Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.

Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

[tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

then

[tex]\sqrt{500}[/tex]

= [tex]\sqrt{100(5)}[/tex]

= [tex]\sqrt{100}[/tex] × [tex]\sqrt{5}[/tex]

= 10 × 2.24

= 22.4

-------------------------------

[tex]\sqrt{0.5}[/tex]

= [tex]\sqrt{\frac{50}{100} }[/tex]

= [tex]\frac{\sqrt{50} }{\sqrt{100} }[/tex]

= [tex]\frac{\sqrt{50} }{10}[/tex]

= [tex]\frac{7.07}{10}[/tex]

= 0.707

The base case of [tex]n=1[/tex] is trivially true, since

[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]

but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle

[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]

with equality if [tex]E_1\cap E_2=\emptyset[/tex].

Now assume the case of [tex]n=k[/tex] is true, that

[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]

We want to use this to prove the claim for [tex]n=k+1[/tex], that

[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

The I/EP tells us

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]

and by the same argument as in the [tex]n=2[/tex] case, this leads to

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]

By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

Answer:

Hence the age of Mikhail is 37 and the age of Grabrielle is 47

Answer:

Here;

Gabrielle age= 10yrs older that M..= 16 + 10= 26yrs old.

Sum of their age= 84

Now;

100 - 84

16,,

Using logic concepts, the correct statement is given by:

[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.

The events are:

The statement is:

Henri is wearing a red or blue shirt today with jeans.

A red or blue shirt can be represent by p or not p, that is:

[tex](p \vee \neg p)[/tex]

Jeans is not khaki, hence the second part is:

[tex]\neg q[/tex]

Combining the statements, we have that the expression is:

[tex](p \vee \neg p) \wedge \neg q[/tex]

Since p and q are true, [tex]\neg q[/tex] is false, and the entire statement is false. Hence the correct option is:

[tex](p \vee \neg p) \wedge \neg q[/tex]. FALSE.

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Answer:

5 and a 250,000

Step-by-step explanation:

A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000

Answer:

It is: 5,250,000

The length of PR = 18 .

A chord is a line segment whose both points lie on the circle.

When a chord is extended it is called secant .

When two chords meet outside the circle , the product of length of the secant and its external segment is equal to the product of length of other secant and its external segment.

According to the given data

FR and FP are the secants of the circle

To determine the measure of PR

From the secant theorem

(7+9) * 9 = (5x+8) * 8

16 * 9 = (5x+8) *8

2 *9 = 5x+8

18 = 5x+8

5x = 10

x = 2

Therefore the length of PR = 5x+8 = 10+8 = 18

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:2x - 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: (f - g)(x)[/tex]

[tex]\qquad \tt \rightarrow \: f(x) - g(x)[/tex]

Simple procedure :

[tex]\qquad \tt \rightarrow \: 3x - 1 - (x + 2)[/tex]

[tex]\qquad \tt \rightarrow \: 3x - 1 - x - 2[/tex]

[tex]\qquad \tt \rightarrow \: 3x - x - 1 - 2[/tex]

[tex]\qquad \tt \rightarrow \: 2x - 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The statements that are true from the graph are:

Given the graph, we can note some things:

c is the value of the y- coordinates the line passes through.

The line passes through (0, 4 ) with a y- coordinate of 4

Therefore, the equation of the line of y= 4

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The logical conclusion from the statement is that

B. The opposite sides of a rhombus are congruent.

From the information given, if shape is a parallelogram, then opposite angles are congruent.

In this case, since the rhombus is a parallelogram, then the opposite sides of a rhombus are congruent.

In conclusion, the correct option is B.

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Answer:

x = 4

Step-by-step explanation:

6x - 8 = 16 (add 8 to both sides)

6x = 24 (divide by 6 on both sides)

x = 4

Brainliest, please :)

Step-by-step explanation:

6x=16+8

6x=24

6x/6=24/6

x=4

so the answer is 4

If he picks 1965, then the Gross earning will be $85.55.

The missing part of the question is given below.

If he picks 1965, then Calculate the Gross earning.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Calculate the gross earning for an apple picker based on the following differential pay scale:

     1 – 1000: $0.03 each

1001 – 1600: $0.06 each

  over 1600: $0.07 each

Total apples picked by Lindbergh = 1965

So, for 1000 apples, he will get =1000 × 0.03 = $30

Now, remaining apples = 1965 – 1000 = 965

Now for next 600 apples (from 1001-1600), he will get = 600 × 0.05 =$30

Now, remaining apples = 965 – 600 = 365

So, for remaining 365 (above 1600) apples, he will get = 365 × 0.07 = $25.55

So, total gross earning = $30 + $30 + $25.55

⇒ $85.55 is total gross earning

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The worker's expected weekly bonus is $30.0

The amounts and the probabilities are given as:

x    $10       $50

P(x)  0.75    0.25

The worker's expected weekly bonus is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

E(x) = $10 * 0.75 + $50 * 0.25

Evaluate the product

E(x) = $17.5 + $12.5

Evaluate the sum

E(x) = $30.0

Hence, the worker's expected weekly bonus is $30.0

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The two transformations for fx and gx would be to shift by 6 units and also go up by 18.

