Im confused on domain and range

Hello,

The temperature changes at rate of -1.5 degree celsius every hours and the reading of temperatures starts at 0 degree celsius which can be modeled into the linear equation of f(t) = -1.5t where f(t) is the temperature function and t is time.

The problem then asks, “what was the temperature 7 hours ago?” This question asks for the temperature 7 hours ago which means t = -7 in this case since we are solving for temperature 7 hours ago, not next 7 hours.

Time being negative in this scenario means in past or hours ago, generally time cannot be negative as it’s scalar quantity.

Substitute t = -7 in the temperature function, this’ll result in:

Therefore, 7 hours ago, the temperature was at 10.5 degree celsius. Please let me know if you have any questions!

#1

y=x+5

#2

y=3/8

#3

Reflection by y axis as x will be negative and shifting 2 units right

#4

y=6x+1

#5

y=x-11

#6

y=8x

Horizontally streched by 1/8 factor

Answer:

1.  Translated 5 units left.

2.  Vertical stretch by a factor of 3/8.

3.  Reflection in the x-axis, then translated 2 units down.

4.  Vertical stretch by a factor of 6, then translated 1 unit up.

5.  Translated 11 units down.

6.  Vertical stretch by a factor of 8.

7.  Vertical stretch by a factor of 1/3, then reflection in the x-axis.

Step-by-step explanation:

Transformations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.\)

\(f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.\)

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.\)

\(a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}.\)

\(f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}.\)

\(-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}.\)

\(f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}.\)

Parent function:

\(y=x\)

\(\textsf{1.} \quad y=x+5\)

Translated 5 units left.

\(\textsf{2.} \quad y=\dfrac{3}{8}x\)

Vertical stretch by a factor of 3/8.

\(\textsf{3.} \quad y=-x-2\)

Reflection in the x-axis, then translated 2 units down.

\(\textsf{4.} \quad y=6x+1\)

Vertical stretch by a factor of 6, then translated 1 unit up.

\(\textsf{5.} \quad y=x-11\)

Translated 11 units down.

\(\textsf{6.} \quad y=8x\)

Vertical stretch by a factor of 8.

\(\textsf{7.} \quad y=-\dfrac{1}{3}x\)

Vertical stretch by a factor of 1/3, then a reflection in the x-axis.

About $684.08 billion will be spent on restaurants in 2016 if the trend continues.

The amount of money spent at restaurants in a certain country since 2004 has increased at a rate of 8% per annum. In 2004, about $280 billion was spent at restaurants.

To solve this problem, use the formula below to calculate the amount of money spent on restaurants in 2016:P = P₀ (1 + r)ⁿ

Where P is the amount spent on restaurants in 2016, P₀ is the initial amount spent in 2004, r is the rate of increase, and n is the number of years from 2004 to 2016.

We know that P₀ = $280 billion, r = 8% = 0.08, and n = 2016 - 2004 = 12.

Substituting these values into the formula:P = $280 billion (1 + 0.08)¹²P = $280 billion (1.08)¹²P = $280 billion (2.441)P ≈ $684.08 billion

Therefore, about $684.08 billion will be spent on restaurants in 2016 if the trend continues.

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b is the correct answer. Q is 3 units away from the origin along the y-axis.

Given point Q(2,3) is 2 units away from the origin along the x-axis and 3 units away from the origin along the y-axis.

a is incorrect as Q is not 2 units away from the origin along the y-axis.

b is correct as Q is 3 units away from the origin along the y-axis.

c is incorrect as Q is not 5 units away from the origin along the x-axis.

d is incorrect as Q is not 1 unit away from the origin along the x-axis.

Therefore, the correct answer is b.

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Answer:

138 cars.

Step-by-step explanation:

15 percent is .15 decimal form.

Multiply the two and add.

120*.15 is 18 120+18 is 138.

The value of the equation is A = ⁵√32,768 is A = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ⁵√32,768   be equation (1)

On simplifying the equation , we get

A = 8 x 8 x 8 x 8 x 8 = 32,768

So , the 5th root of ( 32,768 ) is 8

Therefore , the value of A = 8

Hence , the equation is A = 8

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Answer:

4 pencils

Step-by-step explanation:

Note=  pencils costing 0. 90p

Given data

Balance= £10

pen= 3*1.45= £4.35

pencils=0.90p

change= £2.05

2.05= 10-4.35-90p

solve for p

2.05= 5.65-90p

collect like terms

5.65-2.05= 0.90p

3.6=90p

divide both sides by 90

p=3.6/0.90

p=4

The matrix a is not invertible.

We can use the fact that a matrix is invertible if and only if its determinant is non-zero.

Let λ be an eigenvalue of a with corresponding eigenvector x. Then we have:

a x = λ x

Multiplying both sides by a, we get:

\(a^2\)x = λ a x

Substituting a x = λ x, we get:

\(a^2\\\) x = λ² x

Similarly, we can show that:

\(a^3\) x = λ³ x  and

\(a^4\) x = λ⁴ x

Substituting these results into the characteristic polynomial, we get:

det(a - λI) = (λ⁴+λ³+λ²+λ) = λ(λ³+λ²+λ+1)

Since the characteristic polynomial has degree 4, we know that a must have 4 eigenvalues (counting multiplicity).

Suppose a were invertible. Then all of its eigenvalues would be non-zero, and so we would have:

det(a - λI) = (λ - λ1)(λ - λ2)(λ - λ3)(λ - λ4)

where λ1, λ2, λ3, λ4 are the eigenvalues of a.

But we just saw that the characteristic polynomial has a factor of λ, so at least one of the eigenvalues must be zero. This is a contradiction, so our assumption that a is invertible must be false.

Therefore, a is not invertible.

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The probability that all coins show heads up is 1/16.

The probability of one is 1/2: Half of the time (on average, as all numbers in this answer will be) it will show heads.

Of those times it shows heads, only half of the time will the second coin also show heads. We're down to a quarter of the time now.

Of those times the second coin shows heads, only half of the time will the third coin also show heads. This is 1/8.

And, of the times the third coin also shows heads, only half of the time will the fourth coin also show heads. Half of 1/8 is 1/16.

You can simplify this by calculating (1/2)^4.

= 1/16

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Take all coins that are still on tails and keep flipping them until they land on heads. We flip 4 coins simultaneously. What is the probability that all coins show heads up?

Answer:

yes it would be

The poem For Want of a Nail is a warning about how small things can have large and unforeseen consequences. The lack of a horseshoe could lead to the loss of a horse, which could result in the loss of a rider, which could lead to the loss of a battle.

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Answer:

63,360 people

Step-by-step explanation:

the area of space =

5280 × 20 = 105,600 sq. ft

15 people occupied 25 sq ft

so, the sum of people will aoccupy the space =

105,600/25 × 15 = 63,360 people

Answer:

63,360 people

Step-by-step explanation:

5280ft × 20ft = 105600 ft²

If 15 people occupied a 25 ft² space, to find how many people occupied 105600 ft² space, divide 105600 by 25 then multiply by 15:

\(\begin{aligned}\implies \sf \dfrac{105600}{25} \times 15 & = \sf 4224 \times 15\\ &= \sf63360 \end{aligned}\)

Answer: The function that represents exponential decay is:

D. f(x) = 268(0.86)^x

This function has a base of 0.86, which is less than 1. As x increases, the value of the function decreases exponentially. This is the characteristic of exponential decay, where the value of a quantity decreases at a constant percentage rate over time.

Option A, f(x) = 0.25(1.06), represents exponential growth, as the base (1.06) is greater than 1.

Option B, f(x) = 18 + 0.9x, represents linear growth, as the value of the function increases linearly with x.

Option C, f(x) = 412 + 1.03x, also represents linear growth, as the value of the function increases linearly with x.

Step-by-step explanation:

If A is center of the circle, the radius of the circle from the given figure is Option C and D.

A circle is a geometric shape that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape. A circle comprising of all points in a plane that are at a given distance from a given point, the center. It is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The radius of a circle is the distance from the center of the circle to any point on its circumference and is usually denoted by 'R' or 'r'. Hence, in the given figure if A is center of the circle, the radius of the circle would be any distance or segment connecting the center to the circumference.

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Answer:

A. 0

General Formulas and Concepts:

Perpendicular Lines always have 1 solution.

Parallel Lines always have no solution.

Same Lines always have infinite amount of solutions.

Step-by-step explanation:

We see from the graph given that the 2 lines are parallel. Since they are parallel, they will never intersect.

Therefore, we would have no solution, or 0 solutions, as our answer.

He argues that teachers and administrators often label students based on their behavior, appearance, or other factors, which can have a profound impact on students' self-perceptions and future opportunities.

Theoretical perspectives are perspectives that sociologists use to help them better understand and explain human social behavior.

These perspectives encompass various theories and approaches to the study of education.

The following is an overview of three major theoretical perspectives and their associated classic studies of education:

Functionalism perspective

The functionalist perspective is a theoretical approach that views society as a complex system composed of various parts that work together to maintain social order.

Functionalism is also known as structural functionalism.

According to functionalists, education plays an important role in society by providing students with necessary skills and knowledge to become productive members of society.

Classic study of education:

Durkheim's study of education in "The Division of Labor in Society."

In this classic study, Durkheim argues that education serves a crucial function in socializing young people into shared cultural values, beliefs, and norms.

According to symbolic interactionists, education is a process of social interaction in which students learn to make sense of the world around them.

Classic study of education: Becker's study of labeling in "Becoming a Marijuana User.

"In this classic study, Becker demonstrates how schools play an important role in shaping student identities.

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Based on the ending balance and the various receipts and payments, the beginning balance must have been $4,418.10

The beginning balance can be found in the formula:

Ending balance = Beginning balance + Receipts - Withdrawals

Solving would give:

5,191.63 = Beginning + 1,584.52 deposit + 3.24 earned - 789.23 checks - 25 fee

5,191.63 = Beginning + 773.01

Beginning = 5,191.63 - 773.01

= $4,418.10

In conclusion, the balance was $4,418.10

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Answer:

Step-by-step explanation:

Since we are to construct the fence around the park, to determine the length of the fence, we will find the perimeter of the rectangular car park.

Perimeter of the car park = 2(Length  + Width)

Given

Width of car park = 12m

Length of the car park = 34 m

Substituting the given data into the formula;

Perimeter of the park = 2(12+34)

Perimeter of the park = 2(46)

Perimeter of the park = 92m

Hence the length of fence that should be ordered to guarantee that there will be enough to surround the car park is 92m

QQTv = 0.

When we multiply QQT by qi, which belongs to the subspace spanned by 91, 92, ..., 9m, the result will be qi itself. Hence, QQTqi = qi.

QQT is a projector, specifically an orthoprojector.

a) To show that QQTv = 0 if u is orthogonal to 91, 92, ..., 9m, we can use the property of orthogonality. If u is orthogonal to 91, 92, ..., 9m, then the dot product of u with each column vector 91, 92, ..., 9m will be zero. Since Q is an isometry with columns 91, 92, ..., 9m, multiplying Q by its transpose Q^T will preserve the dot product. Therefore, when we multiply QQTv, each column of Q will dot product with v, resulting in zero for the columns 91, 92, ..., 9m since they are orthogonal to u.

b) To show that QQTqi = qi, we can observe that QQT behaves like the identity matrix on the subspace spanned by the columns 91, 92, ..., 9m. Since Q is an isometry, multiplying Q by its transpose Q^T results in an identity-like transformation on the subspace spanned by its columns.

c) To show that (QQT)^2 = QQT, we can multiply QQT by itself and observe that the result is equal to QQT. Since QQT behaves like an identity matrix on the subspace spanned by 91, 92, ..., 9m, the square of QQT will also behave like the identity matrix on that subspace. Hence, (QQT)^2 = QQT.

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Answer:

X >4 x − 21

Step-by-step explanation:

Answer: The answer is A, y-intercept.

Step-by-step explanation:

Answer:

first term is 8 and common difference d is -4

Step-by-step explanation:

nth term of an arithmetic sequence is: aₙ=12-4n

First term is putting n=1:

aₙ=12-4n

a₁=12-4(1)

a₁=12-4

a₁=8

So, first term a₁= 8

Now finding second term to find common difference

Second term is: n=2

aₙ=12-4n

a₂=12-4(2)

a₂=12-8

a₂=4

So, second term is: 4

The common difference is: a₂-a₁= 4-8 = -4

So, first term is 8 and common difference d is -4 if nth term is 12-4n

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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3/8 is classified as a rational number.

All fractions, positive or negative, are rational numbers.

Natural numbers, whole numbers, and integers don't include fractions.

Answer:

Rational

Step-by-step explanation:

A natural number is a whole number, so that eliminates natural and whole. An integer is a whole number that includes negative numbers. Since 3/8 is not a whole number, we can eliminate that too. Rational numbers are fractions that don't go on forever. 3/8 is a rational number.

The digit 8 in the number 2,980.7 has a value that is 1/10 times as great as the digit 8 in the number 2,980.72.

To determine in which number the digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.72, we need to compare the place value of the digit 8 in each number.

Let's break down the place values for the digit 8 in each number:

Number: 2,980.72

Thousands place: 8 has a value of 8,000

Hundredths place: 8 has a value of 0.08

Number: 2,980.7

Thousands place: 8 has a value of 8,000

Tenths place: 8 has a value of 0.8

From the above comparison, we can see that in the number 2,980.7, the digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.72.

This is because the digit 8 in the tenths place is 1/10 times the value of the digit 8 in the hundredths place.

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Answer: 30 meters

Step-by-step explanation:

Volume of a cylinder = πr^2h

2,827.43 = πr^2(4)

2,827.43 = 3.14(4)r^2

2,827.43 = 12.56*r^2

2,827.43/12.56 = (12.56*r^2)/12.56

225.11 = r^2, find square root of both sides

r = 15

diameter = 30

The multiplication of 2x and \(\rm x^2+2x-6\) is \(\rm 2x^3+4x^2-12x\).

The correct option is A.

Given

Multiply 2x(x2 + 2x - 6).

Multiplication is the process of calculating the product of two or more numbers.

The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

Then,

The multiplication of 2x and \(\rm x^2+2x-6\) is;

\(\rm= 2x\times (x^2+2x-6)\\\\= 2x\times x^2+2x\times 2x+2x\times (-6)\\\\= 2x^3+4x^2-12x\)

Hence, the multiplication of 2x and \(\rm x^2+2x-6\) is \(\rm 2x^3+4x^2-12x\).

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Answer:

The image does not pop up for me because im on a laptop so im sorry

Step-by-step explanation:

i kinda just need point