The sample space for a child choosing one entrée and one side is A) BA, BF, CA, CF, PA, PF, SA, SF.So, the correct answer is A). Probability of a child choosing pizza or spaghetti with mixed vegetables is 2/15 or 0.1333 (rounded to four decimal places) or approximately 13.33%.
The sample space represents choose of one entrée and one side for his or her meal is BA, BF, CA, CF, PA, PF, SA, SF. So, the correct option is A).
After the addition of grilled cheese as an entrée choice and mixed vegetables as a side choice, there are now five entrée choices (B, C, P, S, G) and three side choices (A, F, MV). The total number of possible meal combinations is 5*3 = 15.
The number of meal combinations where the child chooses pizza or spaghetti with mixed vegetables is 2 (pizza with mixed vegetables and spaghetti with mixed vegetables). Therefore, the probability of choosing spaghetti or pizza with mixed vegetables for her or his meal is
P(pizza or spaghetti with mixed vegetables) = 2/15 = 0.1333 (rounded to four decimal places) or approximately 13.33%.
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--The given question is incomplete, the complete question is given
"At a restaurant, a children's meal gives a choice of four entrées: burger (B), chicken (C), pizza (P), or spaghetti (S), and two sides: apple (A) or fries (F).
Part A
Which sample space represents all the ways a child could choose one entrée and one side for his or her meal?
A) BA, BF, CA, CF, PA, PF, SA, SF
B) BA, CA, PA, SA
C) BF, CF, PF, SF
D) B, C, P, S, A, F
Part B
The restaurant decides to add another choice for the entrée and another choice for the side on the children's menu. The additional entrée choice is grilled cheese and the additional side choice is mixed vegetables. What is the probability that a child will choose pizza or spaghetti with mixed vegetables for his or her meal?"--
Step 2: Construct regular polygons inscribed in a circle.
B) The completed construction of a regular hexagon is shown below. Explain why △ACF is 30°-60°-90° triangle. (10 points)
The explanation on why △ACF is 30°-60°-90° triangle is given below.
How to explain the informationWith a regular hexagon, each of its sides and angles are equal in measure. Consider the centre of the encompassing circle, connected to two neighbouring vertices - labeled A and B here. This then creates a radius wherein the length of AB is basically equal to any other side, denoted as 's'. Furthermore, △ABF will be an isosceles triangle (with AB = BF).
From these facts, we can produce △ACF which is a right angled triangle – with AC being its hypotenuse, A F and FB both equating to s/2, finally concluding that ∠AFB is equivalent to 120°/2 = 60° while establishing that ∠ACF is also a right angle constituent making △ACF essentially a 30°-60°-90° triangle.
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The iterative function that describes how your new car loses value over time is f(t)=0. 75t, where t is the number of years since you purchased the car. If you paid $25,000 for your car and you sell it after owning the car for 3 years, how much is the car worth?
t_3=$14,062. 50
t_3=$10,546. 88
t_3=$7,910. 15
t_3=$18,750
If you paid $25,000 for your car and you sell it after owning the car for 3 years, then the worth of the car is t₃=$7,910. 15 (option c).
To find the value of your car after owning it for 3 years, we need to evaluate the function at t=3. This means we need to substitute t=3 into the function and simplify the expression.
f(3) = 0.75(3) = 2.25
The output of the function when t=3 is 2.25. But what does this number mean? It represents the fraction of the original value of the car that remains after owning it for 3 years.
To find the actual value of the car, we need to multiply this fraction by the original value of the car, which is given as $25,000.
Value of car after 3 years = 2.25 x $25,000 = $56,250
Therefore, the value of the car after owning it for 3 years is $7,910.15. This is the option (C) in the given choices.
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Savas easybrigde use the gcf and the distributive property to find the sum.
22 + 33
write each number as a product using the gcf as a factor, and apply the distributive property.
22 + 33 = ?
To use the GCF and distributive property to find the sum of 22 + 33, we first need to identify the GCF of both numbers, which is 11.
We can then write each number as a product using the GCF as a factor: 22 = 11 x 2 and 33 = 11 x 3. Next, we can apply the distributive property by multiplying the GCF by the sum of the other factors in each number: 11 x (2 + 3).
Finally, we can simplify the expression by adding the sum of the other factors, which is 5: 11 x 5 = 55. Therefore, the sum of 22 + 33 using the GCF and distributive property is 55.
In summary, to find the sum of 22 + 33 using the GCF and distributive property, we first identify the GCF as 11 and write each number as a product using the GCF as a factor.
We then apply the distributive property by multiplying the GCF by the sum of the other factors in each number. Finally, we simplify the expression by adding the sum of the other factors and arrive at the answer of 55. This method can be helpful when working with larger numbers or more complex expressions.
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Evaluate. (3/5)3 enter your answer by filling in the boxes.
the final answer is 27/125.
To evaluate [tex](3/5)^3[/tex], we simply need to multiply (3/5) by itself three times:
[tex](3/5)^3 = (3/5) * (3/5) * (3/5)[/tex]
To simplify, we can first multiply the numerators together and the denominators together:
[tex](3/5)^3 = 27/125[/tex]
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Use the Generalized Power Rule to find the derivative of the function.
f(x) = (3x + 1)^5(3x - 1)^6
This is the derivative of the given function f(x) = (3x + 1)^5(3x - 1)^6 using the Generalized Power Rule.
To find the derivative of the function f(x) = (3x + 1)^5(3x - 1)^6 using the Generalized Power Rule, we will need to apply both the Product Rule and the Chain Rule.
The Product Rule states that if you have a function f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x).
First, let's identify g(x) and h(x) in your function:
g(x) = (3x + 1)^5
h(x) = (3x - 1)^6
Next, we'll find the derivatives g'(x) and h'(x) using the Chain Rule, which states that if you have a function y = [u(x)]^n, then y' = n[u(x)]^(n-1) * u'(x).
For g'(x):
u(x) = 3x + 1
n = 5
u'(x) = 3
g'(x) = 5(3x + 1)^(5-1) * 3 = 15(3x + 1)^4
For h'(x):
u(x) = 3x - 1
n = 6
u'(x) = 3
h'(x) = 6(3x - 1)^(6-1) * 3 = 18(3x - 1)^5
Now, we apply the Product Rule:
f'(x) = g'(x)h(x) + g(x)h'(x) = 15(3x + 1)^4(3x - 1)^6 + (3x + 1)^5 * 18(3x - 1)^5
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Aaden is driving to a concert and needs to pay for parking. There is an automatic fee of $9 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $2 for every hour he had his car in the lot. How much total money would Aaden have to pay for parking if he left his car in the lot for 3 hours? How much would Aaden have to pay if he left his car in the lot for
�
t hours?
Answer:
$15.
Step-by-step explanation:
9 + 3*2
= $15.
Given that abcd is a rhombus, determine the length of each diagonal, ac, and bd if m∠ade=20° and ad = 8cm. please help and show me how you did it
The length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
Rhombus is a special type of parallelogram in which all four sides are congruent. The opposite angles of a rhombus are also congruent, and the diagonals bisect each other at right angles.
Now, let's consider the given rhombus abcd, where ad = 8cm and m∠ade=20°. We need to determine the length of diagonals ac and bd.
First, let's use the law of cosines to find the length of side ae. We know that ad = 8cm, and m∠ade=20°, so we can use the formula:
ae² = ad² + de² - 2ad(de)cos(m∠ade)
Substituting the values, we get:
ae² = 8² + de² - 2(8)(de)cos(20°)
Next, we can use the fact that a rhombus has all sides congruent to find the length of side de. Since abcd is a rhombus, we know that ac and bd are also congruent diagonals that bisect each other at right angles. Therefore, we can draw diagonal ac and use the Pythagorean theorem to find the length of ac:
ac² = (ae/2)² + (de/2)²
Substituting ae² from the previous equation, we get:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Simplifying the equation and using the fact that ac and bd are congruent, we get:
bd² = ac² = (8² + de² - 2(8)(de)cos(20°))/2
Finally, we can use the Pythagorean theorem to find the length of diagonal bd:
bd² = ab² + ad²
Substituting ab = ac/2 and ad = 8cm, we get:
bd² = (ac/2)² + 8²
Substituting ac² from the previous equation, we get:
bd² = ((8² + de² - 2(8)(de)cos(20°))/8)² + 8²
Simplifying the equation, we get:
bd ≈ 12.22 cm
Similarly, we can solve for ac using the equation we derived earlier:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Substituting de ≈ 9.84cm (which we can solve for from the equation ae² = 8² + de² - 2ad(de)cos(m∠ade)), we get:
ac ≈ 15.58 cm
Therefore, the length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
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We feed the okapi about 5,024 cubic centimeters of pellets and hay
each day. How many times a day would we have to fill the container
shown below?
80 times
40 times
16 times
4 times
HELPPPPP PLEASEEEEEE!!!!!!!
