The Sine Function

If you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?

Let x be the amount invested at 10%;

SO we have;

.10x=amount invested at 10%

(4000-x).12=amount invested at 12%

So our equation would be;

.10x+(4000-x).12=460

Distribute the 12%;

.10x+480-.12x=460

Put like terms together so you can see them better;

.10x-.12x+480=460

-.02x+480=460;

subtract 480 from both sides;

-.02x=-20

Multiply each side by -.02;

x=1000

Now that we know what was invested at 10% we can subtract that from $4000 to get what was invested at 12%;

$4000-$1000=$3000

Hope you understand

=)

Answer:

The first law: multiplication. If the two terms have the same base (in this case. ...

The second law: division. If the two terms have the same base (in this case. ...

The third law: brackets. If a term with a power is itself raised to a power then the powers are multiplied together. ...

Negative powers. ...

Power of zero. ...

Fractional powers.

Step-by-step explanation:

Answer:

Grapes are less expensive

Step-by-step explanation:

First, find how much money 1 pound of each fruit is:

Bananas: $1.47 / 3 = $0.49

Grapes: $1.18 / 2 = $0.59

Compare:

0.49 < 0.59

So grapes are less expensive

Answer:

G. 25%

Step-by-step explanation:

given : The price of a video game was reduced from $60 to $45 .

$60 - $45 = $15

then, the percentage was the price of the video game reduced :-

reduction in price/previous price x 100 = 15/60 x 100 = 25%

the percentage was the price of the video game reduced = 25%

Answer: You get to keep 1,673.24

You pay 272.38 in taxes.

Answer: Section formula

Step-by-step explanation:

Given

The line segment AB with endpoints [tex]A(2,2)[/tex] and [tex]B(14,14)[/tex] is divided by a point X in the ratio 1:2

To verify that X divides the line segment in the ratio 1:2, we will use section formula. Section formula tells the coordinates of the point which divide the line segment in the certain ratio or vice-versa.

We will assume that X divides AB in k:1 and insert the values in the section formula. If the ratio k:1 comes out to be 1:2, then it verifies the claim.

Step-by-step explanation:

The parabola has a line of symmetry at x=0 so that means we can reflect the function across the y axis and it will remain unchanged so the answer is even function.

Answer:

of the students who live more than one mile

away, about 76% ride a bike.

Step-by-step explanation:

Answer:

He gets 630 dollars a week so the answer is D.

Step-by-step explanation:

[tex]93 \times 22minutes = 2046 \\ \frac{2046}{10} = 204.6minutes[/tex]

Answer:

The average salary  of the Diamondbacks players  does not differ from that of all players in the National League.

Step-by-step explanation:

1) Formulate null and alternate hypothesis

H0: u1= u2 Ha: u1 ≠ u2

The null hypothesis is that the average salary of the Diamondbacks players does not differ from that of all players in the National League

against the claim

that the average salary of the Diamondbacks players differ from that of all players in the National League

The data given is

x1`= $2,308,488,  s1=  $3,427,508   and  n1 = 27

x2`=  $2,585,804,      s2=$3,500,708   and n2 = 27

2) The test statistic is

z= x1-x2/ sqrt( σ1 ²/n1 + σ2²/n2)

Putting the values

z = $2,308,488- $2,585,804/ sqrt( 3,427,508²/27 + 3,500,708²/27)

z= -0.294

3) The significance level is 0.05

The critical region is Z  =±1.96

4) Since the calculated value of z=  -0.294 is less than the z ∝=±1.96 we  do not reject H0.

5) the P-value can be calculated using the calculator.

The p-value is p = 0.7687

The average salary  of the Diamondbacks players  does not differ from that of all players in the National League.

Is this a true or false?

Answer:

50 times in 1 second

Step-by-step explanation:

I don't know what your specific question, but I'm guessing you wanted divide to see how many times they flap their wings in 1 second. :)

Answer:

Purchases are not withdrawn immediately from bank

Step-by-step explanation:

In case of credit cards, purchases are not withdrawn immediately from bank in fact the transaction needs approval and verification from the bank. Once the bank verify with the customer regarding the transaction requested, it will not allow money to flow from one account to other.

Answer:

-3 and -8

Step-by-step explanation:

Let the two numbers be called a and b respectively. We can say that ab=-24, and a+b=-11.

If a+b=-11, a=-11-b.

ab=-24

(-11-b)b=-24

b²+11b+24=0

(b+3)(b+8)=0

b=-3, b=-8

a=-11-b=-11+3=-8

a=-11-b=-11+8=-3

So the numbers are -3 and -8

Answer:

Step-by-step explanation:

8 cm

Answer:

too difficult 99%(95%) fraction and decimal of 26.5 and (-36)

Answer:

1:2 all you have to do is simplify

Answer:

24p

Step-by-step explanation:

I'm pretty sure that this is the answer because the question was "What is the value P(24)?" which means you have to use the commutative property to reorder the terms.

Hope this helped!

Answer: 6r^3 - 15r

Step-by-step explanation:

(3r) (2r^2 - 5)

Distribute.

6r^3 - 15r

Hope this helped.

Answer:

11/8 and 21/16

Step-by-step explanation:

3 x 1 = 3

4 x 2= 8

3/8+3/4(convert to eighth's)

3/8+6/8=11/8

1 1/8 = 9/8

9 x 1 = 9

8 x 2 = 16

9/16+3/4(convert to sixteenth's)

9/16+12/16

21/16

---

hope it helps

=3/4 × 1/2 + 3/4

=3/8 + 3/4

=9/8

2nd questions ans

=1×1/2 + 3/4

=1/2 + 3/4

=5/4

Answer: The width of the rectangle is 10.2 inches, the perimeter is 71.4 inches,  the area is 260.1 inches.

