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The warmest temperature or "maximum" temperature means we need to find the derivative of the function.

T = -(t^2)/2 + 8t + 32

dT/dt = -t +8

A maximum/minimum occurs when the derivate(gradient) = 0

Therefore, dT/dt = 0

0 = -t + 8

t = 8

Putting t = 8 back into the original equation gives.

T(8) = 64 degF

So the warmest temperature is 64 degF 8 hours after 6am so at 2pm

Answer: a.

Step-by-step explanation:

The amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

Amount of money taken as a loan = $10000

The rate of interest = 2%

The time period of interest is 18 months = 1.5 year

Interst = prt/100

= 10000x 2 x 1.5/100

= 300

Therefore, the amount of interest he would pay for a  loan of $10,000 with a 2% interest rate and for 18 months is $300

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The Angle-Side-Angle Postulate (ASA) asserts that two triangles are congruent if their two angles and included sides are congruent with each other.

We are given that,

BC = EF

∠B = ∠E

∠C = ∠F

We say that by ASA criterion: Δ ABC ≅ ΔDEF.

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The measures of the angles are m∠1 = 69° and m∠2 = 29°

How to find the measures of an angle?

*Triangles always have angles that add up to 180 degrees. As a result, you may find the unknown angles by taking the specified angles of a triangle and subtracting them from 180.

*Finding Unknown Measurements Using Exterior Angles

Two angles that together total 180 degrees are known as supplementary angles. These two angles combine to form a straight angle when put side by side

m∠1 = (4x-7)°

m∠2 = (x+12)°

As the two angles are complementary

4x-7+x+12=90°

5x+5=90°

5x=90-5

5x=85

x=[tex]\frac{85}{5}[/tex]

x=17

Therefore

m∠1 = 4(17)-7

m∠1 = 61°

m∠2 = 17+12

m∠2= 29°

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The volume, to the nearest cubic inch, of the tower is 2,347.

Brandon made a model of a tower, as shown in the figure. The tower is composed of a square prism and a square pyramid. The height of the pyramid is 2 inches. The height of the prism is 3 feet = 36 inches and the base of the prism is 8 inches long. Let the volumes of the tower, prism, and pyramid be represented by the variables V, V1, and V2.

V1 = L*B*H

V1 = 8*8*36

V1 = 2,304

The volume of the square prism is 2,304 cubic inches.

V2 = (1/3)a²h

V2 = (1/3)(8)²(2)

V2 = 42.67

The volume of the square pyramid is 42.67 cubic inches.

The volume of the tower is the sum of the volumes of the square prism and the square pyramid.

V = V1 + V2

V = 2,304 + 42.67

V = 2,346.67

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Answer:

Step-by-step explanation:

1/4 is already less than 1.

When you divide 1/4 by 274, you get much less than 1.

Much less than 1

The equation of line in slope - intercept form is, y = 2x - 13.

What is slope-intercept form of the line?

Using a straight line's slope and the location of its y-axis intersection, the slope intercept equation can be used to determine the general equation of the line. y = mx + b is the equation in slope intercept form.

Consider the given equation of line y = 2x + 1.

And the point given is, (6, -1).

We have to find the equation of line parallel to the given line and passes through the point (6, -1).

First we have to find the slope of the parallel line.

Since, Slope of the parallel line is same as the slope of the given line.

Here, the slope of the line is 2.

So, the slope of the parallel line is also 2.

Now consider the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1)=(6, -1) , m = 2[/tex]

⇒

[tex]y-(-1)=2(x-6)\\y+1=2x-12\\y=2x-12-1\\y=2x-13[/tex]

Hence, the equation of the line parallel to the given line in slope intercept form is, y = 2x - 13.

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Answer:

0.41

Step-by-step explanation:

$4.94/12=0.41

Answer: $0.39.

Step-by-step explanation: $4.94. Divided by 13 = $0.38

Answer:

Step-by-step explanation:

1. x^2 + 4x + 5/x-1

2. x^3-3x^2 + 9x-2 + 3/x+3

3. 2x^2 - 2x+5- 14/3x+1

4.3x2^2- 4x+3 - 13/ 2x-1

5. 3x^2 + 6x + 7 + 12/2x-3

The value of the function f(5) is - 17.

A linear function is a function that represents a straight line on the coordinate plane.

