A tree has a shadow that is 9 feet long. Otis is 4 feet tall, and he is standing next to the tree. Otis has a shadow that is 4.5 feet long.

Answer:

30.6

Step-by-step explanation:

The following data were obtained from the question:

Angle θ = 23°

Opposite = 13

Adjacent = y

The value of y can be obtained by using the following trig ratio:

Tan θ = Opposite /Adjacent

Tan 23° = 13/y

Cross multiply

y × Tan 23° = 13

Divide both side by Tan 23°

y = 13/Tan 23°

y = 30.6

Therefore, the value of y in the diagram above is 30.6

Answer:

the height of the prism =3cm

Step-by-step explanation:

From the question :there is 30 square centimeters, we can deduce this is the area due to the unit

the volume is 90 cubic centimeters

Volume of prism = Area of base × height

We are to determine the height

90cm³ = 30cm² × height

divide both sides by 30cm²

height = 90cm³/30cm²

height = 3cm

Therefore the height of the prism is 3centimeters

Answer: C

Step-by-step explanation:

[tex]2x+4y<16\\=4y<-2x+16\\=y<-\frac{1}{2} x+4[/tex]

Since we are not dividing by a negative at any point during the simplification, the inequality sign won't change.

"<" means that the line will be dashed and shaded below.

Hope this helps!

The description of the inequality is (c) dashed line, shaded below

The inequality is given as:

2x + 4y < 16

The inequality is represented as less than (<)

When the less than sign is used in an inequality, the graph of the inequality would be a dashed line shaded below

Hence, the true statement is (c) dashed line, shaded below

Read more about inequalities at:

https://brainly.com/question/11234618

[tex](1-3i)(1-i)(1+i)(1+3i)=\\(1^2-(3i)^2)(1^2-i^2)=\\(1+9)(1+1)=\\10\cdot2=20[/tex]

Answer:

[tex]\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}[/tex]

Step-by-step explanation:

[tex](1-3i)(1-i)(1+i)(1+3i)\\\\\text{use the commutative property}\\\\=(1-3i)(1+3i)(1-i)(1+i)\\\\\text{use the associative property}\\\\=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\\\\=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\\\\\text{use}\ i=\sqrt{-1}\to i^2=-1\\\\=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\\\\=\bigg(1+9\bigg)\bigg(1+1\bigg)\\\\=(10)(2)\\\\=20[/tex]

Answer:

208 cm²

Step-by-step explanation:

First, you take the area of the whole rectangle, to do this you simply multiply 30 by 15, meaning that the big rectangle’s area is 450 cm².

Then, you take the area of the small rectangle (the unshaded one), to do this, you simply figure out the sides (they end up being 11 cm and 22 cm, you can find this out through subtracting) and to find the area of this rectangle, you multiply 11 by 22, which gives you 242 cm²

Now all that is left to do is to subtract the unshaded area by the whole rectangles area to find the shaded part! This will look like this: 450-242= 208 cm²

Answer:

Step-by-step explanation:

A radius to the tangent point always forms a right angle with the tangent:

m∠XWY = 90°

So:

  90° + 58° + x - 7° = 180°

    141° + x = 180°

        x = 39°

Answer:

m∠6 = 90°

Step-by-step explanation:

∠1 and ∠2 are a linear pair.  This means they are supplementary, or their measures sum to 180°.  To find m∠2, we subtract m∠1 from 180:

180-140 = 40°

The measure of ∠2 is 40°.

The sum of the measures of the angles in a triangle is 180°.  We have ∠2 and ∠3; to find the measure of ∠6, we subtract these two from 180:

180-(40+50) = 180-90 = 90°

Answer:

(i) False

(ii) Selecting a 5 or a spade are not independent.

Step-by-step explanation:

(i)

Independent events are those events that occur at the same time, i.e. the occurrence of one event does not effects the occurrence of the other.

If A and B are independent events then: [tex]P(A\cap B)=P(A)\times P(B)[/tex]

Whereas as if two events are mutually exclusive, then the probability of them both taking place at the same time is 0.

Then for events A and B: [tex]P(A\cap B)=0[/tex]

Thus, the statement is False.

(ii)

In a standard deck of 52 cards there are:

Spades = 13

Diamond = 13

Heart = 13

Clubs = 13

And each of these 13 cards are:

K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A

If a card labelled as 5 is selected then it could also be a Spade.

And if a spade is selected then the card could be labelled as 5.

So, selecting a 5 or a spade are not independent.

Answer:

$10.5 dollars

Step-by-step explanation:

Keep your brains.

Using the data given:

(18+4+12+8)÷4=

42÷4=

$10.5 dollars

Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Step-by-step explanation:

There are three measures of the center: 1) Mean   2) Median  3) Mode

Mean : Average value of the data

Mode = The most repeated value.

Median is the middlemost value in a well-ordered data.

It measures the center of the data.

Hence, the completed statement would be:

The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Answer:

First ____ is median

Second ____ is center

Step-by-step explanation:

The median is the middle value of a set of numbers, and is found in the center.

Answer:

Line y = −x + 4 intersects the line y = 3x + 3.

Step-by-step explanation:

Please Help! Which description best describes the solution to the following system of equations?

y = −x + 4

y = 3x + 3

Line y = −x + 4 intersects the line y = 3x + 3.

This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.

Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.

Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.

Line y = −x + 4 intersects the origin.

Answer:

[tex]\boxed{\mathrm{x=53\° \: \: \: y=33\°}}[/tex]

Step-by-step explanation:

Apply these rules to solve:

• Angles on a straight line add up to 180 degrees.

• Angles in a triangle add up to 180 degrees.

• Opposite angles in a parallelogram are equal.

• Angles in a quadrilateral add up to 360 degrees.

Answer:

55°

Step-by-step explanation:

The following data were obtained from the diagram given above:

Adjacent = 4

Hypothenus = 7

Angle A =?

The value of angle A can be obtained as follow:

Cos A = Adjacent / Hypothenus

Cos A = 4/7

Take the inverse of Cos.

A = Cos¯¹(4/7)

A = 55.1° ≈ 55°

Therefore, the value of angle A is approximately 55°.

Answer:

If I'm not mistaken your graph is supposed to be like this

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

2.4 bags

Step-by-step explanation:

Uh you can keep your brains.

Using the data table, we get:

1, 2, 2, 3, 4 as our data.

Finding the mean:

(1+2+2+3+4)÷5=

12÷5=

2.4 bags

Answer:

           [tex]\bold{P(A) =\dfrac{11}{20}}[/tex]

Step-by-step explanation:

A - an occurrence that Steve encounters the green light

number of all counted ligths:    |Ω| = 20

number of counted green ligths:  |A| = 11

Probability that Steve encounters a green light on any given day:

[tex]P(A) = \dfrac{|A|}{|\Omega|}=\dfrac{11}{20}[/tex]

Answer:

C is the correct answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

have a good day

Answer:

  [tex]\dfrac{3(6)-1}{2(6)+1}[/tex]

Step-by-step explanation:

For ...

The expression (r/s)(6) is ...

  [tex]\left(\dfrac{r}{s}\right)(6) = \left.\dfrac{3x-1}{2x+1}\right|_{x=6}=\boxed{\dfrac{3(6)-1}{2(6)+1}}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Given

[tex]\frac{30b}{6b}[/tex]

Cancel the b on the numerator/ denominator.

Also the 30 and 6 can both be cancelled by 6 , thus

[tex]\frac{30b}{6b}[/tex] = [tex]\frac{30}{6}[/tex] = 5

Answer:

[tex]\boxed{5}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{30b}{6b}[/tex]

[tex]\sf Simplify[/tex]

[tex]\displaystyle \frac{30}{6} \times \frac{b}{b}[/tex]

[tex]5 \times 1[/tex]

[tex]=5[/tex]

Answer:

(0-5)=-5

-5-5 = 0

x=0

Step-by-step explanation:

Answer:

Total consumer spending is 160

Step-by-step explanation:

Here , we are interested in calculating the total consumer spending.

In a long run perfect competition market, price interest with MC and minimum point of AC

Hence , P = AC

this means that Q = 40,000/P = 40,000/150 = 266.67 which is approximately 267 potatoes will be consumed

The total consumer spending is thus 267 * 0.6 = 160

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Resolving Parenthesis

[tex](-5-7)^2-(10)^2\\(-12)^2-100\\144-100[/tex]

=> 44

Answer:

[tex]\boxed{44}[/tex]

Step-by-step explanation:

[tex][-5+(-7)]^2-(7+3)^2[/tex]

Solve for brackets first.

[tex][-12]^2-(10)^2[/tex]

Solve the exponent or power.

[tex]144-100[/tex]

Subtract the numbers.

[tex]=44[/tex]

cos (x - π/3) = cos (π/2)

Then we need x - π/3 = π/2

Solving the equation:

x - π/3 = π/2

x = π/2 + π/3

x = 5π/6

Answer:

706.86 cm

Step-by-step explanation:

=4pi(r^2)

=12.56(r^2)

=12.56(7.5^2)

=12.56(56.25)

=706.86

Answer:

35 degrees.

Step-by-step explanation:

m < TSK = 180 - 22 - 123

= 180 - 145

= 35.

Answer:

b=3a/8

a=8b/3

Step-by-step explanation:

b/a=k ( k is the constant proportional)

3/8=9/24=15/40

b/a=3/8

b=3a/8

a=8b/3

I hope this is right answer

Answer:

b

Step-by-step explanation:

trust me

Answer:

A

Step-by-step explanation:

Answer:

1.475

Step-by-step explanation:

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           Hi my lil bunny!

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                    [tex]\boxed{x = 7}[/tex]

Move 1 to the left side of the equation by subtracting it from both sides.

[tex]\sqrt{2x -5 - 2 - 1 = 0 }[/tex]

Subtract 1 from -2.

[tex]\sqrt{2x -5 - 3 = 0 }[/tex]

Add 3 to both sides of the equation.

[tex]\sqrt{2x - 5 = 3}[/tex]

To remove the radical on the left side of the equation, square both sides of the equation.

[tex]\sqrt{2x - 5^3 = 3^2}[/tex]

Simplify each side of the equation.

Multiply the exponents in [tex](( 2x - 5) ^\frac{1}{2})^2[/tex] .

Apply the power rule and multiply exponents, [tex](a^m)^n = a^mn[/tex]

[tex](2x -5)^\frac{1}{2}.2 = 3^2[/tex]

Cancel the common factor of 2.

[tex](2x - 5)^1 = 3^2[/tex]

Simplify.

[tex]2x - 5 = 3^2[/tex]

Raise 3 to the power of 2.

[tex]2x - 5 = 9[/tex]

Solve for x

Move all terms not containing x to the right side of the equation.

Add 5  to both sides of the equation.

[tex]2x = 9 + 5[/tex]

Add 9 and 5.

[tex]2x = 14[/tex]

Divide each term by 2  and simplify.

Divide each term in 2x = 14 by 2.

[tex]\frac{2x}{2} = \frac{14}{2}[/tex]

Cancel the common factor of 2.

[tex]x = \frac{14}{2}[/tex]

Divide 14 by 2.

[tex]x = 7[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

root of f(x) =  -0.7419124700395855 to about 16 figures

Step-by-step explanation:

given

f(x) = 2x^5-x^2+1 = 0

The polynomial is prime, so cannot solve by factoring.

Since it is a 5th degree polynomial, it has at least one real root.

Graphing helps locate where roots are, if more than one.

(refer to first graph)

So there is a real root between -1 and 0.

We will use numerical methods to find the root to a good degree of accuracy.  The technique applies to any univariable function which is differentiable and continuous near the roots.  This requirement is true for all polynomials.

However, we must know approximately where the root is, usually found by graphing.

The formula used is a recursive one, which gives a better approximation (x1) from the initial (x0) one , and can be repeated until the required accuracy is reached.

Here, we see that the slope of the function at the root is quite steep, so convergence will be rapid.

The formula is

x1 = x0 - f(x0) / f'(x0), where

x1 = new approximation

x0 = initial (or previous) approximation

f(x0) = value of function when x=x0

f'(x0) = value of derivative of function when x=x0

For the given function

f(x) = 2x^5-x^2+1 = 0

f'(x) = 10x^4-2x = 2x(5x^3-1)

From the graph of f(x), we can take an initial approximation as

x0 = -1

x1 = -1 - (-2)/12 = -5/6

Repeat using x0=-5/6

x1 = -5/6 - ( 2(-5/6)^5 - (-5/6)^2 + 1 ) / (2(-5/6(5(-5/6)^3-1))

= 0.7565596512088784

Repeat again, multiple times

x1 = -0.7423377914518363

x1 = -0.7419128371988212

x1 = -0.7419124700398593

x1 = -0.7419124700395855

x1 = -0.7419124700395855

So we see that the root of f(x) = x1 = -0.7419124700395855 to about 16 figures

Note that the accuracy of the iterations approximately doubles every time.