You order CDs for $14.25 each and the website charges $4.50 for each shipment.
The expression $14.25p + $4.50 represents the cost of p CDs. Find the total cost for
ordering 4 CDs.

Answer:

22.08 cm

Step-by-step explanation:

Area = pi*r^2*(angle/360)

r=11.04, d=22.08

Answer:

Part A:

[tex]x+y=27 \\4x+y = 45[/tex]

Part B:

Number of vanilla wafers packets bought = 6  and

Number of chocolate wafers packets bought = 21

Step-by-step explanation:

Given:

Cost of each packet of vanilla wafer = $4

Cost of each packet of chocolate wafer = $1

Total number of packets bought = 27

Total money spent = $45

Part A:

To write a system of equations for the given situation.

Here, we do not know the number of packets bought for each type of wafer.

We just know that total number of packets bought and the total money spent in buying those packets.

Let us suppose,

Number of packets of vanilla wafers bought = [tex]x[/tex] and

Number of packets of chocolate wafers bought = [tex]y[/tex]

Total number of packets = Number of packets of vanilla wafers bought Plus Number of packets of chocolate wafers bought:

i.e. [tex]x+y=27 ...... (1)[/tex]

Money spent on vanilla wafers packets = [tex]4 \times x[/tex]

Money spent on chocolate wafers packets = [tex]1 \times y[/tex]

Total money spent = [tex]4x+y = 45 ...... (2)[/tex]

So, the system of equations is:

[tex]x+y=27 \\4x+y = 45[/tex]

Part B:

To find number of packets bought for each flavor = ?

Here, we have two equations and two variables [tex]x[/tex] and [tex]y[/tex].

As, the coefficients of [tex]y[/tex] in both the equations are same.

Let us subtract equation (1) from (2):

[tex]4x+y-x-y=45-27\\\Rightarrow 3x = 18\\\Rightarrow \bold{x =6}[/tex]

By equation (1), putting the value of [tex]x[/tex] and solving for [tex]y[/tex]:

[tex]6+y=27\\\Rightarrow \bold{y =21}[/tex]

So, number of vanilla wafers packets bought = 6  and

number of chocolate wafers packets bought = 21

Answer:

I believe it's D. histogram ; continuous

Step-by-step explanation:

Answer:  (i) 3

(ii) 10

(iii) 1080

Step-by-step explanation:

(i) Coefficient is the number written before any variable.

Coefficient of x in [tex]3x+10=36[/tex] is 3.

(ii) Constant is a numerical term written without any variable.

Constant in [tex]2x+10=5x[/tex] is 10.

(iii) Let x be the number of miles Katie's family drive.

Since they charge $30 combined with $0.25 per mile drive.

So, Total charge = 0.25 x +30 ( in dollars)

If they charged $300, then

[tex]0.25 x +30 =300[/tex]

Subtract 30 from both sides, we get

[tex]0.25x=270[/tex]

Divide both sides by 0.25, we get

[tex]x=1080[/tex]

Hence, Katie drove 1080 miles.

Answer:

c. p(10)=26,327(1+0.024)^10

Step-by-step explanation:

its just the answer

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

The problem is exponential growth.

[tex]a(1+r)^t[/tex]

[tex]a = \sf initial \ amount[/tex]

[tex]r = \sf rate[/tex]

[tex]t= \sf time[/tex]

The third option is right.

[tex]P(10)=26237(1+2.4\%)^{10}[/tex]

[tex]P(10)=26237(1+0.024)^{10}[/tex]

Answer:

Yes, PQR ~ TSV with a scale of 1 : [tex]\sqrt{3}[/tex]

Step-by-step explanation:

Yes the triangles are congruent for the statement given in option C

The scale 1 : [tex]\sqrt{3}[/tex] shows that the side lengths are proportional

PQ/TS = QR/SV

3[tex]\sqrt{3}[/tex]/6/[tex]\sqrt{3}[/tex] and that's simplified as 1/[tex]\sqrt{3}[/tex]

Answer:

[tex]x + y = - 5[/tex]

Step-by-step explanation:

hopefully it is clear and makes sense

:)

Answer:

sinF = [tex]\frac{11}{61}[/tex]

Step-by-step explanation:

sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{EG}{FE}[/tex] = [tex]\frac{11}{61}[/tex]

The ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

In a right angled triangle, the sine of an angle is the length of the side opposite the angle divided by the length of the hypotenuse.

sin θ = opposite side w.r.t θ / hypotenuse

According to the given question

We have

A right angle triangle EFG, in which

∠G = 90 degree

EG = 11

FE = 61

and,  GF = 60

Now, the opposite side with respect to ∠F is GE

and the hypotenuse is EF

Therefore, sine of ∠F = side which is opposite w.r.t ∠F/ hypotenuse

⇒ [tex]sinF=\frac{GE}{EF}[/tex]

⇒ [tex]SinF=\frac{11}{61}[/tex]

Hence, the ratio which represents the sine of ∠F is [tex]\frac{11}{61}[/tex].

Learn more about sine of an angle here:

https://brainly.com/question/13656175

#SPJ2

Answer:

sin C= 5/13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin C= 5/13

1. The first step here is to arrange the data set's form least to greatest,

Sherelle:  26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85

Venita:  44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79

Now we can determine our 5 - number summary based on the numbers respective positions.

First Data Set,

(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85

Second Data Set,

(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79

2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.

3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -

Sherelle:  1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985

Venita:  1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979

( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.

( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,

Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,

Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5

( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.

Answer:

26 is the answer

Step-by-step explanation:

hope this helps you

Answer:

Complementary effect

Step-by-step explanation:

Answer:

1) one and two-thirds hour

2) 2.4 miles

Answer:

I am not good at word problems but I think I found some good examples

Step-by-step explanation:

Durain beans cost $9 per pound and they sold 11 pounds.

Multiply the cost by the amount sold: 9 x 11 = $99

Subtract that from the total sold:

196 - 99 = $97

Now divide the amount left by the cost per pound for Ice cream beans:

97 / 10 = 9.7 pounds.

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] \mathsf{3(2x - 5)}[/tex]

Distribute 3 through the parentheses

⇒[tex] \mathsf{3 \times 2x - 3 \times 5}[/tex]

Calculate the product

⇒[tex]6x - 15[/tex]

Hope I helped!

Best regards!!

Answer:

a. [tex]\mathbf{P(Y \leq 60) = 0.3333}[/tex]

b. P(Y>50) = 0.8889

c. E(y) = 67.5 and  Standard deviation [tex]\sigma[/tex] = 12.99

Step-by-step explanation:

From the information given :

an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to [tex]1\frac{1}{2}[/tex]hours.

The objective is to determine  the probability that the painting time will be less than or equal to an hour?

since 60 minutes make an hour;

[tex]1\frac{1}{2}[/tex]hours = 60 +30 minutes = 90 minutes

Let Y be the painting time of the automobile; then,

the probability that  the painting time will be less than or equal to an hour ca be  computed as :

[tex]P(Y \leq 60) = \int ^{60}_{45} f(y) dy \\ \\ \\ P(Y \leq 60) = \int ^{60}_{45} \dfrac{1}{45} dy \\ \\ \\ P(Y \leq 60) = \dfrac{1}{45} \begin {pmatrix} x\end {pmatrix}^{60}_{45} \\ \\ \\ P(Y \leq 60) = \dfrac{60-45}{45 } \\ \\ \\ P(Y \leq 60) = \dfrac{15}{45} \\ \\ \\ P(Y \leq 60) = \dfrac{1}{3} \\ \\ \\ P(Y \leq 60) = 0.3333[/tex]

What is the probability that the painting time will be more than 50 minutes?

The probability that the painting will be more than 50 minutes is P(Y>50)

So;

[tex]P(Y>50) = \int \limits ^{90}_{50} f(y) dy[/tex]

[tex]P(Y>50) = \int \limits ^{90}_{50} \dfrac {1}{45} dy[/tex]

[tex]P(Y>50) = \dfrac{1}{45}[x]^{90}_{50}[/tex]

[tex]P(Y>50) = (\dfrac{90-50}{45})[/tex]

[tex]P(Y>50) = \dfrac{40}{45}[/tex]

P(Y>50) = 0.8889

Determine the expected painting time and its standard deviation.

