Exponential Functions

Answer:

62

Step-by-step explanation:

Use the Law of Sines: sinA/a = sinB/b = sinC/c, where A, B, and C are the angles and a, b, and c are the sidelengths opposite of their corresponding angles.

If angle G = 66 and angle H = 30, then angle F = 180-66-30 = 84 degrees.

Therefore sin84/67 = sin66/g.

Multiple both sides by g and divde by sin84/7 to get

g = sin66/(sin84/67) = 61.5... which is about 62 inches.

the linear correlation coefficient given to determine the coefficient of determination,  R² = 0.0784.

The strength of the linear link between two variables, x and y, is measured by the linear correlation coefficient, which is a number derived from the supplied data. The linear link between variables x and y is indicated by the sign of the linear correlation coefficient.

In order to examine the relationship between two quantitative variables, correlation and linear regression are the two methods that are most frequently utilised. As opposed to regression, which expresses the connection as an equation, correlation measures the strength of the linear relationship between two variables.

The linear correlation coefficient is given as:

r = -0.28

Calculation of coefficient of determination:

R² = r²

R² = (-0.28)²

or, R² = 0.0784

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Cynthia was twice as old as Abigail 3 years ago.

Let x be the number of years ago when Cynthia was twice as old as Abigail

If Abigail is 15 years old and Cynthia is 27 years old today, then "x" years ago, the algebraic expression that represents their age was"15 - x" and "27 - x", respectively.

If "x" years ago, Cynthia was twice as old as Abigail, then the equation will be

27 - x = 2(15 - x)

Simplify the equation and solve for the value of x.

27 - x = 30 - 2x

x = 3

Therefore, 3 years ago, Cynthia was twice as old as Abigail.

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A country's population in 1995 was 23 million. In 2001 it was 25 million, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

For this problem, we have the final population P, the starting population A, and the time passed t.

We still need to determine the value of the growth factor k.

This can be done using the information for the years 1995 and 2001.

In this case, A will be 23 million (the population in 1995), P will be 25 million (the population in 2001), and t will be 6 years (the number of years between 1995 and2001):

[tex]P=Ae^{kt}[/tex]

[tex]25=23e^{k 6}[/tex]

[tex]e^{6k} =\frac{25}{23}[/tex]

[tex]k = \frac{ln(25) - ln(23)}{6}[/tex]

k = 0.013897

Now, let's use this information to determine P in 2013.

A will still be 23 million, but t will be 18 years.

[tex]P= 23e^{0.013897*18} \\P= 23e^{0.250146} \\P=23 * 1.28421\\P=29.5368\\[/tex]

Therefore, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

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The total amount of deposits shown is, $713.29.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The graph of a passbook is shown in figure.

Now, By figure,

The total amount of deposits is,

⇒ $310.58 + $402.71

⇒ $713.29.

Thus, The total amount of deposits shown is, $713.29.

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The second and third image will be congruent to the pre-image. The solution has been obtained by applying the concept of transformations.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Pre-image or "inverse image" refers to the two-dimensional shape that exists before any change. The transformed shape is represented by the image.

1. This is not congruent because both the coordinates are dilated and after dilation the size of the image is not the same as of original figure.

2. This is congruent because there is only translation which means it is same as the original figure but the position is different.

3. This is congruent because only translation has taken place which means it is same as the original figure but the position is different.

4. This is not congruent because one coordinate i.e. x has been dilated and after dilation the size of the image is not the same as of original figure.

Hence, second and third are congruent to the pre-image.

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The number of complete days that 4 packs of treats will last, we need to determine the total number of packs each day and divide it into the total number of packs Mrs. Mills has bought.

Let's call the number of days the treats will last "d".

Then, the number of packs Fluff eats in "d" days is d * (1/6 of a pack per day) = (1/6)d.

Similarly, the number of packs Tigger eats in "d" days is d * (1/5 of a pack per day) = (1/5)d.

The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

Since "d" must be a whole number, we round down to get 10 complete days that the 4 packs of treats will last.

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The total number of packs they eat in "d" days is (1/6)d + (1/5)d = (11/30)d.

Since Mrs. Mills has bought 4 packs, we have 4 = (11/30)d.

Finally, solving for "d", we have d = (30/11) * 4 = 120/11 days.

The shape is a triangular prism and the volume of the shape is 45 ft^3.

A triangular prism is a 3-dimensional shape with two parallel triangular bases and three rectangular sides connecting the bases. It has six faces and nine edges in total.

The volume of the triangular prism is;

V = 1/2(b * h * l)

b = base

h = height

l = length

V = 0.5 (6 * 3 * 5)

= 45 ft^3

Thus, we can see that the kind of shape that have been modelled in the image has six faces and corresponds to the triangular prism with a volume of 45 ft^3.

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The right solution is option C, which is Y'(1, -4) and Z'(-2, -1).

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's interior angles equals 180 degrees, which is its most essential feature. This is known as the angle sum property of a triangle.

