The frequency table represents data gathered about how much time some farmers spend tending to their land each week. Complete the conditional relative frequency table by row by identifying the values for each letter. a = b = c = d =

Answer:

Therefore the total of all profit earned by the end of of the the first 5 years is $19,058.542.

Step-by-step explanation:

To find total profit earned per year, we need to use the compound growth formula.

The compound growth formula:

[tex]A= P(1+r)^t[/tex]

A= Amount after t years

P= initial amount

r= rate of growth

t= time in year.

Given that,

New business made a profit during the first year of $3000.

If the profit increased 12% per year.

Here P= $3,000 and r =12%=0.12 , t=1 years

Plugging all value in the above  formula:

[tex]A=3000(1+0.12)^1[/tex]

   =3000(1.12)

  =$3360

Profit after 2 year is $3,360.

Now, P= $3,000 and r =12%=0.12 , t=3 years

[tex]A=3000(1+0.12)^2[/tex]

   =3000(1.12)²

   =$3763.2

Similar the profit at 4 year is

[tex]A=3000(1+0.12)^3[/tex]

   =3000(1.12)³

   =$4214.784

The profit at 5th year is

[tex]A=3000(1+0.12)^4[/tex]

   =3000(1.12)⁴

   =$4720.558

Therefore the total of all profit earned by the end of of the the first 5 years is=$(3,000+3360+3763.2+4214.784+4720.558)

          =$19,058.542

Answer:

The first one 24/4

Step-by-step explanation:

Into usually means divide when it's used as a math term,

therefore 24 into fourths means 24 divide by 4.

Answer:

the answer is 24 divided by 4

Step-by-step explanation:

To find the height of the office building and the angle of elevation to the top of the tower, we can use the tangent function and solve two equations simultaneously.

To find the height of the office building and the angle of elevation from the base to the top of the tower, we can use the Tangent function.

Tan(angle) = Opposite/Adjacent

For the first angle (37 degrees), the opposite side is the height of the tower (1964 feet) and the adjacent side is the height of the office building.

So, tan(37) = 1964/Adjacent.

For the second angle (19 degrees), the opposite side is again the height of the tower (1964 feet) and the adjacent side is the height of the office building + the height from the roof to the top of the tower.

So, tan(19) = 1964/(Adjacent + Roof Height).

We can solve these two equations simultaneously to find the height of the office building and the height from the roof to the top of the tower.

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Answer:

Its the first option

40,000,000(0.9)x.

Step-by-step explanation:

90% recognise her each year so after 1 year so the number (N) is:

N = 40,000,000(0.90)^1 = 36,000,000 recognise her after 1 year.

N = 40,000,000(0.90)^2 = 32,400,000 recognise her after 2 yeas

- and so on.

After x years:

N = 40,000,000(0.90)^x.  

Note the x is a power and is best written as ^x.

The correct equation to represent the given scenario is [tex]y = 40,000,000(0.9)^x[/tex]. This equation represents a geometric sequence, with the initial quantity being 40,000,000 and decreasing by 10% each year.

The scenario is a geometric sequence, where the number of people who still recognize Britney Spears each year is decreasing by 10%. To represent this situation mathematically, we can use a geometric equation: [tex]y = a \cdot r^x[/tex]where 'a' is the initial quantity, 'r' is the ratio of decrease or increase, and 'x' is the number of time periods.

In this case, 'a' is 40,000,000 (the initial amount of people), 'r' is 0.9 (representing a 10% decrease each year), and 'x' will represent the number of years since her prime. Thus, the correct equation out of the options to represent the scenario is [tex]y = 40,000,000(0.9)^x.[/tex]

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I think the answer is 6(2n-3)

Answer:

5 weeks until they have the same

Arie and Olga have the same amount in their accounts in 8 weeks.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Amount in Arie's account = $46

Arie's each week savings = $8.50

Amount in Olga 's account = $14

Olga 's each week savings = $12.50

Let x be the number of weeks when Arie and Olga will have the same amount in their accounts

Total savings of Arie = 8.5x

Total savings of Olga = 12.5x

Amount in Arie's account = 8.5x + 46

Amount in Olga's account = 12.5x + 14

For, Arie and Olga have the same amount in their accounts

8.5x + 46 = 12.5x + 14

Taking alike terms together,

12.5x - 8.5x = 46 - 14

⇒ 4x = 32

Dividing both side by 4 we get,

x =8 weeks

which is the required number of weeks.

