A pension fund owns 11,000 shares in a stock mutual fund and a bond mutual fund. Currently the stock fund sells for $12 per share and the bond sells fund sells for $15 per share. How many shares of each does the pension fund own if the value of the securities is $150,000?

Fund owns:
Stock fund shares
Bond fund shares

​

The completed blanks in Nyala's solution that is used to prove that the measure of angle x is 40° is as follows;

If we perform a 180° rotation about the point O the following happens

Ray \(\overleftrightarrow{EF}\) maps unto ray \(\overleftrightarrow{GH}\)

Ray \(\overleftrightarrow{GH}\) maps unto ray \(\overleftrightarrow{FE}\)x

\(\overleftrightarrow{FG}\) maps unto itself

Therefore, the image of angle x will be exactly where the pre-image of 40° was. Since rotation preserve angle measure, the measure of angle x must be 40°.

The measure of an angle is the degree of rotation between the initial side and the terminal side of the angle.

The details of the method Nyala used to prove that the measure of the angle x is 40° can be found as follows;

The rotation of a line 180° about the center of the line maps onto itself, and the rotation of a line about a non colinear point, is parallel to the original line.

Whereby the center of rotation of the line \(\overleftrightarrow{EF}\) is equidistant from both the line \(\overleftrightarrow{GH}\) which is parallel to the line \(\overleftrightarrow{EF}\), the image of the line \(\overleftrightarrow{EF}\) maps to the line \(\overleftrightarrow{GH}\) following a 180° rotation about the point O, and the rotation of the line \(\overleftrightarrow{FG}\) about the point O maps unto itself, such that the angle x maps to the angle 40°, therefore;

∠x ≅ 40° (A rotation transformation is a rigid transformation)

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Answer:

-18000000

Step-by-step explanation:

Don't even ask the zeros hurt me.

It's probably wrong isnt it

Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

Answer:

The expected value of a ticket is of -$5.

Step-by-step explanation:

The expected value of the ticked is the probability of earning each prize multiplied by the prize, and subtracted by the value of the ticket.

Value of the ticket:

$10.

100 tickets are sold. They will award one first prize of $300, one second prize of $150, and one third prize of $50.

Thus, 1/100 probability of earning $300, 1/100 probability of 150 and 1/100 probability of 50. So

\(E = \frac{1}{100}300 + \frac{1}{100}150 + \frac{1}{100}{50} - 10 = 3 + 1.5 + 0.5 - 10 = -5\)

The expected value of a ticket is of -$5.

Answer:

the answer is 67.4545454545

Step-by-step explanation:

Answer:

B) It is irrational and equal to \( = 4\sqrt{2} \)

Step-by-step explanation:

The expression, \( \sqrt{18} + \sqrt{2} \) , is an irrational expression because it contains two irrational numbers, \( \sqrt{18} \) and \( \sqrt{2} \) . Both number are not perfect square. there is no whole number that would be squared that will give you 18 nor 2.

The expression can be equals the following:

\( \sqrt{18} + \sqrt{2} \)

\( = \sqrt{9*2} + \sqrt{2} \)

\( = \sqrt{9}*\sqrt{2} + \sqrt{2} \)

\( = 3\sqrt{2} + \sqrt{2} \)

\( = 4\sqrt{2} \)

Answer:

4 root 2

Step-by-step explanation:

Answer:

no the relation is not a function because it has -2 for two functions its supposed to be 1 input and 1 output

Step-by-step explanation:

Answer:

Option D) 5

Step-by-step explanation:

In the given graph of a parabola, and the equation in vertex form, y = (x - k )²: The variable k represents the x-coordinate of the vertex, and the point where the axis of symmetry lies on the graph.  In the given graph, the vertex is the minimum point, occurring at point (5, 0). The x-coordinate of the vertex is also the value of k = 5.

Therefore, the correct answer is Option D) k = 5.

Answer:

4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

2x - (4y - 3) + 5xz

x = -3

y = 2

z = -1

Step 2: Evaluate

Answer:

Vertex is (-3,2)

Step-by-step explanation:

The vertex is either the absolute minimum or maximum of a function, depending on how the function opens.

In this case, since this absolute value function opens upward, the vertex is the absolute minimum of the function, which is found at (-3,2).

Therefore, the vertex of the absolute value graph is (-3,2).

Answer:

12.5pages

Step-by-step explanation:

50pages ×6hours=300 and then we divide by 8 to get 37.5(the number of pages printed by david in 6 hours)

subtract 37.5 from 50 to find the number of pages printed by andy

Answer:

Its normal value would be 50 beats per minute.

Step-by-step explanation:

20% = 10bpm

40% = 20bpm

60% = 30bpm

80% = 40bpm

100% = 50bpm

we must multiply 3 four times

The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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════════ ∘◦❁◦∘ ════════

════════════════════

y = -2x² - 8x + 3

════════════════════

#First, find the x coordinate first by using the formula of -b/2a

x = -b/2a = -(-8)/2(-2) = 8/-4 = -2

#After getting the x, find the y

y = -2(-2)² - 8(-2) + 3

y = -2×4 +16 + 3

y = -8 + 16 + 3

y = 11

So the vertex is

(-2,11)

════════════════════

Answer:

the vertex is (-2, 11)

Step-by-step explanation:

F(x) = -2X^2 - 8X + 3 can be rewritten as -2(x^2 + 4x) + 3.

We complete the square of x^2 + 4x, obtaining x^2 + 4x + 4 - 4 = (x + 2)^2 - 4

and then we substitute this last result into F(x) = -2(x^2 + 4x) + 3:

F(x) = -2[ (x + 2)^2 - 4 ] + 3, which simplifies to:

F(x) = -2(x + 2)^2 + 8 + 3, or F(x) = -2(x + 2)^2 + 11

Comparing this to the vertex equation (x + h)^2 + k, we see that h must be -2 and k must be 11.  

Thus, the vertex is (-2, 11).

The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

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Answer:

andrew gets 15 dollars a hour

and andr

Answer:

\(y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)\)

OR

\(y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\)

Step-by-step explanation:

Hi there!

Point-slope form: \(y-y_1=m(x-x_1)\) where \((x_1,y_1)\) is a point and \(m\) is the slope

1) Determine the slope

\(m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}\) where two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (-2, 6) and (3,-2):

\(m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}\)

Therefore, the slope of the line is \(-\frac{\displaystyle 8}{\displaystyle 5}\). Plug this into \(y-y_1=m(x-x_1)\):

\(y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)\)

2) Plug in a point \((x_1,y_1)\)

\(y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)\)

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

\(y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)\)

OR

\(y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\)

I hope this helps!

Answer:

Step-by-step explanation:

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

Answer:

total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils

= 17 pencils

P (g n y) = 4/17 + 8/17

= 0.706

Step-by-step explanation:

1. first find the total number of pencils

2. since there is a replacement the demoinator remains the same

3. find the probability of each green and yellow

4. add the two probability

Answer:

10145

Step-by-step explanation:

5 times 950 equals 4750

and 6.5 times 830 equals 5395

add first and second value

4750 + 5395 equals 10145

there is no arguing

Answer:

10145 km

Step-by-step explanation:

Time x speed = Distance

5 x 950 = 4750

6.5 x 830 = 5395

add together = 10145

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Answer:

The image is (-16,-14)

Step-by-step explanation:

Given

Represent the point with A

\(A = (-8,-7)\)

\(Scale\ factor = 2\)

Required

Determine the image (A')

The image is calculated as:

\(A' = A * Scale\ factor\)

\(A' = (-8,-7) * 2\)

So, we have:

\(A' = (-8* 2,-7* 2)\)

\(A' = (-16,-14)\)

Hence, the image is (-16,-14)

Answer:

dddddddddv

Step-by-step explanation:

Answer:

1 2 3

Step-by-step explanation:

Answer:

x not given

therefore no answer for x

Answer:

The answer to the question is Sixteen.

Answer:ok so 133 monkey

Step-by-step explanation:

Answer:

133 and a monkey ^w^

Step-by-step explanation:

Brainliest maybe? owo

Answer:

there is no circle

Step-by-step explanation:

you can add a photo with the lil link looking thing when you first ask the question

Answer:

srry no circle. I'd be happy to help if you update it tho.

Step-by-step explanation: