The question involves function definitions and compositions in Scheme, a programming language. 'Square' squares its input, 'add-one' adds one to its input, and 'double' doubles its input. The composed function applies these operations sequentially.
Explanation:The student's question involves programming in the Scheme language, a dialect of Lisp. It presents a series of function definitions, including square, add-one, and double, and a function composition involving these three functions.
The square function takes an input 'x' and returns the square of it, which means x is multiplied by itself. In programming, this multiplication can be symbolized as (* x x). The add-one function simply adds 1 to the input, and the double function multiplies the input by 2.
Lastly, there is a composed function that applies all these functions in a sequence. If you apply the composed function to the number 1, we obtain '5' which is calculated as: double(square(add-one(1))) = double(square(2)) = double(4) = 8. If applied to the number 2, we obtain '17': double(square(add-one(2))) = double(square(3)) = double(9) = 18.
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In the diagram, the base of the tower is at point H, and the top of the tower is at point F. If the distance from the base of the tower to point G is 7x feet and the distance from the base of the tower to point E is 6x + 12 feet, find GE, the distance across the lake.
A. 84 feet
B.
94 feet
C. 168 feet
D. 186 feet
A metal rod is 38 meters long. It will be cut into pieces that are each 148
meters long. How many pieces will be made from the rod?
solve by substitution 3x+2y=-5, 2x-5y=-16
The solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
let's solve the system of equations using the substitution method.
Given:
1. [tex]\(3x + 2y = -5\)[/tex]
2.[tex]\(2x - 5y = -16\)[/tex]
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve equation 1 for [tex]\(x\):[/tex]
[tex]\[3x = -2y - 5\][/tex]
[tex]\[x = \frac{-2y - 5}{3}\][/tex]
Step 2: Substitute the expression for [tex]\(x\)[/tex]from step 1 into the other equation.
Substitute [tex]\(x = \frac{-2y - 5}{3}\)[/tex] into equation 2:
[tex]\[2\left(\frac{-2y - 5}{3}\right) - 5y = -16\][/tex]
Step 3: Solve for [tex]\(y\).[/tex]
[tex]\[ \frac{-4y - 10}{3} - 5y = -16 \][/tex]
[tex]\[ -4y - 10 - 15y = -48 \][/tex]
[tex]\[ -19y - 10 = -48 \][/tex]
[tex]\[ -19y = -38 \][/tex]
[tex]\[ y = 2 \][/tex]
Step 4: Substitute the value of [tex]\(y\)[/tex] into one of the original equations to solve for [tex]\(x\).[/tex]
Let's use equation 1:
[tex]\[3x + 2(2) = -5\][/tex]
[tex]\[3x + 4 = -5\][/tex]
[tex]\[3x = -9\][/tex]
[tex]\[x = -3\][/tex]
So, the solution to the system of equations is [tex]\(x = -3\)[/tex] and [tex]\(y = 2\).[/tex]
Complete question:
solve by substitution 3x+2y=-5, 2x-5y=-16
Monica is shopping for candy for her wedding and needs lollipops and gummy bears for a display she is making for the reception. Lollipops are $1 per pound and gummy bears are $0.75 per pound. She knows she wants to spend exactly $15 on candy. If she spent $9 on lollipops, which of the following is the number of pounds of gummy bears she purchased?
6 8 9 12
We have been given that she wants to spend exactly $15 on candy.
Also, she spent $9 on lollipops. It means she spent [tex]15-9= $6[/tex] on gummy bears.
Also, we have been given that the cost of gummy bears are $0.75 per pound.
Thus, in 1$ she can purchase [tex]\frac{0.75}{6}[/tex] pounds of gummy bears.
Hence, in $6, she can purchase
[tex]\frac{1}{0.75} \times 6\\ \\ =8[/tex]
Therefore, she purchased 8 pounds of gummy bears.
determine the domain of the function h(x)= 9x/x(x^2-36)
Final answer:
The domain of the function h(x)=9x/x(x²-36) is all real numbers except 0, 6, and -6, because the function is undefined at these points.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
Explanation:
The question asks to determine the domain of the function h(x) = 9x / x(x² - 36).
The domain of a function consists of all the real numbers x for which the function is defined. In this case, the function will be undefined when the denominator is zero because division by zero is not defined in mathematics.
