The table below shows a
proportional relationship. Fill
in the missing values.
Servings
12
4
16
18
the last one it wouldnt fit plesse I need help will mark brainest ​ ounces 21 ? ? ?

Answer:

a) [tex]\bar X= \frac{\sum_{i=1}^n X_i}{10} =19.4[/tex]

[tex] s^2 = \frac{\sum_{i=1}^n (x_i -\bar x)^2}{n-1}=5.438[/tex]

[tex] s= \sqrt{5.438}=2.332[/tex]

b) [tex]19.4-2.262\frac{2.332}{\sqrt{10}}=17.732[/tex]    

[tex]19.4+2.262\frac{2.332}{\sqrt{10}}=21.068[/tex]    

So on this case the 95% confidence interval would be given by (17.732;21.068)    

c) [tex]t=\frac{19.4-22.5}{\frac{2.332}{\sqrt{10}}}=-4.203[/tex]  

Since is a two-sided test the p value would be:  

[tex]p_v =2*P(t_{9}<-4.203)=0.00230[/tex]  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 22.5 minutes.  

Step-by-step explanation:

Part a

We have the following data given: 22.2, 23.7, 16.8, 18.3, 19.7, 16.9, 17.2, 18.5, 21.0, and 19.7

We can calculate the sample mean with this formula:

[tex]\bar X= \frac{\sum_{i=1}^n X_i}{10} =19.4[/tex]

And the sample variance with this formula:

[tex] s^2 = \frac{\sum_{i=1}^n (x_i -\bar x)^2}{n-1}=5.438[/tex]

And the sample deviation would be just the square root of the sample variance

[tex] s= \sqrt{5.438}=2.332[/tex]

Part b

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 =19.4[/tex] represent the sample mean

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

s=2.332 represent the sample standard deviation

n=10 represent the sample size

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

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

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=10-1=9[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that [tex]t_{\alpha/2}=2.262[/tex]

Now we have everything in order to replace into formula (1):

[tex]19.4-2.262\frac{2.332}{\sqrt{10}}=17.732[/tex]    

[tex]19.4+2.262\frac{2.332}{\sqrt{10}}=21.068[/tex]    

So on this case the 95% confidence interval would be given by (17.732;21.068)    

Part c

Null hypothesis:[tex]\mu =22.5[/tex]  

Alternative hypothesis:[tex]\mu \neq 22.5[/tex]  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

[tex]t=\frac{19.4-22.5}{\frac{2.332}{\sqrt{10}}}=-4.203[/tex]  

P-value  

Since is a two-sided test the p value would be:  

[tex]p_v =2*P(t_{9}<-4.203)=0.00230[/tex]  

Conclusion  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 22.5 minutes.  

Final answer:

The mean, variance, and standard deviation of a sample of ten students' test completion times are 19.0 minutes, 3.3 minutes² , and 1.82 minutes, respectively.

Explanation:

a. To find the mean, add up all the times and divide by the number of students: (22.2 + 23.7 + 16.8 + 18.3 + 19.7 + 16.9 + 17.2 + 18.5 + 21.0 + 19.7) / 10 = 19.0 minutes.

To find the variance, subtract the mean from each time, square the differences, and find the average: [(22.2-19.0)² + (23.7-19.0)² + ... + (19.7-19.0)²] / 10 = 3.3 minutes².

To find the standard deviation, take the square root of the variance: √(3.3) = 1.82 minutes.

b. To construct a 95% confidence interval, we need to know the critical value for a sample size of 10. The critical value for a 95% confidence interval with 10 degrees of freedom is 2.262.

The margin of error can be calculated as the critical value multiplied by the standard deviation: 2.262 * (1.82 / √10) = 1.29 minutes. The confidence interval is then [19.0 - 1.29, 19.0 + 1.29] = [17.71, 20.29].

c. To test if the population mean time to complete the test is 22.5 minutes, we can use a t-test. The t-value can be calculated as the difference between the sample mean and the hypothesized population mean divided by the standard deviation divided by the square root of the sample size: (19.0 - 22.5) / (1.82 / √10) = -5.44. T

he degrees of freedom for this test is 9. Using a t-distribution table, we find that the critical t-value for a two-tailed test at a significance level of 0.05 is approximately ±2.262. Since -5.44 is outside of this range, we can reject the null hypothesis that the population mean time is 22.5 minutes.

