The graph shows the density of a substance. Find the density in grams per milliliter.

The total amount earned after 3 years at 8% rate is $5580

Interest is the price you pay to borrow money or the cost you charge to lend money.

Given that, $4500 is invested at 8% for 3 year,

SI = PxRxT/100

= 4500x8x3/100

= 1080

Amount = interest + principal

Amount = 1080 + 4500 = 5580

Hence, The total amount earned after 3 years at 8% rate is $5580

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A linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

The mathematical assertion that two linear expressions, or a linear expression and a constant, are not equal is made via a linear equation.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept).

Therefore, a linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.

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Answer:

A. [tex] {5}^{7} [/tex]

B. [tex] ( { - 7})^{5} [/tex]

C. [tex] {3}^{9} [/tex]

D. [tex] {27}^{2} [/tex]

E. [tex] ({ - 2})^{9} [/tex]

F. [tex] {3}^{14} [/tex]

G. [tex] {( - 4)}^{14} [/tex]

H. [tex] {2}^{8} [/tex]

I. [tex] {(0.25)}^{5} [/tex]

J. [tex] {7}^{6} [/tex]

Step-by-step explanation:

A.

[tex] {5}^{3} \times {5}^{4} \\ = {5}^{3 + 4} \\ = {5}^{7} [/tex]

B.

[tex]( { - 7})^{2} \times ( { - 7})^{3} \\ = ( { - 7})^{2 + 3} \\ = ( { - 7})^{5} [/tex]

C.

[tex] {3}^{6} \times {3}^{3} \\ = {3}^{6 + 3} \\ = {3}^{9} [/tex]

D.

[tex] {27}^{0} \times {27}^{2} \\ = {27}^{0 + 2} \\ = {27}^{2} [/tex]

E.

[tex]( { - 2})^{2} \times ( { - 2})^{3} \times ( { - 2})^{4} \\ = ( { - 2})^{2 + 3 + 4} \\ = ({ - 2})^{9} [/tex]

F.

[tex] {3}^{4} \times {9}^{2} \times ( { - 3})^{6} \\ = {3}^{4} \times {3}^{2 \times 2} \times {3}^{6} \\ = {3}^{4} \times {3}^{4} \times {3}^{6} \\ = {3}^{4 + 4 + 6} \\ = {3}^{14} [/tex]

G.

[tex] {( - 4)}^{6} \times {( - 4)}^{5} \times {( - 4)}^{3} \\ = {( - 4)}^{6 + 5 + 3} \\ = {( - 4)}^{14} [/tex]

H.

[tex] ( - 8) \times ( - 8) \times {2}^{2} \\ = 8 \times 8 \times {2}^{2} \\ = {2}^{3} \times {2}^{3} \times {2}^{2} \\ = {2}^{3 + 3 + 2} \\ = {2}^{8} [/tex]

I.

[tex] 0.25 \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = {(0.25)}^{1} \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = \times {(0.25)}^{1+4+0} \\ = \times {(0.25)}^{5} [/tex]

J.

[tex] {7}^{3} \times {7}^{2} \times 7 \\ = {7}^{3} \times {7}^{2} \times {7}^{1} \\ = {7}^{3+2+1} \\ = {7}^{6} [/tex]

Answer:

[tex] \frac{7}{6} [/tex]

The alkali metals, which are located in Group 1A of the periodic table, are the most reactive metals.

The blue column on the left of the periodic table contains the alkali metals, which are the most reactive metals. As we move down column (group) one, which is depicted in blue, their responsiveness improves.

What are Alkali metals ?

Alkali metals are those that react with water to produce strong bases.

It is composed of six elements collectively referred to as the lithium family. These metals have one electron in their outermost shell, making them extremely reactive elements of the periodic table.

A few instances of alkali metal

lithium (Li), sodium (Na), rubidium (Rb), potassium (K), francium (Fr) and  Caesium  (Cs).

