Answer:
350
Step-by-step explanation:
Using the proportion from part (a):
14/n = 20/500
Cross-multiplying, we get:
20n = 14 × 500
Dividing both sides by 20, we get:
n = 14 × 500 / 20 = 350
Therefore, about 350 seventh graders participate in the contest.
Convert the Cartesian equation 2 xy = 1 in polar equation form.
The Cartesian equation 2xy = 1 has the following polar equation r²·sen2θ = 1.
To convert the Cartesian equation 2xy = 1 into polar equation form, we need to use the relationships between Cartesian coordinates and polar coordinates. The relationships are as follows:
x = r cos θy = r sin θSubstituting these relations in the Cartesian equation, we proceed to solve:
2 (r·cosθ)(r·sinθ) = 1
2r²·cosθ·sinθ = 1
r²·(2cosθ·sinθ) = 1
r²·sen2θ = 1
In conclusion, the polar equation has the following form: r²·sen2θ = 1.
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Pizzazz Pizza is selling pizzas during lunch time at a festival. From 10:00 to 2:00 they served a steady stream of
customers, selling approximately 376 pizzas during the shift. Tomorrow they are also serving dinner, from 5:00 -
7:00. If sales continue at the same rate, how many pizzas will they sell TOTAL for both days?
Answer:
Step-by-step explanation:
So if they sell approximately 376 pizzas the first shift and then the same amount for the second, all you have to do is add 376 by 367 or multiply by 2 because adding the same number twice is like multiplying the number by 2.
Answer: 564
Step-by-step explanation: From 10-2 they sell 376 pizzas. So, in 4 hours they sell 376 pizzas, and they sell 94 pizzas per hour, because 376/4 is 94. So from 5-7, 2 hours, they should sell 94 times 2 pizzas, which is 188 pizzas. So 188+376 is 564.
Answer the question for lots of points
The angle of depression from an airplane to the top of an air traffic control tower is 56°. If the tower is 320 feet tall and the the airplane is flying at an altitude of 7,450 feet, how far away is the airplane from the control tower? Round to the nearest tenth.
Find the angle of depression from the top of a lighthouse 275 feet above water to a boat 1,324 feet off shore. Round to the nearest whole number.
Answer:
1) 7995.9 feet
2) 12 degrees
Step-by-step explanation:
1)
We can start by drawing a diagram of the situation. Let's label the height of the tower as "h", the distance from the airplane to the tower as "d", and the angle of depression as 56°.
C (top of tower)
/|
/ |
/ |h
/ |
/θ |
A_____/_____|
d B
In this diagram, point A represents the airplane, point B represents the base of the tower, and point C represents the top of the tower. The angle θ is the angle of depression from the airplane to the top of the tower.
We can use trigonometry to solve for the distance "d" from the airplane to the tower. In particular, we know that:
tan(θ) = h / d
We can rearrange this equation to solve for "d":
d = h / tan(θ)
Substituting the values we know, we get:
d = 320 / tan(56°)
Using a calculator, we can evaluate this to get:
d ≈ 215.8 feet
However, the airplane is flying at an altitude of 7,450 feet, so we need to add this to the height of the tower to get the total distance from the airplane to the ground:
total distance = d + 320 + 7,450
Plugging in the value we found for "d", we get:
total distance ≈ 7995.8 feet
Rounding to the nearest tenth, we get:
total distance ≈ 7995.8 ≈ 7995.9 feet
2)
We can use the tangent function to find the angle of depression. Let theta be the angle of depression. Then:
tan(theta) = (275 / 1324)
We can solve for theta by taking the inverse tangent (or arctan) of both sides:
theta = arctan(275 / 1324)
Using a calculator, we find:
theta ≈ 11.92 degrees
Rounding to the nearest whole number, we get:
The angle of depression is approximately 12 degrees.
Help please…………………………………..
Answer:
35
Step-by-step explanation:
DUDE JUST PLUG IN THE NUMBER.
