Verify that the vector X is a solution of the given homogeneous system. X' = −1 1 25 1 −1 X; X = −1 5 e−6t/5 For X = −1 5 e−6t/5, one has

Answer:

m = 1/2 and b = 1.

Step-by-step explanation:

The y intercept (b)  is at y = 1 so we have

y = mx + 1  so b = 1

The m is the slope of the line.

The graph passes through the point (4, 2)

From the graph, the slope  = 2/4 = 1/2.

So it is y = 1/2x + 1.

Answer:

x=4

Step-by-step explanation:

19=7X+3-3x

Combine like terms

19 = 4x +3

Subtract 3 from each side

19-3 = 4x+3-3

16 = 4x

Divide each side by 4

16/4 = 4x/4

4 =x

Answer:

45 / 15 = 3

Step-by-step explanation:

Required

Steps to divide 45 by 15 using integer tiles

Step 1: We start by writing out 45 items;

See attachment 1 where I used 45 boxes as illustration

Step 2: Then, we group these 45 items into groups (15 per groups)

See attachment 2 for illustration

Step 3: Count the number of groups

There are 3 groups;

Hence, 45 / 15 = 3

Answer:

The answer is B

Step-by-step explanation:

bc its 45/15 :)

Answer:

The value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].

Step-by-step explanation:

In this problem, we need to evaluate [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex]. Here, c and d are variable with exponents.

Taking both c together

[tex]=(10c^6{\cdot} 2c^{-5})\\\\=20(c^6{\cdot} c^{-5})\\\\=20c^{6-5}\\\\=20[/tex]

Taking both d together

[tex]=(d^{-5}{\cdot}d^4)\\\\=d^{-5+4}\\\\=d^{-1}[/tex]

So,

[tex](10c^6d^{-5})(2c^{-5} d^4)=20d^{-1}[/tex]

Hence, the value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].

Answer:

Step-by-step explanation:

This problem is on the mensuration of flat shapes, a rectangular shape

we are required to solve for the length and width of the rectangular ball court

we know that the perimeter is expressed as

[tex]P= 2(L)+2(W)[/tex]

let the width be x

hence the length is 2x

Given data

perimeter = 64 meters

length l= 2x

width w= x

Substituting our data  and solving for x we have

[tex]64= 2(2x)+2(x)\\\\64= 4x+2x\\\\64= 6x[/tex]

Dividing both sides by 6 we have

[tex]x=\frac{64}{6}\\\\ x= 10.66[/tex]

Hence the width is 10.66 meters

The length is 2x= 2(10.66)= 21.33 meters

Answer:

7 + 8x

Step-by-step explanation:

-11 + 2 (4x -1) + 6

=> -11 + 8x -2 + 6

=> -13 + 8x + 6

=> -7 + 8x

So, the simplified expression is 7 + 8x.

Answer:

0

Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

= 8[6561/4]∫(cosθsinθ)dθ

= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

= 13122/2[-cos2θ]/2 from 0 to 2π

13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]

= -13122/4[cos4π - cos(0)]

= -13122/4[1 - 1]

= -13122/4 × 0

= 0

Answer: Choice A

Note: the range should be [tex][-5, \infty)[/tex]. See explanation below.

===================================================

We can plug in any real number for x to get some output for y. The domain is the set of all real numbers in which we say [tex](-\infty, \infty)[/tex] which is interval notation. It represents the interval from negative infinity to positive infinity.

The range is the set of possible outputs. The smallest output possible is y = -5 which occurs at the vertex (3,-5). We can get this y value or larger. So we can describe the range as the set of y values such that [tex]y \ge -5[/tex] and that translates to the interval notation [tex][-5, \infty)[/tex].

The square bracket says "include this endpoint" while the curved parenthesis says to exclude the endpoint. Your teacher mistakenly wrote [tex](-5, \infty)[/tex] for choice A, when they should have written [tex][-5, \infty)[/tex]

I think either your teacher made a typo or somehow the formatting messed up. Either way, choice A is the closest to the answer.

Option A is the correct choice .

Domain will be → all real numbers .

Range will be → y belongs to R : y greater than or equal to -5 .

