please
help with part b
QUESTION 2 [5 marks] A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. a) Use

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.

In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:

For the first pair (2 hours, 8 miles):

Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour

For the second pair (4 hours, 16 miles):

Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour

For the third pair (6 hours, 24 miles):

Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour

For the fourth pair (8 hours, 32 miles):

Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour

As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.

Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.

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Answer:

x>2

Step-by-step explanation:

Longer than two hours is >.

Answer:

4/3

Step-by-step explanation:

7x + 4 = 10x

4 = 3x

x = 4/3

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

Due to the fact that mass is the quantity of matter contained in an item and does not change with gravity, mass is always the same. As long as the amount of matter in an object doesn't change, its mass will remain constant. In contrast, an object's weight refers to the force of gravity acting on it.

No matter where you are in the cosmos, you have the same mass since mass is a measurement of how much matter is in an object. But because weight measures the force between an object and the body it is resting on, it fluctuates (whether that body is the Earth, the Moon, Mars, et cetera).

Given : A mass of student 40 kg

length is represented by l

Position of the pivot point from the board = l/3

The student should stand at 2L/9 you will see it tip over so as to weigh of 60kg.

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Answer:

60% increase

Step-by-step explanation:

Take the new minus the original

48-30 = 18

Divide by the original

18/30

.6

Change to percent form

60% increase

Answer: C: 0.4

Step-by-step explanation:

1/5 is 0.2 and double that is 0.4 since there are 2 half hours in an hour :)

Answer:

D

Step-by-step explanation:

16m-(5+8m)

this expression change like

16m-5-8m

Answer:

5x-y=-9

Step-by-step explanation:

When x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

1)  We are aware that only when x is positive is a logarithmic function, log x, defined. i.e., x>0 . Therefore, when x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

2) Order from smallest to largest:

     \(log^{200}_{20} < log 100 < log^{5}_{40} < log^{3}_{60} < log^{2}_{16}\)

3)

           \(\(2A=A(1+\frac{0.09}{52})^{n}\\\\ 2=(1+\frac{0.09}{52})^{n}\\\\ log2=log(1+\frac{0.09}{52})^{n}\\\\ log2=nlog(1+\frac{0.09}{52})\\\\ n=log2\div log(1+\frac{0.09}{52})\\\)\)

log(2)/log(1+0.09/52 = 400.831511360387616 weeks

400.831511360387616/52 = 7.708298295392069538

7.7 years

Hence, It take 7.7 years for deposit to double.

4)

a)

          \(S= 86 \ log d+112\\\\S= 86 log 50 +112\\\\S = 86*1.7+112\\\\S= 258.2\)

          S = 258.2 mph

b)

S = 258.2 mph ;  find d

258 =86 log10 (d) + 112

146 = 86 log10 (d)

 1.7 = log10 (d)

 d = 50.118

Change from Log Form to Exponential Form

50.118 miles = d   Rounded is 181 miles

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Answer:

They will spend less at the sunny side hotel

Step-by-step explanation:

The attachment completes the question.

From the question, we understand that there are 4 individuals involved.

And they will spend one night

First, we need to calculate the expenses in Traveler's hotel.

\(Rate = \$107.10\) (for 3 people)

\(Additional\ Person = \$21.55\) (for 1 person)

\(Breakfast = \$8.75 * 4\) (for 4 people)

\(Tax = \$16.85\)

Total Expenses

\(Total = \$107.10 + \$21.55 + \$8.75* 4 + \$16.85\)

\(Total = \$107.10 + \$21.55 + \$35.00 + \$16.85\)

\(Total = \$108.50\)

For Sunny Side hotel:

\(Rate = \$152.95\) (for 4 people)

\(Tax = \$21.34\)

Total Expenses:

\(Total = \$152.95 + \$21.34\)

\(Total = \$174.29\)

By comparison, they will spend less at the sunny side hotel.

The condition characterized by cyanosis and pain in the fingers due to extreme vasoconstriction in the digits resulting from excessive sympathetic stimulation is called Raynaud's phenomenon.

Raynaud's phenomenon occurs when blood vessels, specifically the small arteries that supply blood to the fingers, constrict excessively in response to cold or emotional stress. This constriction reduces blood flow to the affected areas, leading to cyanosis (bluish discoloration), pain, and numbness in the fingers.

The underlying cause of Raynaud's phenomenon is an imbalance in the autonomic nervous system, particularly an overactivity of the sympathetic nervous system. This system is responsible for the "fight or flight" response and, when stimulated, can cause blood vessels to constrict.

Raynaud's phenomenon is characterized by:
1. Cyanosis: Bluish discoloration of the fingers due to reduced blood flow.
2. Pain and numbness in the fingers.
3. Extreme vasoconstriction: Constriction of small arteries supplying blood to the digits.
4. Excessive sympathetic stimulation: Overactivity of the sympathetic nervous system leads to constriction of blood vessels.
If you experience symptoms of Raynaud's phenomenon, it is essential to consult with a medical professional for proper diagnosis and treatment.

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Answer:

\(\textsf{Mean}\:\overline{X}=\sf \dfrac{\textsf{sum of all the data values}}{\textsf{total number of data values}}\)

\(\implies \sf Mean\:(Nilo)=\dfrac{5+6+14+15}{4}=\dfrac{40}{4}=10\)

\(\implies \sf Mean\:(Lisa)=\dfrac{8+9+11+12}{4}=\dfrac{40}{4}=10\)

\(\displaystyle \textsf{Standard Deviation }s=\sqrt{\dfrac{\sum X^2-\dfrac{(\sum X)^2}{n}}{n-1}}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}\)

\(\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}\)

Nilo has a mean score of 10 and a standard deviation of 5.23.

Lisa has a mean score of 10 and a standard deviation of 1.83.

The mean scores are the same.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more spread out that Lisa's, which means Lisa's test scores are more consistent.

Answer:

4/20=1/5

Step-by-step explanation:

Answer:

The answer is 1/5 of the students are blond girls, since 1/3 of 3/5 is 1/5.  

Divide 3/5 by 3, which is 1/5.  

Hope this helps!

Step-by-step explanation:

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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Answer:

y = x² - 9x + 14

Step-by-step explanation:

Given the zeros x = 7 and x = 2, then the corresponding factors are

(x - 7) and (x - 2)

The function is then the product of its factors, that is

y = (x - 7)(x - 2) ← expand using FOIL

  = x² - 9x + 14

The quadratic function with zeros 7 and 2 in standard form is

f(x) = x² - 9x + 14

If a quadratic function has zeros of a and b, then the quadratic function can be formed as:

f(x) = (x - a)(x - b)

For a function with zeros 7 and 2:

a = 7, b = 2

Substitute a = 7 and b = 2 into the quadratic function f(x) = (x - a)(x - b)

f(x)  = (x  - 7)(x  -  2)

Expand the expression

f(x) = x² - 2x - 7x + 14

f(x) = x² - 9x + 14

The quadratic function with zeros 7 and 2 in standard form is f(x) = x² - 9x + 14

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The appropriate label for the analysis of the data described in the study by Roediger and Karpicke (2006) is a "2x3 between-groups ANOVA." This designation accurately reflects the experimental design and the factors involved in the investigation.

In their study, the researchers randomly assigned participants to one of two study conditions: study-study or study-test. Additionally, participants were assigned to one of three retention interval conditions: 5 minutes, 2 days, or 1 week.

The dependent variable measured was the proportion of idea units recalled from an encyclopedia passage.

The first factor, study condition, is a between-groups variable as it was manipulated by assigning participants to one of the two study conditions. The two levels of this factor are study-study and study-test. Participants in each group underwent the designated study method.

The second factor, retention interval condition, is also a between-groups variable. Participants were assigned to one of the three retention intervals: 5 minutes, 2 days, or 1 week. This factor explores the effect of time duration on the participants' memory retention.

The notation "2x3" indicates that there are two independent variables in the study, each with multiple levels. The first variable, study condition, has two levels, while the second variable, retention interval condition, has three levels.

The interaction between these variables is of interest to understand their combined effects on memory recall.

Considering the between-groups design and the multiple levels of the two factors, the appropriate label for the analysis is a "2x3 between-groups ANOVA."

This type of analysis allows for examining the main effects of each factor, as well as their interaction effect on the proportion of idea units recalled.

By employing this statistical method, the researchers can investigate the potential differences in memory performance based on the study condition and the retention interval condition, providing valuable insights into the test-enhanced learning effect and repeated exposure to material.

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Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

\(f(x)=x^3\)

If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.

\(f(x)=(x-8)^3\)

graph shifted toward right by \(8\) units right

\(f(x)=(x-8)^3+3\)

graph shifted toward right by \(3\) units up

Thus the new function is:

\(g(x)=(x-8)^3+3\)

Answer:

w^2 + 13w + 39

Step-by-step explanation:

Multiplying Polynomials (FOIL- Firsts, Outs, Inners, Lasts)

(w+9) (w+4)          Multiply- Firsts (w*w)   Outs (w*4)   Inners (9*w)   Lasts (9*4)

w*w + w*4 + 9*w + 9*4     Multiply the FOIL

w^2 + 4w + 9w + 36          Combine like terms (same variables, numbers)

w^2 + 13w + 39

If 5 wholes are divided into pieces that are each \($\frac{1}{4}$\) start fraction, 1, divided by, 4, end fraction of a whole, there are 20 pieces.

In mathematics, a fraction represents a part of a whole or a collection of equal parts. It is a way of representing a number as a ratio of two integers, where the top number is called the numerator and the bottom number is called the denominator.

If 5 wholes are divided into pieces that are each \($\frac{1}{4}$\) of a whole, we can find the total number of pieces by multiplying the number of pieces in one whole by the number of wholes:

Number of pieces in one whole=

\($\frac{1}{\frac{1}{4}} = 4$\)

Number of pieces in 5 wholes = 5 x 4 = 20

Therefore, there are 20 pieces.

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The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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Answer:

y = 0.5,  1,  1.5,  2

Step-by-step explanation:

x is twice as much as y, so when you multiply the input for y by 2, it should get the value of x. Example: if y is 1, then x is 2, because 1*2 = 2

hope this helped!

Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

There are two different translations we can apply to a function graph. In addition, they are scaling. If you count reflections, there are three, but reflections are really a specific instance of the second translation.

Transformations:

Reflecting a function on X-axis  : Change y in function to -y.

Reflecting aa function on Y-axis : Change x in function to -x.

Shifting right by a:  Replace x by (x-a)

Shifting left by a:  Replace x by (x+a).

Shifting up by a: Replace y by (y-a).

Shifting down by a: Replace y by (y+a).

Scaling up by  n times: Multiply n

Step1: Vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by \(\frac{1}{7}\) .

So, we have:

\(y=\frac{1}{7}x^3\);

Step2:Horizontal shift by 8 units to the left, we need to add 8 to x.

So, we have:

\(y=\frac{1}{7}(x+8)^3\);

Step3:Reflection over the x-axis, we need to Replace y by -y.

So, we have:

\(y=-\frac{1}{7}(x+8)^3\)

Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

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Answer:

a) x = 1.5 or x = -0.3

b) x = 5 or x = -8

Explanation:

Quadratic formula:

\(\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0\)

Here given equation: 5x² - 6x  - 2 = 0

Identify variable constants: a = 5, b = -6, c = -2

Putting these values into equation:

\(\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}\)

\(\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}\)

\(\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}\)

\(\sf x = \dfrac{ 3\pm \sqrt{76}}{5}\)

\(\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}\)

In one decimal point:

\(\sf x = 1.5 \quad or \quad -0.3\)

b) Here use "middle term split" method

⇒ x² + 3x = 40

relocate

⇒ x² + 3x - 40 = 0

The factors of 40 are 8 and 5

⇒ x² + 8x - 5x - 40 = 0

factor common terms

⇒ x(x + 8) - 5(x + 8) = 0

collect into groups

⇒ (x - 5)(x + 8) = 0

set to zero

⇒ x - 5 = 0 or x + 8 = 0

relocate

⇒ x = 5 or x = -8

Step-by-step explanation:

a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) for a quadratic equation of the form \(ax^2+bx+c=0\).

In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.

\(x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}\)

This means that the value of x is both \(\frac{3+\sqrt{19}}5\) and \(\frac{3-\sqrt{19}}5\), since both values make x equal to 0. Putting both into the calculator, we get that \(x=1.5\) or \(x=-0.3\).

b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.

\(x^2+3x-40=0\)

Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.

we can now make our factors x+8 and x-5

\((x+8)(x-5)=0\)

If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.

\(x+8=0\\x=-8\)    \(x-5=0\\x=5\)

This makes our solutions x=-8 and x=5.

If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.

Answer:Simplify the expression.

Exact Form:

35

8

Decimal Form:

4.375

Mixed Number Form:

4  3/8

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

\(h(3)= 3(3)^2-2(3)+13= \\\\3(9)-6+13=\\\\27+7=\\\\34\)

Hope this helps!

Answer:

34

Step-by-step explanation:

3*9-6+13

27-6+13

you do the math

Answer:

c=7

Step-by-step explanation:

−5c+5=4c−58

Subtract 4c from both sides.

−5c+5−4c=4c−58−4c

−9c+5=−58

Subtract 5 from both sides.

−9c+5−5=−58−5

−9c=−63

Divide both sides by -9.

-9c/-9= -63/-9

c=7

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Answer:

m+22-22=30-22

m=8

7/7 y=28/7

y=4

12-12+3p=-3-12

3p=-15

3/3 p=-15/3

p=-5