Four students took an exam the fraction of the total possible points that each received is given which students had the highest score. If students receive a whole number of points on every exam item can the exam be worth 80 points

Answer:

x =  \(\frac{-6}{7+\sqrt{13}}\)

r =  \(\frac{1+\sqrt{13} }{2}\)

Step-by-step explanation:

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio.

For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

-----

Let's take r=ratio of the geometric sequence

in first term, x is multiplied by  \(r^{0}\)

First term:                   x \(r^{0}\)

Second term: 4x+3 = x \(r^{1}\)

Third term:     7x+3 = x \(r^{2}\)

From the last 2 equation, we have to obtain r and x values.

Second equation - First equation:

3x = x r (r - 1)

Let's state: x different from 0, so we can simplify x, obtaining:

3 = \(r^{2}\) - r

0 = \(r^{2}\) - r - 3

r =  \(\frac{1+\sqrt{13} }{2}\)  (only the positive value of r counts)

so, going to second term of the sequence:

4x+3 = x \(r^{1}\) => x (4 - \(\frac{1+\sqrt{13} }{2}\) ) = -3

x (\(\frac{7+\sqrt{13} }{2}\) ) = -3  =>  x =  \(\frac{-6}{7+\sqrt{13}}\)

hope it helps..

The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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Answer:

3

Step-by-step explanation:

\(1 \div \frac{2}{6} \\ \\ = 1 \times \frac{6}{2} \\ \\ = 1 \times 3 \\ \\ = 3\)

a) The statement " The intersection of two events A and B can be larger than the union of the same two events A and B" is False.

b) The statement " The probability of a single event A must be smaller than or equal to the union of two events A and B" is False.

c) The statement " The condition probability of A given B must be smaller than the intersection of the same two events A and B"  is False.

(a) False. The intersection of two events A and B represents the set of outcomes that are common to both A and B, while the union of the same two events A and B represents the set of outcomes that belong to either A or B or both. Hence, it cannot be larger than the union of A and B.

(b) False. The probability of an event A must be between 0 and 1 (inclusive), while the union of two events A and B represents the set of outcomes that belong to either A or B or both. The probability of the union of A and B is the sum of the probabilities of A and B, which can be larger than the probability of A.

(c) False. The conditional probability of A given B, denoted as P(A|B), represents the probability of event A occurring given that event B has already occurred.  Since the intersection of A and B must be less than or equal to 1, the conditional probability of A given B must also be less than or equal to 1.

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Answer:

40 liters of 30% solution.

20 liters of 60% solution.

Step-by-step explanation:

Let x = amount of 30% solution.

Let y = amount of 60% solution.

Equation of amounts of solutions.

x + y = 60

Equation of amounts of alcohol in the solutions.

0.3x + 0.6y = 0.4 × 60

x = 60 - y

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

x + y = 60

x + 20 = 60

x = 40

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Let 30% solution = m

Let 60% solution = n

Now,

A scientist needs 60 liters of a 40% solution of alcohol.

He has a 30% solution and a 60% solution available.

This means,

m + n = 60 _____(1)

30% of m + 60% of n = 40% of 60

0.30m + 0.60n = 0.40 x 60

0.30m + 0.60n = 24 ____(2)

From (1) and (2) we get,

m + n = 60

m = 60 - n _____(3)

Putting (3) in (2) we get,

0.30m + 0.60n = 24

0.30(60 - n) + 0.60n = 24

18 - 0.30n + 0.60n = 24

18 + 0.30n = 24

0.30n = 24 - 18

0.30n = 6

n = 6/0.30

n = 20

Putting n = 20 in (3) we get,

m = 60 - 20

m = 40

Now,

The number of liters of the 30% solution is 40.

The number of liters of the 60% solution is 20.

Thus,

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

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The simplified sum of the second and forth integers are; -1 + 5 = 4

An integer is defined as a whole number that can be positive, negative, or zero. Examples of integers are: -7, 2, 9, 18, 125, and 9803

Now, we are given the consecutive integer sequence as;

x, 1, 3, 5

Now, since the integers are consecutive, then the common difference is the same. Thus;

1 - x = 3 - 1

1 - x = 2

x = 1 - 2

x = -1

Sum of first and fourth term = -1 + 5 = 4

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Answer:

Step-by-step explanation:

the objects which have less density than water will float

and the objects which have more density than the density of liquid will sink in liquid or will not float.

Answer:

option c is the correct answer

first take y raised to the power 4 common then cancel its power by y raised to the power 3

you get your answer

Answer:

16 Times Greater

Step-by-step explanation:

Smaller cylinder:

radius = 6 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)6^2(8)

radius = 24 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)24^2(8)

.

[(3.14)6^2(8)] / [(3.14)24^2(8)]

[6^2(8)] / [24^2(8)]

[6^2] / [24^2]

[36] / [576]

16 times greater

Answer:

Step-by-step explanation:

Smaller cylinder:

h = 6 ft

r = 6 ft

Volume of smaller cylinder = πr²h

                                             = π * 6 * 6 * 6 cubic ft

Bigger cylinder:

r = 6 * 2 = 12 ft

h = 6 ft

Volume of bigger cylinder = π * 12 * 12 * 6 cubic ft

Volume of bigger cylinder = π * 12 * 12 * 6

Volume of smaller cylinder    π * 6 * 6 * 6

                                           = \(\frac{2 * 2}{1*1}\\\)

                                           = 4 : 1

The volume of greater cylinder is 4 times than the smaller cylinder.

Answer:

hmmm I guess it has to be e. if I 'm wrong

Answer:

17.137193922

Step-by-step explanation:

I did the math and got this

\(\bf{Tan\left(\dfrac{2\pi}{3}\right) }\)

Apply the reference angle to find the angle with the equivalent trigonometric values in the first quadrant. Make the expression negative because the tangent is negative in the second quadrant.

\(\bf{-tan\left(\dfrac{\pi}{3}\right) }\)

The exact value of \(\bf{tan\left(\dfrac{\pi}{3}\right) \ is \ \sqrt{3} }\).

\(\bf{-\sqrt{3} }\)

The result can be displayed in multiple ways.

Exact form:

\(\bf{-\sqrt{3} }\)

Decimal form:

-1.73205080...

\(\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

Using the percentage principle, the estimated and actual sale price of the Home are $275, 000 and $307,000 respectively.

Estimated commison = $8250

Let Estimated sale price = P

3% × P = 8250

0.03p = 8250

p = 8250 / 3

p = $275000

Actual commission earned = $9210

Let Actual sale price = P

3% × P = 9210

0.03p = 9210

p = 9210 / 3

p = $307,000

Therefore, the estimated and actual sale price are $275,000 and $307,000 respectively.

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The length of the arc on a circle of mentioned radius intercepted by the central angle is 3π feet.

The formula to calculate the arc angle from radius and central angle is simply by finding their product. The formula for arc length is -

S = r×theta, where r is radius and theta is the central angle

Now we are given angle in degree and we need to convert it in radian. So the formula is -

Central angle = 60 × π/180

Central angle = π/3 radians

Keep the values in formula

S = 9 × π/3

Performing division

S = 3π

Thus, the arc length is 3π.

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Answer:

(a)

\(\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

(b)

\(\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right]\)

1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal will give the desired mixture.

Step-by-step explanation:

Given the mixture of cereals below:

\(\left|\begin{array}{c|c|c}&$General Mills &$Quaker \\$Nutrient&$Cherrios &100\% $Natural Cereal\\----&---&---\\$Calories&110&130\\$Protein (g)&4&3\\$Carbhydrate (g)&20&18\\$Fat (g)&2&5\end{array}\right|\)

Suppose a mixture of these two portions of cereals is to be prepared that contain exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat.

(a)Let x be the number of servings of Cheerios

Let y be the number of servings of Natural Cereal

From the table above, we have

\(110x+130y=295\\4x+3y=9\\20x+18y=48\\2x+5y=8\)

Then a vector equation for this problem is:

\(\left[\begin{array}{ccc}110\\4\\20\\2\end{array}\right] x+\left[\begin{array}{ccc}130\\3\\18\\5\end{array}\right] y=\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

(b) Next, we obtain an equivalent matrix equation of the data

\(\left[\begin{array}{ccc}110&130\\4&3\\20&18\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}295\\9\\48\\8\end{array}\right]\)

This is of the form AX=B. To solve for X we, therefore have an equivalence matrix:

\(\left[\begin{array}{ccc}110&130&295\\4&3&9\\20&18&48\\2&5&8\end{array}\right]\)

Next, we row reduce the matrix using a calculator to obtain the matrix:

\(\left[\begin{array}{ccc}1&0&1.5\\0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

Therefore:

1x+0=1.5

0x+y=1

x=1.5 and y=1

To get the required mixture, we use 1.5 servings of cheerios and 1 serving of Quaker 100% natural cereal.

Answer:

6,12,18,24,30,36,42,48,54,69

Answer:

she runs 2 miles

Step-by-step explanation:

basic math

Answer:

$9.08

Step-by-step explanation:

A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:

a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.

The z-score formula is given by: z = (x - μ) / σ

where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).

z = (5 - 10) / 3 = -5/3 ≈ -1.67

Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.

b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.

z = (10 - 10) / 3 = 0

The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.

c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.

z1 = (8 - 10) / 3 = -2/3 ≈ -0.67

z2 = (12 - 10) / 3 = 2/3 ≈ 0.67

Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.

d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.

The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.

Now, we can convert the z-score back to the original time scale:

z = (x - μ) / σ

-0.84 = (x - 10) / 3

Solving for x, we have:

-0.84 * 3 = x - 10

-2.52 = x - 10

x = 10 - 2.52

x ≈ 7.48

Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.

In summary:

a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.

b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%

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Answer:

-8

Step-by-step explanation:

adding a negative makes it subtraction

so -5-2=-7

-7+1=-6

-6-2=-8

Answer:

352sq.cm.

Step-by-step explanation:

There are a total of 5 cubes.

To find the surface area of the corner cubes, we have have to multiply 4^2 * 5 because one of the surface is attached to the other cube's surface. 16*5 is one cube's surface area, so times 2 gives us 160.

To find the surface area of the cubes in the middle, we have to multiply 4^2 * 4 because two of their sides are attached to other cube's side. So 16*3 = 64 and we have 3 of them so it's 192.

Now adding all the surface area, 192 + 160, we get a total of 352 for the surface area of that figure.

Answer:

constant is - 19

Step-by-step explanation:

the constant is the term in an expression with no variable attached to it.

12r + \(\frac{r}{2}\) - 19

the only term without the variable r attached to it is - 19

then the constant term is - 19

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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The absolute value inequality that models the function is given by:

\(|x| = x, x \geq 0\)

\(|x| = -x, x < 0\)

In this problem, the leading candidate will receive 52% of the votes with a margin of error of no more than 5%. Hence, the difference between his percentage of votes x and 0.52 should be at most plus/minus 0.05, that is:

\(|x - 0.52| \leq 0.05\)

Hence, option b is correct.

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The regression equation is Y = −12.201 + 2.195x.

In the given question,

A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

We have to find the regression equation.

Given that,

Coefficient of Intercept(a) = −12.201

Coefficient of Number of contacts(b) = 2.195

The regression equation is,

Y = a + bx

Y = −12.201 + 2.195x

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The right question is:

A sales manager for an advertising agency believes there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results.

                                    Coefficients       Standard Error       t-Stat      p-value

Intercept                        −12.201                     6.560            −1.860       0.100

Number of contacts         2.195                      0.176             12.505      0.000

What is the regression equation?