An evergreen nursery usually sells a certain shrub after 7 years of growth and shaping. The growth rate during those 7 years is approximated by dh/dt = 1.3t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 17 centimeters tall when planted (t = 0). (a) Find the height after t years. h(t) = (b) How tall are the shrubs when they are sold? cm

Answer:

x= -12  y= 4

Step-by-step explanation:

Answer:

Y=4

x=-12

Step-by-step explanation:

Answer:

77.34% of students will score below 555 in a typical year

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.

SAT:

[tex]\mu = 480, \sigma = 100[/tex]

(a) An engineering school sets 555 as the minimum SAT math score for new students. What percentage of students will score below 555 in a typical year?

This is the pvalue of Z when X = 555. So

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

[tex]Z = \frac{555 - 480}{100}[/tex]

[tex]Z = 0.75[/tex]

[tex]Z = 0.75[/tex] has a pvalue of 0.7734.

77.34% of students will score below 555 in a typical year

Answer:

3x+15

Step-by-step explanation:

When it says "the sum of a number three times", it means 3x, because the x stands for multiplication and the problem says the sum sum is between 3x and the number 15. So your equation is 3x+15. Hope this helps ;)

Answer:

There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.

P-value=0.01923.

Step-by-step explanation:

We have to test the hypothesis that the proportion of defective circuits is under 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

We will assume a level of significance of 0.05.

The sample, of size n=1000, has 35 defecteive circuits, so the sample proportion is:

[tex]p=35/1000=0.035[/tex]

The standard error is calculated as if the null hypothesis is true, so it is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1000}}}=\sqrt{0.0000475}=0.007[/tex]

The z-statistic can be calculated as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.035-0.050+0.5/1000}{0.007}=\dfrac{-0.0145}{0.007}= -2.07[/tex]

For this one-tailed test, the P-value is:

[tex]P-value=P(z<-2.07)=0.01923[/tex]

As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected. There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.

Answer:

B

Step-by-step explanation:

Null hypothesis is not rejected if the test statistics show that the difference between observed and expected value is not significant and any difference is only due to chance.

So there is sufficient evidence from statistics that null hypothesis is true and the standard deviation in the pressure required to open a certain valve has not changed.

since evidence has to be there when null hypothesis is tested, optionC,  D and E are rejected.

There is no change in standard deviation so option A and F are rejected.

Answer:

add -x to 6x to get 5x then divide by 5 to get 2 x is 2

Step-by-step explanation:hope this helps god bless

Step-by-step explanation:

I think you have to find value of x

-x + 6x = 10

5x = 10

x = 10 / 5 = 2

x = 2

Answer: the z- score when x= 186 is 2.643

the mean is 149

this z score tells you that x= 186 is 2.643 standard dev. to the right of the mean

Answer:

Step-by-step explanation:

Hello!

You have two variables of interest

X₁: failure stress of a NiCrAlZr coating after nine 1-hr cycles.

X₂: failure stress of a NiCrAlZr coating after six 1-hr cycles.

a)

To be able to estimate the difference between the means using a confidence interval, you need that both variables have a normal distribution and to determine whether or not the population variances are equal.

If the population variances are equal, σ₁²=σ₂², you can use a pooled variance t-test

If the population variances are different, σ₁²≠σ₂², you have to use Welch's t-test

Using α: 0.05

The normality test for X₁ shows a p-value of 0.7449 ⇒ You can assume it has a normal distribution.

The normality test for X₂ shows a p-value of 0.9980 ⇒ You can assume it has a normal distribution.

The F-test for variance homogeneity shows a p-value of 0.6968 (H₀:σ₁²=σ₂²) ⇒You can assume both population variances are equal.

b) and c)

You need to test if both population means are the same, the hypotheses are:

H₀: μ₁=μ₂

H₁: μ₁≠μ₂

α: 0.05

[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{8*4.28+5*5.62}{9+6-2} }= \sqrt{4.7953}= 2.189= 2.19[/tex]

[tex]t_{H_0}= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } = \frac{(16.36-11.48)-0}{2.19*\sqrt{\frac{1}{9} +\frac{1}{6} } } = 4.23[/tex]

The distribution of this test is a t with 13 degrees of freedom and the test is two-tailed, so to calculate the p-value you have to do the following:

P(t₁₃≤-4.23)+P(t₁₃≥4.23)= P(t₁₃≤-4.23)+[1-P(t₁₃<4.23)]=  0.000492 + (1-0.999508)= 2*0.000492= 0.000984≅ 0.001

The p-value: 0.001 is less than α: 0.05, the decision is to reject the null hypothesis.

I hope it helps!

