Isaiah's total earnings after picking 10 baskets of apples and peaches each is: $117
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
We are told that Isaiah as already earned $24 picking apples and $18 picking peaches.
Amount for each basket of apple = $3 each
Amount for each basket of Peach = $4.5 each
Thus, for 10 baskets each:
Apples = 10 * 3 = $30
a = 24 + 30
a = $54
Peaches = 10 * 4.5 = $45
p = 18 + 45
p = $63
Total earnings = a + p
= $54 + $63
= $117
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Complete question is:
Isaiah picks fruit at a local orchard. He has already earned $24 picking apples and $18 picking peaches. He earns $3 for each basket of apples and $4.50 for each basket of peaches picked.
Isaiah wants to compute his total earnings after picking 10 baskets of each fruit.
Complete the equations and find Isaiah's total earnings. Enter your answers in the boxes.
Apples: 10 x ____ = ____
24+ ___ = a
Peaches: 10 x ____ =
18+____= p
Total: a+p=$ ___
One of the byproducts of nuclear power generation is Uranium-233. Uranium is decaying at a constant 32% rate per day. If 12,880 pounds are produced from a power plant, what will the amount be in 20 days?
Answer:
The amount of Uranium-233 produced after 20 days will be approximately 65.1 pounds.
Step-by-step explanation:
Solve the following for θ, in radians, where 0≤θ<2π.
4sin2(θ)+7sin(θ)−5=0
Select all that apply:
2.57
1.37
1.05
2.35
0.58
1.88
Answer:θ ≈ 2.57 radians
θ ≈ 0.58 radians
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:
4sin^2(θ) + 7sin(θ) - 5 = 0
(4sin(θ) - 1)(sin(θ) + 5) = 0
Therefore, either:
4sin(θ) - 1 = 0
sin(θ) = 1/4
or:
sin(θ) + 5 = 0
sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)
So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:
θ = arcsin(1/4)
Using a calculator, we find:
θ ≈ 0.2531 or θ ≈ 2.8887
Therefore, in radians, the solutions for θ are approximately:
0.2531 (which is less than 2π)
2.8887 (which is greater than 2π)
So the only answer that satisfies 0 ≤ θ < 2π is:
whats the improper fraction 17/9 as a mixed number
The improper fraction 17/9 as a mixed number is A = 1 8/9
Given data ,
Let the mixed number be represented as A
Now , the improper fraction is n = 17/9
On simplifying , we get
The improper fraction 17/9 can be converted to a mixed number by dividing the numerator (17) by the denominator (9) and expressing the quotient as a whole number and a proper fraction.
So , A = 1 8/9
Hence , the mixed number is A = 1 8/9
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what 7 coins make 82 cents
Answer:
1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
Step-by-step explanation:
One possible set of 7 coins that make 82 cents is:
1 quarter (25 cents)
2 dimes (10 cents each)
1 nickel (5 cents)
3 pennies (1 cent each)
Adding up the values of these coins:
25 + 10 + 10 + 5 + 1 + 1 + 1 = 82
Therefore, a set of 1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.
Which of the following functions has the largest value when x = 3 (1 point)?
c(x) = 3x2 + 5x + 22
j(x) = 12x
a(x) = 9x
Group of answer choices
All the functions are equal at x = 3.
c(x)
j(x)
a(x)
Answer:
x = 3
c(x) = 3x² + 5x + 22
⇒ c(3) = 3(3²) + 5(3) + 22
⇒ c(3) = 3(9) + 15 + 22
⇒ c(3) = 27 + 15 + 22
⇒ c(3) = 64
j(x) = 12x
⇒ j(3) = 12(3)
⇒ j(3) = 36
a(x) = 9x
⇒ a(3) = 9(3)
⇒ a(3) = 27
c(x) = 3x² + 5x + 22 is the function that has the largest value when x = 3.
False. Not all functions are equal at x = 3.
A small box in the shape of a cube for packaging has a volume of 216 cubic inches.
(a) For a medium box, the length, width, and height are all tripled. What is the ratio of the sides, area of
the bases, and volumes of the boxes? Show your work.
(b) What is the volume of a medium box? Show your work.
The ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1 and the volume of the medium box is 5832 cubic inches.