A linear function in slope intercept form is as follows:

y = mx + b

where

Therefore, for the linear function,  f(4) = −13 and  f(−4) = 19.

f(5) can be found as follows;

-13  = 4m + b

19 = -4m + b

2b = 6

b = 6  /2

b = 3

-13 - 3 = 4m

-16 = 4m

m = -4

Hence,

f(5) = -4(5) + 3

f(5) = -20 + 3

f(5) = - 17

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Answer:

$0

Step-by-step explanation:

Answer:

She will owe 2,391

Step-by-step explanation:

760-60x12

The equation to find rent difference C from given values of E and L is 1.75M + 3.25. After adding the values of E and L.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its translations into various languages can vary slightly.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables.

Let E represent Economy

Let L represent Luxury

Let M be the number of miles driven

Let C be how much it cost to rent a luxury car than economy

E = -0.70M + 11.95

L = 1.25M + 17.30

C = L - E

C =(1.25M + 17.30) - (-0.70M + 11.95)

C = 1.25M + 17.30 + 0.70M - 11.95

collect like terms

C = 1.25M + 0.70M + 18.20 - 14.95

C = 1.95M + 3.25

The rent difference between luxury car and economy car is 1.95M +3.25 .

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The equation that best represent the relationship on the scatter plot is y = 6 / 5 x + 18 / 5.

The line of best fit is used to express a relationship in a scatter plot of different data points.

The line of best fit (or trendline) is an educated guess about where a linear equation might fall in a set of data plotted on a scatter plot.

Therefore, the line of best fit will pass through (2, 6)(7, 12) and (12, 18).

Therefore, the equation of the line can be represented as follows;

y = mx + b

where

Therefore,

m = 12 - 6 / 7 - 2

m = 6 / 5

Let's find y-intercept using (2, 6)

6 = 6 / 5(2) + b

6 - 12 / 5 = b

b = 18 / 5

Therefore, the equation is y = 6 / 5 x + 18 / 5

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Answer:

The slope would be 1/9.

Step-by-step explanation:

From 3 to 4 it would be 1. From -4 to 5 it would be 9, the equation for slope is y/x so it would be 1/9.

solution

slope M =(Y' - Y)/(x' - x)

Indicated by (-4, 3) and (5 , 4)

x = -4 , x' = 5 , y = 3 , y' = 4

M = (4 - 3)/( 5 + 4)

M = 1/9 Ans

Answer: -√7 because it will cancel out to equal 0

Answer:

16.25

65 x 0.25 = 16.25

If another type of question the total price would be 48.75 :)

Answer:

16

Step-by-step explanation:

12+1=13

13+1=14
14+1=15
15+1=16

1+1=2
2+1=3
3+1=4

---------
4+6=10

10+6=16

(6+6=12)

1. If you multiply the first equation by 2, the number to multiply the second equation by eliminating the y terms when making a linear combination is -3.

2a) The price per pound of apples is $1.25.

b) The price per pound of bananas is $0.75.

A system of equations involves two or more equations solved together.

Such equations are also known as simultaneous equations.

5x + 3y = 8.5 ... Equation 1

3x + 2y = 5.25 ... Equation 2

Multiply Equation 1 by 2:

5x + 3y = 8.5 ... (x 2)

= 10x + 6x = 17 ... Equation 3

Multiply Equation 2 by -3:

3x + 2y = 5.25 ... (x -3)

-9x -6y = -15.75 ... Equation 4

Add Equations 3 and 4:

10x + 6x = 17

+

-9x -6y = -15.75

= x = 1.25

Substitute x = 1.25 in Equation 1:

5x + 3y = 8.5

6.25 + 3y = 8.5

3y = 2.25

y = 0.75

Check variables in Equation 2:

3x + 2y = 5.25

= 3(1.25) + 2(0.75) = 5.25

= 3.75 + 1.5 = 5.25

5.25 = 5.25

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5x + 3y = 8.5

3x + 2y = 5.25

1. If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination?

2. Complete the multiplication and add the equations. What is the result?

What is the price per pound of apples? $

What is the price per pound of bananas?

The height of the CN Tower on scale drawing is 0.05.

A scale is a group of levels or numbers that are applied to a certain system of measurement or comparison.

Given that,

The height of CN Tower = 550 m,

Also, the scale is 1/11000

Let the height of the CN Tower in the scale is x,

Then,

x/550 = 1/11000

⇒x= =550/11000

⇒x = 0.05

The height of the CN Tower on scale drawing is 0.05.

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The probability of a female being born to a couple using this​ technique is 0.923.

Yes, it is effective in increasing the likelihood that a baby will be a​ female.

Given:

In a test of a​ sex-selection technique, results consisted of 215 female babies and 18 male babies.

Total = 215+18

= 233

1.

