The graph models the temperature, in degrees Fahrenheit, of a cup of hot water placed in a refrigerator.

Based on the graph, what was the original temperature, in degrees Fahrenheit, of the cup of hot water?

The area of the triangle ΔKLM, obtained using Routh's theorem is 4/13

Routh Theorem outlines the ratio relationship between the triangle formed by three cevians of a triangle and the area of the original triangle.

Mathematically it states that the ratios (x, y, and z) of the segments formed the intersection of the cevians and the three sides of the triangle produces the area of the triangle when expressed in the form;

A = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1)).

The specified dimensions are;

BD : DC = CE : EA = A_F: FB  = 1 : 3

The point of intersection of AD, BE and CF = K, L, and M

Area of triangle ΔABC = 1

The area of triangle ΔKLM is found as follows;

Where the length of AB = 4 units, we get;

Length of A_F = 1 unit and the length of FB = 3 units

We get;

BD/DC = x, CE/EA = y, A_F/FB = z

x = y = z = 1/3

Routh's theorem states that the area of the triangle formed by AD, BE, and CF is obtained using the formula;

Area of ΔKLM = (x·y·z - 1)² ÷ ((x·y + y + 1)·(y·z + z + 1)·(z·x + x + 1))

Plugging in the values of x, y, z, we get;

x = y = z, therefore;

Area of ΔKLM, A = (x³ - 1)² ÷ ((x² + x + 1)·(x² + x + 1)·(x² + x + 1))

A = (x³ - 1)² ÷ ((x² + x + 1)³)

x = 1/3, therefore;

A = ((1/3)³ - 1)² ÷ (((1/3)² + (1/3) + 1)³) = 4/13

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1 and 7/12

Divide the 2 fractions (multiply by reciprocal.)

1/4 + 1/2 × 8/3

1/4 + 8/6

Find common denominators.

6/24 + 32/24

38/24

Turn that into a mixed number.

1 14/24

Simplify.

1 7/12

Answer: The answer is 3

Step-by-step explanation:

(-7)-(-10)

=(-7)+10

=10-7

=3

Answer: 3

Step-by-step explanation: First, to make this easy, let's rewrite the equation:

-7 + 10

I did this because whenever you change subtraction to an addition problem, with decimals, you need to change the sign of the number on the right side (always) So, (-7) - (-10) is the same as (-7) + 10.

So, to make this even easier, we can model this as 10 - 7, which is 3. As we know, it's the same as (-7) + 10 because we are adding 10 more to (-7) which is 3. Also, if you can, using a numberline really helps to! I hope this helped!

Answer:

We know that the distance between Paris and Nice is about 920,000 meters. To convert this distance to kilometers we divide by 1000: 920,000/1000= 920 kilometers

We also know that the train travels at a speed of 230 kilometers per hour. To find out how long it will take Lola to travel from Paris to Nice, we divide the distance by the speed:

920/230 = 4 hours

So it will take Lola 4 hours to travel from Paris to Nice by train.

Answer: 4 hours actually kinda ez not gonna lie

Step-by-step explanation: 230 kilometers = 230000 meters. 230 * 1000 = 230000. Distance / speed = time. 920000/230000 = T(as in time). T = 4

As per the given distance, he surrounded around 20 miles

Here we have given that Pete drives from his house to the store and then to the fair.

While we have given the distance covered by the Pete driver as,

=> 6, 5, 4, 3, 2

Then the total travelling distance is calculated by sum up all the details,

Then  we get,

=> 6 + 5 + 4 + 3 + 2

=> 20 units.

Here we have also given that 1 unit is equal to 1 miles.

Therefore, the resulting distance is 20 miles.

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The population in this study would be adolescent boys.

The researcher is interested in the effect of the electrolytic sports drink on the endurance of adolescent boys. The sample of 30 boys that are selected for the study is representative of the larger population of adolescent boys, and the results of the study will be generalized to this population. The study is designed to draw inferences about the population of adolescent boys based on the sample that is selected.

The population in this study would be adolescent boys.

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Two fractions are equivalent if they represent the same decimal number. For example, the three previous fractions represent the same decimal: 0.5. 1/2 is 1 between 2, which is 0.5

The converse is:

If a number is a whole number, then it is a natural number.

The following information should be considered:

Considering the conditional:

In the case when the number is a natural number, then it is a whole number.

>If a number is not a whole number, then it is not a rational number. The converse is false. ( converse must be true)

>If a number is a rational number, then it is a whole number. The converse is false. (converse must be true)

>If a number is not a rational number, then it is a whole number. The converse is false. (hypothesis should've been "then it is not a whole number")

In the Law of Detachment, if both conditional and hypothesis are true, then the conclusion is true.

All whole numbers are rational numbers.

