One is looking to invest 10 thousand dollars among 5 opportunities. Each investment should be integral in units of 500 dollars ($10K = 20 units). A portfolio corresponds to an investment policy. For example, (5,6,3,2,4) is a portfolio that invests 5 units in the first opportunity, 6 units in the second, 3 units in the third, 2 units in the fourth, and 4 units in the fifth opportunity. The investor has to invest all $10K, and at least one unit in each opportunity. The total number of portfolios is:

Answer: Janelle can fill 6 feeders.

Step-by-step explanation:

To find the number of feeders Janelle can fill, we need to divide the total amount of bird food she has by the amount of bird food each feeder can hold.

First, let's convert the total amount of bird food from cups to half-cups:

3 cups / 2 = 6 half-cups

So, Janelle has 6 half-cups of bird food, and each feeder can hold 1 half-cup.

Therefore, she can fill:

6 half-cups / 1 half-cup per feeder = 6 feeders.

So, Janelle can fill 6 feeders.

The two smaller angles are 39 degrees each. The other angle is 106

The measure of the angles would be found using the formula

2*x + 24 = 180

This is because the sum of angles that are in a triangle is = 180

the two equal angles are x + x = 2x

the other angle is 24 greater than 2x

2x + 24 = 180

2x = 180 - 24

2x = 156

x = 78

eaxh of the two equal angles are 78 degrees

while the other angle is 78 + 24 = 106

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.

It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.

Let the number of adults in the group = x

number of adults in the group = y

Total number of  people paid an entry fee = 100

So the equation becomes : x + y = 100

 or x = 100 - y

Cost for adult ticket = $12

Cost for child ticket = $8

Total entry fee paid = $1,056

Second equation = 12x + 8y = 1056

putting value of x from equation 1

12(100 - y) + 8y = 1056

1200 - 12y + 8y = 1056

4y = 144

y = 36

x = 100 - 36 = 64

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Answer:

[tex]6\pi[/tex]

Step-by-step explanation:

There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.

The area of a circle can be calculated using the formula: [tex]A=\pi r^2[/tex] where "r" is the radius, equal to half the diameter.

Since we're dealing with the semi-circles, we can just divide this area by two to get: [tex]A=\frac{\pi r^2}{2}[/tex]

Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.

So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: [tex]A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi[/tex]

One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.

So now let's calculate the area of the inner semi-circle: [tex]A=\frac{\pi (2)^2}{2}=2\pi[/tex]

Now let's just subtract the areas: [tex]8\pi - 2\pi = 6\pi[/tex], so the area is 6 pi

Answer:

Step-by-step explanation:

The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.

If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:

y = -9x + 11

y = -9 * 0 + 11

y = 11

So, the y-intercept of the original graph is (0, 11).

Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:

y = -9x + 14

y = -9 * 0 + 14

y = 14

So, the y-intercept of the new graph is (0, 14).

Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).

Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.

Answer:

j1gru3hek3n

Step-by-step explanation:

bso2jw4usk8

According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.

The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.

Rate of change for Pennsylvania  [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]

Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]

As a result, Nevada's property prices have grown more rapidly.

b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]

c) Pennsylvania[tex]= 42400 + 1092x[/tex]

Nevada[tex]= 53700 + 1816x[/tex]

[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]

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The volume of the composite figure is 12 cubic in.

How to calculate the Volume of Composite Shapes?

Composite shapes have a volume that is made up of basic shapes. We can calculate the volume of the composite shapes using the steps listed below:

Step 1: Break down the compound shape into different components.

Step 2: Determine the volume of each basic shape.

Step 3: Combine the volumes of all the basic shapes.

Step 4: Write the solution in cubic units.

Firstly we can divide the figure into two rectangular prisms A and B. Then add these two to total volume the volumes of each prism.

The volume of prism A = length × width × height

V = 4 * 2 * 1

V = 8 cubic in.

The volume of prism B = length × width × height

V  = 1 * 2 * 2

V = 4 cubic in.

