Aunt Eloise’s house is always 20°C. She has just made a fresh cup of tea (tea is made with boiling water and water boils at 100°C) five minutes after she made the tea her mad scientist nephew came in, stuck a thermometer in the cup and announced that the tea was now only 70°C. She had gotten involved with her book and forgot to have even a sip of her tea. Now she won’t drink it because it isn’t piping hot anymore.Write and equation that models this problem and use it to predict the temperature of the tea 20 minutes after it was taken off the stove.

Anisha used the substitution method to solve the system of equations.

She is missing the value of y.

To find it we plut the value of x in the first equation, then:

Therefore the solution is (4,-1)

Answer:

Alternative D - 8 sin(35°)

Step-by-step explanation:

Sin(x) is defined as:

In this exercise,

BC is the opposite side to 35°

AC is the hypotenuse and measures 8 in

Then:

Given the picture, we have:

Enclosed area: A = x*y

Fence Length: F= 2x+y

Answer:

Yes, because if you divide the two numbers, you get a whole number which means it is. Also, since the last numbers are 56, 8 can go into 56 so yes.

Step-by-step explanation:

The product of the slopes of the perpendicular lines is -1, which means if the slope of one of them is m, then the slope of the perpendicular line is -1/m

In triangle ABC

The perpendicular bisector of the side BC is drawn from the opposite vertex A

Then to find it find the slope of BC and reciprocal it and change its sign to get its slope and find the midpoint of BC to use it in the equation of the perpendicular bisector

Since B = (7, 3) and C = (4, 6)

Let us find the slope of BC, using the rule of the slope

Let (x1, y1) = (7, 3) and (x2, y2) = (4, 6)

Now to find the slope of the perpendicular line to BC reciprocal it and change its sign

Since the reciprocal of 1 is 1 and the opposite of negative is positive, then

Then the slope of the perpendicular line is 1

Now, let us find the mid-point of BC

The rule of the midpoint is

Then the mid-point of BC is

Now we can form the equation of the perpendicular bisector of BC using its slope 1 and the point (5.5, 4.5)

The form of the equation using a point and a slope is

m is the slope and (x1, y1) is a point on the line

Since m = 1 and (x1, y1) = (5.5, 4.5), then

Add 4.5 to both sides

The equation of the perpendicular bisector of BC is

We will do the same to AB and AC

Average rate is f(a+266)-f(a))/266

so f(a+266) equals (0.16 x 266) + f(a)

f (a+266)= (0.16 x 266) + 92.39

Given:

Required:

To find the correct one.

Explanation:

The given quation is:

4 + x +8 =24

Subtract 8 on both sides

4 + x +8 - 8 = 24 -8

4 + x = 16

Final Answer:

Thus the first option is the correct answer.

Note that if plane N and plane M intersects each other in two points (say A and B) it follows that they intersects each other in the line that contains A and B. So they cannot intersect exactly in only two points. Postulate number 10

This is a simple question to solve when we use the calculator (as the question allows us to use it).

For this problem when we have :

It can be read as "log base 10 of pi", and using a calculator we find:

And that is the final answer.

NOTE: this result means that:

.

Answer:

C 109

Step-by-step explanation:

First add all the known angles inside the triangle first to get 109°

Then since all angles in a triangle add to 180°

you take away 109 from 180 so

180-109 which equals 71

Then since all angles on a straight line add up to 180°

you take 71 from 180 so

180-71 = 109

so x = 109°

The Approximation of 14 plus cube root of 81 to the nearest tenth is 18.0

The concept that will be used to solve this is finding cube root of 81 which same thing as [tex]81^{\frac{1}{3} }[/tex].

Firstly we will need to find the  cube root of 81, which can be expressed as this: [tex]\sqrt[3]{81}[/tex]  and this can be calculated as 4.33.

This implies that the cube root of 81 will now be 4.33.

Then we can proceed to the simplification that was asked from the question which is 14 plus cube root of 81 and this can be expressed as ( 14) + (4.33) = 18.33

Then we were told to express in the the nearest tenth which is 18.0

Therefore, the third option is correct.