Step-by-step explanation:

25.5/5=5.1

5.1*2=10.2

The width is 10.2 inches

25.5*2+10.2*2=71.4

The perimeter is 71.4 inches

20.5*10.2=260.1

The area is 260.1

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in.

[tex]P=2\times(l+w)[/tex]

where, 'l' is the length of the rectangle

'w' is the width of the rectangle

[tex]A=l\times w[/tex]

For given example,

The sides of a rectangle are in the ratio 2:5

The longer side of the rectangle is 25.5 in.

This means the length of the rectangle is [tex]l=25.5~in.[/tex]

Let 'x' represents the width of the rectangle.

⇒ [tex]\frac{2}{5} =\frac{x}{25.5}[/tex]

⇒ 2 × 25.5 = 5 × 'x'

⇒ 51 = 5x

⇒ x = 51/5

⇒ x = 10.2 in.

This means the width of the rectangle is 10.2 in.

⇒ [tex]l=25.5~in,~w=10.2~in.[/tex]

Using the formula of perimeter of the rectangle,

⇒ P = 2 × (25.5 + 10.2)

⇒ P = 2 × 35.7

⇒ P = 71.4 in.

Using the formula of area of the rectangle,

⇒ A = 10.2 × 25.5

⇒ A = 260.1 sq. in.

Therefore, the width of the rectangle is 10.2 in.

The perimeter of the rectangle is 71.4 in.

The area of the rectangle is 260.1 sq.in.

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Answer:

V≈3619.11cm³

Step-by-step explanation:

Answer:

3619.11 cm³

Step-by-step explanation:

V = πr²h

π · 12² · 8

3619.11 cm³

9514 1404 393Answer:

Step-by-step explanation:

Let c and w represent the per-picture cost of the class picture and a wallet-size picture, respectively. The two packages can be described by ...

  c +10w = 19

  2c +15w = 31

Subtracting the second equation from twice the first, we get ...

  2(c +10w) -(2c +15w) = 2(19) -31

  5w = 7

  w = 1.40

Substituting into the first equation, we can find the cost of a class picture.

  c + 10(1.40) = 19

  c = 5 . . . . . . . . . . . subtract 14

A class picture costs $5; a wallet-size picture costs $1.40.

Answer:

(1)

[tex]a = \frac{3\sqrt 3}{2}[/tex]

[tex]b = \frac{3}{2}[/tex]

(2)

[tex]a = \sqrt 6[/tex]

[tex]b = \sqrt 2[/tex]

Step-by-step explanation:

Solving (1):

Considering

[tex]\theta = 60^o[/tex]

We have:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

This gives:

[tex]\sin(60^o) = \frac{a}{3}[/tex]

Solve for a

[tex]a = 3 * \sin(60^o)[/tex]

[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]

So:

[tex]a = 3 * \frac{\sqrt 3}{2}[/tex]

[tex]a = \frac{3\sqrt 3}{2}[/tex]

To solve for b, we make use of Pythagoras theorem

[tex]3^2 = a^2 + b^2[/tex]

This gives

[tex]3^2 = (\frac{3\sqrt 3}{2})^2 + b^2[/tex]

[tex]9 = \frac{9*3}{4} + b^2[/tex]

[tex]9 = \frac{27}{4} + b^2[/tex]

Collect like terms

[tex]b^2 = 9 - \frac{27}{4}[/tex]

Take LCM and solve

[tex]b^2 = \frac{36 - 27}{4}[/tex]

[tex]b^2 = \frac{9}{4}[/tex]

Take square roots

[tex]b = \frac{3}{2}[/tex]

Solving (2):

Considering

[tex]\theta = 60^o[/tex]

We have:

[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]

This gives:

[tex]\sin(60^o) = \frac{a}{2\sqrt 2}[/tex]

Solve for a

[tex]a = 2\sqrt 2 * \sin(60^o)[/tex]

[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]

So:

[tex]a = 2\sqrt 2 * \frac{\sqrt 3}{2}[/tex]

[tex]a = \sqrt 2 * \sqrt 3[/tex]

[tex]a = \sqrt 6[/tex]

To solve for b, we make use of Pythagoras theorem

[tex](2\sqrt 2)^2 = a^2 + b^2[/tex]

This gives

[tex](2\sqrt 2)^2 = (\sqrt 6)^2 + b^2[/tex]

[tex]8 = 6 + b^2[/tex]

Collect like terms

[tex]b^2 = 8 - 6[/tex]

[tex]b^2 = 2[/tex]

Take square roots

[tex]b = \sqrt 2[/tex]

Answer:

whats this? can you provide more context?

Step-by-step explanation:

Answer:

The answer is in the picture I couldn't type it sorry.

Step-by-step explanation:

Answer:

Unless I'm misunderstanding it should be 100% or 1/1  because something that is 100% likely to happen will always happen.

Step-by-step explanation:

If there is anything else that may change my understanding of this please send it otherwise I hope this helps.

The value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

If event A is certain to occur.

As we know,

From the definition of probability, the ratio of the number of favorable outcomes to the total number of outcomes

The value of the probability lies between 0 to 1 or [0, 1]

If the probability of any event is 0 that means that event cannot happen.

If the probability of any event is 1 that means that event is certain to occur.

Event A is certain to occure.

P(A) = 1

Thus, the value of P(A) is 1 where A is the event that is certain to occur because the probability of any event is 1 which means that event is certain to occur.

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