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The summation notation of the sum is given as follows:

[tex]\sum_{i = 1}^{6} \frac{(-1)^{i-1}}{3^i}[/tex]

The summation notation of the sum is written considering the patterns of the terms that compose the terms.

First we look at the fact that the sum has six terms, and the first term is considered as having index 1, hence:

[tex]\sum_{i = 1}^{6}[/tex]

Then we consider that the signal is alternating, with the terms with odd indices being positive and those with even indices being negative, hence the numerator is of:

[tex](-1)^{i - 1}[/tex]

(any of -1 or +1 would work here).

Then we considering that the denominator is composed by the powers of 3, hence it is given by:

[tex]3^i[/tex]

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The base of the triangle is decreasing at the rate of 1.6 cm/min.

Given

dh/dt = 1 cm/min

dA/dt = 2 cm2/min

When A = 100 cm2, h = 10 cm

We know that

A = 1/2 × b × h

b = 20 cm

Let us differentiate both sides

dA/dt = 1/2 [b dh/dt + h db/dt]

Substituting the values

2 = 1/2 [20 × 1 + 10 × db/dt]

By further simplification

4 = 20 + 10 db/dt

db/dt = -1.6 cm/min

Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.

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The expression that can be used to determine how long it will take for the tank to fill completely is C. 1 over 4 . 12.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B). This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

In this case, the oil company fills 1 over 12 of a tank in 1 over 4 hour with gasoline.

The rate will be:

= 1/4 ÷ 1/12

= 1/4 × 12

= 3

The correct option is C

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2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]

To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:

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Answer:

It looks like you have an inequality equation with one variable, but the equation is incomplete. In order to solve the inequality, we need to have a complete equation with a left-hand side and a right-hand side.

For example, if we wanted to solve the inequality 8y - 5 < 3, we could complete the equation by adding 5 to both sides:

8y - 5 + 5 < 3 + 5

8y < 8

Then, we could divide both sides of the inequality by 8 to solve for y:

8y/8 < 8/8

y < 1

Therefore, the solution to the inequality 8y - 5 < 3 is y < 1.

The predicted value of the twin born first has an IQ of 104 is 106.2..

We have given that,

sample size n = 10

x = 98.13

y = 100.6

r = 0.904

p-value = 0.000

y'= 14.68 + 0.88x

significance level = 0.05

and we have to find predicted value of the twin born first has an IQ of 104.

We know that x represents the IQ score of the twin born first.

Therefore value of x is 104.

Hence the predicted value P will be,

P = 14.68 + 0.88(104)

  = 14.68 + 91.52

P = 106.2

Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.

The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.

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Answer: QB≈4.24

Step-by-step explanation:

Q(1,0)    B(-2,-3)   QB=?

[tex]\boxed{L=\sqrt{(x_2-x_1)+(y_2-y_1)^2} }\\\\x_1=1\ \ \ \ x_2=-2\ \ \ \ y_1=0\ \ \ \ y_2=-3[/tex]

Hence,

[tex]QB=\sqrt{(-2-1)^2+(-3-0)^2} \\\\QB=\sqrt{(-3)^2+(-3)^2} \\\\QB=\sqrt{9+9} \\\\QB=\sqrt{18} \\\\QB=\sqrt{9(2)} \\\\QB=\sqrt{3^2(2)} \\\\QB=3\sqrt{2} \\\\QB\approx4.24[/tex]

Answer:

3 x y (y + x)

Step-by-step explanation:

Factor the following:

(y + x)^3 - (y^3 + x^3)

Factor the sum of two cubes. y^3 + x^3 = (y + x) (y^2 - x y + x^2):

(y + x)^3 - ((y + x) (y^2 - x y + x^2))

Factor y + x out of (y + x)^3 - (y + x) (y^2 - x y + x^2), resulting in (y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2)):

(y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2))

3 - 1 = 2:

(y + x) ((y + x)^2 - (y^2 - x y + x^2))

(y + x) (y + x) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = y^2 + 2 x y + x^2:

(y + x) ((y^2 + 2 x y + x^2) - (y^2 - x y + x^2))

