A cold front moves through the area quickly. In the morning, the temperature is 82
degrees F and after 6 hours the temperature has dropped to 58 degrees F. If the
temperature dropped at a steady rate, how much did it drop each hour?

Upon answering the query  Thus, the athletes devote a total of 21/4 equation hours, or 5 1/4 hours, to lacrosse practise each week.

An equation in math is an expression that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between each of the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The sign and only one variable are frequently the same. as in, 2x - 4 equals 2, for instance.

On Monday, Wednesday and Friday, the Seneca Nation athletes practise lacrosse for 1 3/4 hours daily.

[tex]1 3/4 hours + 1 3/4 hours + 1 3/4 hours1 3/4 = 7/4\\7/4 + 7/4 + 7/4\\7/4 + 7/4 + 7/4 = (7+7+7)/4 = 21/4\\[/tex]

Thus, the athletes devote a total of 21/4 hours, or 5 1/4 hours, to lacrosse practise each week.

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Tyler invested $5800 in the first account and $3900 in the second account.

Simple interest is interest that is calculated solely on a loan's or investment's principal amount, without taking into account any interest that has accrued over time. For instance, regardless of how long you keep the money in the account, if you deposit $1,000 in a savings account that offers 5% simple interest annually, you will make $50 in interest each year. Contrarily, compound interest accounts for both the original principal and the interest that has accrued over time. This means that interest is calculated on the new, higher balance after the interest collected during each period is applied to the principal amount.

Let us suppose the amount invested in first account = x.

The amount in second account = y.

Thus, according to the statements we have:

x + y = 9700 (total amount invested is $9700)

0.10x + 0.09y = 931

Now from the first equation we can write:

y = 9700 - x

Substituting the value of y we have:

0.10x + 0.09(9700 - x) = 931

0.10x + 873 - 0.09x = 931

0.01x = 58

x = 5800

Now, substituting the value of x we have:

y = 9700 - 5800

y = 3900

Hence, Tyler invested $5800 in the first account and $3900 in the second account.

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Answer: B

Step-by-step explanation:

The external angle is = to the sum of the other 2 angles so <x=125

and <y=55 Because of the supplemental rule.

So answer is B

To solve for x, we need to isolate the variable (x) on one side of the equation. We can do that by first subtracting 3 from both sides of the equation to get:

11 - 3 = 4x

Simplifying the left side gives:

8 = 4x

Finally, dividing both sides by 4 gives:

x = 2

Therefore, the solution to the equation 11=3+4x is x=2.

the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x = 2[/tex] X = 2.

The equation [tex]11=3+4x[/tex] 11=3+4x is a linear equation in one variable [tex](x)[/tex](x) with coefficients and constants that are real numbers.

It can be simplified by performing basic algebraic operations, such as isolating the variable term [tex](4x)[/tex] (4x) and solving for the value of [tex]x[/tex] x.

to solve for x in the equation  [tex]11=3+4x[/tex] 11=3+4x, we will follow the steps of algebraic manipulation:

First, we will isolate the variable term [tex](4x)[/tex] (4x)  by subtracting 3 from both sides of the equation:

[tex]11 - 3 = 4x[/tex] 11 - 3 = 4x

[tex]8 = 4x[/tex] 8 = 4x

Next, we will isolate x by dividing both sides by 4:

 [tex]8/4 = x[/tex] 8/4 = x

   [tex]2 = x[/tex] 2 = x

Therefore, the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x=2[/tex] x=2.

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In summary |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

How to solve?

|-13.5 - (-4 1/5)| = |-13.5 + 4 1/5| [Subtracting a negative is equivalent to adding a positive]

= |-9 4/5|

= 9 4/5

Now, we can substitute the values and simplify the expression:

|-13.5 - (-4 1/5)| × 1.4 + (-2)²2

= 9 4/5 × 1.4 + (-2)²2

= 13 3/5 + 4

= 17 3/5

Therefore, |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), connected by an equal sign (=).

For example, the equation 3x + 5 = 14 is an equation that shows that the expression 3x + 5 is equal to the expression 14. This equation can be solved for x to find the value of x that makes the equation true.

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Answer:

Step-by-step explanation:

(0,0)

i hope this helps

From the given dimensions, it seems like the figure is a trapezoid.Therefore, the surface area of the figure is 300 square feet.

Surface area is the measure of the total area that the surface of an object occupies. It is calculated by adding the area of all the faces or surfaces of the object.

A trapezoid is a four-sided geometric shape that has one pair of parallel sides. It is also called a trapezium. The parallel sides are called bases and the non-parallel sides are called legs.

According to the given information:

To calculate the surface area of the figure, we need to split it into smaller shapes and then calculate their individual areas. From the given dimensions, it seems like the figure is a trapezoid.

The formula for the surface area of a trapezoid is (1/2) × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the height.

Using this formula, we can calculate the surface area of the trapezoid:

Surface Area = (1/2) × (15 + 9) × 15 + 2 × 15 × 4

= (1/2) × 24 × 15 + 2 × 15 × 4

= 180 + 120

= 300ft²

Therefore, the surface area of the figure is 300 square feet.

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Answer:4

4 What percentage of students got a 100% on their math quiz? Round to the nearest whole percent?

Step-by-stepStep-by-stepStep-by-step explanation: 4 What percentage of students got a 100% on their math quiz? Round to the nearest whole percent?

Answer:

The algebraic expression for "Subtract 5x−2 from x−1" is:

(x - 1) - (5x - 2)

Simplifying this expression:

x - 1 - 5x + 2

= -4x + 1

Therefore, the simplified algebraic expression is -4x + 1.

Answer: C. 3/(t-1)

Step-by-step explanation:

Answer:

[tex] \dfrac{3}{t - 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{t^2 - 2t - 3}{t^2 - 1} \cdot \dfrac{3t - 3}{t^2 - 4t + 3} = [/tex]

Start by factoring every numerator and denominator.

[tex] = \dfrac{(t - 3)(t + 1)}{(t + 1)(t - 1)} \cdot \dfrac{3(t - 1)}{(t - 3)(t - 1)} [/tex]

Every factor that exists in both a numerator and denominator can be eliminated.

[tex] = \dfrac{1}{t - 1} \cdot \dfrac{3}{1} [/tex]

Multiply numerators together. Multiply denominators together.

[tex] = \dfrac{3}{t - 1} [/tex]

The value of s in the given logarithmic functions is 19683.

A logarithmic equation is an equation that involves logarithmic functions.

Logarithms are the inverse functions of exponential functions and are used to solve for an unknown variable that appears as an exponent in an exponential equation.

For the given logarithm function, the value of s is calculated by applying the following steps;

log₃s = 9

rewrite the equation in exponential form:

3⁹ = s

3⁹ = 19683

So, the value of s is 19683.

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Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

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Answer: It is not possible for the length of the third side of a triangle to be an integer when the lengths of the other two sides are not integer.

Step-by-step explanation:

When the other two sides of a triangle are 5.3 and 0.4 in length, the third side cannot possibly have an integer length. This is so because any two sides of a triangle must have lengths that are greater than the length of the third side. In this instance, 5.3 + 0.4 = 5.7, which still falls short of any integer number for the third side's length.

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Answer: 5

Step-by-step explanation:

5.3+0.4=5.7

5.3-0.4=4.9

4.9<x<5.7

The only possible integer between these two numbers is 5, so the correct answer is 5.

Answer:

The completed statements are:

The y-intercept represents the base price of $200.

The slope represents a cost of 30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their airfare. (y = 200 + 0.30x, where x is the distance traveled in miles)

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,000 miles. (500 = 200 + 0.30x, solving for x gives x = 1,000)

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x. (The slope remains the same, while the y-intercept changes to 50.)

Note that the statement "According to the equation given, someone who traveled 2000 miles from NYC would pay $2500 for their airfare" is incorrect. The correct calculation using the given equation y = 200 + 0.30x is:

y = 200 + 0.30(2000) = 800

Therefore, someone who traveled 2000 miles from NYC would pay $800 for their airfare.

The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.

To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.

Let's calculate the length of each side:

Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.

Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.

Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.

Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.

Now, let's sum up the lengths of all four sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

Perimeter = 7 + 7 + 7 + 7

Perimeter = 28 units

Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.

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Answer:

A = 15.87 m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6.9 and h = 4.6 , then

A = [tex]\frac{1}{2}[/tex] × 6.9 × 4.6 = 3.45 × 4.6 = 15.87 m²

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Answer:

the abswer is D

Step-by-step explanation:

[f○g](x)=(9x+12)/9+8/3=x+8/3

[g○f](x)=9(x/9 + 4/3)+12=x+24

so for the same x they are not inverses

Answer:

1/5

Step-by-step explanation:

-2/5 - (-9/15) make like denominators

-6/15 - (-9/15) negative and negative make positive

-6/15 + 9/15 solve

3/15 simplify

1/5

Answer:

x= 51°

Step-by-step explanation:

Fist find the measure of angle y.

A straight angle measures 180°

180 - 57 - 61 = 60

y = 62

The sum of the interior angles of a triangle also equals 180

180 - 62 - 67 = 51

x= 51°

Helping in the name of Jesus.

The evaluations of the given expressions are:

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵) = -5

From the question, we are to evaluate the given expressions.

The given expressions contain natural logarithm and exponential functions.

