Consider the following 8 numbers, where one labelled x is unknown.
24, 4, 1 ,x, 39, 5 ,37, 48.
Given that the range of numbers is 66, work out two values of x.

Answer:

[tex]f^{-1} = \frac{x-1}{2}[/tex]

Step-by-step explanation:

[tex]f(x) = 2x+1[/tex]

Replace it with y

[tex]y = 2x+1[/tex]

Exchange the values of  x and y

[tex]x = 2y+1[/tex]

Solve for y

[tex]x = 2y+1[/tex]

Subtracting 1 from both sides

[tex]2y = x-1[/tex]

Dividing both sides by 2

[tex]y = \frac{x-1}{2}[/tex]

Replace it by [tex]f^{-1}[/tex]

So,

[tex]f^{-1} = \frac{x-1}{2}[/tex]

Answer:

[tex]\displaystyle f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]

Step-by-step explanation:

f(x) = 2x + 1

f(x) = y (output)

y = 2x + 1

Solve for x.

y - 1 = 2x

Divide 2 on both sides.

y/2 - 1/2 = x

1/2y - 1/2 = x

Switch variables.

1/2x - 1/2 = y

[tex]f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]

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▹ Answer

Exponential

▹ Step-by-Step Explanation

Every time 1 is added to x, y multiples by 2.

0 + 1 = 1

1 + 1 = 2

2 + 1 = 3

3 + 1 = 4

-2 * 2 = -4

-4 * 2 = -8

-8 * 2 = -16

-16 * 2 = -32

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Answer:

[tex] P(38.6 <X <57.8)[/tex]

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

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

And replacing we got:

[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]

[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]

We can find the probability of interest using the normal standard table and with the following difference:

[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]

Step-by-step explanation:

Let X the random variable who represent the expense and we assume the following parameters:

[tex]\mu = 45, \sigma 16[/tex]

And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:

[tex] P(38.6 <X <57.8)[/tex]

And we can assume a normal distribution and then we can solve the problem with the z score formula given by:

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

And replacing we got:

[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]

[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]

We can find the probability of interest using the normal standard table and with the following difference:

[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]

Complete Question is;

Write a polar equation of a conic with the focus at the origin and the given data. hyperbola, eccentricity 3.5, directrix y =2

Answer:

r = 14/(2 + 7(sinθ))

Step-by-step explanation:

We are given;

Eccentricity;e = 3.5

Directrix; y = 2

This means that d = 2

We are told that the focus is at the origin, so since the directrix is at y = 2,then the part of the hyperbola that is closest to this focus will open downwards and the equation is given by;

r = ed/(1 + e•sinθ)

Plugging in the relevant values, we have;

r = (3.5 × 2)/(1 + 3.5(sinθ))

r = 7/(1 + 3.5(sinθ))

To make every figure a whole number, let's multiply numerator and denominator by 2 to give;

r = 14/(2 + 7(sinθ))

Answer:

Well I took it"s Reflect the intermediate image.  and Multiply the vertices of polygon ABCD by One-half.

Step-by-step explanation:

Answer:

2 and 5 or B and E

Step-by-step explanation:

i did it on edge! ; )

Answer:

The least five digit number is

Hope this helps you

Answer:

a(x) * b(x)  will give a quadratic function

Step-by-step explanation:

A quadratic function is one with an x^2 term

a(x) = 2x - 4 and b(x) = x + 2

a(x) + b(x) will only have an term with the highest power of x

a(x) - b(x) will only have an term with the highest power of x

a(x) * b(x) will only have an term with the highest power of x^2

Answer:

Both Brittany and Sid are correct.

Step-by-step explanation:

Since both heights drawn would be equal to each other because they are the same triangle (but in different locations), the heights would equal each other.

Answer:

They are both correct

Step-by-step explanation:

The height is how tall the figure is.

They represent the height.

Answer:

  270

Step-by-step explanation:

  f(5) = 7 +4·5 = 27

  g(5) = 1/(2·5) = 1/10

The ratio of functions is the ratio of their individual values:

  (f/g)(5) = f(5)/g(5) = 27/(1/10)

  (f/g)(5) = 270

Answer:

6 -6r

Step-by-step explanation:

8 - (6r + 2)

Distribute the minus sign

8 - 6r -2

Combine like terms

6 -6r

Answer:

A. -6r+6

Step-by-step explanation:

We are given the expression:

8-(6r+2)

First, let's distribute the negative sign. Multiply each term inside the parentheses by -1.

8+ (-1*6r) + (-1*2)

8-6r-2

Now, combine like terms. Add the constants, or terms without a variable.

-6r + (8+-2)

-6r + (8-2)

-6r + (6)

-6r+6

The answer is A. -6r+6

Explanation:

Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)

r = radius

h = height of cone

In this case,

r = 8 is the radius

h = 41

So,

SA = surface area

SA = pi*r^2 + pi*r*sqrt(r^2+h^2)

SA = pi*8^2 + pi*8*sqrt(8^2+41^2)

SA = 1250.936884057 use a calculator for this step

SA = 1251 square meters approximately

Answer:

m∠1 = 99°

Step-by-step explanation:

∠2 and ∠81° are Corresponding Angles, so they are equal to each other:

∠2 = 81°

∠1 and ∠2 are Supplementary Angles, so they add up to 180°:

180 - m∠2 = m∠1

180 - 81 = 99°

Answer:

The answer is C (j' 1,4). It is not B J'(4, 1) because the new coordinate is moving 90 degrees clockwise not 180 degrees.

Step-by-step explanation:

J' will have coordinates (1, 4) after  90° clockwise rotation

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Rectangle JKLM is rotated 90° clockwise about the origin.

On a coordinate plane, rectangle J K L M has points (-4, 1), (-1, 1), (- 1, - 1), (- 4, - 1).

After rotating the rectangle 90° clockwise about the origin, the point J(-4, 1) will be transformed to a new point J' with coordinates (y, -x).

Thus, J' will have coordinates (1, 4).

Therefore,  J' will have coordinates (1, 4) after  90° clockwise rotation

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Answer:

the probability that 7 out 10 Internet users will order something online is 0.78 or 78%

Step-by-step explanation:

Given that:

Internet users who order something online = 85%

To find:

Probability that 7 out of 10 Internet users will order something online ?

Solution:

This problem is of binomial distribution of probability.

where, p = 0.85

q = 1-p = 0.15

r = 7 and

n = 10

Formula is given as:

[tex]P(x = r) = _nC_r q^{n-r}p^r[/tex]

Putting all the values:

[tex]P(x = 7) = _{10}C_7 0.15^{10-7}\times 0.85^7\\P(x = 7) = _{10}C_3 0.15^{3}\times 0.85^7\\P(x = 7) = 10\times 9 \times 8 \times 0.15^{3}\times0.85^7\\P(x = 7) = 720 \times .0034 \times0.32\\P(x = 7) = 0.78[/tex]

So, the probability that 7 out 10 Internet users will order something online is 0.78 or 78%.

Answer:

14 = n - 6

Step-by-step explanation:

"Is" indicates equal to. "Less" means subtract.

The equation that shows this relationship would be; 14 = n - 6.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

We have been given a statement "Fourteen is 6 less a number (n)."

So  here, "Is" indicates equal to sign. "Less" means subtract.

The equation form would be;

14 = n - 6

The equation that shows this relationship would be; 14 = n - 6.

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Answer:

43.68cm²

Step-by-step explanation:

area of a parallelogram=base×height

8.4cm×5.2cm

43.68cm²

Answer:

A= 43.68 cm²

Step-by-step explanation:

Area of Parallelogram =  base × height

Step 1: Plug in the values ⇒  A= 8.4 × 5.2

Step 2: Simplify ⇒ A= 43.68

Step 3: Units ⇒ A= 43.68 cm²

Answer:

  -17.67 +3.43i

Step-by-step explanation:

Carry out the indicated math:

  18 cis 169° = (18·cos(169°) +i·18·sin(169°)) = (18·(-0.9816) +i·18·0.1908)

  = -17.67 +i·3.43

Answer:

The rectangular form is z = -17.67 + i 3.43

Step-by-step explanation:

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▹ Answer

r = 4

▹ Step-by-Step Explanation

15r - 6r = 36

Collect like terms

9r = 36

Divide

r = 4

Final Answer

r = 4

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Answer: The answer would be 4, which is B, hopefully this helps.

Answer:

([tex]\sqrt{15}[/tex])/7

Step-by-step explanation:

Let b be the tird side of the triangle

tanθ= b/c

using the pythagorian theorem we get :

a²+b²= c² ⇒ b²= c²-a²= 8²-7²=15 ⇒b=√15

so: tanθ= √15/7

Answer:

A)

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is  significant difference between in drug resistance between the two states

B)

The calculated value Z =  2.7261 > 2.054 at 0.02 level of significance

Rejected H₀

There is a significant difference in drug resistance between the two states.

C)

P - value = 0.0066

P - value = 0.0066 < 0.02

D)

1) Reject H₀  

There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 174

Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.

First sample proportion

                    [tex]p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632[/tex]

Given second sample size n₂ = 375

Given data  Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant

Second sample proportion

                 [tex]p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186[/tex]

Step(ii):-

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is  significant difference between in drug resistance between the two states

Test statistic

          [tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

       Where

        [tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }[/tex]

       [tex]P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } = \frac{17.9718}{549} = 0.0327[/tex]

      Q = 1 - P = 1 - 0.0327 = 0.9673

Step(iii):-

 Test statistic

          [tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

         [tex]Z = \frac{0.0632-0.0186 }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }[/tex]

      Z  =   2.7261

Level of significance = 0.02 or 0.98

The z-value = 2.054

The calculated value Z =  2.7261 > 2.054 at 0.02 level of significance

   Reject H₀  

There is a significant difference in drug resistance between the two states.

 P- value

P( Z > 2.7261) = 1 - P( Z < 2.726)

                        = 1 - ( 0.5 + A (2.72))

                        = 0.5 - 0.4967

                         = 0.0033

we will use two tailed test

2 P( Z > 2.7261)  = 2 × 0.0033

                           = 0.0066

P - value = 0.0066 < 0.02

 Reject H₀  

There is a significant difference in drug resistance between the two states.

Answer:

a. Country Z's GDP will double in 23 years' time, given the experts prediction of 5% growth for 3 and 3% thereafter.

b. Z's GDP 's growth rate would be 39%.

This growth rate is calculated by determining Z's GDP from the end of 2025 as 292,000.  So, (292,000 - 210,000)/210,000 x 100 = 39% from the 2019 base year.

Step-by-step explanation:

a) 2019 Country Z's GDP = 210,000

2019 Growth rate = 5%

Future growth rate:

2019 - 2022 = 5%

2022- 2025 = 3%

2025 - so on = 1%

Let Country Z's GDP in 2019 = G₀ = 210,000

n = number of years from 2019

g = growth rate = 5%

(1 + g)ⁿ = increase in GDP as a result of the growth rate and number of years

Gⁿ = GDP in n years

Therefore, Gⁿ = G₀(1 + g)ⁿ

b) With GDP growth of 5% from 2019 to 2022, the GDP will be

= 210,000 (1 + 5%)³

= 210,000 x 1.158

= 243,000 approx.

c) From 2022 to 2025 at 3%, the GDP will be

= 243,000 (1 + 3%)∧20

= 243,000 x 1.817

= 441,531

d) Z's GDP from 2025 with 1% growth and so on, will become double at:

Gⁿ = 265,600(1 + 1%)∧48

= 265,600 x 1.61

= 428,000

48 + 6 = 54 years.

Answer:

(a)

(i) The probability of getting at least one 3 when 9 fair dice are thrown is 0.8062.

(ii) The value of n is 12.

(b) The probability that Ronnie wins the game is 0.3572.

Step-by-step explanation:

(a)

(i)

The probability of getting a 3 on a single die roll is, [tex]p=\frac{1}{6}[/tex].

It is provided that n = 9 fair dice are thrown together.

The outcomes of each die is independent of the others.

The random variable X can be defined as the number of die with outcome as 3.

The random variable X follows a Binomial distribution with parameters n = 9 and [tex]p=\frac{1}{6}[/tex].

Compute the probability of getting at least one 3 as follows:

[tex]P(X\geq 1)=1-P(X=0)[/tex]

                [tex]=1-[{9\choose 0}(\frac{1}{6})^{0}(1-\frac{1}{6})^{9-0}]\\\\=1-(\frac{5}{6})^{9}\\\\=1-0.19381\\\\=0.80619\\\\\approx 0.8062[/tex]

Thus, the probability of getting at least one 3 when 9 fair dice are thrown is 0.8062.

(ii)

It is provided that:

P (X ≥ 1) > 0.90

Compute the value of n as follows:

[tex]P (X \geq 1) > 0.90\\\\1-(\frac{5}{6})^{n}>0.90\\\\(\frac{5}{6})^{n}<0.10\\\\n\cdot \ln (\frac{5}{6})<\ln (0.10)\\\\n<\frac{\ln (0.10)}{\ln (5/6)}\\\\n<12.63\\\\n\approx 12[/tex]

Thus, the value of n is 12.

(b)

It is provided that the bag contains 5 green balls and 3 yellow balls.

Ronnie and Julie play a game in which they take turns to draw a ball from the bag at random without replacement.

The winner of the game is the first person to draw a yellow ball.

Also provided that Julie draws the first ball.

P (Ronnie Wins) = P (The 1st yellow ball is selected at an even draw)

                          = P (The 1st yellow ball is drawn at 2nd, 4th and 6th draw)

                          = P (1st yellow ball is drawn at 2nd)

                                  + P (1st yellow ball is drawn at 4th)

                                        + P (1st yellow ball is drawn at 6th)

                          [tex]=[\frac{5}{8}\times \frac{3}{7}]+[\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}\times \frac{2}{5}]+[\frac{5}{8}\times \frac{3}{7}\times \frac{4}{6}\times \frac{2}{5}\times \frac{1}{4}\times 1]\\\\=0.2679+0.0714+0.0179\\\\=0.3572[/tex]

Thus, the probability that Ronnie wins the game is 0.3572.

Answer:

9

i got it right on my test

The equivalent expressions to 243 Superscript two-fifths will be 9.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple, we simplify it.

Simplification usually involves making the expression simple and easy to use later,

The given expression is;

[tex]243^{2/5}[/tex]

We know that 2/3 = 0.4

So, the equivalent expressions to the given function;

[tex]243^{0.4}\\\\= 9[/tex]

Thus, The equivalent expressions to 243 Superscript two-fifths will be 9.

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Answer:

Step-by-step explanation:

1. Given the integral function [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex], using trigonometric substitution, the substitution that will be most helpful in this case is substituting x as [tex]asin \theta[/tex] i.e [tex]x = a sin\theta[/tex].

All integrals in the form [tex]\int\limits {\sqrt{a^{2} -x^{2} } } \, dx[/tex] are always evaluated using the substitute given where 'a' is any constant.

From the given integral, [tex]\int\limits {7\sqrt{49-x^{2} } } \, dx = \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx[/tex] where a = 7 in this case.

The substitute will therefore be   [tex]x = 7 sin\theta[/tex]

2.) Given [tex]x = 7 sin\theta[/tex]

[tex]\frac{dx}{d \theta} = 7cos \theta[/tex]

cross multiplying

[tex]dx = 7cos\theta d\theta[/tex]

3.) Rewriting the given integral using the substiution will result into;

[tex]\int\limits {7\sqrt{49-x^{2} } } \, dx \\= \int\limits {7\sqrt{7^{2} -x^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -(7sin\theta)^{2} } } \, dx\\= \int\limits {7\sqrt{7^{2} -49sin^{2}\theta } } \, dx\\= \int\limits {7\sqrt{49(1-sin^{2}\theta)} } } \, dx\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, dx\\since\ dx = 7cos\theta d\theta\\= \int\limits {7\sqrt{49(cos^{2}\theta)} } } \, 7cos\theta d\theta\\= \int\limits {7\{7(cos\theta)} }}} \, 7cos\theta d\theta\\[/tex]

[tex]= \int\limits343 cos^{2} \theta \, d\theta[/tex]

Answer:

2x-y=4

Step-by-step explanation:

Standard form of a line: Ax+by=c

Use slope intercept form: y=mx+b

slope= 2

y=2x-4

Add 4 to both sides.

y+4=2x

subtract y from both sides.

4=2x-y

Rotate the equation

2x-y=4

Answer:

2x-y=4

Step-by-step explanation:

y=2x-4 is the slope intercept.

y-2x=-4

-2x+y=-4

2x-y=4

Answer:

D. 17 11/20 tubs

Step-by-step explanation:

Convert the cones into scoops.

234 regular cones = 468 scoops; 156 large cones = 468

So in total, Richard scooped 936 scoops. Since each scoop is 3 oz:

936 scoops * 3 oz = 2808 oz

Because a tub is 10 pounds or 160 oz:

2808 / 160 = 17.55 tubs

The answer is D. Here is how I found the answer:

Hope this helps!

Answer:

See bolded below.

Step-by-step explanation:

Take a look at the attachment below. It represents circle x and y, with respect to each of their radii. In each of the options we are given, we would have to translate and dilate the circles, by a fixed scale factor -

Now the first thing one would do is translate the circles so that they share a common center point, or in other words the center of one circle rests on the edge of the other circle. That way when dilating circle y, it may fit into circle x as it expands.

The second point is how much this smaller circle ( circle y ) has to expand. The radius of circle y being 2, has to increase by 3 times the value to equal the radius of circle x, and hence has to dilate by a scale factor of 3 as to match circle x,

Solution = " Translate the circles so the center of one circle rests on the edge of the other circle, and dilate circle Y by a scale factor of 3 " / Option D

Answer:

[tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex]

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

[tex]y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\[/tex]

[tex]\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}[/tex]

Therefore;

[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }[/tex]

Since x = cos y from the above substitute;

[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }[/tex]

Hence, [tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex] gives the required proof

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