If the graph of the parent function f(x) = x is 7 units up and stretched vertically by a factor of 3

Given:

Total distance = 60 km

Upstream time = 5 hours

Downstream time = 3 hours

Find-:

The rate of boat in still water.

Explanation-:

Let

The speed of the boat in still water is"x"

The speed of the water is "y"

For upstream ( Against the current )

Speed of boat is:

Use the formula:

For upstream speed is:

For downstream,

Use the formula of distance

From eq(2) put the value of "y" in eq(1) then the value is:

The rate of the boat in still water is 16 km/hour

day 1  4 cm

day 2  8 cm

day 3  12 cm

day 4  16 cm

day 5  20 cm

day 6  24 cm

day 7  28 cm

????

The graph of the linear inequality is given by the image presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The function for this problem is given as follows:

y = -3x/4 + 2.

Hence the graph crosses the y-axis at y = 2, and when x increases by 4, y decays by 3.

The inequality is given as follows:

y < -3x/4 + 2.

Meaning that points below the dashed line are the solution to the inequality.

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11. The length of side AC is approximately 4.41 yards.

12. The measure of angle C is equal to arcsin(sin(α)).

What is law of sines?

The law of sines and the law of cosines are two trigonometric formulae that are frequently used to determine the lengths and angles in scalene triangles. The rule of sines can be applied to surfaces with constant curvature in higher dimensions.

11. In triangle ABC, we have the following information:

BC = 8 yd (opposite to angle A)

angle B = 38 degrees

angle A = 82 degrees

We can use the law of sines to find the length of side AC:

sin(A)/BC = sin(B)/AC

First, we need to convert the angles from degrees to radians:

A = 82 degrees = (82/180) * pi radians = 1.43 radians

B = 38 degrees = (38/180) * pi radians = 0.66 radians

Substituting the given values into the formula, we get:

sin(1.43)/8 = sin(0.66)/AC

Solving for AC, we get:

AC = 8 * sin(0.66) / sin(1.43) ≈ 4.41 yd

Therefore, the length of side AC is approximately 4.41 yards.

12. In triangle ABC, we have the following information:

BC = 23 m (opposite to angle A)

angle A = 116 degrees

Let angle B be denoted as angle α, and angle C be denoted as angle β. Then we can use the law of sines to relate the side lengths to the angles:

sin(α)/23 = sin(β)/AB

We know that the sum of the angles in a triangle is 180 degrees, so we can use this fact to solve for angle β:

β = 180 - A - α

Substituting this into the equation for the law of sines, we get:

sin(α)/23 = sin(180 - A - α)/AB

Simplifying the expression using the trigonometric identity sin(180 - x) = sin(x), we get:

sin(α)/23 = sin(A + α)/AB

Solving for AB, we get:

AB = 23 * sin(A + α) / sin(α)

Substituting the given values, we get:

AB = 23 * sin(116 + α) / sin(α)

To solve for angle β, we need to find angle α. We can use the fact that the sum of the angles in a triangle is 180 degrees, so:

α + β + A = 180

Substituting the given values, we get:

α + β + 116 = 180

β = 180 - α - 116

β = 64 - α

Substituting this into the expression for AB, we get:

AB = 23 * sin(116 + α) / sin(α)

AB = 23 * sin(116 + (64 - β)) / sin(β - 64)

AB = 23 * sin(180 - β) / sin(β - 64)

AB = 23 * sin(β) / sin(β - 64)

Now we can use the law of sines to relate the side lengths to the angles:

sin(β)/AB = sin(C)/BC

Solving for sin(C), we get:

sin(C) = BC * sin(β) / AB

Substituting the given values, we get:

sin(C) = 23 * sin(β) / (23 * sin(β) / sin(β - 64))

Simplifying, we get:

sin(C) = sin(β - 64)

Using the inverse sine function, we get:

C = arcsin(sin(β - 64))

Substituting the value for β in terms of α, we get:

C = arcsin(sin((α + 64) - 64))

C = arcsin(sin(α))

Therefore, the measure of angle C is equal to arcsin(sin(α)).

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Answer:

7 schools have fewer than 50 classrooms.