The natural logarithm is the inverse of the exponential function.

Thus,

ln eˣ = x

Likewise

e^(ln x) = x

Applying these rules to the given expressions, we get

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵)

This can be written as

ln (e⁻⁵) = -5

Thus,

ln (1 / e⁵) = -5

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Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.

What is investment?

Property acquired or invested in to build wealth and save hard-earned income or appreciation is called investment.

Let's start by assigning variables to represent the amounts invested in each type of account:

Let x be the amount invested in CDs.

Let y be the amount invested in bonds.

Let z be the amount invested in stocks.

From the problem statement, we know that:

Here total invested amount is $95,000,

So, we have

[tex]x + y + z = 95,000.[/tex]

The amount invested in bonds is $35,000 more than the amount invested in CDs,

So we have

[tex]y = x + 35,000.[/tex]

The annual income from the investments is $6,845, which we can express as:

0.0475x + 0.042y + 0.112z = 6,845........ (1)

Now we can use the system of equations formed by the three equations above to solve for x, y, and z. First, we can substitute [tex]y = x + 35,000.[/tex] into the equation [tex]x + y + z = 95,000[/tex] to get,

[tex]x + (x + 35,000) + z = 95,000[/tex]

Simplifying this equation, we get:

2x + z = 60,000........ (2)

Next, we can substitute y = x + 35,000 and simplify the equation (1) using equation (2) to get:

[tex]0.0475x + 0.042(x + 35,000) + 0.112z = 6,845[/tex]

Simplifying and rearranging this equation, we get:

0.0895x + 0.112z = 8,545 ..........(3)

Let's use substitution by solving equation (2) for z and substituting into equation (3):

Now, z = 60,000 - 2x

So, 0.0895x + 0.112(60,000 - 2x) = 8,545

Simplifying and solving for x, we get:

x = 18,000

Substituting this value of x into equation (2) to solve for z, we get:

2(18,000) + z = 60,000

z = 24,000

Finally, we can use equation (1) to solve for y:

[tex]0.0475(18,000) + 0.042(y) + 0.112(24,000) = 6,845[/tex]

Simplifying and solving for y, we get:

y = 32,000

Therefore, Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.

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Answer:

9207 divided by 4 = 2301 with a remainder of 3

Step-by-step explanation:

  (check the attached document)

The probability of forming this committee with equal representation is approximately 0.570 or 57.0%.

The total number of individuals in the ATU COVID-19 team of Marshalls is 50 (13+15+10+12). To form an executive committee of 16 with equal representation, we need to choose 4 individuals from each group (4 lecturers, 4 students, 4 administrative staff, and 4 medical personnel).
Using the combination formula, we can calculate the number of ways to choose 4 individuals from each group:
C(13,4) × C(15,4) × C(10,4) × C(12,4) = 715 × 1,455 × 2,385 × 4,095 = 7,976,476,875
Therefore, there are 7,976,476,875 possible ways to form the executive committee with equal representation.
To calculate the probability of forming this committee, we need to divide the number of possible ways by the total number of ways to choose any 16 individuals from the ATU COVID-19 team of Marshalls:
C(50,16) = 13,983,816
The probability of forming the executive committee with equal representation is:
7,976,476,875 / 13,983,816 = 0.570

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1. Depreciation expense = $7,400 per year

2. Incremental net operating income = $10,000 per year

3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

4. The simple rate of return on the new bottling machine is 13.5%.

Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.

Annual Depreciation Expense:

The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:

Depreciation expense = (Cost of the machine - Salvage value) / Useful life

Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year

Annual Incremental Net Operating Income:

To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.

Annual operating cost of the old machine = $19,000

Annual operating cost of the new machine = $9,000

Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine

Incremental net operating income = $19,000 - $9,000 = $10,000 per year

Initial Investment:

The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

Simple Rate of Return:

The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.

Simple rate of return = Annual incremental net operating income / Initial investment

Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)

Therefore, the simple rate of return on the new bottling machine is 13.5%.

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1. Depreciation expense = $7,400 per year

2. Incremental net operating income = $10,000 per year

3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

4. The simple rate of return on the new bottling machine is 13.5%.

What is investment?

Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.

Annual Depreciation Expense:

The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:

Depreciation expense = (Cost of the machine - Salvage value) / Useful life

Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year

Annual Incremental Net Operating Income:

To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.

Annual operating cost of the old machine = $19,000

Annual operating cost of the new machine = $9,000

Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine

Incremental net operating income = $19,000 - $9,000 = $10,000 per year

Initial Investment:

The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

Simple Rate of Return:

The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.

Simple rate of return = Annual incremental net operating income / Initial investment

Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)

Therefore, the simple rate of return on the new bottling machine is 13.5%.

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Check the picture below.