You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 95%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 25 years.

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

The volume of the glass bead formed by a rectangular prism with a smaller prism removed can be found by subtracting the volume of the smaller prism from the larger prism. As an example, a larger prism of volume 60 cubic cm and smaller prism of volume 8 cubic cm gives a bead of volume 52 cubic cm.

The volume of the glass bead formed by a rectangular prism with a smaller rectangular prism removed can be calculated using the formula for the volume of a rectangular prism, which is length × width × height. The volume of the glass bead would then be the volume of the larger prism minus the volume of the smaller prism.

As an example, if the larger prism has a length of 5cm, width of 4cm, and height of 3cm, its volume would be 5cm × 4cm × 3cm = 60 cubic cm. If the smaller prism removed has a length of 2 cm, width of 2 cm, and height of 2 cm, its volume would be 2cm × 2cm × 2cm = 8 cubic cm. Subtracting the volume of the smaller prism from the larger one gives a volume of 60 cubic cm - 8 cubic cm = 52 cubic cm which is the volume of the glass bead.

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The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.

Calculating the Volume of a Glass Bead

To find the volume of a glass bead with the shape of a rectangular prism with a smaller rectangular prism removed, follow these steps:

For example, if the dimensions of the larger rectangular prism are 10 cm (length), 5 cm (width), and 4 cm (height), its volume will be 200 cm³. If the smaller removed prism has dimensions of 3 cm (length), 2 cm (width), and 1 cm (height), its volume will be 6 cm³. The volume of the glass bead is then 200 cm³ - 6 cm³ = 194 cm³.

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:

Type I error: Concluding μ ≠ 40, when in fact μ = 40.

Type II error: Concluding μ = 40, when in fact μ ≠ 40.

Step-by-step explanation:

In this case we need to determine whether the mean amperage at which the 40-amp fuses burn out is 40.

The hypothesis to test this can be defined as follows:

H₀: The mean amperage at which the 40-amp fuses burn out is 40, i.e. μ = 40.

Hₐ: The mean amperage at which the 40-amp fuses burn out is different from 40, i.e. μ ≠ 40.

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

In this context, a type I error will be committed if we conclude that the mean amperage at which the 40-amp fuses burn out is different from 40, when in fact it is 40.

And a type II error will be committed if we conclude that the mean amperage at which the 40-amp fuses burn out is 40, when in fact it is different from 40.

The null hypothesis for the manufacturer of 40-amp fuses is that the mean amperage at which fuses burn out is 40 amps, while the alternative hypothesis is that the mean is not 40 amps. A Type I error is incorrectly rejecting a true null hypothesis, and a Type II error is failing to reject a false null hypothesis, both of which have consequences for the manufacturer in terms of production and safety.

A manufacturer of 40-amp fuses is interested in ensuring the mean amperage at which its fuses burn out is indeed 40 amps. To validate this, a sample of fuses must be tested, and a hypothesis test applied to the results. The null hypothesis (H0) of interest would state that the mean amperage at which the fuses burn out is 40 amps, formulated as H0: μ = 40, where μ is the population mean. The alternative hypothesis (H1) would indicate that the mean amperage is not 40 amps: H1: μ ≠ 40.

In this scenario, a Type I error would occur if the hypothesis test incorrectly rejects the null hypothesis when in fact the fuses do burn out at the mean of 40 amps. This could result in unnecessary production changes and costs for the manufacturer. Alternatively, a Type II error would occur if the test fails to reject the null hypothesis when the true mean amperage at which the fuses burn out is actually different from 40 amps. In such a case, the manufacturer might continue producing fuses that could either require frequent replacement or pose a risk of damage to electrical systems.

The determination of the true mean amperage is relevant because of the role of fuses and circuit breakers in protecting appliances and residents from harm due to large currents and because they are designed to tolerate high currents for brief periods, or in some cases like electric motors, for a longer duration. Thus, ensuring fuses operate correctly at their intended amperage is crucial for safety and functionality.

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Answer:

D. x + 8

Step-by-step explanation:

factor. Find factors of x² and 48, in which, when combined, will equal 2x:

x² + 2x - 48

x               8

x              -6

(x + 8)(x - 6)

D. x + 8 is your answer.

~

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:

0.225

Step-by-step explanation:

Total outcomes of choosing 5 out of 18 members = 18C5

Outcomes of choosing 2 out 11 favourers, 3 out of 7 members  =          11C2 & 7C3

Probability = Favourable outcomes / Total outcomes

= ( 11C2 x 7C3 ) / 18C5

[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ]

       [ 18 ! / 5! 13! ]

( 55 x 35 ) /  8568

1925 / 8568

= 0.2246 ≈ 0.225

In the given scenario, when the shoe company makes 360 black shoes, they will also make 270 blue shoes as the ratio was provided as 3:4.

The problem involves the concept of ratio proportion. Given the ratio of blue shoes to black shoes is 3:4, this means for every 3 blue shoes, 4 black shoes are made. If the company makes 360 black shoes, this is like 90 sets of 4 black shoes (360/4). That means 90 sets of 3 blue shoes must also be made. Therefore, the company will make 270 (90*3) blue shoes when 360 black shoes are made.

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Step-by-step explanation:

9 + x - 7

Solving like terms

x + 2

If we find the value of x

X + 2 = 0

x = - 2

Answer:

If its the sum then, 0+0 if its an quotient, 0 divided by 0 if its a multiply problem, 0 times 0.

Step-by-step explanation:

0 can only be the answer of a problem if its used on itself or if its multiplies by another.

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.

first find the greatest possible length:

9 + 6 > x

15 > x

x < 15

Then find the lowest possible length:

x + 6 > 9

x > 9 - 6

x > 3

3 < x < 15

To determine the range of possible lengths of the third side of a sail, use the triangle inequality theorem. The range is 3 feet to 15 feet.

To determine the range of possible lengths of the third side of the sail, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the two given sides are 9 feet and 6 feet. So, the third side must be less than the sum of these two sides and greater than the difference between these two sides.

Therefore, the range of possible lengths of the third side of the sail is 3 feet to 15 feet.

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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:

Amount invested in first account = $1,000

Amount invested in second account = $29,000

Step-by-step explanation:

Jina had total amount of $30,000 to invest last year.

Let x be the amount that Jina invested in the first account at interest rate of 9%

Mathematically,

0.09x

she invested the remaining amount in the second account at an interest rate of 5%

Mathematically,

0.05(30,000 - x)

Jina received $1540 in interest.

0.09x + 0.05(30,000 - x) = 1540

0.09x + 1500 - 0.05x = 1540

0.04x = 1540 - 1500

0.04x = 40

x = 40/0.04

x = $1,000

Therefore, Jina invested an amount of $1,000 in the first account at interest rate of 9%  

The remaining amount that she invested in the second account is

Amount invested in second account = $30,000 - $1,000

Amount invested in second account = $29,000

Therefore, Jina invested an amount of $29,000 in the second account at interest rate of 5%

Verification:

0.09x + 0.05(30,000 - x) = 1540

0.09(1000) + 0.05(30,000 - 1000) = 1540

90 + 1450 = 1540

1540 = 1540  (satisfied)

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

Answer:

do you have a picture of the line graph ?

Answer is 4,000

Step-by-step explanation:

Answer:

Easy! The cool thing about correlations is you can easily determine them by reading your graph, no hard brain work involved!

It should be A.

Step-by-step explanation:

By looking at the graph, you can already determine that the correlation is negative, since it's going down, not up.

Now, you need to read what is happening on the graph. As the price (X-Axis) is increasing, less people are spending their money, presumably because it's not priced affordably. So as you can see according to your Y-Axis, the amount of people buying is lowered.

Hopefully this isn't confusing!

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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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.

Shouldn't the equation read " (x - 4)² = 81 ", instead of "(1 - 4)² = 81" ?

If so, then the solutions are  x = -5  and  x = 13 .

If it's really "(1 - 4)² = 81", then that's not even an equation, and there's no solution.

The solutions to the given equation are x = -5 and x = 13.

The correct solutions to the given equation are x = -5 and x = 13.

To solve the equation (1 - 4)2 = 81:

Answer: M≤ $15

Step-by-step explanation:

The answer is [ m ≤ $15 ]

The question states, "If you have no more than $15." This means that you can only have up to $15 and no more.

So, the solutions to the set are all real numbers except the numbers after 15.

Let's say you had $9. If we were to substitute 9 with m in the inequality, we would get; 9 ≤ 15. This satisfies the inequality since the number is less than 15.

Best of Luck!

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:

Final answer:

The number 7,790,200 has zero decimal places as it is a whole number with no fractional part and ends in the unit's place.

Explanation:

The student asked how many decimal places are in 7,790,200. This question is related to place value and decimals in mathematics. The number 7,790,200 has no decimal part since it is a whole number and ends in the unit's place. Therefore, it contains zero decimal places. To expand on place value, when expressing numbers in decimal form, the position of a digit represents its value in powers of ten. For instance, the number 1837 can be decomposed as (1 × 10³) + (8 × 10²) + (3 × 10¹) + (7 × 10⁰), which shows the ones, tens, hundreds, and thousands places respectively.

Answer:

5 faces

Step-by-step explanation:

Answer:

The probability that the sample mean weight will be more than 262 lb is 0.0047.

Step-by-step explanation:

The random variable X can be defined as the weight of National Football League (NFL) players now.

The mean weight is, μ = 252.8 lb.

The standard deviation of the weights is, σ = 25 lb.

A random sample of n = 50 NFL players are selected.

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The sample of players selected is quite large, i.e. n = 50 > 30, so the central limit theorem can be used to approximate the distribution of sample means.

[tex]\bar X\sim N(\mu_{\bar x}=252.8,\ \sigma_{\bar x}=3.536)[/tex]

Compute the probability that the sample mean weight will be more than 262 lb as follows:

[tex]P(\bar X>262)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{262-252.8}{3.536})\\\\=P(Z>2.60)\\\\=1-P(Z<2.60)\\\\=1-0.99534\\\\=0.00466\\\\\approx 0.0047[/tex]

*Use a z-table for the probability.

Thus, the probability that the sample mean weight will be more than 262 lb is 0.0047.

To find the probability that the sample mean will be more than 262 lb, calculate the z-score using the sample mean, population mean, standard deviation, and sample size. Then, find the corresponding probability using the standard normal distribution table. Subtract the probability from 1 to get the final result, which is approximately 0.2%.

To solve this problem, we need to use the z-score formula and the standard normal distribution table. First, calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, x = 262 lb, μ = 252.8 lb, σ = 25 lb, and n = 50. Plug in these values and calculate the z-score. Next, find the corresponding probability using the standard normal distribution table. Look up the z-score and find the corresponding probability. The probability that the sample mean will be more than 262 lb can be found by subtracting the probability you found from 1.

Calculating the z-score:

z = (262 - 252.8) / (25 / sqrt(50)) = 2.901.

Using the standard normal distribution table, the probability corresponding to a z-score of 2.901 is approximately 0.998. Therefore, the probability that the sample mean will be more than 262 lb is approximately 1 - 0.998 = 0.002, or 0.2%.

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Answer:

[tex]z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123[/tex]  

The p value for a left tailed test would be:  

[tex]p_v =P(z<-1.123)=0.131[/tex]  

Since the p value is very higher we can conclude that the true proportion  of teenagers who floss twice a day is NOT less than 40%.

Step-by-step explanation:

Information given

n=400 represent the random sample given

X=149 represent the floss twice a day

[tex]\hat p=\frac{149}{400}=0.3725[/tex] estimated proportion of floss twice a day

[tex]p_o=0.4[/tex] is the value the proportion that we want to check

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to check proportion of teenagers who floss twice a day is less than 40%, so then the system of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.4[/tex]  

Alternative hypothesis:[tex]p < 0.4[/tex]  

For the one sample proportion test the statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

If we replace the info given we got:

[tex]z=\frac{0.3725 -0.4}{\sqrt{\frac{0.4(1-0.4)}{400}}}=-1.123[/tex]  

The p value for a left tailed test would be:  

[tex]p_v =P(z<-1.123)=0.131[/tex]  

Since the p value is very higher we can conclude that the true proportion  of teenagers who floss twice a day is NOT less than 40%.

We have been given that a baseball player threw 82 strikes out of 103 pitches. We are asked to find the percentage of pitches that were strikes.

To solve our given problem, we need to find strikes are what percent of pitches.

[tex]\text{Percentage of pitches that were strikes}=\frac{82}{103}\times 100\%[/tex]

[tex]\text{Percentage of pitches that were strikes}=0.7961165\times 100\%[/tex]

[tex]\text{Percentage of pitches that were strikes}=79.61165\%[/tex]

[tex]\text{Percentage of pitches that were strikes}\approx 79.6\%[/tex]

Therefore, approximately [tex]79.6\%[/tex] of pitches were strikes.

Answer:

10:00 AM

Step-by-step explanation:

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]