What is the perimeter of a regular pentagon with a
side whose length is x +4?
1 x2 +16
2 4x + 16
3 5x + 4
4 5x + 20

Answer:sdxfrcgtvyhujikokjhgfdsasdfghjknbv 6yujhgtrfgb         srry .\.

Answer:

The shorter piece   x  =  8.4 in

The longer one    y  =  15.6 in

Step-by-step explanation:

If we cut  a string length  L  in to unequal  pieces we get two pieces

first one with length  x  and the other one with length  y

Let call  x  the smaller piece,  then   y = L  -  x will be the longer one

If   x  =  35 %    then

x  =  0,35* L     and

y = L -  x  =  L - 0,35*L      ⇒  y  =  0,65 L     ⇒ y  =  0.65*24

Now if L  =  24  in

x  =  0,35*24          ⇒               x = 8.4 in

and

L  -  x  =  0.65*L      ⇒       L - x  =  0.65*24     y  =  L  -  x  =  15.6 in

as way of verification you can add the length of the two pieces and find:

8.4  +  15.6  = 24 in

Final answer:

The ratio of the length of the small piece to the big piece is found to be 7/13 after calculating the lengths of each piece, with the small piece being 28 inches and the big piece being 52 inches.

Explanation:

Given that the length of the small piece is 35% of the total length L, we can denote the length of the small piece as 0.35L. The big piece is 24 inches longer than the small piece, so the length of the big piece is 0.35L + 24 inches. Since the string is cut into only two pieces, the total length L is the sum of the lengths of the two pieces, which means L = 0.35L + (0.35L + 24).

Simplifying, we have L = 0.7L + 24. Subtracting 0.7L from both sides gives 0.3L = 24 inches. Therefore, the total length of the string is L = 24 / 0.3 = 80 inches. So the small piece is 0.35L = 0.35 * 80 = 28 inches, and the big piece is 28 + 24 = 52 inches.

To find the ratio of the lengths of the small piece to the big piece, we divide the length of the small piece by the length of the big piece: 28/52. Simplifying this ratio by dividing both the numerator and denominator by 4 gives us 7/13. Therefore, the ratio of the length of the small piece to the big piece in its lowest terms is 7/13.

Answer: the employee worked for 41 hours

Step-by-step explanation:

Let x represent the total number of hours that the employee worked. An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. Let y represent the amount earned for x hours. Therefore

y = 7×35 + 10.5(x - 35)

y = 245 + 10.5x - 367.5

One week's paycheck (before deduction) was for $308.00. This means that y = $308.00. Therefore,

308 =245 + 10.5x - 367.5

308 = 10.5x - 122.5

10.5x = 308 + 122.5 = 430.5

x = 430.5/10.5

x = 41

Answer:

The radii of the circles are 12 cm and 7cm.

Step-by-step explanation:

Let the radii of the circles be [tex]r_{1}\ and\ r_{2}[/tex]

Given:

Sum of circumference of two circles= 38π cm

Formula for circumference of a circle with radius r = 2πr

[tex]2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19[/tex]------------1

Sum of areas of two circles= 193π cm²

Area of circle with radius r = πr²

[tex]\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193[/tex]-------2

Substituting r2 = 19 - r1 in equation 2 we get:

[tex]r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7[/tex]

Then r2 = 19 - r1

[tex]r_{2}=12\ or\ 7[/tex]

Answer: Infrequent decisions and long lasting decisions

Step-by-step explanation:

Infrequent: decisions made infrequently, they are not urgent, and deeper consideration is appropriate (ex., product strategy, international expansion).

Long-lasting: Once made, these decisions are unlikely to change not immediately but at least in the short term (e.g., commitment to a standard technology platform, commitment to organizational realignment around Value Streams)

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

Answer:

3

Step-by-step explanation:

Simplify :

(5-4i)-(2-4i)

5-4i-(2-4i)

=3

Answer:

The cost of a 12 minute call to France is $ 3.63

Step-by-step explanation:

given:

The cost of 15 minute call to France = $ 4.29

The cost of 10 minute call to France   = $ 3.19

To Find :

The cost of a 12 minute call to France = ?

Solution:

Let the flat fee be X

and the cost per minute be Y

so the  15 minute call to France will be

X + 15(Y) = 4.29---------------------------(1)

the  10 minute call to France will be

X + 10(X) = 3.19----------------------------(2)

Subtracting (2) from (1)

X + 15(Y) = 4.29

X + 10(Y) = 3.19

-      -           -

---------------------------------

      5Y = 1.10

--------------------------------

[tex]Y =\frac{1.10}{5}[/tex]

Y = 0.22

So the cost per minute of a call = $0.22

substituting the values in (1)

X + 15(0.22) = 4.29

X + 3.3 = 4.29

X = 4.29 -3.3

X = 0.99

Now the cost of 12 minute call is

=>X + 12(Y)

=> 0.99 + 12(0.22)

=> 0.99 + 2.64

=> 3.63

Answer: Two-sample t-test

Step-by-step explanation:

The Two-sample t-test is used to test the difference between two random and distinct population means. It help test whether the difference between the two populations is statistically significant.

In the case above the researcher wants to determine whether there is a difference in mean number of minutes of television viewing between men and women which makes it a Two-sample t-test.

Answer:

  -1/2

Step-by-step explanation:

Slope is calculated as ...

   (change in y)/(change in x) = (y2 -y1)/(x2 -x1)

   = (-4 -1)/(0 -(-10)) = -5/10 = -1/2

The slope of the line is -1/2.

Answer: the length is 6 feet. The width is 2 feet

Step-by-step explanation:

The garden pool is rectangular in shape.

Let L represent the length of the rectangular garden.

Let W represent the width of the rectangular garden.

The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that

L× W = 12 - - - - - - - - - - 1

The length of the pool needs to be 2ft more than twice that width. This means that

L = 2W + 2 - - - - - - - - - - - 2

Substituting equation 2 into equation 1, it becomes

W(2W + 2) = 12

2W^2 + 2W = 12

2W^2 + 2W - 12 = 0

W^2 + W - 6 = 0

W^2 + 3W - 2W - 6 = 0

W(W + 3) - 2(W + 3) = 0

W - 2 = 0 or W + 3 = 0

W = 2 or W = - 3

Since the Width cannot be negative, then the width is 2 feet

Substituting W = 2 into equation 2. It becomes

L = 2×2 + 2 = 6 feet

Answer:

- √5

Step-by-step explanation:

Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.

To get the answer to the question,  

The first step is to find the hypotenuse, we have to use the Pythagoras theorem  where, Hypotenuse = opposite raise to power two + adjacent raise to power.  

(I.e. h= O² + A²)

H = 6² + (-3)2

H = 36 + 9

H = 45

We then convert the answer to surds form.  

H = 3√5

The next step is to find the value of secant theta.  

To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant  

We have  

Sec ø = - (hypotenuse/adjacent)  

Sec ø = - (3√5/ 3)

Sec ø = - √5

Answer:

-√5

Step-by-step explanation:

Answer: The value of 528 would change by 40 if 6 replaced 2

Step-by-step explanation:

The given number is 528. If we replace 2 by 6, the new number becomes 568. This is greater than the previous number. The difference between the new number and the previous number would be

568 - 528 = 40

Answer:

The profits for firma A and B will decrease.

Step-by-step explanation:

Oligopoly by definition "is a market structure with a small number of firms, none of which can keep the others from having significant influence. The concentration ratio measures the market share of the largest firms".

If the costs remain the same for both companies and both firms decrease the prices then we will have a decrease of profits, we can see this on the figure attached.

We have an equilibrium price (let's assume X) and when we decrease a price and we have the same level of output the area below the curve would be lower and then we will have less profits for both companies.

Answer:

k-5

Step-by-step explanation:

"k and 12" : (k + 12)

"17 less than k and 12" : (k + 12) - 17

simplifying:

(k + 12) - 17

= k + 12 - 17

= k-5

Question is Incomplete, Complete question is given below:

In Triangle ABC shown below, side AB is 6 and side AC is 4.

Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Answer

Segment AD is 3 and segment AE is 2.

Segment AD is 3 and segment AE is 4.

Segment AD is 12 and segment AE is 4.

Segment AD is 12 and segment AE is 8.

Answer:

Segment AD is 3 and segment AE is 2.

Step-by-step explanation:

Given:

side AB = 6

side AC = 4

Now we need to prove  that segment DE is parallel to segment BC and half its length.

Solution:

Now AD + DB = AB also AE + EC = AC

DB = AB - AD also EC = AC - AE

Now we take first option Segment AD is 3 and segment AE is 2.

Substituting we get;

DB = 6-3 = 3 also EC = 4-2 =2

From above we can say that;

AD = DB and EC = AE

So we can say that segment DE bisects Segment AB and AC equally.

Hence From Midpoint theorem which states that;

"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."

Hence Proved.

Answer:

y + b > 15

Step-by-step explanation:

given data

positive integers = x, y, a, b

x divided by y then remainder = 6

a divided by b then remainder = 9

to find out

possible value for y + b

solution

we know that here when  x divided by y then remainder is 6

its mean y is greater than 6 and when a divided by b then remainder is 9

so its mean b is greater than 9

and we know remainder is less than divisor

so here y + b must be greater than = 6 + 9

y + b > 15

Answer:

Domain: set of all real numbers; (-∞, ∞)

Range : {y | y f > 2}

Check the attached figure to visualize the graph.

Step-by-step explanation:

The graph of the given function is attached. Please check the attached figure.

As the function is given as:

                                              [tex]f(x) = (\frac{1}{3})^{x} +2[/tex]

As the table of some of the values of x and y values for [tex]f(x) = (\frac{1}{3})^{x} +2[/tex] is given as follows:

               -2                    11

                -1                    5

                 0                   3

                 1                   2.33

                  2                  2.111

Hence, it is clear that the function is defined for every input value of x. So, domain is the set of all real numbers.

Domain: set of all real numbers; (-∞, ∞)

If we carefully analyze the graph of this function, it is clear that no matter what input value of x we put, range or y-value of this function would always be be greater than 2. Check the attached graph figure to better visualize the range of the function.

Range can also be denoted as: Range : {y | y f > 2}

Keywords: graph, function, domain and range

Learn more about domain and range from brainly.com/question/1581653

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Answer:

4/33

Step-by-step explanation:

x=0.121212...

100x=12.1212...

100 x-x=12

99 x=12

x=12/99=4/33

Given a decimal number 0.12, we have that its expression as a fraction in its simplest form is mathematically given as x=4/33

A fraction is simply a numerical quantity or use of integers in a form that is not in a whole number form.

Question Parameter(s):

X=0.121212...

Generally, the equation for the statement  is mathematically given as

x=0.121212

Therefore

100x=12.1212...

100 x-x=12

99 x=12

x=12/99

x=4/33

In conclusion, X=0.121212 as a fraction is x=4/33.

Read more about Arithmetic

https://brainly.com/question/22568180

Answer:

[tex]18x+12y\geq 300[/tex]

Step-by-step explanation:

Let

x ---> the number of an adult tickets

y ---> the number of a child tickets

Remember that the word "at least" means "greater than or equal to"

so

The number of an adult tickets multiplied by its price ($18) plus the number of a child tickets multiplied by its price ($12) must be greater than or equal to $300

The inequality that represent this situation is

[tex]18x+12y\geq 300[/tex]

using a graphing tool

the solution is the shaded area

Remember that the number of tickets cannot be a negative number

see the attached figure

Answer:

Step-by-step explanation:

let length=x

width=y

area A=xy

[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]

area is decreasing at the rate of 1.5 cm^2/sec

The rate of change in the area of the rectangle when the length is 10 cm and the width is 7 cm, with their rates of change being 0.5 cm/sec and -0.5 cm/sec respectively, is -1.5 cm²/sec.

To determine the rate of change in the area of a rectangle where the length is increasing at 0.5 cm/sec and the width is decreasing at 0.5 cm/sec, we can use the concept of derivatives from calculus.

Let L be the length and W be the width of the rectangle. The area A of the rectangle is given by A = L * W. Given that the length is increasing at 0.5 cm/sec (dL/dt = 0.5 cm/sec) and the width is decreasing at 0.5 cm/sec (dW/dt = -0.5 cm/sec) the rate of change of the area with respect to time can be found using the product rule for derivatives: dA/dt = (dL/dt) * W + L * (dW/dt).

At the moment when the length L is 10 cm and the width W is 7 cm, we can plug these values into the formula: dA/dt = (0.5 cm/sec) * 7 cm + 10 cm * (-0.5 cm/sec). This simplifies to dA/dt = 3.5 cm2/sec - 5 cm2/sec, giving us the rate of change in the area as dA/dt = -1.5 cm2/sec.

Answer:

Andrew walks more steps than Sarah.

Step-by-step explanation:

The question is incomplete. The complete question is :

Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andrew and Sarah each walk for a total of 5 hours. Who walks more steps?

Solution:

Given:

Andrew walks 6000 steps in 50 minutes.

Number of steps Sarah walks is given by the equation :

[tex]y=118x[/tex]

where [tex]y[/tex] is the number of steps and [tex]x[/tex] is the number of minutes she walks.

Finding the number of steps each walks in 5 hours.

Total number of minutes in 5 hours = [tex]5\times 60 = 300\ min[/tex]

For Andrew:

Using unitary method:

If in 50 minutes Andrew walks = 6000 steps.

In 1 minute he will walk = [tex]\frac{6000}{50}[/tex] = 120 steps

In 300 minutes he will walk = [tex]120\times 300 = 36000[/tex] steps

Thus, Andrew will walk 36,000 steps in 5 hours.

For Sarah:

We will plugin [tex]x=300[/tex] in the equation and solve for [tex]y[/tex].

We have:

[tex]y=118(300)[/tex]

∴ [tex]y=35400[/tex]

Thus, Sarah will walk 35,400 steps in 5 hours.

Therefore, Andrew walks more steps than Sarah as [tex]36,000>35,400[/tex].

Answer:

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Step-by-step explanation:

Given:

[tex]x^{3}+7x^{2} +12x= 0[/tex]

To Find:

All  the Roots = ?

Solution:

As the degree of the polynomial is THREE then the number of root are also THREE.

[tex]x^{3}+7x^{2} +12x= 0\\\\x(x^{2}+7x +12)= 0\\\\x=0\\or\\x^{2}+7x +12= 0\\[/tex]

Now one root is Zero For other we need to Factorize

So by Splitting the middle term

i.e Factor of 12 such that sum should be 7

i.e 3 × 4 = 12  and 3 + 4 = 7

∴ [tex]x^{2}+7x +12= 0\\x^{2}+3x+4x +12= 0\\x(x+3)+4(x+3)=0\\(x+3)(x+4)=0\\\\x+3=0\ or\ x+4 = 0\\\\\therefore x=-3\ or x=-4\ \textrm{Which are the roots}[/tex]

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Answer:

Option B is right

Step-by-step explanation:

Given that in the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.

                      Males              Females

                        48%                    52%

25 or more

age                  40%                     20%

One student in the class is randomly selected,

to find the probability that he or she will be less than 25 years old

= Prob (male and less than 25 years old)+Prob (female and less than 25 years old)

(since mutually exclusive and exhaustive)

= [tex]0.48(1-0.4) + 0.52(1-0.20)\\= 0.288+ 0.416\\= 0.704\\[/tex]

After rounding off to 1 one decimal

we get 0.7

Option B is right

Answer:

C. 122

Step-by-step explanation:

Given,

Dimension of the cake:

Length = 12 in      Width = 16 in      Height = 4 in

We have to find out the area of the tray that is not covered by the cake.

Indra centered the cake on a circular tray.

Radius of the tray = 10 in.

So area of the tray is equal to π times square of the radius.

Framing in equation form, we get;

Area of tray =[tex]\pi\times r^2=3.14\times{10}^2=3.14\times 100=314\ in^2[/tex]

Since the cake is placed in circular tray.

That means only base area of cake has covered the tray.

Base Area of cake = [tex]length\times width=12\times 16=192\ in^2[/tex]

Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.

We can frame it in equation form as;

Area of the tray that is not covered by the cake = Area of tray - Base Area of cake

Area of the tray that is not covered by the cake =[tex]314-192=122\ in^2[/tex]

Hence The area of the tray that is not covered by the cake is 122 sq. in.

Answer:

The money Rachael plan to collect for the shelter is $350.

Step-by-step explanation:

Given:

Rachel is collecting donations for the local animal shelter.

So far she has collected $245, which is 70% of what she hopes to collect.

Now, to find the money Rachael plan to collect for the shelter.

Let the total amount Rachael plan to collect be [tex]x[/tex].

Amount she collected = $245.

Percentage of amount she collected = 70%.

Now, to get the amount Rachael plan to collect we put an equation:

[tex]70\%\ of\ x=\$245.[/tex]

⇒ [tex]\frac{70}{100} \times x=245[/tex]

⇒ [tex]0.70\times x=245[/tex]

⇒ [tex]0.70x=245[/tex]

Dividing both sides by 0.70 we get:

⇒ [tex]x=\$350.[/tex]

Therefore, the money Rachael plan to collect for the shelter is $350.

Answer:

  1000

Step-by-step explanation:

Each value of the first digit can be paired with any value of the second digit, so there are 10×10 = 100 possible pairs of the first two digits. Each of those can be combined with any third digit to give a total of ...

  10×10×10 = 1000

possible combinations.

Final answer:

A combination lock with a 3-digit code where each digit can be 0-9 allows for 1000 different combinations, as calculated by 10 x 10 x 10, which equals 10³ or 1000.

Explanation:

The question asks how many different 3-digit combinations are possible with a combination lock where each digit can range from 0-9. Each digit of the code is independent and can take any of the ten possible values (0-9), leading to a total combination of possibilities calculated by multiplying the number of choices for each digit position. Given that there are three digit positions and each can be any of the ten digits, the calculation is as follows:

10 (choices for first digit) × 10 (choices for second digit) × 10 (choices for third digit) = 10³

Therefore, there are 1000 different possible combinations for the lock, ranging from 000 to 999.

Answer:

No solution , The line's are parallel

Step-by-step explanation:

Given set of equations are y = 56x + 2 and y = 56x - 2

If we observe carefully these lines are in the form of y=mx+c where m is the slope of the line and c is the y-intercept

Here both the line's have slope m = 56

We also know that two lines are parallel only if their slopes are equal ie m1=m2

Here the two line's have same slope, so the giventwo line's are parallel And they don't have a solution So jane is wrong.

[tex]\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}[/tex]

Step-by-step explanation:

A, B and C are integers between 1 and 10  such that A<B<C.

The value of A can be minimum 1 and maximum 8.

If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).

If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).

If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).

If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).

If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).

If A = 1, B = 7, then C has 3 options (8, 9, 10).

If A = 1, B = 8, then C has 2 options (9, 10).

If A = 1, B = 9, then C has 1 option (10).

So, if A = 1, then the number of combinations is

[tex]n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.[/tex]

Similarly, if A = 2, then the number of combinations is

[tex]n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.[/tex]

If A = 3, then the number of combinations is

[tex]n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.[/tex]

If A = 4, then the number of combinations is

[tex]n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.[/tex]

If A = 5, then the number of combinations is

[tex]n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.[/tex]

If A = 6, then the number of combinations is

[tex]n_6=1+2+3=\dfrac{3(3+1)}{2}=6.[/tex]

If A = 7, then the number of combinations is

[tex]n_7=1+2=\dfrac{2(2+1)}{2}=3.[/tex]

If A = 3, then the number of combinations is

[tex]n_8=1.[/tex]

Therefore, the total number of combinations is

[tex]n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.[/tex]

Thus, the required number of different combinations is 120.

Learn more#

Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?

Link : https://brainly.in/question/4909567.

Answer:

78/2,652, or 0.0294, or 2.94%.