Answer:

a) The range of lengths from 28.3 cm to 43.3 cm covers almost all (99.7%) of this distribution.

b) 16% of women over 20 have upper arm lengths less than 33.3 cm.

Step-by-step explanation:

The Empirical Rule(68-95-99.7 Rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 35.8 cm

Standard deviation = 2.5 cm

(a) What range of lengths covers almost all (99.7%) of this distribution?

This range is from 3 standard deviations below the mean to three standard deviations above the mean.

So from 35.8 - 3*2.5 = 28.3 cm to 35.8 + 3*2.5 = 43.3 cm

The range of lengths from 28.3 cm to 43.3 cm covers almost all (99.7%) of this distribution.

(b) What percent of women over 20 have upper arm lengths less than 33.3 cm?

68% of the women over 20 have upper arm length between 33.3 cm and 38.3 cm. The other 32% have upper arm length lower than 33.3 cm or higher than 38.3. The distribution is symmetric, so 16% of the have upper arm length lower than 33.3 cm and 16% have upper arm length higher than 38.3 cm

So 16% of women over 20 have upper arm lengths less than 33.3 cm.

Answer:

There are 6,151,600,000 different 7-place license plates are possible when 3 of the entries are letters and 4 are digits,

Step-by-step explanation:

For each of the entries which are letters, there are 26 possible outcomes.

For each of the entries which are digits, there are 10 possible outcomes.

These outcomes can be permutated.

For example, ABC1234 is a different outcome than A1B2C34. This means that we need to use the permutations formula.

The number of permutations of n, divided into two groups of size a and b, is:

[tex]P_{a,b}^{n} = \frac{n!}{a!b!}[/tex].

In this problem, we have a permutation of 7, divided into a group of 4(digits) and 3(letters).

How many different 7-place license plates are possible when 3 of the entries are letters and 4 are digits?

This is [tex]P_{3,4}^{7}*(26)^{3}*10^{4} = 35*(26)^{3}*10^{4} = 6,151,600,000[/tex]

There are 6,151,600,000 different 7-place license plates are possible when 3 of the entries are letters and 4 are digits,

Final answer:

The number of different 7-place license plates possible with 3 letters and 4 digits, where repetition is allowed, is 175,760,000.

Explanation:

To calculate the number of different 7-place license plates possible with 3 letters and 4 digits where repetition is allowed, we need to use the fundamental counting principle. For the three letters, assuming an English alphabet of 26 letters, each position can be filled in 26 different ways. Since there are 3 positions for letters, the number of combinations for the letter part is 26 × 26 × 26.

For the four digits, each position can be filled in 10 different ways (0 to 9). Therefore, the number of combinations for the digit part is 10 × 10 × 10 × 10.

To find the total number of combinations for the license plates, we multiply the combinations of letters by the combinations of digits: (26 × 26 × 26) × (10 × 10 × 10 × 10) = 175,760,000 different 7-place license plates possible.

Answer:

[k*(k+1)*(2*k+1)] / 6

Step-by-step explanation:

We have balls numbered as: 1, 2, 3, ... , k with probabilities as: c, 2*c, 3*c, ... , k*c

Let Y be the discrete random variable defined as: Y = ball number

We know that Expected value of discrete Random Variable is:

E[X] =  Σ₁ⁿ xₐ*f(xₐ)            ,where f(xₐ) is probability of xₐ

then,

E[Y] = 1*c + 2*2*c + 3*3*c + ... + k*k*c

E[Y] = c*(1 + 2*2 + 3*3 + ... + k*k)

E[Y] = c*(1^2 + 2^2 + 3^2 + ... + k^2)

consider c = 1  (because it's constant so you can suppose any you wish)

E[Y] = 1^2 + 2^2 + 3^2 + ... + k^2

using formula of first n squares natural numbers (as attached picture)

E[Y] = [k*(k+1)*(2*k+1)] / 6

Step-by-step explanation:

We can not exactly predict the values of mean and median of the data un till and unless we know about the skewness of the data.

Skewness represents the asymmetry or tapering in  the distribution of data  sample. If skewness is

Negative skew: median > mean:

Positive skew: mean > median :

Although this generalization is not always true.

Answer:

standard deviation =3.11

Step-by-step explanation:

data given is ungrouped data

standard deviation =√ [∑ (x-μ)² / n]

mean (μ)=∑x/n

           = [tex]\frac{10+15+12+18+19+16+12}{7}[/tex]

          =14.57

x-μ   for data 10, 15, 12, 18, 19, 16, 12 will be

                     -4.57, 0.43, -2.57, 3.43, 4.43,1.43, -2.57

(x-μ)² will be 20.88, 0.1849, 6.6049, 11.7649,19.6249, 2.0449, 6.6049

∑ (x-μ)² will be = 67.7049

standard deviation = √(67.7049 / 7)

                      =3.11

Final answer:

The standard deviation for the given data is approximately 3.11.

Explanation:

To calculate the standard deviation (s) of the set of scores 10, 15, 12, 18, 19, 16, 12, you would follow these steps:

Here's how to carry out each step with the provided scores:

Therefore, the standard deviation of the scores is about 3.11.

Answer:

division for me im probably wrong tbh

Step-by-step explanation:

Complete Question :

  The question is shown on the first uploaded image

Answer:

The solution is the second uploaded image

Step-by-step explanation:

The step by step explanation is on the third, fourth and fifth uploaded image

Answer:

a) Alpha

Step-by-step explanation:

The correct option is alpha because alpha known as type I error is the probability of reject the null hypothesis when null  hypothesis is true. If we take alpha 5%, it means that we are taking 5 out of 100 chance of rejecting the null hypothesis when it is true.

So, statistician controls alpha by establishing the risk of rejecting a null hypothesis when its true.

Answer:

-$80

Step-by-step explanation:

Assuming that the variation in the number of shirts per day is -1 hundred shirs, the variation in profit with respect to time is given by the derivate of the profit equation:

[tex]p=-40x^2+581x-520\\\frac{dp}{dx}=-80x+581[/tex]

Let x be the number of shirts sold in a day, then x-1 is the number of shirts sold in the following day, the change in profit is:

[tex]p'(x) - p'(x-1)=-80x+581 - (-80(x-1)+581)\\p'(x) - p'(x-1)=-80(x-x+1) = -80[/tex]

The profit is changing by -$80 per day.

Answer: 3, 4,5 and 17, 15,8

give the measures of the legs and hypotenuse of a right triangle.

Step-by-step explanation:

In order for the measures of the legs and hypotenuse given to form a right angle triangle, they must be Pythagorean triples. A Pythagoras triple is a set of numbers that perfectly satisfy the Pythagorean theorem. The Pythagorean theorem is expressed as

Hypotenuse² = opposite side² + adjacent side². We will apply the theorem to each set of numbers given.

1) 3, 4, 5

5² = 3² + 4² = 9 + 16

25 = 25

It is a Pythagorean triple

2) 4, 11, 14

14² = 11² + 4² = 121 + 16

196 = 137

It is a Pythagorean triple

3) 9, 14, 17

17² = 14² + 9² = 196 + 81

289 = 277

It is not a Pythagorean triple

4) 8, 14, 16

16² = 14² + 8² = 196 + 64

256 = 260

It is not a Pythagorean triple

5) 8, 15 , 17

17² = 15² + 8²

289 = 225 + 64

289 = 289

It is a Pythagorean triple

Therefore, 3, 4,5 and 17, 15,8

give the measures of the legs and hypotenuse of a right triangle.

Answer: he purchased 5 small file cabinets and 8 large file cabinets.

Step-by-step explanation:

Let x represent the number of small file cabinets that he purchased.

Let y represent the number of large file cabinets that he purchased.

Luis bought 13 new small and large file cabinets. This means that

x + y = 13

Small file cabinets cost $43.50 and large file cabinets cost $65.95. He spent a total of $745.10. This means that

43.5x + 65.95y = 745.1 - - - - - - - -1

Substituting x = 13 - y into equation 1, it becomes

43.5(13 - y) + 65.95y = 745.1

565.5 - 43.5y + 65.95y = 745.1

- 43.5y + 65.95y = 745.1 - 565.5

22.45y = 179.6

y = 179.6/22.45

y = 8

x = 13 - y = 13 - 8

x = 5

The problem can be solved by creating a system of linear equations based on the given information, then solved using methods such as substitution or elimination to find out the number of small and large cabinets.

This is a problem related to the system of linear equations. So let's define the variables: Let 's' represent the number of small cabinets and 'l' the number of large cabinets. So we form two equations, one based on the total amount spent, and the other based on the total number of cabinets.

The first equation is $43.50s + $65.95l = $745.10, presenting the total amount of money spent by Luis. The second one is s + l = 13, representing the total number of cabinets.

Now, we can solve these equations simultaneously using any method, substitution or elimination, to find the values of 's' and 'l'.

https://brainly.com/question/20379472

#SPJ12

Answer:

b. 0.1216

Step-by-step explanation:

Given that a sample of  15 from a normal population yields a sample mean of 43 and a sample standard deviation of 4.7.

We have to check the p value for the claim that mean <45

[tex]H_0: \mu =45\\H_a: \mu <45[/tex]

(Left tailed test for population mean)

Sample size n = 15

Sample mean = 45

Sample std dev s = 4.7

Since sample std deviation is being used, we use t test only

Std error of mean = [tex]\frac{s}{\sqrt{n} } \\=1.214[/tex]

Mean difference = 43-45 = -2

t statistic = mean difference/std error

= -1.176

df = n-1 = 14

p value = 0.1216

Answer:

[tex] W= 34.3 \frac{kg}{s^2} (4^2-0^2)m^2 =548.8 \frac{kg m^2}{s^2} =548.8 J[/tex]

Step-by-step explanation:

Data Given: m = 70 kg , g = 9.8 ms^-2, h =10m.

For this case we can use the following formula:

[tex] W = \int_{x_i}^{x_f} F(x) dx[/tex]

For this case we need to find an expression for the force in terms of the distance. And since on this case the total distance is 10 m long we can write the expression like this:

[tex] F(x) = \frac{ma}{10m}= \frac{mg}{10m} x[/tex]

The only acceleration on this case is the gravity and if we replace the values given we got:

[tex] \frac{70 kg *9.8 m/s^2}{10m} x=68.6 x\frac{kg}{s^2}[/tex]

Now we can find the required work with the following integral:

[tex] W= 68.6 \frac{kg}{s^2} \int_{0}^4 x dx[/tex]

[tex] W= 34.3 \frac{kg}{s^2} x^2 \Big|_0^4[/tex]

[tex] W= 34.3 \frac{kg}{s^2} (4^2-0^2)m^2 =548.8 \frac{kg m^2}{s^2} =548.8 J[/tex]

The amount of work that is required to raise one end of the chain is 548.8 Joules.

Given the following data:

To calculate the amount of work that is required to raise one end of the chain:

We would solve for the magnitude of the force acting on the chain with respect to the distance and this is given by this expression:

[tex]Force = \frac{mgx}{10} \\\\Force = \frac{70 \times 9.8 \times x}{10}[/tex]

Force = 68.6x Newton.

Now, we can calculate the amount of work by using this formula:

[tex]W=\int\limits^{x_2}_{x_1} F({x}) \, dx \\\\W= 68.6 \int\limits^{4}_{0} x \, dx\\\\W= 34.3 x^2 |^4_0\\\\W=34.3 [4^2 -0^]\\\\W=34.3 \times 16[/tex]

W = 548.8 Joules.