To find these values, we set the denominator equal to zero and solve the resulting equation:
x(x² - 36) = 0.This can be factored further as x(x - 6)(x + 6) = 0, which gives us the zero points of x = 0, x = 6, and x = -6.
Therefore, the domain of h(x) is all real numbers except 0, 6, and -6.
In conclusion, the domain of h(x) is x ∈ ℝ, x ≠ 0, x ≠ 6, x ≠ -6.
A tennis player lands 25 out of 40 first serves in bounds for a success rate of 62.5%. How many more consecutive first serves must she land in bounds to increase her success rate to 70%.
The tennis player must consecutively land 10 more first serves in bounds to raise their success rate from 62.5% to 70%.
First, let's define the variables:
x = number of additional successful serves needed
40 + x = total number of serves after additional successful serves
25 + x = total number of successful serves after additional successful serves
We set up the equation with the desired success rate of 70%:
(25 + x) / (40 + x) = 0.70
To solve this equation, follow these steps:
Multiply both sides by (40 + x):
25 + x = 0.70 * (40 + x)
Distribute 0.70 on the right side:
25 + x = 28 + 0.70x
Isolate the variable x by subtracting 0.70x from both sides:
25 + x - 0.70x = 28
Combine like terms:
0.30x = 3
Solve for x by dividing both sides by 0.30:
x = 10
Thus, the tennis player must land 10 more consecutive first serves in bounds to increase her success rate to 70%.
2 blue shirts
1 white shirt
1 red shirt
2 black slacks
1 white pair of pants
1 pair of jeans
1 pair of sandals
2 pairs of running shoes
Alex is on vacation and has the clothes listed above with her. She is trying to pick out an outfit. What is the probability she chooses a red shirt and a pair of jeans?
A) 0.01 B) 0.06 C) 0.08 D) 0.5
5% of all widgets are defective. there is a 30% chance that a widget was produced at the foo factory. if a widget was produced at the foo factory, then there is a 4% chance that the widget is defective.
a.) what is the probability that a widget was produced at the foo factory AND is defective?
b.) are "produced at the foo factory" and "defective" independent events? justify.
Use a change of variables to find the indefinite integral xe^(x^2) dx
Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale
A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no
What is the greatest possible error when measuring to the nearest quarter of an inch? 1/8 in. 1/4 in. 1/2 in.
The greatest possible error when measuring to the nearest quarter of an inch is:
1/8 in.
What is the greatest possible error when measuring to the nearest quarter of an inch?Error in measurement is the difference between the measured value of a quantity and its true value. It is an inevitable part of any measurement, and there are many different sources of error.
The greatest possible error when measuring to the nearest quarter of an inch is 1/8 of an inch.
This is because the smallest measurement interval is 1/4 of an inch, and the greatest possible error is half of the smallest measurement interval.
Therefore, the greatest possible error when measuring to the nearest quarter of an inch is 1/8 in.
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Use the X method to find the solutions of 6x2 + 2x – 20 = 0. x = x =
The solutions of the given quadratic equations is 5/3 and -2
Given the quadratic function expressed as:
6x^2 + 2x – 20 = 0Factorizing the function we will have:
6x^2 + 2x – 20 = 0
3x^2 + x - 10 = 0
3x^2 +6x - 5x - 10 = 0
3x(x+2) 5(x+2) = 0
Group the function;
(3x-5)(x+2) = 0
Find the factors
3x- 5 = 0 and x + 2 = 0
x = 5/3 and -2
The solutions of the given quadratic equations is 5/3 and -2
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Graph 12x-9y=36 please???
Answer:
The graph for 12x-9y=36 is given below
Step-by-step explanation:
The graph for 12x-9y=36 is given below.
[tex]12x-9y=36\\\frac{12x}{36}+\frac{9y}{-36}=1\\\frac{x}{3}+\frac{y}{-4}=1[/tex]
So x intercept is 3 and y intercept is -4.
The required graph is shown below which represents the equation 12x - 9y = 36.
To graph the equation 12x-9y=36, we can rearrange it to slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.
First, solve for y by subtracting 12x from both sides and then dividing by -9. This gives us y=-4/3x+4.
