Find A x B, where A=(5i+j) , B=（i-5j)

Answer:

(6,2)

Step-by-step explanation:

1) convert both equations  to slope intercept form:

y=-x+8

and

y=x-4

now graph both equations separately by intercepts:

x int:  0=-x+8

-8=-x

8=x

y int:  y=0+8

y=8

so the two coordinate points for first equation are (0,8) and (8,0)

lets move on two second equation: y=x-4

x int:  0=x-4

4=x

y int y=0-4

y=-4

so the 2 coordinate points are (4,0) and (0,4)

lets graph these two equations and see where they intersect:

(see graph below), the intersection is at (6,2) so (6,2) is our answer

hope this helps

Answer:

[tex]\boxed{\sf \ \ \text{Jori is 42} \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's not J Jori's age

Pamela is 7 years older than Jori so here age is J + 7

The sum of their age is 91 so

J + ( J + 7 ) = 91

<=>

2J + 7 = 91  subtract 7

2J = 91 - 7 = 84  divide by 2

J = 84/2 = 42

So Jori is 42 and Pamela is 49

hope this helps

Answer:

  (x, y, z) = (45°, 57°, 78°)

Step-by-step explanation:

The problem statement tells you ...

  x + y + z = 180

  -3x +y +z = 0

  0x -y +z = 21

__

Subtracting the second equation from the first gives ...

  4x = 180

  x = 45 . . . . . . divide by 4

Substituting this into the first equation and adding the third equation gives ...

  (45 +y +z) +(-y +z) = (180) +(21)

  2z = 156 . . . . simplify, subtract 45

  z = 78 . . . . . . divide by 2

  y = z -21 = 57

The angle measures are ...

  (x, y, z) = (45°, 57°, 78°)

Answer:

1.875

Step-by-step explanation:

To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.

In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:

[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]

[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]

[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]

Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:

[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]

[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]

[tex]E_2 = 1 + \frac{7}{8}[/tex]

[tex]E_2 = \frac{15}{8} = 1.875[/tex]

Answer:

all real numbers greater than or equal to zero

Step-by-step explanation:

The domain of the real function f(x) = sqrt(x) is

all real numbers greater than or equal to zero

because when x < 0, then f(x) will become complex, which does not belong to a real function.

Answer:

  2.908 s

Step-by-step explanation:

The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.

For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...

  h(t) = -16t² +v₀t +s₀

where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.

  0 = -16t² +65sin(44°) +4

Dividing by -16 gives ...

  0 = t^2 -2.82205t -0.2500

Using the quadratic formula, we find ...

  t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099

  t ≈ 2.90802

It will take about 2.908 seconds for the discus to reach the ground.

_____

Comment on the question

You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.

Answer:

  [tex]f(x)\to 1[/tex]

Step-by-step explanation:

The function approaches its horizontal asymptote in both directions as the magnitude of x gets large. The limit is y = 1.

Answer:

A. y=-2x-4

Step-by-step explanation:

The slope is negative when the line is going down from up.

Options B and D are wrong.

The y-intercept is (0, -4) as shown in the graph.

Option C is wrong.

y = mx + b

y = -2x - 4

Answer:

Proved

Step-by-step explanation:

Given

Prove that

[tex]\frac{cos x}{1 - sin x} = sec x + tan x[/tex]

[tex]\frac{cos x}{1 - sin x}[/tex]

Multiply the numerator and denominator by 1 + sinx

[tex]\frac{cos x}{1 - sin x} * \frac{1 + sin x}{1 + sin x}[/tex]

Combine both fractions to form 1

[tex]\frac{cos x (1 + sin x)}{(1 - sin x)(1 + sin x)}[/tex]

Expand the denominator using difference of two squares;

[tex]i.e.\ (a - b)(a + b) = a^2 - b^2[/tex]

The expression becomes

[tex]\frac{cos x (1 + sin x)}{(1^2 - sin^2 x)}[/tex]

[tex]\frac{cos x (1 + sin x)}{(1 - sin^2 x)}[/tex]

From trigonometry; [tex]1 - sin^2x = cos^2x[/tex]

The expression becomes

[tex]\frac{cos x (1 + sin x)}{(cos^2 x)}[/tex]

Divide the numerator and the denominator by cos x

[tex]\frac{(1 + sin x)}{(cos x)}[/tex]

Split fraction

[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex]

From trigonometry; [tex]\frac{1}{cos x} = sec x \ and\ \frac{sin\ x}{cos\ x} = tan\ x[/tex]

So;

[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex] = [tex]sec x + tan x[/tex]

Answer:

The order in which you solve the operations will provide different results and to be able to get the right answer you have to be familiar with the order of operations to know the appropiate steps to solve an operation. According to the order of operations in mathematics, exponents are given precedence over addition and multiplication. Because of that, the exponent is the first you have to solve.

