The correct answer is option c. There are no real-valued functions that have a domain of all real numbers and a range of all integers.
A function maps an input (or domain) to a unique output (or range). In order for a function to have a domain of all real numbers, it must take any real number as an input and provide a unique output. However, for a function to have a range of all integers, it must be the case that every output is an integer.
Since the real numbers are not countable and the integers are countable, there can be no function that maps every real number to a unique integer. In other words, there is no one-to-one correspondence between the real numbers and the integers, which means that it is not possible to find a function that maps every real number to an integer.
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Complete Question:
which function(s) has the following properties? there may be more than one answer, so select all that apply.
the domain is all real numbersthe range is all integersnone of the abovePlease please help
7 A cylinder of height h metres is inscribed in a sphere of constant radius R metres.
a If the cylinder has radius r metres, show that r? = R? - ]h?.
b Show that the volume of the cylinder is given by V = Ih (4R? - h).
c Show that the volume of the cylinder is maximised when h = §v3R.
d Hence show that the ratio of the volume of the sphere to the maximum volume of the cylinder is V3: 1.
12 A canned fruit producer wishes to minimise the area of sheet metal used in manufacturing cylindrical cans of a given volume. Find the ratio of radius to height for the desired can.
10 A rectangle is inscribed in a quadrant of a circle of radius r so that two of its sides are along the bounding radii of the quadrant.
a If the rectangle has length x and width y, show that its area is given by A = yVr2 - y
b Show that the maximum possible area of the rectangle is †r?
Answer:
7a) To show that r^2 = R^2 - h^2, one can use the Pythagorean theorem and the fact that the distance from the center of the sphere to the surface of the cylinder is h/2.
7b) To find the volume of the cylinder, one can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height.
7c) To find the maximum volume of the cylinder, one can differentiate the expression for the volume with respect to h, set the derivative equal to zero, and solve for h.
7d) The ratio of the volume of the sphere to the maximum volume of the cylinder can be found by dividing the volume of the sphere by the maximum volume of the cylinder.
To find the ratio of radius to height for the desired can, one can set up an expression for the surface area of the can and differentiate it with respect to the radius and height. Setting the partial derivatives equal to zero, one can find the critical points, and evaluate which one is the minimum.
10a) To find the area of the rectangle, one can use the formula for the area of a rectangle, A = xy, where x is the length and y is the width.
10b) To find the maximum area of the rectangle, one can differentiate the expression for the area with respect to x and y, set the partial derivatives equal to zero, and solve for x and y.
Step-by-step explanation:
Jane and Sarah share £28.
Jane receives 1/4 of the money
Find how much money Sarah receives.
what are three subcategories in the previous scratch list? high-end linens, affordability, food and drink free snacks, shampoo, and conditioner; high-end linens; double-thick bath towels 600-thread-count sheets, coffeemaker and selected teas, $100/night four-star rooms
The three subcategories in the previous scratch list are high-end linens, affordability, and food and drink-free snacks.
High-end linens include double-thick bath towels and 600-thread-count sheets. Affordability includes $100/night for four-star rooms. Food and drink-free snacks include coffeemakers and selected teas.
This scratch list provides guests with luxurious amenities and convenience. High-end linens enhance the comfort of a room, while affordability makes it accessible to many.
Food and drink-free snacks add to the convenience of a stay by providing guests with refreshments. All of these amenities contribute to a pleasant and comfortable stay.
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Find 1 sequences that are geometric and then write the recursive form and the explicit equation. I
The geometric sequence is given as follows:
1, 2, 4, 6, 8, ...
The recursive formula is given as follows:
f(n) = 2 x f(n - 1).f(1) = 1.The explicit formula is given as follows:
[tex]f(n) = 2^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.
The explicit formula of a geometric sequence is given by:
[tex]f(n) = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For the recursive formula, we have that:
f(n) = q x f(n - 1).
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PLEASE ME WITH MY MATH THE QUESTION IS IN THE PICTURE
sum of roots is 0 , -5 , 4
product of roots is -9, 25/4, 8
Discriminant = 36, 0 , - 16
What are quadratic Equation ?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
When a quadratic equation is solved, the two values of x that result are known as the roots of the equation. The zeros in the equation are another name for these quadratic equation roots. For instance, x = -1 and x = 4 are the roots of the equation x² - 3x - 4 = 0 since they each fulfill it.
