Answer: To find the value of the car after 8 years, we can use the given information to create a linear equation in the form:
y - y1 = m(x - x1)
Where:
y is the value of the car after 8 years (what we want to find)
y1 is the value of the car after a given time (either 3 or 5 years)
x is the given time (either 3 or 5 years)
x1 is the starting time (when the car was purchased)
m is the rate of decrease (slope of the line)
We can use the two given data points to find the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (11,000 - 15,000) / (5 - 3)
m = -2,000 per year
Now, we can use one of the data points to solve for the y-intercept of the line:
y - y1 = m(x - x1)
y - 15,000 = (-2,000)(3 - x1)
y - 15,000 = (-2,000)(3 - x1)
y - 15,000 = (-6,000 + 2,000x1)
y = 2,000x1 - 6,000 + 15,000
y = 2,000x1 + 9,000
So the linear equation that represents the value of the car after x years is:
y - 15,000 = (-2,000)(x - 3)
Simplifying this equation gives:
y - 15,000 = -2,000x + 6,000
Now, we can use x = 8 to find the value of y:
y - 15,000 = -2,000(8) + 6,000
y - 15,000 = -2,000
y = $13,000
Therefore, the value of the car after 8 years will be $13,000.
So the completed expression is:
y - 15,000 = -2,000(x - 3)
The value of the car after 8 years will be $13,000.
Step-by-step explanation:
My question is in the form of a picture see attached below.
A semicircle rotated around its axis gives sphere, rectangle rotated around its axis gives sphere . and a right triangle rotated around its axis gives sphere
what is rectangle?
A rectangle is a four-sided flat shape with straight sides and four right angles. It is a type of parallelogram, with opposite sides equal in length and parallel to each other. The area of a rectangle can be calculated by multiplying its length and width, while its perimeter can be found by adding the lengths of all four sides.
In the given question,
A semicircle rotated around its axis gives sphere,
A rectangle rotated around its axis gives sphere .
A right triangle rotated around its axis gives sphere
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I need help with math AGAIN
8 goes into 70, 8 times with a remainder of 6.
What is remainder?
In general, if we want to divide a number by another number, say a by b, we want to find out how many times b goes into a, and what the remainder is. We can represent this as:
a = b × q + r
where:
a: the dividend
b: the divisor
q: the quotient (how many times b goes into a)
r: the remainder (what is left over after we divide as many times as possible)
Now, let's apply this to the specific problem:
We want to divide 70 by 8, so we can write:
70 = 8 × q + r
We want to find out what q and r are.
To find q, we can start with the largest multiple of 8 that is less than or equal to 70, which is 64 (8 times 8). We can see that 8 goes into 64 exactly 8 times:
64 = 8 × 8 + 0
So q = 8.
To find r, we can subtract 64 from 70:
70 - 64 = 6
So the remainder is 6.
Putting it all together, we have:
70 = 8 × 8 + 6
So 8 goes into 70 8 times with a remainder of 6.
What is dividend?
In division, the dividend is the number that is being divided into equal parts or groups. It is the number that appears before the division symbol. For example, in the division problem 12 ÷ 3 = 4, 12 is the dividend.
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Complete question is: 8 goes into 70, 8 times with a remainder of 6.
"3. Select all the relationships that demonstrate a negative association between variables.
• Miles you drive and the amount of gas in your tank.
• The number of miles you ran over time.
2 Craine.e The level of water in a water tank being drained over time.
wiver da The speed of a train at a constant speed over the next 6 hours. heigh. Number of cups in a stack and the stack height.
Answer(s):
- miles you drive and the amount of gas in your tank
- the level of water in a water tank being drained over time
Step-by-step explanation:
1. The more miles that you drive, the less gas that is in your tank, so this one has a negative association between its variables.
2. The more time you spend running, the more miles you'll have ran, so that's a positive association, not a negative association.
3. The longer a water tank is drained, the less water it'll have in it, so this one has a negative association between its variables.
4. The speed of a train at a constant speed over the next 6 hours can be modeled by a graph with a horizontal line (which has a slope of zero), representing that as the x increases, the y does not change, so there is not a negative association between the variables.
5. The more cups in the stack, the taller it will be, so that's a positive association, not a negative association.
A marine biologist would like to estimate the mean weight of all mahi mahi on the Treasure Coast, using a
90% confidence interval. The standard deviation of the weights of all mahi mahi on the Treasure Coast is
known to be 7.6 pounds. How large a sample of mahi mahi should the marine biologist select so that the
estimate is within 1.48 pounds of the true population mean. Round the solution up to the nearest whole
number.
n=
The marine biologist should select a sample of 38 mahi mahi to estimate the population means within 1.48 pounds with 90% confidence.
