Given the exponential growth function f ( x ) = 75 ( 1.02 ) x f ( x ) = 75 ( 1.02 ) x What is the initial value of the function? What is the growth factor, or growth rate of the function (as a percent)? %

The value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]

The summation expression is given as:

[tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex]

Rewrite as:

[tex]38 + 3 + \frac{22}{75} + \frac{11}{15}[/tex]

Evaluate the sum and take LCM

[tex]41 + \frac{22 + 5 * 11}{75}[/tex]

Evaluate the sum

[tex]41 + \frac{77}{75}[/tex]

Express as mixed number

[tex]41 + 1\frac{2}{75}[/tex]

Add

[tex]42\frac{2}{75}[/tex]

Hence, the value of [tex]38 \frac{22}{75} + 3\frac{11}{15}[/tex] is [tex]42\frac{2}{75}[/tex]

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The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The rate of gas will be calculated as:-

Suppose the hours are represented by x and the gallons are represented by y.

The rate of the gas will be the slope so the slope will be calculated as:-

[tex]m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \dfrac{2-20}{3-0}[/tex]

[tex]m =\dfrac{-18}{3}[/tex]

m = -6

The equation will be given as:-

y = mx + c

y  = -6x + 20

Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

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Answer:

16.19

Step-by-step explanation:

Use the cosine rule:

[tex]\sqrt{a^{2} +b^{2} -2abcosy} \\\\\sqrt{16^{2} +20^{2} -(2)(16)(20)cos(52)} \\\\\\= 16.19cm[/tex]

The slope-intercept expression for the line is, y=2x-6

The slope-intercept formula is the one we require for this issue.

y = mx + b is the expression that provides the answer.

where 'm' is the equation's scale's slope and 'b' is the y-intercept, or the point on the y-axis in which the line intersects, respectively.

Since, the x-intercept of the line 2x-3y=6 is (3, 0), we desire the following line's expression, which has a slope of 2, to pass over the position (3,0).

Use the formula y=mx +b, x=3, y=0 to get 'b'.

Hence,

0 = 2(3) + b

⇒ b= -6,

∴The expression for the line is y= 2x-6.

This line will cross at x=3 and 2x-3y=6.

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Answer:

1.a.  skew

1.b.  parallel

1.c.  none of the above

1.d.  perpendicular

1.e.  parallel

1.f.  skew

2.a.  never

2.b.  always

2.c.  always

2.d.  sometimes, sometimes, sometimes

Step-by-step explanation:

For these questions, it is critical to know the definitions of each of the terms.

Problem Breakdown

1.a.  skew  [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]

Point E is not on line AB.  Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar.  Point F is not in plane ABE.  Since line EF and line AB do not intersect and are not coplanar, they are skew.

1.b.  parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]

Line CD is parallel to line AB, and line AB is parallel to line EH.  Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.

1.c.  none of the above  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]

Line AC and line GA share point A, necessarily intersecting at A.  Therefore, line AC and line GA cannot be parallel or skew.

Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle?  If the figure is cube-shaped, as depicted, then no.

Note that each line segment AC, AG, and CG are all the diagonal of a cube face.  A cube has equal edge lengths, so each of those diagonals would be equal.  Thus, triangle ACG is an equilateral triangle.

All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle).  So, lines AC and GA are not perpendicular.  (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)

"none of the above"

1.d.  perpendicular  [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]

Line DG and line HG share point G, so they intersect.  Both lines are the edges of a face, so they intersect at a right angle.  Perpendicular

1.e.  parallel  [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]

Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face.  They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.

1.f.  skew  [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]

Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar.  Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.

2.a.  Two lines on the top of a cube face are never skew

Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face.  By definition, skew lines are not coplanar.  Therefore, these can never be skew.

2.b.  Two parallel lines are always coplanar.

If two lines are parallel, by definition of parallel lines, they are coplanar.

2.c.  Two perpendicular lines are always coplanar

If two lines AB and CD are perpendicular, they form a right angle.  To form a right angle, they must intersect at the right angle's vertex (point P).

Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P.  Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines.  Therefore, they must always be coplanar.

2.d.  A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular

Consider each of the following cases:

These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above.  So, those two lines are neither "always", nor "never", one of those choices.  Therefore, they are each "sometimes" one of them.

Using the normal distribution, it is found that 0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 5.43, \sigma = 0.54[/tex]

The proportion of rainy days have rainfall with pH below 5.0 is the p-value of Z when X = 5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5 - 5.43}{0.54}[/tex]

Z = -0.8

Z = -0.8 has a p-value of 0.2119.

0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.

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Answer:

Anita= 25 years old

Sumbo= 10 years old

Step-by-step explanation:

Start by forming 2 equations that represent the given information.

Let Anu's and Sumbo's ages be A and S respectively.

A= S +15 -----(1)

A² +S²= 725 -----(2)

Now, solve for A and S by substitution.

Substitute (1) into (2):

(S +15)² +S²= 725

Expand:

S² +2(S)(15) +15² +S²= 725

2S² +30S +225= 725

-725 on both sides:

2S² +30S -500= 0

Divide both sides by 2:

S² +15S -250= 0

Factorise:

(S +25)(S -10)= 0

S +25= 0             or            S -10= 0

S= -25 (reject)     or            S= 10

Sumbo's age cannot be a negative value hence -25 is rejected.

Substitute S= 10 into (1):

A= S +15

A= 10 +15

A= 25

A. all real numbers

the doman are the x values and in this equation they are infinite making the domain all real numbers

Using the concepts of domain and range of a function, the correct statement regarding the graph of the function f(x) = -(x + 3)(x - 1) is given by:

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

In a graph:

The graph of f(x) = -(x + 3)(x - 1) is given at the end of the answer, hence:

Hence the correct statement is:

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

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Answer:

180

Step-by-step explanation:

Find the LCM of 12, 18, and 20

[tex]12 = 2 \times 2 \times 3[/tex]

[tex]18 = 2 \times 3 \times 3[/tex]

[tex]20 = 2 \times 2 \times 5[/tex]

LCM = 2 × 2 × 3 × 3 × 5 = 180

Answer:

Step-by-step explanation:

hello :

Answer:

The first, third and last sequences

Answer:

See below

Step-by-step explanation:

Here is one way

cos^2 + sin^2 = 1

cos^2 = 1 - sin^2  

For angle A      cos^2 = 1 - (10/26)^2

                          cos ^2 = 1 - 100/676

                                       =  576/676

                              cos A = 24/26   = 12/13

Another way would be to use the Pythagorean theorem to find length of AB .... then cos A =   length AB / 26

The number of pairs of parallel sides of the polygon have no parallel sides if n is odd and n/2 pair of parallel sides if n is even.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

A regular polygon has n sides.

Then the number of pairs of parallel sides of the polygon will be

IF n is odd, then none of the sides are parallel.

If n is even, then the number of pair of parallel sides will be n / 2.

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The formula for finding the area of the triangle ΔABC will be half of the product of the base and height. Then the formula is A = 1/2 x BC x  AD.

The area of the triangle is given as

A = 1/2 x B x H

Where B is the base and H is the height of the triangle.

The triangle is given below,

We have

B = BC

H = AD

Then we have

A = 1/2 x BC x AD

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Step-by-step explanation:

as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.

v(t) = 60×ln(t + 1)

V(t) = 60 × integral(ln(t + 1)) between 0 and 5.

integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C

V(t) = 60 × ((t + 1)ln(t + 1) - t + C)

the distance traveled between t = 0 and t = 5 is then

60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =

= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =

= 60×(5.750556815... + C) - 60×C =

= 60×5.750556815... = 345.0334089... ≈ 345 km

Y=x+8

Table

[tex]\boxed{\begin{array}{c|c}\bf x&\bf y\\ \rm 2&\rm 10\\ \rm 0&\rm 8\\ \rm 4&\rm 12\end{array}}[/tex]

How?

x=2

x=0

x=4

Answer:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Given rule:

[tex]y=x+8[/tex]

The rule tells us that to the corresponding y-values, simply substitute the given value of x into the given rule:

[tex]x=2 \implies y=2+8=10[/tex]

[tex]x=0 \implies y=0+8=8[/tex]

[tex]x=4 \implies y=4+8=12[/tex]

Therefore, the completed table is:

[tex]\large\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 2 & 10 \\\cline{1-2} 0 & 8 \\\cline{1-2} 4 & 12 \\\cline{1-2}\end{array}[/tex]

Answer:

1/2 - 1/3,

1 - 1/2,

1/4 + 1/2

Step-by-step explanation:

1/4 + 1/2 = 1/4 + 2/4 = 3/4

1/2 - 1/3 = 3/6 - 2/6 = 1/6

1 - 1/2 = 2/2 - 1/2 = 1/2

Hence, the desired order is

1/2 - 1/3,

1 - 1/2,

1/4 + 1/2

Answer:

you got that

Step-by-step explanation:

wet wet wet

Answer:

{ x : x > 2 }

Step-by-step explanation:

4x - 3 + 6x > 5x + 7 , that is

10x - 3 > 5x + 7 ( subtract 5x from both sides )

5x - 3 > 7 ( add 3 to both sides )

5x > 10 ( divide both sides by 5 )

x > 2

Answer:

the answers are all right

The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.

On the basis of given data

The number given is 2,4,7

Size of the sample = 2 with replacement

The Total outcome with replacement will be given by

3² = 9

Possible outcome can be

2,2   2,4   2,7   4,4  4,2  4,7  7,7  7,2  7,4

The sample mean can be calculated as

(a+b)/2

(2+2)/2 = 2

similarly the mean of the samples will be  2 , 4.5 , 3 , 7 , 4

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Answer:

Step-by-step explanation:

Answer:

200 cans.

Step-by-step explanation:

f(c)=10r + 120

Put t=8 into it

T(c) = 10 x 8 + 120

=200 cans

(Use substitution method)

Answer:

9

Step-by-step explanation:

The Pythagorean Theorem is a² + b² = c². c² is the hypotenuse while a² and b² are the legs.

So plugging it into the equation,

a² + 12² = 15²

a² + 144 = 225

a² = 81

a = 9

steps:

1. square the values

2. isolate the missing value

3. take the square root of both sides

Answer:

x=50

Step-by-step explanation:

3x-5=145(vertically opposite angle)

3x=145+5

3x=150

x=150/3

x=50

DON'T FORGET TO WRITE DEGREE

Answer:

x = 50

Step-by-step explanation:

Vertically opposite angles are of equal measure.

3x - 5 = 145

3x = 145 + 5

3x = 150

x = 50

That's all i know, Hope it helps!

The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.

Probability refers to a possibility that deals with the occurrence of random events.

The marketing team has gathered data from a random month, in which there were 2039 class attendees.

The probability that a class attendee is a non-member of the gym and is attending a barre class

= 185/2039

= 0.09

The probability that a class attendee is a member of the gym and is attending a boot camp class

= 204/2039

= 0.10004

The probability for both the event would be

= 0.09 x 0.10004

= 0.009

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The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a statement:

Which of the following probabilities is the greatest for a standard normal distribution:

The options are:

P(-1.5 ≤ z ≤ -0.5)

P(-0.5 ≤ z ≤ 0.5)

P(0.5 ≤ z ≤ 1.5)

P(1.5 ≤ z ≤ 2.5)

As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.

From the Z-curve:

P(-1.5 ≤ z ≤ -0.5)  = 9.2% + 15% = 24.2%

P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%

P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%

P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%

Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

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Answer:

B) P (-0.5 <= z <= 0.5)

Step-by-step explanation:

Step-by-step explanation:

I'm going to assume you mean

[tex]log(5^{125})[/tex] which can be rewritten as [tex]125 log(5)[/tex] since if you start with [tex]log(a) = x = > 10^x=a\\(10^x)^c=a^c\\c *log(a^c)[/tex]since when you do (10^x)^c you're just multiplying the exponent which is represented by the x but is equal to the log you just multiply the log which is why you can bring it in front.

You can then approximate the value of log(5) using a calculator and multiply by 125 to get around 87.371

The matching is done below

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

1) 3 is the difference of 2 times d minus 3.

As, 2*d - 3

=2*3 - 3

=6 - 3

= 3

2) 4 is 4 added to the difference of d minus 3.

or, 4 + (d - 3)

or, 4 + (3 - 3)

or, 4 + 0 = 4

3) 0 is  the difference of d minus 3 divided by 2.

(d - 3)/2

= (3 - 3)/2

= 0/2

= 0

4) 2 is the quotient of 12 divided by the difference of 3 times d minus 3.

12/(3d - 3)

=12/(3*3 - 3)

=12/(9 - 3)

=12/6

= 2

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