Some water is placed in a bottle inside a refrigerator. Suppose the water's temperature (in °C) after x minutes can be modeled with an exponential function. The
graph of this function is shown below.
Use the model to answer the parts to the right.

The value of sinθ is 15/17.

What are the trigonometric functions?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given:

Cosθ = 8/17

We apply here trignometric functions.

Sinθ = √1 - cos²θ

Sinθ = √1 - (8/17)²

Sinθ = √(289 - 64)289

Sinθ = √225/289

Sinθ = 15/17

Hence, the value of Sinθ is 15/17.

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Sum is an aggregation of the numbers, quantities etc. It is write as 4 + 4 = 8 ( plus symbol (+ ) represent the sum). Similarly, ∑ (sigma) also represents the sum of numbers.

Addition is an important topic in Mathematics. When we add two or more numbers, the result is defined as the SUM. The added numbers are called addends. The sum of two or more numbers make a new number say total. A plus symbol (+) is used when we add the numbers. Summation (or) sum formula is the sum of consecutive terms of a sequence. To write the sum of more terms, say n terms, of a sequence {an} , we use the summation notation instead of writing the whole sum manually. That is summation symbol which represent the sum is ∑ (sigma). For example, Sum of two numbers say 6 and 7 is equals to 6 + 7 = 13. But in case of "n" numbers the sum is determined as following way. Consider the first n even numbers, i.e., 2,4,6,....,n and we have to calculate the sum of it. As we see the above sequence is in AP with first term, a = 2 and common difference, d= 2. Then the sum formula in AP is S = n/2[ 2a + (n -1)d ]

=> S = n/2 [ 4 + (n-1)2 ]

=> S = n/2 [ 4 + 2n - 2 ]

=> S = n(n+1) or ∑n( n+1,) ; n = 1,2,.......

Hence, the sum of first n even numbers can be written as ∑n( n+1,) ; n = 1,2,.......

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The rate of change for the linear is -5 and the initial value  is -1

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function. We'll go into great detail about what a linear function is in this article, along with its table, graph, formulas, traits, and examples.

The rate of change refers to the slope of the linear function, because the slope is actually a ration between the two variables. So, to find the slope, we use its definition:

m = [tex]y^{2}[/tex]-[tex]y^{1}[/tex]/[tex]x^{2}[/tex]-[tex]x^{1}[/tex]

Now we replace the given points, being C the first point and D the second point:

m= -11-(-1)/2-0= -5

Therefore, the rate of change is -5, where the negative sign refers to a decreasing change, it's a decreasing linear function. In addition, the initial values is where the independent variable is zero, which is given in the point C (0;-1), so the initial condition is y = -1

 Therefore ,The rate of change for the linear is -5 and the initial value  is -1

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Part A - The cycle has a total distance travelled of 130 meters.

Part B - The cycle has an acceleration of 0 meters per square second at t = 8 seconds.

In this question we find the case of a graph between time (t), in seconds, and velocity (v), in meters per second, from which we need to determine the total distance travelled (s), in meters, on the cycle and the acceleration (a), in meters per square second, at a given time.

Part A - The total distance travelled is the area below the curve, defined as the sum of the areas of two triangles and rectangle, thus:

s = 0.5 · (6 s) · (10 m / s) + (6 s) · (10 m / s) + 0.5 · (8 s) · (10 m / s)

s = 30 m + 60 m + 40 m

s = 130 m

The total distance traveled by the cycle is 130 meters.

Part B - The acceleration at a given time t is the slope of the curve at point (t, v). In this case, we find that slope can be found by secant line formula:

a = [v(12) - v(6)] / (12 - 6)

a = (0 - 0) / (12 - 6)

a = 0 m / s²

The acceleration of the cycle at t = 8 seconds is equal to 0 meters per square second.

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The statement that is true is that when p(x) is divided by x-n, the remainder is 7.

This statement can be confirmed by solving the equation

p(x)/x-n = q(x) + 7, where q(x) is the quotient. Solving this equation yields the result that q(x) = 2x - 5. This means that when p(x) is divided by x-n, the remainder is 7 and the quotient is 2x - 5.

