An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 70
grams of an alloy that contains 12% copper with 90 grams of pure copper.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?

Given

Answer

The graph is given by y = -3/2|x|

The graph of |y| = x/2

The graph of y = |x|

The graph of -1/2 |y| = x

Using the uniform distribution, it is found that:

a) The probability that the friend is between 10 and 20 minutes late is of 1/3.

b) There is a 30% probability that the friend will arrive within 9 minutes.

The uniform has two bounds, a and b, and each outcome of the distribution is equally as likely.

From the image given at the end of the answer, the bounds are given as follow:

a = 0, b = 30.

The probability of finding a value between c and d in the distribution is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Hence, the probability that the friend is between 10 and 20 minutes late is given as follows:

P(10 <= X <= 20) = (20 - 10)/(30 - 0) = 1/3.

The 30th percentile of the distribution, which is what item b is asking, is given as follows:

0.3 x (30 - 0) = 0.3 x 30 = 9 minutes.

The complete problem is given by the image at the end of the answer.

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Given:

To find:

The height from the ground to the base of the window.

Explanation:

Since the triangles XWY and XVZ are similar by AA similarity.

So we can write,

The dimensions of your mowing plot if x = 13 meters is;

Length = 31 meters

Width = 36 meters

We are told that Your plot has a length which is five more than two times x and the width is three less than three times x

This means that, the length given as words is "5 more than 2 times x" and the width given as words is "3 times x minus 3"

The expression for length would be  2x + 5

The expression for width would be 3x - 3

Now, if x = 13 meters, then we see that;

Length = 2(13) + 5 = 31 meters

Width = 3(13) - 3 = 36 meters

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Answer

The function that describes the height of the rocket in terms of the is

In order to find the margin of error, we need to know that the width of the confidence interval is equal to 2 times the margin of error.

The width of this confidence interval is given by:

If the width is 2 times the margin of error, we have:

The margin of error is equal to 3, therefore the correct option is D.

Answer:

  43%

Step-by-step explanation:

You want to know the percentage of applicants having a rating between 200 and 275, given that applicants have ratings normally distributed with a mean of 200 and a standard deviation of 50.

The given percentage can be found using a spreadsheet, suitable calculator, or table of values of the Normal probability function. The attached calculator display shows the percentage to be ...

  0.433 × 100% = 43.3%

About 43% of applicants will have a rating between 200 and 275.

Step-by-step explanation:

option B is correct answer

Answer: Radius = 5.33

Diameter = 10.66

Area = 89.3

Step-by-step explanation:

Circumference = 2πr

33.5 = 2πr

r = 33.5 / 2π

Diameter = 2r

Area = r²π

Area = 5.33²π

each box costs $3 : The cost of one box = $3

12 boxes of cookies : The total number of boxes = $12

For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes

The total cost of 12 boxes = 12 x $3

The cost of 12 boxes = $36

The cost of 12 boxes of cookies ia $36

Answer : $36

Hello!

For a line with slope '0':

⇒ the equation is 'y = y-coordinate of point that the line passes through'

Since the line passes through (-1, -4) and has the slope of '0'

⇒ y = -4

Hope that helps!

The expression (28 + 70) as a multiple of a sum of whole numbers with no common factor is given as

7x(4+10). This is further explained below.

Generally, An express is a finite combination of symbols that have been formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.

In conclusion, When expressed as a multiple of a total of whole numbers that do not have a common component, the equation (28 + 70) is written as 7 times (4 + 10).

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Thus, t has a greater value than s for the co-ordinates (s, -1) and (t, 3).

How to analyze points of an axis for a two dimensional entity?
We can use the fact that both points on the x-axis to compare the values of s and t for the provided parallelogram. As a result, each point that is closest to the x coordinate reflects a higher value than its equivalent counterparts.

Given, the co-ordinates of the parallelogram are: (-2, 3), (s, -1), (0, -1),
(t, 3).
Also, the co-ordinates of the parallelogram are also shown in the figure below.
To compare for the values of s and t for the given parallelogram,
we can analyze that both s and t represent points on the x-axis, therefore any point that stands rightmost with the x co-ordinate represents a higher value than the corresponding counterparts.
Therefore, t has a greater value than s for the co-ordinates (s, -1) and (t, 3), since t is on the right side from s.

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The perimeter of the square has a value of 260 units

From the question, the given parameters are

Shape = Square

Side lengths = 9x + 11 and 13x - 1

The side lengths of a square are congruent

This means that

9x + 11 = 13x - 1

Collect the like terms in the equation

So, we have

13x - 9x = 11 + 1

Evaluate the like terms

2x = 12

Divide both sides by 2

x = 6

The perimeter of the square is then calculated as

P = 4 * (9x + 11)

Where x = 6

So, we have

P = 4 * (9 x 6 + 11)

Evaluate

P = 260

Hence, the perimeter is 260 units

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Given the function :

we need to find the value of 3f(5) x f(2)

so, to find the value of f(5), substitute with x = 5 at the given function

And to find the value of f(2) , substitute with x = 2 at the given function

so,

The equation that represents the total average decrease in the stock after 4 weeks is 4|−12| = 48 dollars.

When the value of a stock decreases, the number is a negative number. A negative number is a number that is less than zero. A negative number would have a negative sign in front of it. Thus, a $12 stock decrease would be written as -12.

The total stock decrease in 4 weeks can be determined by multiplying $-12 by 4 weeks. Multiplication is the operation that is used to determine the product of two or more numbers.