-(y^2 - x y + x^2) = -y^2 + x y - x^2:

(y + x) (x^2 + 2 x y + y^2 + (-y^2 + x y - x^2))

Grouping like terms, y^2 - y^2 + 2 x y + x y + x^2 - x^2 = (2 x y + x y) + (y^2 - y^2) + (x^2 - x^2):

((2 x y + x y) + (y^2 - y^2) + (x^2 - x^2)) (y + x)

x y 2 + x y = x y×3:

(3 x y + (y^2 - y^2) + (x^2 - x^2)) (y + x)

y^2 - y^2 = 0:

(3 x y + (x^2 - x^2)) (y + x)

x^2 - x^2 = 0:

Answer: 3 x y (y + x)

Length of wall = 10km

side of square= 10km

area of square= 10²= 100km²

radius of circle = 10/2 = 5km

area of circle = 3.14 × 5²

area of circle = 3.14 × 25

area of circla = 78.5 km²

area of square >>> area of circle

For queuing system B, the average time in queue ids going to change significantly as a result of increased utilization.

This is because queuing system B is initially heavily loaded and has less capacity to handle more requests. As a result, an increase in utilization can cause a significant increase in average queue latency on system B compared to system A.

Average Queue Time is a measure of the time a customer or request spends being processed by a server. It is affected by several factors such as server load, customer or request arrival rate, and server service rate. As the load on the queuing system increases, it means that the server is being used more frequently and is no longer available to process incoming requests. This will increase the average time in the queue as more requests accumulate and have to wait to be processed. The greater the increase in occupancy, the greater the impact on average latency.

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The number multiplied by 3 and subtracted by 2 equals 40 is 14.

The Equation that is used to find an unknown value is known as Linear Equation. To find an unknown value or quantity, first form a linear equation according to the conditions that are given the problem, here we use variables like x, y, etc. to represent the unknown value.  

Here we have

A Number is multiplied by 3 and subtracted by 2 equals 40

Let the number be x

Given that 'x' is multiplied by 3 (3x); subtracted by 2 (3x-2) equals to 40

=> 3x - 2 = 40

Add 2 on both sides

=> 3x - 2 + 2 = 40 + 2

=> 3x = 42

Divide by 3 into both sides

=> 3x/3 = 42/3

=>  x = 14

Therefore,

The number multiplied by 3 and subtracted by 2 equals 40 is 14.

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The solution of the expression - 4 - 0.2x + 11 = - 0.8x + 10 is 28.33.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A numerical expression and we have to solve for x or find the value of x.

- 4 - 0.2x + 11 = - 0.8x + 10.

- 0.2x - 7 = - 0.8x + 10.

- 0.2x + 0.8x = 10 + 7.

0.6x = 17.

x = 17/0.6.

x = 28.33.

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The interquartile range IQR for the given data set is IQR=10

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

Finding the median, lower quartile, and upper quartile of a given set of data (Q2, Q1, and Q3) is the first stage in creating a box-and-whisker figure. Now that you know how to calculate the interquartile range (IQR). The distance between the upper and lower quartiles is known as the interquartile range.

Lower data set:

70 73 81 84

Q1=73+81/2=77

Middle data set

65 70 75 80

Q2= 70+75/2=72.5

Upper data set

85 87 90

Q3=87

IQR=Q3-Q1=87-77=10

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The simplified form of the given expression is 3x+5y+4. Here only the constants are simplified since there are no like terms in the expression.

The given expression which is to be simplified is 6+3x-6+4+5y.

Here to simplify the given expression, we need to add or subtract the like terms.

In the given expression, the variables x and y.

They are unlike terms. So, we cannot add or subtract them. But there are three constants. Then, we can add or subtract them.

Thus, the simplified expression for the given expression is

6+3x-6+4+5y = 3x+5y+4

Here 6 and -6 are added so that we get 0.

Hence the answer is 3x+5y+4.

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Answer:

-2,0

very simple it is so easy

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R

Full question is:

Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)

If we have a level surface, then it will give us

f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.

Now let us calculate the ∇ gradient of f at point (0,0,7):

∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)

= (1, 1, 1)

We get the equation for the tangent plane A:

A: 1(x−0) + 1(y−0) + 1(z−7)=0

This can also be written as:

x+y+z = 7 ------------------------------------------------------------------(a)

The equation for the normal line B gives us :

L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)

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Answer:

7a+9b

Step-by-step explanation:

The number is 17.

The first part is "Fifteen less than twice a number".

Let us say that n represents the unknown number.

Twice a number is the same as two times the number or 2n, and fifteen less than 2n is 2n−15.

The next part "is the same as the" part of the word problem indicating that the two parts are equal. So we use an equal sign to represent it⇒2n−15 =

The third part of the problem is "the number plus two". This is the same as n+2

The final equation is 2n-15=n+2

To solve for n, we would add 15 to both sides: 2n=n+17

Then subtract 1n from both sides: n=17

The number is 17.

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The scale factor of the dilation is 2 which can be shown in the details given below.

In geometry, a line segment is bounded with the aid of using awesome factors on a line. Or we are able to say a line phase is a part of the road that connects  factors. A line has no endpoints and extends infinitely in each the course however a line phase has constant or particular endpoints.

QS : QS'

= 4 : 8

= QU : QU'

= 5 : 10

= 1 : 2

Then the scale factor is of the dilation is 2 (magnification).

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Complete question

Line segment SU is dilated to create S'U' using point Q as the center of dilation.

The scale factor of the dilation is:

When the sum of their squares is as largest as possible the numbers are 0 and 20, when the sum of their squares is as small as possible, the numbers are 10 and 10

Sum of the two numbers = 20

First we have to find the sum of their squares is as large as possible

Consider the first number as x and second number as y

To get the largest values the value of x or the value of y should be zero

Then the two numbers are 0 and 20

To get the small as possible

x^2 + (20-x)^2 = x^2 + x^2 - 20x +400

= 2x^2 -20x + 400

= 2(x^2 - 10x + 100)

The one number will be 10 and the other number will be 10

Therefore, to get the largest value the numbers will be 0 and 20 and to get the smallest value the numbers will be 10 and 10

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(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

What are the properties of angles?

The angle properties of lines are:

Vertically opposite angles are equal, for example, a = d, b = c.

Adjacent angles add to 180, for example, a + b = 180, a + c = 180. Corresponding angles are equal, for example, a = e, b = f, c = g, d= h.

(2) In the given figure, m∠BFC = 42°

By using the property of linear pair, we can write

       ∠BFC + ∠CFD = 180

         42 + ∠CFD = 180

        ∠CFD = 58.

(2) Angle CFD and angle AFE are opposite angles and opposite angles are same in measurement so we can write

             m∠AFE = 58°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

Hence,

(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

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Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

A multicore processors is an electronic component that has two or more processor cores attached for higher performance and lower power consumption. These processors also enable more efficient execution of numerous activities, such as with parallelization and multithreading.

Here,

It is because of the following disadvantages:

Although Peterson's technique is effective for two processes, it is the best plan for the important part in user mode.

Additionally, this solution involves busy waiting, wasting CPU time. So that “SPIN LOCK” problem can emerge. And any busy waiting solution may encounter this issue.

Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

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The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁  = 3 + 80

∴ a₂₁  = 83

So, the 21st term in the given arithmetic sequence is 83.

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By information provided in the question, we can say that It is the probability of a Type I error.

The proportion of favorable outcomes to all possible outcomes for an event is known as the probability. The quantity of positive outcomes in an experiment with 'n' outcomes is represented by x. The following equation can be used to determine the likelihood of an event:

Probability (event) = positive outcome / overall outcome = x/n

It refers to the likelihood of a Type I mistake.

The likelihood that a Type I error will occur, or the likelihood that a null hypothesis will be rejected when it is true, determines the degree of significance.

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