Please help me out please

Answer:

- 0.0625

Step-by-step explanation:

Again, I don't know of another way besides Calculus other than letting x = something very tiny.

When you use calculus, the answer approaches - 1/16 = - 0.0625 (I think). So we'll let x = 0.01 and see how that goes.

numerator: 1/(0.01 + 4) - 1/4

(0.24938 - 0.25) / 0.01

- 0.000623 / 0.01 = - 0.0623 which is  pretty close considering what I used for x. You could try it with 0.0001 which will get much closer.

Answer:

B. f -1(x) = x + 2 / 5

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

Step-by-step explanation:

To find the inverse of a function we need to interchange x and y an solve for y.

Since [tex]f(x)=y[/tex], then

[tex]f(x)=5x-2[/tex]

[tex]y=5x-2[/tex]

[tex]x=5y-2[/tex]

Add 2 to both sides

[tex]x+2=5y-2+2[/tex]

[tex]x+2=5y[/tex]

Divide both sides by 5

[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]

[tex]\frac{x+2}{5}=y[/tex]

[tex]y=\frac{x+2}{5}[/tex]

[tex]f^{-1}(x)=\frac{x+2}{5}[/tex]

We can conclude that the correct answer is B. f -1(x) = x + 2 / 5

Answer: The required function would be [tex]x^2+3x-40[/tex]

Step-by-step explanation:

Since we have given that

There are two real zeroes :

x = -8 and x = 5

So, we need to find the function satisfying the above two zeroes:

Let α = -8 and β = 5

So, it means it is a quadratic equation :

[tex]x^2-(\alpha +\beta)x+\alpha \beta \\\\=x^2-(-8+5)x+-8\times 5\\\\=x^2+3x-40[/tex]

Hence, the required function would be [tex]x^2+3x-40[/tex]

Answer:

The answer is A

Step-by-step explanation:

1,0,-1,7,7.

The range always be the Y values

Answer:

The answer would be the large album has 54 more stamps than the small album.

Step-by-step explanation:

... 92 - 38 = 54

Do you need a drawing done though?

19/50 of the baseball caps in the store are blue and on sale.

Let's say there are a total of 100 baseball caps in the store. Then, 2/3 of them are blue, which is:

2/3 x 100 = 66.67 (approximately 67)

So, there are approximately 67 blue baseball caps in the store. Out of these, 4/7 are on sale, which is:

4/7 x 67 = 38 (rounded to the nearest whole number)

Therefore, there are approximately 38 blue baseball caps that are on sale in the store.

The fraction of baseball caps in the store that are blue and on sale is:

38/100 = 19/50

So, 19/50 of the baseball caps in the store are blue and on sale.

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To find the fraction of baseball caps in the store that are blue and on sale, multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

To find the fraction of baseball caps in the store that are blue and on sale, we need to multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

Given that 2/3 of the caps are blue and 4/7 of the blue caps are on sale, we can calculate the fraction of blue caps that are on sale by multiplying 2/3 and 4/7:

2/3 * 4/7 = 8/21

Therefore, 8/21 of the baseball caps in the store are blue and on sale.

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Answer:

12-5.5=h

12-5.5=6.5

Kyle needs to volunteer 6.5 more hours.

Step-by-step explanation:

Answer:

5.5 + h = 12

Step-by-step explanation:

Here, h represents the number of hours, Kyle still needs to volunteer this week,

Given,

He volunteered 5.5 hours at the library this week.

Since, the total number of hours he needs to volunteer = 5.5 + h

According to the question,

5.5 + h = 12

Which is the required equation.

Answer:

the answer is 0.00221184

Step-by-step explanation:

as we can see 3rd term is product of first two terms

4th term is product of third and second term

5th term is the product of fourth and third term

 the next term in the sequence which is the sixth term will be the product of fifth and fourth term

Answer:

The next term of geometric sequence is 0.025 which is the probability of dropped call.      

Step-by-step explanation:

We are given the following information in the question:

The probability of a customer experiencing a dropped call decreases formed the geometric sequence.

The geometric sequence is:

0.8, 0.4, 0.2, 0.1, 0.05

First term = a = 0.8

Common difference = r =[tex]\frac{a_{n}}{a_{n-1}} = \frac{0.4}{0.8} = \frac{1}{2}[/tex]

We have to find the next term of the geometric series to find the next probability.

Next term of sequence =

[tex]a_n = a_{n-1}\times r\\= 0.05\times \displaystyle\frac{1}{2}\\\\= 0.025[/tex]

Hence, the next term of geometric sequence is 0.025 which is the probability of dropped call.

Answer:

Option B) $122,140

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=5\ years\\ P=\$100,000\\ r=0.04[/tex]  

substitute in the formula above  

[tex]A=\$100,000(e)^{0.04*5}=\$122,140.28[/tex]  

Round to the nearest dollar

[tex]\$122,140.28=\$122,140[/tex]  

Answer:

Final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

Step-by-step explanation:

Given expression is [tex](a-\sqrt{2})^8[/tex].

Now we need to find the fourth term of the given expression  [tex](a-\sqrt{2})^8[/tex]. So apply the nth term formula using binomial expansion.

exponent n=8

4th term means we use r=4-1=3

x=2, [tex]y=-\sqrt{2}[/tex]

rth term in expansion of [tex](x+y)^n[/tex] is given by formula:

[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]

[tex]=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3[/tex]

[tex]=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=56\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=-112a^5\cdot\sqrt{2}[/tex]

[tex]=-112\cdot\sqrt{2}a^5[/tex]

Hence final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

Answer:

The Phase Shift is how far the function is shifted horizontally from the usual position.

Step-by-step explanation:

Answer:

60 cm^2

Step-by-step explanation:

The formula for the area of a triangle is ...

A = (1/2)bh

where b is the length of the base, and h is the height. Your triangle shows a base length of 12 cm + 3 cm = 15 cm, and a height of 8 cm. Using these values in the formula, we have ...

A = (1/2)(15 cm)(8 cm) = 60 cm^2

Answer:

A. $4397.9

Explanation:

We are given that Kendra sold 200 shares and that the price per share was $22.1

This means that:

Total value = 200 * 22.1 = $4420

Now, we know that the broker charged 0.5% commission on the total value

This means that:

Broker's charge = 0.5% * 4420 = 0.005 * 4420 = $22.1

Therefore,

Kendra's return = Total value - broker's charge

Kendra's return = 4420 - 22.1 = $4397.9

Hope this helps :)

Answer:

$4,397.90

Step-by-step explanation:

Add all the times together:

27.81 + 26.89 + 26.55 + 25.48 = 106.73 seconds.

1 minute = 60 seconds.

106 - 60 = 46

Total time: 1 minute and 46.73 seconds.

Answer:

106.73

Step-by-step explanation:

27.81 + 26.89 + 26.55 + 25.48 = 106.78

So in conclusion, the answer is 106.78

Answer:

12

Step-by-step explanation:

96 / 8

Answer:

12 Cups are needed!

Step-by-step explanation:

You find the answer by dividing 96 milkshakes by 8 Milkshakes and find that 12 cups are needed.

:)

Answer:

1 is my answer but I could be wrong

Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{4\times 4}{16}\\ h=&4 \end{cases}\implies V=\cfrac{1}{3}(16)(4)\implies V=\cfrac{64}{3}\implies V=21.\overline{3}[/tex]

Answer:

21.03^3  this is the answer.

The volume of the conical perfume bottle is 77.38 cubic centimeters of perfume, answer D.

To calculate the volume of a conical perfume bottle, we use the formula for the volume of a cone, which is V = (1/3)
3.14r²h, where r is the radius and h is the height of the cone. Given the radius of 3.7 centimeters and a height of 5.4 centimeters, we calculate:

V = (1/3)
3.14 * (3.7 cm)² * 5.4 cm
= (1/3) * 3.14 * 13.69 cm2 * 5.4 cm
= (1/3) * 3.14 * 73.926 cm3
= 3.14 * 24.642 cm3
= 77.38 cubic centimeters

Therefore, the perfume bottle can hold approximately 77.38 cubic centimeters of perfume, which corresponds to answer choice D.

Answer:

  $388.16

Step-by-step explanation:

Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...

  $260,000 × 0.038/12 ≈ $823.33

Then the amount applied to the principal is ...

  $1211.49 -823.33 = $388.16

[tex]f(x)=2\sqrt x[/tex] is continuous on [0, 4] and differentiable on (0, 4), so the MVT holds. We have

[tex]f'(x)=\dfrac1{\sqrt x}[/tex]

so that by the MVT, there is some [tex]c\in(0,4)[/tex] such that

[tex]f'(c)=\dfrac{f(4)-f(0)}{4-0}\implies\dfrac1{\sqrt c}=\dfrac{2\sqrt4}4=1[/tex]

[tex]\implies1=\sqrt c\implies \boxed{c=1}[/tex]

Answer:

x= 16/9

Step-by-step explanation:

[tex]f(x) = 2\sqrt{x}[/tex] is differentiable on [0,4] so the Mean Value Theorem For Integrals applies.

Average Value of the Integral:

[tex]\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx = \frac{1}{4-0} \int\limits^4_0 {2\sqrt{x} } \, dx[/tex]

After evaluating you will get  [tex]\frac{8}{3}[/tex]

Now, this is the average value so you still need to find the x-value using the original equation:

[tex]\frac{8}{3} =2\sqrt{x}\\\\\frac{4}{3} = \sqrt{x}\\\\\frac{16}{9} =x[/tex]

Answer:

D

Step-by-step explanation:

C is also possible but it is not purely random and it is not mentioned the mall is in her district.

Answer:  D) Mail a questionnaire to random households.

Step-by-step explanation:

A) You are limited to only listeners of the radio show

B) You are limited to only those that are wiling and able to attend the meeting.

C) You are limited to only shoppers at that particular mall.

D) Randomly selecting households is the least biased method of responses from the district.

Answer:

B

Step-by-step explanation:

The exponential function [tex]y=a^x[/tex] shows the exponential growth if [tex]a>1.[/tex]

Consider choice B.

If x=1, then [tex]y=2=2^1;[/tex]

if x=2, then [tex]y=4=2^2;[/tex]

if x=3, then [tex]y=8=2^3;[/tex]

if x=4, then [tex]y=16=2^4.[/tex]

This means that the function [tex]y=2^x[/tex] represents the table B.

ANSWER

See attachment

EXPLANATION

The table that represent a geometric sequence is the one shown in the attachment with y-values

[tex]2,4,8,16,...[/tex]

We can see that, the subsequent term is obtained by multiplying the previous term by 2.

In other words, there is a bit ratio of 2.

Here the table represents a geometric sequence.

Answer: the answer is C

The histogram and dot plot that represent the order of varying shirt sizes are illustrations of charts

The dataset on the dot plot can be represented using the following frequency table

Shirt size     Frequency

    8                     0  

   10                     1

   12                     3

   14                     3

   16                     5

   18                     4

   20                    2

   22                    1

   24                    1

   26                   0

Since the options are not given, the next step is to plot and upload the histogram using a graphing tool

See attachment for the histogram that represents the dot plot

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Answer:

1

Step-by-step explanation:

y = mx + b

y = 1/2 x - 1

y = 1/2 (4) - 1

y = 2 - 1

y = 1

When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.

To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:

y = (1/2)(4) - 1

y = 2 - 1

y = 1

So, when x = 4, the value of the function y is 1.

In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.

When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.

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Step-by-step Answer:

If trapezium DBCE is one-fourth of the area of the triangle ABC, that means that the area of triange ADE is (1 - 1/4) = three-fourth of ABC.

Since DE is parallel to BC, we can prove that triangles ADE and ABC are similar.

Similar triangles have corresponding sides proportional, and area is proportional to the square of the linear proportions.

From this we can conclude that

(DE/BC)^2 = 3/4

DE/BC = sqrt(3/4) = sqrt(3)/2

DE = sqrt(3)/2 * 20 = 10 sqrt(3) = 17.320508 cm (to 6 decimal places).

On the subject of similar figures/volumes, if we know the ratio of linear dimensions (such as the side of a cube) as k, then the ratio of AREA of similar squares would be k^2.

Example: A square would have a side of 8 (area=8^2=64), and a (similar) square has a side of 10 (area = 10^2= 100).  The

ratio of areas = 64/100 = (8^2/10^2) = (8/10)^2

Here 8/10 is the ratio of linear dimensions = k, and the ratio of areas is k^2 = (8/10)^2 = 64/100.

The same works for cubes (or similar volumes) where the volumes would be proportional to k^3.

Answer:

The difference in investment between the smallest investor an largest investor is $40,000

Step-by-step explanation:

Let

x ---> the contribution of the smallest investor

y ---> the contribution of the middle investor

z ---> the contribution of the largest investor

we know that

x+y+z=140,000 -----> equation A

x/y=3/4 -----> y=(4/3)x ----> equation B

x/z=3/7 ----> z=(7/3)x ----> equation C

substitute equation B and equation C in equation A and solve for x

x+(4/3)x+(7/3)x=140,000

(14/3)x=140,000

x=140,000*3/14

x=$30,000

Find the value of y

y=(4/3)x ----> y=(4/3)(30,000)=$40,000

Find the value of z

z=(7/3)x ----> z=(7/3)(30,000)=$70,000

Find the difference in investment between the smallest investor an largest investor

z-x=$70,000-$30,000=$40,000

X^(3•2) =X^ 6

Think of an example such as :

(2^3)^2=8^2=64 is the same with

2^(3•2) = 2^6 = 64

Answer= x^6

When two exponents are multiplied together the two exponents multiply.

Answer:

  3, -8, 11

Step-by-step explanation:

The first factor is zero when x=3.

The second factor is zero when x=-8.

The third factor is zero when x=11.

Whenever any factor is zero, the polynomial is zero.

The zeros are 3, -8, 11.

A = 0.5 x 10.4 x 16.9

A = 87.88

The area of the triangle is 87.88 ft²

Answer:

B. f(-1)=6

C.  The domain of f(x) is the set {-2.-1,0,1,2,3,4,5,6}

Step-by-step explanation:

To find f(5) from the table means, the y-value that corresponds to x=5.

This value is 12.

This implies that:

f(5)=12

Also the y-value that corresponds to -1 is 6.

Hence f(-1)=6

The domain of f(x) are the set of all the x-values.

The domain is : {-2.-1,0,1,2,3,4,5,6}

The range for f(x) is the set of all the corresponding y-values.

From the table, the range is: {5,6,7,8,9,10,11,12,13}