→ (x+3)^2 It means 0 to infinity

So (x+3)^2-5= (-5, infinity)

→ Range = (-5, infinity )

Answer:

y-11

Step-by-step explanation:

First you divide 3 by 3 to get one. Then you add 12 to -1 to get 11. Then you will have y-11. PEMDAS saves lives.

Answer:

y = - 11

Step-by-step explanation:

Let y - 3/3 + 12 = 0

Multiply through by 3, we have as follow:

3y - 3 + 36 = 0

3y + 33 = 0

3y = - 33

y = -33/3 = -11

Answer:

Mean = $123.8

Range= $72

Variance= $607.344

Standard deviation=$ 24.64

Step by step explanation:

The list of the data of electricity bill on ascending order

$88,$90,$90,$95,$110,$115,$120,$126,$144,$150

Mean = (summation of($88,$90,$90,$95,$110,$115,$120,$126,$144,$150))/10

Mean = 1238/10

Mean = $123.8

Range= highest value- Lowest VA

Range= 150-88

Range= $72

Variance=( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)/10

Variance= (1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)/10

Variance= 6073.44/10

Variance=$ 607.344

Standard deviation= √variance

Standard deviation= √ 607.344

Standard deviation=$ 24.64

The mean monthly electric bill is $123.8

The Range is $72

The variance is $607.344

The standard deviation is $ 24.64

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

Σx = 88+90+90+95+110+115+120+126+144+150

Σx = 1238

Here n = 10

⇒ Mean = Σx/n

⇒ Mean = 1238/10

⇒ Mean = $123.8

Hence, the mean monthly electric bill is $123.8

⇒ Range = Largest value - Least value

⇒ Range = 150-88

⇒ Range= $72

Hence, the Range is $72

⇒ Σ(x -mean)² = ( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)

⇒ Σ(x -mean)² =(1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)

⇒ Σ(x -mean)² = 6073.44

Here n = 10

⇒ Variance = Σ(x -mean)²/10

⇒ Variance = 6073.44/10

⇒ Variance = $607.344

⇒ Standard deviation = √variance

⇒ Standard deviation = √607.344

⇒ Standard deviation = $24.64

Hence, the standard deviation is $24.64.

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The answer should be c) To determine if the relationship is bi-directional.

What is a scatterplot?

Scatterplot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed

To get an initial sense of whether the means of the groups are different from each other. scatterplot is used to show relation between the two variables. So option a is wrong.

To determine the research hypothesis has been proven. Scatterplot is no where related to research hypothesis. so option b is wrong

determine if the relationship is bi-directional. Scatterplot is used to determine that the variables are dependent or not i.e they have a relation or not ,option c is correct

To see if the relationship is postive or negative . Scatterplot is used to show dispersed data, it can't be used to show positive or negative.So option d is wrong

Therefore, option c is correct

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Answer: Experimental probability

Step-by-step explanation:

There are two kinds of probability: Theoretical probability and Experimental probability.

To calculate theoretical probability we divide favorable outcomes by total outcomes.

To calculate experimental probability we divide number of times an event occurs by the total number of trials or times the activity is performed.

Here, A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, which is dependent on the activity he performed, thus it is an experimental probability.

Answer:

Inequality

Step-by-step explanation:

An inequality is mathematical sentence that compares expression that are not equal.

Answer:

18

Step-by-step explanation:

25=7+r     25-7=18     7-7=0

r=18 Do you understand? I really hoped I helped. I was in your position when i was learning that.

Answer:

the answer is -203 i got 100%

Step-by-step explanation:

Answer:

a. c = 2030,

b. n = 1.42,

c. x = 2.875,

d. k = 140

Step-by-step explanation:

a ) 8120 = 4c,

c = 8120 / 4 = 2030

b ) 0.5n = 0.71,

n = 0.71 / 0.5 = 1.42

c ) 8x = 23,

x = 23 / 8 = 2.875

d ) 7 : 6 = k : 120

Here we want to convert this ratio into fraction form,

7 / 6 = k / 120

And now we can cross - multiply to determine the value of k,

6k = 7(120) = 840,

k = 840 / 6 = 140

We can check the value of k, by plugging it back into our ratio, and see if it reduces to 7 : 6,

140 : 120,

14 : 12,

7 : 6

Answer:

Hey there!

Basically, you are either going to North Dakota, New Hampshire, New Jersey, New York, New Mexico or North Carolina, as those are the only two word states beginning with N.

Thus, the chance of picking one of those is 6/50, or 3/25.

You have to choose one state, so this is Mutually Exclusive.

Let me know if this helps :)

Answer:

T = BP

Step-by-step explanation:

Boxes = B

Pack of paper in each box = P

Total number of packs = T

Is the equation for total number of packs of paper

Answer:

Step-by-step explanation:

  1+tan2A(tanA)=sec2A  

Right hand side  

sec2A=1cos2A=1cos2A−sin2A  

=cos2A+sin2Acos2A−sin2A  

=1+tan2A1−tan2A  

=1−tan2A+2tan2A1−tan2A  

=1−tan2A1−tan2A+2tan2A1−tan2A  

=1+2tanA1−tan2A×tanA  

=1+tan2A×tanA  

=Left hand side  

I HOPE THIS WILL HELP YOU

MARK ME AS BRAIN LIST

IF MY ANSWER IS HELP FUL

Answer:

c

Step-by-step explanation:

We need to divide [tex]9x^2-6x+2[/tex] by 3x -1

we know that 2 = 1+1 so

[tex](9x^2-6x+1)+1[/tex]

if you notice the thing that it's inside the parenthesis it's a perfect square

[tex]((3x)^2-2(3x)+1)+1\\=(3x-1)^2+1\\[/tex]

if we divide this by 3x -1 we get

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

so answe is c

Answer:

Well, we know that there exists a function f(x) such that f(x-1) is a direct transformation of its parent function. First we want to set x=x-1. Conceptually, it might be easier just to annotate one of the x’s as a completely different variable, because we know that x doesn’t equal x-1. So let’s rewrite as x=y-1 and solve for y.

We now have y=x+1 where y(x) is actually our parent function and y(x)=f(x+1). So take our equation f(x-1) and substitute each x with (x+1). So f(x)=2(x+1) + 3

f(x)= 2x + 5. We can check this by finding f(x-1) because it should equal 2x+3.

f(x-1)= 2(x-1) + 5

f(x-1)= 2x + 3.

Hoped I helped

Answer:

a) 0.4647

b) 24.6 secs

Step-by-step explanation:

Let T be interval between two successive barges

t(t) = λe^λt where t > 0

The mean of the exponential

E(T) = 1/λ

E(T) = 8

1/λ = 8

λ = 1/8

∴ t(t) = 1/8×e^-t/8   [ t > 0]

Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

= 1 - e^-5/8 = 0.4647

Therefore the probability that the time interval between two successive barges is less than 5 minutes is 0.4647

b)

Now we find t such that;

p[T>t] = 0.95

so

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t  = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

t = 24.6 secs

Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is 24.6 secs

a.) we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.

b.) the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.

Given to us:

exponential distribution with mean = E(T) = 8,

The mean of the exponential

E(T) = 1/λ

 1/λ = 8

λ = 1/8

∴ [tex]t(t) =\frac{1}{8} \times e^\frac{-t}{8} }\ ;\ [ t > 0][/tex]

(a) The probability that the time interval between two successive barges is less than 5 minutes.

Now the probability we need

[tex]\begin{aligned} \ [T<5] &= \int\limits^5_0 {t(t)} \, dt\\&= \int\limits^5_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\\\&= [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^5\\&= - [ e^{-t/8}]_0^5\\&= - [ e^{-5/8} - 1 ]\\&= 1 - e^{-5/8}\\&= 0.4647\end{aligned}[/tex]

So, we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.

b)  Now we find t such that;

[tex]\begin{aligned} \ &p[T>t]=0.95\\ & \int\limits^{10}_0 {t(t)} \, dt=0.95\\& \int\limits^{10}_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt=0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt = 0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt=0.95 \\\\& [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^{10}=0.95\\\\& - [ 0 - e^{-t/8} ] = 0.95&\ \ e^{-t/8} = 0.95\\\end{aligned}[/tex]

taking logs,

t = 24.6 secs

Hence,the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.

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Answer:

5.79%

Step-by-step explanation:

The percentage error in the measurement is obtained by;

|measured temperature - actual temperature|/actual temperature ×100

actual temperature= 95°F

measured temperature= 100.5°F

|100.5 - 95|/95×100

%error= 5.79%

Answer:

im Pretty sure x

Step-by-step explanation: Distribute:

=4x2+−12x+9+−9x2+12x+−4

Combine Like Terms:

=4x2+−12x+9+−9x2+12x+−4

=(4x2+−9x2)+(−12x+12x)+(9+−4)

=−5x2+5

Answer:  −5x2+5

Answer:

200% of tickets handed out this year

Step-by-step explanation:

Let

Tickets handed out last year=x

Tickets handed out this year=2x

The number of tickets handed out this year was what percent of the number handed out last year

Last year was x%

Then, this year would be 200x%

200% tickets was handled out this year

Answer:

x = -5

Step-by-step explanation:

Step 1: Write out equation

15x - 24 - 4x = -79

Step 2: Combine like terms

11x - 24 = -79

Step 3: Add 24 to both sides

11x = -55

Step 4: Divide both sides by 11

x = -5

Step 5: Check step

Plug in -5 into the original equation

15(-5) - 24 - 4(-5) = -79

-75 - 24 + 20 = -79

-99 + 20 = -79

-79 = -79

Answer:

x = -5

Step-by-step explanation:

15x - 24 - 4x = -79

11x - 24 = -79

11x = -55

x = -5

Check:

15 * -5 - 24 - 4 * -5

= -75 - 24 + 20

= -79

Answer:

Yes we reject the null hypothesis

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 9[/tex]

   The  population mean is  [tex]\mu = 40[/tex]

    The  sample  mean is  [tex]\= x = 33[/tex]

    The  standard deviation is [tex]\sigma = 9[/tex]

    The  level of significance is  [tex]\alpha = 0.05[/tex]

For a two-tailed test

The  null hypothesis is  [tex]H_o : \mu = 40[/tex]

The alternative hypothesis is  [tex]H_a : \mu \ne 40[/tex]

Generally the test statistics is mathematically represented as

        [tex]t = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]

=>     [tex]t = \frac{ 33 - 40 }{ \frac{9}{\sqrt{9} } }[/tex]

=>     [tex]t = -2.33[/tex]

The  p-value for the two-tailed test  is mathematically represented as

     [tex]p-value = 2 P(z > |-2.33|)[/tex]

From the z-table  

            [tex]P(z > |-2.33|) = 0.01[/tex]

       [tex]p-value = 2 * 0.01[/tex]

       [tex]p-value = 0.02[/tex]

Given that [tex]p-value < \alpha[/tex] Then we reject the null hypothesis

Answer:

T = 5c +5d,    where unit of the equation is $.

Step-by-step explanation:

Cost of 1 large cheese  pizza = $5

No. of large cheese pizza = c

therefore

cost of c  large cheese pizza = c*Cost of 1 large cheese  pizza = $5c

Cost of 1 large one topping  pizza = $6

No. of large one topping pizza = d

therefore

cost of d  large one topping pizza = d*Cost of 1 large one topping  pizza =             cost of d  large one topping pizza = $6d  

Total cost of  c  large cheese pizza and cost of d  large one topping pizza

= $5c +$6d

total cost is represented by T

thus, T = $5c +$5d  Answer

Answer:

it is an example of an expression

Step-by-step explanation:

it is an example of an expression because it is asking a question without an equal sign. so its not a question, but an expression

Answer:

D. (2, -4),(3, -1), (4, -4)

Step-by-step explanation:

Hello!

When you reflect over the y-axis you reverse the x.

Negatives become positives and positives become negatives

(-2, -4) turns into (2, -4)

(-3, -1) turns into (3, -1)

(-4, -4) turns into (4, -4)

look for the answer that has (2, -4),(3, -1), and (4, -4)

The answer is D

Hope this helps!

Answer:

the answer is D

Step-by-step explanation:

because i said so