4. The temperature of the water in a pot on the stove is taken every 2 minutes, as shown in the
following chart.
Time (Minutes)
0
2
4
6
8
10
12
14
16
18
20
Temperature (°C)
23.2
25.1
29.2
36.8
42.5
47.6
55.9
62.7
72.4
86.1
98.3
Based on an exponential model of the data, what is the predicted temperature of the water at 7
minutes? Use the Desmos calculator to find your answer. Round your answer to the nearest tenth
of a degree.
(1 point)

Based on the calculations, the unknown number (x) is equal to 7.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;

Multiply a number (x) by 5 = 5x

The product is equal to the sum of 20 and 15 = 20 + 15 = 35.

Combining the above information, we have:

5x = 20 + 15

5x = 35

Dividing both sides by 5, we have:

x = 35/5

x = 7.

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In the initial list, there were 4 integers.

We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:

m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).

The initial equation is x = mn.

Therefore, changing x in the other two equations:

m + 2 = (mn + 15) / (n + 1) ..............(1)

m + 1 = (mn + 16) / (n + 2)...............(2)

Based on equation (1):

(m + 2)(n + 1) =  mn + 15

mn + m + 2n + 2 = mn + 15

m + 2n + 2  = 15

m + 2n = 13

m = 13 - 2n.

Now change m in equation (2) to:

13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)

14 - 2n = (13n - 2n^2 + 16) / (n + 2)   Through-multiplication by n + 2:

(14 - 2n)(n + 2) =  13n - 2n^2 + 16

14n + 28 - 2n^2 - 4n =  13n - 2n^2 + 16

10n + 28 = 13n + 16

12 = 3n

n = 4.

Hence, there were 4 integers in the original list.

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Answer:

There are 2 zeros. You know they are zeros because they are the only two points that intercept the x-axis. There is one touch zero and one bounce zero, meaning there are both even and odd multiplicities in the graph.

The answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

Given equation

f(x) = (x − 2)2(x + 1)(x − 3)

f(x) = (x + 2)2(x − 1)(x + 3)

f(x) = (x + 2)2(x + 1)(x + 3)

f(x) = (x − 2)2(x − 1)(x − 3)

Factored form is a product of stayed and linear elements.

by checking of the red line cross the x-axis.it will give you the zero.

it passes at -1, touches at 1, and crosses again at 3.

This implies that the zeroes are -1, 1 and 3.

The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.

Therefore the answer is

f(x) = (x - 1) 2(x +1)(x - 3 ).

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It is true that WXY ≅ WZY.

What is a congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Properties of Congruence

Reflexive Property: An angle is congruent to itself.

Symmetric Property: The order of congruence does not matter.

Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.

Here, It is given that

Angle ZWY is congruent to angle XWY

Segment WZ is congruent to Segment WX

Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.

Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.

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Friday hope that this helps

The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°

In the given question we have,

Radius of circular curve (R) = 225 ft

intersection or central angle in circular curve (I or delta) = 55°

separtion between stakes alaong arc = 50 ft

Angle of deflection is measured from tangent at PC or PT to any point .

deflection angle formula

deflection angle = (Lc /L)(I/2)

where, Lc is long chord and L is lenth of arc , I is central angle

first we find out the value of Lc and L

using formula , R = Lc / 2sin(I/2)

Lc = 225× 2 sin(55°/2) = 208 ft

L = R × I ×π/180°

L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft

put all the vales in deflection angle formula we get ,

deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°

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The value of c is 20.35 (approx).

The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).

The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.

Let the other 2 sides of the triangle be named a and b

Given:- a = 15.5ft

            b = 13.2ft

According to the Pythagorean Theorem, We know that

[tex]a^{2}+b^{2}=c^{2}[/tex]

By substituting the values of a and b we get

[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]

[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]

c is the hypotenuse of the triangle.

Hence the value of c is 20.35

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The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.

29.6 milliliters = 1 fluid ounce

3 liters = 3000 milliliters

3000 milliliters / 29.6 milliliters = 101 fluid ounce

Hence, 3 liters ≈ 101 fluid ounces.

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The final velocity of a vehicle with a mass of 800kg is 20000 m/s.

So, calculate the final velocity as:

Now, we know that:

Insert values in the formula and calculate as follows:

Rounding off: v =  20000 m/s

Therefore, the final velocity of a vehicle with a mass of 800kg is 20000 m/s.