After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

The intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 ) and the y intercept of the parabola is ( 0 , -12 )

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation of the parabola be represented as A

Now , the value of A is

y = x² - 4x - 12   be equation (1)

On simplifying , we get

when y = 0

x² - 4x - 12 = 0

On factorizing the quadratic equation , we get

x² - 6x + 2x - 12 = 0

( x + 2 ) ( x - 6 ) = 0

So , the two values of x are

when ( x + 2 ) = 0

x = -2

And , when ( x - 6 ) = 0

x = 6

So , the x intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 )

The y intercept is when x = 0

So , y = 0 - 0 - 12

y = -12

And , the y intercepts of the parabola are ( 0 , -12 )

Hence , the intercepts of the parabola are solved

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To show that the point (å, ä) is on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ), we need to demonstrate two things: that the point lies on the line segment, and that it is equidistant from the endpoints.

1. Determine the midpoint of the line segment:

  - The midpoint coordinates (\(x_{mid, y_{mid\)) can be found using the midpoint formula:

    \(x_{mid\) = (x1 + x2) / 2 and \(y_mid\) = (y1 + y2) / 2, where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

    In this case, we have (x1, y1) = (Ů, ü) and (x2, y2) = (ĝ, ġ).

2. Calculate the midpoint coordinates:

  - Substitute the values into the midpoint formula to find (x_mid, y_mid).

3. Find the slope of the line segment:

  - Use the slope formula: slope = (y2 - y1) / (x2 - x1).

    Apply the formula to the endpoints (Ů, ü) and (ĝ, ġ) to determine the slope of the line segment.

4. Determine the negative reciprocal of the line segment's slope:

  - Take the negative reciprocal of the slope calculated in the previous step. The negative reciprocal of a slope m is -1/m.

5. Write the equation of the perpendicular bisector:

  - Using the negative reciprocal slope and the midpoint coordinates (\(x_{mid\), \(y_{mid\)), write the equation of the perpendicular bisector in point-slope form: y - \(y_{mid\) = \(m_{perp\) * (x - \(x_{mid\)), where \(m_{perp\) is the negative reciprocal slope.

6. Substitute the point (å, ä) into the equation:

  - Replace x and y in the equation of the perpendicular bisector with the coordinates of the point (å, ä). Simplify the equation.

7. Verify that the equation holds true:

  - If the equation is satisfied when substituting (å, ä), then the point lies on the perpendicular bisector.

By following these steps, you can demonstrate that the point (å, ä) lies on the perpendicular bisector of the line segment with endpoints (Ů, ü) and (ĝ, ġ).

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Check the picture below.

\(\sin( \theta )=\cfrac{\stackrel{opposite}{0.5}}{\underset{hypotenuse}{0.64}} \implies \sin^{-1}(~~\sin( \theta )~~) =\sin^{-1}\left( \cfrac{0.5}{0.64} \right) \\\\\\ \theta =\sin^{-1}\left( \cfrac{0.5}{0.64} \right)\implies \theta \approx 51.4^o\)

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

ANSAWER:

−15+8i

Explanation:

First, you can expand the square of the bynomial:

Answer:

The inequality is;

2x + 3y ≤ 30

Step-by-step explanation:

Here, we want to select which of the inequalities represent all possible combinations of x roses and y carnations.

From the question, we are told that roses cost $3 and carnations cost $2

So, by buying x roses, total amount spent = $3x

By buying y carnations, total amount spent = $2y

Now, we are told that she does not want to spend more than $30, this means she can spend less than $30 or exactly $30 but cannot spend more than $30

So, by mathematical convention, we say the sum of the roses and carnations bought is less than or equal to $30

Thus we have;

2x + 3y ≤ 30

Answer:

2x + 3y ≤ 30

Step-by-step explanation:

Uhh im doing the test rn on it so yea

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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Answer:

796871

Step-by-step explanation:

Based on the given conditions, formulate:

5000 x (1 - (1 + 10%) 10)

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

           1 - (1 + 10%)                                                                          

Evaluate the equation/expression:

796871.23005

Find the closest integer to

798871.23005

=  796871

Answer:

12x-2=60

Step-by-step explanation:

since there are 12 cookies per box, u could multiply it by x boxes, and since she kept 2 you would need to subtract it from your total.