Let consider E to be the expected painting time

Then :

[tex]E(y) = \int \limits ^{90}_{45} y f(y) dy \\ \\ \\ E(y) = \int \limits ^{90}_{45} y \dfrac{1}{45} dy \\ \\ \\ E(y) = \dfrac{1}{45} [\dfrac{y^2}{2}]^{90}_{45} \\ \\ \\ E(y) = \dfrac{1}{45}[\dfrac{(90^2-45^2)}{2}] \\ \\ \\ E(y) = \dfrac{1}{45} (\dfrac{6075}{2}) \\ \\ \\ E(y) = \dfrac{1}{45} \times 3037.8 \\ \\ \\ \mathbf{E(y) = 67.5}[/tex]

[tex]E(y^2) = \int \limits ^{90}_{45} y^2 f(y) dy \\ \\ \\ E(y^2) = \int \limits ^{90}_{45} y^2 \dfrac{1}{45} dy \\ \\ \\ E(y^2) = \dfrac{1}{45} [\dfrac{y^3}{3}]^{90}_{45} \\ \\ \\ E(y^2) = \dfrac{1}{45}[\dfrac{(90^3-45^3)}{3}] \\ \\ \\ E(y^2) = \dfrac{1}{45} (\dfrac{637875}{3}) \\ \\ \\ E(y^2) = \dfrac{1}{45} \times 2126.25 \\ \\ \\ \mathbf{E(y^2) = 4725}[/tex]

To determine the standard deviation, we need to first know what is the value of our variance,

So:

Variance [tex]\sigma^2[/tex] = E(x²) - [E(x)]²

Variance [tex]\sigma^2[/tex] = 4725 - (67.5)²

Variance [tex]\sigma^2[/tex] = 4725 - 4556.25

Variance [tex]\sigma^2[/tex] = 168.75

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{variance}[/tex]

Standard deviation [tex]\sigma[/tex] = [tex]\sqrt{168.75}[/tex]

Standard deviation [tex]\sigma[/tex] = 12.99

Answer:

Below

Step-by-step explanation:

5)

The sequence includes the terms 3,6,9,12,15.. and so on

Notice that each time we add 3.

The first term is 3.

We can see it in a different way

● 3 = 3×1

● 6 = 3×2

● 9 = 3×3

● 12 = 3×4

Let 1 be n. Notice what happens

● 3 = 3n

● 6 = 3 × (n+1)

● 9 = 3 × (n+2)

● 12 = 3 × (n+3)

So we can express it as.

● a1 = 3 × 1 =3

● a2 = 3×2 =6

● a3 = 3×3 = 9

So the third term is a3 wich is 9

● a6 = 3×6 = 18

So the sixth term is 18 .

■■■■■■■■■■■■■■■■■■■■■■■■■■

6)

the sequence is defined by:

● f(n-1) = -0.5 f(n)

Repalce n-1 with n and n with n+1

● f(n) = -0.5 f(n+1)

So to get a term you must multiply the next one by -0.5

The first term in the sequence is 120.

● 120 = -0.5 f(n+1)

● f(n+1) = 120/-0.5

● f(n+1) = -60

So the second term is -60

Answer: A.14x + 6; the answer is a polynomial

Step-by-step explanation:

Since all of the variables have integer exponents that are positive this is a polynomial.

Answer:

Step-by-step explanation:

it shows the maximum rise in temperature.

Answer:

b answer, will show the rise in temperature

Answer:

Alice will have to pay $13.33

Ben will have to pay $23.33

Kelvin will have to pay $43.33

Step-by-step explanation:

Given that

Alice destination is 20 miles away

Ben destination is 30 miles away

Calvin destination is 40 miles away.

For a mile, taxi costs 2 dollars.

To find:

How much each person has to pay if they share the same taxi to their respective destinations?

Solution:

For the first 20 miles, the taxi will be shared by all 3 of them.

Charges for 20 miles = 20 [tex]\times[/tex] 2 = $40

This $40 will be shared among all 3.

Each will pay = [tex]\frac{40}{3} = \$13.33[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33

Charges for Calvin = $13.33

For the next 10 miles, the taxi will be shared by Ben and Calvin.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be shared between Ben and Calvin.

Each will pay = [tex]\frac{20}{2} = \$10[/tex]

Charges for Alice = $13.33

Charges for Ben = $13.33 + 10 = $23.33

Charges for Calvin = $13.33 + 10 = $23.33

For the next 10 miles, Calvin travels alone.

Charges for 10 miles = 10 [tex]\times[/tex] 2 = $20

This $20 will be paid by Calvin alone.

