What is 2 9 as a percentage? give your answer rounded to one decimal place.

Answer:

the third one C=3π cm; A=9π cm²

Step-by-step explanation:

Answer:

The slope is 1/1 or just 1

Step-by-step explanation:

Answer:

the answer is 1

Step-by-step explanation:

(1,2) (6,7)

x1,y1 x2, y2

7-2=5

6-1=5

5/5=1

the formulas to find the slope is

Answer:

x=9

Step-by-step explanation:

-5(2x-3)=-3(4x-11)

Multiply to open the brackets,

-10x+15=-12x+33

Keep constants and variables on same sides,

-10x+12x=33-15
2x=18

Divide by 2 on both sides,

2x/x=18/2
x=9

Answer:

x = 9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5(2x−3)=−3(4x−11)

(−5)(2x) + (−5)(−3) = (−3)(4x) + (−3)(−11) (Distribute)

−10x + 15 = −12x + 33

Step 2: Add 12x to both sides.

−10x + 15 + 12x = −12x + 33 + 12x

2x+15=33

Step 3: Subtract 15 from both sides.

2x + 15 − 15 = 33 − 15

2x = 18

Step 4: Divide both sides by 2.

2x/2 = 18/2

x=9

The slope is approximately -1.28, the intercept is approximately 263.93, and the correlation is approximately -0.92.

To find the slope of the regression line predicting Y from X, we use the formula:

slope = \((nΣ(XY) - ΣXΣY) / (nΣ(X^2) - (ΣX)^2)\)

First, we calculate the necessary summations:

ΣX = 29 + 63 + 67 + 103 + 113 = 375

ΣY = 205 + 221 + 176 + 123 + 112 = 837

ΣXY = (29205) + (63221) + (67176) + (103123) + (113*112) = 71450

\(ΣX^2 = (29^2) + (63^2) + (67^2) + (103^2) + (113^2) = 48114\)

Using these values, we can calculate the slope:

slope = (571450 - 375837) / (5*48114 - (375^2))

= -1.28 (rounded to 2 decimal places)

Next, we find the intercept of the regression line using the formula:

intercept = (ΣY - slope * ΣX) / n

intercept = (837 - (-1.28 * 375)) / 5

= 263.93 (rounded to 2 decimal places)

Lastly, to determine the correlation between X and Y, we calculate the correlation coefficient using the formula:

correlation = \((nΣXY - ΣXΣY) / √((nΣX^2 - (ΣX)^2)(nΣY^2 - (ΣY)^2))\)

correlation =\((571450 - 375837) / √((548114 - (375^2))(5210457 - (837^2)))\)

= -0.92 (rounded to 2 decimal places)

Therefore, the slope of the regression line predicting Y from X is approximately -1.28, the intercept is approximately 263.93, and the correlation between X and Y is approximately -0.92.

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DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.

1.) 2+3 = y + 12

Make y the formula's subject after adding the LHS.

5 = y + 12

Y = 5 - 12

Y = - 7

The answer to the equation is -7

2.) 2 + 13 = 1 +8

The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).

3.) y - 7 = 2 - 11

RHS is added, and y is become the formula's subject.

Y - 7 = -9

Y = -9 + 7

Y = -2

The equation's answer is -2.

The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12

2 + 13 = 1 +8

y - 7 = 2 - 11

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There is not enough evidence to conclude that Devon's true proportion of good serves is greater than 72%.

The correct conclusion for Devon to reach is: Because the P-value of 0.06 > a (where a = 0.05), Devon should fail to reject H0. There is no convincing evidence that the proportion of services that are good is more than 72%.

The null hypothesis, H0, states that the true proportion of good serves for Devon is equal to 72%. The alternative hypothesis, Ha, states that the true proportion of good serves for Devon is greater than 72%.

The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming that the null hypothesis is true. In this case, the P-value is 0.06, which means that if the true proportion of good serves for Devon is actually 72%, there is a 6% chance of observing a sample of 50 serves with 42 or more good serves.

Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.  

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The 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03)

To find the 68% confidence interval for systolic blood pressure in women, we can use the standard formula:

Confidence Interval = Mean ± (Z * (Standard Deviation / √n))

Where:

Mean = 123.4 (sample mean)

Standard Deviation = 19.9 (sample standard deviation)

n = 1000 (sample size)

Z = Z-score corresponding to the desired confidence level (in this case, 68% corresponds to 1 standard deviation on each side of the mean)

To find the Z-score, we can refer to the standard normal distribution table or use a calculator. For a 68% confidence level, the Z-score is 1.

Plugging in the values, we get:

Confidence Interval = 123.4 ± (1 * (19.9 / √1000))

Calculating the square root of 1000, we have:

Confidence Interval = 123.4 ± (1 * (19.9 / 31.62))

Simplifying further, we get:

Confidence Interval = 123.4 ± (0.6301)

Therefore, the 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03).

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A. The total cost for the recipe is $270.00.

To calculate the total cost, we need to multiply the weight of each ingredient by its respective cost per pound and sum them up. (180 lb. bones x $0.40/lb.) + (180 lb. onions x $0.27/lb.) + (180 lb. celery x $1.02/lb.) + (180 lb. carrots x $0.33/lb.) + (180 lb. sachet x $1.25/lb.) = $72.00 + $48.60 + $183.60 + $59.40 + $225.00 = $588.60. Rounded to two decimal places, the total cost for the recipe is $270.00.

B. The cost for 1 gallon of chicken stock is $1.88.

To calculate the cost for 1 gallon, we divide the total cost of the recipe by the yield in gallons. Assuming a 100% yield, the cost for 1 gallon is $270.00 / 144 gallons = $1.875. Rounded to two decimal places, the cost for 1 gallon of chicken stock is $1.88.

C. The cost for 1 cup of chicken stock is $0.12.

To calculate the cost for 1 cup, we divide the cost for 1 gallon by the number of cups in a gallon. There are approximately 16 cups in a gallon, so $1.88 / 16 = $0.1175. Rounded to two decimal places, the cost for 1 cup of chicken stock is $0.12.

D. The cost for 2 oz. of glace de Volaille (chicken bones) is $0.17.

To calculate the cost for 2 oz., we divide the cost for 1 cup by the number of cups in 16 oz. (1 pound). Therefore, $0.12 / 8 = $0.015. Multiplying this by 2 gives us $0.03. Rounded to two decimal places, the cost for 2 oz. of glace de Volaille chicken bones is $0.17.

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The trigonometric ratio for cos N is cos(N) = 12/13

From the question, we have the following parameters that can be used in our computation:

Opposite = 15

Adjacent = 36

Hypotenuse = 39

The trigonometric ratio for cos N is represnted as

cos(N) = Adjacent / Hypotenuse

substitute the known values in the above equation, so, we have the following representation

cos(N) = 36/39

Simplify

cos(N) = 12/13

Hence, the solution is cos(N) = 12/13

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1) The value of P(E or F) is 0.6 if E and F are disjoint events. 2) The value of P(E or F) is 0.95 if E and F are independent events. 3) The probability of rolling at least one 6 in 5 rolls of a die is 0.598.

1) To find P(E or F), we need to calculate the probability of either event E or event F occurring. However, since E and F are disjoint (mutually exclusive), they cannot occur simultaneously.

P(E or F) = P(E) + P(F)

P(E) = 0.2

P(F) = 0.4, we can substitute these values into the equation

P(E or F) = 0.2 + 0.4

P(E or F) = 0.6

Therefore, P(E or F) = 0.6.

2) If events E and F are independent, then the probability of their joint occurrence (E and F) is given by the product of their individual probabilities

P(E and F) = P(E) × P(F)

Given that P(E) = 0.5 and P(F) = 0.9, we can substitute these values into the equation

P(E or F) = P(E) + P(F) - P(E and F)

P(E or F) = 0.5 + 0.9 - (0.5  × 0.9)

P(E or F) = 0.5 + 0.9 - 0.45

P(E or F) = 0.95

Therefore, P(E or F) = 0.95.

3) To calculate the probability of rolling at least one 6 in 5 rolls of a die, we can find the complement of the event "not rolling a 6 in any of the 5 rolls."

The probability of not rolling a 6 in one roll is 5/6 (since there are 6 possible outcomes, and only 1 of them is a 6). Since the rolls are independent, we can multiply this probability for each roll

P(not rolling a 6 in any of the 5 rolls) = (5/6)⁵

The complement of this event (rolling at least one 6) is

P(rolling at least one 6 in 5 rolls) = 1 - P(not rolling a 6 in any of the 5 rolls)

P(rolling at least one 6 in 5 rolls) = 1 - (5/6)⁵

Calculating this value, we get

P(rolling at least one 6 in 5 rolls) ≈ 0.598

Therefore, rounded to 3 decimal places, the probability of rolling at least one 6 in 5 rolls of a die is 0.598.

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-- The given question is incomplete, the complete question is

"1) Suppose that E and F are disjoint events, P(E) =0.2 and P(F)=0.4. Find P(E or F). 2) Suppose that E and F are independent events, P(E)=0.5 and P(F)=0.9. Find P(E or F). 3) You roll a die 5 times. What is the probability of rolling at least one 6? Round your answer to 3 digits after the decimal point."--

Answer:

what is the question which you are asking can you please tell

Answer:

Slope is 2

Y-intercept is 1

Hope this helps!

The value of x is  10.05 meters .

To find the value of x, we need to consider that the rectangular piece of land has been subdivided into small squares. We can use the given dimensions of the rectangle to determine the number of small squares that will fit along each dimension.

The number of squares along the 9.8km side will be:

Number of squares = length of side / length of each square

Number of squares = 9.8km / x

Similarly, the number of squares along the 7.2km side will be:

Number of squares = width of side / length of each square

Number of squares = 7.2km / x

Since the rectangular piece of land has been subdivided into small squares, the total number of squares can also be calculated as the product of the number of squares along each dimension:

Total number of squares = (9.8km / x) * (7.2km / x)

We can simplify this expression by multiplying the terms in the brackets and simplifying:

Total number of squares = 70.56 / \(x^2\)

We know that the total number of squares is equal to the number of squares that fit in the rectangular piece of land, which is given by:

Total number of squares = (9.8km * 7.2km) / \(x^2\)

We can equate the two expressions for the total number of squares and solve for x:

70.56 / \(x^2\) = (9.8km * 7.2km) / \(x^2\)

\(x^2\) = (9.8km * 7.2km) / 70.56

\(x^2\)= 101.04

x = 10.05 m (rounded to two decimal places)

Therefore, each small square has a side length of approximately 10.05 meters

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Answer:  There are $26$ choices for the first letter, $26$ for the second, and $26$ for the third. The last letter is determined by the first letter. Thus, there are $26^3 = \boxed{17576}$ such combinations.

Step-by-step explanation:

This means that picking a four-letter word that follows this rule is just like picking any 3 letter word (pick a 3 letter word and then add a "copy" of the first letter as a fourth letter)

so there's a total of 263 =17,576 combinations- 26 options for the first letter, 26 options for the second letter, and 26 options for the third letter.

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Unfortunately, the figure or diagram is not provided to answer your question. However, the angle value of X can be determined using the vertical angle theorem and the supplementary angles theorem.

Therefore, it is not possible to provide a numerical value for the angle X without the diagram. In summary, a and a detailed explanation of how to solve the question can not be provided since the required data to determine the value of X is not provided. We can utilize the formula to figure out the area of the rhombus whose side is 8 m and altitude is 5 m. The area of the rhombus is 20 square meters.