Read more on work done here: https://brainly.com/question/22599382

Answer:

51

Step-by-step explanation:

The possible components to sum up to 101 can only be divided into 2 groups, 1 is larger than 50 and the other is less than or equals to 50

For example

50 + 51 = 101

52 + 49 = 101

60 + 41 = 101

...

99 + 2 = 101

100 + 1 = 101

Therefore, the worst case scenario is to pick all numbers from only 1 group, either all number less than or equal to 50, which there are 50 of them from 1 to 50, or greater than 50, which there are 50 of them from 51 to 100.

So k has to be at least 51 to guarantee that at least one pair of the selected integers will sum to 101

The smallest value of k that guarantees at least one pair of the selected integers will sum to 101 is 100.

In order to guarantee that at least one pair of the selected integers will sum to 101, we need to find the largest value of k under which it is still possible for all pairs of integers to have a sum less than or equal to 100.

Let's consider the scenario where k is equal to 99. We can select 99 integers between 1 and 100, and it is still possible for none of the pairs to have a sum of 101. Every integer can be paired with one other integer to form a sum less than or equal to 100 (e.g., 1 and 100, 2 and 99, 3 and 98, and so on).

However, if we select one more integer to make k equal to 100, there will be at least one pair that adds up to 101, since we have one extra integer that cannot form a sum less than 101 with any of the other integers.

Therefore, the smallest value of k that guarantees at least one pair of the selected integers will sum to 101 is 100.

Answer: =0.2465

Step-by-step explanation:

Firstly the probability that a random requisition is entered by data entry specialist 1 equals 0.3, by data

entry specialist 2 equals 0.45, by data entry specialist 3 equals 0.25.

probability(p1) =

(0.3 × 0.03

)/(0.3 × 0.03 + 0.45 × 0.05 + 0.25 × 0.02 )= 0.2465

Answer:

Explanation:

1. Given vector:

2. y-component

The y-component may be determined using the sine ratio, the angle from the x-axys (counterclockwise direction), and the magnitude of the vector.

Answer:

∫∫∫1 dV=4\sqrt{3}π

Step-by-step explanation:

From Exercise we have  

z=6-x^{2}-y^{2}

z=x^{2}+y^{2}

we get

2z=6

z=3

x^{2}+y^{2}=3

We use the polar coordinates, we get

x=r cosθ

y=r sinθ

x^{2}+y^{2}&=r^{2}

r^{2}=3

We get at the limits of the variables that well need for our integral

x^{2}+y^{2}≤z≤3

0≤r ≤\sqrt{3}

0≤θ≤2π

Therefore, we get a triple integral

\int \int \int 1\, dV&=\int \int \left(\int_{x^2+y^2}^{3} 1\, dz\right) dA

=\int \int \left(z|_{x^2+y^2}^{3} \right) dA

=\int \int\ \left(3-(x^2+y^2) \right) dA

=\int \int\ \left(3-r^2 \right) dA

=\int_{0}^{2\pi}\int_{0}^{\sqrt{3}} (3-r^2) dr dθ

=3\int_{0}^{2\pi}\int_{0}^{\sqrt{3}}  1 dr dθ-\int_{0}^{2\pi}\int_{0}^{\sqrt{3}} r^2 dr dθ

=3\int_{0}^{2\pi} r|_{0}^{\sqrt{3}}  dθ-\int_{0}^{2\pi} \frac{r^3}{3}|_{0}^{\sqrt{3}}dθ

=3\sqrt{3}\int_{0}^{2\pi} 1 dθ-\sqrt{3}\int_{0}^{2\pi} 1 dθ

=3\sqrt{3} ·2π-\sqrt{3}·2π

=4\sqrt{3}π

We get

∫∫∫1 dV=4\sqrt{3}π

We find the volume of the region D bounded by the paraboloids z = 6 - x² - y² and z = x² + y² by setting up triple iterated integrals. Six different integrals are presented, and one is evaluated using cylindrical coordinates. The volume is determined to be 9π.

To find the volume of the region D bounded by the paraboloids z = 6 - x² - y² and z = x² + y², we need to set up triple iterated integrals.