The missing reasons in the proof that shows that the triangles are congruent by SSS are:

3. Definition or parallelogram

4. Alternate interior angles theorem

5. Reflexive property of congruency

6. SSS Congruence Theorem

The SSS congruence theorem is applicable when two triangles have three pair of corresponding side lengths that are congruent to each other. The SSS congruence theorem states that they are congruent to each other. This theorem can be used in proof where it is established that the three sides of two triangles are equal to each other.

A side is congruent to itself according to the reflexive property of congruency. This means that if two triangles share a common side, the two angles therefore have a pair of corresponding congruent sides in a proof.

Therefore, the missing reasons for the proof are explained below:

Statements                  Reasons                                          

1. AD║BC                    1. Definition or parallelogram

2. ∠ADB ≅ ∠CBD      2. Alternate interior angles theorem

3. AB║CD                   3. Definition or parallelogram

4. ∠ABD ≅ ∠CDB       4. Alternate interior angles theorem

5. DB ≅ DB                 5. Reflexive property of congruency

6. ΔABD ≅ ΔCDB       6. SSS Congruence Theorem

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Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

c² = a² + b²

where

c is the hypotenuse

From the question x is the hypotenuse

So we have

We have the final answer as

Hope this helps you

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

250

Step-by-step explanation:

Answer:

Hope this helps! <3

( Pic Below )

Answer:

800+90+4

Step-by-step explanation:

800+90=890 and 890+4=894

HOPE THIS HELPS

Let's start by drawing a diagram:

css

Copy code

       B

      / \

     /   \

 m /     \ n

   /       \

  /_ _ _ _ _\

 A     c     C

We know that the median m is half the length of ac, so we can label ac as 2m.

We also know that the median m makes an angle of 32 degrees with side ac. Since the median m also bisects bc, we know that angles Cbm and Abm are congruent, so each must measure (180 - 32)/2 = 74 degrees.

Now we can use the fact that the angles of a triangle add up to 180 degrees to solve for angle bac:

java

Copy code

angle BAC = 180 - angle ABC - angle ACB

We can find angle ABC as follows:

java

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angle ABC = angle ABm + angle Cbm

Since Abm is a right angle and Cbm is 74 degrees, we have:

java

Copy code

angle ABC = 90 + 74 = 164

Similarly, we can find angle ACB as follows:

java

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angle ACB = angle ACm + angle CBm

Since ACm is a right angle and CBm is 74 degrees, we have:

java

Copy code

angle ACB = 90 + 74 = 164

Now we can plug in these values to find angle BAC:

java

Copy code

angle BAC = 180 - angle ABC - angle ACB

         = 180 - 164 - 164

         = 180 - 328

         = -148

This answer doesn't make sense since angles are measured between 0 and 180 degrees. So we made a mistake somewhere. Let's check our work.

We found that ABC is 164 degrees, which means that angle BCA must be (180 - 164)/2 = 8 degrees. But this is a problem since angle BCA should be greater than angle ACB, which we found to be 164 degrees. So we made a mistake when we assumed that angles Cbm and Abm are congruent.

Let's try again:

css

Copy code

       B

      / \

     /   \

 m /     \ n

   /       \

  /_ _ _ _ _\

 A     c     C

Since the median m bisects bc, we know that angles Cbm and Abn are congruent, so each must measure (180 - 32)/2 = 74 degrees.

Now we can find angle BAC as follows:

java

Copy code

angle BAC = angle BAm + angle CAM

Since BAm and CAM are congruent, we have:

java

Copy code

angle BAC = 2 * angle BAm

We know that angle BAm is equal to 90 - 32/2 = 74 degrees, so:

java

Copy code

angle BAC = 2 * 74

         = 148

Therefore, the measure of angle bac is 148 degrees.

Answer:

no

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The answer is a no because:

1) If we add a 0 to the 0.98 as a place value holder, then it would turn into 0.980 (This does not change the value of the number.)

