A boat traveled 336 miles downstream and then returned back. The trip downstream took 8 hours. The trip back took 12 hours. What is the speed of the boat in still water? What is the speed of the current? (Distance= rate x time)

Answer:

gradient= y2-y1/x2-x1

-8+10/-8-c=-1/8

2/-8-c=-1/8

-1(-8-c)=8(2)

8+c=16

c=16-8

c=8

Answer:

The amount of the money earned left for the band to split is $357.5

Step-by-step explanation:

The amount the band earned for playing at the concert = $550.00

The percentage of the money earned taken by the manager = 15%

The percentage of the money earned the band is donating to charity = 20%

The amount of the money earned the manager takes = 15/100 × 550 = 82.5

∴ The amount of the money earned the manager takes = $82.5

The amount of the money earned that is donated to charity = 20/100 × 550 = 110

∴ The amount of the money earned that is donated to charity = $110

The amount of the money earned left for the band to split = $550 - $82.5 - $110 = $357.5.

Answer:

It is a scalene triangle because it has unequal sides

Answer:

A scalene triangle

Step-by-step explanation:

I'm just a smart guy

Answer:

gradient = \(\frac{1}{2}\) , y- intercept = - \(\frac{3}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope ( gradient) and c the y- intercept )

given

x - 2y = 3 ( subtract x from both sides )

- 2y = - x + 3 ( divide through by - 2 )

y = \(\frac{-1}{-2}\) x + \(\frac{3}{-2}\) = \(\frac{1}{2}\) x - \(\frac{3}{2}\) ← in slope- intercept form

with gradient m = \(\frac{1}{2}\) and y- intercept c = - \(\frac{3}{2}\)

Answer:

Step-by-step explanation:

The value of M and N from the given expression is -10 and -21 respectively

Sum of functions is the addition of expression. Given the expression below;

M = 5(x + 1) and;

N = (6x - 3)

Take the difference of the expressions

M - N = 10

Substitute

5(x+1) - (6x-2) = 10

Expand the expression to have:

5x + 5 -6x + 2 = 10
5x - 6x + 5 + 2 = 10
-x + 7 = 10
-x = 10 - 7
-x = 3
x = -3

Determine the value of M

M = 5x + 5
M = 5(-3) + 5
M = -15 + 5
M = -10

Determine the value of N

N = 6x - 3
N = 6(-3) - 3
N = -18 - 3
N = -21

Hence the value of M and N from the given expression is -10 and -21 respectively

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

1.

5/3 h

5/3 h

Les résultats sont égaux

2.

5/3

3.

-5/3

Step-by-step explanation:

1.

Femmes: 5 h / 3 = 5/3 h

Hommes: 15 h / 9 = 15/9 h = 5/3 h

Les résultats sont égaux

2.

3 × ... = 5

3 × 5/3 = 5

3.

45 × ... = -75

-75/45 = -5/3

45 × (-5/3) = -75

Answer: We should first use order of operations to multiply 6 and -5. Then we add and subtract from left to right.

Demo:

6 * (-5) = -30

Equation looks like: -2 - 30 + 9

-2 - 30 = -32

-32 + 9 = -23

-23 is the answer to this equation.

Answer:

Y= -2

Step-by-step explanation:

3y+5=(2-3)

3y+5=-1

3y=-5-1

y= -6÷3

y= -2

The equation that models the situation where a data plan costs $19.95 plus $2.95 per gigabyte is C = 19.95 + 2.95G.

The equation to model the situation in which a data plan costs $19.95 plus $2.95 per gigabyte is given below.Let C be the total cost of the data plan, and let G be the number of gigabytes used.C = 19.95 + 2.95G

This equation is used to calculate the total cost of a data plan depending on the number of gigabytes used.

The fixed cost, which is the cost of the data plan itself, is $19.95. Then, the variable cost, which is the cost per gigabyte, is $2.95.The cost of a data plan can be found by multiplying the number of gigabytes used by the cost per gigabyte and adding the fixed cost. Hence, the equation can be written as:

C = G(2.95) + 19.95

In conclusion, the equation that models the situation where a data plan costs $19.95 plus $2.95 per gigabyte is C = 19.95 + 2.95G.

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Answer:

See below

Step-by-step explanation:

The domain of \(f(x)=-4|x-2|+3\) is all real numbers while the range is y≤3.

Compared to \(g(x)=|x|\), the graph of \(f(x)\) is shifted two units to the right, jas a reflection across the x-axis, has a vertical compression by a factor of 1/4, and is shifted three units up.

