Dog in a Ditch
Oscar and Rasheed are identical twins. They are both 6 feet tall. They are on opposite sides of
a ditch that is 30 feet wide. Their dog, Earl, is at the bottom of the ditch and is walking away
from Oscar towards Rasheed. Earl can get out if he wants to. When Oscar looks at Earl, his line
of sight makes a 75° angle below the horizontal. When Rasheed looks at Earl, his line of sight
makes a 40° angle below horizontal. Earl has walked % of the way across the ditch. How deep
is the ditch?

Answer:

C) 20.97 AED

Step-by-step explanation:

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as [tex]\displaystyle E(X)=\mu=\sum xP(x)[/tex].

Here, x represents values of the random variable X, [tex]P(x)[/tex] represents the corresponding probability, and symbol [tex]\displaystyle \sum[/tex] represents the sum of all products [tex]xP(x)[/tex]. Here we use the symbol [tex]\mu[/tex] for the mean because it is a parameter. It represents the mean of a population.

In this case, the expected value of the ticket is [tex]\displaystyle E(X)=\mu=\sum xP(x)=12(0.08)+18(0.15)+20(0.31)+22(0.08)+24(0.15)+25(0.23)=20.97[/tex]

This means that Ahmad can expect to win 20.97 AED for the ticket.

Answer:

maybe option 2 is the correct answer

Answer:

1 and 3/8 or C

Step-by-step explanation:

the longer pencil is 5 and 2/8 and the length of the shorter pencil is 3 and 7/8

5 2/8 - 3 7/8= 11/8 or 1 and 3/8

I hope this helps!!!

Answer:

10.16

Step-by-step explanation:

average change =  9.16 - 4.35 / 2020 - 1996  = 0.2

Cost = 9.16 + (2025 -2020) x 0.2 = 10.16

So the answer is $10.16

The slope within two sets of points is calculated using the slope equation [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

The slope of a line or points is the rate of change of the line.

This in other words means that, the vertical change per unit horizontal change

Assume that the points are given as:

(x1, y1) and (x2, y2)

The slope (m) of the points is:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

Hence, the equation of two sets of points is [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

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There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

To find the total number of different sundaes possible, we need to multiply the number of choices for each category: ice cream flavors, toppings, and sizes.

Number of ice cream flavors = 20

Number of toppings = 5

Number of sizes = 3

Total number of sundaes = Number of ice cream flavors × Number of toppings × Number of sizes

Total number of sundaes = 20 × 5 × 3

Total number of sundaes = 300

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

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[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =36 \end{cases}\implies s=\cfrac{(36)\pi (2)}{180}\implies s=\cfrac{2\pi }{5}\implies s\approx 1.26~in[/tex]

Answer: 60

Step-by-step explanation:

The opposite side of the right angle triangle by using Tan.

[tex]tan \: 22 = \frac{x}{12} [/tex]

[tex]x = 12 \times tan \: 22[/tex]

[tex]x = 4.8 \: cm[/tex]

Therefore, the opposite side of the right angle triangle is 4.8 centimeters

x/12

x= 12*tan 22

x= 4.8 cm

hope this helps

Answer:

Step-by-step explanation:

A linear function that models the remaining amount he would have to repay is y =620 - 50x. The slope is -50 and the y-intercept is 620.

A linear function is a function in which there is only one variable that is raised to the power of one. Linear functions usually have the form: mx + b.

Where:

The first step is to determine the amount that would be repaid each month: (620 - 320) / 6 = $50

The linear function:  =620 - 50x.

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The two angles are supplementary angles and form a straight line which equals 180 degrees

x = 180 - 125

X = 55 degrees

Answer:

hope this will help you

Step-by-step explanation:

x+125=180

x=180-125

x=55°

Answer:

∠A≅∠Z         AB≅ZX

∠B≅∠X          AC≅ZY

∠C≅∠Y          BC≅XY

ΔCBA≅ΔYXZ

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Let me know if you ever need help !

Answer:

3/8

Step-by-step explanation:

1/8 + 1/4 = 1/8 + 2/8 = 3/8

Note that 1/4 = 1/4 * 2/2 = 1*2 / 4*2 = 2/8

Step-by-step explanation:

−3(x−4)+x+1

Evaluate this with x=−6

−3(−6−4)+−6+1

=25

Hey there!

[tex] \displaystyle \red{ \boxed{ \green{25}}}[/tex]

-3(x - 4) + x + 1

>> Substitute -6 for x :

⇒ -3(-6 - 4) + (-6) + 1

⇒ -3(-10) - 6 + 1

⇒ 30 - 6 + 1

⇒ 24 + 1

⇒ 25

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Answer:

See below in bold.

Step-by-step explanation:

Let t be the number of tulips you buy and r be the number of rose bushes.

a.

The system is:

t + r = 13

4t + 10r = 100

b.

Solving:

4t + 10r = 100

t + r = 13           Multiply this by 4:

4t + 4r = 52      Subtract this from the first equation:

0 + 6r = 48

r = 8.

Now substitute for r in  t + r = 13:

t + 8 = 13

t = 5.

c.

To  buy 13 plants and spend  $100 you need to buy 5 tulips and 6 rose bushes.

Both the tangents are equal to each other. Then the length of BC will be 5.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

A tangent to a circle is a line that passes through the centre of the circle precisely once.

As illustrated in the diagram, there are precisely two tangents to a circle that may be drawn from a location just outside of the circle.

Then both the tangents are equal to each other.

The length of BC will be 5.

The diagram is shown below.

More about the circle link is given below.

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Answer:

6

Step-by-step explanation:

The ratio of boys to girls is 2:5

let the number of boys be 2x -------(i)

and number of girls be 5x

and the total number of students is 21

therefore we know that..

2x+5x = 21

on solving for x,

7x=21

x= 21/7

x=3

now, by putting the value of x in (i),

2x = 2×3 = 6

therefore, there are 6 boys in the classroom.

you find the no. of girls similarly.

hope it helps !!...

PLEASE MARK BRAINLIEST ♡

x = -2/3 or -4

see the attachment for solution

hope it helps...!!!

Based on the calculation below, the amount that can be withdrawn each month for 10 years is a. $769.27.

First, we calculate the future value (FV) of the amount after 20 years using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:

FV = A * (((1 + r)^n – 1) / r) ................................. (1)

Where,

FV = Future value of the amount after 20 years =?

A = Monthly deposit = $235.15

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 20 * 12 = 240

Substituting the values into equation (1), we have:

FV = $235.15 * (((1 + 0.00266666666666667)^240 – 1) / 0.00266666666666667) = $78,910.41

The amount planned to be withdrawn on monthly basis can be calculated using the formula for calculating the present value (PV) of an ordinary annuity as follows:

P = PV / ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

P = Monthly withdrawal or payment = ?

PV = Present value = FV calculated above = $78,910.41

r = Monthly interest rate = 3.2% / 12 = 0.00266666666666667

n = number of months = 10 * 12 = 120

Substitute the values into equation (2), we have:

P = $78,910.41PV / ((1 - (1 / (1 + 0.00266666666666667))^120) / 0.00266666666666667) = $769.27

Therefore, the amount that can be withdrawn each month for 10 years is $769.27.

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The answer is A: $769.27

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Have a great day and God bless! :D

Answer:

15.24 millimeters

Step-by-step explanation:

6 * 2.54 = 15.24 mm.

Answer: should be 15.24

Step-by-step explanation: quick maths

Answer:

2 ounces

Step-by-step explanation:

2 pounds and 2 tons are a lot of weight to assume the weight of a pen.

What percent of students prefer aerobic excersize: 53%

88+69 /350= 0.5257 x 100

52.57 round up 53

53%

Answer:

2

Step-by-step explanation:

0.75*32=24 is 75% of 32

0.8*32=25.6 is 80% of 32

you need to round to 26 as you cant get .6 of a mark

26-24=2

Answer:

a. 1 triangle

Step-by-step explanation:

measure line QS=8.cm measure 85°on side Q

Answer:

will construct 1 triangle

Step-by-step explanation:

construct a line of Q to S 8cm

SQR let the angle stay in the middle of the letter (Q)

Q to R is 5cm

Answer:

B

Step-by-step explanation:

We know that AB has endpoints at A(4, -3) and B(3, 7).

To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.

So, let's find the slope of AB using the slope formula:

Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:

So, the slope of AB is -10.

Remember that the slopes of perpendicular lines are negative reciprocals of each other.

Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.

So, Line D has a slope of 1/10.

Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.

To find the midpoint, we can use the midpoint formula:

We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:

Evaluate. So, the midpoint is:

Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:

Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:

This is the same as choice C. So, choice C is indeed an equation of Line D.

We can distribute the right to obtain:

Add 2 to both sides to acquire:

This is the same as choice D. So, choice D is indeed an equation of Line D.

Moreover, we can put this into standard form by multiply everything by 10, which gives:

Subtracting x from both sides yields:

This is the same as A. So, choice A is also an equation of Line D.

There is no way to acquire choice B. So, B is not an equation of Line D.

Therefore, our answer is B.

And we're done!

Answer:

8$

Step-by-step explanation:

4 students contribute 12$ Each.

So, total amount becomes 12 x 4 = 48$

If two more students contribute it makes a total of 6 students.
so we now divide the 48$ by 6
48/6=8$

Answer:

BC = 6 units

Step-by-step explanation:

given that B is between A and C , then

AB + BC = AC ( substitute values )

3x + 4x - 2 = 12

7x - 2 = 12 ( add 2 to both sides )

7x = 14 ( divide both sides by 7 )

x = 2

Then

BC = 4x - 2 = 4(2) - 2 = 8 - 2 = 6

Answer:

6

Step-by-step explanation:

from the question, since point B is between Ac

AC = AB + BC

12 = 3X+4X -2

3X+4X-2 = 12

7X = 12+2

7X = 14

dividing bothsides by 7

7X/7 = 14/7

X = 2

the length BC = 4X-2 = 4(2)-2 = 8-2= 6

length of BC = 6

Answer:

volume = l×b×h = 1.6 × 1.6 × 1.6 = 4.096cm³