This is the term that is used in mathematics to describe the manipulation of a line or a shape.

a. The possible transformations that can be gotten here would be to shift to the left by 6 units from what we have in the graph and also shift to the top by 18.

g of x = f(x - k) then

g(x)= f(x) + k

C. The value of k should be based on the way it changes based on the given points.

Vertically, g(x)=f(x) +18

Horizontally , g(x)=f(x-6)

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Answer:

Unknown

Step-by-step explanation:

Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!

hope this helps :)

Answer:

[tex]\boxed {192 cm^{2}}[/tex]

Step-by-step explanation:

Find the volume of separate cuboids :

Volume (top cuboid) :

⇒ V = 2 x 6 x (10 - 2)

⇒ V = 12 x 8

⇒ V = 96 cm²

Volume (lower cuboid) :

⇒ V = 8 x 6 x 2

⇒ V = 48 x 2

⇒ V = 96 cm²

Volume (prism) :

⇒ 96 + 96

⇒ 192 cm²

Answer:

4

Step-by-step explanation:

[tex] \frac{9 - 1}{3 - 1} = 4[/tex]

The average rate of change on the interval [3, 9] will be 4.

The average rate of change between two points is given by the slope formula:

 m = average rate of change = (y2 -y1)/(x2 -x1)

The sequence an = 1(3)n − 1 is graphed below:

 m = (9 -1)/(3 -1) = 8/2

 m = 4

The average rate of change on the interval [3, 9] will be 4.

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Answer:

6

Step-by-step explanation:

the blue factors are all the factors 12 and 18 have in common.

An undefined term in geometry is (b) A term that has no formal definition, but is used to define other terms

In geometry, there are four undefined terms.

These terms are:

The above items do not have a specific or formal definition. However, they are used to define other terms in geometry

This is the reason they are referred to as undefined terms.

Hence, an undefined term in geometry is (b)

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Answer:

AC = 2x - 13 Cm

BC = 3x + 4 Cm

AB = 36 Cm

AB = AC + BC

BC = AB - AC

= 36 - (2x - 13)

= 36 - 2x + 13

= 49 - 2x

but, BC = 3x + 4

so equating both the equation we get

3x + 4 = 49 - 2x

3x + 2x = 49 + 4

5x = 53

x = 53/5

x = 10.6

BC = 49- 10.6*2

= 49- 21.2

= 27.8 CM

Answer:

BC = 31 cm

Step-by-step explanation:

from the diagram

AC + CB = AB ( substitute values )

2x - 13 + 3x + 4 = 36

5x - 9 = 36 ( add 9 to both sides )

5x = 45 ( divide both sides by 5 )

x = 9

then

BC = 3x + 4 = 3(9) + 4 = 27 + 4 = 31 cm

Answer:

p = 2

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]

[tex](8^{9}) ^{2}[/tex] = [tex]8^{9(2)}[/tex] = [tex]8^{18}[/tex]

so value of p = 2

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

Answer:

5

Step-by-step explanation:

We need to isolate the variable, aka make y on one side. So, if we divide 8 on both sides, it will be

y8=40

y8/8=40/8

y=5

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

Here we have the quadratic function:

[tex]f(x) = -x^2 - 4x + 5[/tex]

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

[tex]f(x) = -x^2 - 4x + 5[/tex]

So the vertex is at:

[tex]x = 4/(2*-1) = -2\\[/tex]

Then the y-value of the vertex is:

[tex]f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9[/tex]

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

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Answer: 20/63

Step-by-step explanation:

Multiplying these probabilities, we get (16/28)(15/27) = 20/63

Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

The opening price of the stock in the beginning of the day will be $75.

The quantity of anything is stated as though it were a fraction of a hundred.

The stock of Company A lost 2% today to $73.50.

Let x be the opening price of the stock in the beginning of the day.

Then the opening price of the stock in the beginning of the day will be

0.98 · x = 73.5

         x = 73.5 / 0.98

         x = $75

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Answer:

33

Step-by-step explanation:

3² = 3.3 = 9 => 24 + 9 = 33