The intersection of the two surfaces occurs when 6 - x² - y² = x² + y²,

which simplifies to 6 = 2(x² + y²) or x² + y² = 3, defining a circle of radius √3 in the xy-plane.

Possible Triple Iterated Integrals

Here are six different triple iterated integrals to find the volume of the region D:

Evaluating One of the Integrals

[tex]\int_{0}^{2\pi} \int_{0}^{\sqrt{3}} \int_{r^2}^{6 - r^2} r \, dz \, dr \, d\theta[/tex]

[tex]\int_{r^2}^{6 - r^2}\, dz = \left[ z \right]_{z=r^2}^{z=6-r^2}[/tex]

[tex]= (6-r^2) - (r^2)[/tex]

[tex]= 6-2r^2[/tex]

[tex]int_{0}^{\sqrt{3}} r(6 - 2r^2) dr = \int_{0}^{\sqrt{3}} (6r - 2r^3) dr[/tex]

[tex]= \left[ 3r^2 - \frac{1}{2}r^4 \right]_{r=0}^{r= \sqrt{3}}[/tex]

[tex]= \left[ 3(3) - \frac{1}{2}(9) \right][/tex]

= 9 - 4.5

= 4.5

[tex]\int_{0}^{2\pi} 4.5 \, d\theta = 4.5 \cdot 2\pi = 9\pi[/tex]

So the volume of the region D is 9π.

Answer:

The slope of the graph of y=x(t)

Step-by-step explanation:

The speed's equation is the derivative of the position.

Position

y = x(t)

Linear function.

So

y = ax(t)

In which a is the slope

The derivative of y is:

y = a

Which is the slope

This means that the speed of the particle is constant.

So the answer is:

The slope of the graph of y=x(t)

Let p be the true proportion of  registered voters wish to see Mayor Waffleskate defeated.

As per given , we have

[tex]H_0: p\leq0.27\\\\ H_a: p >0.27[/tex]

Sample size : n= 447

Number of of registered voters wish to see Mayor Waffleskate defeated = 157

I.e. sample proportion :  [tex]\hat{p}=\dfrac{157}{447}\approx0.3512[/tex]

Confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

, where n= sample size

[tex]\hat{p}[/tex] = sample proportion

z* = critical z-value.

Critical z-value for 98% confidence interval is 2.33.  (By z-table)

Then, the 98% confidence interval for the proportion of registered voters who wish to see Waffleskate defeated will be :

[tex]0.3512\pm2.33\sqrt{\dfrac{0.3512(1-0.3512)}{447}}\\\\=0.3512\pm (2.33)(0.022577656)\\\\=0.3512\pm 0.05260593848\\\\=(0.3512-0.05260593848,\ 0.3512+0.05260593848)\\\\=(0.29859406152,\ 0.40380593848)\approx(0.299,\ 0.404)[/tex]

Since the 0.27 < 0.299 , it means 0.27 does not belong to the above confidence interval.

So , we reject the null hypothesis ([tex]H_0[/tex]).

So ,  98% confidence interval does not support the claim.

Final answer:

The tomato hits the ground at a speed of approximately 80 ft/s. It takes approximately 1.58 seconds for the tomato to travel the last 10 feet.

Explanation:

To find the speed at which the tomato hits the ground, we can use the equation:

v^2 = u^2 + 2as

Where:

Plugging in these values, we get:

v^2 = 0 + 2(-32)(100)

v^2 = -6400

Taking the square root of both sides, we find that the speed at which the tomato hits the ground is approximately 80 ft/s.

To find the time it takes for the tomato to travel the last 10 feet, we can use the equation:

s = ut + (1/2)at^2

Where:

Plugging in these values, we get:

10 = 0 + (1/2)(-32)t^2

20 = -16t^2

t^2 = -20/16

Taking the square root of both sides, we find that the time it takes for the tomato to travel the last 10 feet is approximately 1.58 seconds.

Answer:

[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16[/tex]

Step-by-step explanation:

The general equation of a sphere is as follows:

[tex](x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}[/tex]

In which the center is [tex](x_{c}, y_{c}, z_{c})[/tex], and r is the radius.