The probability of a female being born to a couple using this​ technique is:

p = 215/233

p = 0.923.

hence the probability of the female being born to a couple is 0.923.

2.

Yes it is effective in increasing the likelihood that a baby will be a​ female because the probability of female is higher than the probability of male to be born.

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a. Roster form: { 3, 4,5, 6}

b. Set-builder form : {x | x is an integer, where x ≥ -5}

What is a Roster form?

A list of the elements of a set, each separated by a comma, enclosed in a group of curly brackets, can be used to describe the contents of the set. Roster form is the term for this method of describing a collection.

What is a set-builder form?

Set builder notation is defining a set by expressing its properties rather than simply listing its constituents. One or more variables and a rule specifying which elements are part of the set and which are not are included in the set builder notation.

Here,

a. It is given the set is A={x:x is an integer 3 ≤ x ≤ 6}.

Then the integers lying between 3 and 6 are 3,4,5,6.

So the roster form is

A={3,4,5,6}.

b. It is given that  A = { -5, -4, -3, -2......}

then the set-builder form is

A = {x | x is an integer, where x≤ -5}

Hence,

a. Roster form: { 3, 4,5, 6}

b. Set-builder form : {x | x is an integer, where x ≥ -5}

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Answer:

-3x + 4y = 3

Step-by-step explanation:

Ax + By = C  standard form

y + 3 = 3/4 (x + 5)        | ×4

4(y + 3) = 3(x + 5)

4y + 4·3 = 3x + 3·5

4y + 12 = 3x + 15

-3x + 4y = 15 - 12

The equation in standard form is    -3x + 4y = 3

241,864,704  many different passwords are possible.

The total characters of the password is six in which it is given that first character should start with W, X, Y or Z. So the first character can be filled in 4 ways.

For next five characters it can be any letter of the alphabet or any numeric digit so it will be 26 + 10 = 36.

So second, third, fourth, fifth and sixth space can be taken by 36 characters.

Therefore the total no. of passwords will be 4 * 36 * 36 * 36 * 36 * 36 that is equal to 241,864,704.

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Answer:

a.) The relation is linear

b.) Plot the given (x,y) coordinates on the given graph and connect them.

c.) The y-intercept is at y=2.

d.) m=4

e.) y=4x+2

Step-by-step explanation:

a.) The relation is linear because the values in the sequence of first differences are all equal:

6-2=4   10-6=4   14-10=4   18-14=4

c.) The y-intercept is the point on the graph where x=0.  According to the given points, the y-intercept must be y=2.

d.)

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\(x_1,y_1)=(0,2)\\(x_2,y_2)=(4,18)\\m=\frac{18-2}{4-0}\\m=4[/tex]

e.) Plug slope (m) and y-intercept into the slope-intercept form to get y=4x+2.

For a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°.

As per the question statement, a parallelogram has (∠1 and ∠3) and         (∠2 and ∠4) as the two pairs of opposite angles, and [∠2 = (4x - 20)] and [∠4 = (3x - 11)],

Then, we are required to calculate the measure of ∠1.

To solve this question, first we will need to know about two important properties of a parallelogram,

(a) The sum of all the four interior angles of a parallelogram is equal to 360°,

(b) Opposite angles of a parallelogram are equal.

Now since our concerned parallelogram has (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles,

Therefore, (∠1 = ∠3) and (∠2 = ∠4),

And [(4x - 20) = (3x - 11)]...[∵(∠2 = ∠4)]

Or, [(4x - 3x) = (20 - 11)]

Or, [x = 9]

Therefore, [∠2 = ∠4 = (4x - 20) = 16°].

Now, [(∠1 + ∠2 + ∠3 + ∠4) = 360°]

Or, [(∠1 + ∠2 + ∠1 + ∠2) = 360°]...[∵(∠1 = ∠3) and (∠2 = ∠4)]

Or, [{(∠1 + ∠1 ) + (∠2 + ∠2)} = 360°]

Or, [(2∠1 + 2∠2) = 360°]

Or, [2∠1 = {360 - (2 * 16)}°]

Or, [2∠1 = (360 - 32)°]

Or, [2∠1 = 328°]

Or, [∠1 = (328/2)°]

Or, [∠1 = 164°]

That is, for a parallelogram having (∠1 and ∠3) and (∠2 and ∠4) as the two pairs of opposite angles, if [∠2 = (4x - 20)] and [∠4 = (3x - 11)], then the measure of ∠1 will be 164°

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Answer:

52 / (1/2)

Step-by-step explanation:

Divide the total height by the thickness of each book.

52 / (1/2)