What is the sample size?To determine the sample size needed for estimating the population mean within a certain margin of error with a 90% confidence level, we can use the following formula:
n = (z*(σ/√n))/E
where:
z = the z-score corresponding to the desired confidence level (in this case, 1.645 for 90%)
σ = the population standard deviation (7.6 pounds)
E = the desired margin of error (1.48 pounds)
n = the sample size
Substituting the given values, we get:
n = (1.645*(7.6/√n))/1.48
Simplifying
n = 3.841n/3.501
n = 1.097n
n ≈ 37.8
Rounding up to the nearest whole number, we get:
n = 38
Therefore, the marine biologist should select a sample of 38 mahi mahi to estimate the population means within 1.48 pounds with 90% confidence.
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Each free throw in a game of basketball is worth 1 point and each field goal is worth 2 points. George's team scores a total of 16 points. They make a free throws and y field goals.
Answer: 4 free throws and 6 field goals
Step-by-step explanation:
4x1=4
6x2=12
12+4=16
Answer:
4 free throws and 6 field goals
Step-by-step explanation:
FINDING UNKNOWN ANGLE MEASURES-SUPPLEMENTARY ANGLES--#6
The measure of angle B is indeed 70°, and the two angles are Supplementary
Step 1: Understand supplementary angles
Supplementary angles are two angles whose sum equals 180 degrees. In other words, if two angles are supplementary, then their measures add up to 180°.
Step 2: Set up the equation
Let's say you have two supplementary angles, angle A and angle B. You know the measure of angle A, but you need to find the measure of angle B. To do this, you can set up the following equation:
angle A + angle B = 180°
Step 3: Insert the known angle measure
Since you know the measure of angle A, you can insert its value into the equation. For example, if angle A measures 110°, the equation would be:
110° + angle B = 180°
Step 4: Solve for the unknown angle
Now, you can solve the equation to find the measure of angle B. Using the example above:
110° + angle B = 180°
Subtract 110° from both sides:
angle B = 70°
Step 5: Verify your answer
To make sure your answer is correct, you can add the measures of angle A and angle B together. If they equal 180°, then your answer is correct. In this example:
110° + 70° = 180°
So, the measure of angle B is indeed 70°, and the two angles are supplementary.
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Determine how many real solutions the quadratic equation has:
a. one
b. can't be determined
c. zero
d. two
real solutions or roots or zeros from a graphic standpoint, are simply the x-intercepts, because that's what a zero or root is, nothing but an x-intercept, hmm well, from the picture above, how many times does the graph touch the x-axis? hell, is really above it, it never touches it, so it doesn't have any real solutions.
(3) Find the area.
Uptoko
3 in
6 in
3 in
Answer: A = 18 in²
Step-by-step explanation:
To find the area, we will use this formula:
A = LW
➜ A = Area
➜ L = Length
➜ W = Width
We will substitute known values and solve by multiplying.
A = LW
A = (6 in)(3 in)
A = 18 in²
a rectangular prism has volume $12$ cubic inches. a triangular pyramid is cut off the cube as shown in the diagram. what is the volume of the remaining piece in cubic inches?
Once the dimensions of the triangular pyramid are provided, we can perform these calculations to find the volume of the remaining piece in cubic inches.
To determine the volume of the remaining piece, we need to find the volume of the triangular pyramid that was cut off and then subtract it from the original volume of the rectangular prism.
Here are the steps:
Step 1: Determine the volume of the rectangular prism.
The student question already provides this information: 12 cubic inches.
Step 2: Determine the volume of the triangular pyramid.
In order to do this, we need the base area and the height of the pyramid.
However, the diagram is not provided in the question. Please provide the dimensions of the base and height of the triangular pyramid.
Step 3: Calculate the volume of the triangular pyramid using the formula:
Volume = (1/3) × Base area × Height
Step 4: Subtract the volume of the triangular pyramid from the volume of the rectangular prism to find the volume of the remaining piece:
Remaining Volume = Volume of Rectangular Prism - Volume of Triangular Pyramid.
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for halloween, bernie bought a jumbo bag of jolly lollipops. cherry is the most popular flavor, and about 25% of the lollipops are cherry flavored. when the first group of trick-or-treaters arrives, bernie opens the bag and pulls out 3 lollipops. how likely is it that all of the lollipops are cherry flavored? which simulation could be used to fairly represent the situation?