Here,

To translate a triangle, you need to add the same value to each x-coordinate and each y-coordinate. In this case, the translation moves each point 2 units to the left and 3 units down, so the new coordinates of Y and Z would be:

Y'(3 - 2, -1 - 3) = Y'(1, -4)

Z'(0 - 2, 2 - 3) = Z'(-2, -1)

The correct answer is Y'(1, -4) and Z'(-2, -1) that is option C.

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Answer: 44.6 yards

Step-by-step explanation: The formula for the circumference of a circle is C = 2 * π * r, where r is the radius. We can rearrange the formula to solve for r:

r = C / (2 * π) = 279.46 / (2 * π) = 44.6 yards

So, the radius of the field is approximately 44.6 yards.

p.s. sorry it might be 44.6 yards or / 44.5 yards :)

The measure of angle B from the given hexagon ABCDEF is 108°.

In geometry, a hexagon or sexagon is a six-sided polygon or 6-gon creating the outline of a cube. The total of the internal angles of any simple hexagon is 720°.

In the given hexagon ABCDEF, ∠A=170°, ∠C=133°, ∠D=102°, ∠E=117° and ∠F=90°.

Here, ∠A+∠B+∠C+∠D+∠E+∠F=720°

170°+∠B+133°+102°+117°+90°=720°

612°+∠B=720°

∠B=720°-612°

∠B=108°

Therefore, the measure of angle B from the given hexagon ABCDEF is 108°.

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The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = √(2x + 6) - 3

The parent function is given as,

f(x) = √x

Multiply by 4, then we have

f(x) = 4√x

f(x) = √2x

Shift the function 3 units downwards and 6 units left.

f(x) = √(2x + 6) - 3

The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.

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The complete question is given below.

5.228 written as fraction is 1307/250

Albert have 9/4 cups of cheese in the mixture.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing.

Given,

Amount of cheddar = 2/3 cup

Amount of mozzarella = 5/6 cup

Amount of parmesan = 3/4 cup

Total cups of cheese

= cheddar + mozzarella + parmesan

= 2/3 + 5/6 + 3/4

= 8 + 10 + 9 /12

= 27/12

= 9/4

There is 9/4 cups of cheese in the mixture.

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Answer:

The ratio they are asking for is Model height to actual height. Rewritten that is:

Model Height: Actual Height

So the ratio after plugging in numbers is;

15:605

Ratios can be simplified by dividing both sides.

Both numbers are divisible by 5.

Therefore the ratio is;

3:121

(this is the simplest form of the ratio because 121

is not evenly divisible by 3)

Now, that is not an answer you can select,

however you can also multiply both sides by theKalius Call be simple by uviuiny po siues. Both numbers are divisible by 5.

Therefore the ratio is;

3:121

(this is the simplest form of the ratio because 121 is not evenly divisible by 3)

Now, that is not an answer you can select, however you can also multiply both sides by the same number. Take 4 for example (I'm choosing 4 because 3*4=12)

12:484

change the function f(x) and interval a=1/3 , b=1 in above code (remaining same code) in the iteration

clear all;

s=1200;

h=20;

f(x)= x-2^(-x) ;

a=1/3;

b=1;

format long

eps_ abs = 0.000005;

eps_ step = 0.000005;

n=0;

while ((b - a)/2 >= eps_ step || ( abs( f(a) ) >= eps_ abs && abs( f(b) ) >= eps_ abs )&& n~=100 )

n=n+1;

c = (a + b)/2;

if ( f(c) == 0 )

break;

else if ( f(a)*f(c) < 0 )

b = c;

else

a = c;

end

err=abs( (b-a)/2);

end

n

c

err

out put

n = iteration

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Answer:

7

Step-by-step explanation:

30÷6=5

$5 per mow

35÷5=7

7

(bonus) prove the equation ∃x(a(x) ∧ ¬b(x)) ∀x(a(x) −→ c(x)) ∴ ∃x(c(x) ∧ ¬b(x))

Proof by Contradiction:Assume that ∃x(c(x) ∧ ¬b(x)) is false.

Therefore, we can conclude that ∀x(c(x) ∧ ¬b(x)) is true.

This implies that for all x, either c(x) is false or b(x) is true.

But, from our assumption, we know that ∃x(a(x) ∧ ¬b(x)) is true.

Therefore, there must exist an x such that a(x) is true and b(x) is false.

Since a(x) is true, we can conclude from ∀x(a(x) −→ c(x)) that c(x) must also be true.

But this is a contradiction since we previously assumed that the equation ∀x(c(x) ∧ ¬b(x)) is true, which implies that c(x) must be false.

Therefore, our initial assumption must be false, and we can conclude that ∃x(c(x) ∧ ¬

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The original points for the parent function of f(x) = -2|1/4(x-1)| +3 is (0, 0)

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

f(x) = -2|1/4(x-1)| + 3

The above function is an absoluute value function

The parent function of an absolute value function is represented as

y = |x|

When x = 0. we haeve

y = 0

This means that (0, 0) is the point on the parent function

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Answer: Rounding degrees is similar as to answering decimals. How ever, there is 60 minutes in a degree. If the numbers is less than 30, you round down to the nearest degree, and if its 30 or up, you round up to the nearest degrees.

