slope:
y-intercept:
HELP PLS
20 points

Vic and Dan are 2, 897m apart.

It is important to note that the distance between Vic and Dan is the base of CN

Let's say the distance to Dan is x

The distance to Vic is y

Using cosine ratio, we have

cos α = opposite / adjacent

α = 72°

opposite = 553. 3cm

Adjacent = x

cos  72° = [tex]\frac{553. 3}{x}[/tex]

Cross multiply

[tex]cos 72[/tex] × [tex]x[/tex] = [tex]553. 3[/tex]

[tex]0. 3090x= 553. 3[/tex]

[tex]x = \frac{553. 3}{0. 3090}[/tex]

[tex]x = 1, 790. 61[/tex] m

The distance to Vic is y

Using the cosine ratio, we have

[tex]cos 60 = \frac{553. 3}{y}[/tex]

Cross multiply

[tex]0. 5y = 553. 3[/tex]

[tex]y = \frac{553. 3}{0. 5}[/tex]

[tex]y = 1,106. 6[/tex]m

To determine how far apart Vic and Dan, we use = x + y

= 1790. 61 + 1106. 6

= 2, 897. 21m

= 2, 897m

Thus, Vic and Dan are 2, 897m apart.

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Each element in a population has an equal chance of being chosen is Random selection.

Given that each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process.

Sampling is an umbrella term for all methods used to take samples from populations. The main purpose of sampling is to ensure that a chosen sample reflects the desired characteristics of a population so that a statistical study can produce accurate and reasonable results. Sampling techniques include random sampling, stratified sampling and many others.

As we know, random selection is the process of selecting a small group of people from a larger group to participate in a study. Each person has an equal chance of being selected, giving each person in the group an equal chance to participate.

Hence, Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process is known as random selection.

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Answer:

[tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

Step-by-step explanation:

to obtain a common denominator

multiply the numerator/denominator of the first fraction by x + 7

multiply the numerator/denominator of the second fraction by x - 4

= [tex]\frac{2(x+7)}{(x-4)(x+7)}[/tex] + [tex]\frac{3(x-4)}{(x-4)(x+7)}[/tex]

simplify and add numerators leaving the common denominator

= [tex]\frac{2x+14+3x-12}{(x-4)(x+7)}[/tex]

= [tex]\frac{5x+2}{(x-4)(x+7)}[/tex]

3 is the scale factor that was changed from the previous scale to the new scale.

What is  the scale factor?

The scale factor is a way to compare figures that appear to be similar but actually have distinct scales or measurements. Let's say two circles have similar appearances but different radii. A figure's scale factor indicates how much larger or smaller it is than the original figure.

What is the change in the scale factor?

A scale drawing is a condensed representation of an original image, structure, or object in terms of dimensions. The scale drawing is typically shrunk at a fixed dimension.

The change in the scale factor = larger scale / smaller scale

3.3 / 1.1 = 3

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Answer: 3

Step-by-step explanation:

The area of the shaded part in figure A and B are 2m² and 49 m² respectively.

To determine the area, we must know the shape of the shaded part.

After identifying the shape, we move further to know the formula for such shape

From the figures given in A, we can see that the shaded region is in form of a triangle

a. The area of a right angle is given as;

The base multiplied by the half the height and vice versa

It is written mathematically as;

Area = 1/ 2 × base × height

Where

base = 2m

height = 2m

Substitute into the formula

Area = 1/ 2 × 2 × 2

Area = 2m²

For figure B, the shaded part is a rectangle

The formula for area of a rectangle is given as;

the width multiplied by the length

Area = width × length

Where width = 7m

length = 7m

Area = 7 × 7

Area = 49m ²

Thus, the area of the shaded part in figure A and B are 2m² and 49 m² respectively.

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Step 1. You need x isolated.
[tex]x < 13+7[/tex]

When you move a number from the left to right (and its addition or subtraction, the sign stays (< ≤ > and ≥ is signs).
x<20 or in words, x is less than 20, and cannot be 20.

Answer:

x < 20

Any number less than 20 is a solution

Step-by-step explanation:

x-7 < 13

The first step to solve this inequality is to add 7 to each side

x-7+7 < 13+7

x < 20

Any number less than 20 is a solution

Using the Factor Theorem, the expression 3x² + 2 is factored as follows:

[tex]3x^2 + 2 = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the expression is:

3x² + 2.

The roots are found as follows:

[tex]3x^2 + 2 = 0[/tex]

[tex]x^2 = -\frac{2}{3}[/tex]

[tex]x = \pm \sqrt{-\frac{2}{3}}[/tex]

[tex]x_1 = -i\sqrt{\frac{2}{3}}[/tex]

[tex]x_2 = i\sqrt{\frac{2}{3}}[/tex]

Hence the factored expression is:

[tex]3x^2 + 2 = \left(x + i\sqrt{\frac{2}{3}}\right)(x - 1\sqrt{\frac{2}{3}}\right) = (\sqrt{3}x + i\sqrt{2})((\sqrt{3}x - i\sqrt{2}))[/tex]

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Answer:

Step-by-step explanation:

Similar Triangle:

Triangle ABC has angles of 53 and 62 degrees....the sum is 115 degrees.  The third angle must be 180 - 115 = 65 degrees.

A triangle with one angle = 61 degrees cannot be similar

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Answer: The triangles are not similar; no expression for x can be found.

Answer:

Se below

Step-by-step explanation:

The two angles form a straight line which is 180° angle

4z + z = 180

5z = 180

z = 36  °            4z = 144°

For easy estimation, option A = nearest hundred,B = nearest ten, C = nearest hundred and D= nearest thousand.

3529 and 3689

3529 to the nearest hundred = 3500 and,

3689 to the nearest hundred = 3700

∴ Required sum = (3500+3700) = 7200

33 and 99

33 to the nearest ten = 30 and,

99 to the nearest ten = 90

∴ Required sum = (30+90) = 120

120777 × 523

777 to the nearest hundred = 800 and,

523 to the nearest hundred = 500

∴ Required sum = (800+500) = 1300

1300495420 and 123512

495420 to the nearest thousand = 495000 and,

123512 to the nearest thousand = 124000

∴ Required sum = (495000 + 124000 ) = 619000

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Used formula

Answer:

6x+5

Step-by-step explanation:

the derivative of a sum is equal to the sum of derivatives:

(3x^2 + 5x + 2)' = (3x^2)' + (5x)' + (2)' = 6x + 5

Q.E.D.

Answer:

[tex]\huge\boxed{\sf A = 78.5\ ft\²}[/tex]

Step-by-step explanation:

Circumference = C = 31.4 ft

We know that,

Where, r is the radius

31.4 = 2(3.14)r

31.4 = 6.28(r)

Divide 6.28 to both sides

31.4/6.28 = r

5 ft. = r

Now,

A = πr²

A = (3.14)(5)²

A = (3.14)(25)

[tex]\rule[225]{225}{2}[/tex]

Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, [tex]\sin{2\theta}[/tex] is always positive.

It is given by:

[tex]\sin{2\theta} = 2\sin{\theta}\cos{\theta}[/tex]

In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and [tex]\sin{2\theta}[/tex] is always positive.

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Answer: 18.6 feet

Step-by-step explanation: Horizontal distance = 17 feet and the angle

of elevation = 24°

Using the binomial distribution, it is found that the standard deviation of the distribution is of 0.67.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The parameters are:

n = 5, p = 0.1.

Hence the standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5 \times 0.1 \times 0.9} = 0.67[/tex]

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Answer:

Step-by-step explanation:

6^0 + 6^0 + 6^0 + 6

= 1+1+1+6

= 9.

Answer:

The speed of the boat in still water is 18 mph.

The speed of the current is 2 mph

Step-by-step explanation:

Let x constitute the charge of the boat in nonetheless water.

Let y constitute the rate of the contemporary.

When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that

x - y = 16  (equation 1)

Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that

x + y = 20  (equation 2)

Adding each equation, it becomes

2x = 36

x = 36/2

x = 18 mph

Substituting x = 18 into equation 1, it will become

18 - y = 16

y = 18 - 16

y = 2 mph

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The factored expression of the polynomial is (x - 3)(x + 4)

The polynomial expression is given as;

x^2 + x - 12

Expand the expression

x^2 + 4x - 3x - 12

Factorize the expression

x(x + 4) -3(x + 4)

Factor out x + 4

(x - 3)(x + 4)

Hence, the factored expression of the polynomial is (x - 3)(x + 4)

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Excel uses VAR function for determining the residual variance.

The variation of any error is known as residual variance, also known as unexplained variance or error variance.

Depending on the type of analysis you're doing, the precise definition will vary. For instance, random fluctuations in regression analysis produce volatility around the "actual" regression line.There are two components to a regression line's total variance: variation that can be explained and variance that cannot. Simply put, the residual variance after deducting the variation resulting from the regression from the total variance of the dependent variable is the residual variance.

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The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

According to the statement

There is a region where the range of values of the independent variables in the data used to estimate the regression model.

AND

Those region is called EXPERIMENTAL REGION

So, Experimental region is called a those region in which the region within which we can make valid predictions and doesn't go outside of the bounds of the data we were provided.

So, The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

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Answer:

C = 364.24

Step-by-step explanation:

Comment

The circumference and the radius are related to one another. The constant relating them is pi which is a fixed number of 3.14 The formula for the circumference is C = 2*pi * r

Givens

pi = 3.14

r = 58 cm

Circumference = ?

Formula

C = 2*pi * r

C = 2 * 3.14 * 58

C = 364.24

ANSWER:

Quadrant ll

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The probability that a particular passenger chooses chips and soda as a snack is 0.25 or 25%.

In mathematics, probability is considered as the chances a specific situation or event occurs. For example, you can calculate the probability that it rains tomorrow based on general weather patterns.

Now, let's multiply these probabilities:

This means the  probability of a passenger choosing chips and soda as a snack is 0.25 or 25%.

Note: This question is incomplete; here is the missing section:

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Answer:

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).

We have,

Matrix A becomes singular (i.e., its determinant is zero).

The given matrix A is:

A = | 3x  -6 |

      | -4  x |

Using the determinant formula for a 2x2 matrix, we have:

det(A) = (3x * x) - (-6 * -4)

Simplifying the expression:

det(A) = 3x^2 - 24

To find the value of x for which det(A) = 0, we set the determinant equal to zero:

3x^2 - 24 = 0

Now, we can solve this quadratic equation for x:

3x^2 = 24

x^2 = 8

x = ±√8

Therefore,

The matrix A becomes singular when x is equal to ±√8 (positive or negative square root of 8).

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Answer:

[tex]y=-\frac{3}{2}x + 6[/tex]

Step-by-step explanation:

For perpendicular lines, we use the same y-intercept. Though, to find the slope of perpendicular lines, we use opposite reciprocals. The opposite reciprocal of [tex]\frac{2}{3}[/tex] is [tex]-\frac{3}{2}[/tex].

Using it's concept, the probability that a student attended the game, given that the student if fro North Beach is:

B. 0.65.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that 170 people attended the game, out of which 110 are from North Beach, hence the probability is:

p = 110/170 = 0.65.

Hence option B is correct.

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Answer:0.55 is the correct answer

Step-by-step explanation:

Answer:

area of A'B'C'D' = 18.4 units²

Step-by-step explanation:

given 2 similar figures with

ratio of corresponding sides = a : b , then

ratio of areas = a² : b²

here ratio of sides = 5 : 2

ratio of areas = 5² : 2² = 25 : 4

let x be the area of A'B'C'D' , then by proportion

[tex]\frac{25}{115}[/tex] = [tex]\frac{4}{x}[/tex] ( cross- multiply )

25x = 460 ( divide both sides by 25 )

x = 18.4

area of A'B'C'D' = 18.4 units²

The height of the water depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.

According to the two cases described in the statement, we have clear example of sinusoidal model for the height as a function of time. In this case, we can make use of the following equation:

h = a + A · sin (2π · t/T + B)     (1)

Where:

Now we proceed to derive the equations for each case:

Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):

A = (20 m - 8 m)/2

A = 6 m

a = 14 m

Phase

20 = 14 + 6 · sin B

6 = 6 · sin B

sin B = 1

B = π/2

h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.

Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):

A = (40 m - 2 m)/2

A = 19 m

a = 21 m

Phase

2 = 21 + 19 · sin B

- 19 = 19 · sin B

sin B = - 1

B = - π/2

h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.

Lastly, we proceed to graph each case in the figures attached below.

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