Now we can see that the slope is -4/3 and the y-intercept is 4.
To graph this line, we can start at the y-intercept of (0,4) and then use the slope to find another point.
Since the slope is negative, we can move down 4 units (which is the denominator of the slope) and then move to the right 3 units (which is the numerator of the slope) to get another point at (3,0).
We can then draw a straight line through these two points to graph the equation.
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Adam charges 20$ to mow his neighbor's lawn every 2 weeks for the 18 weeks of grass growing season. he wants to but a new
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
To calculate how much Adam will earn this season, subtract his expenses from his total earnings.
Earnings per mowing session: $20
Number of mowing sessions in the grass-growing season: 18 weeks / 2 weeks = 9 sessions
Total earnings: $20 per session * 9 sessions = $180
Expenses:
Cost of the lawn mower: $165
Cost of gasoline per session: $2.50 per session * 9 sessions = $22.50
Total expenses: $165 + $22.50 = $187.50
To find Adam's net earnings, subtract his expenses from his total earnings:
Net earnings = Total earnings - Total expenses
Net earnings = $180 - $187.50
Net earnings = -$7.50
Since Adam's expenses exceed his earnings, he will have a negative net earnings. Therefore, Adam will not earn any money this season. In fact, he will have a net loss of $7.50.
Adam charges $20 to mow his neighbors lawn every 2 weeks for the 18 weeks of grass-growing season. He wants to buy a nice lawn mower for $165 and gasoline costs $2.50 every 2 weeks. How much will Adam earn this season?
What is the domain of the function?
The domain of the function is (-∞, ∞).
Definition of function
A function is an expression that shows the relationship between variables as well as numbers.
The domain of a function is the set of all possible inputs for the function.
From the graph, the domain is the set of all x values, hence:
Domain = (-∞, ∞)
The domain of the function is (-∞, ∞).
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ABCD and DECF are both squares. If AC = 28 millimeters, what is the perimeter of DECF?
Blue cassests hold 45 min. Of music
Green cassets hold 55 min. Of music
If Niko has 16 cassets containing 830 min. Of music
How many are blue? And how many are green?
Which expression has a value closest to 1? (Use 3.14 as the value of .)
Answer:
C)square 37 - square root 26
Step-by-step explanation:
Hey can you please help me posted picture of question
Factor 4x^2-20x-144
1.
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.
To find the new balance on January 1, we need to calculate the total balance after considering purchases, returns, payments, and finance charges.
Calculate the total charges:
Total charges = Previous balance + New purchases − Returns
Total charges = $205.84 + $98.42 − $18.63
Total charges = $285.63
After the payment, ascertain the extra amount due:
Unpaid balance = Total charges − Payment
Unpaid balance = $285.63 − $25
Unpaid balance = $260.63
Calculate the finance charges:
Finance charges=Unpaid balance×Monthly interest rate
Monthly interest rate = 1.5% = 0.015
Finance charges = $260.63 × 0.015
Finance charges ≈ $3.91
Calculate the new balance:
New balance = Unpaid balance + Finance charges
New balance = $260.63 + $3.91
New balance = $264.54
So, the new balance on January 1 is approximately $264.54.
To calculate Brent Tyson's new balance on January 1, we first determine the total charges by adding new purchases and subtracting returns from the previous balance.
Then, we deduct his payment to find the unpaid balance.
Next, we calculate finance charges at a rate of 1.5% per month on the unpaid balance.
Finally, we add the finance charges to the unpaid balance to get the new balance.
After these steps, Brent Tyson's new balance on January 1 is $264.54.
This process ensures we account for all transactions and interest charges to accurately determine the updated balance on his Discover card.
Complete Question:
The balance on Brent Tyson’s Discover card on December 1 is $205.84.
In December, he charges an additional $98.42 of purchases, has returns of $18.63, and makes a payment of $25.
If the finance charges are calculated at 1.5% per month on the unpaid balance, find the new balance on January 1.
Using the law of cosines, a=2.2
Use your answer above to find m<B, to the nearest degree. m<B=__
Answer:
81
Step-by-step explanation:
19. # Q Find the missing side length
Kendrick travel 2/3 mile to his friend’s house.He cycles 3/4 of his distance and walks the rest of the way.What fraction of a mile did he cycle?