The probability of pulling out three cherry-flavored lollipops from a bag where 25% of the lollipops are cherry-flavored is very low at only about 1.5625%.
If 25% of the lollipops are cherry flavored, then the probability that any one lollipop is cherry flavored is 0.25. Since Bernie pulls out 3 lollipops, the probability that all of them are cherry flavored is:
0.25 x 0.25 x 0.25 = 0.015625 or 1.5625%
So the probability that all three lollipops are cherry flavored is very low, only about 1.5625%.
As for which simulation could be used to fairly represent the situation, one possible approach is to create a virtual bag of lollipops with 25% cherry flavored ones and randomly draw 3 lollipops from the bag multiple times to simulate the process.
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I NEED HELP ON THIS ASAP!!!
The deli sold a total of 80 sandwiches. How many salami sandwiches were sold?
4
16
64
20
Using percentages, we can find that out of the 80 sandwiches sold 16 were salami sandwiches.
Option B is correct.
Define percentage?The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100."
Here, the total number of sandwiches sold = 80.
In the chart we can see that out of 80 sold sandwiches, 205 of the sandwiches were salami.
So, 20% of 80
= 20/100 × 80
= 1600/100
= 16.
Therefore, 16 salami sandwiches were sold out of the 80.
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The complete question is:
The deli sold a total of 80 sandwiches. How many salami sandwiches were sold?
4
16
64
20
Whats the equation if the circle if it's centered at (4,7) with a radius of 5
Answer:
Answer: (x + 2.5)² + (y + 4.4)² = 49/16.
Step-by-step explanation:
need today its the deadline is tom
Answer:
1. a. [tex]\frac{2}{13}[/tex]
2. c. [tex]\frac{3}{6}[/tex]
3. d. [tex]\frac{1}{10}[/tex]
4. b. [tex]\frac{1}{8}[/tex]
Hope it helps you!
Please help I need these differential equations done by today and cannot do it.
the particular solution to the given differential equation with the initial condition [tex]y(pi)=-5[/tex] is: [tex]y = -2 + [(3sec^2(x)-1)/3][/tex]
What is the differential equation?To find the particular solution to the given differential equation with the initial condition, we can use the method of separation of variables and integrate both sides with respect to x.
Starting with the given differential equation:
[tex]dy/dx = sec^2(x)(2+y)^2[/tex]
We can separate variables and write:
[tex](2+y)^(-2)dy = sec^2(x)dx[/tex]
Integrating both sides, we have:
[tex](2+y)^(-1) = tan(x) + C[/tex]
where C is an arbitrary constant of integration.
To find the value of C, we can use the initial condition y(pi)=-5:
[tex](2+(-5))^(-1) = tan(pi) + C[/tex]
[tex](2-5)^(-1) = 0 + C[/tex]
[tex]C = -1/3[/tex]
Substituting this value of C back into the general solution we obtained earlier, we get:
[tex](2+y)^(-1) = tan(x) - 1/3[/tex]
Multiplying both sides by [tex](2+y)[/tex] , we can solve for y:
[tex]y = -2 ± [(3sec^2(x)-1)/3][/tex]
Therefore, the particular solution to the given differential equation with the initial condition [tex]y(pi)=-5[/tex] is: [tex]y = -2 + [(3sec^2(x)-1)/3][/tex]
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Which of the following proportions is false
12/15 = 20/25
25/45 = 50/90
20/50 = 40/100
18/48 = 30/50
Answer:
The proportion that is false is 18/48 = 30/50.
Step-by-step explanation:
To determine which of the given proportions is false, rewrite the fractions on both sides each equation so that the denominators are the same.
[tex]\dfrac{12}{15}=\dfrac{20}{25} \implies \dfrac{12 \div 3}{15 \div 3}=\dfrac{20 \div 5}{25 \div 5}\implies \dfrac{4}{5}=\dfrac{4}{5}\qquad \boxed{\sf True}[/tex]
[tex]\dfrac{25}{45}=\dfrac{50}{90} \implies \dfrac{25 \div 5}{45\div 5}=\dfrac{50\div 10}{90\div 10}\implies \dfrac{5}{9}=\dfrac{5}{9}\qquad \boxed{\sf True}[/tex]
[tex]\dfrac{20}{50}=\dfrac{40}{100} \implies \dfrac{20\div 10}{50\div 10}=\dfrac{40\div20}{100\div 20}\implies \dfrac{2}{5}=\dfrac{2}{5}\qquad \boxed{\sf True}[/tex]
[tex]\dfrac{18}{48}=\dfrac{30}{50} \implies \dfrac{18\times 25}{48\times 25}=\dfrac{30\times 24}{50 \times24}\implies \dfrac{450}{1200}= \dfrac{720}{1200}\qquad \boxed{\sf False}[/tex]
Therefore, the proportion that is false is 18/48 = 30/50.
The value of the 3 in 140,395 is how many times the value of the 3 in 241,638 ?
Answer:
100
Step-by-step explanation:
30 x 100 = 300
Helping in the name of Jesus.
8. if our slope is 3 and our intercept is 14, how many months would a convict with 11 priors expect to receive ?
Answer:47
Step-by-step explanation:
Try it
Proving the Parallelogram Side Theorem
Given: ABCD is a parallelogram.
Prove: AB CD and BC = DA
A
□
Hint
Angles Segments Triangles Statements Reasons
ASA
CPCTC
reflexive property
given
Statements
✓ 3. BC || DA
4. draw AC
✔✓ 5. AC AC
SE
6. BCA and DAC
are alt. interior angles
7.
DAC
✓8. ZDCA and
are alt. interior angles/
DCA
✓9.
Reasons
3. def. of parallelogram
4. unique line postulate
5. reflexive property
6. def. of alt. interior angles
7. alternate interior angles theorem
8. def. of alt. interior angles
9. alternate interior angles theorem
Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.
What is parallelogram?A parallelogram is a four-sided polygon (a flat, closed shape) with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles of a parallelogram are also equal. Parallelograms can have different shapes and orientations, but they always have these defining properties of parallel sides and equal opposite angles and sides. Examples of shapes that are parallelograms include rectangles, squares, and rhombuses.
Given: ABCD is a parallelogram.
Draw diagonal AC.
1. By definition of a parallelogram, BC || DA.
2. By the Unique Line Postulate, there is exactly one line through A that is parallel to BC.
3. By the Reflexive Property of Congruence, AC is congruent to itself.
4. By the definition of alternate interior angles, angle BCA is congruent to angle DAC.
5. By the Alternate Interior Angles Theorem, angle DAC is congruent to angle ZDCA.
6. By the definition of alternate interior angles, angle DCA is congruent to angle ZDCA.
7. By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle CDA.
8. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), AB is congruent to CD and BC is congruent to DA.
Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.
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amy shoots 9 arrows at a target. each arrow hits the target (independently) with probability 0.6. if exactly 6 arrows hit the target, what is the probability that 6 specified arrows hit the target?
The probability that 6 specified arrows hit the target is 0.321.
Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say whether it will happen or not. The result often has good applications in sports, and business as a result of forecasting, and the result is also widely used in the field of new intelligence.
Given that:
She shoot 9 arrows,
the probability of each arrow being fitted 0.6.
Therefore,
The probability that 6 specified arrows hit the target is:
(⁸₄) ×(0.6)⁶ ×(0.4)⁶ = 0.321
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what is the consequence of a type ii error? group of answer choices concluding that a treatment has an effect when it really does concluding that a treatment has an effect when it really has no effect concluding that a treatment has no effect when it really does concluding that a treatment has no effect when it really has no effect
The consequence of a type II error can be conclude that option (c) has no effect when it really does concluding that a treatment
A Type II error is a statistical error that occurs when a null hypothesis is not rejected when it should be. Specifically, it is when a researcher concludes that there is no effect of a treatment when there actually is one. This error can have serious consequences, as it may result in missed opportunities to implement effective treatments or interventions.
To minimize the likelihood of Type II errors, researchers can increase the sample size or adjust the statistical significance level of the test. Overall, it is important to be aware of the potential for Type II errors and to take steps to minimize their occurrence.
Therefore, the correct option is (c) has no effect when it really does concluding that a treatment
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The given question is incomplete, the complete question is:
what is the consequence of a type ii error? group of answer choices concluding that a treatment
a) has an effect when it really does concluding that a treatment b) has an effect when it really has no effect concluding that a treatment c) has no effect when it really does concluding that a treatment d) has no effect when it really has no effect
Examine the plot below showing the decrease of a thirty-year loan balance over time. After how many years will the loan be half-paid? A. 15 years B. 18 years C. 21 years D. 24 years
Answer: b. 18
Mark me brainliest
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the inequality and describe the solution set. y – 6 ≥ 12
The solution of the given linear inequality will be y ≥ 18.
What are linear inequalities, exactly?
Linear inequalities are mathematical expressions that involve linear functions and the symbols "<", ">", "<=", ">=", or "≠". They are used to describe a range of possible values that a variable can take.
For example, the inequality 3x + 2 > 10 is a linear inequality, where x is a variable. It means that the possible values of x that satisfy the inequality are those that make the expression 3x + 2 greater than 10. The solution set for this inequality is x > 2.
Now,
To solve the inequality y - 6 ≥ 12, we need to isolate y on one side of the inequality sign. We can do this by adding 6 to both sides of the inequality:
y - 6 + 6 ≥ 12 + 6
Simplifying the left side, we get:
y ≥ 18
So the solution set for this inequality is all values of y that are greater than or equal to 18. We can represent this graphically on a number line by shading all values to the right of and including 18:
---|================================>
18
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‼️WILL MARK BRAINLIEST‼️
Answer:
4.The median coast for beach parking is $35: This means that half of the beach parking costs are below $35 and half of them are above $35.
5. The IQR of weights of dishes of frozen yogurt is 3.5 ounces: This means that the middle 50% of weights of dishes of frozen yogurt fall within a range of 3.5 ounces.
6.The mean weight for an adult loggerhead sea turtle is 275 pounds: This means that the average weight of an adult loggerhead sea turtle is 275 pounds.
7. The range of the length of adult manatees was 5 feet: This means that the difference between the maximum and minimum lengths of adult manatees is 5 feet.
What is the value of (x-5)(x+2) when it is equal to 0
When (x-5)(x+2) is equal to 0, the value of x can be either 5 or -2.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
If (x-5)(x+2) is equal to 0, then either (x-5) = 0 or (x+2) = 0, because the product of two factors is equal to 0 only when at least one of them is equal to 0. Therefore, we have:
x - 5 = 0 or x + 2 = 0
Solving these equations for x, we get:
x = 5 or x = -2
Therefore, when (x-5)(x+2) is equal to 0, the value of x can be either 5 or -2.
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what is P?(less than 7?)
According to the given figure number of possible outcome is 2 and total number of outcome is 4 therefore the probability of an event P(e) less than 7 would be ½.
There are a total of 4 numbers so the No total outcome would be 4.
No of possible outcome = 2 (as there are only two numbers less than 2)
Probability of event, P(e) = no of possible outcome / No of total outcome
This,
P(less than 7) = 2/4
P(less than 7) = ½
Hence The probability of an event P(e) less than 7 would be ½.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will learn the potential outcomes for a random experiment using this fundamental theorem of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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convert 17pi/9 to degrees
Answer:
Step-by-step explanation:
pi = 180°
[tex]\frac{17*180}{9} = \frac{3060}{9}= 340[/tex]
the shape of a rectangle has an area of 1/5 square mile. the length of the field 1/2 mile. what is the width of the field.
Answer: 1/10
1/5 divided by 1/2 = 0.1 = 1/10
when the positive integers are arranged in order, filling in the successive diagonals of an infinite grid from top to bottom, as shown, the integer $41$ is in the $(5, 5)$ spot. what integer would we see in the $(10, 10)$ spot if the rest of the grid were visible?
To fill in the successive diagonals of the infinite grid, we start with $1$ in the $(1,1)$ spot. The second diagonal starts with $2$ in the $(1,2)$ spot and $3$ in the $(2,1)$ spot.
The third diagonal starts with $4$ in the $(1,3)$ spot, $5$ in the $(2,2)$ spot, and $6$ in the $(3,1)$ spot. And so on. Since $41$ is in the $(5,5)$ spot, it means it is the $41$st integer to be filled in the diagonals of the grid. To find the integer in the $(10,10)$ spot, we need to count $9$ diagonals that come before the diagonal that contains $(10,10)$.
Each diagonal contains one more integer than the previous diagonal. So, the $n$th diagonal contains $n$ integers.Therefore, the $10$th diagonal contains $10$ integers, starting with the integer in the $(1,10)$ spot and ending with the integer in the $(10,1)$ spot.
The integer in the $(10,10)$ spot is the last integer in the $10$th diagonal, which is $10+9+8+7+6+5+4+3+2+1 = \boxed{55}$.
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Based on climate data that have been collected in Bar Harbor, Maine, the average monthly
temperature, in degrees F, can be modeled by the equation
B(x)= 23.914 sin(0.508x-2.116) + 55.300. The same governmental agency collected average
monthly temperature data for Phoenix, Arizona, and found the temperatures could be
modeled by the equation P(x) = 20.238 sin(0.525x-2.148) + 86.729. Which statement can not
be concluded based on the average monthly temperature models x months after starting data
collection?
The statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."
Describe Equation?Equations can be simple or complex, and they can involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Equations can also be represented graphically using curves or surfaces.
We can compare the two given temperature models to make conclusions about the average monthly temperature variations in Bar Harbor and Phoenix.
First, let's compare the midline temperatures:
Midline temperature for Bar Harbor = 55.300 degrees F
Midline temperature for Phoenix = 86.729 degrees F
Since the midline temperature for Phoenix is higher than that of Bar Harbor, we can conclude that statement 2 cannot be concluded.
Next, let's compare the amplitude of the temperature variations:
Amplitude of temperature variation in Bar Harbor = 23.914 degrees F
Amplitude of temperature variation in Phoenix = 20.238 degrees F
Since the amplitude of temperature variation in Bar Harbor is greater than that of Phoenix, we can conclude that statement 1 is true.
Finally, let's use the temperature models to find the maximum and minimum temperatures:
Maximum temperature in Bar Harbor = 23.914 sin(0.508x-2.116)+55.300
To find the maximum temperature, we need to find the maximum value of the sine function, which is 1. Therefore, the maximum temperature occurs when:
0.508x-2.116 = 90 degrees
Solving for x, we get:
x = (90 + 2.116)/0.508 = 177.066
Plugging this value into the temperature model, we get:
Maximum temperature in Bar Harbor = 23.914 sin(0.508(177.066)-2.116)+55.300 = 78.986 degrees F
Therefore, statement 3 is false.
Minimum temperature in Phoenix = 20.238 sin(0.525x-2.148) + 86.729
To find the minimum temperature, we need to find the minimum value of the sine function, which is -1. Therefore, the minimum temperature occurs when:
0.525x-2.148 = 270 degrees
Solving for x, we get:
x = (270 + 2.148)/0.525 = 517.657
Plugging this value into the temperature model, we get:
Minimum temperature in Phoenix = 20.238 sin(0.525(517.657)-2.148) + 86.729 = 65.983 degrees F
Therefore, statement 4 is false.
Therefore, the statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."
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Statement 2: "The midline average monthly climate for Bar Harbor is less than the midline temperature for Phoenix," cannot be proven based on the provided temperature models.
Describe Equation?In addition to variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, equations can be simple or complex. Equations can also be graphically represented using surfaces or curves.
To draw conclusions regarding the average monthly temperature variations in Bar Harbor and Phoenix, we can compare the two provided temperature models.
Let's start by contrasting the midline temperatures:
Midline temperature for Bar Harbor = 55.300 degrees F
Phoenix's midline temperature = 86.729 degrees F
We can infer from the fact that Phoenix's median temperature is greater than Bar Harbor's that assertion 2 cannot be drawn.
Let's compare the temperature variations' amplitude next:
Bar Harbor's temperature variations' severity = 23.914 degrees F
The intensity of Phoenix's temperature variations = 20.238 degrees F
We can infer that assertion 1 is accurate since the amplitude of temperature change in Bar Harbor is bigger than that in Phoenix.
Let's use the temperature models to determine the highest and lowest temperatures.
Bar Harbor's highest temperature is equal to 23.914 sin (0.508x-2.116) + 55.300.
We need to determine the sine function's maximum value, which is 1, in order to determine the maximum temperature. Consequently, the highest temperature is reached when:
0.508x-2.116 = 90 degrees
Solving for x, we get:
x = (90 + 2.116)/0.508 = 177.066
When this value is entered into the temperature model, we obtain:
Bar Harbor's highest temperature record
= 23.914 sin(0.508(177.066)-2.116)+55.300
= 78.986 degrees F
Therefore, statement 3 is false.
Phoenix's low temperature = 20.238 sin(0.525x-2.148) + 86.729
We need to determine the sine function's minimal value, which is -1, in order to determine the minimum temperature. Consequently, the lowest temperature is reached when:
0.525x-2.148 = 270 degrees
Solving for x, we get:
x = (270 + 2.148)/0.525 = 517.657
When this value is entered into the temperature model, we obtain:
Phoenix's low temperature
= 20.238 sin(0.525(517.657)-2.148) + 86.729
= 65.983 degrees F
Therefore, statement 4 is false.
Statement 2: "The midline average month climate for Bar Harbor is lower than the midline temperature for Phoenix," cannot be proved based on the provided temperature models.
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