3 + 2 * 3^2

3+2*9

Then, mutiplication is given precedence over addition:

3+18

Now, you can solve the addition and the result is: 21

Because of this, the answer is:

• 3 +( 2 * (3^2)) = 21

Answer:

(7, -3)

Step-by-step explanation:

Isolate x for 2x +7y = -7:

x = (-7 - 7y)/2

Substitute:

-4((-7 - 7y) / 2) - 3y = -19

Solve for y:

-2(-7y - 7) - 3y =

14y + 14 - 3y =

11y + 14 = -19

11y = -33

y = -3

Substitute -3:

x = (-7 - 7(-3))/2

  = 14/2

x = 7

Answer:

(7,-3)

Step-by-step explanation:

Answer: Albert is wrong

Step-by-step explanation:

You first have to subtract Plant B's measurement from Plant A's measurement.

3 7/8-2 1/4 => 3 7/8-2 2/8

If you solve it you get 1 5/8. Since it cannot be reduced this is the final answer.

The table of the probability is missing, so i have attached it.

Answer:

μ = 0.919

The interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

Step-by-step explanation:

The expected value which is also called mean value is denoted by the symbol μ. It is defined as the sum of the product of each possibility x with it's probability P(x) as the formula;

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Thus, the interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

The interpretation of the mean of the random variable X is 0.919.

Here the interpretation should represent the average and it should be individual aged 15 years or more so it should be involved in 0.919 marriage.

Now the mean is

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Hence, The interpretation of the mean of the random variable X is 0.919.

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Answer:

Answer: (0.4356,0.4844)

Step-by-step explanation:

Use Ti 84

use function "1-PropZInt".

Enter x = 736

         n = 1600

         c= 0.95

Answer: (0.4356,0.4844)

Answer:

z-test.

Step-by-step explanation:

We want to perform an hypothesis test for a population mean.

In the case that the standard deviation of the population is known and the population distribution is normal, even if the sample is small, we will use a z-test.

The usual case is to not know the standard deviation of the population, in which case a t-test is adequate instead of a z-test, taking into account the degrees of freedom of the sample.

Answer:

Step-by-step explanation:

The divisors of a number are the numbers that divide it exactly.

60/2

2/30

3/3

5/5

one

divisors = 1,2,3,, 4,5,6,10,12,15,20,30,60.

answer:

1, 2, 3, 6, 10, 30, 60

Step-by-step explanation:

i am pretty sure!

Answer:

it takes

[tex]\boxed {\red {2 \: \: months}}[/tex]

for 10 builders

Step-by-step explanation:

[tex]4 \: \: \: builders = 5 \: month \\ 10 \: builders = x[/tex]

Let us solve

[tex]4 = 5 \\ 10 = x[/tex]

so

[tex]4 = x \\ 10 = 5[/tex]

use cross multiplication

[tex]5 \times 4 = 10 \times x \\ 20 = 10x \\ \frac{20}{10} = \frac{10x}{10} \\ \green {x = 2}[/tex]

Answer:

[tex]\boxed{2months}[/tex]

Step-by-step explanation:

B1 = 4

M1 = 5

B2 = 10

M2 = x (we have to find this)

Since it is an inverse proportion (more builders will take less time and vive versa), we'll write it in the order of

=> B1 : B2 = M2 : M1

=> 4:10 = x : 5

Product of Means = Product of Extremes

=> 10*x = 4*5

=> 10x = 20

Dividing both sides by 10

=> x = 2 months

So, it will take 2 months to build classrooms by 10 builders.

Answer:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=20, p=1-0.42=0.58)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

The probability of exactly eight successful trials is 0.0486 and this can be determined by using the formula of the probability mass function.

Given :

According to the binomial distribution, the probability mass function is given by:

[tex]\rm P(X) = \; (^nC_x )(p^x)(1-p)^{n-x}[/tex]

where the value of n is 20 and the value of (p = 1 - 0.42 = 0.58).

Now, substitute the values of known terms in the above expression of probability mass function.

[tex]\rm P(X=8) = \; (^{20}C_8 )((0.58)^8)(1-0.58)^{20-8}[/tex]

Simplify the above expression in order to determine the probability of exactly eight successful trials.

P(X = 8) = 0.0486

For more information, refer to the link given below:

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Answer:

Mean increase or decrease (same quantity) according to the quantity of the increment or reduction

As all elements were equally affected the standard deviation will remain the same

Step-by-step explanation:

For the original set of salaries: ( In thousands of $ )

51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46

Mean = μ₀ = 47,92

Standard deviation  =  σ = 9,56

If we raise all salaries in the same amount  ( 5 000 $ ), the nw set becomes

56,58,53,67,39,39,56,58,53,35,67,56,51

Mean   =  μ₀´  = 52,92

Standard deviation  =  σ´ = 9,56

And if we reduce salaries in the same quantity ( 2000 $ ) the set is

49,51,46,60,32,32,49,51,46,28,60,49,44

Mean μ₀´´ = 45,92

Standard deviation  σ´´ = 9,56

What we observe

1.-The uniform increase of salaries, increase the mean in the same amount

2.-The uniform reduction of salaries, reduce the mean in the same quantity

3.-The standard deviation in all the sets remains the same.

We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the  data spread around the mean will be the same

Any uniform change in the data will directly affect the mean value

Uniform changes in values in data set will keep standard deviation constant

Answer:

t = 5.6 day

t =5 days 14 hours 24 minutes

Step-by-step explanation:

Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.

N = N•e(-kt)

N• = 25

K = 0.1229

Then

N = 25/2 = 12.5

The reason because at the half life , it's original value will decrease to half.

Let's solve for the half life t

N = N•e(-kt)

12.5 = 25e(-0.1229t)

12.5/25 = e(-0.1229t)

0.5 = e(-0.1229t)

In 0.5 =-0.1229t

-0.69314 = -0.1229t

-0.69314/-0.1229 = t

5.6399 = t

To the nearest tenth

5.6 days = t

Answer:

line passes through the vertex

Step-by-step explanation:

f(x)=-3(x+2)^2+4

x=-2 it is the x of the vertex

Answer:

Step-by-step explanation

p - the price of pizza

c- the price of a bottle of coke

p = c+3.2

3p + c=19.4

3* (c+3.2)+c=19.4

3*c+3*3.2+c=19.4

3c+c+9.6=19.4

4c+9.6=19.4

-9.6 -9.6

4c=9.8

:4. :4

c=2.45

p=2.45+3.2=5.65

verify : 3*5.65+2.45=16.95+2.45=19.40

Answer:

QUESTION 2 -> Correct option: A.

QUESTION 3 -> Correct option: C.

Step-by-step explanation:

QUESTION 2

To find the amount of tax we just need to multiply the tax rate by the original price of the product:

[tex]Tax = 29\% * 53.93[/tex]

[tex]Tax = 0.29 * 53.93[/tex]

[tex]Tax =\$15.64[/tex]

Then, to find the total selling price, we need to sum the original price to the tax value:

[tex]Total = tax + price[/tex]

[tex]Total = 15.64 + 53.93[/tex]

[tex]Total = \$69.57[/tex]

Correct option: A.

QUESTION 3

To find the final value after 2 years, we can use the formula:

[tex]P = Po * (1 + r*t)[/tex]

Where P is the final value, Po is the inicial value, r is the interest and t is the amount of time. Then, we have that:

[tex]P = 10000 * (1 + 0.08 * 2)[/tex]

[tex]P = \$11600[/tex]

Correct option: C.

Answer:

It has one solution (0, 1).

Step-by-step explanation:

Easiest and fastest way to solve the systems of equation is to graph them on a graphing calc and analyzing where the 2 graphs intersect (if they are not parallel).

Answer:  18 in²

Step-by-step explanation:

S(fig1)=32 in² . We know that the figures are similar and  the correspondonding sides are a1=12  and a2=9

So the coefficient of similarity is k=9/12=3/4

S(fig2)=S(fig1)*k²

S(fig2)=32*(3/4)²=32*9/16=18 in²

The solution is A = 18 inches²

The proportion relation is given by k = 3/4 and the value of A = 18 inches²

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the constant of proportionality be k

From the figures , the two figures are similar

Constant of proportionality k = ( side of first figure / side of second figure)

k = 9/12

k = 3/4

Now , the area of the first figure A = 32 ( k )²

On simplifying the equation , we get

A = 32 ( 3/4 )²

A = ( 32 x 9 ) / 16

A = 2 x 9

A = 18 inches²

Therefore , the value of A is 18 inches²

Hence , the proportion is A = 18

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Answer:

[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]

Step-by-step explanation:

[tex]$\frac{6x}{x-3} -\frac{5}{x} $[/tex]

[tex]$\frac{6x(x)}{x(x-3)} -\frac{5(x-3)}{x(x-3)} $[/tex]

[tex]$\frac{6x^2}{x^2-3x} -\frac{5x-15}{x^2-3x} $[/tex]

[tex]$ \frac{6x^2-5x+15 }{x^2-3x} $[/tex]

The answer is Ferris wheel, since it is a circular object and will display symmetry even when rotated.

Answer:

In both cases, the spider has already crawled up 3 feet. In order for the answer to be 0 the spider must crawl down 3 feet because 3 - 3 = 0, therefore the answer is the first story.

Answer:

Question 1

Step-by-step explanation:

1) The spider is 3 feet above the patio : +3

Now, due to strong wind, it crawls down 3 feet: -3

+ 3 - 3 = 0