Total stock decrease = decrease per week x number of weeks

-12 x 4 = -48 or |-48| dollars

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Setting h=0 and solving for t we get:

Since t<0 does not have real meaning, we get that:

Answer: 6.5 seconds.

THe diagonal, BD divides the rectangle into two right angle triangles.

BD represents the hypotenuse

BC represents the opposite side

DC represents the adjacent side

We would determine BD by applying the pythagorean theorem which is expressed as

The length of the diagonal, BD is 13.9m to the nearest tenth

The solution for the algebraic expression is [tex]3\frac{3}{8}[/tex].

The problem we are dealing with is related to the PEMDAS order of operations, where P stand for parentheses, E  stands for Exponents, M  stands for Multiplying, D stands for Divide, A stands for Add, and last S  stands for Subtract. It's the order we follow to solve a rational algebraic expression.

For the given expression  3/4.9/2, we start solving it from the direction left to right, according to PEMDAS  we multiply first  followed by dividing

=3x9/4 x2

=27/4/2

=27/8

simplifying the improper fraction to a mixed number

= [tex]3\frac{3}{8}[/tex]

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Any integer that cannot be divided into twos is considered an odd number. Five computers, for instance, cannot be arranged in pairs only. 5 is therefore an odd number.

The next three numbers in the pattern is 16,21,26. The pattern is odd.

Any integer that cannot be divided into twos is considered an odd number. Five computers, for instance, cannot be arranged in pairs only. 5 is therefore an odd number.

An even number is one that can be divided by two and leaves residue of zero. The even numbers include 2, 4, 6, 8, 10, and so on. Let's say, for instance, that you have ten chocolates. There are two groups of these chocolates that each include five chocolates. Ten is therefore an even number.

An even number is produced by adding two even numbers. In this case, 12 + 8 equals 20.

Odd numbers are created by adding odd numbers to even numbers. For example, 6 + 7 equals 13.

The outcome of adding two odd numbers is an even number. For an instance, 15 + 11 = 26.

Now for the above question,

The next three numbers: 16, 21, 26.

Number pattern is odd, because 5 is odd number.

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The 30-60-90 ratio is a special right triangle that always has angles with measures: 30º, 60º, and 90º. Its side lengths have also the same relationship one with another.

For any 30-60-90 the ratio is as follows:

The side opposite to the 30º angle has length: z

The side opposite to the 60º angle has a length z√3

The side opposite to the 90º angle has a length: 2z

Following these ratios, you can determine the side lengths of the triangle.

The measure opposite to the 60º angle is z√3 = 9√3 → From this we can determine the value of z, which is z=9

Once we know the value of z, we can calculate the values of the sides opposite to the other angles.

The side opposite to the 30º angle is y= z= 9

The side opposite to the 90º angle is x= 2z= 2*9 = 18

Based on the calculations, the value of function g(f(x)) is equal to: g(f(x)) = x + 10.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).

In this exercise, you're required to determine the value of g(f(x)) and we are given the following functions:

f(x) = (x + 3)²        ........function 1.

g(x) = √x + 7        ........function 2.

Next, we would substitute function 1 into function 2 as follows:

g(f(x)) = √((x + 3)²) + 7

g(f(x)) = (x + 3) + 7

g(f(x)) = x + 3 + 7

g(f(x)) = x + 10

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Carmella has 9 albums and 4410 cards.

The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.

Due to that,

There are 315 cards in each box.

14, the number of boxes.

(b) Total number of cards is the sum of the boxes plus the number of cards in each box.

= 14 × 315

= 4410

(a) Carmella purchased a six-album set of 500 cards since she thought she had 3,000 cards. Six albums are not enough because she calculated the quantity of cards incorrectly. There are 4410 cards in total, but she thought there were only 3000.

(c). Total number of albums required = [tex]\dfrac{Total number of cards}{Number of card 1 album can hold}[/tex]

                                                             = [tex]\frac{4410}{500}[/tex]

                                                             = 8.82 ≅9

Carmella have 4410 cards, 9 albums.

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For a quadratic [tex]ax^2+bx+c[/tex], the sign of its determinant, given by

[tex]\Delta = b^2 - 4ac[/tex]

"determines" the nature of its roots. In particular, if [tex]\Delta<0[/tex], then the quadratic has two distinct non-real roots.

Now, we have

[tex]3z^2 - 9z = n-3 \implies 3z^2 - 9z - (n-3) = 0[/tex]

with determinant

[tex]\Delta = (-9)^2 - 4\cdot3(n-3) = 117 - 12n[/tex]

Solve for [tex]n[/tex] such that [tex]\Delta<0[/tex].

[tex]\Delta = 117 - 12n < 0 \implies 12n > 117 \implies n > \dfrac{117}{12} \\\\ ~~~~ \implies \boxed{n > \dfrac{39}4}[/tex].

Answer:

- 200,5

Some words for 20 symbols

Answer:

  C.  100

Step-by-step explanation:

If 60 songs are played in 3 hours, 80 songs in 4 hours, and 120 songs in 6 hours, you want to know the number played in 5 hours.

Considering the rate of change of songs per hour, we find ...

  hours 3-4: 80-60 = 20 songs, over the 1-hour period

  hours 4-6: 120 -80 = 40 songs, over the 2-hour period

It appears that the number of songs being played is steady at 20 songs per hour. Then 5×20 = 100 songs were played in 5 hours.

Adding the two equations will be adding similar terms to both equations. That is:

8x + (-8x) = 0

-10y + (-6y) = -16y

20 + (-4) = 16

Therefore, adding the two equations will look like -16y = 16. (Option 3)