12. A staffs shadow is 8 feet and a tree's shadow is 16 feet. If the staff is 9 feet tall, how tall is the tree?
A. 15 ft
B. 18 ft
C. 12 ft
D. 9 ft

The value of the limit of the function given when the value of x tends to zero is 0

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.

Given the function limit below;

lim x→0 [1 − cos(2x) /x]

Substitute the value of x into the expression to have;

f(0) = 1-cos2(0)/0
f(0) = 1-1/0

f(0) = 0/0 (ind)

Apply the L'hospital rule to have:

lim x→0 [ − (-2sin2x)) /1]

Substitute the value of x into the result

f(0) = 2sin2(0)/1

f(0) = 2(0)

f(0) = 0

Hence the value of the limit of the function given when the value of x tends to zero is 0

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Answer:

The value of tan M = 15/8

Step-by-step explanation:

[tex]tan \: m \: = \frac{p}{b} \\ tan \: m \: = \frac{15}{8} [/tex]

You don't shade a region when graphing just a line, but you do when graphing an inequality.

It should be noted that a graph is a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

It should be noted that an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

This is used most often to compare the two numbers on the number line by their size.

On the other hand, the graphing inequalities shows what part of the number line contains values that will be able to satisfy the given inequality.

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Answer:

x = 22°

Step-by-step explanation:

Between two parallel lines, the opposite inside angles will be congruent. So, x is equal to angle V. The sum of the angles of any triangle will be 180°. Therefore, you can find the value of x by setting all the angles of the triangle SRV equal to 180°.

S = 5x + 4

R = 44

V = x

S + R + V = 180                                         <----- General equation

(5x + 4) + 44 + x = 180                              <----- Insert values

5x + 48 + x = 180                                      <----- Add 4 and 44

6x + 48 = 180                                           <----- Add 5x and x

6x = 132                                                    <----- Subtract 48 from both sides

x = 22                                                      <----- Divide both sides by 6

The probability that a three shows on at least one of the dice is 11/36.

It should be noted that of probability means the likelihood of the occurence of an event.

The probability that a three shows on at least one of the dice will be:

= 11/36

This can be seen from the table that is attached.

The probability that the total is less than 8 will be:

= 21/36

= 7/12

Here, there are 21 places where the total is less than 8.

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Answer:

a) ∠VUW

b) VY

c) XYV

d) 180°

e) 65°

Step-by-step explanation:

A central angle is an angle that creates an arc in a circle, while also having its vertex as the center of the circle.

Here the center is U. So, the vertex of the angle must include U.

This means that there are multiple answers to part a.

The answers can be:

∠VUW

∠WUX

∠XUV

A minor arc is any arc that doesn't exceed 180°.

The possible answers for part b, using this definition are:

WV

VY

XY

The answer you inputted here is incorrect.

The order of the letters matter.

A tip for you to never mess these up is to trace the letters you've chosen with your finger and see if that image you make with your finger matches up with the shape you wanted to make.

An arc that makes a semicircle is an arc that connects the endpoints of the diameter. The diameter in this case is VX.

This means that your answer must start with V and end with X, or the other way around. (Meaning you could start with x and end with v, but always make sure you keep the endpoints of the diameter as the endpoints of the arc.)

The possible answers for this part are either:

VYX or VWX

This arc intercepts the diameter, which is a straight line and a central angle.

The angle of a diameter is 180°.

The arc of an intercepted central angle has the same measure of the central angle itself.

So, the measure of VWX is 180°.

If an arc intercepts a central angle, then the arc has the same measure as the central angle.

This rule works the other way around, too.

So, the central angle has the same measure as the minor arc that it intercepts.

Measure of arc VUW is 65°, so m∠VUW is also 65°.

A) The Period is 30 seconds

D) The amplitude is 25 m

A) Since the Ferris wheel makes 2 rotations every minute, then we can say that the period is;

T = 1/2 = 0.5 minutes = 30 seconds

B) Let t be time in seconds and let h be height and as such, we have the formula; h = 25 - 25 cos ((2π/30)t)

Thus, the table is attached showing input values of t and their corresponding h values.

C) The graph of the table above is as attached below.