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2(-x - 5) = 12

Step 1 : Expand the bracket.

=> -2x - 10 = 12

Step 2 :Add both side by 10.

=> -2x - 10 + 10 = 12 + 10
=> -2x = 22

Step 3 : Divide both side by -2.

=> -2x : (-2) = 22 : (-2)
=> x = -11

Therefore, x = -11.

Answer:

x = - 11

Step-by-step explanation:

2(- x - 5) = 12 ( divide both sides by 2 )

- x - 5 = 6 ( add 5 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

Step-by-step explanation:

so the ticket booth had $150 so $1254 -$150=$1104

so $1104 ÷ by $3 each person = to 368 people paid the admission

Had: $150

Tickets :368

Total :$1254

An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.

What is a rectangle?

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 22in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (22) = JG

11 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.  

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The measure of the side MK of the triangle is 109.6.

The scale factor is defined as the proportion of the new image's size to that of the previous image. The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.

For the triangles, the scale factor will be calculated as,

Scale factor = 57 /13

The measure of the side MK will be calculated as,

57 / 13 = MK / 25

MK = ( 57 x 25 ) / 13

MK = 1425 / 13

MK = 109.61

Therefore, the measure of the side MK of the triangle is 109.6.

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Answer:

h(8) = 2

Step-by-step explanation:

substitute x = 8 into h(x) , that is

h(8) = 2(8 - 7) = 2(1) = 2

The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.

Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:

= 4 / 24

= 1/6

= 1:6

Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:

= 2/12.

= 1/6

= 1:6

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The domain of the function f(x) = 3x is (b) All positive integers less than or equal to 4

From the question, we have the following equation of the function that can be used in our computation:

f(x) = 3x

In this case, the notations are given as

x = Number of splits

f(x) = number of new roots in each split

From the question, we have

Splits = 4

This means that the maximum value of x is 4

The other values of x would be

x = 1, 2, 3, 4

This can be represented as

0 ≤ x ≤ 4

The interpretation of the above notation is all positive values less than or equal to 4

Hence, the domain value is option (b)

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Answer:

When you round the number to 5

Step-by-step explanation:

The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

A golf ball is fabricated so that assuming it is dropped from A feet over the ground onto a hard surface, the most extreme level of each skip will be one portion of the level of the past bob.

Then the equation is given as,

h = a (1/2)ˣ

Where 'a' is the initial height.

The exponential equation that gives the height h the ball will attain during the nth bounce will be given as,

h = a (1/2)ⁿ

If the ball is dropped from 13 feet above the ground onto hard a surface. Then the height on the 5th bounce will be given as,

h = 13 (1/2)⁵

h = 13 x 1 / 32

h = 0.40625 feet

The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.

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The area of the David's pantry = 10 square feet.

The length of the pantry = 5 feet.

For the given question.

Thus,

Area of kitchen  = 6 x area of the pantry

60 = 6 x area of the pantry

area of the pantry = 60 / 6 = 10 square feet.

Area of the pantry = length x breadth

10 = length x 2

length = 10/2 = 5 feet.

Thus, the length of the pantry is found as the 5 feet.

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Answer: Your answer is $7.30

Step-by-step explanation:

Finding the amount for a tip is simple!

all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)

36.50×.2= $7.30

Yes. The residuals' distribution pattern resembles a haphazard dispersion around the horizontal line at 0.

The horizontal plot in this instance comprises points that are unstructured and randomly dispersed around the horizontal mean line.

These are also points below the mean above the mean. This shows that some points in the distribution of data points are above and some are below the least square line, which crosses through the distribution.

The least-square line model would not produce adequate results if, in a residual plot, the majority of the data points are located roughly in a straight line or on either side of the horizontal line.

A residual plot must have data points randomly distributed on both sides of the horizontal mean line in order to produce good results.

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COMPLETE QUESTION:

if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. is this the case for the residual plot?

Answer:

B

Step-by-step explanation:

∠ ADB and ∠ AOB sum to 180° , that is

56° + ∠ AOB = 180° ( subtract 56° from both sides )

∠ AOB = 124°

An angle on the circle is half the central angle subtended on the same arc , so

∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°

Answer: 64.95

Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95