Alice collected donations of $50, $125, $10, $210, $50, $24, and $175 for charity. What is the mean of her collections?
Answer:92
Step-by-step explanation:
92
simplify the expression
Kite ABCD represents a softball field that is being built. If AC = 48 meters, what is the perimeter of the field? 40 meters 70 meters 140 meters 218 meters
Answer:
140 m
Step-by-step explanation:
A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length.
The perimeter of the kite is the sum of the length of all its sides. So, the perimeter of kite ABCD can be expressed as:
[tex]\sf Perimeter = AB + BC + CD + DA[/tex]
As BC = AB and CD = DA, then:
[tex]\sf Perimeter = BC + BC + CD + CD\\\\Perimeter = 2(BC + CD)[/tex]
Therefore, to find the perimeter of kite ABCD, we need to determine the lengths of sides BC and CD.
The diagonals of a kite intersect to form two pairs of congruent right triangles, where the sides of the kite are the hypotenuses of these triangles.
in kite ABCD:
Diagonal AC = 48 mDiagonal BD = 18 + 32 = 50 mThe longer diagonal of a kite always bisects the shorter diagonal at a right angle.
Let M be the point of intersection of the diagonals. Therefore:
AM = MC = 24 m
Side BC is the hypotenuse of right triangle BMC, with legs measuring 18 m and 24 m, while side CD is the hypotenuse of right triangle CMD, with legs measuring 32 m and 24 m.
To find the lengths of sides BC and CD, we can use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two legs.
[tex]\sf BC^2=18^2+24^2 \\\\BC^2=324+576 \\\\BC^2=900\\\\BC=\sqrt{900}\\\\BC=30\; m[/tex]
[tex]\sf CD^2=32^2+24^2 \\\\CD^2=1024+576 \\\\CD^2=1600\\\\CD=\sqrt{1600}\\\\CD=40\; m[/tex]
Now we have determined the length of sides BC and CD, we can substitute them into the perimeter formula:
[tex]\sf Perimeter = 2(30+40) \\\\ Perimeter = 2(70) \\\\ Perimeter = 140 \; m[/tex]
Therefore, the perimeter of kite ABCD is:
[tex]\LARGE\boxed{\boxed{\sf 140\; m}}[/tex]
15 points!!! GEOMETRY help please!!
Questions attached!
A person whose eye level is 1.5 meters above the ground is standing 75 meters from the base of the jin mao building in shanghai, china. the person estimates the angle of elevation to the top of the building is about 80º. what is the approximate height of the building
The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building from the ground is 426.85 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
As it is given that the angle of elevation from the person's view is 80°, while the distance between the person and the base of the building is 75 meters, therefore, using the trigonometric function the height of the building top from the person eye level is,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\\\Tan(80^o) = \dfrac{\text{Height of the building}}{75\ meters}\\\\\\\text{Height of the building} = 75 \times tan(80^o) = 425.35\ meters[/tex]
Now, we know the height of the building top from a person's eye level, and we also know the person's eye level as well, therefore, the height of the building can be written as,
[tex]\text{Height of the building} = 425.35 + 1.5 = 426.85\rm\ meters[/tex]
Hence, the height of the building from the ground is 426.85 meters.
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Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?
By continuing the pattern of Amy increasing her volunteer hours by 2 each month, she will work for 30 hours in December.
Explanation:To find out how many hours Amy will work in December, we must first identify the number of terms between June and December.
Counting inclusively, we see that there are seven months between June and December (June, July, August, September, October, November, December), which means we should look for the 7th term after June to find the number of hours Amy will work in December.
Since we have established an increase of 2 hours each month, we can calculate this by adding 7 terms of an arithmetic progression to Amy's last known volunteering hours.
To do this, we use the explicit formula for an arithmetic sequence:
Tn = a + (n - 1) * d,
where Tn is the term we wish to find, a is the first term in the sequence, n is the position of the term in the sequence, and d is the common difference between terms. Amy's last known volunteering hours in June (the 4th term in the sequence) were 16, with a common difference of 2.
Adding 7 intervals of 2 hours each gives us 14 additional hours by December.
Therefore, we add this to the 16 hours she worked in June: 16 + 14 = 30 hours.
Amy is expected to volunteer for 30 hours in December.