In this problem, we have that:

[tex]x_{c} = 5, y_{c} = 4, z_{c} = 1[/tex]

So

[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = r^{2}[/tex]

Interior contained in the first octant:

The first octant is bounded by:

The xy plane, in which z is 0. The distance from the center of the sphere to the xy plane is 9.

The xz plane, in which y is 0. The distance from the center of the sphere to the xz plane is 4.

The yz plane, in which x is 0. The distance from the center of the sphere to the yz plane is 5.

This means that if the radius is higher than four, the sphere will cross into a different octant.

So the radius for the largest sphere is 4.

The equation is

[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 4^{2}[/tex]

[tex](x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16[/tex]

Answer:

[tex]m = -7[/tex]

Step-by-step explanation:

The objective is to find all values [tex]m[/tex] so that the function [tex]y=e^{mx}[/tex] is a solution of the differential equation [tex]y'+7y =0[/tex].

If [tex]y=e^{mx}[/tex] is a solution of the given differential equation, then it and its first derivative must satisfy the given equation. Let's calculate the derivative.

                      [tex]y = e^{mx} \implies y' = e^{mx} \overset{\text{Chain Rule}}{\cdot} (mx)' = me^{mx}[/tex]

Substituting [tex]e^{mx}[/tex]  for [tex]y[/tex] and [tex]me^{mx}[/tex] for [tex]y'[/tex] in the equation gives

                          [tex]me^{mx} + 7e^{mx} = 0 \iff e^{mx}(m+7) = 0[/tex]

We can divide both sides by [tex]e^{mx}[/tex], since [tex]e^{mx} > 0, \; \forall x,m \in \mathbb{R} \implies e^{mx} \neq 0[/tex]. Thus,

                                     [tex]m +7 = 0 \implies m = -7[/tex]

Therefore, the function [tex]y = e^{-7x}[/tex] is a solution of the differential equation [tex]y'+7y = 0.[/tex]

Answer:

A. Attachment

Step-by-step explanation:

The powerful survival impulse that leads infants to seek closeness to their caregivers is called Attachment. The infant can count on the caregiver possibly parent(s) for care which gives the infant a solid foundation for dependence and survival.

Final answer:

The instinctual behavior that drives infants to seek closeness with their caregivers is known as A) attachment. It's fostered by reflexes that ensure physical contact and is crucial for an infant's survival, ensuring they receive the necessary care, protection, and opportunity to develop securely.

Explanation:

The powerful survival impulse that leads infants to seek closeness to their caregivers is called A) attachment. This is an intrinsic part of human development and is crucial for the infant's survival. Infants have a set of innate behaviors and reflexes that promote closeness and contact with their caregivers, such as the Moro reflex and the grasping reflex, which help the infant to hold onto the caregiver and thus reduce the risk of falling.

Additionally, behaviors such as crying and the sucking reflex are instinctive methods for infants to express needs and receive care. Furthermore, the rooting reflex is an instinctive behavior that helps the infant find the nipple to feed by touching. John Bowlby's evolutionary theory underscores the importance of attachment by suggesting that the ability to maintain proximity to an attachment figure would have increased the chances of an infant surviving to reproductive age.

Attachments are not just reactions to the provision of food and warmth by the caregivers but are biological imperatives that ensure an infant remains close to those who provide security, learning, and protection, thereby enhancing their chance of survival.

Answer:

175/1001

Step-by-step explanation:

(a.)

Freshman: 5 Combination 2

sophomores: 7 Combination 3

Junior: 4 Combination 1

The combination of three groups :

=5c2 × 7c3 × 4c1

=10 × 35 × 4

=1400 ways

(b.)

=5+7+4=16

=2+3+1

Which is (16 combination 6)

The probability will be:

=(5c2 × 7c3 × 4c1) / 16c6

=1400/8008

=175/1001

The groups can be formed in multiple ways, calculated by the combination formula, and the probability of forming a specific group is calculated by dividing the number of ways to form that specific group by the total number of possible groups.

