solve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7

We have sufficient evidence to conclude that the over all percentages of 3 categories are not same.

The percentage refers to a specific percentage out of a hundred. It is a fraction with the denominator 100, and the sign for it is 1%.

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.

Category    Observed([tex]O_{i}[/tex])          Expected([tex]E_{i}[/tex])              ([tex]O_{i}[/tex]-[tex]E_{i}[/tex])²/[tex]E_{i}[/tex]

A or B           100                           120                          3.333

C                   130                           105                          5.9524

D or F             70                            75                            0.056

Total               300                        300                         9.3417

H₀:over percentages are same at UC Davis and at SSC

H₁:They are not same

Test statistic

X²=∑  ([tex]O_{i}[/tex]-[tex]E_{i}[/tex])²/[tex]E_{i}[/tex]

=9.3417

P-value=P(X²(n-1)>9.3417)

=0.0094

Here we can see that the P-value is very low(<0.05 and <0.01)

So, we reject the null hypothesis H₀.

Therefore, we have sufficient evidence to conclude that the over all percentages of 3 categories are not same.

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Answer:

12.8

Step-by-step explanation:

You can see that triangle DAF and BED are equal.

So lineAF is lineDE.

6.4*2=12.8.

a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

Answer:

5cm. 8cm

Step-by-step explanation:

Label all the vertices then use Pythagorean theorem

c² = a² + b²

The graph that shows the equation, y = -5x + 45, that represents the scenario given is shown in the attachment.

Determine the slope (m) and the y-intercept (b), then input the values in the equation, y = mx + b, to write the equation of the line that would be graphed.

Given the information above, we have the following:

Let x = hours, and y = quantity  of gallons of paint left

Slope (m) = -5

Y-intercept (b) = 45

Write the equation of the graph by substituting m = 5 and b = 45 into y = mx + b:

y = -5x + 45

The graph shown below for y = 5x + 45 would be labelled as follows:

x-axis = hours

y-axis = quantity of paint (in gallons)

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To maximize the profit 29.6 units must be produced.

What is the maxima or minima?

The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.

We have given,

The revenue function is,

R(x)=3x

Cost function,

C(x)=0.05x^2+0.04x+10,

Where

x = number of units produced.

Thus, profit = revenue - cost

P(x) = 3x - (0.05x^2+0.04x+10)

= -0.05x^2 + 2.96x - 10

Differentiating with respect to x,

P'(x) = -0.1x + 2.96

Again differentiating with respect to x,

P''(x) = -0.1

For maxima or minima,

P'(x) = 0,

0 = -0.1x + 2.96

-0.1x = -2.96

x = 2.96/0.1

For x = 29.6,

P''(x) = negative,

Hence, to maximize the profit 29.6 units must be produced.

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By solving a quadratic equation, it can be calculated that

Length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

What is a quadratic equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as quadratic  equation.

Here a quadratic equation needs to be solved.

Let the length be l ft. and the width be b ft.

Perimeter = 2(l + b) ft.

By the problem,

2(l + b) = 200

l + b = [tex]\frac{200}{2}[/tex]

l + b = 100

b = (100 - l) ft.

Now,

Area = l [tex]\times[/tex] b sq. ft.

        = [tex]l \times (100 - l)[/tex]

By the problem,

[tex]l \times (100 - l) = 1275\\100l - l^2=1275\\l^2 -100l+1275 = 0\\l^2 - 85l -15l + 1275 = 0\\l(l -85) - 15(l - 85) = 0\\(l -85)(l -15) =0\\l -85 = 0 \ or \ l -15 = 0\\l =85 \ or \ l =15[/tex]

If l = 15 ft.

b = 100 - 15 = 85 ft.

Which is not possible as length is always greater than the width

So, length of the plot = 85 ft.

Width of the plot = 100 - 85 = 15 ft.

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The system of equations are

The solution of the equation from the graph is

The system of equations is derived from the statements as interpreted below

If x represents the number of hours lifeguarding and y represents the number of hours tutoring

number of hours lifeguarding = x  

number of hours tutoring = y

she can work no more than 11 total hours

x + y not more than 11 hours

x + y < 11

making $14 per hour lifeguarding and making $25 per hour tutoring and must earn no less than $200

$14x + $25y no less than $200

14x + 25y > 200

The required equations are

14x + 25y > 200

x + y < 11

The graph is attached

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Answer: 2/11

Step-by-step explanation: there are 11 letters and 2 of them are p so the chances of getting p is 2/11

Answer:

2/11

Step-by-step explanation:

The total amount of tiles is 11. There are only 2 tiles that have the letter P on them.

Theoretical probability is the probability that should occur over many, many trials.

Theoretical probability = favorable outcomes / total outcomes.

In this scenario, the favorable outcome is the letter P. which there are two of. The total outcomes would be all the letters that make up the word MISSISSIPPI, or 11.

So your theoretical probability would be 2/11.

The height of the kite assuming that there is no slack in the string is 86.6 m.

We have given that,

the string of a kite is 100 meters long and it makes an angle of 60°.

and we have to find the height of the kite.

So therefore we know the formula for right angled triangle,

i.e. sinθ = Opposite side/ Hypotenuse

Here θ = 60°

Opposite side = height of the kite = h (say)

Hypotenuse = length of string = 100 m

⇒ sin60° = [tex]\frac{h}{100}[/tex]

           h = 100sin60°

              = 100 × [tex]\frac{\sqrt{3} }{2}[/tex]

              = 50 × 1.732

           h = 86.6 m

Hence the height of the kite is 86.6 m.

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The length of the other leg of the given right triangle is [tex]\sqrt{70}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The question gives:

Therefore, from the Pythagorean Theorem, you will find the value of the other leg. See below.

[tex]9^2={\sqrt{11}^2 +{leg_2}^2[/tex]

[tex]81=11 +{leg_2}^2[/tex]

[tex]{leg_2}^2=81-11\\ \\ {leg_2}^2=70\\ \\ leg_2=\sqrt{70}[/tex]

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ΔXYZ will also be an equilateral triangle.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.

As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic

Hence XYZ will also be an equilateral triangle

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An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

When two equal expressions are added together with the aid of the equal sign "=," an equation is created.

Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,

V ∝ T

V = kT

Substituting the volume and time in the equation,

60,000 gallons = 2.5 hours × k

Solving the equation for k,

k = 60,000 gallons / 2.5 hours

k = 24,000 gallons per hour

Now, the equation for the relationship can be written as,

V = 24,000 gallons per hour × T

Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,

V = 24,000 gallons per hour × T

108,000 gallons = 24,000 gallons per hour × T

108,000 gallons / 24,000 gallons per hour = T

T = 4.5 hours

Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

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The value of x = 6cm.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object refers to the space occupied by its outer surface.

From the given figure,

Surface area(A) = [tex]192cm^{2}[/tex]

Height = 8cm

a base side = 6 cm

b base side = 10 cm

c base side = x cm

Therefore,  TSA= 2B +Px = [tex]2 \times\frac{1}{2} \times8\times6 +(6+10+8)x[/tex]

                                          =48+24x

Thus, 60+24x=192

                     [tex]x=\frac{192-48}{24}[/tex]

                      x= 6cm

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zeroes are 2,-2,

vertical asymptotes are -1,3

plotted on the number line

---------|---------|---------|---------|---------|---------|

      -2          -1          0          1          2         3

What is vertical asymptote?

A vertical asymptote is a line that appears to correspond with a function's graph but never really touches the curve. When graphing a function, the vertical asymptote of the function is crucial.

