The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.
I assume that the question is to describe or graph the equation r² - 15 = t + 19.
The given equation r² - 15 = t + 19 is the equation of a parabola with vertex at (h, k) = (0, -34) and focal length |p| = 1/4.
4p(y - k) = (x - h)² is the common equation for a parabola that faces up and down and has a vertex at (h, k) and a focal length of |p|.
Let us re-write the given equation in the standard form.
r² - 15 = t + 19
⇒ r² = t + 19 + 15
⇒ r² = t + 34
⇒ (r - 0)² = t + 34 (r can be written as r - 0)
⇒ (r - 0)² = t - (-34) (+34 is written as -(-34))
⇒ (r - 0)² = 4 × 1/4 × (t - (-34))
(4 × 1/4 is equal to 1. The given equation is unaffected by a multiplication by 1.)
⇒ 4 × 1/4 × (t - (-34)) = (r - 0)² this equation is in the standard form. And here we have |p| = 1/4 and (h, k) = (0, -34).
Refer to the attached image for the graph of this equation.
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Sometimes Zach's teammates arrive late to basketball practice. The following dot plot shows how many times each teammate was late to practice last week.
Find the mean number of times Zach's teammates were late to practice last week.
BRAINLIEST!!!!!
Answer:
3.5.
Step-by-step explanation:
Zach's teammates were late to practice last week. According to Khan Academy the answer is 3.5.
The mean number of times Zach's teammates were late to practice last week is 3.5
What is dot plot?A dot plot visually groups the number of data points in a data set based on the value of each point.
Given that, the following dot plot shows how many times each teammate was late to practice last week.
We need to find mean,
Total elements = 2 + 4 + 4 + 4 = 14
Data points = 4
Mean = 14 / 4 = 3.5
Hence, the mean number of times Zach's teammates were late to practice last week is 3.5
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Which of the following is not a step in finding the area of an unknown figure?
- Calculate the areas of the smaller figures.
- Plug all dimensions into the formula: SA=Ixwxh.
- Divide the figure into smaller, known figures.
- Add up the areas of the smaller figures.
The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B
Which is not a step in finding the area of an unknown figure?It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.
This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.
The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.
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Answer:
B) Plug all dimensions into the formula: SA=Ixwxh.
Step-by-step explanation:
Determine the equation of the parabola that opens to the right, has focus (13,-6),
and a focal diameter of 28.
The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.
To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:
\((x - h)^2 = 4p(y - k)\)
Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).
Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).
We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.
We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.
Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.
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in Lindsay's class, there were three students who scored 90 on a test and six students who scored 40 on a test. what is the mean of the scores in the class?
Answer:
((90*3)+(40*6))/9
=(90+90+90+40+40+40+40+40+40)/9
=66.66
Step-by-step explanation:
A, higher than her sisters score
6th grade math I mark as brainliest
Answer: 1/32 pounds
Step-by-step explanation:
1/4 divided by 8 = 1/32
Answer:
1/32
Explanation:
1/4 / 8 = 1/32
integrate (2x ^ 2 + x - 1)/(x - 2) dx from 1 to 2
the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.
How to solve it?
To solve this integral, we can use partial fraction decomposition. We first write:
(2x²2 + x - 1)/(x - 2) = A + B/(x - 2)
Multiplying both sides by (x - 2), we get:
2x²2 + x - 1 = A(x - 2) + B
Substituting x = 2, we get:
7A + B = 7
Substituting x = 1, we get:
-A + B = -2
Solving these equations simultaneously, we get:
A = -3 and B = 10
So we have:
(2x²2 + x - 1)/(x - 2) = -3 + 10/(x - 2)
Now we can integrate this expression:
∫[-3 + 10/(x - 2)] dx from 1 to 2
= [-3x + 10 ln|x - 2|] from 1 to 2
= [-3(2) + 10 ln|2 - 2|] - [-3(1) + 10 ln|1 - 2|]
Since ln|0| is undefined, we know that the natural logarithm term evaluates to zero. Therefore, we get:
= -6 + 3 + 0
= -3
So the value of the definite integral of (2x²2 + x - 1)/(x - 2) from 1 to 2 is -3.
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Kallie works at a pet store. Part of her job is to add the correct amount of water conditioner to each fish tank the list below provides information about the number of fish tanks and the amount of water conditioner she uses.
1: there are 12 fish tanks that need water conditioner
2: Each fish tank is filled with 20 quarts of water
3: for every 10 gallon of water, Kallie uses 1 teaspoon of water conditioner
What is the total number of teaspoons of water conditioner kallie will use for all the water in 12 fish tanks?
Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.
Here,
First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:
12 fish tanks * 20 quarts per fish tank = 240 quarts of water
To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):
240 quarts / 4 quarts per gallon = 60 gallons of water
Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:
60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner
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Please help ASAP math question
The compound amount after 3 years is $2275.22.