Let's denote the side length of the small cube as "s". Since it is a cube, all sides are equal.
Given that the volume of the small box is 216 cubic inches, we can set up the equation;
Volume of small box = s³ = 216
Taking the cube root of both sides, we get;
s = ∛216 = 6 inches
So, the side length of the small cube is 6 inches.
For the medium box, the length, width, and height are all tripled, so the new side length of the medium cube is 3 times the side length of the small cube:
Side length of medium cube = 3s = 3 × 6 = 18 inches
Now, let's calculate the ratio of the sides, area of the bases, and volumes of the small and medium boxes;
Ratio of sides: Side length of medium cube / Side length of small cube = 18 / 6 = 3
Ratio of area of bases: (Side length of medium cube)² / (Side length of small cube)² = (18)² / (6)² = 9
Ratio of volumes: (Volume of medium box) / (Volume of small box) = (Side length of medium cube)³ / (Side length of small cube)³ = (18)³ / (6)³ = 27
So, the ratio of the sides of the medium box to the small box is 3:1, the ratio of the area of the bases is 9:1, and the ratio of the volumes is 27:1.
The volume of the medium box is given by;
Volume of medium box = (Side length of medium cube)³ = 18³
= 5832 cubic inches
Therefore, the volume of the medium box is 5832 cubic inches.
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Jessica is buying several bunches of bananas to make desserts for a fundraiser. She can buy 10 pounds of bananas for $14.90 or 8 pounds of bananas for $12.08.
Part A
How much does each pound of bananas cost in each case?
Drag the tile with the cost of each pound to the correct box.
Each tile may be used once or not at all.
Cost of Each Pound
$1.21 $1.49 $1.51 $1.86 10 pounds for $14.90
8 pounds for $12.08
Part B
Use the information in Part A to choose the better buy.
The
choose:
-10 punds
-8 pounds
of bananas is the better buy because
choose:
-$1.49
-$1.86
-$1.51
-$1.21
is the cheaper price per pound.
Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.
The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.
We have,
Part A:
To find the cost of each pound of bananas in each case,
We can use the unit rate.
- For 10 pounds of bananas at $14.90, the cost per pound is:
$14.90 ÷ 10 pounds
= $1.49 per pound
- For 8 pounds of bananas at $12.08, the cost per pound is:
$12.08 ÷ 8 pounds
= $1.51 per pound
Part B:
The better buy is the one with the lower cost per pound.
Since $1.49 is less than $1.51, the 10-pound package is the better buy.
The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.
Therefore,
Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.
The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.
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1 point
Find the area of the following composite figures, round your answer to the nearest tenth:
Line AD = 6
Line DC = 6
Line AB - 20
Type your answer...
The area of the following composite figures is 78 square units.
How the area is computed:The area of the square is computed as 36 (length x width) or 2(Length).
The area of the triangle is computed as (base x height) ÷ 2.
The areas of the composite figures are added to determine the total area.
Line AD = 6
Line DC = 6
Line AB = 20
Base of the triangle = 14 (20 - 6)
Area of triangle = (h x b) ÷ 2
= (6 x 14) ÷ 2
= 42
Area of square portion = 36 (6 x 6)
Total area = 78 square units
Thus, we can conclude that the area of the composite figures are 78 square units.
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A group of student athletes were asked which organized sport they participate in. Each athlete participates in exactly 1 sport. The results are shown in this frequency table. How many baseball and basketball players are there? Enter your answer in the box. players
14
6
9
8
12
10
12 baseball and 9 basketball players are there. The frequency of a value in the data is its occurrence.
One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table. The frequency of a value in the data is its occurrence. We can immediately see how frequently each value appears in a table. 12 baseball and 9 basketball players are there.
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Solve the following for θ, in radians, where 0≤θ<2π.
−sin2(θ)−2sin(θ)+1=0
Select all that apply:
0.75
2.5
2.71
0.95
0.43
2.04
Answer:2.71
0.43 are correct
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
-u^2 - 2u + 1 = 0
Multiplying both sides by -1, we get:
u^2 + 2u - 1 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 2, and c = -1. Substituting these values, we get:
u = (-2 ± sqrt(4 + 4)) / 2
u = (-2 ± 2sqrt(2)) / 2
Therefore, either:
ASAP!!!