D) The amplitude is;

Amplitude = (Maximum Point - Minimum Point)/2

Amplitude = (50 - 0)/2

Amplitude = 25

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The critical points of the function graphed are given as follows:

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

In a graph, they are turning points, and are classified as follows:

Looking at the graph, the turning points are approximately:

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Answer: c, y ≤ -3x+6

Step-by-step explanation:

for example we could use a point on the graph such as (-2, 0)

now we would insert the numbers into the inequality:

y ≤ -3x+6

= 0 ≤ -3(-2) +6

= 0 ≤ 6+6

= 0 ≤ 12

which is true! therefore it is y ≤ -3x+6

Answer:

[tex] \sf{b. \frac{x}{2} <3}[/tex]

step by step explanation:

We will try one by one.

A. x + 5 < 3

Step 1. Subtitution Value of x

= 4 + 5 < 3

Step 2. Add by 4 with 5

= 9 < 5

A is wrong because 9 is bigger then 5

B. x/2 < 3

= 4/2 < 3

= 2 < 3

is true because 2 is smaller than 3

C. 9x > 36

9(4) > 36

36 > 36

is wrong, should 36 = 36

D. 18 < 8

is wrong because 18 is bigger than 8

Answer:

73.0 m²

Step-by-step explanation:

[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]

[tex] A = \dfrac{130^\circ}{360^\circ}\pi (8.02~m)^2 [/tex]

[tex] A = 73.0~m^2 [/tex]

Using it's concept, the probability that the teenager picked at random is male and their favorite hobby is playing video games is:

[tex]\frac{1}{16}[/tex].

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

Researching this problem on the internet, it is found that out of 32 teenagers, 2 are males who prefer playing videogames, hence the probability is:

[tex]p = \frac{2}{32} = \frac{1}{16}[/tex]

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Answer:

1. 60%

2. He paid Rs. 1285.71

Step-by-step explanation:

1.

He buys an item for x.

He sells the item with a 25% of the marked price, and he still makes a 20% profit over his cost x.

He must sell for x + 20% of x which is the same as 1.2x.

Let the markup be y%.

Since he gives a 25% discount over the marked price, he sells for 75% of the marked price.

0.75(x + y% of x) = 1.2x

0.75(x + xy/100) = 1.2x

x + xy/100 = 1.6x

Divide both sides by x.

1 + y/100 = 1.6

Multiply both sides by 100.

100 + y = 160

y = 60

Remember that y is in percent, so the markup must be 60%.

Check:

He buys an item for $10.

He applies a markup of 60%. 1.6 × $10 = $16.

He has a price of $16 for this item.

Now he gives a 25% discount. That means the discounted price is 75% of the marked price.

75% of $16 = $12

He sells at a 25% discount for $12.

Compare the actual selling price after the 25% discount with this cost.

$12 compared to $10.

$12/$10 = 1.2 = 120%

Since he sells for 120% of the original price, the markup is 20% which is what he wanted.

2.

The cost to the seller is x.

If he sells it at a 20% profit, then he sells it for 1.2x

Now he gives a discount of 5%, so the final selling price after discount is

0.95(1.2x)

The profit is the difference between what he sold it for, 0.95(1.2x), and what he bought is for, x, and it is Rs. 180.

0.95(1.2x) - x = 180

1.14x - x = 180

0.14x = 180

x = 1285.71

Answer: He paid Rs. 1285.71

Answer:

[tex]\bf m = - 1[/tex]

Step-by-step explanation:

[tex]\bf m= −(4+m)+2[/tex]

First of all, let's Rearrange the given terms :-

[tex]\bf m = - ( m +4) + 2[/tex]

Now, let's distribute:-

[tex]\bf m = - m - 4 + 2[/tex]

Add numbers -4 + 2 = -2

[tex]\bf m = - m - 2[/tex]

Add m to both sides, and combine like terms :-

[tex]\bf 2m = - 2[/tex]

Divide both sides by 2 :-

[tex]\bf m = - 1[/tex]

Answer:

The ANSWER is 1/2 x (3/5) : (9/15) (-6/4) : (4/1) = -3/16 = -0.1875

Step-by-step explanation:

Multiple: 1/2 * 3/5 = 1 · 3/2 · 5 = 3/10

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 10) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by three fifths is three tenths.

Divide: the result of step No. 1 : 9/15 = 3/10 : 9/15 = 3/10 · 15/9 = 3 · 15/10 · 9 = 45/90 = 45 · 1/45 · 2 = 1/2

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 9/

15 is 15/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 45 gives 1/2.

In other words - three tenths divided by nine fifteenths is one half.

the result of step No. 2 * (-6/4) = 1/2* (-6/4) = 1 · (-6)/2 · 4 = -6/8 = -3 · 2/4 · 2= -3/4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-6, 8) = 2. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by minus six quarters is minus three quarters.

Divide: the result of step No. 3 : 4 = -3/

4 : 4 = -3/4 · 1/4 = -3 · 1/4 · 4 = -3/16

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/

1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - minus three quarters divided by four is minus three sixteenths.

Answer:

The intersection of L and J or simply (L ∩ J)= ∅

or { }

Step-by-step explanation:

Hello!

The intersection operation is denoted by the symbol ∩. The set A ∩ B—read “A intersection B” or “the intersection of A and B”—is defined as the set composed of all elements that belong to both A and B.

Thus, at this situation there is no similar terms between the to set elements of L and J.

Answer:

shown in explanation

Step-by-step explanation:

a) ∆EPB similar to ∆ERG

b) angle BEP = angle GER (common angle shared)

angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)

therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG

or explanation can also be shortened to

∆EPB is similar to ∆ERG (AA, similarity)

c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal

[tex] \frac{pb}{rg} = \frac{ep}{er} [/tex]

RG = 200+300=500m

[tex] \frac{200}{500} = \frac{ep}{ep + 350} [/tex]

cross multiply (from what I've learnt)

2ep+700=5ep

ep= 700/3 = 233 ⅓m (answer for length EP)

Do the same for length BE(using ratio of corresponding sides)

[tex] \frac{be}{ge} = \frac{pb}{rg} [/tex]

[tex] \frac{be}{be + 400} = \frac{200}{500} [/tex]

cross multiply again to get:

5BE = 2BE + 800

BE = 800/3 = 266 ⅔ m (answer for length BE)

The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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Answer:

Graph attached.

Step-by-step explanation:

Given equation:

[tex]y=\dfrac{1}{3}x+5[/tex]

The given equation is a linear equation in slope-intercept form, where 1/3 is the slope and 5 is the y-intercept.

To graph the equation, find and plot at least two points, then draw a straight line through them.

To find the points on the line, input values of x into the equation:

[tex]x = 0 \implies y=\dfrac{1}{3}(0)+5 \implies (0,5)[/tex]

[tex]x=3 \implies y=\dfrac{1}{3}(3)+5 \implies (3,6)[/tex]

[tex]x=6 \implies y=\dfrac{1}{3}(6)+5 \implies (6,7)[/tex]

See attachment for the graph of the given equation.

Find some points

x=0

x=3

x=-3

Graph attached

Answer: equation: y=-4x+1

slope: -4

y intercept:1

The test statistic based on the probability illustrated is -3.22.

Based on the information, the test statistic will be:

= (0.4 - 0.5)/[✓0.5(1 - 0.5)/260]

= -3.22

The p value using the distribution table is 0.0012.

The conclusion is to reject the null hypothesis as there's sufficient evidence to warrant rejection.

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The solution of the equations y=[tex]x^{2}[/tex]-x-22 and y=x-7 is that x=-3,5 and y=-10,-2.

Given equations y=[tex]x^{2} -x-22[/tex], y=x-7.

We are required to solve these equations for the value of x and y.

Equation is relationship between two or more variables expressed in equal to form.Equations of two variables look like ax+by=c.It may be a linear equation, quadratic equation and cubic equations.

The given equations are:

y=[tex]x^{2}[/tex]-x-22-----------1

y=x-7----------------2

Put the value of y from second equation in first equation.

x-7=[tex]x^{2}[/tex]-x-22

Solving

[tex]x^{2}[/tex]-x-x-22+7=0

[tex]x^{2}[/tex]-2x-15=0

[tex]x^{2}[/tex]-5x+3x-15=0

x(x-5)+3(x-5)=0

(x+3)(x-5)=0

x=-3,5

Put the values of x=-3 and 5 one by one to get the two values of y in second equation.

y=x-7

x=-3

y=-3-7

=-10

x=5

y=5-7

=-2

Values of y are -10 and -2.