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Answer:

Step-by-step explanation:

x: Andre's Age

(x+3): Andre's Brother's Age

(x−2): Andre's Sister's Age

3(x+3): Andre's Mom's Age

87: The Sum of All Four Ages

Answer:

x = 5

y = -4

Step-by-step explanation:

3x+4y = -1

-2x-5y = 10

We time the first equation by 2 and the second equation by 3

6x + 8y = -2

-6x -15y = 30

-7y = 28

y = -4

Now put -4 back in for y and solve for x

3x+4(-4) = -1

3x - 16 = -1

3x = 15

x = 5

Let's check

3(5) + 4(-4) = -1

15 - 16 = -1

-1 = -1

So, x = 5 & y = -4 is the correct answer.

The cost of pizza and salad will be $8.54 and $2.64 respectively.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The equation will be represented as;

Let p = pizza

Let s = salad

2p + 3s = 25

3p + 2s = 30.90

Multiply equation i by 3

Multiply equation ii by 2

6p + 9s = 75

6p + 4s = 61.80

Subtract.

5s = 13.20

Divide

s = 13.20 / 5

s = $2.64

Pizza will be

2p + 3s = 25

2p + 3(2.64) = 25

2p = 25 - 7.92

p = 17.08 / 2

p = 8.54

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l

Complete question

Two groups of students went to pizza delight one group paid 25 dollars 2 pizzas and 5 salads the other group paid 30.90 dollars for 3 pizzas and 2 salads. Find the cost of the pizza and salad.

Answer:

formula:

c^2 = a^2 + b^2 - 2abcos(C)

where c is the length of the diagonal, a and b are the lengths of the legs of the triangle (the non-parallel sides of the trapezoid), and C is the angle between them.

In this case, a = b = 7 feet and C = (180 - 140)/2 = 20 degrees. We can plug these values into the formula to find:

c^2 = 7^2 + 7^2 - 2(7)(7)cos(20)

c = sqrt(98 + 49cos(20))

To use the Law of Sines to find the length of the shorter base, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.

Since we know a and b, we can use the formula to find:

x/sin(140) = 7/sin(20)

x = 7sin(140) / sin(20)

Note that the value of c will be in squared units, so you need to take the square root to get the actual length of the diagonal.

The probability that the hand contains 4 jacks is solved to be

0.003697

Probability is solved using the formula

= required outcome / possible outcome

The required outcome

= number of ways of picking 4 jacks * number of ways of 10 cards from 48

= ⁴C₄ * ⁴⁸C₁₀

= 1 * 6540715896

= 6540715896

The possible outcome

= number of ways of picking 14 card from possible 52 cards

= ⁵²C₁₄

= 1.768966345 * 10¹²

The probability

= required outcome / possible outcome

=  6540715896 / 1.768966345 * 10¹²

= 11 / 2975

= 0.00369747

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One of the right triangles that are given which can be used to approximate PQ of the given triangle above is triangle labelled 3 and it's value = 9.5.

A right triangle is defined as the triangle that is has one of its angle equal to 90 degrees.

Therefore, the value of the side of the triangle PQ can be obtained using the Pythagorean formula;

c² = a² + b²

c² = PR = 7²

a² = 6.4²

b² = PQ = ?

b² = c² - a²

b² = 49+40.96

b² = 89.96

b= √ 89.96

b = 9.5.

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The missing coefficient of the linear equation 4 · x + 10 = __ · x + 8 such that it has no solutions is equal to 4.

In this problem we find a linear equation of the form a · x + b = c · x + d, where a, b, c, d are real coefficients. This kind of equation has no solution for the case when a = c. The complete procedure is shown below.

First, write the incomplete expression:

4 · x + 10 = __ · x + 8

Second, add the missing coefficient according to the definition for linear equations with no solutions:

4 · x + 10 = 4 · x + 8

Third, use algebra properties to simplify the expression:

10 = 8 (CRASH!)

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The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

This graph will show the rate of infection for each virus and the total amount of virus present in the culture at any given time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters infected cells with either virus A or virus B and then sampled the mixture at five-minute intervals. After removing the intact cells, the number of viruses per milliliter of culture was determined and plotted on a graph over time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

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Answer:

Step-by-step explanation:

There are 529 students standing in the assembly hall, and since there are as many students in a row as there are rows in the hall, there must be an equal number of students in each row. Therefore, each row must have 529/rows = 529/rows students in it.

The sample size that would be required for the width of 99% is 2653.

The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.

The following details are given:

Margin of error, E = 0.025; Significance Level, = 0.01

The proportion p is estimated to be p = 0.53.

The significance level with a critical value of 0.01 is 2.58.

The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:

n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2

As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that

n >= 2652.97 and that it must be an integer value.

Sample size is 2653.

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Nature of roots of the quadratic equation 4x^2 - 12x - 9 = 0 are real and unequal by Discriminant method.