This statement can also be verified by using synthetic division. By using synthetic division with 2x2 - 5x + 10 as the dividend and x - n as the divisor, the remainder after the division is 7. This confirms that when p(x) is divided by x-n, the remainder is 7.

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The number of zeros and nature of zeros for the functions,

g(x) =  8x⁶ - 9x² - 6x⁵        ⇒ 6 Roots and 4 real & 2 imaginary roots

h(x) = -4x² - 3x - 1              ⇒  2 Roots and both are imaginary

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

Functions,

g(x) =  8x⁶ - 9x² - 6x⁵

h(x) = -4x² - 3x - 1

Number of roots and nature of roots = ?

First take,

g(x) =  8x⁶ - 9x² - 6x⁵

8x⁶ - 9x² - 6x⁵  = 0

x² = 0

its two of the zeros are 0, 0

After plotting graph for the given function

It can be say that,

It is intersecting x axis at 3 places

So it will have total 6 roots, 4 real roots and two imaginary roots

h(x) = -4x² - 3x - 1

D  = b² - 4ac

   =  9  - 4 × -4 × -1

   =  9  - 16

D =  -7

D is  negative so it will have 2 roots and nature will be imaginary

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The coordinates of the midpoint of PQ is (5/8, 1/8)

i. To find the slope of the line l1, you can rearrange the equation 4x - 3y + 5 = 0 to the standard form of y = mx+ b, where m is the slope and b is the y-intercept.

4x - 3y + 5 = 0

3y = -4x + 5

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

So the slope of the line l1 is m = -4/3.

ii. To find an equation of the line l2, which passes through the point (1, 2) and is perpendicular to the line l1, you can use the slope-intercept form of a line y = mx + b, where m is the slope and b is the y-intercept. Since line l2 is perpendicular to line l1, the slope of l2 is the negative reciprocal of the slope of l1.

m = -1/(-4/3) = 3/4

We can substitute point (1, 2) into the equation

2 = 3/4 * 1 + b

b = 2 - 3/4

So the equation of the line l2 is y = 3/4 x + (2 - 3/4) = 3/4 x + 1/4

iii. To find the coordinates of the point where line l1 crosses the x-axis, we can set y to 0 and solve for x.

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

0 = (-4/3)x + (5/3)

x = 5/4

The point where line l1 crosses the x-axis is (5/4, 0)

Similarly, to find the point where line l2 crosses the y-axis, we can set x to 0 and solve for y.

y = 3/4 x + 1/4

y = 3/4 * 0 + 1/4

y = 1/4

The point where line l2 crosses the y-axis is (0, 1/4)

The midpoint of two points can be found by taking the average of the x and y coordinates.

Midpoint of P and Q = ( (5/4 + 0) / 2, (0 + 1/4) / 2) = (5/8, 1/8)

So the coordinate of the midpoint of PQ is (5/8, 1/8).

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The closest correlation coefficient of the scatterplot is 0.8

From the question, we have the following parameters that can be used in our computation:

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Because the points appear to be on a straight line, but they are not on a straight line, the r value will most likely be between 0.7 and 0.9

The closest value to this is 0.8

Hence, the r value is 0.8

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The amount of money that the farmer will make after the deduction of percentage of service fees would be = $783.75

A contract earning is defined as the amount of money an individual or company earns for a period of time which only lasts till the end of the contract.

FROM the question,

1 acre /year = 0.11 metric tons

50 acre/year = 0.11 × 50

= 5.5 metric tons

For ten years contract = 5.5 × 10 = 55 metric tons

The amount earned per metric ton = $15

Therefore, 55 metric tons = 15×55 = $825

Deductions of service charge;

5% of 825 = 5/100 × 825

= 4125/100

= $41.25

The balance after deduction of service fees = 825 - 41.25 = $783.75

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The answer is 2500 - 45W = B

2500 is the total amount

45 is taken out a week, so let w be the variable

B is the total bank balance

So 2500 - 45W = B

I hope this was able to help you :D

The equation 2x + 3y = 13 has infinitely many solutions.

We know that a linear equation in two variables is of the form ax + by + c = 0, where a, b, c are non-zero real numbers.

Here we have been given a linear equation in two variables 2x + 3y = 13

To find the solution of equation 2x+3y=13, first we solve equation for x and then for any real value of y we find value of x.

We solve this equation for x,

Consider 2x + 3y = 13

2x + 3y - 3y = 13 - 3y            .........(subtract 3y from each side of equation)

2x/2 = (13 - 3y)/2                   .........(divide each side by 2)

x = (13 - 3y)/2

for any real value of y we can find value of x.

This means, an equation 2x + 3y = 13 has infintely many solutions.

The graph of 2x + 3y = 13 is shown below.

From the graph, the y-intercept of line 2x + 3y = 13 is (0, 4.333)

and the x-intercept of line 2x + 3y = 13 is (8, 0)

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The complete question is:

What is the solution of 2x + 3y =13?.

Answer:

Step-by-step explanation: Since both the numerator and the denominator have a minus (-), they even each other out and the minus signs can be removed. Then we are left with this:

13

23

Now that both the dividend and divisor are positive numbers, we can simply divide 13 by 23 as follows:

13 ÷ 23 = 0.565217391304348

Which means that this is the answer to "What is negative 13 divided by negative 23?":

(-13) ÷ (-23) = 0.565217391304348

Answer:

t = -299

Step-by-step explanation:

[tex]\frac{t}{-13} = 23\\\\ t = 23 * -13\\\\t = -299\\\\Check:\\-\frac{-299}{-13} = 23[/tex]

The product of radicals is C) x[tex]\sqrt[12]{x^5}[/tex]

What is product of radical form?

The term "simplest radical form" refers to the most basic representation of a number or algebraic expression. It indicates that we should multiply the radicals when they are placed next to one another in this manner. Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Here the given form is

=> [tex]\sqrt[3]{x^2} \sqrt[4]{x^3}[/tex]

Now use [tex]\sqrt[n]{a}= \sqrt[mn]{a^m}[/tex] to expand the expression then

=> [tex]\sqrt[12]{x^8} .\sqrt[12]{x^9}[/tex]

Now the product of roots with the same index is equal to the root of the product then

=> [tex]\sqrt[12]{x^8x^9}[/tex]

=> [tex]\sqrt[12]{x^{17}}[/tex]

=> x[tex]\sqrt[12]{x^5}[/tex]

Hence the correct option is C) x[tex]\sqrt[12]{x^5}[/tex]

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The inequality which represents the possible additional amounts Dan will spend is; c ≤ 17.

As evident in the task content; the possible additional amounts Dan will spend is to be determined from the information given in the task content.

Since it is stated that Dan can spend at most $32 in which case, he has spent $15 already.

Let c be the additional amount Dan would spend.

Therefore the inequality which represents the situation is;

c + 15 ≤ 32

Ultimately, the solution set which represents the possible additional amounts he will spend is;

c ≤ 17.

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Of the two methods for area calculation, the preferred method is the second method because the objects around the polygon are smaller, and easier to calculate their area.

There are several ways to calculate the area of a polygon. Two of them were carried out by the two students in the problem:

Of the two methods for the area of a polygon calculation, the preferred method is the second method because the objects around the polygon are smaller and easier to calculate their area.

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Answer: 3c + r + 2.5s + 5

Step-by-step explanation:

Im not gonna explain it thats too much.

Answer:

the answer is (-3)

Step-by-step explanation:

its to make it work

The total fee that Ratnam should pay the agency for a journey of 50 kilometers, using a linear equation, is A. x + 10y.

The total fee is a function of summing the fixed charge for the first 40 kilometers and the variable charge for additional kilometers traveled.

In this situation, the variable charge per km represents the slope or the unit rate while the fixed charge for 40 kilometers represents the constant in a linear equation.

Flat charge up to 40 kilometers = Rs. x

Variable charge per kilometer after 40 km = Rs. y

Total distance traveled = 50 kilometers

Total fee paid = Rs. x + (50 - 40)y

= x + 10y

Thus, the correct fee that Ratnam should pay is represented by Option A.

