Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1

Answer:

  [8, 44]

Step-by-step explanation:

The average of equally-weighted values is their sum divided by their number.

For some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...

  70 ≤ (91 +88 +93 +x)/4 ≤ 79

Multiplying by 4, we have ...

  280 ≤ 272 +x ≤ 316

  8 ≤ x ≤ 44 . . . . . . . . . . subtract 272

Paul will get a C if his fourth test score is in the interval [8, 44].

The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:

Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X = B(n,p)

The probability that out of n trials, there'd be x successes is given by

P(X=x)  = [tex]^nC_xp^x(1-p)^{n-x}[/tex]

Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.

Let we say

Success= Probability of a diseased person tagged as diseased by the clinic

Failure = Probability of a diseased person tagged as not diseased by the clinic.

Then,

P(Success) = p = 72% = 0.72 (of a single person)

P(Failure) = q = 1-p = 0.28

Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)

Calculating the needed probabilities, we get:

a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)

P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]

P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378

b)  P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)

P (X ≤ 4) =

[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]

[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]

P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719

P (X ≤ 4) =  0.0342

Thus,

The probabilities of considered events are:

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The factored inequality is  [tex]x^2-3x+6\geq 0[/tex]

The given inequality is:

[tex]-x^2+3x-6\leq 0[/tex]

This can be further simplified as:

[tex]-(x^2-3x+6)\leq 0[/tex]

The inequality can be re-written as:

[tex]x^2-3x+6\geq 0[/tex]

Since the question does not state that we should solve the inequality, the simplest we can get after factoring is [tex]x^2-3x+6\geq 0[/tex]

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The value of x in the equation is x=-44.

The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].

An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.

Firstly, apply the distributive property as a(b+c)=ab+ac and get

[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]

Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as

[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]

Further, simplify the above expression by taking L.C.M as

[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]

Then, multiply both sides with 4 and get

[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]

Furthermore, cross multiply both sides and get

[tex]x=-44[/tex]

Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.

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Answer:

Average rate of change = 4/3

Step-by-step explanation:

We have to calculate the average rate of change of the graph at x = 2 to x = 5.

From the graph attached,

At x = 2,

f(2) = 3

At x = 5,

f(5) = 7

Since, average rate of change of the function between x = a and x = b is defined by,

Average rate of change = f (b)-f (a) / b - a
                                         

Therefore, average rate of change of the function represented by the graph will be =7-3/5-2

          = 4/3

Answer:

sin=-3/5
cos=4/5

tan-3/4

csc=5/-3

sec=5/4

cot=4/-3

Step-by-step explanation:

you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.

Answer:

  7/9

Step-by-step explanation:

In order to write the fraction without any units (as a pure number), we must have units in the numerator and denominator that are the same. Then the units cancel.

We are given the conversion ...

  4 quarts = 1 gallon

Multiplying by 7, we see ...

  28 quarts = 7 gallons

This lets us write the desired fraction as ...

  (28 quarts)/(9 gallons) = (7 gallons)/(9 gallons) = 7/9

The ratio in simplest form is 7/9.

Answer: 3

Step-by-step explanation:

Using proportions, it is found that 78 students would prefer long jump.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Out of 300 students, 26% would prefer long jump, hence the amount is given by:

n = 0.26 x 300 = 78 students.

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Answer: 123/32 or 3 27/32 sticks

Step-by-step explanation:

41/8*3/4 =

41*3/8*4 =

123/32 =

3 27/32

The moving average of the stock for the end of day 7 is 53

Note that

Average = Day 1 + Day 2 + Day3 + Day 4 = Day 5 + Day 6 + Day 7/ 7

We have

Average = 32 + 56 + 50 + 60 + 59 + 55 + 59 /7

Average = 371/ 7

Average = 53

Therefore, the moving average of the stock for the end of day 7 is 53

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Answer:

Step-by-step explanation:

(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].

(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].

So, the combined areas of the four semicircles is [tex]241\pi[/tex].

The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].

Answer:

[tex] \boxed{\bf \cfrac{\boxed{c}}{\boxed{a }+ b}} [/tex]

Step-by-step explanation:

Given:

[tex] \tt (x_1,y_1) : A (0,0)[/tex]

[tex]\tt (x_2,y_2) : C (a+b, c) [/tex]

[tex]\boxed{\tt Slope= \cfrac{y_2,y_1}{x_2,x_1}} [/tex]

[tex]\tt \cfrac{c - 0}{a + b - 0} [/tex]

Add zero (Anything plus zero gives itself).

