A tree is growing such that its trunk forms a 98 degree angle with the ground. At a point 27 meters from the tree, the angle of elevation to the top of the tree is 24 degrees. If a bug crawls from the base of the tree all the way to the top, how far has it gone? (i.e. how tall is the tree?)A. 46 metersB. 13 metersC. 54 metersD. 56 meters

Answer:

Option D.

Step-by-step explanation:

Cost of truck = $16000

Residual value after 5 years = $1000

Depreciated value of a truck in 5 year is

[tex]Depreciation=16000-1000=15000[/tex]

In straight-line method, the value of a fixed asset depreciate by a constant rate.

Since depreciation of truck in 5 years is $15000, therefore, the depression of one year is

1 year Depreciation = [tex]\dfrac{15000}{5}=3000[/tex]

From July 3 to end of fist year = 1/2 year

1/2 year Depreciation = [tex]\dfrac{3000}{5}=1500[/tex]

So, the value at the end of year 1 using straight-line rate is

[tex]Value=16000-1500=14,500[/tex]

Therefore, the correct option is D.

Answer:

  y(x) = e^(-2x +3)

Step-by-step explanation:

The graphed line has a "y-intercept" of 3 and a slope of -2, so its equation is ...

  ln(y) = -2x +3

Taking antilogs, we get ...

  y(x) = e^(-2x +3)

Answer:

Step-by-step explanation:

Lines p and line r are parallel. This actually means that they will extend continuously without meeting at a point.

Let us assign an alphabet to an angle to make it easy for reference. The diagram is shown in the attached photo

From the photo,

Angle T is equal to 34 degrees. This is because angle T and 34 degrees are corresponding angles.

Angle G = angle T. This is because angle T is vertically opposite to angle G. Therefore

G = 34 degrees

Answer:

A. pay for each individuals tipping fee at landfills with taxes

Step-by-step explanation:

Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a  municipality wanting to waste management so Curbside recycling can be used.

Municipal should attract business that utilize source reduction in their manufacturing.

They should offer much to its resident.

They maintain a hazardous waste collection site for its residents as well.

Answer: No

Step-by-step explanation:

X does not represent the cost of fabric. X represents the number of yards of fabric used.

15x + 250

Could be read as ($15 × # of yards) + $250

So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.

She could use an additional variable to represent the cost of fabric.

Example: Y

Y= 15x

Cost of fabric is equal to $15 per yard × # of yards.

The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.

C = 50 + 20x

Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.

Answer:

  C)  28√17

Step-by-step explanation:

The perimeter is twice the sum of the two given side lengths, so is ...

  P = 2(L +W) = 2(2√153 +4√68)

  = 2(6√17 +8√17) = 2(14√17)

  P = 28√17 . . . . . matches choice C

_____

This is about simplifying radicals. The applicable rules are ...

  √(ab) = (√a)(√b)

  √(a²) = |a|

__

  153 = 9×17, so √153 = (√9)(√17) = 3√17

  68 = 4×17, so √68 = (√4)(√17) = 2√17

_____

Comment on the problem presentation

It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.

In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)

∠A = ∠B

6x + 12 = 3x + 63

6x - 3x = 63 - 12

3x = 51

x = 51 ÷ 3

x = 17

6(17) + 12

102 + 12

∠A = 114°

Answer:

114

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have four equations here.  Let's actually solve them, using factoring if possible and some other method if factoring is not possible.

A)  x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.

B)  x^2 + 6x + 9 factors into (x + 3)^2.

C) x^2 + 3x - 4 factors into (x + 4)(x - 1).

D) x^2 - x - 6 factors into (x - 3)(x + 2)

x^2 + 5x - 4 = 0 can be solved, but not by factoring.

Answer:

Step-by-step explanation:

If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards.  The general vertex form of a parabola of this type is

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

We have the x, y, h, and k.  We will plug all those in and solve for a.  That looks like this:

[tex]-5=a(6-4)^2-13[/tex] which simplifies to

-5 = 4a - 13 and

8 = 4a so

a = 2

That means that the paraobola in vertex form is

[tex]y=2(x-4)^2-13[/tex]

Answer:

a)550

b)910

c)730

Step-by-step explanation:

The given model is

[tex]v(t) = 10t^2 ft/s[/tex]

Use the interval [0,6], with n=6 rectangles

Then, the interval width is

[tex]\Delta t = \frac{b-a}{n}[/tex]

[tex]\Delta t = \frac{6-0}{6}[/tex]= 1

so, the sub intervals are

[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]

Now evaluating the function values

[tex]f(t_0)= f(0) = 0[/tex]

[tex]f(t_1)= f(1) = 10[/tex]

[tex]f(t_2)= f(2) = 40[/tex]

[tex]f(t_3)= f(3) = 90[/tex]

[tex]f(t_4)= f(4) = 160[/tex]

[tex]f(t_5)= f(5) = 250[/tex]

[tex]f(t_6)= f(6) = 360[/tex]

a) left hand sum is

L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]

=[tex]1 [0+ 10+40+90+160+250][/tex]

= 550

b) right hand sum

R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]

= [tex]1 [10+40+90+160+250+360][/tex]

= 910

c) average of two sums is

[tex]\frac{L_5+R_5}{2}[/tex]

= [tex]\frac{550+910}{2}[/tex]

=730

Answer:

she will need to dance for 26 hours

Step-by-step explanation:

500=15(26)+110

Answer:

26 hours

Step-by-step explanation:

One group will donate $15 per hour, while the other is offering a flat sum of $110. She wants $500, so we can set up the equation

15x + 110 = 500 (with x being the number of hours Traci dances). You subtract 110 from 500 to isolate the variable with its coefficient, resulting in

15x = 390 . Then, dividing 390 by 15 to get x by itself, the answer of 26 hours is found.

Answer:

b) 0.2464

c) 0.0580

d) 0.2952

Step-by-step explanation:

Probability of those that purchased regular gas = 88% = 0.88

2% purchased mid grade gas

10% purchased premium gad

Given that a driver bought regular gas, 28% paid with credit card

Given that a driver bought mid grade gas, 34% paid with credit card

Given that a driver bought premium gas, 42% paid with credit card

Let R represent drivers that bought regular gas

Let M represent drivers that bought mid grade gas

Let P represent drivers that bought premium gas

Let C represent credit card payment

Let NC represent non-credit card payment

Pr(R) = 88% = 0.88

Pr(M) = 2% = 0.02

Pr(P) = 10% = 0.10

Pr(C|R) = 28%= 0.28

Pr(C|M) = 34%= 0.34

Pr(C|P) = 42%= 0.42

Pr(NC|R) = 1 - 0.28= 0.72

Pr(NC|M) = 1 - 0.34 = 0.66

Pr(NC|P) = 1 - 0.42 = 0.58

Using multiplication rule

Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)

Using conditional probability,

P(B|A) = Pr(AnB) / Pr(A)

Pr(CnR) = Pr(R) * Pr(C|R)

= 0.88*0.28

= 0.2464

Pr(CnM) = Pr(M) * Pr(C|M)

= 0.02*0.34

= 0.0068

Pr(CnP) = Pr(P) * Pr(C|P)

= 0.10*0.42

= 0.0420

b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =

Pr(CnR)

= 0.2464

c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)

= 0.58 * 0.10

= 0.0580

d) The probability of those that paid with credit card is given as

Pr(CnR) + Pr(CnM) + Pr(CnP)

= 0.2464 + 0.0068 + 0.042

= 0.2952

This problem involves calculating different probabilities pertaining to customers' selection of gas type and payment method. These probabilities are found by multiplying corresponding probabilities together for intersecting events, and adding different possibilities together for compound events.

The subject of this question is probability, used in Mathematics. Let's solve each part step-by-step:

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Answer:

Part 1 : Figure show the graph of triangle

Part 2 : The area of triangle is 4 sqaure units

Step-by-step explanation:

Given points A(1, -3), B(3, -1) and C(5, -3) make triangle.

Part 1:

Figure show the graph of triangle with A(1, -3), B(3, -1) and C(5, -3)  as vertices.

Part 2: Find the area of the triangle.

The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]

From figure, Take base as length of AC

Length of line is given by L=[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]

Now, Base = length of AC

Base =[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]

        =[tex]\sqrt{(1-5)^{2}+((-3)-(-3))^{2}}[/tex]

        =[tex]\sqrt{(-4)^{2}+(0)^{2}}[/tex]

        =[tex]\sqrt{16}[/tex]

        =4units

and Height as difference of y-component of point A and point B

Height = (y of component of point B)- (y of component of point A)

           = (-1)- (-3)

           = 2units

Therefore, The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]

A=[tex]\frac{(4)(2)}{2}[/tex]

A=4 sqaure units

Answer:

a) 95% confidence interval estimate of the true weight is (3.026, 3.274)

b) 99% confidence interval estimate of the true weight is (2.944, 3.356)

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

And margin of error (ME) can be calculated using the formula

ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where

Using the numbers 95% confidence interval estimate of the true weight is:

3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124

And 99% confidence interval estimate of the true weight is:

3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206

Answer:

easey

Step-by-step explanation:

Answer:

B) x + y = 3

Step-by-step explanation:

This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:

[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]

I am joyous to assist you anytime.

Answer:

option C) (7, -2)

Step-by-step explanation:

By the graph, the initial coordinates of point A are ( -5, -4)

first reflection along the line x=1, only the x coordinate will change.

the new x coordinate is = x = 7

thus the point becomes (7, -4)

similarly, reflection along y= -3, only the y coordinate will change.

the new y coordinate is = y = -2

thus the final coordinates are (7, -2)

Answer:

The worth of the automobile after an year with 15% depreciation  is $22,100.

Step-by-step explanation:

The current cost of the automobile car = $26,000

The percentage of depreciation  = 15%

Now, calculating the depreciated amount:

15% of $26,000  = [tex]\frac{15}{100}  \times 26,000 = 3,900[/tex]

So, the depreciated amount of the car in the next year = $3,900.

Now, the worth of the car after an year

= CURRENT WORTH - THE DEPRECIATED AMOUNT

= $26,000 - $3,900.

= $22,100

Hence, the worth of the automobile after an year  is $22,100.

If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.

If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.

The coefficient of determination, denoted as r², is equal to the square of the correlation coefficient, r. It represents the percentage of variation in the dependent variable, y, that can be explained by variation in the independent variable, x, using the regression line. When r² is positive, it indicates a positive relationship between x and y, but it does not specify the direction of the slope.

Therefore, if the coefficient of determination is positive, the regression equation could have either a positive or a negative slope.

Answer:

1: C(n) = 2.50 + 16n

2: $66.50

Step-by-step explanation:

Part 1

Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.

There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is

C(n) = 2.50 + 16n

Part 2

For n = 4, the expression evaluates to

C(4) = 2.50 + 16 (4) = $66.50

Answer:

the answer is (-4,2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is (-4,2)

Answer:

a)[tex]P(X\geq 11) = 0.198[/tex]

b)[tex]P(X\leq 2) = 0.000565[/tex]

c) Mean = 8.8

Step-by-step explanation:

1) Previous concepts

Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".

The Binomial distribution is a type of Bernoulli experiment with following properties:

a)There are two possible outcomes; success or failure.

b) Outcomes are independent on preceding result of a trial.

c) The probability of success remains constant throughout the experiment.

d)The number of successes are fixed.

The probability mass function for the Binomial distribution is given by:

[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]

Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.

[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing

[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing

[tex]n=16[/tex] random sample selected

2) Part a

The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]

On this case we want the following probability, and since says greater or equal than 11 we can express like this:

[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]

[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]

[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]

[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]

[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]

[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]

[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]

[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]

3) Part b

[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]

[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]

[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]

[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]

[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]

4) Part c

The expected value for the binomial distribution is given by the following formula:

[tex] E(X)=np=16*0.55=8.8[/tex]

So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.

Answer:

four bouquets

Step-by-step explanation:

The way of solving this problem is tell Abigail to keep the relation between flowers constant, that is

We have  16 roses   and 20 carnations

16  2       16  =  2⁴      20  2     20 = 2² * 5

8   2                           10   2

4   2                            5   5

2   2                             1

1

So we will make bouquets of 4 roses and 5 carnations

so we will have  4 bouquets using all flowers

Final answer:

The stone is approximately 583 feet high 4 seconds later.

Explanation:

To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:

h = h0 + v0t + (1/2)gt^2

Where:

h = height at time t

h0 = initial height

v0 = initial velocity

g = acceleration due to gravity

t = time

Substituting the given values:

h = 775 + 16(4) + (1/2)(-32)(4)^2

h = 775 + 64 - 256

h = 583 feet

Therefore, the stone is approximately 583 feet high 4 seconds later.

Answer:

From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .  

Step-by-step explanation:

Given as :

To Proof : Triangle Δ ABC and Triangle Δ DEF are similar

There are three methods for two Triangles to be similar

A ) SAS  i.e side angle side

B ) AA i.e angle angle

C ) SSS i.e side side side

Now,

A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E

and , [tex]\dfrac{AB}{DE}[/tex] =  [tex]\dfrac{BC}{EF}[/tex]

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e SAS   similarity

B ) If two triangles have equal corresponding angles , then triangles are similar .

So, If in  Δ ABC and  Δ DEF

∠ B = ∠ E   and   ∠ A = ∠ D

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e AA similarity

C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .

So, If in  Δ ABC and  Δ DEF

[tex]\dfrac{AB}{DE}[/tex] =  [tex]\dfrac{BC}{EF}[/tex] = [tex]\dfrac{AC}{DF}[/tex]

Then Δ ABC  [tex]\sim[/tex] Δ DEF

I.e SSS similarity

Hence From three condition the it is proved that Δ ABC and  Δ DEF are similar Triangles .   answer

Answer: Neither

Step-by-step explanation:

Got it wrong bc of the person it top of me but yea

Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.

Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.

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Answer:

The value of x is 3 cm.

Step-by-step explanation:

Given,

Total surface area of cuboid = 112 cm^2

Height of cuboid = 10 cm

Breadth of cuboid = 2 cm

Length of cuboid = x cm

Solution,

Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]

∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]

Thus the length of cuboid is 3 cm.

Answer:

The answer to your question is x = 4

Step-by-step explanation:

                                   2x² - bx - 20 = 0

One root is -2.5

Process

Get the value of the equation when x = -2.5

                                   2(-2.5)² - b(-2.5) - 20 = 0

                                   2(6.25) + 2.5b  - 20 = 0

                                   12.5 + 2.5b - 20 = 0

                                   2.5b = 20 - 12.5

                                   2.5b = 7.5

                                   b = 7.5 / 2.5

                                  b = 3

Then

                                  2x² - 3x - 20 = 0

Factor the polynomial

                                  2 x -20 = -40

                                  2x² -8x + 5x - 20 = 0

                                  2x(x - 4) + 5(x - 4) = 0

                                  (x - 4)(2x + 5) = 0

                                  x₁ - 4 = 0               2x₂ + 5 = 0

                                 x₁ = 4                     x₂ = -5/2

                                                               x₂ = -2.5

Answer:

The "other" or "second" root is 4.

Step-by-step explanation:

We are told that -2.5 is a root of the equation.  The coefficient b of the x term is unknown, and must be determined.  Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.

Setting up synthetic division, we arrive at:

-2.5    /    2    -b    -20

                     -5     +12.5 + 2.5b

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

                2   -5-b    -7.5 + 2.5b

The remainer, -7.5 + 2.5b, must be zero (0).  Thus, 2.5b = 7.5, and b = 3.

Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.

The other factor is 2x - 8, which, if set equal to 0, yields x = 4.  This is the "other root."