how many solutions are there to this non-linear systems/graph a. one solution,b.two solutions,c.no solutions

Answer: a. $40,800 b. 36

Step-by-step explanation:

Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].

[tex]\sigma= \$14,900[/tex]

a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.

Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]

= 40,800

hence, the point estimate of the mean salary for all college graduates in this town = $40,800

b.  Since  lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.

Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]

Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.

z-value for 99% confidence level  = 2.576

So,

[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]

The sample size used for the analysis =36

Answer:

Three

Step-by-step explanation:

Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

Answer:

[tex]\boxed{108d}[/tex]

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³.  Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

[tex]\frac{216}{108}=2[/tex]

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is [tex]\boxed{108d}[/tex].

Answer:

Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.

Step-by-step explanation:

We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.

Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.

This means that the two events A and B are independent if;

P(A) [tex]\times[/tex] P(B) = P(A and B)

Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94

So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)

      0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94

This shows that event a and event B are not independent.

So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.

Answer:

Shawn is correct

Step-by-step explanation:

Find the circumference:

Circumference = 2 x PI x radius:

Circumference = 2 x 3.14 x 16 = 100.48 inches.

A full circle is 360 degrees, a 45 degree angle is 1/8 of a full circle.

Arc length = 100.48 / 8 = 12.56 inches.

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

The area is given by the integral

[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]

where C is the curve and [tex]dS[/tex] is the line element,

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]

[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]

[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]

So the area is

[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]

Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:

[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]

Answer:

1, 7

Step-by-step explanation:

Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7

Answer:

b . sphere

Step-by-step explanation:

Answer:

18 - 8 * n = -6 * n

The number is 9

Step-by-step explanation:

Let n equal the number

Look for key words such as is which means equals

minus is subtract

18 - 8 * n = -6 * n

18 -8n = -6n

Add 8n to each side

18-8n +8n = -6n+8n

18 =2n

Divide each side by 2

18/2 = 2n/2

9 =n

The number is 9

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▹ Answer

n = 9

▹ Step-by-Step Explanation

18 - 8 * n = -6 * n

Simple numerical terms are written last:

-8n + 18 = -6n

Group all variable terms on one side and all constant terms on the other side:

(-8n + 18) + 8n = -6n + 8n

n = 9

Hope this helps!

CloutAnswers ❁

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▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

Answer:

2^11

Step-by-step explanation:

since the bases are the same, we can add the exponents

a^b * a^c = a^(b+c)

2^6 * 2^5

2^(6+5)

2^11

Answer:

Option (2)

Step-by-step explanation:

If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.

By using this property,

Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.

By applying Pythagoras theorem in right triangle KNJ,

(KJ)² = (KN)² + (NJ)²

(33)² = (6√10)² + (NJ)²

NJ = [tex]\sqrt{1089-360}[/tex]

NJ = [tex]\sqrt{729}[/tex]

    = 27 units

Since, GJ = 2(NJ)

GJ = 2 × 27

GJ = 54 units

Option (2) will be the answer.

Answer:

42  headbands per dancer

Step-by-step explanation:

Selling 1260 headband

Divide by the three coaches

1260/3

420 per coach

Divide by each dancer under a coach

420/10 = 42

Each dancer must sell 42 headbands

Complete question is;

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:

Do the results support the manufacturer's claim?

Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed

Answer:

We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Step-by-step explanation:

For the first sample, we have;

Mean; x'1 = 1160 ft

standard deviation; σ1 = 32 feet

Sample size; n1 = 19

For the second sample, we have;

Mean; x'2 = 1130 ft

Standard deviation; σ2 = 30 ft

Sample size; n2 = 11

The hypotheses are;

Null Hypothesis; H0; μ1 = μ2

Alternative hypothesis; Ha; μ1 > μ2

The test statistic formula for this is;

z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]

Plugging in the relevant values, we have;

z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]

z = 2.58

From the z-table attached, we have a p-value = 0.99506

This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200

Answer:

[tex]p = 2[/tex] if given vectors must be linearly independent.

Step-by-step explanation:

A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:

[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]

In other words, the following system of equations must be satisfied:

[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)

[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)

[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)

By Eq. 1:

[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]

Eq. 1 in Eqs. 2-3:

[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]

[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]

[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)

[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)

By Eq. 3b:

[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]

Eq. 3b in Eq. 2b:

[tex](p-2)\cdot \alpha_{2} = 0[/tex]

If [tex]p = 2[/tex] if given vectors must be linearly independent.

Answer:

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Step-by-step explanation:

Mean x`= 518 +548 +561 +523 + 536 + 499+  538 + 557+ 528 +563 /10

x`= 537.1

The Variance is  = 20.70

H0 μ≤ 520

Ha μ > 520

Significance level is set at ∝= 0.05

The critical region is t ( with df=9) for a right tailed test is 1.8331

The test statistic under H0 is

t=x`- x/ s/ √n

Which has t distribution with n-1 degrees of freedom which is equal to 9

t=x`- x/ s/ √n

t = 537.1- 520 / 20.7 / √10

t= 17.1 / 20.7/ 3.16227

t= 17.1/ 6.5459

t= 2.6122

As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05

If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821

then we would accept H0. The test would not support the claim at ∝= 0.01

Answer:

The second option.

Step-by-step explanation:

The first option consists of a line that extends at both opposite sides to infinity, with no precise end.

The third option is a ray that has an endpoint of A, and extends to infinity towards B.

The fourth option is a line segment. It has two endpoints, B and A.

The second portion is a ray that has an endpoint B, and extends towards A in one direction, to infinity.

The answer is the 2nd option.

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

[tex]B' = (-96,-24)[/tex]

Step-by-step explanation:

Given

[tex]A(0,6)[/tex]

[tex]B(-8,-2)[/tex]

[tex]C(8,-2)[/tex]

Required

Determine the coordinates of B' if dilated by a scale factor of 12

The new coordinates of a dilated coordinates can be calculated using the following formula;

New Coordinates = Old Coordinates * Scale Factor

So;

[tex]B' = B * 12[/tex]

Substitute (-8,-2) for B

[tex]B' = (-8,-2) * 12[/tex]

Open Bracket

[tex]B' = (-8 * 12,-2 * 12)[/tex]

[tex]B' = (-96,-24)[/tex]

Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]

Answer:

Bit late but the answer is (-4,-1)

Step-by-step explanation:

Took the test in k12

Answer:

2x

Step-by-step explanation:

These are like terms so we can combine them

4x-2x

2x

Answer:

2x

Explanation:

Since both terms in this equation are common, we can simply subtract them.

4x - 2x = ?

4x - 2x = 2x

Therefore, the correct answer should be 2x.

Answer:

135 degrees

Step-by-step explanation:

3x+15 = 5x - 5 because of the alternate interior angles theorem.

20 = 2x

x = 10

3(10) + 15 = 30+15 = 45

Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.

180-45 = 135.

Answer and Step-by-step explanation: The null and alternative hypothesis for this test are:

[tex]H_{0}: s_{1}^{2} = s_{2}^{2}[/tex]

[tex]H_{a}: s_{1}^{2} > s_{2}^{2}[/tex]

To test it, use F-test statistics and compare variances of each treatment.

Calculate F-value:

[tex]F=\frac{s^{2}_{1}}{s^{2}_{2}}[/tex]

[tex]F=\frac{1.26^{2}}{0.93^{2}}[/tex]

[tex]F=\frac{1.5876}{0.8649}[/tex]

F = 1.8356

The critical value of F is given by a F-distribution table with:

degree of freedom (row): 20 - 1 = 19

degree of freedom (column): 20 - 1 = 19

And a significance level: α = 0.05

[tex]F_{critical}[/tex] = 2.2341

Comparing both values of F:

1.856 < 2.2341

i.e. F-value calculated is less than F-value of the table.

Therefore, failed to reject [tex]H_{0}[/tex], meaning there is no sufficient data to support the claim that sham treatment have pain reductions which vary more than for those using magnets treatment.

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

"4" is the number of variable terms that are in the expression 3x3y + 5x2 _ 4y + z + 9. The four variable terms in the expression are "xy", "x^2", "y" and "z". I hope that this is the answer that you were looking for and the answer has actually come to your desired help. If you need any clarification, you can always ask.