The question is about how many unique ways a study group can be formed from a given set of students and determining the probability of a specific group formation.

To solve Part (a), we use the concept of combinations. The number of ways to select 2 freshmen out of 5 is 5C2, for 3 sophomores out of 7 is 7C3, and for 1 junior out of 4 is 4C1. Multiply these together to get the total number of ways, which is (5C2)*(7C3)*(4C1).

For Part (b), the total number of ways to select a group of 6 students from 16 is 16C6. The probability of selecting 2 freshmen, 3 sophomores, and 1 junior, is the result from Part (a) divided by this total number, or [(5C2)*(7C3)*(4C1)] /(16C6).

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Answer:

Step-by-step explanation:

square

quadrilateral - all of these

polygon - squares

trapezoid - others - non square

rhombus - squares

hope this helps.

Answer:

F(x=11)= (-31)

Step-by-step explanation:

for the function

F(x) = x² - 13*x + 22/x-11 , for x ≠ 11

then in order to define F(x=11) so  F is continuous (see Note below) . By definition of continuity of a function:

F(x) is continuous in x=11 if lim F(x)=F(a) when x→a

then

when x→a , lim x² - 13x + 22/x-11 = lim 11² - 13*11 + 22/11 -11 = -3*11 + 2 = -31 = F(x=11)

then

F(x=11)= (-31)

Note:

F is not continuous in all x since

when x→0⁺ ,  lim (0⁺) ² - 13*0⁺  + 22/0⁺ -11 = (+∞)

when x→0⁻,  lim (0⁻) ² - 13*0⁻  + 22/0⁻ -11 = (-∞)

then

limit F(x) , when x→0 does not exist since the limit from the left and from the right do not converge → since the limit does not exist , the function is not continuous  in x=0

Answer:

There is a 10.9375% probability that their first child will have green eyes and the second will not.

Step-by-step explanation:

We have these following probabilities:

0.75 probability of having children with brown eyes, 0.125 probability of having children with blue eyes, and 0.125 probability of having children with green eyes.

(a) What is the probability that their first child will have green eyes and the second will not?

There is a 0.125 probability a child will have green eyes and an 1-0.125 = 0.875 probability a child will not have green eyes.

So

0.125*0.875 = 0.109375

There is a 10.9375% probability that their first child will have green eyes and the second will not.

Answer:

a) 117.4

b) 117.9

c) Option A)  When there is rounding or grouping, the median can be highly sensitive to small change

Step-by-step explanation:

We are given the following data set in the question:

108.6, 117.4, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2

[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]

n = 9

a) Median of the reported blood pressure values

Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.4, 120.0, 121.5, 123.2, 128.4

Median =

[tex]\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.4[/tex]

b) New median of the reported values

Data: 108.6, 117.9, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2

Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.9, 120.0, 121.5, 123.2, 128.4

New Median =

[tex]\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.9[/tex]

c) Since median is a position based descriptive statistics, a small change in values can bring a change in the median value as the order of the data may change.

Option A)  When there is rounding or grouping, the median can be highly sensitive to small change

The median of the reported blood pressure values is 117.4. If the blood pressure of the second individual is changed to 117.9, the new median would be 117.9. This shows that the median is not sensitive to small changes in rounding or grouping.

(a) What is the median of the reported blood pressure values?

To find the median, we need to arrange the blood pressure values in numerical order: 98.3, 103.7, 108.6, 112.0, 117.4, 120.0, 121.5, 123.2, 128.4. Since there are 9 values, the middle value is the 5th value, which is 117.4.

(b) Suppose the blood pressure of the second individual is 117.9 rather than 117.4. What is the new median of the reported values?

If we change the second individual's blood pressure to 117.9, the new order is: 98.3, 103.7, 108.6, 112.0, 117.9, 120.0, 121.5, 123.2, 128.4. Now, there are 9 values and the middle value is the 5th value, which is 117.9. So the new median would be 117.9.

(c) What does this say about the sensitivity of the median to rounding or grouping in the data?

C. When there is rounding or grouping, the median is not sensitive to small changes.

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