Thus, Arie and Olga will have the same amount in their accounts in 8 weeks.

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6(-4x - 7) - 4(x - 6)       Distribute 6 into (-4x - 7) and -4 into (x - 6)

(6)(-4x) + (6)(-7) + (-4)x + (-4)(-6)  (two negative signs cancel each other out and become positive)

-24x - 42 - 4x + 24    Combine like terms(terms that have the same variable and power/exponent)

-24x - 4x - 42 + 24    (I rearranged the terms to be next to their like term)

-28x - 18      Your answer is D

Answer:

a) CD = 6a + 4.5b

b) k = 4

Step-by-step explanation:

CD = CA + AB

CA = -AC

CD = -3b + 6a + 7.5b

CD = 6a + 4.5b

BC is parallel to CD

BC = BA + AC

BC = ka + 3b

BC is a scalar multiple of CD

Scale factor:

3/4.5 = 2/3

k = ⅔(6)

k = 4

Answer:

1. x = +/- 2[tex]\sqrt{2}[/tex] - 7

2. x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]

3. n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]

Step-by-step explanation:

1. Divide both sides by 2: (x + 7)^2 = 8

Square root both sides: x + 7 = +/- 2[tex]\sqrt{2}[/tex]

Subtract 7 from both sides: x = +/- 2[tex]\sqrt{2}[/tex] - 7

2. Square root both sides: x - 3 = [tex]\sqrt{-12}[/tex]

Since there is a negative inside the radical, we need to have an imaginary number: [tex]i=\sqrt{-1}[/tex] . So, [tex]\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}[/tex]

Add 3 to both sides: x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]

3. Divide by -5 from both sides: (n - 2)^2 = -2

Square root both sides: n - 2 = [tex]\sqrt{-2}[/tex]

Again, we have to use i: [tex]n-2=\sqrt{-2} =i\sqrt{2}[/tex]

Add 2 to both sides: n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]

Hope this helps!

Answer:

1. x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. No real solutions

x = 3 + 2sqrt(3) i, 3 - 2sqrt(3) i

3. No real solutions

n = 3 + sqrt(2) i, 3 - sqrt(2) i

Step-by-step explanation:

1. 2(x + 7)² = 16

(x + 7)² = 8

x + 7 = +/- sqrt(8) = +/- 2sqrt(2(

x = 2sqrt(2) - 7, -2sqrt(2) - 7

2. (x - 3)² = -12

A perfect square can never be negative for real values of x

(x - 3) = +/- i × sqrt(12)

x - 3 = +/- i × 2sqrt(3)

x = 3 +/- i × 2sqrt(3)

3. -5(n - 3)² = 10

(n - 3)² = -2

A perfect square can never be negative for real values of x

n - 3 = +/- i × sqrt(2)

n = 3 +/- i × sqrt(2)

Answer:

integers

Step-by-step explanation:

Answer:

Intergers

Step-by-step explanation:

Intergers are a whole number meaning a number that's not a fraction.

Answer:

Circular shapes - They are those planner shapes that represent the locus of all the points that has a constant distance from a fixed point on the plane. This constant distance is termed as the radius of the circle and the fixed point is known as the center of the circle.

The center of the circle is enclosed by all the points on its periphery.

The circumference of the circle is the total length of its periphery around the center.

Concentric circles are two circles that have the same center

Step-by-step explanation:

just put them how u normally wuld 1 is

3 is 6

4 is 5

2 is 8

5 is 13

Answer: area of the rectangle = 256

area of triangle 1 = 24

area of triangle 2 = 16

area of triangle 3 = 96

area of the trapezoid = 120

Jeremy will have 72 baseball cards in April.

A consecutive pattern refers to a sequence or order of numbers, letters, or other objects in which each follows in direct and uninterrupted succession from the one that precedes it.

We have,

To solve this problem, we need to determine the pattern of how many cards Jeremy adds to his collection each month.

To do this, we can find the difference between consecutive months:

February minus January: 48 - 36 = 12

March minus February: 60 - 48 = 12

We can see that Jeremy is adding 12 cards to his collection each month.