In this case, you are given:
Principle = $2,000
rate = 0.0353
time = 3
You need to find A, the compound amount after 3 years.
To do this, you need to plug in the values of P, r and t into the formula and use a calculator:
A=P×e^rt
A=2000×(e)^0.0353×3
A≈2275.22
Therefore, by the compound interest the answer will be $2275.22.
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3y=4x+7
-4x-4y=28
Solve the system of equations
Drag each tile to the correct box. Consider the given functions f, g, and h. x -1 0 1 2 3 4 f(x) -2 1 4 7 10 13 A graph of function g on a coordinate plane where the function intersects the Y-axis at 1 and the X-axis at minus 4. Place the tiles in order from least to greatest according to the average rate of change of the functions over the interval [0, 3]. function h function g function f , ,
Answer:
G, F, H
Step-by-step explanation:
geometric mean of 1/3 and 3
Answer:
-1 or 1
Step-by-step explanation:
^
Answer:
how many ninths are there in 9 2/3
Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 8 people, and small rooms that can hold 6 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 88 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
The number of small rooms reserved is 4.
The number of large rooms reserved is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Small rooms are denoted as S.
Large rooms are denoted as L.
Now,
We will make two equations.
L = 2S _____(1)
8L + 6S = 88 ______(2)
Putting (1) in (2) we get,
8L + 6S = 88
8 x (2S) + 6S = 88
16S + 6S = 88
22S = 88
S = 88/22
S = 8/2
S = 4
Now,
Putting S = 4 in (1) we get,
L = 2 x 4
L = 8
Thus,
The number of small rooms and large rooms reserved is 4 and 8.
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Lines MN and GH are parallel. If the measure of angle 6 is 45°, what is measure of angle 4?
Answer: It will be A that is the best answers
5.4(24 - 3.88x)
expression
What is the exact value of sin pi/3?
The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.
The exact value of sin(pi/3) can be determined using trigonometric properties and identities.
First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.
To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.
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Simplify the expression.
2+2 4+3
O 6
o 7
o 21
067
Yall help this is worth 30 points
The number of bacteria in a refrigerated food product is given by N ( T ) = 29 T 2 − 160 T + 77 , 5 < T < 35 where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 8 t + 1.2 , where t is the time in hours. Find the composite function N ( T ( t ) ) : N ( T ( t ) ) = Find the number of bacteria after 4.1 hours. Give your answer accurate to the nearest whole value. bacteria
Given:
The number of bacteria in a refrigerated food product is given by:
\(N(T)=29T^2-160T+77\)where (T) is the temperature of the food.
When the food is removed from the refrigerator, the temperature is given by:
\(T(t)=8t+1.2\)where (t) is the time in hours.
We will find the composite function N(T(t))
So, we will substitute the function (T) into the function (N):
\(N(T(t))=29(8t+1.2)^2-160(8t+1.2)+77\)Expand the function then simplify it:
\(\begin{gathered} N(T(t))=29(64t^2+19.2t+1.44)-160(8t+1.2)+77 \\ N(T(t))=1856t^2+556.8t+41.76-1280t-192+77 \\ \\ N(T(t))=1856t^2-723.2t-73.24 \end{gathered}\)So, the composite function will be:
\(N(T(t))=1,856t^{2}-723.2t-73.24\)Now, we will find the number of bacteria after 4.1 hours.
So, substitute t = 4.1 into the composite function
\(\begin{gathered} N(T(t)=1856(4.1)^2-723.2(4.1)-73.24 \\ N(T(t))=28161 \end{gathered}\)So, the answer will be:
The number of bacteria after 4.1 hours = 28161 bacteria
Rebotar Inc.makes basketballs.Their fixed costs are $3,450.
Variable costs are $12per basketball.
if the basketball is priced at $25 and 300 basketballs are sold,did Rebotar break even?How do you know?Show all work.
Answer:
Since the profit is positive, Rebotar not only broke even, they had earnings.
Step-by-step explanation:
Function Modeling
The costs, incomes, and profits of Rebotar Inc. can be modeled by means of the appropriate function according to known conditions of the market.
It's known their fixed costs are $3,450 and their variable costs are $12 per basketball produced and sold. Thus, the total cost of Rebotar is:
C(x) = 12x + 3,450
Where x is the number of basketballs sold.
It's also known each basketball is sold at $25, thus the revenue (income) function is:
R(x) = 25x
The profit function is the difference between the costs and revenue:
P(x) = 25x - (12x + 3,450)
Operating:
P(x) = 25x - 12x - 3,450
P(x) = 13x - 3,450
If x=300 basketballs are sold, the profits are:
P(300) = 13(300) - 3,450
P(300) = 3,900 - 3,450
P(300) = 450
Since the profit is positive, Rebotar not only broke even, they had earnings.
3x+(8x-16) simplest form
Step-by-step explanation:
3x × 8x- 3x×16
24x -48x
-24x
Is 83.77 an integer?
Answer:
It is not a integer, it is a rational number
Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!