Total volume = volume of prism A + volume of prism B

= 8 cubic in + 4 cubic in

= 12 cubic in

Hence, the volume of the composite figure is 12 cubic in.

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One inequality that is equivalent to 3x<1 and 6x<2 is 3x<1/2.

To see why this is true, we can divide both sides of the second inequality by 2, which gives 3x<1/3. However, we want an inequality that is equivalent to both 3x<1 and 6x<2, so we need to find a common solution.

Notice that if 3x<1, then x<1/3. And if 6x<2, then x<1/3 as well (since 1/3 is less than 2/6). Therefore, the intersection of the solutions for these two inequalities is x<1/3.

But we want an inequality in the form of 3x<a, where a is some constant. To find this value, we need to solve for x in the intersection of the two solutions:

x<1/3

Multiplying both sides by 3 gives:

3x<1

So we can choose a=1/2, which gives us the final inequality:

3x<1/2

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In  linear equation, 2 miles per hour is the rate in miles per hour .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Divide the distance by the time.

(1/5 miles) / (1/10 hour)

= 10(1/5) miles per hour

= 2 miles per hour

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Answer:

B

Step-by-step explanation:

c=d*π

c=8*π

c=25.1 inches

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The measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangles; ∆ABC with hypotenuse = 45 and adjacent = BC, the triangle ∆ADC with hypotenuse = BC and adjacent = 9 with the angle C we can solve for BC as follows:

for ∆ABC;

cosC = 9/BC {adjacent/hypotenuse}

for ∆ADC;

cosC = BC/45 {adjacent/hypotenuse}

9/BC = BC/45

BC² = 9 × 45 {cross multiplication}

BC² = 405

BC = √405 {take square root of both sides}

BC = 20.1246

Therefore, the measure of the length of x is equal to 20.1246 using the trigonometric ratios of cosine for angle C

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Answer:

Rowan collects

3x + 4

Step-by-step explanation:

Maribel collects x sea shells.

Rowan collects 4 more (this is the +4)

than 3 times Maribels (this is the 3x)



Maribel = x

Rowan = 3x + 4

Answer:

its actually 4x + 3

Step-by-step explanation:

Answer:

11 bat and 8 helmets.

Step-by-step explanation:

Let x = the number of bats

Let y = the number of batting helmets

x + y = 19  Rewrite as y = 19 - x

18.25x + 24.50y = 369.75  Multiply by 100

1825x + 2450y = 36975  Substitute 19 - x for y

1825x + 2450(19 -x) = 39675   Distribute the 2450

1825x + 46550 - 2450x = 39675  combine like terms

-625x + 46550 = 39675  subtract 46550 from both sides

-625x = -6875  Divide both sides by -625

x = 11

He bought 11 bats

x + y = 19  Substitute 11 for x to solve for y

11 + y = 19  Subtract 11 from both sides

y = 8

He bought 8 helmets.

The equation is f(x) = -0.4x + 60. The solution has been obtained by using slope - intercept form.

What is slope-intercept form?

The graph of the equation y = mx + b is a line with a slope of m and a y-intercept of b. The form of the linear equation is called the slope-intercept form, and the values of m and b are real integers.

We are given that f(-10) = 64 and f(15) = 54.

So, we get the points as (-10 , 64) and (15 , 54)

Using the slope intercept form, we get

Slope(m) = (54 - 64)/(15 + 10)

Slope(m) = -0.4

We know that y = mx + b

For calculating b. we will put in the values

⇒64 = -0.4(-10) + b

⇒64 = 4 + b

⇒b = 60

From this we get the equation as

f(x) = -0.4x + 60

Hence, the equation is f(x) = -0.4x + 60.

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300 people read neither​ of the papers.

Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental theory in mathematics and can be used as a foundation for all other areas of mathematics.

Total population n(ξ) = 5000

Number of people reading Concord, n(C) = 2800

Number of people reading Guardian, n(G) = 2300

Number of people reading both = n(C ∩ G)] = 400

Number of people reading any of the newspaper = n(C ∪ G)] = n(C) + n(G) - n(C ∩ G) = 2800 + 2300 - 400 = 4700.

Number of people reading none of them is equal to = Total population - Number of people reading any of the newspaper = 5000 - 4700 = 300

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a. The probability that all the marbles are red is calculated as follows:

(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429

So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.

b. The probability that none of the marbles are red is calculated as follows:

(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696

So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.

Answer: 5.26

Step-by-step explanation:

Answer:

= 0.190

Solution:

Change the divisor 2.63 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.

We then have the equations:

50 ÷ 263 = 0.190

and therefore:

0.5 ÷ 2.63 = 0.190

Both calculated to 3 decimal places.

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Answer: 12.8 cm

Step-by-step explanation:

Multiply 3.2 by the scale of 4 to get 12.8.

Answer:

the IQR is the best measure which equals 16

Step-by-step explanation:

the 2nd option is not correct because, while the range is 45, there are only two out of eleven data items above 45, which is not representative of the majority of the data

the 3rd option is incorrect because the IQR does not equal 45, it's 16

the 4th option is incorrect because the range does not equal 16, it's 45

The null hypothesis H0 in this case would be that the standard deviation of the number of accidents per day is equal to 0.04, while the alternative hypothesis Ha would be that the standard deviation of the number of accidents per day is not equal to 0.04.

The null hypothesis represents the status quo or the default assumption, which is that there has been no change in the standard deviation of the number of accidents per day. The alternative hypothesis represents the claim made by the actuaries, which is that there has been a change in the standard deviation.

Mathematically, the null and alternative hypotheses can be expressed as follows:

H0: σ = 0.04

Ha: σ ≠ 0.04

where σ represents the standard deviation of the number of accidents per day.

The hypothesis test would be used to determine whether there is evidence to support the actuaries' claim that the standard deviation has changed, or whether there is not enough evidence to reject the null hypothesis that the standard deviation remains equal to 0.04.

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

g(x) = 4ˣ

The function is shifting up 2 and shifting right 5. Then the function is given as,

g(x) = 4⁽ˣ⁺⁵⁾ + 2

The function after reflecting over the x-axis is given as,

- g(x) = 4⁽ˣ⁺⁵⁾ + 2

g(x) = - 4⁽ˣ⁺⁵⁾ - 2

And then horizontally compressing by a factor of 5. Then the function is given as,

f(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

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Answer:

6)  x = 6

7) x = 4

8) x = 4

9) x = 6

10) x = 6

Step-by-step explanation:

This is based on Dr. Henry Borenson's method of using pawns to explain algebraic equations.  Frankl I find using variables more intuitive

Let each pawn represent an x in the equations

6.
x + 8 = 10 + 4

x = 10 + 4 - 8

x = 14 - 8 = 6

7.  

x + x = 4 + x
2x = 4 + x
2x - x = 4

x = 4

8.

x + x + x + 2 = 7 + 7
3x + 2 = 14

3x = 14 - 2

3x = 12

x = 12/3

x = 4

9.

2x + 4 = x + 10

2x - x = 10 - 4

x = 6

10

3x = x + 10 + 2

3x = x + 12

3x - x = 12

2x = 12

x = 6

Answer:

0.89

Step-by-step explanation:

As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89

Answer:0.89

Step-by-step explanation:

G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.

Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.

As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.

Since f(x) = axe + b is the typical slope-intercept form of a linear function,

an is the slope (rate of change), and b is the y-intercept (initial value).

g = -12x + 100 is the necessary linear function, which is what has been presented.

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Explanation:

Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.

Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.

Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.

The result of the command should be 350

To verify you can manually add up the values to check the answer is correct.

Answer:

X = 7+2+5+9+6+10+9+8+4

X= 50

Y = 2+5+7+4+2+9+9+4+10

Y = 52

Now ,

Σ(xy)= 50×52

= 2600

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