Answer: [tex]A = 100[/tex] square unit

Step-by-step explanation:

The formula for calculating the area of a square when the diagonal is given is :

[tex]Area = d^{2} / 2[/tex]

That is :

[tex]A = \frac{(10\sqrt{2})^{2}}{2}[/tex]

[tex]A = \frac{100(2)}{2}[/tex]

[tex]A = 100[/tex] square unit

Answer:

since the rate at  which concentration inside the cell is proportional to the difference in the concentration of the solute in the blood stream and the concentration within the cell, then the rate of change of concentration within the cell is equals to K(L-C).

Thus, the  required differential equation is Δc/Δt = K( L - C ).

Step-by-step explanation:

The differential equation that models solute diffusion in osmosis is dC/dt = k*(L - C), representing the idea that the rate of change of the solute's concentration within the cell is proportional to the difference between the external and internal concentrations.

The differential equation that models this situation based on osmosis is expressed as dC/dt = k*(L - C), where C is the concentration of a solute within the cell, L is the constant level concentration in the bloodstream, and k is the constant of proportionality.

This equation is a simple expression of the rate of change being proportional to the difference between the outside and inside concentration levels. In this case, the rate of change of the concentration of solutes, dC/dt, is proportional to the difference between the concentration outside the cell, L, and the concentration inside the cell, C. The constant of proportionality is k.

This differential equation is a first order linear differential equation and represents processes that occur widely in nature, including in the diffusion of solutes through membranes in osmosis.

Learn more about Differential Equation here:

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Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

Where

σ = population standard Deviation

n = number of samples

From the information given

1) x = 32

σ = 6

n = 50

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.90 = 0.1

α/2 = 0.1/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645

Margin of error = 1.645 × 6/√50 = 1.4

Confidence interval = 32 ± 1.4

The lower end of the confidence interval is

32 - 1.4 = 30.6

The upper end of the confidence interval is

32 + 1.4 = 33.4

Answer:

Part 1

(a) 0.28434

(b) 0.43441

(c) 29.9 mm

Part 2

(a) 0.97722

Step-by-step explanation:

There are two questions here. We'll break them into two.

Part 1.

This is a normal distribution problem healthy children having the size of their left atrial diameters normally distributed with

Mean = μ = 26.4 mm

Standard deviation = σ = 4.2 mm

a) proportion of healthy children have left atrial diameters less than 24 mm

P(x < 24)

We first normalize/standardize 24 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (24 - 26.4)/4.2 = -0.57

The required probability

P(x < 24) = P(z < -0.57)

We'll use data from the normal probability table for these probabilities

P(x < 24) = P(z < -0.57) = 0.28434

b) proportion of healthy children have left atrial diameters between 25 and 30 mm

P(25 < x < 30)

We first normalize/standardize 25 mm and 30 mm

For 25 mm

z = (x - μ)/σ = (25 - 26.4)/4.2 = -0.33

For 30 mm

z = (x - μ)/σ = (30 - 26.4)/4.2 = 0.86

The required probability

P(25 < x < 30) = P(-0.33 < z < 0.86)

We'll use data from the normal probability table for these probabilities

P(25 < x < 30) = P(-0.33 < z < 0.86)

= P(z < 0.86) - P(z < -0.33)

= 0.80511 - 0.37070 = 0.43441

c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter.

Let the value be x' and its z-score be z'

P(x > x') = P(z > z') = 20% = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 0.80

Using normal distribution tables

z' = 0.842

z' = (x' - μ)/σ

0.842 = (x' - 26.4)/4.2

x' = 29.9364 = 29.9 mm

Part 2

Population mean = μ = 65 mm

Population Standard deviation = σ = 5 mm

The central limit theory explains that the sampling distribution extracted from this distribution will approximate a normal distribution with

Sample mean = Population mean

¯x = μₓ = μ = 65 mm

Standard deviation of the distribution of sample means = σₓ = (σ/√n)

where n = Sample size = 100

σₓ = (5/√100) = 0.5 mm

So, probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm = P(64 < x < 67)

We first normalize/standardize 64 mm and 67 mm

For 64 mm

z = (x - μ)/σ = (64 - 65)/0.5 = -2.00

For 67 mm

z = (x - μ)/σ = (67 - 65)/0.5 = 4.00

The required probability

P(64 < x < 67) = P(-2.00 < z < 4.00)

We'll use data from the normal probability table for these probabilities

P(64 < x < 67) = P(-2.00 < z < 4.00)

= P(z < 4.00) - P(z < -2.00)

= 0.99997 - 0.02275 = 0.97722

Hope this Helps!!!

Answer:

radius-4

Step-by-step explanation:

the radius is half of the diameter

Answer:

On this case we want to test if the mean age of the​ agency's customers is over 20, so the system of hypothesis would be:

Null hypothesis: [tex]\mu \leq 20[/tex]

Alternative hypothesis: [tex]\mu >20[/tex]

If he concludes the mean age is over 20 when it is​ not, he makes a​ type I error . If he concludes the mean age is not over 20 when it​ is, he makes a​ Type II error error.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

On this case we want to test if the mean age of the​ agency's customers is over 20, so the system of hypothesis would be:

Null hypothesis: [tex]\mu \leq 20[/tex]

Alternative hypothesis: [tex]\mu >20[/tex]

If he concludes the mean age is over 20 when it is​ not, he makes a​ type I error . If he concludes the mean age is not over 20 when it​ is, he makes a​ Type II error error.

When the travel agency owner concludes the mean age is over 20 when it's not, it's called a Type I error. If he concludes it's not over 20 when it is, it is a Type II error.

The scenario described involves a hypothesis test concerning the mean age of customers at a travel agency. When the travel agency owner incorrectly concludes that the mean age is over 20 when in fact it is not, he is making a Type I error. Conversely, if he concludes that the mean age is not over 20 when it actually is, that would be a Type II error. Understanding the consequences of these errors is critical in statistics because they affect decision-making processes based on data analysis.

Answer:

Is the #6 in the row. Is this a riddle

Answer:

its 1/720 i just took it

Step-by-step explanation:

Answer:

Step-by-step explanation:

Friend sells x cups

You sell 3x cups

Total cups sold:: 4x

Ans: x/4x = 1/4 = 25%

Final answer:

The fraction of cups sold by your friend is x/4x, which gives us 25% of the total sales when converted to a percentage.

Explanation:

To find out what percent of the cups sold were sold by your friend, we can set up a simple ratio.

Let's assume your friend sold x cups.

According to the problem, you sold three times as many cups, so you sold 3x cups.

The total number of cups sold is the sum of the cups you both sold, which is x + 3x = 4x cups.

Now, we want to find out what fraction of the total sales x represents.

Since your friend sold x cups out of the total 4x, the fraction is x/4x.

To convert this fraction to a percentage, we multiply it by 100%.

Therefore, the percentage of cups sold by your friend is (x/4x) × 100% = 25%.

This calculation shows that your friend sold 25% of the cups.

Step-by-step explanation:

Circumference of the circle= 2πr

=2×3.14×8 cm

= 50.24cm

= 50.2 cm

Answer:

50.27

rounded : 50.3

Step-by-step explanation:

2 times 3.14 times 8

hope this helped

brainliest is appreciated :)

Given:

The base of the triangle = 15 yd

The height of the circle = 12 yd

To find the area of the triangle.

Formula

The area of the triangle is

[tex]A=\frac{1}{2} bh[/tex]

where, b be the base of the triangle

h be the height of the triangle

Now,

Putting, b= 15 and h=12 we get,

[tex]A=\frac{1}{2} (15)(12)[/tex] sq yd

or, [tex]A = 90[/tex] sq yd

Hence,

The area of the triangle is 90 sq yd.

Answer:

A =90 yd^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

A = 1/2(15)*12

A =90 yd^2

The question asks for various measures of an exponentially distributed statistic, the distance between flaws on a cable. To find these, we use formulas specific to the exponential distribution; for example, the median is calculated as ln(2) * mean, and the standard deviation is equal to the mean, computed with the formula σ = √variance = √mean.

The problem can be modeled using the exponential distribution in statistics. The exponential distribution is often used to model the time elapsed between events in a Poisson point process, or in our case, the distance between the flaws in the cable.

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In this problem, we're calculating properties of an exponential distribution representing the distances between flaws in a cable. The probability that a given distance is more than 15m is 22.31%, and between 8m and 20m is 48.57%. The median distance is around 8.317m, the standard deviation is 12m, and the 65th percentile is about 14.791m.

In this problem, the distance between flaws on a long cable is exponentially distributed with a mean of 12 m. That means the lambda (λ) parameter's rate of occurring flaws per meter is 1/mean, or approximately 0.0833.

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a)

[tex]2a+(3a-7)=2a+3a-7=5a-7[/tex]

b)

[tex](2x-3)+x=2x-3+x=3x-3[/tex]

c)

[tex]7-(5x+4)=7-5x-4=3-5x[/tex]

d)

[tex]3x-(y-2x)=3x-y+2x=5x-y[/tex]

e)

[tex]-(3a+6)-4=-3a-6-4=-3a-10[/tex]

f)

[tex]-(x-2y)-3x=-x+2y-3x=2y-4x[/tex]

g)

[tex](2p-1)+(3+5p)=2p-1+3+5p=7p+2[/tex]

h)

[tex](4-2x)-(7x-2)=4-2x-7x+2=6-9x[/tex]

i)

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

j)

[tex](2m+4n)+(m-0,5n)=2m+4n+m-0,5n=3m+3,5n[/tex]

k)

[tex](4a-7b)-(2a+3b)=4a-7b-2a-3b=2a-10b[/tex]

l)

[tex]-(2p-r)-(2r-p)=-2p+r-2r+p=-p-r[/tex]

Answer:

Sorry about that answer, some people are plain rude, but the correct answer is -5.

Step-by-step explanation:

Hope this Helps! Good Luck!

Answer: k=-5 is correct because if you were to divide -10/-2 it would give you -5

I hope this simplifies your question for the answer.

Answer:

a = 1

Step-by-step explanation:

x = 8

3x - y = 9

3(8) - y = 9

24 - y = 9

-y = 9 - 24

-y = -15

y = 15

ax + y = 23

a(8) + 15 = 23

8a = 23 - 15

8a = 8

a = 8/8

a = 1

Answer:

Step-by-step explanation:

Answer:

19.5 inches or 19.685 inches for length

Step-by-step explanation:

50•0.39. 50÷3

19.5. 19.685

how to convert centimeters to inches:

multiply the centimeter by 0.39. example 10•0.39= 3.9 inches.

If you want centimeters to inches as length, then divide the centimeters by 3. example: 10÷3= 3.3333333333 inches

Given:

Given that ABCD is a parallelogram.

The length of AB is 3y - 2.

The length of BC is x + 12.

The length of CD is y + 6.

The length of AD is 2x - 4.

We need to determine the length of AB and BC.

Value of y:

We know the property that opposite sides of a parallelogram are congruent, then, we have;

[tex]AB=CD[/tex]

Substituting the values, we get;

[tex]3y-2=y+6[/tex]

[tex]2y-2=6[/tex]

     [tex]2y=8[/tex]

       [tex]y=4[/tex]

Thus, the value of y is 4.

Value of x:

We know the property that opposite sides of a parallelogram are congruent, then, we have;

[tex]AD=BC[/tex]

Substituting the values, we get;

[tex]2x-4=x+12[/tex]

 [tex]x-4=12[/tex]

       [tex]x=16[/tex]

Thus, the value of x is 16.

Length of AB:

The length of AB can be determined by substituting the value of y in the expression 3y - 2.

Thus, we have;

[tex]AB=3(4)-2[/tex]

     [tex]=12-2[/tex]

[tex]AB=10[/tex]

Thus, the length of AB is 10 units.

Length of BC:

The length of BC can be determined by substituting the value of x in the expression x + 12.

Thus, we have;

[tex]BC=16+12[/tex]

[tex]BC=28[/tex]

Thus, the length of BC is 28 units.

Hence, the length of AB and BC are 10 units and 28 units respectively.

Answer:

k=9

Step-by-step explanation:

The formula for direct variation is

y = kx

We know y and x

27 = k*3

Divide each side by 3

27/3 = 3k/3

9 =k

Answer:

The difference is 15.

Step-by-step explanation:

30-15=15

45-30=15

60-45=15

Answer:

I agree the difference is 15.

Step-by-step explanation:

Answer:

The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the student t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995([tex]t_{995}[/tex]). So we have T = 2.797

The margin of error is:

M = T*s = 2.797*0.2 = 0.56

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 12.1 - 0.56 = 11.54 fluid ounces.

The upper end of the interval is the sample mean added to M. So it is 12.1 + 0.56 = 12.66 fluid ounces.

The 99% confidence interval for the average fluid content of a can is between 11.54 and 12.66 fluid ounces.

Answer:

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Or equivalently:

[tex]\bar X \pm ME[/tex]

For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:

[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

Or equivalently:

[tex]\bar X \pm ME[/tex]

For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:

[tex]ME= \frac{Upper -Lower}{2}= \frac{7.7-3.9}{2}= 1.9[/tex]

Answer:

The answer is ten bouquets

Step-by-step explanation:

1 dozen is 12 if you were multiply 12 by 10 you would get 120. Now multiply 10 by twelve instead you get the same answer

Final answer:

When the price of each bouquet increased from $10 to $12, the flower stand sold 10 bouquets to make the same total sales of $120 as the previous day.

Explanation:

The question at hand involves a basic mathematical calculation of how changes in price affect the number of units sold to achieve the same total revenue. If a flower stand sold a dozen bouquets for $10 each yesterday, they made $120 in total sales (12 bouquets  imes $10 per bouquet). Today, with the price increase to $12 per bouquet, we need to find out how many bouquets were sold to still make $120 in total sales. The calculation is as follows:

Total Sales = Number of Bouquets Sold  imes Price per Bouquet

We know that the Total Sales should still be $120, and the Price per Bouquet is now $12. Therefore:

$120 = Number of Bouquets Sold  imes $12

Number of Bouquets Sold = $120 / $12

Number of Bouquets Sold = 10 bouquets

Thus, the flower stand sold 10 bouquets today to make the same amount of money as yesterday after increasing the price to $12 each.