Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. On the way there it took him 10 hours against a river current of 3 km/ hr. On the way back, the same distance took him 5 hours with the same 3 km/hr current.

Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:

5 = (90 cm - x)/x     (1)

5 · x = 90 cm - x

6 · x = 90 cm

x = 15 cm

Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.

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The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.

In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:

(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)

Which is equivalent to this system of linear equations:

α₁ + 2 · α₂ - α₃ = 4

3 · α₁ + 8 · α₂ - 5 · α₃ = 6

- 4 · α₁ - 5 · α₂ = 3

α₁ - α₂ + 2 · α₃ - t = 0

Whose solution is (α₁, α₂, α₃, t) = (38, - 31,  - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.

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Answer:

multiple triangles

Step-by-step explanation:

add the numbers up it adds to 180 which is the sum of a triangle and could create other triangles

There are 14 yellow blocks in the box

The given parameters are:

The number of yellow blocks is calculated as:

Yellow = (1 - P(Red) - P(Red and Yellow)) * n

So, we have:

Yellow = (1 - 1/3 - 1/12) * 24

Evaluate

Yellow = 14

Hence, there are 14 yellow blocks in the box

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Complete question

A box contains a group of 24 blocks. Some are red, some are yellow, and some are a mixture of the two colors. The probability of drawing a red block is 1/3. The probability of drawing a red and yellow block is 1/12. Determine the number of yellow blocks.

The zeros of the polynomial function are -1.728, 0.56 and 5.167

The polynomial function is given as:

x^3 - 4x^2 - 7x + 5

Next, we plot the graph of the polynomial

From the graph, the polynomial cross the x-axis when

x = -1.728, 0.56 and 5.167

Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167

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Answer:

Step-by-step explanation:

$274 for 40 hours of work as a unit rate

in practice you look for the hourly wage, you find it by dividing the wages divided by the working hours

274 : 40 = 6.85 units per hour

Answer:

8,9,5

Step-by-step explanation:

Sofia will order 7 more rolls of sushi (84 pieces) and pay $56St

Step-by-step explanation: im right

The cost of one ounce of peanuts is $0.20

The cost of one ounce of cashew is $0.35

15p + 5c = 4.75 equation 1

5p + 15c = 6.25 equation 2

Where:

Multiply equation 2 by 3

15p + 45c = 18.75 equation 3

Subtract equation 1 from equation 3

40c = 14

c = 14/40

c = $0.35

Substitute for c in equation 1

15p + (5 x 0.35) = $4.75

15p + 1.75 = 4.75

15p = 4.75 - 1.75

15p = 3

p = 3/15

p = $0.20

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Answer:

hold shift then press the lil right  arrow next to the question mark

Step-by-step explanation:

Answer:

shift  +  >

Step-by-step explanation:

Hope this helps

The expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

From the question, we are to determine the expression that shows the best use of the associative and commutative properties

The given expression is

[tex]\frac{3}{4}-5+9 -\frac{2}{4}+2[/tex]

To easier simplify the expression, we can group the fractions together and group the whole numbers together

That is,

[tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

Hence, the expression that shows the best use of the associative and commutative properties is [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]. The correct option is C. [tex][\frac{3}{4}+(-\frac{2}{4})]+[9 +2+(-5)][/tex]

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Considering the definition of an equation and the way to solve it, 43 female contestants have signed up to compete.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "m" the number of male contestants, and knowing that:

the equation in this case is:

m + (m+36) = 50

Solving:

m + m = 50 - 36

2m= 14

m= 14 ÷ 2

m= 7

Since there are 36 more female contestants than male contestants, then m +36= 7 + 36= 43

Finally, 43 female contestants have signed up to compete.

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The solutions to the system of equations are (4, 15) and (-1,-1)

The system of equations is given as:

y=3x+2

y=x^2-4+2

Substitute y=3x+2 in y=x^2-4+2

3x + 2=x^2-4+2

Simplify

x^2 - 3x - 4 = 0

Expand

x^2 + x - 4x - 4x = 0

Factorize

x(x + 1) - 4(x + 1) = 0

This gives

(x - 4)(x + 1) = 0

Solve for x

x = 4 and x = -1

Substitute these values in y=3x+2

y = 3(4)+2 = 15

y = 3(-1)+2 = -1

Hence, the solutions to the system of equations are (4, 15) and (-1,-1)

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The statements that correctly compare the sum and product of the function are:

A linear function simply means a function that represents a straight line on the coordinate plane.

In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.

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The conclusion is P(pass l morning) = 0.56

P(pass l afternoon) = 0.72

Conclusion: a student taking the test in the afternoon has a greater probability of passing than a student taking the test in the morning.

Probability is the odds that a random event would happen. The odds that the event would happen lies between 0 and 1. The closer the probability is to one, the more likely it is for the event to happen.

P(pass l morning) = number of students who took the test in the morning and passed / total number of students that took the exam in the morning

28 / 50 =  0.56

P(pass l afternoon) = number of students who took the test in the afternoon and passed / total number of students that took the exam in the afternoon  = 36 / 50 = 0.72

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Answer:

C

Step-by-step explanation:

Just took the quiz

Answer:

C & D

Step-by-step explanation:

A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.

B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.

C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.

D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.

Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.

From the equation of simple interest; I = PRT

Given that;

I = PRT

I = $4,500 × 0.0275 × 8/12

I = $82.50

Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.

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The value of x in the similar triangles is 18

Similar triangles have the same shapes but may have different sizes.

Corresponding side of similar triangles are a ratio of each other.

Therefore,

UV / BC = AU / AB

Hence,

UV = 444 units

BC = 703

AU = 20x + 108

AB = 20x + 108 + 273 = 20x + 381

Therefore,

444 / 703 = 20x + 108 /  20x + 381

cross multiply

444( 20x + 381) = 703(20x + 108)

8880x + 169164 = 14060x + 75924

8880x  - 14060x  = 75924 -  169164

-5180x = -93240

x = -93240 / -5180

x = 18

Therefore, the value of x in the similar triangles is 18

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Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=

[tex] \sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} } [/tex]

Also, for example the distance between A(a,b) and B(c,d)

is

[tex] \sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} } [/tex]

Answer:

[tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

Step-by-step explanation:

To find the distance between two points, we can use the Distance Formula.

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given:

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

[tex]\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}[/tex]

The distance between points P and Q is [tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

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The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)

We are given the quadratic equation;

81x² - 100

Now, according to quadratic identities, we know that;

(a + b) * (a - b) = a² - b²

Now, our equation can also be expressed as;

81x² - 100 = 9²x² - 10²

Thus, applying the quadratic identity gives us;

(9x + 10)(9x - 10)

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The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?

From the information given, it can be seen that 1/2 is divided by 2/5.

In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?

In this case, the length is multiplied by width to get the area.

Therefore, the correct option is A.

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Answer:

  (c)  45°

Step-by-step explanation:

A protractor is used to measure angles by aligning one of the sides of the angle with the 0 mark on the protractor scale. Then the value of the angle is read from the same scale where it is crossed by the other side of the angle.

Here, ray BA crosses the outer scale at 0. The other ray of the angle, BC, crosses the outer scale halfway between 40 and 50, obscuring the mark at 45°.

The measure of angle ABC is 45°.

C. 45°

When measuring with a protractor one of the rays should line up with the straight edge of the protractor, then match up the second ray to the tick marks. However, it can be confusing to tell how to read a protractor.

Clockwise

This angle moves clockwise. This means that the second ray is clockwise to the ray at the bottom. When using a protractor that opens up to the left like this, read the top row of the protractor. The second ray matches the 45-degree mark.

Acute vs Obtuse

There is another way to tell which row of numbers to read. By looking at the drawn angle we can tell the angle is acute (smaller than a right angle). So, the measurement must be less than 90. Therefore, the top row must apply in this situation, meaning the angle is 45°.

Answer:

Step-by-step explanation:

(a). A = 5x( 7x - 2 ) - 3x( 2x + 4 )

(b). A = 35x² - 10x - 6x² - 12x = 29x² - 22x

A = 29x² - 22x

The number of steps they climbed can be represented by positive

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

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The first day when he would do these activities on the same day is December 7, 2023.

In order to determine which day Mr. Carson would wash his car, check his oils and check the tire pressure, the multiple of 8, 7, and 9 have to be determined.

A multiple of a number is the product of an integer and that number. A common multiple is a number that is common to all three numbers. The lowest common multiple of 8, 7 and 9 is 504. So, in 504 days he would do all three activities on the same day.

In order to convert 504 days, take note of the following:

365 days = 1 year

12 month = 1 year

1 month = 4 weeks

30 days = 1 month

504 / 365 = 1 year 139 days

139 days / 30 days  = 4 months 19 days

504 days = 1 year, 4 months and 19 days

1 year, 4 months and 19 days + July 18, 2022 = December 7, 2023

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Answer:

Angle = 59.03 degrees

Length = 58.3 inches

Step-by-step explanation:

The number of marriage licenses were issued in 2003 is 21586.

According to the statement

we have to find the number of marriage licenses were issued in 2003

and the given equation is y=3.405x^2-17674x+21533000

And in this equation x represent the time

And Y represent the number of marriage certificate issued.

So, in given equation

y=3.405x^2-17674x+21533000

we fill the value of X and find the value of Y means tne number of marriage license is issued in 2003

We know that X = 3 from 2000 to 2003

Then put X=3 in the given equation.

Then

This is the equation (1) represent the change

y=3.405(3)^2-17674(3)+21533000 -(1)

y = 30.645+53022+21533000

y = 21586052.645

On nearest hundred the value becomes 21586.

So, The number of marriage licenses were issued in 2003 is 21586.

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DISCLAIMER: The question was incomplete. please find the full content below.

QUESTION:

According to the model, how many marriage licenses were issued in 2003? Round your answer to the nearest hundred.

The number of marriage licenses issued by Clark county Nevada, the county where Las Vegas is located, has been decreasing since the year 2000. This can be modeled by y=3.405x^2-17674x+21533000 where x is the year and y is the number of marriage licenses issued.

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Answer: A. 137,000

Step-by-step explanation: I did the quiz.

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.02

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

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