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The scale of the picture is 1 in,: 3 cm, and the length of the Thermos in the picture is 4 inches, which indicates that the actual length of the Thermos is 12 centimeters

A scale factor is a number by which the dimensions of an actual or original image are multiplied to obtain the dimensions of the image.

The dimensions of the image are proportionately smaller or larger than the actual dimensions of the image.

The scale of the drawing is 1 inch is equivalent to 3 centimeters

Therefore, each inch of theThermos flask in the drawing is equivalent to 3 centimeter length of the actual Thermos flask.

The dimensions of the thermos flask in the drawing = 4 inches

Therefore;

Length of the thermos flask in the diagram ÷ Actual length of the thermos flask = 1 in./3 cm

Actual length = Image length × 3 cm/1 in.

Actual length = 4 inches × 3 cm/(1 inch) = 12 cm

The actual length of the thermos flask is 12 centimeters

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we can conclude that the probability for the first apple than the peach fruit is 10/39.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Given that there are 8 apples and 5 peaches in a basket.

Total Fruits = 13

For the first event, the probability of getting an apple is,

P(A) = 8/13

Now, Total Fruits = 12

For the second event, the probability of getting peach is,

P(B) = 5/12

The probability for both events is given below.

P = P(A)×P(B)

P = 8/13 ×  5/12

P = 40/156 = 10/39

Hence we can conclude that the probability for the first apple than the peach fruit is 10/39.

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Answer:

vertical line x = -3

horizontal line y =  -9

Step-by-step explanation:

Answer:

Solutions 1 and 2.

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle so first option,

A. m∠4 = m∠1 + m∠2

is correct.

m∠3 and m∠4 are supplementary angles because they make a straight line and their sum is equal 180°, so third option,

C. m∠4 = 180 - m∠3

is also correct.

f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

After answering the provided question, we can conclude that The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

"Scatter plots are graphs that show the relationship between two variables in a data set. Data points are represented by a two-dimensional plane or a Cartesian system. The independent variable or characteristic is represented by the X-axis, while the dependent variable is represented by the Y-axis. These plots are also known as scatter graphs or scatter diagrams."

The y-intercept of the line of fit is approximately 80 based on the scatter plot and line of fit.

The y-intercept in the context of the data represents the predicted test score for a student who did not study at all for the test.

It should be noted that this prediction is based on the linear relationship observed in the sample data and may not be applicable to the entire population. This prediction also assumes that all other factors influencing test performance (such as natural ability, prior knowledge, and test-taking skills) are constant, which may not be the case in real-world situations.

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Answer:

60; a student who studies for 0 hours is predicted to earn 60% on the test

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

Since we are given what y is, we can plug in y into the first equation.

[tex]3x-2(\frac{3}{2} x-\frac{5}{4} )=8[/tex]                    [distribute]

[tex]3x-3x+\frac{5}{2} =8[/tex]                         [subtract]

[tex]\frac{5}{2}\neq8[/tex]

Since this is false, then the only option is that we have no solution.

Answer:

Tax paid on video game: $4.20

Total price of game w/tax: $64.19

Step-by-step explanation:

7% of 59.99 = 4.20

59.99+4.20=64.19

Answer:

4/

Step-by-step explanation:

gradient=y2-y1/x2-x1

-2-2/-5-2=

-4/-7

=4/

When it comes to static characteristics, there are many desirable attributes that can make a product or service stand out from the competition.

Quality and reliability are essential and desirable, as these are the main factors customers will consider when making a purchasing decision.

Durability is also important, as it ensures that a product will continue to perform to its highest standards over time.

Additionally, value for money is key, as customers want to be sure that they are getting a product or service that is worth the cost.

Furthermore, flexibility is highly desirable, as customers often need the ability to customize products or services according to their specific needs.

Finally, a good customer service experience is an essential static characteristic, as a positive customer experience can increase customer satisfaction and loyalty.

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The method of simplification of the radical trinomial is described below.

Particularly those polynomials that are persistent under the influence of the perpendicular group are referred to as radical polynomials. A rated subalgebra of the circle of all polynomials is the circle of radical polynomials.

Utilize the Product Property to condense a radical phrase.

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