Step-by-step explanation:
the three data sets show the number of text messages sent by jada, and diego, and lin over 6 days. one of the data sets has a mean of 4, one has a mean of 5, and one has a mean of 6.
1. which data set has which mean? what does this tell you about the text messages sent by the three students?
2. which data set has the greatest variabillity? Explain
1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.
2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
Question 1.
In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;
Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6
Mean number of text for Jada = 30/6
Mean number of text for Jada = 5.
Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6
Mean number of text for Diego = 36/6
Mean number of text for Diego = 6.
Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6
Mean number of text for Lin = 24/6
Mean number of text for Lin = 4.
Question 2.
In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;
Standard deviation = √(1/n × ∑(xi - u₁)²)
Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]
Standard deviation for Jada = √(6/6) = 1
Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]
Standard deviation for Diego = √(14/6) = 1.53
Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]
Standard deviation for Lin = √(76/6) = 3.6
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Solve in substitution
Kodak cut a pizza into eight equal slices and ate
three of them. If his meal had 450 calories, how
many calories were in the entire pizza?
Answer:1200 calories
Step-by-step explanation:look at pic to see how it was solved :)
Answer:
8-3=5 slice not eaten
450÷3=150 in each slice he ate
150×5=750=750 calories in entire pizza
What is the volume of a solid that is 2 cm wide, 2 cm long, and 2 cm high?
The volume of a solid with the given dimensions is 8 cm³.
The dimensions of a solid that is 2 cm wide, 2 cm long, and 2 cm high.
What is the volume of solid?The volume of a solid is the measure of how many regions of space is occupied by an object. It is measured by the number of unit cubes it takes to fill up the solid. It is decided by counting the unit cubes in the solid.
The volume of the solid can be solid using length × Width × Height.
That is, 2 × 2 × 2 = 8 cm³
Therefore, the volume of a solid with the given dimensions is 8 cm³.
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A circle of radius 16 units is divided into 8 congruent slices.
What is the arc length of each slice?
4π units
3π units
2π units
π units
Answer:
4π
Step-by-step explanation:
Circumference = π X D (D = diameter = 2 X radius).
Diameter = 32.
Circumference = π (32) = 32π.
Divided into 8 slices = 1/8 of the circumference = 32π/8 = 4π.
Keisha has her own bakery, she makes 5 pans of donuts each day. If her bakery is open 7 days a week, how many pans of donuts she makes per week?
Answer: 35 pans per week
Step-by-step explanation:
5 pans of donuts per day, 7 days a week
5 (7) = 35
35 pans per week
Answer:
The answer is 35 pans of donuts per week.
Step-by-step explanation:
5 x 7 = 35.
OR
5 + 5 + 5 + 5 + 5 + 5 + 5 = 35.
Review the image below. Based on the image, what type of transformation is
this? Be specific and detailed and explain how/why you know. Use details, correct
vocabulary and coordinates to justify your reasoning. Your answer should be in
paragraph form using complete sentences.
Answer:
When you read a sentence, you may first look for the subject or what the sentence is about. The subject usually appears at the beginning of a sentence as a noun or a pronoun. A noun is a word that identifies a person, place, thing, or idea. A pronoun is a word that replaces a noun. Common pronouns are I, he, she, it, you, they, and we. In the following sentences, the subject is underlined once.
Step-by-step explanation:
You will often read a sentence that has more than one noun or pronoun in it. You may encounter a group of words that includes a preposition with a noun or a pronoun. Prepositions connect a noun, pronoun, or verb to another word that describes or modifies that noun, pronoun, or verb. Common prepositions include in, on, under, near, by, with, and about. A group of words that begin with a preposition is called a prepositional phrase. A prepositional phrase begins with a preposition and modifies or describes a word. It cannot act as the subject of a sentence. The following circled phrases are examples of prepositional phrases.
Answer:
this is a rotation. you can tell because point Z is (-5,2) and Z' is (2,5)
Point X was (-5,7) and X' is (7,5) and Point Y was (-2, 2) and Y' is (2,2).
by looking at the picture it was rotated 90 degrees counterclockwise
Step-by-step explanation:
Jason can water all the plants at the botanical
garden in 32 minutes. Celia can water them in
25 minutes. If they work together, about how long
will it take for them to water the plants?
Answer:
If they water the plants in the garden together then it will take about 15 minutes because when they do it seperatly it takes about 30 minutes. So if they do it together, they are cutting work in half. And half of 30 is 15.
Step-by-step explanation:
32 rounded is 30.
25 rounded is 30.
30/ 2 = 15
Given P(A) = 9⁄25, P(B) = 21⁄50 and P(A ∩ Bc ) = 4⁄25. Find P(A ∩ B).
A) 0.94
B) 0.24
C) 0.21
D) 0.20
E) 0.36
F) None of the above.
un corral de vacas tiene forma de cuadrado y su perímetro es de 99 metros¿ cuál es la medida de cada uno de sus lados?