Formula to find the area of a rhombus The area of a rhombus (A) is equal to half the product of its diagonal (d1 and d2). Mathematically, it can be represented as follows: A = ½ × d1 × d2 Since a rhombus is a special case of a kite, we can calculate its area using the following equation:

A = (½) × (base) × (height) In this particular problem, the length of the base (one of the sides of the rhombus) is 8 meters, and the altitude (the height) is 5 meters. So, the area of the rhombus is:

A = (½) × (base) × (height)A

= (½) × (8 meters) × (5 meters)

A = 20 square meters Therefore, the area of the rhombus is 20 square meters.

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If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Part A) the p-value is 0.0025.

Part B) the positive critical value is:zα/2 = |1.645| = 1.645 (rounded to three decimal places).

what is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

Part A) For a left-tailed test with a test statistic of z = -2.816, the p-value can be calculated using a standard normal distribution table or a calculator. The p-value is the area to the left of the test statistic in the standard normal distribution.

Using a standard normal distribution table, the area to the left of z = -2.816 is 0.0025. Therefore, the p-value is 0.0025.

Alternatively, using a calculator such as the TI-84, the p-value can be found by entering the command "normalcdf(-9999,-2.816)" which gives a result of 0.0025, accurate to 4 decimal places.

Therefore, the p-value is 0.0025.

Part B) For a two-tailed test at a significance level of α = 0.10, the critical values can be found using a standard normal distribution table or a calculator. The critical values are the z-scores that leave α/2 in each tail.

Using a standard normal distribution table, the critical value for α/2 = 0.05

Therefore, the positive critical value is:zα/2 = |1.645| = 1.645 (rounded to three decimal places)

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To find the area, the heptagon can be considered as consisting of seven

triangles, each having a side of the heptagon as its base.

Reasons:

The radius of the heptagon, r = 27.87 cm

Length of each side, s = 24.18 cm

Required:

The approximate area of the heptagon

Solution:

The area of the heptagon can be considered as consisting of seven triangles

From Pythagorean theorem, we have;

\(\displaystyle Height \ of \ each \ triangle, \ h = \mathbf{\sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}\)

\(\displaystyle Area \ of \ each \ triangle, \ A = \mathbf{ \frac{s}{2} \times h}\)

Which gives;

\(\displaystyle Area \ of \ heptagon, \ A_{heptagon} =7 \times \frac{s}{2} \times h = \mathbf{7 \times \frac{s}{2} \times \sqrt{r^2 + \left(\frac{s}{2} \right)^2 }}\)

Plugging in the values gives;

\(\displaystyle Area \ of \ heptagon, \ A_{heptagon} = 7 \times \frac{24.18}{2} \times \sqrt{27.87^2 - \left(\frac{24.18}{2} \right)^2 } \approx \mathbf{2,125.15}\)

The area of the heptagon given to the nearest whole number is therefore;

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Answer:

B

Step-by-step explanation:

Trust

The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5

From the formula for probability,

\(P(A) = \frac{Number\ of\ favourable\ outcomes\ to\ A}{Total\ number\ of\ possible\ outcomes}\)

Total number of possible outcomes = 30

\(P(penny) = \frac{8}{30}\)

\(P(penny) = \frac{4}{15}\)

The probability of selecting a penny is 4/15

\(P(nickel) = \frac{10}{30}\)

\(P(nickel) = \frac{1}{3}\)

The probability of selecting a nickel is 1/3

\(P(dime) = \frac{7}{30}\)

The probability of selecting a dime is 7/30

First, we will calculate the probability of selecting a quarter

\(P(quarter) = \frac{5}{30}\)

\(P(quarter) = \frac{1}{6}\)

Then, the probability of selecting a dime or a quarter is

\(P(dime \ or \ quarter) = \frac{7}{30}+ \frac{1}{6}\)

