Johnny just became a personal trainer and is finalizing his pricing plans. One plan is to charge $74 for the initial consultation and then $64 per session. Another plan is to charge $20 for the consultation and $66 per session. Johnny realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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The solution of the system of equation 2x + 4y = 16, 2x - 4y = 0 is (4, 2). The correct option is A.

System of equations can be solved using different method such as substitution method, elimination method and graphical method. The system of equation can be solved with the elimination method as follows:

2x + 4y = 162x - 4y = 0

add equation(ii) to equation(i)

2x + 2x  = 16 + 04x = 16

divide both sides by 4x = 16

x = 4

Let's find y

2x - 4y = 0-4

y = -2x-4y = -2(4)

-4y = -8

divide both sides by -4y = -8 / -4y = 2

Therefore, the solution is (4, 2)

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Her total salary for the month would be $8300.

We have a women with $3,200 as a base salary each month. She gets 8.5% of everything she sells. If she sold $60,000 worth of items this month.

Assume her total salary to be y = $(3200 + x). Then, we can write -

y = $(3200 + {8.5/100} x 60000}

y = $(3200 + 5100)

y = $8300

Therefore, her total salary for the month would be $8300.

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The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7

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

f(x) = 12(x + 6)² - 3

The transformation is given as

11 units to the right and 4 units down

This is represented as

(x - 11, y - 4)

So, we have the following representation

g(x) = 12(x + 6 - 11)² - 3 - 4

Evaluate

g(x) = 12(x - 5)² - 7

Hence, the function is g(x) = 12(x - 5)² - 7

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Option 'a' is the correct answer.

Z0.05 represents the z-score, the value of the standard normal distribution, at which the probability of being greater than that value is 0.05. The value is Z0.05 =1.65.

In a normal distribution, data points are referred to as x, whereas in a z-distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations a given number (x) is from the mean:

Every z score has a corresponding p-value that indicates the likelihood that all values below or above that z score will occur.

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The distance between John's friend and the building is 14.9 metres.

From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop.

Therefore, the distance of John's friend from the building can be calculated as follows:

This situation forms a right angle triangle.

Hence, using trigonometric ratios,

tan 50 = opposite / adjacent

tan 50 = 16 + 1.8 / x

tan 50° = 17.8 / x

cross multiply

x tan 50° = 17.8

x = 17.8 / tan 50

x = 17.8 / 1.19175359259

x = 14.9359734675

x = 14.9 metres

Therefore,

distance of John's friend to the building  = 14.9m

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The probability to determine the time needed to complete the project, we simply added the time required for activities 1 and 2.

1 (1): the chance that a given event will occur

 (2): the ratio of the number of outcomes in an exhaustive set of equally     likely outcomes that produce a given event to the total number of possible outcomes a branch of mathematics concerned with the study of probabilities

2 : something (such as an event or circumstance) that is probable

3: the quality or state of being probable

4: a logical relation between statements such that evidence confirming one confirms the other to some degree

The best-case scenario's calculation of the project's completion time is displayed below;

= Week spent on Activities A1 +  Week spent on Activities A2.

= 5 weeks plus 7 weeks.

= 12

To determine the time needed to complete the project, we simply added the time required for activities 1 and 2.

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Considering the definition of perpendicular line, the equation of the perpendicular line is y= 1/5x - 13/5.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= -5x +1.

In this case, the line has a slope of  -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:

(-5)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-5)

slope perpendicular line= 1/5

So, the perpendicular line has a form of: y= 1/5x + b

The line passes through the point (2, -1). Replacing in the expression for perpendicular line:

-1= 1/5× 2 + b

-1= 2/5 + b

-1- 2/5= b

-13/5= b

Finally, the perpendicular line is y= 1/5x - 13/5.

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Answer:

Step-by-step explanation:

its ab

Answer:

x = 6 units

Step-by-step explanation:

We know that, By pythagoras theorem,

Hypotenuse2 = base2 + perpendicular2

Given, Hypotenuse = 6.5

perpendicular = 2.5

base = x

So, by putting the values,

6.52 = 2.52 + x2

42.25 = 6.25 + x2

36 = x2  

Hence, x = 6 units

A logarithmic function is defined by f(x) = [tex]log_a[/tex]x(r) y = [tex]log_a[/tex]x, where a > 0 and y = [tex]log_a[/tex]x. It is the inverse of the exponential function [tex]a^{y}[/tex] = x.

During the 16th century, Scottish mathematician, scientist, and astronomer John Napier discovered logarithms. The technique is widely used in astronomical and scientific calculations involving huge numbers. As an inverse of exponential functions, logarithmic functions are closely related to exponential functions. By transforming [tex]a^{x}[/tex] = N into [tex]log_a[/tex] N = x, the exponential function is transformed into a logarithmic function.

Let's say that y=[tex]10^{\log x}[/tex]

see this, 100=[tex]10^2[/tex],

then [tex]log _{10}[/tex] 100 = 2

therefore, [tex]log _{10}[/tex] y=[tex]\log _{10}[/tex] xy = x

[tex]10^{\log x}[/tex] = x

Hence, proved.

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Answer: In ΔABF & ΔACE

AB/FB = AC/EC   (As both the triangles are similar)

as B is the midpoint of AC = 48

AB = 24

So,

24/23 = 48 / EC

EC = 46

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The value of EC is equal to 69 units

Triangle Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

Given here, AX=24 And FB=23

Now applying the triangle midpoint theorem we get the value of

AC =3×23

      = 69 units

Hence, The value of EC is equal to 69 units

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Answer:a=6,25

Step-by-step explanation:

i did the test yesterday

The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

34(2a − 6) + 12 = 25(3a + 20) + a

Simplify the equation, then the value of the variable 'a' is given as,

34(2a − 6) + 12 = 25(3a + 20) + a

68a − 204 + 12 = 75a + 500 + a

68a − 192 = 76a + 500

Simplify the equation further, then the value of the variable 'a' is given as,

76a − 68a = − 192 − 500

8a = − 692

a = − 692 / 8

a = −86.5

The solution of the equation 34(2a − 6) + 12 = 25(3a + 20) + a will be negative 86.5.

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The maximum value of x in the figure given is of:

x = 33º.

The maximum value of x is obtained when the segment traced represents a bisection of the angle at the vertex of the quadrilateral.

A bisection is defined as a segment that splits an angle measure into two equal measures.

The angle measures for this problem are given as follows, from the image:

Then the maximum value of x is obtained when these two measures are equal, as follows:

2x + 5 = 71

2x = 71 - 5

2x = 66

x = 66/2

x = 33º.

(the bisection concepts means that the larger angle, which would be of 2 x 71 = 142º, would be split into two angles with an equal measure of 71º).

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Answer:

22/55 = 40% = 0.4

Step-by-step explanation:

22/55

Reduce the fraction by dividing the numerator and denominator by 11.

22/55 = 2/5

Now use a calculator, or long division, to divide 2 by 5.

22/55 = 2/5 = 0.4

To change a decimal to a percent, multiply the decimal by 100%.

0.4 × 100% = 40%

Answer: 22/55 = 40% = 0.4

Answer:

8−72+12−8

Step-by-step explanation:

Answer: n = 4

9 = x

y = 2

Step-by-step explanation:

2 ( x + 5 ) = 3x + 1

2x +10 = 3x + 1

10 = 1x + 1

- 1       -1

9 = 1x

9 = x

3y - 4 = 6 - 2y

5y -4 =6

5y = 10

y = 2

3 (n + 2) = 9 ( 6-n)

3n + 6 = 54 -9n

3n +9n = 54 - 6

12n =54 -6

12n =48

n = 4

Answer: 75 minutes to 25 minutes

Step-by-step explanation:

To find the ratio between 1 1/4 hours and 25 minutes, we first need to convert both quantities to the same unit of time. Since 1 hour is equal to 60 minutes, 1 1/4 hours is equal to 1.25 * 60 = 75 minutes. Therefore, the ratio between 1 1/4 hours and 25 minutes is 75 minutes to 25 minutes, or 3 to 1.

Answer:

Step-by-step explanation:

The required graph of the given function d(x)=−1/2x−3 has been shown.

Given that, to plot the graph of the linear function,  d(x)=−1/2x−3.

What is the graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,

The graph of the liner function d(x)=−1/2x−3 can be plot by putting the values of the x in the equation which gives the value of y by calculating such an ordered pair we can plot the curve of the liner equation on the graph. i.e.

At x = 0

d(0) = -1/2 * (0) - 3

d(0) = -3

So, the ordered pair will be (0, -3).

Now, put x = 2

d(2) = -1/2 * 2 - 3

d(2) = -1 - 3

d(2) = - 4

So the ordered pair will be (2, -4)

joining these two points will show the graph of the given equation d(x)=−1/2x−3.

Thus, the required graph of the given function d(x)=−1/2x−3 has been shown.

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The function g(x) = √x + 4 is the result of a vertical translation 4 units up of the function f(x) = √x. (Right choice: B)

In this problem we find the definition of a function f(x) and its image g(x). Both f(x) and g(x) are radical functions and we need to determine the transformation rule to obtain the latter function. By direct inspection, g(x) is the result of applying a vertical translation, whose definition is shown below:

g(x) = f(x) + k

Where:

Please notice that k indicates a translation in the +y direction. k > 0 indicantes a vertical shift k units up.

Then, g(x) is the result of a vertical translation (4 units up) on f(x).

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Answer:

D

Step-by-step explanation:

To find the solutions, let's calculate the determinant:

Δ = (-1)²-4(-2)(-1) = 1-8 = -7

the solution is: (1 ±√-7)/(-4)

√-7 indicates there are two complex solutions

For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.

A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.

Using a standard normal table the area to the right of z = 1.75 is given by

P(z > 1.75) = .0401

Therefore, the correct option is a.

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The distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.

Distance is the total movement of an object without any regard to direction.

To calculate the approximate reaction distance, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitiute these values into equation 1

Hence, the distance of the reaction is 11.73 m.

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583 times the length of jeff's ride was larry's bike ride

Word problem in maths is a maths question written as one sentence or more that requires children to apply their maths knowledge to a ‘real-life’ scenario. a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.Word problems are usually made up of a few sentences describing a scenario that needs to be solved through maths. These scenarios are usually ‘real-life- ones, situations that people might find themselves in every day. For example, it could be the division of pizza between party members or working out how long a train might take from one place to another.

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.

Given,jeff jogged 4 miles today, and larry biked 2 1/3 miles.

Let x times the length of jeff's ride was larry's bike ride.

4x= 7/3

x=.583 times

So, .583 times the length of jeff's ride was larry's bike ride.

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The information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.

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Answer:

Sum of G.P. series is given by,

Sum=

r−1

a(r

n

−1)

when r>1

Where a= first term, n=n

th

term and r is common ratio.

Here, a=1,n=10,r=

3

S

10

=

(

3

−1)

1×{(

3

)

10

−1}

=

(

3

−1)

(3

5

−1)

×

(

3

+1)

(

3

+1)

=

(3−1)

242(

3

+1)

=121(

3

+1).

Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:

The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).

The graph of the inverse function is a reflection in the line y = x.

Therefore, the endpoints of the inverse function are:

The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Step-by-step explanation:

Answer: -10

Step-by-step explanation:

y2-y1

---------

x2-x1

The distances between the points are given as follows:

As these two distances are equal, point A is equidistant from the endpoints of segment BC.

The distance between points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the distance of point A to the endpoint B is calculated as follows:

[tex]D = \sqrt{(7 - (-7))^2 + (0 - 8)^2} = \sqrt{260}[/tex]

The distance of point A to the endpoint C is calculated as follows:

[tex]D = \sqrt{(-5 - (-7))^2 + (-8 - 8)^2} = \sqrt{260}[/tex]

As the distance from point A to point B is equals to the distance from point A to point C, the point A is equidistant from the endpoints of segment BC.

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The value of x = 50

Exterior angle:

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.

In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

given that

m∠6 = x

m∠7 = x-20

m∠11 = 80

we solve this by using exterior angles

sum of 2 interior angles is equal to one  exterior angle

m∠6 + m ∠7 = m∠11

x + x - 20 = 80

2x = 80 + 20

2x = 100

x = 100/2

the value of x = 50

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