To determine how many times a day we would need to fill the container shown below, we need to calculate its capacity in cubic centimeters. Let's assume that the container is a rectangular prism with dimensions of 30 centimeters (length) x 20 centimeters (width) x 25 centimeters (height). The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
Plugging in the values we have, we get:
Volume = 30 cm x 20 cm x 25 cm
Volume = 15,000 cubic centimeters
Therefore, the container has a capacity of 15,000 cubic centimeters. To determine how many times we would need to fill it each day, we need to divide the amount of pellets and hay we feed the okapi daily (5,024 cubic centimeters) by the capacity of the container (15,000 cubic centimeters):
5,024 / 15,000 = 0.3356
This means that we would need to fill the container approximately 0.3356 times a day, which is not a practical answer. We need to round this up to the nearest whole number.
The options given to us are 80 times, 40 times, 16 times, and 4 times. Out of these options, the closest whole number to 0.3356 is 1, which means we would need to fill the container once a day.
Therefore, the answer is that we would need to fill the container shown below 1 time a day to feed the okapi their daily amount of pellets and hay.
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Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?
The expression to represent the situation is 2.85g + 3.15c.
How to represent sentence with an expression?Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can.
An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.
Therefore, the expression that can be used to determine the total amount Joe spent on gasoline and oil can be calculated as follows:
Therefore,
total cost = 2.85g + 3.15c
where
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Joe and Mike ran the same race. Joe finished the race 4 minutes before Mike. If Mike finished the race at 4:02 p.m., what time did Joe finish the race?
Answer:3:58 p.m.
Step-by-step explanation:
For thousands of years, gold has been considered one of the Earth's most precious metals. One hundred percent pure gold is 24-karat gold, which is too soft to be made into jewelry. Most gold jewelry is 14-karat gold, approximately 58% gold. If 18 karat-gold is 75% gold and 12-karat gold, how much of each should be used to make a 14-karat gold bracelet weighing 500 grams
The solution is: 14 karat gold is 58.3333...% gold
We have given that;
75% gold and 50% gold and we need to make 200 grams of 58.3333...% gold.
Since, A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
A) x + y = 200
B) .75x + .50y = ( (14/24) * 200)
We multiply equation B) by -1.3333... and get
B) -x -.6666...y = -155.5555... then adding A)
A) x + y = 200 we get
.3333...y = 44.4444...
y = 133.3333... grams 12 karat gold
x = 66.6666... grams 18 karat gold
Double-Checking the answer
133.3333... * .5 = 66.6666...
66.6666 * .75 = 50.0000...
Hence, Concentration of final solution = (66.6666... + 50) / 200 = 58.3333...% which is 14 karat gold
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I need help what is the approximate area, in square feet, of the shaded region in this figure use 3. 14
To find the approximate area of the shaded region in this figure, we need to subtract the area of the smaller circle from the area of the larger circle. The radius of the larger circle is 6 feet and the radius of the smaller circle is 3 feet.
The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius.
So, the area of the larger circle is A = 3.14 x 6^2 = 113.04 square feet.
The area of the smaller circle is A = 3.14 x 3^2 = 28.26 square feet.
To find the area of the shaded region, we subtract the area of the smaller circle from the area of the larger circle:
Area of shaded region = 113.04 - 28.26 = 84.78 square feet (rounded to two decimal places).
Therefore, the approximate area of the shaded region in this figure is 84.78 square feet.
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An initial amount of $600 is invested in a compound savings account with an annual interest rate of 3. 5%.
1. Define variables
2. Substitute into formula
3. Evaluate
Formula=A = P(1+r)t
What is the total amount after 2 years?
What is the total amount after 4 years?
After 2 years, the total amount is approximately $642.45. After 4 years, the total amount is approximately $690.27.
1. Define variables:
A = total amount after a certain number of years
P = initial amount ($600)
r = annual interest rate (3.5% or 0.035)
t = number of years
2. Substitute into formula:
A = 600(1+0.035)^t
3. Evaluate:
For 2 years (t=2):
A = 600(1+0.035)^2
A = 600(1.035)^2
A ≈ 642.45
The total amount after 2 years is approximately $642.45.
For 4 years (t=4):
A = 600(1+0.035)^4
A = 600(1.035)^4
A ≈ 690.27
The total amount after 4 years is approximately $690.27.
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PLEASE HELP!!!!!!! Line M is represented by the following equation: x + y = −1 What is most likely the equation for line P so the set of equations has infinitely many solutions? (4 points) Question 5 options: 1) 2x + 2y = 2 2) 2x + 2y = 4 3) 2x + 2y = −2 4) x − y = 1
The equation for line P such that the system has an infinite number of solutions is given as follows:
3) 2x + 2y = -2.
How to obtain the equation?The first equation for the system of equations is given as follows:
x + y = -1.
A system of equations has an infinite number of solutions when the two equations are multiples.
Multiplying the equation by 2, we have that:
2x + 2y = -2.
Meaning that equation 3 is correct.
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You are going to make a password that starts with two letters from the alphabet, followed by three digits (for example, AB-123). Digits may be numbers 0
through 9
If you are allowed to repeat letters or numbers, you can make
passwords.
If you don't repeat any letters or numbers, you can make
passwords
When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.
To create a password that starts with two letters from the alphabet, followed by three digits (for example, AB-123), you can make a different number of passwords depending on whether you are allowed to repeat letters or numbers.
1. If you are allowed to repeat letters or numbers, you can make:
- 26 (alphabet letters) x 26 (alphabet letters) x 10 (digits 0-9) x 10 (digits 0-9) x 10 (digits 0-9) = 676,000 passwords.
2. If you don't repeat any letters or numbers, you can make:
- 26 (alphabet letters) x 25 (remaining alphabet letters) x 10 (digits 0-9) x 9 (remaining digits 0-9) x 8 (remaining digits 0-9) = 468,000 passwords.
Your answer: When allowing repetition, you can make 676,000 passwords, and without repetition, you can make 468,000 passwords.
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Chelsea Menken, of Providence, Rhode Island, recently graduated with a degree in food science and now works for a major consumer foods company earning $70,000 per year with about $58,000 in take-home pay. She rents an apartment for $1,100 per month. While in school, she accumulated about $38,000 in student loan debt on which she pays $385 per month. During her last fall semester in school, she had an internship in a city about 100 miles from her campus. She used her credit card for her extra expenses and has a current debt on the account of $8,000. She has been making the minimum payment on the account of about $240 a month. She has assets of $14,000. Calculate Chelsea’s debt-to-income ratio. Comment on Chelsea’s debt situation and her use of student loans and credit cards while in college
1. Chelsea Menken's debt-to-income ratio is 35.7%.
2. Her debt situation is concerning because she accumulated significant student loan debt and credit card debt.
What is Chelsea debt-to-income ratio?The debt-to-income ratio means percentage of gross monthly income that goes to paying your monthly debt payments
Her total monthly debt payments is:
= $385 (Student loans) + $240 (Credit card) + $1,100 (Rent)
= $1,725.
Her total monthly income after taxes is:
= $58,000 / 12 months
= $4,833.33 per month.
The debt-to-income ratio will be:
= Total monthly debt payments / Monthly income after taxes
= $1,725 / $4,833.33
= 0.357
= 35.7%.
Her debt situation is concerning, so, it important for to develop a plan to pay off the debts in order to avoid accruing more interest and damaging her credit score.
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3) Graph polygon G(-3,-2) R(-4,4) E(0,1) A(1, -2) T(-1, -3) and it’s image G’R’E’A’T’=R (GREAT)
A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:
(x, y) → (-y, x)
Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)
Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)
Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)
Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)
Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)
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suppose you are playing poker with a non-standard deck of cards. the deck has 5 suits, each of which contains 12 values (so the deck has 60 cards total). how many 6-card hands are there, where you have at least one card from each suit?
The number of 6-card hands in which at least one card from each suit is equal to 8,184,220.
Total number of 6-card hands that can be formed from a deck of 60 cards is,
Using combination formula,
C(60, 6) = 50,063,860
Now, subtract the number of 6-card hands that do not contain at least one card from each suit.
There are 5 ways to choose the suit that will be missing from the hand.
Once this suit is chosen, there are 48 cards remaining in the other suits.
Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suit is,
C(48, 6) = 12,271,512
Overcounted the number of hands that are missing more than one suit.
There are C(5, 2) ways to choose 2 suits that will be missing from the hand.
Once these suits are chosen, there are 36 cards remaining in the other 3 suits.
Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suits is,
C(36, 6) = 1,947,792
We cannot have a 6-card hand that is missing more than 2 suits.
3 suits with no cards in the hand, which is not allowed.
Number of 6-card hands that have at least one card from each suit is,
C(60, 6) - 5×C(48, 6) + C(5, 2)×C(36, 6)
=50,063,860 - 5× 12,271,512 + 10 × 1,947,792
= 50,063,860 -61,357,560 + 19,477,920
= 8,184,220
Therefore, there are 8,184,220 of 6-card hands that have at least one card from each suit.
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Claire flips a coin 4 times. Using the table, what is the probability that the coin will show tails at least once?
2.
Number of Tails
Probability
0
0. 06
1
0. 25
3
0. 25
4
0. 06
?
O 0. 06
O 0. 25
0. 69
O 0. 94
Mark this and return
Save and Exit
Next
Sunmit
The probability that the coin will show tails at least once is 0.56.
To find the probability that the coin will show tails at least once, you can sum the probabilities of getting 1, 3, or 4 tails, as shown in the table:
Probability of 1 tail: 0.25
Probability of 3 tails: 0.25
Probability of 4 tails: 0.06
Now, add these probabilities together:
0.25 + 0.25 + 0.06 = 0.56
So, the probability that the coin will show tails at least once is 0.56.
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The population P of an organism
is growing exponentially. Select all
the functions that could represent
the population.
A. P = 400(0.85)t
B. P = 2(1.35)t
C. P = 10(1.15)t
D. P = 215(0.95)t
E. P = 75(2.85)t
F. P = 900(0.05)t
Answer: B, C and E
Step-by-step explanation: the term growing means the value is increasing, and a number multiplied by 1 gives the same number; therefore in order for that number to increase, it need to be multiplied by a bigger number which is greater than 1, in this case it can not be a number less than 0 like 0.85, so all the number which are greater than 1 in the bracket are correct.
the number before the bracket is the population before increasing, so you can substitute any value for t and try out different outcomes, you will get only B, C and E as number greater than the original number
Ive been stuck on this one question for a long time can someone help me learn how to solve this?
The calculated value of x is 8 and the perimeter is 80 units
Calculating the value of x and the perimeterFrom the question, we have the following parameters that can be used in our computation:
The figure
If the lines that appear to be tangent are tangent, then we have the following equation
x = 26 - 18
Evaluate the like terms
x = 8
The perimeter is the sum of the side lengths
So, we have
Perimeter = 26 + 18 + 14 + 14 + x
This gives
Perimeter = 26 + 18 + 14 + 14 + 8
Evaluate
Perimeter = 80
Hence, the perimeter is 80 units
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What is the sum of 2 / 10 + 6/100 not simplified
Answer: 26/100 OR 0.26 (I would put the answer as a fraction)
Step-by-step explanation:
We need both fractions to have the same denominator before we add them. The denominator of 6/100 is 100. The denominator of 2/10 is 10. We need to turn 10 into 100. To do that, we can do 10*10. This gives us 100. However what we do to the bottom must be done to the top therefore we have 20/100 + 6/100
Now the two fractions can be added together. 20/100 + 6/100 = 26/100.
Normally we would simplify this down to 13/50 but if you want it unsimplified 26/100 would be your answer.
Solve for x Trigonometry
The size of the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
For the given triangle;
sin X = 3/5 {opposite/hypotenuse}
X = sin⁻¹(3/5) {cross multiplication}
X = 36.8699°
Therefore, the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine
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The ratio of an objects weight on earth to its weight on the moon is 6:1 the first person to walk on the moon was neil armstrong. he weighed 165 pounds on earth. what would be the proportion of this word problem?
The proportion of this word problem is 6 : 1 where Neil Armstrong weighed approximately 27.5 pounds on the moon.
The proportion of a word problem represents the relationship between two or more quantities. In this case, the proportion can be set up as:
Weight on Earth : Weight on Moon = 6 : 1
Using the information provided in the problem, we know that Neil Armstrong weighed 165 pounds on Earth. We can use this information to find his weight on the moon by setting up a proportion:
165 : x = 6 : 1
where x represents his weight on the moon. To solve for x, we can cross-multiply and simplify:
165 * 1 = 6 * x
x = 165/6
x ≈ 27.5
Therefore, Neil Armstrong weighed approximately 27.5 pounds on the moon.
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Identify the volume of the composite figure. The figure shows a rectangular prism with a cube removed. The prism is 9 meters long, 8 meters wide, and 3 meters high. The cube has a side of 4 meters
The volume of the composite figure is 152 m³.
How to solve for the volume of the shapeThe volume of a rectangular prism can be found using the formula V = lwh, where l is the length, w is the width, and h is the height.