Arthur cuts a 24° slice from a pizza 22 inches in diameter. Find the length of AB.
(See attached photo)
The length of AB is 4.6 inches.
What is the length of an arc?An arc is a part of a circle i.e. an incomplete circle. It can be either a major arc or a minor arc of a given circle.
The length of an arc can be determined by;
length of an arc = (θ/ 360)*2πr
Where r is the radius of the circle, and θ is the measure of its central angle.
In the given diagram, the arc AB is a minor arc. So that;
AB = (θ/ 360)*2πr
r = d/2
= 22/2
r = 11 inches
AB = (24/ 360)*2*3.14*11
= 4.6053
AB = 4.6 inches
The length of arc AB is 4.6 inches.
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128 3 мы - 5 20 14 ) 448 320 (20X14) 128 80 (5х16) 48 -48 (3 XI) vaku С
2y+3y-18=-83?????????????
The table of values below represent an exponential function. Write an exponential equation that models the data. x y -2 26 -1 18.2 0 12.74 1 8.918 2 6.2426 a. y = 18.2 (1.7) Superscript x c. y = 26 (0.7) Superscript x b. y = 12.74 (1.3) Superscript x d. y = 12.74 (0.7) Superscript x
An exponential equation of the function that models the data given is y = 12.74 (0.7)ˣ.
Given a table of values that represent an exponential function.
An exponential equation is of the form,
y = a (b)ˣ
When x = 0, y = 12.74
12.74 = a (b)⁰
12.74 = a [since b⁰ = 1]
So a = 12.74
When x = 1, y = 8.918
Substituting,
12.74 b = 8.918
b = 8.918 / 12.74
b = 0.7
Hence the equation is option D) y = 12.74 (0.7)ˣ.
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Find the area of a triangle with base of
inches and a height of
inches.
A
100100100 square inches
B
505050 square inches
C
252525 square inches
D
12.512.512.5 square inches
The area of the triangle with base of 5 inches and a height of 10 inches is 25 square inches. The correct answer is C.
The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base, and h is the height. Using this formula, we can calculate the area of the triangle in question.
Given that the base of the triangle is 5 inches and the height is 10 inches, we can plug these values into the formula and solve for A:
A = 1/2 * b * h
A = 1/2 * 5 * 10
A = 25
Therefore, correct answer is C.
The height of a triangle is the perpendicular distance between the base and the opposite vertex. The base is the side of the triangle on which the height is measured.
By multiplying the base and the height and dividing the result by 2, we can find the area of a triangle. This formula works for all types of triangles, regardless of their size or shape.
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Complete question is:
Find the area of a triangle with base of 5 inches and a height of 10 inches.
A 100 square inches
B 50 square inches
C 25 square inches
D 12.5 square inches
Find the equation for the tangent plane to the surface z=8x^2-9y^2 at the point (2,1,23)
The equation of tangent plane to the surfacez = 8x² - 9y² at the point (2,1,23) is 32(x - 2) - 18(y - 1) -1(z - 23) = 0
Here, the equation of the surface is
z = 8x² - 9y²
Let us assume that f(x, y, z) = 8x² - 9y² - z
The partial derivative of f(x, y, z) would be:
[tex]\frac{\partial f}{\partial x}[/tex] = 16x
[tex]\frac{\partial f}{\partial y}[/tex] = -18y
[tex]\frac{\partial f}{\partial z}[/tex] = -1
At point (2, 1, 23) the partial derivative of f(x, y, z),
[tex]\frac{\partial f}{\partial x}[/tex] = 32
[tex]\frac{\partial f}{\partial y}[/tex] = -18
[tex]\frac{\partial f}{\partial z}[/tex] = -1
So, the equation of tangent plane would be,
32(x - 2) - 18(y - 1) -1(z - 23) = 0
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Use the change of base formula to express log subscript9 6 using In, the natural logarithm.
Step-by-step explanation:
there is the general rule of logarithms :
loga(x) = logb(x)/logb(a)
for any a and b.
so,
log9(6) = ln(6)/ln(9)
Larry Sergio Katrina Jim Ian Tyrone Maria and Sarah are invited to a dinner party.