The curve is neither touched or crossed by a vertical asymptote, which is a vertical line along which the function becomes unbounded (either y tends to or -). K is NOT present in the domain of the function if x = k is the vertical asymptote of a function y = f(x). Any quantity of vertical asymptotes is possible for a function. i.e., it may have 0 vertical asymptote, 1, 2,..., or a limitless amount. If the y-axis represents the vertical asymptote, we often do not portray it by a dotted line. Instead, we represent a vertical asymptote by a vertical dotted line.

1)

zeros means that the value were g(x) is zero

that means (x-2) and (x+2) = 0

x = 2 ,-2

2)

for vertical asymptote (x+1)and (x-3) = 0

x = -1,3

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The value of x from the inequality equation | 4x + 1 | ≤ 6 , is

-7/4 ≤ x ≤ 5/4

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the equation be A

The value of the equation A is | 4x + 1 | ≤ 6   be equation (1)

From the modulus function rule , we know

If , | x | ≤ a , then -a ≤ x ≤ a

So , on simplifying the equation , we get

-6 ≤ 4x + 1 ≤ 6

Now , the two values are

4x + 1 ≥ -6   be equation (2)

4x + 1 ≤ 6    be equation (3)

From equation (2) , 4x + 1 ≥ -6

Subtracting 1 on both sides , we get

4x ≥ -7

Divide by 4 , we get

x ≥ -7/4

And , From equation (3) , 4x + 1 ≤ 6

Subtracting 1 on both sides , we get

4x ≤ 5

Divide by 4 on both sides , we get

x ≤ 5/4

Therefore , the solution is -7/4 ≤ x ≤ 5/4 and the graph is given below

Hence , The value of x from the inequality equation | 4x + 1 | ≤ 6 , is

-7/4 ≤ x ≤ 5/4

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The mean lifetime of a bulb is 149.37 hours.

What is the meaning of mean?

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined. Mean is equal to (Sum of All Observations/Total Observations).

The given table represents a continuous data.

The table attached in below. To get mean lifetime of a bulb, find the mean of the given table.

The formula for mean is = Σ fm/N

Where f is frequency and m is midpoint of the class.

N is total number of observation.

From the table, Σ fm = 53175

Total number of bulb is 356.

The mean lifetime is 53175/ 356 = 149.37 hours

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Answer:

15 cats

Step-by-step explanation:

c:d

3:5

5=25

25/5=5

5*3=15

15 cats

======================================================

Explanation:

The tape diagram is shown below.

"C" represents a sub-group of cats, and "D" represents a sub-group of dogs. Each sub-group has the same number of animals.

There are 3 copies of "C" and 5 copies of "D" to represent the ratio 3:5 of cats to dogs. For every 3 cats, there are 5 dogs.

We are told there are 25 dogs available for adoption. This consists of all five blocks of "D" combined. If each "D" is the same number of dogs, then there must be 25/5 = 5 dogs per "D" block. By extension, there are 5 cats per "C" block.

In short, each block has 5 animals.

3 blocks of C = 3*5 = 15 cats are available.

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

Another approach:

C = number of cats available = unknown

D = number of dogs available = 25

C/D = 3/5

C/25 = 3/5

5C = 25*3 ... cross multiply

5C = 75

C = 75/5

C = 15 cats are available

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

A third approach:

The ratio 3:5 scales up to 15:25 after multiplying both parts by 5. This is so the "5" in "3:5" becomes "25".

The ratio of cats to dogs of 15:25 reduces to 3:5 when you divide both parts by the GCF 5.

So this is another way to see how 15 cats are available.

The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

Given that,

He makes paths that follow Line segments A and B, X and Y, and Z and Y through the garden.

We have to find which accurately compares the pathways' lengths.

We know that,

The length of the third side in a triangle is proportional to the angle Ф  if the lengths of the two sides that make up the angle Ф are fixed.

XY > YZ because XY's opposing angle (79°) is greater than YZ's (65°).

As before, YZ > AB because the opposing angle of YZ (65°) is greater than that of AB (36°).

Since both sides of the angle are the same length (8 feet),

As a result, assertion A. is accurate. (Answer)

Therefore, The journey along Line segment X Y is longer than the path along Line segment Z Y, and the path along Line segment Z Y is longer than the path along Line segment A B, hence Option-A is the correct answer.

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Answer:

It's A

Step-by-step explanation:

I got 100 on the quiz

The linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Given, data for a classroom of students who measured each (approximately) in inches.

Femur Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3

Tibia Length  15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8

we have to find a linear correlation between the two variables,

linear correlation be,

(y - 15.8)/(x - 18.7) = (15.8 - 21.0)/(18.7 - 14.2)

(y - 15.8)/(x - 18.7) = (- 5.2)/4.5

4.5y - 71.1 = -5.2x + 97.24

4.5y + 5.2x = 168.34

So, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Hence, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

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The amount of money that Margret needs to deposit to reach this amount is $8.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since Margret has $32.00 in a savings account. Margret wants to have a balance of $40.00 in the account, the amount needed will be:

= $40 - $32

= $8

She'll need $8 more.

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The angles ∠BCD and ∠BAD are opposite interior angles of a parallelogram. in which the alternate interior angles  ∠BAC  and  ∠ACD and ∠BCA and ∠DAC are congruent, from which by angle addition property, ∠BCD ≅ ∠BAD

Alternate interior angles are angles formed by the transversal to two parallel lines on the inside of the parallel lines, and on opposite sides of the transversal.

The two column-method used to  prove that ∠BCA is congruent to ∠DAC can be presented as follows;

Step       [tex]{}[/tex]         Statement                                          Reason

1.        [tex]\overline{BC}[/tex]║ [tex]\overline{AD}[/tex],  [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex]   [tex]{}[/tex]       Given

2. [tex]{}[/tex]    ∠BCA ≅ ∠DAC                  ║ lines cut by a trans. form ≅ int.  ∠s

3. [tex]{}[/tex]    [tex]\overline{AC}[/tex]║[tex]\overline{CA}[/tex]     [tex]{}[/tex]                         Reflexive Property

4.     ∠BAC ≅ ∠ACD [tex]{}[/tex]                  Alternate interion angles

5.     ∠BCA = ∠DAC[tex]{}[/tex]                    Definition of congruency

[tex]{}[/tex]        ∠BAC = ∠ACD

6.    ∠BCD = ∠BCA + ∠ACD[tex]{}[/tex]       Angle addition property

      ∠BAD = ∠BAC + ∠DAC

7.    ∠BCD = ∠BCA + ∠ACD  [tex]{}[/tex]       Substitution property

8. [tex]{}[/tex]   ∠BCD = ∠BAD   [tex]{}[/tex]                    Substitution property

9.    ∠BCD ≅ ∠BAD   [tex]{}[/tex]                    Definition of congruency

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Answer:

18k +37

Step-by-step explanation:

13k + 7 + 5(k + 6)

13k + 7 + 5k + 30

13k + 5k + 7 + 30

18k +37

By using the concept of maxima, it can be calculated that

Volume is maximum if the radius of the cone is 40 cm

What is maxima of a function?

Maxima of a function gives the maximum value of the function on a certain interval or on the whole domain.

Let the height of the cylinder be h and radius be r

Sum of height and circumference = h + 2πr

By the problem,

h + 2πr = 60

h = 60 -2πr

Volume(V) = π[tex]r^2[/tex] h

             = π[tex]r^2[/tex](60 - r)

             = 60π[tex]r^2[/tex] - π[tex]r^3[/tex]

[tex]\frac{dV}{dr} = 120\pi r - 3 \pi r^2[/tex]

For maximum volume

[tex]\frac{dV}{dr} = 0[/tex]

[tex]120\pi r - 3 \pi r^2 = 0\\[/tex]

[tex]3 r^2 = 120 r\\3r = 120 [r \neq 0]\\r = \frac{120}{3}\\r = 40 \ cm[/tex]

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi r\\[/tex]

Putting r = 40

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi \times 40\\\frac{d^2V}{dr^2} =120\pi - 240 \pi\\\frac{d^2V}{dr^2} = -120\pi < 0[/tex]

Hence Volume is maximum

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Answer: 12cm^2

Step-by-step explanation: We use the equation 1/2(bh) to get the area. If you put the number in the equation you will get the answer 12.

The statemet 2, the variable K represent carrying capacity and the variable N represent population size, is correct.

In the given question we have to review the video to determine whether each statement about the following equation is true or false.

The given equation is:

[tex]\frac{dN}{dt}=rN(\frac{K-N}{K})[/tex]

The given equation is used to find the annual growth of population.

In which, dN/dt = the annual increase for the population,

r = the annual growth rate,

N = the population size, and

K = the carrying capacity.

So the statemet two, the variable K represent carrying capacity and the variable N represent population size, is correct.

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Answer:

(i)  See below for proof.

(ii)  x = 1.823,   x = -0.823

Step-by-step explanation:

Given equation:

[tex]\dfrac{x+2}{x+1}+\dfrac{3}{x}=3[/tex]

Make the denominators of the fractions the same:

[tex]\implies \dfrac{x+2}{x+1}\cdot \dfrac{x}{x}+\dfrac{3}{x}\cdot \dfrac{x+1}{x+1}=3[/tex]

[tex]\implies \dfrac{x(x+2)}{x(x+1)}+\dfrac{3(x+1)}{x(x+1)}=3[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \dfrac{x(x+2)+3(x+1)}{x(x+1)}=3[/tex]

Multiply both sides of the equation by x(x + 1) to eliminate the denominator of the fraction on the LHS:

[tex]\implies x(x+2)+3(x+1)=3x(x+1)[/tex]

Expand the brackets:

[tex]\implies x^2+2x+3x+3=3x^2+3x[/tex]

[tex]\implies x^2+5x+3=3x^2+3x[/tex]

Subtract x² from both sides:

[tex]\implies 5x+3=2x^2+3x[/tex]

Subtract 5x from both sides:

[tex]\implies 3=2x^2-2x[/tex]

Subtract 3 from both sides:

[tex]\implies 0=2x^2-2x-3[/tex]

[tex]\implies 2x^2-2x-3=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

To solve the quadratic equation  [tex]2x^2-2x-3=0[/tex],  use the quadratic formula.

Therefore:

Substitute these values into the formula and solve for x:

[tex]\implies x=\dfrac{-(-2) \pm \sqrt{(-2)^2-4(2)(-3)}}{2(2)}[/tex]

[tex]\implies x=\dfrac{2 \pm \sqrt{4+24}}{4}[/tex]

[tex]\implies x=\dfrac{2 \pm \sqrt{28}}{4}[/tex]

[tex]\implies x=\dfrac{2 \pm \sqrt{4 \cdot 7}}{4}[/tex]

[tex]\implies x=\dfrac{2 \pm \sqrt{4} \sqrt{7}}{4}[/tex]

[tex]\implies x=\dfrac{2 \pm 2 \sqrt{7}}{4}[/tex]

[tex]\implies x=\dfrac{1 \pm \sqrt{7}}{2}[/tex]

Therefore, the solutions correct to 3 decimal places are:

[tex]x=1.823,\;\; x= -0.823[/tex]

The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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In this Trigonometric Functions F(x) = 1 + cos(1/X):  n=3 (12.01, 8.10),  n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

F(x) = 1 + cos(1/X)

for n=3

Upper sum = 12.01

Lower sum = 8.10

Δx = (b-a)/n = 2π / 3

for n=4

Upper sum = 11.65

Lower sum = 8.50

Δx = (b-a)/n = π / 2

for n=6

Upper sum = 11.24

Lower sum = 9.12

Δx = (b-a)/n = π / 3

Hence, n=3 (12.01, 8.10),  n=4 (11.65,8.50), and n=6 (11.24, 9.12), with their upper and lower value.

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