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Given:

The original selling price of 1 swimsuit = $44.95

The selling price of 1 marked down swimsuit = $16.90

Using the provided formula:

Where,

M is the markdown

S is the original selling price

N is the reduced price

Substituting we have:

Solving for N:

Hence, the reduced price is $28.05

Answer:

$28.05

In order to solve for x, we need to use the tangent relation of the angle 48°.

The tangent relation is equal to the length of the opposite leg to the angle over the length of the adjacent leg to the angle.

So we have:

Rounding to the nearest tenth, we have x = 18.9.

Given in the scenario:

a.) Helen ran 15 1/4 kilometers last week.

b.) Riley ran 4 1/12 less kilometers than Helen.

c.) Derrick ran 7 3/8 more kilometers than Riley.

d.) Their goal is to run 60 kilometers in total.

To be able to determine how much further do they need to run to get 60 kilometers in total, we must first determine how many kilometers did Riley and Derrick run.

We get,

A.)

Recall: To be able to subtract mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.

The LCM of 4 and 12 is 12. We get,

Let's now proceed with the subtraction,

Conclusion: Riley ran 11 1/6 kilometers.

B.)

Recall: To be able to add mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.

The LCM of 6 and 8 is 24. We get,

Let's now proceed with the addition,

Conclusion: Derrick ran 18 13/24 kilometers.

C.) To be able to determine how much further do they need to run to get 60 kilometers in total, we subtract 60 by the sum of distance the three people ran.

We get,

The same process that we did, convert all numbers into similar fractions.

The LCM of 4, 6 and 24 is 24. We get,

Let's proceed with the operation,

Therefore, they need to run a total of 361/24 kilometers to be able to meet their goal.

To find the step where the error was made, we are going to correctly solve the equation:

We need to solve for x, first we subtract 3 from each side:

We divide by 2 each side:

The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.

Answer: B. Step 2

The map of Roaring River shows1 inch to be an equivalent of 25 miles. If therefore, the river is shown as 5.5 inches long on the map;

The river is "actually" 137.5 miles long

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Substituting with c = 9 and a = 5, we get:

1. Quadratic curve

2. Odd degree function

3. TWO REAL ZEROS

We know that a function has a unique value of y for each value in x so the correct statement is:

c. it is not a function because there are multiple y values for a given x value

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

Let the rate of change of  the edge length x, y, and z of a closed rectangular box are:

dx/dt= 1m/s

dy/dt= -2 m/s

dz/dt= 0.5 m/s

a) The volume of the box

From the formula of the volume,

V=xyz

Then,

differentiate w.r.t t

[tex]\frac{dV}{dt} = xy\frac{dz}{dt} + yz\frac{dx}{dt} +xz\frac{dy}{dt}[/tex]

[tex]\frac{dV}{dt} = xy(0.5)+ yz(1)+xz(-2)[/tex]

put the value of x, y, z , then we get

[tex]\frac{dV}{dt} = 2.3.(0.5)+ 3.5.(1)+2.5.(-2)[/tex]

[tex]\frac{dV}{dt} = 3+ 15 - 10[/tex]

[tex]\frac{dV}{dt} = 8m^3/s[/tex]

The rate of change of the volume of the box is 8m³/s.

b) surface area of the box

surface area of the rectangular box is

s = 2xy + 2yz + 2zx

differentiate w.r.t t

[tex]\frac{ds}{dt} = 2(y + z)\frac{dx}{dt} + 2(z + x)\frac{dy}{dt} +2(x + y)\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 2(y + z)(1) + 2(z + x)(-2)+2(x + y)(0.5)[/tex]

[tex]\frac{ds}{dt} = 2(3 + 5)(1) + 2(5 + 2)(-2)+2(2 + 3)(0.5)[/tex]

[tex]\frac{ds}{dt} = 16 -40 + 5[/tex]

[tex]\frac{ds}{dt} = -19m^2/s[/tex]

The rate of change of the surface area of the box is -19m²/s.