Observe the graphs attached below for more information

Answer:

7

Step-by-step explanation:

2x2 - 5

= (2x3x2)-5

= 12-5

= 7

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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Answer:

Unit Price at Grocery Mart = $1.50

Unit Price at Baldwin Hills = $1.33

Step-by-step explanation:

Unit price in this case will be the price divided by number of pounds

Let u1 be the unit price of Grocery Mart and u2 be the unit price at Baldwin Hills

Given

\(s_1 = 2.99\\w_1 = 2\\s_2 = 3.99\\w_2 = 3\)

The unit price for Grocery Mart is:

\(u_1 = \frac{s_1}{w_1}\\= \frac{2.99}{2}\\= 1.495\)

Rounding off to nearest penny

u1 = $1.50 per lbs

Unit price for Baldwin Hills is:

\(u_2 = \frac{s_2}{w_2}\\=\frac{3.99}{3}\\=1.33\)

u2  = $1.33 per lbs

Hence,

Unit Price at Grocery Mart = $1.50

Unit Price at Baldwin Hills = $1.33

Answer:

$30

Step-by-step explanation:

first, take 25% of 120

then, turn the percent to a decimal (move the percent to the left twice, equals 0.25)

0.25 times 120

this equals 0.3

then turn the decimal to a whole number by moving the decimal to the right two times

0.3= 30

$30

The curve is an ellipse with the Cartesian equation x²/1 + y²/1 = 1.

To convert the given polar equation r² cos 2θ = 1 to a Cartesian equation, we can use the following relationships between polar and Cartesian coordinates:

x = r cos(θ)

y = r sin(θ)

Substitute these values into the given polar equation:

r² cos 2θ = 1

(r cos θ)² - (r sin θ)² = 1

use the identity cos² θ - sin² θ = 1 to simplify further:

(cos θ)² - (sin θ)² = 1

Replace (cos θ)² with x² and (sin θ)² with y²:

x² - y² = 1

Rearrange the equation to put it in standard form for an ellipse:

x²/1 - y²/1 = 1

The equation represents an ellipse with a major axis along the x-axis and a minor axis along the y-axis.

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Complete question:

Find a Cartesian equation for the curve and identify it.

r2 cos 2θ = 1

circle ellipse hyperbola limaçon parabola

Answer: D

Step-by-step explanation:

2x - 14 + x= 46

3x = 60

x= 20

Answer:

75 mL.

Step-by-step explanation:

3/(3+2) = 3/5 of the solution is concentrate.

So the answer is 125 * 3/5

= 3*25

= 75 mL.

Statement 1. \(\angle BCA\cong\angle DAC.\)

Reason 1. Alternate interior angles formed when two parallel lines are cut by a transversal are congruent.

Statement 2. \(\overline{AC}\cong\overline{AC}.\)

Reason 2. Reflexive congruence of segments (a segment is congruent to itself).

Statement 3. \(\triangle ACD \cong\triangle CAB.\)

Reason 3. SAS congruence (using our two congruences above and the given congruence).

Statement 4. \(\angle ACD=\angle CAB.\)

Reason 4. Corresponding parts of congruent triangles are congruent.

Statement 5. \(\overline{AB}\parallel\overline{CD}.\)

Reason 5. If the alternate interior angles formed when two lines are cut by a transversal are congruent, then the lines are parallel.

Statement 6. \(ABCD\) is a parallelogram.

Reason 6. The quadrilateral satisfies the definition of a parallelogram: a quadrilateral where both pairs of opposite sides are parallel.

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

The average best secret swimming hole is Rio Secreto in Playa del Carmen, Mexico, which features aa bedrock-carved natural waterslide with a 3-foot-deep pool at the end.

Rio Secreto is a hidden gem located in Playa del Carmen, Mexico. It is a natural underground river that features a unique natural waterslide carved out of bedrock. This waterslide leads to a 3-foot-deep pool at the end that is perfect for swimming. It is a great spot for adventurous travelers looking to explore the Mexican outdoors while taking a dip. The underground river is surrounded by lush vegetation, making it the ideal spot to relax and take in the stunning views. The crystal clear waters allow for excellent visibility and make it an ideal spot for snorkeling and swimming. Rio Secreto is sure to add a sensational soak to any dream vacation.

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The probability of getting a heart on the fourth card but not before that is 0.2278

The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.

The probability of not getting a heart in the first three cards can be calculated as follows:

(39/52) * (38/51) * (37/50) = 0.862

where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).

The probability of getting a heart on the fourth card can be calculated as follows:

13/49 = 0.265

where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).

So, the probability of getting a heart on the fourth card, but not before, can be calculated as:

0.862 * 0.265 = 0.2278

So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.

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Answer:

x = 10

Step-by-step explanation:

Given question is incomplete; here is the complete question.

A man (M) is standing halfway between a tree (T) and a lamppost (L). What is the value of x.

TM = (2x + 8)

ML = (3x - 2)

Since, a man M is standing halfway between a tree and a lamppost,

measure of TM = measure of ML

(2x + 8) = (3x - 2)

3x - 2x = 8 + 2

x = 10

Therefore, x = 10 will be the answer.

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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