Given quadratic equation is 4x^2 - 12x - 9 = 0

Comparing the given equation with the standard form i.e ax^2 - bx - c = 0.

 Here we have, a = 4

                           b = -12  and

                           c = -9

Now discriminant, D = b^2 - 4ac

                                  = (-12)^2 - 4(4)(-9)

                                  = 144 - (-144)

                               D = 288    

Now check for discriminant D, D=288 and 288 >0

                                 Therefore, (D>0)

Hence the roots of given equation are real and unequal.

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The coin will be worth $299.23 in 11 years when increasing at the rate of 11% Option A is the correct answer.

A steady rate of expansion that is proportionate to the quantity's current size is referred to as exponential growth. In other words, a quantity expands more quickly the larger it is. The exponential function, which has the formula y = ab raised to x, can be used to mathematically represent exponential growth. Here, "a" stands for the beginning quantity or value, "b" is the growth factor or base, and "x" stands for the duration or number of growth periods. Population expansion, compound interest, and the spread of infectious illnesses are a few examples of real-world processes that show exponential growth.

The exponential growth is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

For the given situation we have:  (P) = $115, the interest rate (r) = 11% or 0.11, and the number of years (t) = 11.

Thus,

[tex]A = $115(1 + 0.11/1)^{(1*11)}\\A = $115(1.11)^{11}[/tex]

A = $299.23

Hence, the coin will be worth $299.23 in 11 years. Option A is the correct answer.

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The vertex form is

y = (x - 1)^2 - 4.

Generally, The equation of a parabola, which is a kind of quadratic function, may be written in a particular format known as the vertex form. The equation of the parabola may be written out in vertex form as follows:

y = a(x - h)^2 + k

If the vertex of the parabola is located at (h, k), and the leading coefficient is denoted by a. If an is positive, the parabola will have its lowest point at the vertex, and if an is negative, the vertex will have its highest point.

The vertex form is important because it makes it simple to determine where the vertex of a parabola is located, and it may also be used to establish the direction in which the parabola is pointing.

The vertex form of the equation y = x^2 - 2x - 3 is

y = (x - 1)^2 - 4.

The vertex of this parabola is at the point (1, -4).

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The exact value of the trigonometric expression sin(x - y) is given as follows:

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

The trigonometric expression in the context of this problem is defined as follows:

sin(x - y).

The identity used to obtain the sine of the subtraction of two angles is given as follows:

[tex]sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

Considering the sine of x, the cosine of x is obtained as follows:

[tex]\sin^2{x} + \cos^2{x} = 1[/tex]

[tex]\left(\frac{\sqrt{28}}{6}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\frac{28}{36} + \cos^2{x} = 1[/tex]

[tex]\cos^{2}{x} = \frac{7}{9}[/tex]

[tex]\cos{x} = \frac{\sqrt{7}}{3}[/tex]

The angle y, with a tangent of [tex]\frac{1}{\sqrt{3}}[/tex], is the angle of 30º, hence the sine and cosine are given as follows:

Hence the trigonometric expression is given as follows:

[tex]\sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

[tex]\sin{(x - y)} = \left(\frac{\sqrt{28}}{6}\right) \times \frac{\sqrt{3}}{2} - \frac{\sqrt{7}}{3} \times \frac{1}{2}[/tex]

[tex]\sin{(x - y)} = \frac{\sqrt{84}}{12} - \frac{2\sqrt{7}}{12}[/tex]

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

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Answer:[tex]x = 18[/tex]

* also think you meant x instead of c*

Step-by-step explanation:

[tex]\frac{x}{6} - 7 = -4[/tex] --> +7 on both sides

[tex]\frac{x}{6} - 7 + 7 = -4 + 7[/tex]

[tex]\frac{x}{6} = 3[/tex] --> multiple by 6 by both sides

[tex]6 * \frac{x}{6} = 3 * 6[/tex] --> the 6 and the [tex]\frac{x}{6}[/tex] cancel out

[tex]x = 18[/tex]

The size of the final unknown interior angle is 157°

Given the interior angles of a polygon are 162°,115°,125°,138°,105°, and 98°.

Considering the given polygon to be 7-sided,

The sum of the interior angles of a polygon is:

(n-2) x 180

where n= number of sides of the polygon

Substituting the values:

(7 - 2) x 180

= 5 x 180

= 900

Let the unknown angle be x°

So,

162+115+125+138+105+98+x = 900

x = 900 - 743

x = 157°

Thus the final interior angle is 157°

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Step-by-step explanation and Answer

Since the interest rate is 5%, and the first loan was borrowed on May 1, we can calculate the interest on the first loan by using the formula:

Interest = Principal x Rate x Time

In this case, the principal is 2000, the rate is 5% (expressed as a decimal), and the time is (September 24 - May 1) = 4.5 months

So, Interest = 2000 x 0.05 x 4.5/12 = 50

The same applies to the second loan of 1000, so the interest on this loan is:

Interest = 1000 x 0.05 x (4.5/12) = 25

To find the total amount returned, we add the interest on both loans to the total principal borrowed:

total = 2000 + 1000 + 50 + 25 = 3075

Therefore, the total amount returned is Ks 3075

The area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse is 84 cm.