The easiest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula. The quadratic equation's roots also aid in determining the quadratic equation's sum of roots and product of roots. The quadratic formula's two roots are shown as a single statement.
The equation are :
x² - 9 = 0 ⇒ (x-3)(x+3) = 0 ,
sum of roots is 0
product of roots is -9
Discriminant = 0² - 4*3(-3) = 36
The second equation :
4x² + 25 = - 20x ⇒ 4x² + 20x + 25 = 0 ⇒ 4x² + 10x + 10x + 25 ⇒2x(2x + 5) +5(2x+5) = 0 ⇒ (2x +5)²
sum of roots is -5
product of roots is 25/4
Discriminant = 0
x²/2 - 2x + 4 = 0 ⇒ x² - 4x + 8 = 0
Sum of roots 4
Product of roots 8
Discriminant = (-4)² - 4*1*8 = 16 - 32 = -16
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Select all the equations where c=9c=9c, equals, 9 is a solution.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
4-c=54−c=54, minus, c, equals, 5
(Choice B)
B
20=14+c20=14+c20, equals, 14, plus, c
(Choice C)
C
15=c-615=c−615, equals, c, minus, 6
(Choice D)
D
\dfrac{c}{3}=3
3
c
=3start fraction, c, divided by, 3, end fraction, equals, 3
(Choice E)
E
36=4c36=4c
The equations that are solutions when c = 9 are B and C, and D and E.
When c = 9, the solutions for the equations are:
(A) 4 - c = 5: substituting 9 for c, we get 4 - 9 = -5, which is not true, so this equation is not a solution.
(B) 20 = 14 + c: substituting 9 for c, we get 20 = 14 + 9, which is true, so this equation is a solution.
(C) 15 = c - 6: substituting 9 for c, we get 15 = 9 - 6, which is true, so this equation is a solution.
(D) c/3 = 3: substituting 9 for c, we get 9/3 = 3, which is true, so this equation is a solution.
(E) 36 = 4c: substituting 9 for c, we get 36 = 4 * 9, which is true, so this equation is a solution.
So the equations that are solutions when c = 9 are B and C, and D and E.
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Answer:
Step-by-step explanation:
The first credit card that you got charges 12.5 % interest to its customers and compounds the interest monthly. Within one day of getting your first credit card you max out the credit limit by spending $1,200.00. If you do not buy anything else on the card and you do not make any payments, how much money would you owe the company after 6 months?
The amount company will make in 6 months is $24327.43.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given the interest rate = 12.5% = 0.125
principal = $12,000
time period = 6 months
CI is given by,
CI = [tex]p(1 + \frac{r}{n})^{nt}[/tex]
n = 1
substitute the values,
A = 12000(1 + (0.125/1))¹ˣ⁶
A = 12000(1.125)⁶
A = 24327.43
A = $24327.43
Hence the amount will be $24327.43.
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or
Watch a video
Find the cosine of ∠U.
28
45
53
U
V
T
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.
The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.
cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53
So, the cosine of ∠U is 28/53, written as a proper fraction.
Now let's convert cosine of ∠U is 28/53 in improper fraction:
The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.
gcd(28, 53) = 1, so the fraction cannot be further simplified.
Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.
Now let's convert cosine of ∠U is 28/53 in whole number:
The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.
28 ÷ 53 = 0.526087
So, the cosine of ∠U expressed as a whole number is approximately 0.52609
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_____ The given question is not correct, so correct Question is:
Find the cosine of ∠U in Triangle UTV with side:
UV=28
VT=45
TU=53
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
the data were collected from a statistics class. the column head gives the variable, and each of the rows represent a student in the class. find the frequency, proportion, and percentage of women
Step 1: Count the total number of students
The total number of students in the statistics class is 8.
Step 2: Count the number of women
There are 4 women in the statistics class.
Step 3: Calculate the frequency, proportion, and percentage of women
Frequency: The frequency of women in the statistics class is 4.
Proportion: The proportion of women in the statistics class is 4/8, or 0.5.
Percentage: The percentage of women in the statistics class is 50%.
The information in the question is not significant to calculate the frequency, proportion and percentage of women.