[tex]x^4 -3x^3 + x -3\\(-2)^4 - 3(-2)^3 + (-2) -3\\16 + 24 -2 - 3\\35[/tex]
2.) Emmanuel is at a sporting goods store. The store
offers a 9% discount on all items. At checkout a 6%
sales tax is added to the discounted price. Select the
two that apply.
A. $25 pants cost $24.12 at checkout
B. $89 cleats cost $76.50 at checkout
C. A $29 basketball costs $37.97 at checkout.
D. $189 glove costs $183.33 at checkout
Circle � ′ A ′ A, prime is the result of rotating circle � AA by 18 0 ∘ 180 ∘ 180, degrees about point � PP. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. Select all of the correct statements about the unchanged properties of circle � AA and circle � ′ A ′ A, prime. Choose all answers that apply: Choose all answers that apply: (Choice A) A Circle � AA and circle � ′ A ′ A, prime have the same circumference. (Choice B) B The radii of circle � AA and circle � ′ A ′ A, prime have the same lengths. (Choice C) C Points � AA and � ′ A ′ A, prime are both on the � xx-axis. (Choice D) D None of the above
Circle A and circle A' have the same circumference and the radii of circle A and circle A' have the same lengths. Therefore, options A and B are the correct answers.
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, circle A' is the result of rotating circle A by 180° about point P.
When we rotate any object its shape and size does not change, only its position changes.
Therefore, options A and B are the correct answers.
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Find the measure of angle B
Equation form
The measure of the angle B in the triangle is 51.34 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.
The angle of a right triangle can be found using trigonometric ratios as follows:
tan B = opposite / adjacent
tan B = 25 / 20
B = tan⁻¹ 5 / 4
B = tan⁻¹ 1.25
B = 51.3401917459
Therefore,
B = 51.34 degrees
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Which four statements that are true?
y=e" and y = ln x are inverses.
are not equivalent.
In een
In(x) = log. (x)
ln e = 1
In (x) = log10 (x)
In e = 10
In(e) and en both equal x.
The statements are:
y=e" and y = ln x are inverses.
This is false. The inverse of y = e^x is y = ln x, and the inverse of y = ln x is y = e^x. So, the two functions y = e^x and y = ln x are inverses of each other, but y = e^x and y = e^ln x are not.
In een In(x) = log. (x)
This is false. The statement should be: e^ln(x) = x, which is true by the definition of logarithms.
ln e = 1
This is true. The natural logarithm of e is 1.
In (x) = log10 (x)
This is false. The statement should be: log10(x) = log(x) / log(10).
In e = 10
This is false. The natural logarithm of e is 1.
In(e) and en both equal x.
This is false. In(e) = 1, and e^n = x does not necessarily imply that In(e) = x.
5) After surveying a sample of high school teachers, Enrique concluded that
adults like to eat dinner at The Bistro more than other restaurants in town.
Terry disagreed with Enrique's conclusion, saying that Enrique's population
was too specific for such a broad question. Which question would have
been more appropriate for Enrique's survey of high school teachers?
The question that would be more appropriate for Enrique's survey of high school teachers is Among high school teachers, what is the most popular restaurant to eat dinner at in town?
The appropriate question for Enrique's survey of high school teachersEnrique's conclusion about adults liking to eat dinner at The Bistro more than other restaurants in town may not be accurate since his survey was only limited to high school teachers.
To make his conclusion more reliable, Enrique could have asked a more specific question that is relevant to high school teachers. Here are a few examples of more appropriate questions for Enrique's survey of high school teachers:
Among high school teachers, what is the most popular restaurant to eat dinner at in town?
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Samantha has two anthills in her yard. The first anthill has 982 ants. The second PLEASE HELP QUICKLY // anthill has one and one-third the amount of ants of the first hill. Which statement correctly compares the two anthills?
The first anthill is one and one-third times as many than the second anthill.
The first anthill is equal in size to the second anthill.
The second anthill is one and one-third times as many than the first anthill.
The second anthill is one and one-third times fewer ants than the first anthill.
The statement that correctly compares the two anthills is "the second anthill is one and one-third times as many ants as the first anthill."
Which statement correctly compares the two anthills?From the question, we have the following parameters that can be used in our computation:
The first anthill has 982 antsThe second anthill has one and one-third the amount of ants of the first hillUsing the above as a guide, we have the following:
First = 982
Second = 1 1/3 * First
This means that "the second anthill is one and one-third times as many ants as the first anthill."
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Brianna surveyed a representative sample of students at her school to collect data about the numbers of Internet-compatible devices they own. Use the data in the table. Select all the valid inferences.
Internet-Compatible Devices
Number of Devices Number of Students
1 18
2 25
3 or more 7
Students are more likely to own exactly 2 devices than any other number.
More students own 3 devices than own more than 3 devices.
Less than half as many students own 3 or more devices as compared to students who own 1 device.
10 more students own 1 device than own 3 or more devices.
None of the students own exactly 5 devices.
The statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Students are more likely to own exactly 2 devices than any other number is
true because the number of students own exactly 2 devices is greater than the other categories.
Less than half as many students own 3 or more devices as compared to students who own 1 device is true because 18 students own 1 device, the half of them is 9, and the number of students own 3 or more devices is 7 which is less than 9.
About 10 more students own 1 device than own 3 or more devices is true because the difference between students own 1 device and those own 3 or more devices = 18 - 7 = 11 which is about 10 more.
Hence, the statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.
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n the metric system, each millimeter increment is equal to _____.A. 1/1000 of a centimeterB. 1/100 of a centimeterC. 1/10 of a centimeterD. 10 centimeters
The answer is C. 1/10 of a centimeter.
Situation:
A geologist in South America discovers a
bird skeleton that contains 61% of its
original amount of C-14.
N = Noe-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
Transcribed image text: Situation: Find the age of the bird skeleton to the nearest A geologist in South America discovers a bird skeleton that contains 74% of its original amount of C-14. Enter the correct answer. N-Noekt No-inital amount of C.14 (at time t 0) N amount of C-14 at time t k 0.000 t time, in years.
a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points, M=$3,509.71. loan b: 390,000, 15 year-fixed, 0 discount points, M=3,659.86. how much does the hole buyer save in total by choosing loan A? a) 27,027 b) 11,427 c) 26,351.02 d) 42,627.05
The amount the the home buyer saves in total by choosing Loan A is most closest to $11,427. The Option B is correct.
How much does the buyer save by choosing Loan A?In order to compare the total cost of each loan, we need to consider both the monthly payment and the discount points.
For Loan A, we have Loan amount: $390,000, Loan term: 15 years, Discount points: 4 and Monthly payment: $3,509.71. For Loan B, we have Loan amount: $390,000, Loan term: 15 years Discount points: 0 and Monthly payment: $3,659.86.
The total cost of Loan A is the sum of the discounted upfront cost (discount points) and the total of all monthly payments over the life of the loan:
= (4% of $390,000) + ($3,509.71 x 180)
= $15,600 + $631,948.80
= $647,548.80
The total cost of Loan B is the total of all monthly payments over the life of the loan:
= ($3,659.86 x 180)
= $658,574.80
Now, the amount saved by choosing Loan A over Loan B is the difference between their total costs which equals:
= Total cost of Loan B - Total cost of Loan A
= $658,574.80 - $647,548.80
= $11,026
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Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given a scatter plot in terms of the time the player spent practicing and the number of points he scored in the game.
A scatter plot uses dots to represent values for two different numeric variables.
The position of each dot on the horizontal and vertical axis indicates values for an individual data point.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
3,203 cm2
2,295 cm2
1,020 cm2
731 cm2
Answer:
2,295 cm2
Step-by-step explanation:
Answer:
(b) 2295 cm²
Step-by-step explanation:
You want the area of icing on a cake 13 cm high and 17 cm in radius.
Icing areaThe area of the top is ...
A = πr²
The area of the side is ...
A = 2πrh
Then the total area of icing on the cake is ...
πr² +2πrh = πr(r +2h)
= 3.14(17 cm)(17 cm + 2·13 cm) = 2295.34 cm²
The area of icing needed for the cake is about 2295 cm².
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What is interval of increase and decrease
Interval of increase and decrease refers to a period of time in which a quantity rises or falls. For example, a stock market index may have an interval of increase and decrease over a certain period, such as a month or a year.
Interval of increase and decrease is a term used to describe a period during which a certain quantity either increases or decreases. This phenomenon is commonly seen in financial markets, such as the stock market, where indices may go up and down over a certain period of time. This interval of increase and decrease can be measured using different measures such as time, percentage growth, and movement. This interval helps investors and analysts to determine how the stock market is performing and if there are any changes in the market. It also helps them to predict future trends and make better investment decisions. During this interval, it is important to monitor the stock market and any changes that may occur. This helps to ensure that investments are made with the best possible outcome.
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Amy has a job that pays according to the function P(h) = 9.5h. If Amy is only allowed to work
40 hours per week, what are the domain and range of the function P?
Answer:
well in 9.5 40 you have to multiply which is 40 times 9.5h
solve for x,
3x+10
3x+2
If the numerator of a fraction is multiplied by 4 and the denominator is reduced by 2,the result is 4. If the numerator of the fraction is increased by 15 and 2 subtracted from the double of the denominator, the result is 5/4. Find the fraction.
Answer:
To solve this problem, we need to start by setting up an equation. The equation should express the fact that the result of the two operations on the fractions is both 4 and 5/4.
We can do this by writing:
4x/(x-2) = 4
5x/2(x-2) = 5/4
Solving for x, we get x=16. Therefore, the fraction we are looking for is 4/14, since 4 times 16 divided by 16 minus 2 equals 4 and 5 times 16 divided by 2 times 16 minus 2 equals 5/4.
SOH CAH TOA TRIG RATIOS
Answer:
HI: 57.4 cm; KM: 0.4 mil
Step-by-step explanation:
Question 17:
ΔGHI is a right-angled triangle
where:
Side GI = Hypotenuse
α = 55°
With respect to 55° angle:
Side HI = Adjacent side
∴Trigonometric function used: Cosα (CAH)
Cos55° = [tex]\frac{Side HI}{100cm}[/tex]
Cross-multiplication is applied:
Side HI = (Cos55°)×(100 cm)
Side HI = 57.4 cm (Rounded to 3 significant figures)
Question 18:
ΔKLM is a right-angled triangle
where:
Side KL = Hypotenuse
β = 27°
With respect to 27° angle:
Side KM = Opposite side
∴Trigonometric function used: Sinβ (SOH)
Sin27° = [tex]\frac{Side KM}{0.8 mil}[/tex]
Cross-multiplication is applied:
Side KM = (Sin27°)×(0.8 mil)
Side KM = 0.4 cm (Rounded to 1 decimal places)
Jose pays 10% of his balance each month. If Jose borrowed $5000 with no interest, how much does he still owe after 1 year?
Answer: 1,422
Step-by-step explanation:
Help please I don’t think I have any idea with what I’m doing
If the triangles are similar but no congruent, then the triangles have different size, thus the only correct option is the dilation (first option).
Which transformation is the correct one?We know that two figures are congruent if the figures have the same shape and size, while two figures are similar only if have the same shape (but the figures can have different size).
Here we know that the triangles are similar but no congruent, so the triangles must have different size. From the given transformations, the only one that changes the size is the first option, a dilation.
And for example, if we apply a dilation AND the other transformations, then we still will get a similar figure, but if we apply a reflection/rotation/translation alones, we will get a congruent triangle.
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Given the equation y = -2x + 4, complete the table.
0
1
2
3
Answer:
0: 4
1: 2
2: 0
3: -2
Step-by-step explanation:
To find out the values of 0, 1, 2 and 3 we have to substitute these numbers into the place of x
0...
y = -2(0) + 4 = 4
1...
y = -2(1) + 4 = 2
2...
y = -2(2) + 4 = 0
3...
y = -2(3) + 4 = -2
TIP:
We can see that there is a pattern of decreasing of 2 so to keep finding the following values we just have to keep subtracting 2. For any question like this, if we see a pattern to make it easier and quicker all we have to do is follow the pattern!
Hope this helps, have a lovely day! :)
Which statements correctly describe the relationships between x and y for each table? Responses Table A represents an additive relationship because y is 2.5 more than x, and Table B represents a multiplicative relationship because y is 9.2 times x. Table A represents an additive relationship because , y, is 2.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 9.2 times , x, . Both tables represent additive relationships. In Table A, y is 2.5 more than x, and in Table B, y is 8.2 more than x. Both tables represent additive relationships. In Table A, , y, is 2.5 more than , x, , and in Table B, , y, is 8.2 more than , x, . Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x. Both data sets represent multiplicative relationships. In Table A, , y, is 3.5 times , x, , and in Table B, , y, is 9.2 times , x, . Table A represents a multiplicative relationship because y is 3.5 times x, and Table B represents an additive relationship because y is 8.2 more than x.
The requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describe the relationships between x and y for each table. Option C is correct.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
In Table A, y is 2.5 more than x, and in Table B, y is 3 more than x. Both tables represent additive relationships. the requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describing the relationships between x and y for each table. Option C is correct.
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What is the volume of each hemisphere in the picture below? (Use 3.14 for)
Answer:
The answer is C.
106.0 in^3
Answer:
106.0 in^3
Step-by-step explanation:
Change 1.5 to fraction with working
Answer:
³/₂
Step-by-step explanation:
1.5 = ¹⁵/₁₀
= ³/₂
Compare and contrast the parabolas with these definitions:
parabola A: points that are the same distance from (0,4) and the x-axis
parabola B: points that are the same distance from (0, -6) and the x-axis
Parabola A and parabola B are similar in that they are both vertically oriented parabolas with the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix, which means they have different equations and open in different directions.
What are the similarity and difference of both parabolaBoth parabola A and parabola B are examples of vertically oriented parabolas that have the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix.
Parabola A has its vertex at (0, 0) and its focus at (0, 4). The directrix is the line y = -4, which is a horizontal line 4 units below the vertex. This means that any point on parabola A is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.
Parabola B has its vertex at (0, 0) and its focus at (0, -6). The directrix is the line y = 6, which is a horizontal line 6 units above the vertex. This means that any point on parabola B is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.
In terms of their equations, the equation of parabola A is y^2 = 16x, while the equation of parabola B is y^2 = -24x. Notice that parabola B has a negative coefficient of x, which means it opens to the left instead of the right like parabola A.
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Which of the following forms are best to use if we want to identify the vertex of a
quadratic equation?
Step-by-step explanation:
[tex]y = a(x - h) {}^{2} + k[/tex]
El costo de combustible por hora que un tren gasta en su recorrido es de [tex]V^2/5[/tex] pesos donde v es la velocidad en kilómetros por hora Note que el costo depende del cuadrado de la velocidad Otros costos, incluyendo el de mano de obra, son de $400 por hora. Expresa el costo total de un viaje de 500 kilómetros como una función de la velocidad v
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Distance = 500 km
Velocity = v km/h
Now,
Velocity = Distance /Time
Time = distance/velocity
= 500 / v
The total cost of the trip.
Cost = fuel cost per hour x time + other costs per hour x time
= v² x 500/v + 400 x 500/v
= 500 v + 400/v
Thus,
The total cost of the trip is a function of the velocity v is:
Cost (v) = 500v + 400/v
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The complete question.
The cost of fuel per hour that a train spends on its journey is v^2 pesos, where v is the velocity in kilometers per hour. Note that the cost depends on the square of the velocity.
Other costs, including labor, are $400 per hour.
Express the total cost of a 500-kilometer trip as a function of the velocity v.