Hence the values of x are-3 and 5 and values of y are -10,-2.

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The measure of Angle EDH = 50°.

The angle EDH exists given as 5x° and the angle HDG exists given as 4x°. The angles EDG and FGD exist at right angles. That signifies both angles exist equivalent to 90°.

Angle EDH = 5x°

Angle HDG = 4x°

Angle EDG = 90°

5x + 4x = 90

9x = 90

Divide both sides by 9

x = 90/9

x = 10°

Angle EDH = 5x = 5 × 10 = 50°

The measure of Angle EDH = 50°.

Therefore, the correct answer is option c) 50°.

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The exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

From the figure, we have the values of the sides to be;

Let's use Pythagorean theorem to find the hypotenuse(x)

Hypotebuse square = opposite side square + adjacent side square

Substitute the values deduced from the figures given

x² = 5² + 4²

x² = 25 + 16

x² = 41

x = [tex]\sqrt{41}[/tex]

x = 6. 4

sin θ = opposite/hypotenuse

Substitute the values

sin θ = 5/ 6. 4

tan θ = opposite/ adjacent

Substitute the values

tan θ = 5/ 4

sec θ = hypotenuse/ adjacent

substitute the values

sec θ = 6. 4/ 4

Thus, the exact values of sec θ, tan θ and sin θ are 6.4/4, 5/4 and 5/ 6.4 respectively.

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The solution to the Questions are

where

u=13

n^2=0.16

[tex]\sigma=\sqrt{0.16}\\\\\sigma=0.4[/tex]

a)

Generally, the equation for is  mathematically given as

[tex]X-N(u=13,\sigma=0.4)[/tex]

p(x<14)=P(z<\frac{13-13}{0.4})

P(z<0)

P=0.5

Therefore

P(z<0)=50%

b)

In conclusion

W=(u+2\sigma)

W=(13+2*0.4)

W=13+0.8

W=18.08oz

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The value of x such that the vertices 3x + 10 and x + 60 are equal is 25

Vertices are the endpoints or corners of a shape (such as triangle, square, rectangle and related shapes)

The two vertices are given as:

3x + 10 and x + 60

The condition on the two vertices are not given.

So, we assume that the vertices are equal (as in the base angles of an isosceles triangle)

So, we have the following equation

3x + 10 = x + 60

Subtract x from both sides of the equation

2x + 10 = 60

Subtract 10 from both sides of the equation

2x = 50

Divide both sides of the equation by 2

x = 50/2

Evaluate the quotient

x = 25

Hence, the value of x such that the vertices 3x + 10 and x + 60 are equal is 25

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The factor of the polynomial expression 4x^3 – 12x^2 + 4x by using GCF method is  4x(x^2 - 3x + 1).

The factors of a given number are those numbers that are divisible by the given number without a remainder.

By using the GCF method in an algebraic, i.e. the factors of the algebraic equation will be dependent on the greatest common factor.

From the given information, we are to factorize the following expression by using the GCF method as follows.

1.

4x^3 – 12x^2 + 4x

Here; the common expression in all the three variables is 4x. So, we have:

= 4x(x^2 - 3x + 1)

Option A is correct

2.

9x^4 + 4x^3 - 27x^2 + 12x

The common expression here is (x); So,

= x(9x^3 +4x^2 - 27x + 12)

Option B is correct

3.

x^2 - 3x + 4

This polynomial expression cannot be factored.

Option F is correct.

4.

17x^5 + 51x^2 - 34

= 17(x^5 + 3x^2 - 2)

Option D is correct.

The factorization of a quadratic equation (polynomial expression) in the form (ax^2 + bx + c) by grouping results into two factors that if multiplied together result back into the original equation.

Given that:

5.

x^2 – 2x + 1

Factors are two numbers that if the multiplied result in (ac) and if added it gives us (b)

By grouping, the polynomial expression is:

= (x - 1)(x - 1)

Option A is correct

6.

x^2 + 2x - 15

= (x + 5) (x - 3)

Option C is correct

7.

x^2 – 3x – 18

=(x + 3)(x - 6)

Option B is correct

8.

8x^2 + 47x + 28

= This polynomial expression cannot be factored in as it contains rational numbers.

Option A is correct.

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