Statistical models for calculating gender through frequency involve counting the number of individuals in a population that identify as each gender. This can be done by collecting data on gender from surveys, census data, or other sources of information. The data collected is then used to calculate the frequency, proportion, and percentage of each gender in the population. This information can be used to better understand gender dynamics in a population and inform policies and practices that promote gender equity.
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for the stem and leaf plot created in question 9 are there any extreme values? if so, what are they?
As a result, the extreme stem values may contain fewer rows than the other stem values. In our graph, the extreme stem values are 1 and 4, and they both have fewer rows than the middle values (2 and 3).
The shape and spread of a continuous data distribution are depicted by stem and leaf plots. These graphs are similar to histograms, but instead of bars, they display numbers.
Statistical software packages use an algorithm to improve our ability to read stem and leaf plots by displaying multiple rows of each stem value based on the properties of the data, as shown in the body fat percentage graph. There are two ones, five twos, five threes, and four fours.
The graph divides stem values into five rows for the body fat percentage data. Each row only has two leaf values (e.g., 0 and 1, 2 and 3, etc.) The leaf values terminate at the dataset's minimum and maximum values.
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there are four boys to every seven girls in an introductory geology course. if there are 374 students enrolled in the course, how many are boys?
There are 172 boys in the introductory geology course.
The ratio of boys to girls is 4:5. We can know that the number of boys in the class is four multiplied by the common value that the ratio is based on.
We can call this usual value x and say that the number of boys in the class is 4x. Applying the same logic to the girls, we can say that there are 5x girls in the class. Hence, a total of 9x children. We divide the total value by 9 to get x, which equals 43.
We can then calculate the number of boys by calculating 4x, which equals 172.
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A segment is connected to two sides of a triangle so that itnis parallel to the third side. Solve for x. A. 5 B. 4 C. 6 D. 9
The value of x in the angle is 56 degrees
How to detrmine the value of xFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we have teh following equation
64 + x + 60 = 130
The above is by the sum of angle theorem
So, we have
124 + x = 130
Evaluate the like terms
x = 6
Hence, the value of x is 6
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Does anyone know the answer ?
Answer:
6
Step-by-step explanation:
As you can see from the graph, it intercepts the y-axis at -4 and x-axis at 6
write the numbers in descending order 0.516,0.615,0.609,0.506
Answer:
0.615, 0.609, 0.516, 0.506
A triangular prism has a height of 5.9 meters and volume 86.376 cubic meters. What is the area of the base of the prism?
Answer: 14.64m^2
Step-by-step explanation:
Base area = volume/height
Substitute:
86.376/5.9 = 14.64cm^2
Hope that helps!
What is the volume and the surface area of the right solid whose base is shown
if the sides are 1 foot high? What is the volume of a cone that has the same base
and the same altitude? Dimensions are in feet.
The volume of the cone = 0.262 feet³.
What is cone?The word "cone" is derived from the Greek word "konos," which denotes a peak or a wedge. Apex and base both refer to the pointy end, which is referred to as the apex. A cone is a three-dimensional geometric structure with a smooth transition from a flat, generally circular base to the apex or vertex, a point that creates an axis to the base's center.
Given that,
base of the cone = 1 foot
thus, radius (r) = 0.5 foot
altitude = 1 foot
thus, volume (V) = 1/3 πr²h
or, V = 1/3 π × (0.5)² × 1
or, V = 0.262 feet³
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3. It takes Devin 4.2 minutes to walk a lap
around a track. How long does it take for
Devin to complete 5.8 laps?
The required time taken by the Devin to complete 5.8 laps is 24.36 minutes.
How to find time to complete 5.8 laps?To find out how long it takes Devin to complete 5.8 laps, we need to multiply the time it takes to complete one lap by the number of laps. If it takes Devin 4.2 minutes to walk a lap, then to complete 5.8 laps, it would take.
According to question:time = 4.2 minutes/lap * 5.8 laps
= 24.36 minutes.
So, it would take Devin 24.36 minutes to complete 5.8 laps.
This information can be useful for determining Devin's walking pace, comparing his time to that of others, or calculating the total distance he has covered. It's important to note that this calculation assumes that Devin's pace remains constant throughout the entire walk, which may not always be the case.
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principal $3200 rate 2% time 4 years
answer
Interest on amount after 4 years = $256
What is simple interest?Simple interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest for a given time.
Given,
Principal = $3200
Rate = 2% = 0.02
Time = 4 years
Simple Interest = Principal × rate × time
= 3200 × 0.02 × 4
= $256
Hence $256 is simple interest on Principal amount after 4 years.
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Need right away pls!!
The bird is flying at a height of 404.9 feet above the ground
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
Let h represent the height of the bird.
Using trigonometric ratio:
tan(39) = h / 500
h = 500 * tan(39)
h = 404.9 feet
The height of the bird is 404.9 feet
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a toddler crawls 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel?
Soledad buys 5 ounces of frozen yogurt for $2.25. What is the unit price of the frozen yogurt in dollars per ounce?
Answer:
0.45
Step-by-step explanation:
You divided 2.25 by 5
(a) Arrange in order from least to greatest: 3,[tex]3^{2}[/tex], [tex]\sqrt{3}[/tex], -3
(b) which of the numbers in part (a) is irrational?
The order of the numbers from least to greatest is -3, √3, 3, 3².
√3 is an irrational number
How to arrange numbers in order from least to greatest?Arranging numbers in order from least to greatest is the arrangement of numbers in such a way that the smallest number comes first and the highest number comes last.
We have 3, 3², √3, -3
where 3² = 9 and √3 = 1.73
Thus, the order from least to greatest will be:
-3, √3, 3, 3²
Irrational numbers are mostly in the form of square roots, which when evaluated cannot be expressed in the form a/b e.g √7, π, 2/√5, 3√11, etc.
Thus, √3 is irrational
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Look at pic for directions and the triangle
9) What is the area of the triangle?
10) what is the area of the rectangular shaded (lavender) area that lies behind the triangle
11) explain how to find the area of the triangle without using a formula
For the given grid a. The area of the triangle is 21 square units. b. The area of the rectangle is 42 square units.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
Given that the points on the grid are 1 units apart we have:
The height of the triangle is 6 units and the base of the triangle is 7 units.
The area of the triangle is:
A = 1/2 (b)(h)
A = 1/2(7)(6)
A = 21 square units.
The area of the triangle is 21 square units.
The length of the rectangular grid is 7 units and the width is 6 units.
The area of the rectangle is:
A = (l)(b)
A = (7)(6)
A = 42 square units.
The area of the rectangle is 42 square units.
Hence, a. The area of the triangle is 21 square units. b. The area of the rectangle is 42 square units.
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Find the slope of the graph: 4x - 16y = 20.
Please explain the steps!
Answer: y = 1/4x + -5/4
Step-by-step explanation:
Step 1: add -4x to both sides
step 2: Divide both sides by -16.
Answer:
Slope is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Rearranging the equation:
[tex]4x - 20 = 16y[/tex]
The coefficient of y needs to be '+1' for the above equation to be considered as the slope-intercept form:
Dividing both sides of the equation by '16':
[tex]\frac{16}{16}y = \frac{1}{16}(4x -20)[/tex]
[tex]y = \frac{4}{16}x - \frac{20}{16}[/tex]
Divide the numerator and denominator present in the coefficient of x by the Highest Common Factor '4'. Also divide the numerator and denominator present in the coefficient of 'non-x' term by the Highest Common Factor '4':
[tex]y = \frac{1}{4}x - \frac{5}{4}[/tex]
The simplified form of the slope-intercept of the equation has been achieved. The coefficient of x is the slope of the graph:
m = Slope of graph =
Please help me !!!!
This figure shows circle O with chords PM and LN
mPL=10 degrees
mLM= 14 degrees
mLN=24 degrees
PM= 15in.
What is LN
In this question, the length of the chord LN will be 15 inches long. It will be equal to PM.
Given,
At the circle's Centre, the Arc PL subtends an angle of 10 degrees.
At the circle's Centre, the Arc LM subtends an angle of 14 degrees.
At the circle's Centre, the Arc LN subtends a 24 degree angle.
The PM chord measures 15 inches in length.
What are the circle's chord theorems?
Considering the attached figure now,
The angle that the Arc PM creates at the Centre is equal to the sum of the angles that the Arc PL and Arc LM make there.
So,
At the middle, Arc PM will create the following angle: 10+14=24 degree.
We are aware that if the chords that make up the arc are equal, then the angle that it subtends in the Centre of the circle will likewise be equal.
Since, PM= 15 inches, therefore LN will also be 15 inches.
LN is therefore 15 inches as well.
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Triangle 1 is composed of line segments AB¯¯¯¯¯, BC¯¯¯¯¯, and CA¯¯¯¯¯.
Triangle 2 is composed of line segments DE¯¯¯¯¯, EF¯¯¯¯¯, and FD¯¯¯¯¯.
The triangles are similar with a scale of 3:1.
Select the true statement about the proportions of the sides.
Answer:
[tex]\textsf{A)} \quad \dfrac{m\overline{AC}}{m\overline{DF}}=3[/tex]
Step-by-step explanation:
Similar TrianglesIn similar triangles:
corresponding angles are the same size.corresponding sides are always in the same ratio.Given ΔABC ~ ΔDEF with a scale of 3 : 1 then:
[tex]\bullet \quad \overline{AB} = 3\overline{DE}[/tex]
[tex]\bullet \quad \overline{BC} = 3\overline{EF}[/tex]
[tex]\bullet \quad \overline{AC} = 3\overline{DF}[/tex]
Therefore:
[tex]\dfrac{m\overline{AC}}{m\overline{DF}}=3[/tex]
Find the area of the polygon
The area of the polygon is 207.06 unit².
How to find the Area of the Polygon with n-sides?
For finding the area of a polygon which is not regular or its formula is not defined, we split the figure into triangles, squares, trapezium, etc. The purpose is to visualize the given geometry as a combination of geometries for which we know how to calculate the area. We then calculate the area for each of the part and then add them up to obtain the area of the polygon.
Here, we have given a polygon in the combination of a square and a triangle.
So, to find an area of the polygon we need first to find the area of square and triangle.
Area of Polygon Formulas:
Name of the Polygon Area Formula
Triangle = 1/2 × base × height
Square = (side)²
Area of Square = (13)²
= 169 unit².
Area of Triangle = 1/2 × base × height
To find base:
(height)² + (base)² = (hypotenuse)²
(13)² = (11)² + (base)²
169 = 121 + (base)²
(base)² = 169 - 121
base = √48 = 6.9
Area of Triangle = 1/2 × (6.92) × 11
= 38.06 unit².
Area of Polygon = Area of Square + Area of Triangle
= 169 + 38.06
= 207.06 unit².
Therefore, the area of the polygon is 207.06 unit².
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is -6 rational or irrstional
How does the relative
frequency change between
when the spinner is spun 50
times vs. 100 times?
The relative frequency of an event is a way to estimate the probability of that event happening.
For example, if you spin a spinner 50 times and the spinner lands on red 20 times, the relative frequency of getting red would be 20/50 = 0.4. This is a statistical estimate of the probability of the spinner landing on red, and it's based on the limited number of trials (spinning the spinner 50 times). As you increase the number of trials, the relative frequency will become a more accurate estimate of the true probability of the event. So if you spin the spinner 100 times instead of 50 times, and the spinner lands on red 40 times, the relative frequency would be 40/100 = 0.4. This shows that as the number of trials increases, the relative frequency becomes a better estimate of the true probability of the event. The reason for this is that the more trials you have, the more representative your sample is of the population, and the closer your estimate will be to the true probability of the event. In this case, the true probability of the spinner landing on red is unknown, but as you spin it more times, the relative frequency will approach the true probability, providing a more accurate estimate.
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3. Ted is standing on his balcony and sees his dog on the ground. The angle of depression to the dog is 40. Ted's eye level is 16 feet above the groundAt that moment, Ted drops a piece of his donut through the cracks of the balcony floor. How far must his dog walk to get to the donut?
Answer:
Step-by-step explanation:
Ted's balcony
|\
| \
| \ <- 40 degrees
| \
| \ <-- line of sight to the dog
| \
| \
| \
| \
| \
|__________\
Ted's
eye level
Let d be the distance the dog needs to walk to get to the donut. We can use trigonometry to solve for d.
Since the angle of depression from Ted's line of sight to the dog is 40 degrees, the angle between the ground and Ted's line of sight is 90 - 40 = 50 degrees.
We can use the tangent function to find d:
tan(50) = opposite / adjacent
The opposite side is the height of Ted's eye level above the ground, which is 16 feet. The adjacent side is d, the distance the dog needs to walk to get to the donut.
tan(50) = 16 / d
d = 16 / tan(50)
d ≈ 12.6 feet