The number of ways they can is 40,320.
The number of ways Larry can arrive first and Sarah can arrive last is 720.
The probability that Larry arrives first and Sarah arrives last is 0.01786.
We have,
a)
Since each person can arrive at any time, the number of ways they can arrive is equal to the number of permutations of 8 people, which is:
= 8!
= 40,320
b)
To calculate the number of ways Larry can arrive first and Sarah can arrive last, we can fix their positions and then permute the remaining 6 people in the middle.
= 1 x 6! x 1
= 720
c)
To find the probability that Larry arrives first and Sarah arrives last, we need to divide the number of ways they can arrive in the desired order (720) by the total number of ways they can arrive (40,320):
= P(Larry first and Sarah last)
= 720 / 40,320
= 0.01786
So the probability is approximately 0.01786, or about 1.8%.
Thus,
The number of ways they can is 40,320.
The number of ways Larry can arrive first and Sarah can arrive last is 720.
The probability that Larry arrives first and Sarah arrives last is 0.01786.
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What is the solution to 3+x=x+3
Answer:
all real numbers
Step-by-step explanation:
if you subtract x from both sides, you get x=x. This is true for basically any number
Use the mapping shown above to show the value of the function ƒ(x) at each point.
The value of the function ƒ(x) at each point is ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21, the correct option is B.
We are given that;
f(-1)=5 f(0) = 3 f(1) = 5 f(2) = 11 f(3) = 21
Now,
The function ƒ(x) maps each value of x to a corresponding value of y. For example, when x = –1, y = 5, so ƒ(–1) = 5. Similarly, when x = 0, y = 3, so ƒ(0) = 3, and so on. The other options are incorrect because they either reverse the order of x and y, or they do not match the values given in the mapping.
Therefore, by the given domain and range the answer will be ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21.
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The complete question is;
Use the mapping shown above to show the value of the function ƒ(x) at each point. Question options: A) ƒ(1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21B) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 11, ƒ(3) = 21C) ƒ(–1) = 5, ƒ(0) = 3, ƒ(1) = 5, ƒ(2) = 21, ƒ(3) = 11D) ƒ(5) = –1, ƒ(3) = 0, ƒ(5) = 1, ƒ(11) = 2, ƒ(21) = 3.
Nour wants to go on a popular talent TV show. In order to be accepted, her audition must get at least
60
%
60%60, percent positive votes from the people in the crowd.
To make sure she’s not going to embarrass herself, she performed her act in front of
100
100100 random people from her school. About
90
%
90%90, percent of the people said they would give her a positive vote. She calculated the margin of error and found it’s well within the range above
60
%
60%60, percent, so she decided to go and audition
1. The objective of Nour's study is to sample the population to see if there is a correlation between her performance and the audience response.
2. No, because the population she sampled isn't necessarily representative
What is population sample?A population sample is a subgroup of people drawn from a broader population for the purpose of a study.
A population sample is often chosen such that it is a representative of the greater population. Populaton sample should consider factors such as age, gender, income, or level of education.
The answer provided is based on the full question below;
Nour wants to go on a popular TV talent show. In order to be accepted, her audition must get at least 60% positive votes from people in the crowd.
To make sure she's not going to embarrass herself, she performed her act in front of 100 random people from her school. About 90% of the people said they would give her a positive vote. She calculated the margin of error and found it's well within the range above 60%, so she decided to go to the audition.
What is the objective of Nour's study?
Is the study appropriate for the statistical questions it's supposed to answer?
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I need explanation for example 8.
Thankyou
There is a probability of 94/315 that the problem will be solved.
We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.
The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.
The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.
The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.
The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.
To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:
2/7 + 4/7 + 4/9 = 94/315
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I don't get it, pls help!!
The circumference of the circle is 75.4 cm.
What is the circumference of the circle?The circumference of the circle is calculated from the radius of the circle.
Considering the equilateral triangle, each of the interior angle is 60⁰, a line passing the center of any of this angle, divides it into two with each angle 30⁰.
Considering the right triangle inside the equilateral triangle, the hypothenuse is equal to the radius of the circle.