So to find out how many cards he will have in April, we can add 12 to the number he had in March:

April

= 60 + 12

= 72

Therefore,

Jeremy will have 72 baseball cards in April.

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Answer:

¿que hay de ellos?

Answer:

[tex]Volume=0.015625\ yd^3[/tex]

Step-by-step explanation:

-A cube is a 3-D object whose height=length=width.

-To find its volume, we multiply its length by width by height dimensions.

#We can calculate the volume of a cube using the formula:

[tex]V=length\times width\times height\\\\=0.25 \ yd\times 0.25\ yd \times 0.25\ yd\\\\=(0.25\ yd)^3\\\\=0.015625\ yd^3[/tex]

Hence, the volume of the cube is [tex]0.015625\ yd^3[/tex]

To find the volume of a cube with an edge length of 1/4 yard, cube the length of the edge. The volume of the cube is 1/64 cubic yards.

To find the volume of a cube, you need to cube the length of its edge. In this case, the edge length is 1/4 yard. So, the volume formula becomes (1/4)^3 = 1/4 × 1/4 × 1/4 cubic yards. Simplifying further, we have 1/64 cubic yards as the volume of the cube.

Answer: 2.13

Step-by-step explanation:

1.42/2=0.71

1.42+0.71=2.13

Answer:

The answer to your question is £ 2.13

Step-by-step explanation:

Data

Cost of 1 kg or oranges = £1.42

Cost of the oranges in the scales = ?

Process

1.- Determine the weight of the oranges in the scales.

As we can see the weight of the three oranges is 1.5 kg

2.- Use proportions and cross multiplication to find the cost.

                 1 kg of oranges --------------------- £ 1.42

                 1.5 kg of oranges ------------------   x

                           x = (1.5 x 1.42) / 1

                           x = 2.13 / 1

                           x = £ 2.13

Answer:

$15000

Step-by-step explanation:

We have that the value of the truck is $ 3000 and that this payment is equivalent to 20% of the value of a new truck, therefore the value of the new truck would be:

% of value         value

      20               3000

     100                  x

x = 100 * 3000/20

x = 15000

therefore the value of the new truck is $ 15000

Answer:

14 = 2*7

Step-by-step explanation:

2 and 7 are prime.

Answer:

14 = 1 x 14 or 2 x 7. Factors of 14: 1, 2, 7, 14. Prime factorization: 14 = 2 x 7

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The remainder theorem states that if f(x) is divided by (x - h)

The the remainder is f(h)

(a)

Given f(x) is divided by (x - 1) then remainder is f(1), thus

f(1) = [tex]1^{4}[/tex] + 1³ + 2(1)² + a + b = 7, that is

1 + 1 + 2 + a + b = 7

4 + a + b = 7 ( subtract 4 from both sides )

a + b = 3 ← as required → (1)

(b

Given f(x) is divided by (x + 2) then the remainder is f(- 2), thus

f(- 2) = [tex](-2)^{4}[/tex] + (- 2)³ + 2(- 2)² + 2a + b = - 8, that is

16 - 8 + 8 + 2a + b = - 8

16 + 2a + b = - 8 ( subtract 16 from both sides )

2a + b = - 24 → (2)

Multiply (1) by 2

2a + 2b = 6 → (3)

Add (2) and (3) term by term to eliminate the term in a

3b = - 18 ( divide both sides by 3 )

b = - 6

Substitute b = - 6 into (1)

a - 6 = 3 ( add 6 to both sides )

a = 9

Thus a = 9 and b = - 6

Final answer:

To solve for the constants a and b in the polynomial function f(x), we apply the remainder theorem to the given division scenarios. Setting up and solving a system of linear equations using the remainders allows us to find that a is 9 and b is -6.

Explanation:

The given function is f(x) = x^4 + x^3 + 2x^2 + ax + b, and we need to find the constants a and b given that when f(x) is divided by (x - 1), the remainder is 7, and when divided by (x + 2), the remainder is -8.

To find a + b, we apply the remainder theorem. When a polynomial f(x) is divided by (x - p), the remainder is f(p). Therefore, for (x - 1):

f(1) = 1 + 1 + 2 + a + b = 7
4 + a + b = 7
a + b = 3

Similarly, for (x + 2):

f(-2) = (-2)^4 + (-2)^3 + 2(-2)^2 + a(-2) + b = -8
16 - 8 + 8 - 2a + b = -8
16 - 2a + b = -8

We already know that a + b = 3, so we can set up a system of equations:

a + b = 3

-2a + b = -24

Solving for a and b:

Subtracting the first equation from the second: -3a = -27

Divide by -3: a = 9

Substitute a into the first equation: 9 + b = 3

Solve for b: b = -6

Options B and C are the correct answer.

The given trigonometric function is y=3cosx+2.

We need to check which of the given options are equivalent to the function y=3 cos x+2.

The given trigonometric function can be solved using complementary angles and even/odd identities.

Complementary angles are sin x=cos(π/2 -x) and cos x=sin(π/2 -x).

Even/odd identities are sin(-x) =-sin x and cos(-x)= cos x.

Now,

From option A:

y=3 sin(x-π/2) +2

using trigonometry identity, we get

y=3 sin(-(x-π/2)) +2

⇒y=-3 sin(π/2 - x)+2

⇒y=-3 cos x+2

From option B:

y= 3sin(x+ π/2) +2

Using Sin(A+B)= sin A cos B+ cos A sin B, we get

y= 3cosx +2

From option C:

y= 3cos(-x) +2 can be written as y=3cosx+2 (cos(-x)=cosx)

From option D:

y= -3cos x-2

Therefore, options B and C are the correct answer.

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Final answer:

The equivalent functions to y=3 cos x+2 are B: y= 3sin(x+ π/2) +2 and C: y= 3cos(-x) +2, as they use the co-function identity and the even property of the cosine function respectively.

Explanation:

The given function is y=3 cos x+2. We need to find functions that are equivalent to this function. The trigonometric identities necessary for this problem are:

Now, considering the given options:

  D. y= -3cos x-2: This is not equivalent because it represents the reflection of the given function over the x-axis and a vertical translation down by 2 units.

Therefore, the equivalent functions are B and C.

Answer:

3 cylinder will fill 9 cones with water

Step-by-step explanation:

This problem bothers on mensuration of slides, cone and cylinder

We know that the

Volume of a cylinder = πr²h

Volume of a cone = 1/3(πr²h)

Given that both cylinder and cone has same height and radius

From the given expression we can deduce that the cone is 3 times smaller than the cylinder in volume

So if 1 cylinder will fill 3 cones

Then 3 cylinders will fill x cones

By cross multiplication we have

x= 3*3cones

x= 9 cones

Hence 3 cylinder will fill 9 cones with water

Answer:

9 cones

Step-by-step explanation:

The formula to find a volume of a cylinder is:

V1 = pi*r^2*h

Where r is the base radius and h is the height

The formula to find a volume of a cone is:

V2 = (1/3)*pi*r^2*h

So, if they have the same base radius and same height, we have that:

V1/V2 = 1/(1/3) = 3

The volume of the cylinder is 3 times bigger than the volume of the cone, so each cylinder of water can fill 3 cones.

Is Dennis has 3 cylinders, he is able to fill 3*3 = 9 cones with water.

Answer:

The total number of flowers in Mrs. Garcia's garden is 25.

Step-by-step explanation:

The ratio of lilies to daisies is 3:2 and there are 15 lilies. We need to compute the number of daisies first and then add both the number of daisies and lilies to compute the total number of flowers. Using the ratio method:

Lilies : Daisies

  3    :     2

  15   :    x

By cross multiplying we get:

3x = 15*2

3x = 30

x = 10

Hence, the total number of flowers in the garden are:

10 + 15 = 25

The total number of flowers in Mrs. Garcia's garden is 25.

Answer:

25

Step-by-step explanation:

Given that the number of lilies = 15

Given ratio = 3:2

Let the total number of flowers be X

Let the number of daisies be 'a'

3/2 = 15/a

3×a = 2×15

3a = 30

a = 30/3

a = 10

X = number of lilies + number of daisies

X = 15 + 10

X = 25

Answer:

20 x 17 = 340

Step-by-step explanation:

C= cost

P=people

Equation- 20p=c

20 x 17 (people) = cost

:) would appreciate anything

Answer:

$1380

Step-by-step explanation:

The electronics store offers a 40% discount on the printer only when the computer is purchased at the regular price.

Discount on the Printer = 40% of $300 =0.4 X 300 =120

Promotional Price of the Printer = $300-120 =$180

Therefore, the total cost of the computer and the printer at the promotional price

=Regular price of a computer + Promotional Price of the Printer

=1200+180

=$1380

Answer:

point t

Step-by-step explanation:

to reflect over the y-axis, flip the sign of the x coordinate

(6, -4) to (-6, -4)

point t is located at (-6,-4)

Answer:

42 tomatoes

Step-by-step explanation:

tomatoes/boxes = tomatoes/boxes

12/4 = x/14

4x/4 = 168/4

x=42

Answer:

42 rotten tomatoes would likely be found in 14 boxes

Step-by-step explanation:

1) Find how many rotten tomatoes are normally found in one box by dividing the amount of rotten tomatoes by the number of boxes they are found in. [tex]12/4=3[/tex]

2) So, now you know that 3 rotten tomatoes are normally found in one box, but the question is asking how many tomatoes would likely be found in 14 boxes which means you need to multiply the amount of rotten tomatoes found in one box by the amount of boxes you want to know about. [tex]3*14=42[/tex]

Answer:

Yes; because P(S & E)= P(E) • P(E).

Step-by-step explanation:

P(S)=530/1600 = 0.33, P(E)= 1523/1600= 0.95, and P(S & E)= 498/1600= 0.31 = (0.33)(0.95)

Answer:

$45

Step-by-step explanation:

In order to find this we need to understand that every time we bet we are selecting white ball. Because of this we have the chance of getting two times right and two times wrong irrespective of the order. For example we can any of the following orders:

White - White - Black - Black

White - Black - White - Black

Black - White - Black - White

Black - Black - White - White

Irrespective of any of the orders above every time our bet is right (we get white urn) the amount of dollars that we have get increased by half of the current amount. For example on the first turn we are betting $40 (half of initial amount = $80) and if we are right we now have $120 with us. This can be written as

1.5*$80 = $120

Similarly if on first turn we get wrong (black ball) then our amount is half of initial which can be written as

0.5*$80 = $40

So now we know that exactly two times we will be right and exactly two times we will be wrong irrespective of the order because the balls are not replaced hence final solution is:

E(X) = 80*1.5*1.5*0.5*0.5

= $45    

Answer:

[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(z>2.64)=0.0082[/tex]  

And the best answer would be

B 0.0082

Step-by-step explanation:

Data given and notation  

[tex]\bar X=125[/tex] represent the mean height for the sample  

[tex]\sigma=12[/tex] represent the population standard deviation

[tex]n=40[/tex] sample size  

[tex]\mu_o =120[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is 120 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 120[/tex]  

Alternative hypothesis:[tex]\mu \neq 120[/tex]  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z=\frac{125-120}{\frac{12}{\sqrt{40}}}=2.64[/tex]    

P-value

Since is a two sided test the p value would be:  

[tex]p_v =2*P(z>2.64)=0.0082[/tex]  

And the best answer would be

B 0.0082

Answer:

Taak 1.12

Mediaan is 5 en het gemiddelde is 5,67

Taak 2 13

De mediaan is 6

Het gemiddelde is 6

Standaarddeviatie is 3,32

Variantie is 11

Aantal werknemers is 13

Step-by-step explanation:

Taak.1 12 medewerkers is gevraagd naar het aantal verlofdagen. Hier zijn de antwoorden: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Geef de dominante en de mediaan. Taak 2 13 medewerkers is gevraagd naar het aantal vakantiedagen. Hier zijn de antwoorden: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Geef de dominante en mediaan. Zad.3 Bereken de dominante en de mediaan a) Verblijfsafstand in km. b) Aantal werknemers a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15

Taak. 1 12, wordt de mediaan gegeven door

2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8 herschikken, we krijgen

2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8, 14

Daarom is de mediaan 5 en het gemiddelde 5,67

Taak 2 13

2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9 herschikken, we krijgen

2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 14

De mediaan is het zevende nummer in de rij = 6

Het gemiddelde is ook = 6

Standaarddeviatie = 3,32

Variantie = 11

Aantal werknemers = som van frequentie of aantal gegevens = 13.