an understanding of the various postgraduate courses that are available to undergraduates. This data will be used to compare and contrast the learning choices of undergraduates from different disciplines and economic backgrounds.

Finally, the research will use an interpretive approach to analyse the data collected and develop a theory of the factors that influence the learning choices of first-year undergraduates. The theory will be used to inform the design of initiatives to help undergraduates make informed decisions about their learning choices.

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The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

No, it is not

Step-by-step explanation:

It is suppose to be like:

1|4

2|8

3|12

Answer:

no it is not x is not the reason and y us the 6

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

The area of the shaded portion of the composite figure could be easily 25*25 - 1/2*13*10 that is 625 - 65 = 560 feet

When referring to a two-dimensional space or points, in mathematics, the term "area" is used. It refers to a region's or a flat object's size, such a square or rectangle. The area of a form is determined in geometry by dividing the length by the breadth. For example, the area of a square with a side length of 4 units is 4 x 4 = 16 square units. Square units, such as square inches, square feet, or square meters, are used to measure area. Triangles (1/2 x base x height), circles ( x radius squared), and trapezoids (1/2 x (base 1 + base 2) x height) are other basic geometric forms with associated area calculations.

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Answer:

11/61

Step-by-step explanation:

sin K = opp/hyp

sin K = 11/61

Answer: 11/61

Answer:

SinK=11/61

Step-by-step explanation:

The function sin can be found by looking for the side opposite of the angle over the hypotenuse.

Given that

The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.

Explanation -

So the figure will be rotated from its position clockwise as

Since the given points are J(-9, -8)

K(-2, -8)

L(-2, -3)

M(-9, -3)

After rotating the points will be

J(

K(-7, -3)

L(-2, -3)

M(-2, 4)

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)

\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)

⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)

⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)

⤑ \( \sf{ \sqrt{100 - 64}} \)

⤑ \( \sf{ \sqrt{36}} \)

⤑ \( \boxed{ \sf{6\: units}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)

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The quotient when 480 is divided by -60 is 8.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The numbers given are 480 and -60.

Both are in opposite signs, that is one negative and other positive.

So the quotient will be negative.

Now divide 480 by 60.

Since both of the numbers contain 0 at the end, cancel it.

Then it becomes 48 divided by 6.

48 / 6 = 8

Hence the quotient is 8.

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Answer: the answer is

8 (2a + 3b)

Answer:354

Step-by-step explanation:

35335345

Answer:

5 pens

Step-by-step explanation:

$10 - 6$ = $4

$4/$0.80

she can afford 5 pens

Responder:

Expressão monomial de terceiro grau

Explicação passo a passo:

O número de expressões de um termo algébrico. Contém é usado para nomeá-los em:

Monomial = 1 termo.

Binomial = 2 termos

Trinomial e assim por diante; A expressão fornecida acima contém apenas um único termo '7x³', portanto, é uma expressão monomial. A maior potência em que a variável na equação quadrática é elevada é chamada de potência;

A expressão acima é elevada à potência 3. Portanto, a equação quadrática é um monômio elevado à potência 3.

Portanto, é um monômio de terceiro grau.

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer: We can solve this problem by counting the total number of ways to select three members and then subtracting the number of ways to select three members without any officers.

The total number of ways to select three members from a group of 13 is given by the combination formula:

C(13,3) = 286

To count the number of ways to select three members without any officers, we need to choose three members from the 8 non-officers. This can be done in C(8,3) = 56 ways.

Therefore, the number of ways to select three members with at least one officer is:

C(13,3) - C(8,3) = 286 - 56 = 230

There are 230 ways to select three members for the search and rescue mission such that at least one officer is included.

Step-by-step explanation:

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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Answer:

95% confidence interval for the population proportion of adults who ate fast food at least once in the past month

( 0.6226  , 0.6814)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 1000

Given data in a survey of 1,000 adults in a country, 652 said that they had eaten fast food at least once in the past month

Sample proportion

                     \(p^{-} = \frac{x}{n} = \frac{652}{1000} = 0.652\)

Step(ii):-

95% confidence interval for the population proportion of adults who ate fast food at least once in the past month

\(( p^{-} - Z_{0.05} \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p^{-} (1-p^{-} )}{n} })\)

\(( 0.652 - 1.96 \sqrt{\frac{0.652 (1-0.652 )}{1000} } , 0.652 + 1.96 \sqrt{\frac{0.652 (1-0.652)}{1000} })\)

( 0.652 -   0.0294 ,0.652 + 0.0294 )

( 0.6226  , 0.6814)

Final answer:-

95% confidence interval for the population proportion of adults who ate fast food at least once in the past month

( 0.6226  , 0.6814)

Answer:

Explanation:

Formula to calculate the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Therefore, length of CD having coordinates C(3,1) and D(3, 3),

\(CD=\sqrt{(3-3)^2+(1-3)^2}\)

\(=2\) \(units\)

Formula to find the midpoint of CD is,

\(M=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\)

   \(=(\frac{3+3}{2},\frac{1+3}{2})\)

   \(=(3,2)\)

Therefore, length of CD = 2 units and (3, 2) are the coordinates of the midpoint of CD.

Answer:

-12

Step-by-step explanation:

The circles that have their centers in the second quadrant are; Options B and D

The general form of equation of a circle is;

( x - h )² + ( y - k )² = r²

where (h, k) is the center and r is the radius.

Thus;

A. (x - 5)² + (y - 6)² = 25

(h, k) = 5,6 This is Quadrant 1

B. (x + 1)² + (y - 7)² = 16

(h, k) = -1,7 This is Quadrant 2

C. (x - 4)² + (y + 3)²= 32

(h, k) = 4,-3 This is Quadrant 4

D. (x + 2)² + (y - 5)² = 9

(h, k) = -2,5

This is Quadrant 2

The missing circle equations are;

A. (x - 5)² + (y - 6)² = 25

B. (x + 1)² + (y - 7)² = 16

C. (x - 4)² + (y + 3)² = 32

D. (x + 2)² + (y - 5)² = 9

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The length of side x of the pyramid is equal to 47 inches.

Given the following data:

To determine the length of side x of the pyramid, we would apply Pythagorean's Theorem:

Pythagorean theorem is a fundamental mathematical expression in Euclidean geometry that can be used to determine any of the three (3) sides of a right triangle.

Mathematically, Pythagorean's Theorem is given by this formula:

\(c^2 = a^2 + b^2\)

Where:

Substituting the given parameters into the formula, we have:

\(x^2=2^2 +46.5^2\\\\x^2=4+2162.25\\\\x^2=2166.25\\\\x=\sqrt{2166.25}\)

x = 46.54 ≈ 47 inches.

b. To find the length of the support:

Since the support is altitude (y) to the hypotenuse of the right-angled triangle, we have:

Length = \(\frac{12 \times \sqrt{47}} {47}\)

Length = 1.75 ≈ 2 inches.

c. The support would attach to base of the hypotenuse of the plywood, which is the triangle formed by altitude (y) to the hypotenuse of the right-angled triangle.

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