Charges for Alice = $13.33

Charges for Ben = $23.33

Charges for Calvin = $23.33 + 20 = $43.33

Answer:

x=2

y=-3

Step-by-step explanation:

2x+y = 1

3x+2y = 0

Multiply the first equation by -2

-4x-2y = -2

Add this to the second equation

-4x-2y = -2

3x+2y = 0

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

-x = -2

Multiply by -1

x = 2

Now find y

2x+y = 1

2(2) +y = 1

4 +y = 1

Subtract 4 from each side

y = 1-4

y = -3

Answer: y = -2x + 1

Solution to the system: (2,-3)

Step-by-step explanation:

2x + y = 1

3x + 2y = 0

We can solve this using substitution

The first thing that we're going to want to do is solve for y in the first equation

Solve for y

2x + y = 1

Subtract 2x from both sides

y = 1 - 2x

We now have the two equations

y = -2x + 1 and 3x + 2y = 0

The next step in solving the system is to plug in the expression of y ( -2x + 1) into the second equation

3x + 2y = 0

Substitute -2x + 1 for y

3x + 2(-2x + 1) = 0

Now solve for x

Distribute the 2 to the -2x and 1

2 * -2x = -4x

2 * 1 = 2

We now have 3x - 4x + 2 = 0

Combine like terms

-x + 2 = 0

Add x to both sides

2 = x

Now to find the value of y we substitute the value of x into one of the equations and solve for y

2x + y = 1

x = 2

2(2) + y = 1

Multiply

4 + y = 1

Subtract 4 from both sides

y = -3

The solution to the system is (2,-3)

And we are done!

Answer:

area ≈ 12.505

perimeter ≈  16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² =  the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

(u × v) • w makes sense, since u × v is another vector, and so (u × v) • w is a scalar.

u × (v • w) does not make sense, since v • w is a scalar, and the cross product is not defined between a vector and a scalar.

(u × v) × w makes sense, since u × v is a vector and so is w.

u • (v • w) does not make sense, since v • w is scalar, and the dot product is not defined between a vector and a scalar.

Answer:

To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

It's the middle value of a list of numbers arranged in order.

For example the median of the list 1 2 3 4 5 is 3.

If there are an even number of values, the median is the mean of the middle two. For example:

1 3 4 5 7 9:

The middle 2 numbers are 4 and 5 so

the median is  (4 + 5) / 2 = 4.5

Answer:

→To combine the two functions, you have to multiply them together, like so:

h(x) · s(x)

→This can also be shown as:

[tex](103)(1.03)^x^-^1[/tex]

The reason as to why you would multiply the two functions together, and not add, is because of the words accrues. Based on the information given, the interest amount of money, which is $103, accrues, which basically means that the money will increase in a pattern, over time. In addition, when a world problem involves a bank and money, multiplication is usually occurring.

The total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is g(x) = (103)(1.03)^(x-1).

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

Christina has $103 earned from babysitting saved at home, and the amount is modeled by the function,

[tex]h(x) = 103[/tex]

She reads about a bank that has savings accounts that accrue interest according to the function,

[tex]s(x) = (1.03)^{(x-1)}[/tex]

This function means that the interest amount is 3% in value per year in which x represent the number of years.

Now the total amount of money she will have in her bank account as interest accrues will be equal to the product principal and interest rate.

Let the amount of money she will have in her bank account as interest accrues is represented by function g(x). Thus,

[tex]g(x) = (103)(1.03)^{(x-1)}[/tex]

Thus, the total amount of money Christina will have in her bank account as interest accrues after she deposits her $103 is.

[tex]g(x) = (103)(1.03)^{(x-1)}.[/tex]

Learn more about the simple interest here;

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Answer:

no solution

Step-by-step explanation:

1/3(12-6x)=4-2x

4-1.3x=4-2x

4=4-0.7x

0=0.7x

ns

ANSWER:

               It is C

NO EXPLANATION

Answer:

Difference : 4th option

Step-by-step explanation:

The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.

x² + 3x + 2 - Break the expression into groups,

( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,

x( x + 1 ) + 2( x + 2 ) - Group,

( x + 2 )( x + 1 )

This is the same as the denominator of the other fraction, and therefore we can combine the fractions.

x - 1 / ( x + 2 )( x + 1 )

As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE