(1/5) -1 as the exponent

Answer:

15

Explanation:

Note that a regular dodecagon is a 12 sided polygon with internal angles that are equal and sides of the same length.

So determine at what angle the architect should cut to frame the base, we have to divide 360 by 12 and divide the result by 2 as seen below;

The angle that the architect should cut to frame the base is 15 degrees

Explanation

We are given the following information:

• Amount at the beginning of an investment = $5500

• Percent decrease = 24.6%

We want to determine the decreased amount in dollars and the amount in his account at the end of the year.

We can determine the decreased amount with the formula below:

Therefore, the decreased amount can be calculated as:

Hence, the decreased amount is $1353.

At the end of last year, the amount left in his account can be calculated as follows:

Hence, the year-end amount is $4147.

For the given points, vector in component form equals -6i^ - 7j^ and its magnitude is 9.22

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative displacement and velocity indicate that the object is travelling counterclockwise.

Vector in component form -

(-4 -2)i^ + (-2-5)j^

= -6i^ - 7j^

Magnitude of the vector equals =

√(-6)² + (-7)² = √85 = 9.22

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Complete Question -

Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.

Answer:

y2-y1 x2-x1

Step-by-step explanation:

-5-(-1)

--------

0-(-2)

-4

---

2

-2

----

1

Answer:

75?

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

3 divided by 5

0.6x125

Using the concept of volume, 700 milliliters of Solution B was used.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.

Volumes of solutions A and B are here which is unknown.

Put these factors in place for us

Let x = the amount of solution A that was mixed in milliliters.

Let y= the amount of solution B that was mixed in milliliters.

The amount of volume utilized for A is 400 ml less than the amount used

for B.

This can be expressed mathematically as y - x = 400.

Or,

- x + y = 400 [1]

The ratios of alcohol in A and B are provided to us.

A contains 12% alcohol, hence its real alcohol content is 12% of x ml.

= 0.12x (12% = 12/100 = 0.12)

Similar to A, B has an alcohol content of 0.20x.

If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.

and it is said that this amount is 176 ml.

Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].

We create an equation containing only the other term by using both equations and removing either the x or y terms.

We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.

Review the equations now:

- x + y = 400 [1]

0.12x + 0.20y = 176 [2]

x's coefficients should all be the same:

Increase [1] by 0.12

=> -0.12x + 0.12y =

= 0.12 x 400

=> 0.12x + 0.12y = 48 [3]

By adding [2] and [3], the x word is removed.

0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48

0x + 0.32 y = 224

=> 0,32y = 224

Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]

==> y = 700

Therefore, 700 cc of Solution B was utilized.

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The area under a standard normal distribution, which we get on a standard normal table, is the same as the probability on that area.

Thus if the area is 0.125, the probability is 0.125, that is, 12.5%.

The radius(r) of the wheel is;

The perimeter(P) of the wheel is given by the formula below:

The distance travelled by Ivan is 165m.

So, the number(n) of times the wheel is:

Hence, the correct answer is 47.8

The given system of equation:

y = 3x - 5 (1)

y = -6x + 4 (2)

We can solve the system of equation by using elimination method :

Elimination Method: In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Subtract the equation (1) & (2)

So, we get x = 1

Substitute the value of x in the equation (1)

y = (-2)

So, the solution of the system of equations are : (x,y) = (1,-2)

Answer: (x,y) = (1,-2)

Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.

To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:

So, Ken got on base 3 times.

Step 1: We have the following expression:

Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:

Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12

First number: -4

Second number: -3

Therefore, we have now:

2 (x - 4) (x - 3)

Step 4

Given:

an equation is given as y = -8.

Find:

we have to find an equation parallel to the given equation and passing through (-6, -7).

Explanation:

Compare the given equation with y = mx + b,

we find that slope ,m = 0 ,

the equation of the line passing through (-6,-7) is

y - (-7) = m( x - (-6))

y + 7 = 0(x + 6)

y + 7 = 0

y = -7

Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).

The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below

Red line represents the equation y = -8

and blue line represents the equation y = -7 passes through the point (-6,-7).

Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.

Given the function

To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

Step 2: Swap the variables:

Step 3: Solve for y:

But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

The number of cans is proportional to the number of days, because each day it uses 2 c

Each senior citizen ticket costs $7.

One child's ticket costs $14.

Describe algebra.

Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.

S represents the senior citizen ticket cost.

C is the child's ticket cost.

Price is expressed as USD per ticket.

8S + 15C = 266

8S + 8C = 168

Subtract both equations now to get rid of S

8S + 15C = 266

8S + 8C = 168

———————————-

7C = 98

C = 98/7

C = $14

Changing the value of C in the first

8S + 15(14) = 266

8S + 210 = 266

8S = 266 - 210

8S = 56

S = 56 / 8

S = $7

Hence, $7 is the price for senior citizen

And, $14 is the price for child

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Explanations:

Given the following parameters

An initial deposit of Gerard is "d" dollars

For the savings with 5% interest, the interest on "d" dollars will be expressed as;

Get the total savings plus interest in the first account

Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the interest will be added to the first deposit, hence;

In Tabulated form:

1)  The Linear equation that models the average price of a new home is;

y = -800x + 294000.

2) The prediction of the average price of a new hom in the year 2014 is; $256000

We are told that the average price in the year 2004 was $294000

We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.

Since the line must pass through the points (0, 294000) and (7, 288400), it means that;

Slope = (288400 - 294000)/(7 - 0)

Slope = -5600/7

Slope = -800

Now, we know that the general formula for equation in slope intercept form is; y = mx + c

where; m is slope and c is y-intercept.

Thus;

1) Linear equation is; y = -800x + 294000.

2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years

Thus;

y = -800(10) + 294000

y = $256000

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The given equation is

First, we subtract 6 on each side.

Then, we divide the inequality by 4.

Answer:

12

Step-by-step explanation:

First, get all of the x values to one side of the equation so that we can solve for x. One way to do this is subtract 5x from both sides.

Now we have this:

4x - 5x = -12.

Simplify:

-x = -12.

We need positive x, so divide both sides by -1.

x = 12.

Hope this helps! :)

Step 1

From the question, Hailey reads 48 pages of a book

Blake reads half as many as Hailey.

Hence Blake reads;

The answer will be together they read;

Answer; Option C

Using linear functions, it is found that:

a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.

b) The inverse expression is: y = 9x/5 + 32.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function are described as follows:

For the conversion of Fahrenheit to Celsius, we have two points, as follows:

(32,0), (68, 20).

When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:

m = 20/36 = 5/9

Hence:

y = 5/9x + b.

When x = 32, y = 0, hence the intercept b is calculated as follows:

0 = 5/9(32) + b

b = -5 x 32/9

b = -160/9

Hence the equation is:

y = 5/9x - 160/9.

To find the inverse expression, we exchange x and y and then isolate y, as follows:

x = 5/9y - 160/9.

5/9y = x + 160/9

5y = 9x + 160

y = 9x/5 + 32.

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Remember that the coordinates are written in the form (x,y). Plot the points with the given coordinates: A(1,6), B(1,1) and C(5,1):

Draw a right triangle using the same measures for the legs in order to construct ΔDEF, as described below:

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

The probability that a student is female and junior is:

The probability that a student is a junior is:

Finally, The probability that a student is female given that it is a junior is:

The probability that a player dealt with four hearts = 0

Probability is defined as the prediction of the occurrence of an event in a stated set.

This can be expressed in proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

From the question given, the 6 sets include the following;

9, 10, jack, queen, king and ace.

There are no hearts given in the set of the event that occurred, therefore, the probability that a player dealt with four hearts = 0.

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The area of the circle is given as:

plugging the value given we have that:

Now, the circumference is given as:

where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:

Therefore the circumference is 38pi

In a case whereby joeita sees on her activity tracker that it took her 58 minutes to run 6.25 hours miles  the distance she can she run in 40 minutes is  4.31 miles.

This can be solved by the cross multiplication using the rate that given in the question.

We were told that joeita took  58 minutes  of her time to run 6.25 hours miles , then to know the distance she can cover within 40 minutes is

58 minutes  = 6.25 miles

40 minutes = X miles

Let X be the number of miles she want to cover in 40 minutes

we ca cross multiply the expression above as :

( 40 minutes *  6.25 miles ) = (58 minutes  *  X miles)

the X = 4.31 miles

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Using it's concepts, the point estimates for the population are given as follows:

a) Mean: 97 units sold per month.

b) Standard deviation: 16.06 units sold per month.

In the context of this problem, the 5 observations are given as follows:

97, 110, 89, 97, 92.

Hence the mean is given by:

M = (97 + 110 + 89 + 97 + 92)/5 = 97.

Considering the mean of 97 found above, the standard deviation is given as follows:

[tex]S(X) = \sqrt{\frac{(97 - 97)^2 + (110 - 97)^2 + (89 - 97)^2 + (97 - 97)^2 + (92 - 97)^2}{5}} = 16.06[/tex]

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Here is the completed table:

Number of bags purchased           Total weight                  Total Cost

1                                                                 4                                  8

2                                                                8                                  16

3                                                                 12                               24

4                                                                  16                              32

5                                                                   20                             40

One bag of cat food weighs 4 pounds. This means that as the bag increases by 1, the weight of the bag increases by 4.

Weight of 1 bag of cat food = 4

Weight of 2 bags of cat food = 4 x 2 = 8

Weight of 3 bags of cat food = 4 x 3 = 12

Weight of 4 bags of cat food = 4 x 4 = 16

Weight of 5 bags of cat food = 4 x 5 = 20

The cost of cat food is $2 per pound.

Cost of a bag of cat food = number of bags bought x weight of one bag x cost per pound

Cost of 1 bag of cat food = 1 x 4 x 2 = 8

Cost of 2 bags of cat food = 2 x 4 x 2  = 16

Cost of 3 bags of cat food = 3 x 4 x 2  = 24

Cost of 4 bags of cat food = 4 x 4 x 2  = 32

Cost of 5 bags of cat food = 5 x 4 x 2  = 40

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The slope point form is

m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

Remember (-)(-) = (+)

The equation of the line in the slope-point form is y + 4 = -1(x + 5)