For the rectangular prism:
V_prism = lwh = 9m * 8m * 3m = 216 m³
For the cube:
V_cube = s^3 = 4m * 4m * 4m = 64 m³
Now, subtract the volume of the cube from the volume of the prism:
V_composite = V_prism - V_cube = 216 m³ - 64 m³ = 152 m³
The volume of the composite figure is 152 m³.
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Quadrilateral ABCD is a square with diagonals AC and BD. If A(4, 9) and C(3, 2), find the slope of BD.
7 is the slope of BD in Quadrilateral.
What in arithmetic is a quadrilateral?
Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional form. Concave and convex are the two most common forms. Additionally, there are several subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.
There are four closed sides to a quadrilateral. Quadrilaterals are the following figures: produced by Raphael. a quadrilateral form. The form features a single pair of parallel sides and no right angles.
points A(4, 9) and C(3, 2)
slope = y₂ - y₁/x₂ - x₁
= 2 - 9/3 - 4
= - 7/-1
= 7
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Are △abc and △def similar triangles? choose all that apply.
no, the corresponding sides are not proportional.
yes, the corresponding sides are proportional.
yes, the corresponding angles are all congruent.
no, the corresponding angles are not congruent.
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△ABC and △DEF are similar triangles if they have corresponding sides that are proportional and the corresponding angles are all congruent. Thus, the options that are applied are B and C.
Similar shapes are enlargements or shortening of other shapes using a scale factor.
Two triangles are said to be similar if the corresponding sides are proportional and the corresponding angles are the same. There are the following similarity criteria:
1. AA or AAA where all the angles are equal
2. SSS where all the sides are proportional to the corresponding sides
3. SAS where the corresponding sides and the angle between are proportional and congruent.
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A fractal is a geometric figure that has similar characteristics at all levels of
magnification. One example of a fractal is Koch's (sounds like "Cokes")
snowflake. To build this fractal, start with an equilateral triangle whose sides
each have length 1. Then on the middle of each side, create a triangular
"bump" to make a new figure having 12 sides. On the middle of each of
these 12 sides, create a smaller bump, and so on. The upper part of the
illustration shows the first four stages in the construction of a Koch's
snowflake. The "real" snowflake is the result of carrying on this process
forever!
The lower part of the illustration shows how, when a bump is added to any
side, the ležgth you have is multiplied by If a bump is added to every side
of a snowflake figure, then the entire perimeter is multiplied by
The perimeter of Koch's snowflake fractal will be infinite.
Find out how Koch's snowflake fractal is created by adding triangular bumps to the side of an equilateral triangle?Koch's snowflake fractal is created by adding triangular bumps to the sides of an equilateral triangle at progressively smaller scales. At each stage, the number of sides of the resulting figure increases by a factor of 4, and the perimeter of the figure increases as well.
To see how the perimeter changes as bumps are added to all sides of the figure, we can use the fact that each bump adds a segment of length 1/3 to the original side. So if we start with a triangle of side length 1 and add a bump to each side, the new perimeter is:
P = 3(1 + 1/3) = 4
Now we have a figure with 12 sides. If we add a bump to each of these sides, the new perimeter is:
P = 12(1 + 1/3 + 1/9) = 16/3
In the next stage, we have 48 sides, and each side has a length of 1/3^2, so the new perimeter is:
P = 48(1 + 1/3 + 1/9 + 1/27) = 64/3
At each stage, we can see that the perimeter is multiplied by a factor of 4/3. So if we carry on this process forever, the perimeter of Koch's snowflake fractal will be infinite.
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which graph represents the linear equation y= 1/2 x + 2
Answer:
The graph on the top right
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
The equation is y = 1/2x + 2
The y-intercept in this equation is 2, meaning the graph has a point (0,2) on it. Looking at the options, the only graph that has a point (0,2) is the map on the top right, and that is the answer.
1. Does the graph below represent a function? Explain how you know.
Q1
A. Yes; the graph is linear.
B. No; the graph does not pass the vertical line test.
C. Yes; the graph passes the vertical line test.
D. No; the graph intersects the x and y axis.
p.s i might fail and retake 7th grade
C. Yes; the graph passes the vertical line test.
How does the graph below represent a function?The correct answer is C. Yes; the graph passes the vertical line test.
To determine whether a graph represents a function, we apply the vertical line test. The vertical line test states that for a graph to represent a function, no vertical line should intersect the graph in more than one point.
In this case, the graph passes the vertical line test if each vertical line crosses the graph at most once. If this condition is satisfied, then each x-value corresponds to a unique y-value, indicating that the graph represents a function.
Since the question states that the graph passes the vertical line test, we can conclude that it represents a function.
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