Question 65
Find area of figure. Round to the nearest hundredth if necessary.
rectangle with circle taken out
5.0 m
10.4 m
(Use 3.1 4 for a.)

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:

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:

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:

([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:

[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]

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

lllluvyvyvyvtctctvtvtctvtctctctctctctctvtvyvyvyvyvyvyvtvtv

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]

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:

  -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:

Answer:

  [tex]y=\log_3{(x+3)}[/tex]

Step-by-step explanation:

The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.

The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.

The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.

The function is ...

  [tex]\boxed{y=\log_3{(x+3)}}[/tex]

Answer:

215

Step-by-step explanation:

7*(6+2)4-9

7*8*4-9

56*4-9

224-9=215

Answer:

7.12.2= 168

Step-by-step explanation:

168 x 168 =28224

28224-3= 28221

28221 x 28221 = 796424841

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.

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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

Hope this helps!

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Answer:

So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.

Step-by-step explanation:

The sample size is important to find the margin of errror of a confidence interval.

The margin of error is given by a formula in the following format:

[tex]M = \frac{c*s}{\sqrt{n}}[/tex]

In which c is the critical value(depends on the distribution used, can be T or Z), s is the standard deviation(of the sample or the population) and n is the size of the sample.

As n increases, M decreases, which leads to a lower margin of error.

The lower the margin of error, the more precise the interval is.

So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.

Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

Answer:

AB/AD=1/2       AC/AE=1/2

Step-by-step explanation:

The distance between 2 points A(x1; y1)     and  B(x2;  y2) can be calculated as:

AB= sqrt((x1-x2)²+(y1-y2)²)

So in our case AB= sqrt ((1-3)²+(4-1)²)= sqrt(2²+3²)=sqrt(13)

AD=sqrt ((-1-3)²+(7-1)²)= sqrt(4²+6²)=sqrt(52)

AB/AD=sqrt(13)/sqrt(52)= sqrt(13/52)=sqrt(1/4) =1/2

AB/AD =1/2

AC= sqrt ((5-3)²+(3-1)²)= sqrt(2²+2²)=sqrt(8)

AE=sqrt ((7-3)²+(5-1)²)= sqrt(4²+4²)=sqrt(32)

AC/AE=sqrt(8)/sqrt(32)= sqrt(8/32)=sqrt(1/4)=1/2

AC/AE=1/2

Answer:

first one is 1/2

second one is 1/2

Step-by-step explanation:

got it right on edge 2020

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:

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:

[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]

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:

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:

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

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]\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

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:

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:

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°