[tex] \tt \cfrac{c}{a + b + 0} [/tex]

[tex]\tt \cfrac{c}{a + b} [/tex]

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Answer:

x<3−√11 /2 or x > 3 +√11/2

Step-by-step explanation:

Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.

The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.

We have

[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]

[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]

[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x)  - 1 = 0[/tex]

[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]

In the interval [tex]0\le x< 2\pi[/tex], we have

[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]

and

[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]

In order from smallest to largest, that's

[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]

The solution to the Trigonometric equation is given as below.

A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.

The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.

Thus,

18 sin (x) cos (x) - 9 sin (x) = 0

8 sin(x) = 0 or 2 cos (x) - 1 = 0

Sin (x) = 0 or Cos (x) = 1/2

Given the interval of 0 ≤ x ≤ 2π

→ Sin (x) = 0 → x = 0 or x = π

and

Cos (x) = 1/2

→ x = π/3 or x = 5π/3

Arranging the values from the smallest to the largest, we have:

x = 0 or x = π/3

x = π or x = 5π/3

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Using PEDMAS, the value of each expressions are:

a. 1 + 5 × 2 + (1 + 3)² = 27

b. 0.25 × 4³ - 1 = 15

c. 4 + 8(1/4 + 2) = 22

PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.

Let's evaluate the expressions using PEDMAS:

a. 1 + 5 × 2 + (1 + 3)²

1 + 5 × 2 + (4)²

1 + 5 × 2 + 16

1 + 10 + 16

= 27

b. 0.25 × 4³ - 1

0.25 × 64 - 1

16 - 1

= 15

c. 4 + 8(1/4 + 2)

4 + 8(9/4)

4 + 18

= 22.

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Answer:

no

Step-by-step explanation:

the y coordinate 9 repeats twice

If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.

Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.

Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.

formula of polar graph is similar to r= a+ b cos (θ).

Case 1. If a<b or b/a>1

then the curve is a limacon with inner loop.

Case 2. If a>b or b/a<1

Then the limacon does not have an inner loop.

Here given that [tex]r=3+4cos[/tex] (θ)

It is observed that , a<b or b/a>1

Therefore the curve is limacon with an inner loop.

Hence because b/a>1 the curve is a limacon with an inner loop.

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Answer:

The answer is B

Step-by-step explanation:

The angular speed of the turntable is = 4.7 rad/sec.

Angular speed can be defined as the rate at which angular displacement changes with respect to time.

Speed can be defined as the distance traveled by an object at a particular time interval.

The rate of rotation of the turntable = 45 rotations per minute.

That is, the time taken to complete one rotation in seconds = 1/45 ×60sec = 1.34secs

This is taken to be the period of rotation (T)

Therefore, the angular speed is calculated using the formula, 2π/T

= 2×3.14/1.34 = 4.7 rad/sec.

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Answer:

D. all real numbers greater than or equal to 0

Step-by-step explanation:

The range is the set of y-values.

The population of Charlotte is 661,000.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

The population of Charlotte = number of unemployed people / percentage of unemployed

26,440 / 0.04 = 661,000

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The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have shown a square in which a one-fourth circle is shown and making an ellipse.

The perimeter of the circle = 2πr = 2π(8) = 16π cm

The perimeter of the one-fourth is circle = (16π)/4 = 4π cm

The perimeter of 2 one-fourth circle = 2(4π) = 8π cm

The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm

The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm

The area of the shaded region = 2(16π - 32) = 36.53 square cm

or

= 32(π - 2)cm²

Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

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Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:

(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)

The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

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Answer:

B

Step-by-step explanation:

Convert everything to inches first

The floor is 120 inches by 144 inches

The floor can be covered with (120/6) * (144/8) tiles

(120/6) * (144/8) = 20*18=360 tiles, hence b.

Answer:

100+946=1046

Ao the next no. Is 1046

Answer: B. The lines will intersect once.

Step-by-step explanation:

Multiplying the bottom equation by 2, we get 6y+4x=14.

Adding this to the first equation, this gives 9x=18, and thus x=2.

Therefore, since this means there will be 1 solution, the lines will intersect once.

Answer:

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

A) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:

The number of terms from zero to 99 is:

B) This is a AP with the first term of 11 and common difference of 4.

The nth term equation is:

Substitute the values and solve for n:

C) Same as above, the sequence is AP, with the first term 44 and common difference 1.

Applying the nth term formula: