Find the length of the segment indicated.

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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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:

Quadrant ll

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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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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: 18.6 feet

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

of elevation = 24°

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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Answer:

Step-by-step explanation:

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

= 1+1+1+6

= 9.

Answer:

Hello!

independent variable: variable in an experiment that is changed e.g. a plant's exposure to light

dependent variable: variable in an experiment that is measured e.g. a plant's height

The question is just asking to identify these variables.

Hope this helps! Feel free to ask further questions if need be.

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]

The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.

Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).

We are required to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h,k) is given by:

y=a[tex](x-h)^{2}[/tex]+k

In the above equation a is the leading coefficient.

We have been given point (-3,-4).

We have to just put the value of h=-3 and k=-4 and the required equation will be as under:

y=a[tex](x+3)^{2}[/tex]-4

Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.

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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:

y = 120

x = 10.6

Step-by-step explanation:

Given polygons are parallelograms.

In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.

Since two parallelograms are similar:

60 + y = 180 subtract 60 from both sides

y = 120

To find the value of x:

side lengths are proportional because these are similar polygons

[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions

18x + 72 = 264 subtract 72 from both sides

18x = 192 divide both sides by 18

x = 10.6 approximately

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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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: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is [tex]\frac{1}{2}(a+b)h[/tex], where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

[tex]A=\frac{1}{2}(5+9)*3[/tex]

[tex]A=\frac{1}{2}(14)*3[/tex] [Adding in the parentheses]

[tex]A=7*3[/tex] [Multiplying one-half by 14]

[tex]A=21[/tex] [Multiplying 7 and 3]

The area is 21 units².

like the place where you are applying TURNED TRIANGLE.

coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....

I believe the explanation is clear, if not do contact me

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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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].

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°

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]

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:

hello :

P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6

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

Answer: -3/2

Step-by-step explanation:

we could use the two points (2,3) and (0,4) from the graph

y2-y1/x2-x1

= 0-3/4-2

= -3/2

SOLUTION :

a² = hypo² - base²

a² = 13² - 12²

a² = 169 - 144 = 25

a = √25

a = 5 units.

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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 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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Answer:

57?

Step-by-step explanation: