10) An amount of $1500.00 is invested for 3 years at rate of 2% for the first year and 5%, for
the 2nd year and 6% for the 3rd year.
a) Calculate the interest amount you will get if this is simple interest?
b) How much more or less you will get if this is compound interest?

the corresponding angles should be equal

so, [tex] 5x+15=90 \implies 5x=75\implies x=15^{\circ}[/tex]

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.

[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex]  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation [tex]4x+3y=1[/tex]  by 2.

[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]

Now we can add these equations

[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]

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

[tex]5x = 5[/tex]

Dividing both sides by 5, we get [tex]x = 1[/tex].

Now we can substitute x into an equation to find y.

[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]

Hope this helped!

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Answer:

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Step-by-step explanation:

Month       No. of              Mean       Squared

           Fatal Accidents  Deviation   Difference

Jan          8                       -4                  16

Feb        15                        3                   9

Mar         9                       -3                   9

Apr         8                       -4                  16

May       13                        1                    1

Jun         6                      -6                 36

Jul         17                       5                 25

Aug       15                       3                   9

Sep       10                      -2                   4

Oct        9                       -3                   9

Nov    18                          6                 36

Dec    12                          0                   0

Total 140                                         170

Mean = 140/12 = 12    Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set.  It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.

Answer:

6×6 tile

Step-by-step explanation:

First let's calculate the total area Hakim should fill.

Let A be that area.

The area is a rectangle so its area is the product of the length and the width.

● A = 180*150

● A = 27000 mm^2

■■■■■■■■■■■■■■■■■■■■■■■■■■

The tiles Hakim has are all squares with different sides(4,6,8).

Let calculate the area of each tile.

Let A' , A" and A"' be the areas respectively of the 4,6 and 8 squares.

Since all tiles are squares, the area is the side times itself.

■■■■■■■■■■■■■■■■■■■■■■■■■■

● A' = 4^2 = 16 mm^2

● A" = 6^2 = 36 mm^2

● A"' = 8^2 = 64 mm^2

Divide the total area by each area and see wich one will give you a whole number.

●A÷A' = 27000÷16 = 1687.5

This isn't a whole number

● A÷A" = 27000÷36 = 750

This is a whole number, so it is the right tile.

● A+A"' = 27000÷64 = 421.875

This isn't the right tile.

Hakil should use the 6×6 tile

Hakim should use a tile of 6×6 side.

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

Given that, Hakim is making a mosaic from square tiles. The area he needs to fill measures 150 mm by 180 mm. The tiles have side lengths of 4, 6 or 8 mm and are too small to cut.

To know that which tile fits best, we will divide the area of mosaic to the area of the tile, and see if we get a whole number if not a whole number then it should be cut, but we are restricted to do so, therefore we will look for the whole number,

Area of the mosaic = 150×180 = 27000 mm²

Area of the tile with side 4 mm = 4² = 16 mm²

Number of tile = 27000/16 = 1687.5 tiles. (not a whole number)

Area of the tile with side 6 mm = 6² = 36 mm

Number of tile = 27000/36 = 750 tile. (a whole number)

Hence, Hakim should use a tile of 6×6 side.

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Step-by-step explanation:

a.

[tex]s \: = \frac{k}{g} [/tex]

[tex]8 = \frac{k}{1.5} [/tex]

[tex]k \: = 1.5 \times 8 = 12[/tex]

[tex]s = \frac{12}{g} [/tex]

b.

[tex]s = \frac{12}{3} [/tex]

s = 4

Answer:

Size of |E n B| = 2

Size of |B| = 1

Step-by-step explanation:

I'll assume both die are 6 sides

Given

Blue die and Red Die

Required

Sizes of sets

- [tex]|E\ n\ B|[/tex]

- [tex]|B|[/tex]

The question stated the following;

B = Event that blue die comes up with 6

E = Event that both dice come even

So first; we'll list out the sample space of both events

[tex]B = \{6\}[/tex]

[tex]E = \{2,4,6\}[/tex]

Calculating the size of |E n B|

[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]

[tex]|E n B| = \{2,4,6\}[/tex]

The size = 3 because it contains 3 possible outcomes

Calculating the size of |B|

[tex]B = \{6\}[/tex]

The size = 1 because it contains 1 possible outcome

Answer:

The hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

14^2=9^2+c^2.

c^2=196-81.

c^2=115.

c=√115.

c=10.72~11cm

Answer:

[tex]\huge \boxed{6x^2 }[/tex]

Step-by-step explanation:

6 times a number squared.

Let the number be [tex]x[/tex].

6 is multiplied to [tex]x[/tex] squared.

[tex]6 \times x^2[/tex]

Answer:

255.8

Step-by-step explanation:

first

1/6*1535

=255.8

Answer:

(0, -10a)

Step-by-step explanation:

From the picture attached,

Coordinates of a point have been given as (-10a, 0)

x-coordinate → distance of the point from the origin on x-axis

y-coordinate → distance of the point from the origin on y-axis

Therefore, distance of the given point on x-axis = -10a [(-) sign denotes the negative side of the x-axis]

Distance of the other point with unknown coordinates (x, y) (on y-axis) from the origin = y

And y = 10a

Therefore, coordinates of the unknown point will be (0, -10a).

[Here (-) sign denotes the negative side of the y-axis]

Answer:

c. both A and B

Step-by-step explanation:

Given that there are two events A and B.

To find:

Intersection of the two sets represents which of the following events:

a. either A or B occurs but not both

b. neither A nor B occur

c. both A and B occur

d. All of these choices are true. a. b. c. d

Solution:

First of all, let us learn about the concept of intersection.

Intersection of two events means the common part in the two events.

Explanation using set theory:

Let set P contains the outcomes of roll of a dice.

P = {1, 2, 3, 4, 5, 6}

And set Q contains the set of even numbers less than 10.

Q = {2, 4, 6, 8}

Common elements are {2, 4, 6}

So, intersection of P and Q:

[tex]P \cap Q[/tex] = {2, 4, 6}

Explanation using Venn diagram:

Please refer to the image attached in the answer area.

The shaded region is the intersection of the two sets P and Q.

When we apply the above concept in events, we can clearly say from the above explanation that the intersection of two events A and B is the event that occurs when both A and B occur.

So, correct answer is:

c. both A and B

Answer:

C.

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:

10x + 33 = 0 or 11x + 60 = 0

10x = -33 or 11x = -60

x = -33/10 or x = -60/11

Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.

Answer:

There are 6566 ways to choose 22 croissants with at least one plain croissant, at least two cherry croissants, at least three chocolate croissants, at least one almond croissant, at least two apple croissants, and no more than three broccoli croissants.

Step-by-step explanation:

Given:

There are 5 types of croissants:

plain croissants

cherry croissants

chocolate croissants

almond croissant

apple croissants

broccoli croissants

To find:

to choose 22 croissants with:

at least one plain croissant

at least two cherry croissants

at least three chocolate croissants

at least one almond croissant

at least two apple croissants

no more than three broccoli croissants

Solution:

First we select

At least one plain croissant to lets say we first select 1 plain croissant, 2 cherry croissants, 3 chocolate croissants, 1 almond croissant, 2 apple croissants

So

1 + 2 + 3 + 1 + 2  = 9

Total croissants = 22  

So 9 croissants are already selected and 13 remaining croissants are still needed to be selected as 22-9 = 13, without selecting more than three broccoli croissants.

n = 5

r = 13

C(n + r - 1, r)

= C(5 + 13 - 1, 13)

= C(17,13)

[tex]=\frac{17! }{13!(17-13)!}[/tex]

= 355687428096000 / 6227020800 ( 24 )

= 355687428096000 / 149448499200

= 2380

C(17,13) = 2380

C(n + r - 1, r)

= C(5 + 12 - 1, 12)

= C(16,12)

[tex]=\frac{16! }{12!(16-12)!}[/tex]

= 20922789888000 / 479001600 ( 24 )

= 20922789888000  / 11496038400

= 1820

C(16,12) = 1820

C(n + r - 1, r)

= C(5 + 11 - 1, 11)

= C(15,11)

[tex]=\frac{15! }{11!(15-11)!}[/tex]

= 1307674368000 / 39916800 (24)

= 1307674368000 / 958003200

= 1307674368000 / 958003200

= 1365

C(15,11) = 1365

C(n + r - 1, r)

= C(5 + 10 - 1, 10)

= C(14,10)

[tex]=\frac{14! }{10!(14-10)!}[/tex]

= 87178291200 / 3628800 ( 24 )

= 87178291200 / 87091200

= 1001

C(14,10) = 1001

Adding them:

2380 + 1820 + 1365 + 1001 = 6566 ways

Answer:

Option (4)

Step-by-step explanation:

By the property of exterior angle of a triangle,

"Exterior angle of a triangle is equal to the sum of two opposite interior angles."

In the triangle ABC,

∠ACD is an exterior angle and ∠BAC and ∠ABC are the opposite interior angles.

m∠ACD = m∠BAC + m∠ABC

95° = m∠BAC + m∠ABC

Therefore, Option (4) will be the correct option.

Answer:

y = [tex]\sqrt[3]{x-5}[/tex]

Step-by-step explanation:

To find the inverse of any function you basically switch x and y.

function = y = x^3 + 5

Now we switch x and y

x = y^3 +5

Solve for y,

x - 5 = y^3

switch sides,

y^3 = x-5

y = [tex]\sqrt[3]{x-5}[/tex]

Answer:

[tex]\Large \boxed{{f^{-1}(x)=\sqrt[3]{x-5}}}[/tex]

Step-by-step explanation:

The function is given,

[tex]f(x)=x^3 +5[/tex]

The inverse of a function reverses the original function.

Replace f(x) with y.

[tex]y=x^3 +5[/tex]

Switch variables.

[tex]x=y^3 +5[/tex]

Solve for y to find the inverse.

Subtract 5 from both sides.

[tex]x-5=y^3[/tex]

Take the cube root of both sides.

[tex]\sqrt[3]{x-5} =y[/tex]

Answer:

y = 4x + 21

Step-by-step explanation:

Hello!

Point-slope form is y - y1 = m(x - x1)

y1 is the y point

x1 is the x point

m is the slope

Put in what you know

y - -3 = 4(x - -6)

Subtracting a negative is the same as adding

y + 3 = 4(x + 6)

Distribute the 4

y + 3 = 4x + 24

Subtract 3 from both sides

y = 4x + 21

The answer is y = 4x + 21

Hope this helps!

Answer:

[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]

Step-by-step explanation:

There are 12 months in one whole year.

In one year, the person earns $96,600 with bonus.

The person gets a bonus of $6,200 during Christmas.

96,600 - 6,200 = 90,400

The person earns $90,400 yearly.

[tex]\frac{90,400}{12}[/tex] = 7,533.3333

Each month, the person earns $7,533.33, to the nearest cent.

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Answer:

C) A only

Step-by-step explanation:

In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is  the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.

Similarly,

In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .

Given that:

At 95% confidence interval for the  difference between the population means is (1.4, 8.7).

The level of significance = 1 - 0.95 = 0.05  = 5%

So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

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Answer:

[tex]\boxed{Probability=\frac{1}{2} }[/tex]

Step-by-step explanation:

The probability of flipping at least 1 head from flipping 2 coins is:

=> Total sides of the coins = 4

=> Sides which are head = 2

=> Probability = 2/4 = 1/2

Answer:

-19

Step-by-step explanation:

By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6

There are 2 intervals between -10 and -4, so each interval is

6/2 = 3

a gap of 3

This means the number to the left of -4 is -7, then -10 which works.

From there, you count how many intervals there is between -10 and the ?

There are 3 intervals, so you have to decrease -10 by -3x3 or -9

Therefore the ? is -19

Another way is to just count it directly

The number directly left of -10 is going to be -13, then -16 and finally -19

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = - 3cos(t) ⇒ x / - 3 = cos(t)

y = 4sin(t) ⇒ y / 4 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / - 3 )² = cos²(t)

+ ( y / 4 )² = sin²(t)

_____________

x² / 9 + y² / 16 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

[tex]\frac{154}{200} =0.77[/tex]

[tex]1-0.77=0.23[/tex]

[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049

0.77±0.049< 0.819, 0.721

Answer:

Hey there!

The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.

Let me know if this helps :)

The graph that  accurately displays a parabola with its directrix and focus is the first graph.

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.

Therefore, The first graph is the correct answer.

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Answer:

3x+2+x-3+2x+1+2(2x+5)=360

10x+10=360

x=35

Answer:

P (x= 5) =  0.0001

P(x=3) =  0.008699

Step-by-step explanation:

This is a binomial distribution .

Here p = 0.8  q= 1-p = 1-0.8 = 0.2

n= 15

So we find the probability for x taking different values from 0 - 15.

The formula used will be

n Cx p^x q^n-x

Suppose we want  to find the value of x= 5

P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001

P(x=3) = 15C3*(0.2)^12*(0.8)^3 =  9.54 e ^-7= 0.008699

Similarly we can find the values for all the trials from 0 -15  by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.

The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.

It is required to find the sampling distribution if n =15 samples.

It is defined as the probability distribution for the definite sample size the sample is the random data.

We have p =80% = 0.8 and q = 1 - p ⇒ 1 -0.8 ⇒ 0.2

n = 15

We can find the probability for the given x by taking different values from 0 to 15

the formula can be used:

[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]

If we find the value for p(x = 5)

[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001

If we find the value for p(x = 3)

[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒  

Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.

Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

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Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]

[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]

For angle θ:

Calculating:

a) (4,2,-4)

[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6

[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]

[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]

For θ, choose 1st option:

[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]

[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]

b) (0,8,15)

[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17

[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]

[tex]\theta = tan^{-1}\frac{y}{x}[/tex]

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]

c) (√2,1,1)

[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2

[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]

[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]

d) (−2√3,−2,3)

[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5

[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]

Since x < 0, use 2nd option:

[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]

[tex]\theta = \pi + \frac{\pi}{6}[/tex]

[tex]\theta = \frac{7\pi}{6}[/tex]

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

[tex]r=\sqrt{x^{2}+y^{2}}[/tex]

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]

[tex]\theta = tan^{-1}\frac{1}{2}[/tex]

z = -4

b) (0, 8, 15)

[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8

[tex]\theta = \frac{\pi}{2}[/tex]

z = 15

c) (√2,1,1)

[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]

[tex]\theta = \frac{\pi}{3}[/tex]

z = 1

d) (−2√3,−2,3)

[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4

[tex]\theta = \frac{7\pi}{6}[/tex]

z = 3