The area of a right triangle of base b and height h can be calculated using the formula 1/2 × b × h and its perimeter is obtained by just adding all the sides.

Length of one side of the right triangle (p) = 24-inch

Length of the hypotenuse of the right triangle (h) = 25-inch

Therefore, we can calculate the third side (b) of the triangle by applying the Pythagorean theorem

p² + b² = h²

24² + b² = 25²

b² = 625 - 576

b² = 49

b = 7 inch

Now, the area of the right triangle will be

= 1/2 × b × h

= 1/2 × 7 × 24

= 84 inch²

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When the tone's height, h, equals 0, we can determine when the tone will fall to the ground. The equation that expresses the height of the tone as a function of time is as follows:

    h = -16t^2 + 32t + 40

  where t is the number of seconds since the tone was launched, and h is the tone's height in feet.

  We can set the formula equal to 0 because we are aware that h = 0 when the tone strikes the ground:

   -16t^2 + 32t + 40 = 0

Here is the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

where a = -16, b = 32, and c = 40.

With these values entered into the formula, we obtain:

t = (-32 ± √(32^2 - 4(-16)(40))) / 2(-16)

t = (-32 ± √(1024 + 2560)) / (-32)

t = (-32 ± √(3584)) / (-32)

t = (-32 ± 64) / (-32)

t = (32) / (-32) or (-96) / (-32)

t = -1 or 3

The duration of the tone before it reaches the ground is -1 or 3 seconds.  

       However, as there is no such thing as a negative amount of time, it takes 3 seconds for the tone to reach the earth.

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The probability that their total completion time in the maze for all rats is between 5.75 and 6.25

To solve this problem, you would need to use the properties of the normal distribution and the central limit theorem. The central limit theorem states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since the completion time for each rat is normally distributed with a mean of 1.5 and a standard deviation of 0.35, the total completion time for 5 rats will also be normally distributed with a mean of 7.5 (5 x 1.5) and a standard deviation of 0.7 (√(5) x 0.35).

Then, you can use the cumulative distribution function (CDF) of the normal distribution to find the probability that the total completion time is between 5.75 and 6.25. This would involve finding the area under the normal distribution curve between those two values, which can be calculated using a table of the standard normal distribution or a calculator with the normal distribution function.

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Three ratios that are equivalent to 18:21 are 6 : 7, 36 : 42 and 72 : 84

An equivalent ratio is a ratio that represents the same relationship between numbers as another ratio, but with different values.

You can create equivalent ratios by multiplying or dividing both parts of the ratio by the same non-zero number. For example, if a ratio is 4:8, an equivalent ratio would be 2:4.

Thus, 3 ratios that are equivalent to 18:21 can be:

18 : 21 = 6 : 7 (divide both sides by 3)

18 : 21 = 36 : 42 (multiply  both sides by 2)

18 : 21 = 72 : 84 (multiply  both sides by 4)

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Answer:

x^2 +9

Step-by-step explanation:

expand and simplify

(2x-3)^2-3x(x-4)

First expand the squared term

4x^2 -6x -6x+9 -3x(x-4)

Distribute the -3x

4x^2 -6x -6x+9 -3x^2 +12x

Combine like terms

4x^2 -3x^2-6x -6x +12x+9

x^2 +9

Answer:

[tex]{x}^{2} - 12x + 21[/tex]

Step-by-step explanation:

We know that,

[tex] {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]

Accordingly, let us solve the sum.

[tex] {(2x - 3)}^{2} - 3x(x - 4)[/tex]

Expand and solve the brackets.

[tex]4 {x}^{2} - 12x + 9 - 3 {x}^{2} + 12[/tex]

Combine like terms.

[tex] {x}^{2} - 12x + 21[/tex]

The equation for the given quadratic polynomial is f(x) = x^2-33x+242.

When the highest degree term in a second-degree polynomial equals 2, the polynomial is said to be quadratic. A quadratic equation has the generic form ax^2 + bx + c = 0. Here, x is the unknown variable, a and b are coefficients, and c is the constant term.

A polynomial with an exponent degree of 2 or higher is said to be quadratic. A quadratic polynomial has the general form f (x) = ax^2 + bx + c, where a 0 and b a n d c are real numbers. A parabola is the name of the quadratic polynomial's curve.

f(x) = (x-11)(x-22)

f(x) = x^2-33x+242

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