The radius of the circle is calculated as follows;
sin (30) = opp/hypo
sin (30) = 6 cm/r
r = 6 cm / sin (30)
r = 12 cm
The circumference of the circle is calculated as follows;
C = 2πr
C = 2π x (12 cm)
C = 75.4 cm
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Elijah can spend up to $23 on groceries. He wants to buy 3 pounds of tomatoes, 4 pounds of oranges, and x pounds
of lean ground beef. The tomatoes cost $1.35 per pound, the oranges $1.65 per pound, and the ground beef $4.94
per pound. Write an inequality that represents the possible number of pounds of ground beef, x, he can buy. Find
the value of x.
A. 1.35 x 3 +
B. 1.35 x 3 +
1.65 x 4 +
1.65 x 4 +
c.
1.35 x 3 + 1.65 x 4 +
D. 1.35 x 3 + 1.65 x 4 +
4.94x < 23; x<25
4.94x ≤ 23; x ≤ 25
4.94x >
23; x > 25
4.94x ≥
23;x ≥ 25
Answer1.35+ 4:
Step-by-step explanation:
1. On July 15, Piper Company sold $17,000 of merchandise (costing $8,500) for cash. The sales tax rate is 5%. On August 1, Piper sent the sales tax collected from the sale to the government.
2. On November 3, the Milwaukee Bucks sold a six-game pack of advance tickets for $510 cash. On November 20, the Bucks played the first game of the six-game pack (this represented one-sixth of the advance ticket sales).
1. Record entries for the July 15 and August 1 transactions.
2. Record the entries for the November 3 and November 20 transactions.
The table is attached.
A journal entry is used to record financial transactions of the business operations in a company's accounting records.
The journal entries of Piper Co. is recorded below:
The table for the journal entries is attached below for a clear understanding of the narration.
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I need help with math!!!
Please answer this question (picture is provided with question) I just need to find the area.
The value of area of the figure is,
⇒ 10√10 units²
We have to given that;
To find the area of figure.
Here, We have to find length of AD and AB for area of figure.
Coordinate of A = (- 2, 2)
Coordinate of B = (- 4, -4)
Coordinate of D = (3, 2)
Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, Length of AD;
AD = √ (-2 - 3)² + (2 - 2)²
AD = √25
AD = 5
Length of AB;
AB = √ (- 2 + 4)² + (2 + 4)²
AB = √4 + 36
AB = √40
AB = 2√10
Thus, The value of area of the figure is,
⇒ AD x AB
⇒ 5 × 2√10
⇒ 10√10
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Find the value of f (-1).
The value of f (-1) by virtue of the given absolute value function graph as required is; 8.
What is the value of the function instance f (-1)?It follows from the task content that the value of the function instance; f (-1) is required to be determined.
On this note, the value of the function instance can be determined as the point of intersection of the line; x = -1 with the given graph.
Ultimately, the value of the instance f (-1) is; 8.
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Ryan spends 10 hours at work each day.
He has a hour lunch and receives two
hour breaks. How much time does Ryan
spend working?
4
Answer: 7
Step-by-step explanation: he spends 7 hours a day take 3 away from 10.
Write a function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4.
y =
A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8
To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:
y = A sin [(2π/P)(x - C)] + D
where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:
y = A sin [(2π/8)(x + 2)] + D
Simplifying the equation, we get:
y = A sin (π/4 x + π/2) + D
To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:
4 + D ≤ -4 and -4 + D ≥ -12
Solving these inequalities, we get:
-8 ≤ D ≤ 0
Therefore, a function that satisfies the given conditions is:
y = 4 sin (π/4 x + π/2) - 8
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How do you find the p value of -0.24?
The p-value is a probability value for test that measures the strength of evidence against a null hypothesis.
It is a number between 0 and 1 and is typically compared to a significance level (such as 0.05) to determine whether to reject or fail to reject the null hypothesis.
However, a p-value cannot be calculated from a single number like -0.24 alone. A p-value is typically calculated using statistical tests, such as a t-test or ANOVA, which require more information about the data, such as the sample size, mean, and standard deviation.
Therefore, to find the p-value for a specific hypothesis test, you would need to perform a statistical test on the relevant data using appropriate statistical software or formula, and the resulting p-value will be specific to that test and the data analyzed.
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