Solve: 6^2x- 3 = 6^-2x+1

1

1 + 0 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

13 + 21 = 34

21 + 34 = 55

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Hope this helps! :)

The 7th number in the Fibonacci sequence is 13 and the 9th number is 21.

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. The sequence starts with 1, 1, and then each subsequent number is the sum of the two numbers before it.

To find the 7th number in the sequence, we can continue the pattern: 1, 1, 2, 3, 5, 8. So, the 7th number is 13.

To find the 9th number in the sequence, we continue the pattern: 1, 1, 2, 3, 5, 8, 13, 21. So, the 9th number is 21.

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Answer:

A. True

B. True

C. True

D. False

Step-by-step explanation:

Option D is the only clear option that is false.

The S distribution is a statistical tool used to check the homogeneity of two independent estimates when studying population variance.

When using an F distribution, The ratio of the degree of freedom of the numerator to the denominator can be >1, = 1 or < 1.

This implies that degrees of freedom for the denominator can be smaller than the degrees of freedom for the numerator.

This makes option D false and hence the correct answer

Final answer:

The F distribution in ANOVA tests has specific characteristics based on degrees of freedom, with critical values for hypothesis testing.

Explanation:

False statement: d. Degrees of freedom for the denominator cannot be smaller than the degrees of freedom for the numerator.

The F distribution is used in ANOVA tests, with the shape determined by the degrees of freedom for the numerator and denominator. Critical values for the F distribution correspond to different probabilities for hypothesis testing.

Answer:

1. The sample chosen from each of the populations is sufficiently large.

Step-by-step explanation:

ANOVA is known as analysis of variance and it is a statistical process which is used to test the degree to which two or more groups vary or differ in an experiment.

The variances of all the sampled populations are usually equal. The sampled populations all have distributions that are approximately normal and the samples are chosen from each population in an independent manner.

The one that is not a condition required for a valid ANOVA F-test for a completely randomized experiment is A. The sample chosen from each of the populations is sufficiently large.

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Answer:

x + y = 4,000

0.1x + 0.04y = 352

Step-by-step explanation:

Product A represents x and product B represents y. The first equation is the total number of items the store owner buys. The second equation is cost per item for both products. The above system of equations can be used to determine how much product A and product B the store owner bought. 

Answer:

C. [tex]\left \{ {{x+y=4,000} \atop {0.1x+0.04y=352}} \right.[/tex]

Step-by-step explanation:

Edge 2020

Answer:

[tex]\cos'(z) = -\sin(z)[/tex]

Step-by-step explanation:

According to the information given by the problem

[tex]\sin(z) = {\displaystyle \frac{e^{iz} - e^{-iz} }{2i} }[/tex]

[tex]\cos(z) = {\displaystyle \frac{e^{iz} + e^{-iz} }{2} }[/tex]

Now, if you compute the derivative of [tex]\cos[/tex] you get that

[tex]\cos'(z) = {\displaystyle \frac{ ie^{iz}-i e^{iz} }{2} } = {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} }\\\\= {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} } *\frac{i}{i} }\\\\= {\displaystyle - \frac{ e^{iz}- e^{iz} }{2i} } = -\sin(z)[/tex]

Answer:

31.6°

Step-by-step explanation:

<B = arctan (14.1/22.9) = 31.6°

Answer:

[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]

Step-by-step explanation:

[tex]x^2+17x+12=-3x^2[/tex]

Add [tex]3x^2[/tex] on both sides.

[tex]x^2+17x+12+3x^2=-3x^2+3x^2[/tex]

[tex]x^2+17x+12+3x^2=0[/tex]

Combine like terms;

[tex]4x^2+17x+12=0[/tex]

Use the quadratic formula;

a=4

b=17

c=12

[tex]x=\frac{-b\frac{+}{}\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(17)\frac{+}{}\sqrt{(17)^2-4(4)(12)} }{2(4)}[/tex]

[tex]x=\frac{-17\frac{+}{}\sqrt{289-192} }{8}[/tex]

[tex]x=\frac{-17\frac{+}{}\sqrt{97} }{8}[/tex]

[tex]x=-\frac{17}{8}+\frac{\sqrt{97} }{8}[/tex] or [tex]x=-\frac{17}{8}-\frac{\sqrt{97} }{8}[/tex]

Answer:

j / 9 = 5

j = 45

Step-by-step explanation:

j / 9 = 5

Multiply each side by 9

j/9 * 9 = 5*9

j = 45

We have been given that in ΔBCD, the measure of ∠D=90°, the measure of ∠C=42°, and CD = 7.5 feet. We are asked to find the length of DB to nearest tenth of foot.

First of all, we will draw a right triangle using our given information.

We can see from the attachment that DB is opposite side to angle C and CD is adjacent side to angle.

We know that tangent relates opposite side of right triangle to adjacent side of right triangle.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(\angle C)=\frac{DB}{CD}[/tex]

[tex]\text{tan}(42^{\circ})=\frac{DB}{7.5}[/tex]

[tex]7.5\cdot\text{tan}(42^{\circ})=\frac{DB}{7.5}\cdot 7.5[/tex]

[tex]7.5\cdot\text{tan}(42^{\circ})=DB[/tex]

[tex]7.5\cdot0.900404044298=DB[/tex]

[tex]DB=7.5\cdot0.900404044298[/tex]

[tex]DB=6.753030332235\approx 6.8[/tex]

Therefore, the length of DB is approximately 6.8 feet.

Answer:

W=12 area=192 12×16

Area192

Step-by-step explanation:

2(4+w)+2w=56

8+4w=56

-8

4w= 48

/4

W=12

To solve the problem, a system of equations is used based on the given conditions. Through algebraic process, we discover the width (W) to be 8 cm and the length (L) to be 20 cm. Consequently, the rectangle's area is calculated to be 160 cm².

The given problem falls under algebra and can be solved through a system of equations. According to the problem, the length of a rectangle is 4 more than twice the width. So we can denote the length of the rectangle as L and the width as W, forming Equation 1: L = 2W + 4.

The perimeter of a rectangle is known to be 2L + 2W. Given that perimeter is equal to 56 cm, we can plug in L from Equation 1 to Equation 2: 2(2W + 4) + 2W = 56. Simplifying this, we get 6W + 8 = 56. By solving for W, we find W as 8 cm. Substituting W = 8 cm into Equation 1, L comes out as 20 cm.

Next, the area of a rectangle is calculated using the formula L * W, which yields the area as 160 cm².

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The value of sin 45 is  1/ √2

An angle is a combination of two rays (half-lines) with a common endpoint.

As per the diagram,

AC= 1 unit, BC= 1 unit

Applying Pythagoras theorem,

AB² = AC² + BC²

AB² = 1²+ 1²

AB² = 2

AB= √2

Now, sine is the ratio between the opposed side and the hypothenuse.

So, sin 45 = 1/ √2 = √2/√2

In radical form = 0.7071

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Final answer:

The sin of 45 degrees is √2/2. This value is found using the properties of an isosceles right triangle and applying the Pythagorean theorem.

Explanation:

In the case of a 45-degree angle in a right triangle, the sine function can be calculated using the properties of an isosceles right triangle. The sin of 45 degrees is equal to the ratio of the opposite side to the hypotenuse. In an isosceles right triangle where the two legs are equal, this ratio is the same for both legs.

By the Pythagorean theorem, we know that in an isosceles right triangle, if each leg is of length 1, the hypotenuse will be √2. Therefore, sin 45 degrees equals the length of the leg (1) divided by the length of the hypotenuse (√2), which simplifies to √2/2 or 1/√2. Expressing this in simplest radical form, we obtain √2/2.

This value is derived from understanding that the sum of the squares of the lengths of the legs equals the square of the hypotenuse, which gives us the equation 1² + 1² = c², where c is the hypotenuse. Simplifying gives us a hypotenuse of √2, and the sine of 45 degrees equals 1/√2, or √2/2 after rationalizing the denominator.

Explanation:

It depends upon the 'base" of your log. Let us say that is  10 ; we can write:

log _10( x + 7 ) = 1  

using the definition of log we can write:

x + 7 =10 ^1

and:

x = 10 − 7 =3  

if you have a different base use the one you got instead of  10 .

Answer:

10

Step-by-step explanation:

Generally we use the base 10 to any logarithmic function , which is known as common Base

so the base of log (x+7) is 10

Answer: 9.1 - 5.8n

Step-by-step explanation:

All you need to do here is combine like terms.

Lets identify the two sets of like terms:

-3.8n and -2n

AND

3.1 and 6

So, you will add or subtract them as needed.

I will start by combining 3.8n and -2n

= 3.1 -3.8 -2n + 6

= 3.1 + 6 -5.8n

Now combine the 3.1 and 6.

= 9.1 - 5.8n

This is your answer!

Answer:

a) The picture with the normal distribution is attached.

b) The picture with the normal distribution with the region X<54 shaded is attached.

c) The area under the normal curve to the left of X=$54 is 0.1587.

This means that there is a probability P=0.1587 that a randomly picked monthly charge for a cell phone plan is under $54.

It can also be interpreted that approximately 15.87% of the cell phone plans have a monthly charge that is less than $54.

Step-by-step explanation:

Answer:

a) Null hypothesis: [tex]\mu \geq 1936[/tex]

Alternative hypothesis: [tex]\mu <1936[/tex]

b) [tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]

The degrees of freedom are:

[tex] df = n-1= 46-1=45[/tex]

The p value for this case since is a left tailed test is given by:

[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]

And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736

c) [tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]

And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736

d) For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.

Step-by-step explanation:

Part a

We are trying to proof the following system of hypothesis:

Null hypothesis: [tex]\mu \geq 1936[/tex]

Alternative hypothesis: [tex]\mu <1936[/tex]

Part b

We have the following data given:

[tex]\bar X =1736[/tex] minute s = 635; n = 46

And the statistic for this case is given by:

[tex] t = \frac{\bar X- \mu}{\frac{s}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] t = \frac{1736-1936}{\frac{635}{\sqrt{46}}}= -2.136[/tex]

The degrees of freedom are:

[tex] df = n-1= 46-1=45[/tex]

The p value for this case since is a left tailed test is given by:

[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]

And since the p value is lower than the significance level 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 1736

Part c

We have the same statistic t = -2.136

[tex] p_v = P(t_{45} <-2.136) = 0.0191[/tex]

And since the p value is higher than the significance level 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly lower than 1736

Part d

For this case the answer is yes since when we change the significance level from 0.05 to 0.01 we see that the final decision changes.

Null and alternative hypotheses are created for a t-test regarding trip times. The t-test is conducted at two different significance levels (α = 0.05 and α = 0.01). The conclusion may change with adjustments to α.

The hypotheses for this statistical test would be:

To test these hypotheses, we can perform a two-sided t-test. We are given:

For α = 0.05, if the t-statistic's associated p-value is lesser than α, we reject the null hypothesis. Likewise, for α = 0.01, the same process is undertaken.

The conclusion reached will depend on the calculated p-value. If the p-value is less than the chosen α, we will reject the null hypothesis and conclude that the drivers are not following safety regulations. If the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that drivers are not following safety regulations.

The test conclusion may change with changes in α, as α establishes the threshold for rejecting the null hypothesis.

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Answer:

Smax = 676 ft

the maximum altitude (height) the rocket will attain during its flight is 676 ft

Step-by-step explanation:

Given;

The height function S(t) of the rocket as;

S(t) = -16t2 + 208t

The maximum altitude Smax, will occur at dS/dt = 0

differentiating S(t);

dS/dt = -32t + 208 = 0

-32t +208 = 0

32t = 208

t = 208/32

t = 6.5 seconds.

The maximum altitude Smax is;

Substituting t = 6.5 s

Smax = -16(6.5)^2 + 208(6.5)

Smax = 676 ft

the maximum altitude (height) the rocket will attain during its flight is 676 ft

Answer:

We want to find the percentage of values between 147700 and 152300

[tex] P(147700 <X<152300)[/tex]

And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:

[tex] z= \frac{x-\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{147700-150000}{2300}=-1[/tex]

[tex] z=\frac{152300-150000}{2300}=1[/tex]

So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%

Step-by-step explanation:

We define the random variable representing the prices of a certain model as X and the distirbution for this random variable is given by:

[tex] X \sim N(\mu = 150000, \sigma =2300[/tex]

The empirical rule states that within one deviation from the mean we have 68% of the data, within 2 deviations from the mean we have 95% and within 3 deviations 99.7 % of the data.

We want to find the percentage of values between 147700 and 152300

[tex] P(147700 <X<152300)[/tex]

And one way to solve this is use a formula called z score in order to find the number of deviations from the mean for the limits given:

[tex] z= \frac{x-\mu}{\sigma}[/tex]

And replacing we got:

[tex] z=\frac{147700-150000}{2300}=-1[/tex]

[tex] z=\frac{152300-150000}{2300}=1[/tex]

So then we are within 1 deviation from the mean so then we can conclude that the percentage of values between $147,700 and $152,300 is 68%

Final answer:

Using the 68-95-99.7 rule in statistics, about 68% of buyers paid between $147,700 and $152,300 for a new home, given the mean price is $150,000 and the standard deviation is $2,300.

Explanation:

The student is asking a question that involves the application of the 68-95-99.7 rule (also known as the empirical rule) in statistics, which describes how data is distributed in a normal distribution. Specifically, the student wants to know the percentage of buyers who paid between $147,700 and $152,300 for a new home, given that the mean price is $150,000 and the standard deviation is $2,300.

According to the 68-95-99.7 rule, approximately 68% of data within a normal distribution falls within one standard deviation of the mean in both directions, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this scenario, the range from $147,700 to $152,300 is $2,300 away from the mean (which is one standard deviation), so approximately 68% of the home prices would fall within this range.

Answer:

  9

Step-by-step explanation:

If 24 points is half the number of points all other players scored, then the points scored by all other players total 24·2 = 48.

All points together total ...

  24 + 48 = 72

A point is awarded for each game, so there were a total of 72 games.

N players will play a total of (N/2)(N-1) games if they play each opponent once. Here, each opponent is played twice, so the total number of games played by N players is ...

  N(N-1) = 72

  9·8 = 72   ⇒   N = 9

The number of players in the championship was 9.

Answer - 10 meters

10 meters

Explanation:

Using the ratios given, we have the three sides in terms of one side.

(x, x+5, 4x)

The perimeter is the sum of all of them:

65 = x+x+5+4x ; 65 = 6x+5

6x = 60 ; x = 10

x+5 = 15

4x = 40

Answer:

100% probability that Joe Biden wins Yolo county

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For a proportion q in a sample of size n, the mean is [tex]\mu = q[/tex] and the standard deviation is [tex]\sigma = \frac{q(1-q)}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]q = 0.51, n = 1000000[/tex]

So

[tex]\sigma = \sqrt{\frac{0.51*0.49}{\sqrt{1000000}} = 0.0005[/tex]

What is the probability that Joe Biden wins Yolo county?

This is the probability that he gets more than 50% = 0.5 of the votes, so it is 1 subtracted by the pvalue of Z when X = 0.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0.5 - 0.51}{0.0005}[/tex]

[tex]Z = -20[/tex]

[tex]Z = -20[/tex] has a pvalue of 0

1 - 0 = 1

100% probability that Joe Biden wins Yolo county

Answer:

100% probability that Joe Biden wins Yolo county

Step-by-step explanation:

Answer:

c 24%use it thats what I got

The B is A greater percentage of children (28%) use the toothpaste is correct.

For each data value in the table, move the decimal point over 2 spots.

We focus on the children's row only since each answer choice has of children mentioned, and also the instructions make this mention as well.

There are 7 children who use the toothpaste out of 25 children overall.

So 6/25 = 0.24 = 24% of the children use the toothpaste.

The probability is the ratio of the number of outcomes divided by the total number of outcomes.

This is a greater percentage than the adults (11%) who use toothpaste.

The 11% comes from 8 adults out of 75 adults

Total who use the toothpaste,

So 8/75 = 0.1067 = 10.67%

which rounds to 11%.

Therefore the probability for toothpaste is 24% and 11% for adults.

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Answer:

Check the explanation

Step-by-step explanation:

UCL = MEAN + (Z * STDEV / SQRT(N))

MEAN = 65

Z = 1.67

STDEV = 1

N = 100

UCL = 65 + (1.67 * 1 / SQRT(100)) = 65.167

Answer:

acircle has infintely many axes of symmetry

Step-by-step explanation:

Answer:

infinite

Step-by-step explanation:

there are no corners what so ever and a circle is symetric, so no matter how many lines you put it will be correct

Answer:

5 faces

Step-by-step explanation:

To find the diameter of a circle when given the circumference, use the formula d = C/π. Substituting the given circumference of 27 centimeters and using 3.14 for π, the diameter of the circle is approximately 8.6 centimeters.

This problem pertains to the mathematical concept of geometry, specifically dealing with the properties of a circle. Given the circumference of the circle, we can use the formula for the circumference of a circle, which is C = πd where C is the circumference, π is a constant (approximately 3.14), and d is the diameter of the circle. We're told the circumference is 27 centimeters, and we're using 3.14 for π.

To find the diameter, we'll need to rearrange the formula to solve for d, which gives us d = C/π. Substituting the given numbers, we find d = 27 / 3.14. Performing this calculation gives a diameter of approximately 8.6 centimeters when rounded to the nearest tenth.

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To find the diameter of a circle with a circumference of 27 cm, divide the circumference by π (3.14). This results in a diameter of approximately 8.6 cm.

Finding the Diameter of a Circle

To find the diameter of a circle given its circumference,

we use the formula for the circumference:  C = πd

where C is the circumference and d is the diameter.

Given that the circumference C is 27 centimeters and π is approximately 3.14,

we can solve for the diameter as follows:

First, set up the equation: 27 = 3.14d

Next, solve for d by dividing both sides by 3.14: d = 27 / 3.14

Perform the division to get: d ≈ 8.6

Therefore, the diameter of the circle is approximately 8.6 centimeters.

Answer:

(a) [tex]X\sim N(\mu=26,\ \sigma^{2}=13^{2})[/tex].

(b) The probability that a randomly selected LA worker has a commute that is longer than 34 minutes is 0.2676.

(c) The 70th percentile for the commute time of LA workers is 33 minutes.

Step-by-step explanation:

The random variable X is defined as the commute time for LA workers.

The mean commute time is, μ = 26 minutes and the standard deviation of the commute times is, σ = 13 minutes.

(a)

It is provided that the LA commute time fr workers is normally distributed.

Then the distribution of the random variable X can be defined as follows:

[tex]X\sim N(\mu=26,\ \sigma^{2}=13^{2})[/tex].

(b)

Compute the value of P (X > 34) as follows:

[tex]P(X>34)=P(\frac{X-\mu}{\sigma}>\frac{34-26}{13})[/tex]

                 [tex]=P(Z>0.62)\\=1-P(Z<0.62)\\=1-0.73237\\=0.26763\\\approx 0.2676[/tex]

*Use a z-table.

Thus, the probability that a randomly selected LA worker has a commute that is longer than 34 minutes is 0.2676.

(c)

The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.

The 70th percentile for the commute time of LA workers can be written as follows:

P (X < x) = 0.70

⇒ P (Z < z) = 0.70

The value of z for this probability is:

z = 0.53

*Use a z-table.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\0.53=\frac{x-26}{13}\\\\x=26+(0.53\times 13)\\\\x=32.89\\\\x\approx 33[/tex]

Thus, the 70th percentile for the commute time of LA workers is 33 minutes.

The competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates are: a. H0: p1 ≤ p2, Ha: p1 > p2.

Null Hypothesis (H0): This represents the statement we want to test and assume to be true in the absence of evidence to the contrary. The null hypothesis (H0) states that there is no difference between the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs.

Alternative Hypothesis (Ha): This represents the statement we want to disprove or find evidence for against the null hypothesis. The alternative hypothesis (Ha) states that the proportion of supporting votes is greater for the women's incumbent candidate than for the men's incumbent candidate.