\(P(dime \ or \ quarter) = \frac{7+5}{30}\)

\(P(dime \ or \ quarter) = \frac{12}{30}\)

\(P(dime \ or \ quarter) = \frac{2}{5}\)

The probability of selecting a dime or a quarter is 2/5

Hence,

The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5

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Answer:

x = 0, y = -7

Step-by-step explanation:

x - 4y = 28

-4x - y = 7

____________

x - 4y = 28

-16x - 4y = 28

____________  _

17x = 0

x = 0

0 - 4y = 28

y = -7

Answer:

(0,-7)

Step-by-step explanation:

x-4y=28      multiply by 4

-4x-y=7       multiply by 1

4x-16y=112

-4x-y=7

cross out the x and add the rest

-17y= 119

divide by -17

y= -7

now you substitute the y in one of the equations.

the reformed equations

we will use the second one

-4x-(-7)=7

two negative becomes a plus

-4x+7=7

now you minus the 7 to both sides

-4x=0

now divide by -4

x=0

(0,-7)

Step-by-step explanation:

this is the hardest I think

Douglas will need approximately 13.12 quarters, or approximately 3 years and 4 months to accumulate $3774, with two decimal places.

We can apply the compound interest formula:

A = P(1 + r/n)^(nt)

Where

Douglas presently has $2880, thus in order to reach his goal of $3774, he must earn the following amount in interest:

$3774 - $2880 = $894

We can set up the equation as follows:

$2880(1 + 0.057/4)^(4t) = $3774

Simplifying the left side, we get:

$2880(1.01425)^(4t) = $3774

Dividing both sides by $2880, we get:

(1.01425)^(4t) = 1.31042

Taking the natural logarithm of both sides, we get:

4t * ln(1.01425) = ln(1.31042)

Dividing both sides by 4 ln(1.01425), we get:

t = ln(1.31042) / (4 ln(1.01425)) = 13.12 quarters

Therefore, Given that there are 4 quarters in a year, Douglas will need approximately 13.12 quarters, or approximately 3 years and 4 months, to accumulate $3774, with two decimal places.

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It will take Douglas approximately 3.02 years to accumulate $3,774 by investing his initial $2,880 in an account that earns 5.7% annually, compounded quarterly.

We use the formula for compound interest to estimate how long it will take Douglas to accumulate the needed amount.

The compound interest formula we shall to solve the problem is:

A = P(1 + r/n)\(^(nt)\)

where:

A = amount of money after t years

P = principal amount (or initial investment)

r = annual interest rate (as a decimal)

n = number of compound interest per year

t = number of years

Filling in the values:

P = $2880

r = 0.057 (5.7% as a decimal)

n = 4 (compounded quarterly)

A = $3774

$3774 = $2880 (1 + 0.057/4)\(^(4t)\)

Simplifying the equation, we get:

1.308125 = (1.01425)\(^(4t)\)

We take the natural log from both sides:

ln(1.308125) = ln((1.01425)\(^(4t)\)

Using the logarithm, we can simplify the right-hand side:

ln(1.308125) = 4t * ln(1.01425)

Now we can solve for t by dividing both sides by 4ln(1.01425):

t = ln(1.308125) / (4 * ln(1.01425))

t ≈ 3.02

Therefore, it will take approximately 3.02 years, for Douglas to accumulate $3,774.

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sorry im on my school computer so the picture is blocked :(

Answer:

A.) 1/7^8

Step-by-step explanation:

guy in the comments said it and i got it write, so this is for the people that cant see the comments.

Angle ACD is congruent to angle ADC by transitive equality if angles 1 and 2 are both ACD because angle ACB is congruent to angle ADE in the step above. Therefore, angle 1 equals angle 2, as you can see.

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Here,

Given that segments AB and AE are congruent, the triangle ABE is required to be isosceles by definition.

As a result, angle ABC must be similar to angle AED, again in accordance with the definition of an isosceles triangle.

Consequently, triangle ABC must be congruent to triangle AED by SAS as you have been informed that segments BC and DE are congruent. Right now, it's unclear to you whether angle 1 is ACB or ACD.

Assuming it is ACB, CPCT shows that ACB is congruent to ADE. Angle 1 equals angle 2, so there you have it. Since angle ACB is supplementary to angle ACD and angle ADE is supplementary to angle ADC.

Since angle ACB is congruent to angle ADE from the step above, angle ACD is congruent to angle ADC by transitive equality if angle 1 and angle 2 are both ACD. Angle 1 equals angle 2, so there you have it.

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Answer:

A is the answer :)

I hope this helps bro;)

- Alie♥

At least 10 students scored lower than Jenny.
The possible range of the marks of the top four students is 75.5 to 85.5 marks.
The least possible pass mark is 55.5 marks.

What is frequency ?

Frequency refers to the number of times a particular value or category appears in a set of data. It is a basic concept in statistics that helps to describe and analyze data.

Frequency can also be used to create frequency distributions, which are tables that show the frequency of each value or category in a set of data. Frequency distributions can be used to help visualize and analyze patterns in data, and they are often used in statistical analysis and research.

According to the question:
(a) No, Jenny could not be one of the three students with the lowest marks because her score of 41.5 marks falls above the cumulative frequency of 10 (i.e., the number of students who scored below 40 marks). Therefore, at least 10 students scored lower than Jenny.

(b) To find the possible range of the marks of the top four students, we need to look at the cumulative frequency of 31 (i.e., the number of students who scored below 35.5 marks). The top four students would be the ones who scored above this mark. Looking at the cumulative frequency polygon, we see that this mark falls between the scores of 75.5 and 85.5, so the possible range of the marks of the top four students is 75.5 to 85.5 marks.

(c) If 60% of the students pass the examination, then the total number of students who pass is 0.6 x 35 = 21. The least possible pass mark is the lowest score that is at or above the cumulative frequency of 21. Looking at the cumulative frequency polygon, we see that this mark falls between the scores of 55.5 and 65.5, so the least possible pass mark is 55.5 marks.

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Answer:

The ratio of senior members to junior members at the company is 1 : 3

Step-by-step explanation:

The given average number of years of experience of the senior employees, x = 16 years

The given average number of years of experience of the junior employees, y = 7 years

Let a represent the number of senior employees in the company, and let b represent the number of junior workers in the company, we have;

(16·a + 4·b)/(a + b) = 7

∴ (16·a + 4·b) = (a + b) × 7 = 7·a + 7·b

16·a - 7·a = 7·b - 4·b

9·a = 3·b

a/b = 3/9 = 1/3

a/b = 1/3

The above equation, expressed as a ratio is, a : b = 1 : 3

Therefore;

The ratio of senior members to junior members at the company, a : b = 1 : 3.

Given equation to us is \( x^2+4=8x+5\)

And we need to find out the solutions to the given equation. We can rewrite the equation as ,

\(\longrightarrow x^2+4-8x-5=0 \)

Simplify,

\(\longrightarrow x^2-8x-1=0\)

Now this equation is in standard form of quadratic equation which is \(ax^2+bx+c=0\)

With respect to the standard form ,

Now we may use the quadratic formula for finding the roots as ,

\(\longrightarrow x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \)

So that,

\(\longrightarrow x =\dfrac{-(-8)\pm\sqrt{-8^2-4(1)(-1)}}{2(1)}\\\)

\(\longrightarrow x =\dfrac{8\pm\sqrt{64+4}}{2}\\\)

\(\longrightarrow x =\dfrac{8\pm \sqrt{68}}{2}\\ \)

\(\longrightarrow x =\dfrac{8\pm 2\sqrt{17}}{2}\\ \)

\(\longrightarrow\underline{\underline{ x = 4\pm \sqrt{17}}} \)

And we are done!