2) Now, let's compare 0.980 with 0.972, we know 0.980 is greater than 0.972

Therefore, 0.972 is not greater than 0.98

Hope this helps!

Option 2 is the correct graph for the function f(x) = \(4[(1/2)^{x}]\) .

Given ,

f(x) = \(4[(1/2)^{x}]\)

Mathematically the graph will of exponential in nature.

So,

Let us assume few values to understand the nature of graph.

Firstly,

Let x= 1

f(x) = \(4[(1/2)^{1}]\)

f(x) = 2

Let x = 2

f(x) = \(4[(1/2)^{2}]\)

f(x) = 1

Let x = 3

f(x) = \(4[(1/2)^{3}]\)

f(x) = 0.5

Thus from these values of f(x) corresponding to the values of x second graph will be correct .

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Answer:

speed of current = 2.1 mph

Step-by-step explanation:

Let the speed of the current be "c" and the speed of the motorboat in still water be "b".

We know that the boat can maintain a constant speed of 41 miles per hour relative to the water. Therefore, the speed of the boat upstream would be:

b - c = 41 mph

Similarly, the speed of the boat downstream would be:

b + c = 41 mph (since the boat maintains the same speed relative to the water)

Now, we need to use the given times to form equations that relate the distance traveled and the speed. Let the distance to the point be "d".

Upstream:

distance = speed x time

d = (b - c) x (43/60)

Downstream:

distance = speed x time

d = (b + c) x (39/60)

Since the distance traveled in both cases is the same, we can equate the two expressions:

(b - c) x (43/60) = (b + c) x (39/60)

Multiplying both sides by 60/3 gives:

(b - c) x 43 = (b + c) x 39

Expanding both sides gives:

43b - 43c = 39b + 39c

Simplifying:

4b = 82c

b = 20.5c

Substituting this into the first equation we obtained:

b - c = 41

20.5c - c = 41

19.5c = 41

c = 2.1 mph (rounded to one decimal place)

Therefore, the speed of the current is 2.1 mph.

The two expressions are not equivalent.

To simplify the expression (p^2n^1/2)^0 √ p^5n^4, we first need to understand the properties of exponents and radicals.

Recall that any number raised to the power of zero is equal to 1, so (p^2n^1/2)^0 = 1.

Next, we can simplify the radical term by multiplying the exponents inside and outside the radical:

√ p^5n^4 =

(p^5n^4)^(1/2)

= p^(5/2)n^(4/2)

= p^(5/2)n^2

Combining this result with the previous step, we have:

(p^2n^1/2)^0 √ p^5n^4

= 1 * p^(5/2)n^2

= p^(5/2)n^2

This is not equivalent to p^18n^6 √p. In fact, p^(5/2)n^2 cannot be simplified any further without additional information about the expression.  ,

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Answer:

Step-by-step explanation:

Answer:

1 and 4

Step-by-step explanation:

Answer:

1, 4

:):):):):):):):):):):)

Answer:

f(2)=-2

Step-by-step explanation:

Values of a function from a graph

The graph of a function is usually a drawn line that joins a number of points that correspond to the ordered pairs (x,y), where x is a given value, and y is the value calculated through the rule of the function, usually a formula or equation.

If we want to know the value for a specific value of x, we find the corresponding x-coordinate, draw an imaginary vertical line until we meet the graph. The value of y at that point is the required value of the function.

For example, for x=0 the graph crosses the y-axis at y=2, thus the ordered pair is (0,2), and f(0)=2.

For x=2, the function has a value of y=-2, thus:

f(2)=-2

Answer:

-15

Step-by-step explanation:

5(-2)-5

Answer:

7th measurement = -26

Step-by-step explanation:

The sequence is 16, 9, 2, –5, ...,

First term( a)= 16

Second term=9

Common difference (d) = 9-16

Common difference= -7

The sequence is a arithmetic progression

For AP's ,the terms formula is

Term(n) = a + (n-1)d

Where n represent the term to be found

In this case,we Are looking for the 7th term , so n= 7

Term(7) = 16+ (7-1)-7

Term(7)= 16 +6(-7).

Term (7) = 16-42

Term(7) = -26

7th term =-26