c) diagonal of the box

lengths of  the boxes for the diagonal is

s = 2x² + y² + z²

differentiate equation w.r.t t

[tex]\frac{ds}{dt} = 4x\frac{dx}{dt} + 2y\frac{dy}{dt} +2z\frac{dz}{dt}[/tex]

[tex]\frac{ds}{dt} = 4.2.1+ 2.3.(-2) +2.5.(0.5)[/tex]

[tex]\frac{ds}{dt} = 8 -12 + 5[/tex]

[tex]\frac{ds}{dt} =1m/s[/tex]

The rate of change of the diagonal of the box is 1m/s.

a) The rate of change of the volume of the box is 8m³/s.

b) The rate of change of the surface area of the box is -19m²/s.

c) The rate of change of the diagonal of the box is 1m/s.

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the median is 25, because:

the mean value is :

The most appropriate choice for profit will be given by-

Profit percent after selling a bag of garri is 25%

What is profit?

If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit

Profit = SP - CP

Here,

Cost price of a bag of Garri = N320

Selling price of a bag of Garri = N400

Profit = N(400 - 320)

         = N80

Profit Percent = [tex]\frac{80}{320} \times 100[/tex]

                       = 25%

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EXPLANATION

For the event B, the order of the first 3 acts doesn't matter.

So, the number of acts taken from the seven acts when the order doesn't matter is calculated using combinations.

Computing the factorials:

Hence, the number of ways the three acts could be given are 1:C(7,3)

Therefore, the probability of the event B is:

For the event A, the order matters, so the difference between combinations and permutations is ordering. When the order matters we need to use permutations.

The number of ways in which four acts can be scheculed when the order matters is:

The number of ways the magician is first, the comedian is second and the whistler is third are 1:P(7,4)

Therefore, the probability of the event A is.

-11 is an integer number

Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e

The formula to find the equation of straight line is

Substitute the values into the formula of the equation of a straight line

Solve for y i.e make y the subject

Thus, the answer is

Thus, the answer is the last option.

The probability of picking a heart or an ace is 17/52

Here, we want to get the probability

The number of cards in a standard deck is 52 cards

Now, we need to know the number of hearts and the number of ace

There are 13 hearts, and 4 aces

The probability of picking a heart is;

The probability of picking an ace is;

The probability of picking an ace or a heart is the sum of both which is;

Answer: Fanuela walked 2.808 miles.

Step-by-step explanation:

If 3.9 = 100 and we need to work out what 72 is we can do this/

3.9 ÷ 10 = 0.39 which = 10

0.39 ÷ 10 = 0.039 which = 1

so with these calculations we can solve the problem.

To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.

To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.

2.73 + 0.078 = 2.808.

Fanuela walked 2.808 miles.

Hope this helps! Feel free to ask any questions if you're still unsure.

The net loss from accepting the special order at a discount of 25% from the regular price, without the existence of excess capacity is $38,700.

Since Coronado Co. lacks the excess capacity for special orders, it implies that it will incur fixed costs per unit of the special order in addition to the variable costs.

Therefore, the company will incur a per unit cost of $40 ($16 + $12 + $9 + $3) while generating a revenue of $39 per unit.

This results in a loss of $1 per unit.

Selling price per unit = $52

Unit Costs:

Direct Materials = $16

Direct Labor = $12

Variable Overhead = $9 (75% of $12)

Total variable cost per unit = $37

Fixed Overhead = $3 (25% of $12)

Special order price per unit = $39 ($52 x 1 - 75%)

Contribution margin per unit = $2 ($39 - $37)

Total contribution margin = $77,400 ($2 x 38,700)

Fixed Overhead without excess capacity = $116,100 ($3 x 38,700)

Net loss = $38,700 ($77,400 - $116,100)

Thus, without excess capacity, it is inadvisable for Coronado to accept the special order at a total loss of $38,700.

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In order to determine which is the equivalent equation, simplify the given expression:

-2x + 5 - 3x = 5x + 25 simplify like terms left side

-2x - 3x + 5 = 5x + 25

-5x + 5 = 5x + 25 subtract 5x both sides and subtract 5 both sides

-5x - 5x = 25 - 5 simplify both sides

-10x = 20

Hence,the equivalent expression is -10x = 20