Yes, Because the paces are 6 miles/hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Christy went jogging on a saturday. The table shows how far she had jogged after various times.

Now, Based on the given table;

⇒ 4.5 ÷ 0.75

⇒ 6

⇒ 7.5 ÷ 1.25

⇒ 6

Thus, She ran the same pace at 6 miles/hour.

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Using unitary method, turkey's temperature after 55 minutes is 120.815° Also, it will take approximately 68 minutes for the turkey to cool down to 105°.

Now, According to the question:

What is unitary method?

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Reduction in temperature after 30 minutes = 185° - 150° = 35°

Reduction in temperature after 1 minute = 35/30 = 1.167°

Reduction in temperature after 55 minutes = 55 × 1.167 = 64.185°

Temperature after 50 minutes = 185° - 64.185° = 120.815°

Decrease in temperature when the turkey has cooled down to 105° = 185° - 105° = 80°

Time taken by the turkey to cool down 80° = 80/1.167 = 68.55 minutes.

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Answer:

100

1,000

10,000

Step-by-step explanation:

10 times 10 is 100.

10 times 10 times 10 is 1,000

10 times 10 times 10 times 10 is 10,000.

By applying standard equation of a circle concept, it can be concluded that the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

Circle is a collection of points on a plane line that are all the same distance (the radius) from a given point (the center).

Standard equation of a circle can be written as:

(x - h)² + (y - k)² = r²   , where:

(h,k) = center of the circle

r = radius

We know that the radius of the circle has endpoints (-4,3) and (1,-2), which means that one of these points is the center of the circle.

Since we know that its center is in the second quadrant, we can conclude that (-4,3) is the center.

Now we can substitute these values into the equation:

   (x - h)² + (y - k)² = r²

(1 - (-4))² + (-2 - 3)² = r²

              5² + (-5)² = r²

                25 + 25 = r²

                        50 = r²

As we know the r, now we can have the standard equation of the circle:

   (x - h)² + (y - k)² = r²

(x - (-4))² + (y - 3)² = 50

 (x + 4)² + (y - 3)² = 50

Thus the equation that defines the circle is  (x + 4)² + (y - 3)² = 50.

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There are 71515 total number of people to which the health clinic must do outreach.

The term percentage refers to a denominator of 100. Here are some actions we can take to find the people the company needs to get in touch with:

About 27% of elderly persons have weakened immune systems.

So here we do that the total number of people multiplied by the 27 percentage of people,

27/100 x 50,000 people is 13500 people.

And 50,000 - 13500 = 36,500

Now;

11% of persons in this category are under 65 and have immune system impairments;

Eleventh part of 100 which is 36,500 results in 4015 people.

The firm should be able to contact a total of 17515 people that is,

(13500 + 4015).

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The value of x in the system of equations is: x = 11.2.

The value of x can be found by solving the system of equations.

One method is to substitute the value of x from one equation into the other equation, solve for y, then use the value of y to find x.

Starting with the second equation: 5x + 2y = 48

Solve for y: y = (48 - 5x) / 2

Now substitute this expression for y into the first equation:

-5x - 12((48 - 5x) / 2) = -8

-5x - 6(48 - 5x) = -8

-5x - 288 + 30x = -8

25x - 288 = - 8

25x = -8 + 288

25x = 280

x = 280/25

x = 11.2

Finally, solving for x:

x = 11.2

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Answer:

-11.8

Step-by-step explanation:

To find the value of x in this system of equations, we can use substitution or elimination method.

Using substitution:

Solve for one of the variables in one of the equations and substitute it into the other equation. We can start by solving for y in the second equation:

[tex]\sf:\implies{5x + 2y = 48}[/tex]

[tex]\sf:\implies{2y = -5x + 48}[/tex]

[tex]\sf:\implies{y = (-5/2)x + 24}[/tex]

Now, substitute this expression for y into the first equation:

[tex]\sf:\implies{-5x - 12y = -8}[/tex]

[tex]\sf:\implies{-5x - 12((-5/2)x + 24) = -8}[/tex]

[tex]\sf:\implies{-5x + 30x + 288 = -8}[/tex]

[tex]\sf:\implies{25x = -296}[/tex]

[tex]\sf:\implies{x = -11.84}[/tex]

The value of x rounded to the nearest tenth is -11.8.

The required measure of an angle is 73 degrees which supplement is 253.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

The supplement of an angle is equal to 180 degrees minus the angle.

So if we call the angle "x", we can set up an equation as follows:

2x + (180 - x) = 253

Simplifying the equation:

x = 253 - 180

Apply the subtraction operation, and we get

x = 73

So the angle is 73 degrees.

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Answer:

The coefficient a = -1, b = 4, c = -1 and d = 0. To solve for the coefficients, substitute the values from the table into the equation y = ax³ + bx² + cx+d. When x = 0 and y = 0, we get 0 = -1a + 4b + c + d, so d = 0. When x = 1 and y = -2, we get -2 = -1a + 4b + c, so c = -1. When x = 2 and y = -26, we get -26 = -1a + 4b, so b = 4. Finally, when x = 3 and y = -54, we get -54 = -1a, so a = -1.

Step-by-step explanation: