Question 3 of 5
Select the correct answer.
Find the Inverse of the given function.
f-¹ (x) = -7√x + 4
Of-¹(x) = ¹ +4
O f-¹(x) = 42²
O f¹(x) = 7x³ + 4
f(x) = √72-4

Answer:

$34.38

Step-by-step explanation:

Y: A random variable that indicates the amount of money that the seller will receive.

p=2,50$

if  x=0  →  y=0.2,50=0$

if  x=5  →  y=5.2,50  = 12,5  $

if  x=10  →  y=10.2,50= 25$

if  x=15  →  y=15.2,50=  37,5$

if  x=20  →  y=20.2,50=  50  $

if  x=25  →  y=25.2,50=  62,5$

Y=  { 0$ ; 12,5$ ; 25$ ; 37,5$ ; 50$ ; 62,5$ }

E(Y)=  ∑Y.P(Y)

=  0.P(0)+12,5.P(12,5)+  25.P(25)+  37,5.P(37,5)+  50.P(50)+  62,5.P(62,5)

=  0.0,01+  12,5.0,15+  25.0,25+  37,5.0,3+  50.0,25+  62,5.0,04

= 0 + 1,875 + 6,25 + 11,25 + 12,5 + 2,5

= 34,38$ expected value of the amount of money the seller receives.

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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Both observed OR and true OR indicate that migraine headache is associated with increased odds of frequent cell phone use.

We know that,

Currently, In the studies of Migraine and cell phone use:

Researchers have observed that When we use our mobile phone more and more then there are higher chances of developing migraines and other symptoms.

Such as that cellular phones, has been found reason of an opening of the blood-brain barrier that separates the bloodstream from the brain and cerebral spinal fluid.

But, We know that,

Headaches have been associated with the opening of this barrier.

Hence the answer is, Both observed OR and true OR indicate that migraine headache is associated with increased odds of frequent cell phone use.

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Answer:

Given

Given

Transitive

Substitution

Subtraction

Addition

Substitution

Multiplication

Hard to see list of options. But this should help.

Given

Given

Transitive

substitution property of equality

Subtraction property of equality

Addition property of equality

multiplication property of equality

Simplify

simplify

Substitution means putting numbers in place of letters to calculate the value of an expression.

The transitive property states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”

The addition and subtraction property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

According to the given question.

AB = BC and BC = CD              ( Given)

AB = 3x - 1 and CD = 2x + 3      ( Given)

Since,

AB = BC and BC = CD

⇒ AB = CD  (transitive)

Substitute the value of AB and CD in AB = CD

⇒  \(3x - 1 = 2x + 3\)  (substitution property of equality)

⇒  \(x -1= 3\)               (subtraction property of equality)

⇒   \(x = 4\)                     (Addition property of equality)

Since,

AB = BC

⇒ AB= 3x -1        

⇒ \(AB = 3(4) - 1\)                   ( multiplication property of equality)

⇒ \(AB = 11\)                          (simplify)                                  

Therefore,

BC = 11                               (simplify)

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yes 7:15 is proportional relationship

The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

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Answer:

So, the time interval between successive compression from the source is 0.002 seconds.

Step-by-step explanation:

Given that,

Frequency of the tone, f = 500 Hz

It is sitting at a distance of 450 m from the source of sound, d = 450 m

Let t is the time interval between successive compression from the source. We know that the relation between the frequency and the time period is :

\(T=\dfrac{1}{f}T=\dfrac{1}{500}\\\\T = 0.002 s\)

A diagram that models the ratio in the story is shown in the image attached below. If the Capybaras had 80 fans in the stands, the number of Iguanas fans that were in the stands is equal to 96 Iguanas fans.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used for denoting the proportion of two (2) or more quantities with respect to one another and the total quantities. This ultimately implies that, a ratio can be expressed as a quotient.

Let the variable I represent the number of Iguanas fans.

Let the variable C represent the number of Capybaras fans.

Therefore, the ratio of the 6 Iguanas fans to 5 Capybaras fans is given by:

I:C = 6:5

Next, we would determine the number of Iguanas fans if there are 80 Capybaras fans:

6 Iguanas fans = 5 Capybaras fans

x Iguanas fans = 80 Capybaras fans

Cross-multiplying, we have:

x Iguanas fans = (80 × 6)/5

x Iguanas fans = 480/5

x Iguanas fans = 96 Iguanas fans.

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The blanks in each statement about the line segment should be completed as shown below.

Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:

8x + 11 = 12x - 1

Solve for x

We now want to solve for x.

−4x+11=−1

−4x = -12

x= 3

Solve for TU, UV, and TV

This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(3)+11

TU= 35

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Based on the segment addition postulate, we have:

TU+UV=TV

35+35=TV

TV= 70

Find the detailed calculations below;

TU = UV

8x + 11 = 12x - 1

8x + 11 - 11 = 12x - 1 - 11

8x = 12x - 12

8x - 12x = 12x - 12 - 12x

-4x = -12

x = 3

By using the substitution method to substitute the value of x into the expression for TU, we have:

TU = 8x + 11

TU = 8(3) + 11

TU = 24 + 11

TU = 35

By applying the transitive property of equality, we have:

UV = TU and TU = 15, then UV = 35

By applying the segment addition postulate, we have:

TV = TU + UV

TV = 35 + 35

TV = 70

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Answer: f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option

Step-by-step explanation:

Both are quadratic equations: -x^2 or x^2

Blue graph: x^2 since it's facing up

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

Vertex: When x=-1, y=0 ==> 0=(-1+b)^2

0=-1+b

b=1

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

f(x)=(x+1)(x+1)

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

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

Red graph: -x^2 since it's facing down

g(x)=-x^2+b

Vertex: When x=0, y=1 ==> 1=(0)^2+b

1=0+b

b=1

g(x)=-x^2+1

f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option

Answer:

0.53< I just did the quiz.

Step-by-step explanation:

The minimum value for the heights is p1 = -4. To find the best straight line using the given points (0,0), (1,8), (3,8), and (4,20) and the given time points t = 0, 1, 3, and 4, we will use the least squares method.

We'll set up a system of linear equations, A^TAx = A^Tb, and solve for the unknowns.

First, let's define our matrix A, which will have the time points as the first column and 1s as the second column:

A = | 0 1 |
   | 1 1 |
   | 3 1 |
   | 4 1 |

The vector b represents the heights at each time point:

b = | 0  |
   | 8  |
   | 8  |
   | 20 |

Next, we will compute A^T (the transpose of A) and the product A^TA:

A^T = | 0 1 3 4 |
     | 1 1 1 1 |

A^TA = | 26  8 |
      | 8   4 |

Similarly, compute the product A^Tb:

A^Tb = | 104 |
      | 36  |

Now, solve the system A^TAx = A^Tb for the unknowns x:

x = (A^TA)^(-1) * A^Tb = | 2  |
                         | -4 |

So, the best straight line can be described as:

y = 2t - 4

Now we will find the four heights (pi) and four errors (ei):

For t = 0, p1 = 2(0) - 4 = -4, e1 = 0 - (-4) = 4
For t = 1, p2 = 2(1) - 4 = -2, e2 = 8 - (-2) = 10
For t = 3, p3 = 2(3) - 4 = 2,  e3 = 8 - 2 = 6
For t = 4, p4 = 2(4) - 4 = 4,  e4 = 20 - 4 = 16

The minimum value for the heights is p1 = -4.

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Answer:

sorry can't understand this language

Answer:

$8.2225

Step-by-step explanation:

100% - 45% = 55%

then divide 55 by 100 to get .55

lastly multiply .55 to 14.95 to get 8.2225

Answer:

8,000 pounds

Step-by-step explanation:

1 US ton = 2,000 pounds

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

1 ton is 2000 pounds

4 tons = 8000 pounds

The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

478 / 479

Step-by-step explanation:

6% of 368 is 22.08.

5 days = 6% x 5 = 30%.

30% of 368 = 110.4

110.4 + 368 = 478.4

492 people will be infected with the virus in 5 days.

An equation contains one or more terms with variables connected by an equal sign.

We have,

Number of people infected = 368

Rate of spreading = 6%

We can make an equation for the number of people infected in x days.

y = 368 x \((106/100)^x\)

y = 368 x \(1.06^x\)

Substitute x = 5

y = 368 x \(1.06^5\)

y = 492.467

y = 492

Thus,

492 people will be infected with the virus in 5 days.

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Answer:

Step-by-step explanation:

y=-\frac{1}{2}x+\frac{11}{2}

Answer:

See Picture

Step-by-step explanation:

Can you mark me Brainliest for this?

Using the probability concept, it is found that there is a 0.8901 = 89.01% probability that a worker chosen at random was not employed in the manufacturing industry.

The question is incomplete, but the pie-chart can be found in the internet.

Hence:

\(p = \frac{129702}{145717} = 0.8901\)

0.8901 = 89.01% probability that a worker chosen at random was not employed in the manufacturing industry.

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Answer:

(-9c)2 and -9c2 when c=5.

Step-by-step explanation:

(-9c)2= doesn't have an answer and -9c2=-90

Answer:

25.9%

Step-by-step explanation:

Since, the actual dimensions of the cylinder is not given we can assume the some dimension to explain the problem

Let us assume the dimension of the cylinder be

radius= 3in

height= 5 in

The expression for the total surface area of a cylinder is

T. S. A. =2πrh+2πr^2

Let us plug in the values to to find TSA

T. S. A. =2×3.14×3×5+2×3.14×3^2

Solving we get

T. S. A. =94.26+56.556

T. S. A. =150.816 in^2

Now let us find the error

we know that error % is calculated as

%error= [actual value-expected value/expected value]×100

%error= [190 -150.816/150.816]×100

%error= [39.184/150.816]×100

%error= 0.259×100

%error= 25.9%

Answer:

Step-by-step explanation:

1/144

hope this helps :)

The focal length of the lens is 40cm.

The distance between the center of a lens or curved mirror and its focus.

A plane convex lens is made of glass ( n = 1. 5) with one flat surface and the other having a radius of 20 cm.

The focal length of the lens is given by the following formula;

\(\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\Where; \ r_1 =\infty , \ r_2=20, \ and \ n = 1.5\)

Substitute all the values in the formula;

\(\rm \dfrac{1}{f}=(n-1) \left ( \dfrac{1}{r_1}-\dfrac{1}{r_2} \right)\\\\\rm \dfrac{1}{f}=(1.5-1) \left ( \dfrac{1}{\infty}-\dfrac{1}{20} \right)\\\\ \rm \dfrac{1}{f}=(0.5) \left ( 0-\dfrac{1}{20} \right)\\\\ \dfrac{1}{f} = \dfrac{-0.5}{20}\\\\\dfrac{1}{f}=-0.025\\\\f = \dfrac{-1}{0.025}\\\\f=-40\)

Hence, the focal length of the lens is 40cm.

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Answer:

5 dollars and 15 cents

Step-by-step explanation:

answer:

c. 7.2

explanation:

on a number line, move the number 7.4 left to tenths. the result is 7.2.

We would calculate the volume by applying the formula,

Volume = length x width x height

From the information given,

length = 0.000000022

width = 0.000000255

height = 0.00000255

Thus,

Volume = 0.000000022 x 0.000000255 x 0.00000255

Volume = 1.431 x 10^-20 m^3

Answer:

Yes

Step-by-step explanation:

upon graphing it, I discovered that it made a straight line

X-intercept: 0.5

Y-intercept: -2

Answer:

B. The graph of the function starts high and ends low.

Step-by-step explanation:

The correct statement regarding the variation of the two measures is given as follows:

C. Yes, they vary directly. When one quantity increases, the other quantity also increases.

For this problem, we have that when the number of correct answers on the test increases, the score also does, hence the two quantities vary directly, and option c is the correct option for this problem.

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Each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.Option B,E,F.

Each chart has the following three components:

1. B. A center line representing the average: This line is drawn to show the average value or mean of the data being analyzed. It provides a reference point to compare the data points above and below it.

2. E. An upper line representing the maximum acceptable variation upwards: This line is drawn to indicate the upper limit of acceptable variation or deviation from the average. It helps identify if the data points exceed the acceptable range.

3. F. A lower line representing the maximum acceptable variation downwards: This line is drawn to indicate the lower limit of acceptable variation or deviation from the average. It helps identify if the data points fall below the acceptable range.

These three components together create a control chart, which is a graphical representation used in statistical process control. Control charts help monitor and analyze data over time, allowing organizations to identify trends, detect abnormalities, and make data-driven decisions to improve processes and quality.

In summary, each chart consists of a center line representing the average, an upper line indicating the maximum acceptable deviation upwards, and a lower line indicating the maximum acceptable deviation downwards. These components help analyze data and monitor process performance.

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