1.expand and simplify 2(x-4) -3 (x-2)


2.factorise a^2 + a

Answer:

a)  y₂ (x) = e ⁵ˣ  

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

b) particular integral

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Step-by-step explanation:

step(i):-

Given differential equation y''-25y= 4

operator form

             ⇒    D²y - 25 y =4

            ⇒     (D² - 25) y =4

       This is the form of f(D)y = ∝(x)

where f(m) = D² - 25     and ∝(x) =4

The auxiliary equation A(m) =0

                         ⇒ m² - 25 =0

                          m² - 5²  =0

                      ⇒ (m+5)(m-5) =0

                     ⇒ m =-5 , 5

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

This is form of

             [tex]y_{C} = C_{1} y_{1} (x) + C_{2} y_{2} (x)[/tex]

where y₁ (x) = e⁻⁵ˣ   and  y₂ (x) = e ⁵ˣ  

Step(ii):-

Particular integral:-

[tex]P.I = y_{p} = \frac{1}{f(D)} \alpha (x)[/tex]

[tex]P.I = y_{p} = \frac{1}{D^{2} -25} 4[/tex]

      =  [tex]= \frac{1}{D^{2} -25} 4e^{0x}[/tex]

put D = 0

The particular integral

[tex]y_{p} = \frac{1}{ -25} 4[/tex]

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Conclusion:-

General solution of given differential equation

[tex]y = y_{C} +y_{P}[/tex]

[tex]y = C_{1} {e^{-5x} } + C_{2} {e^{5x} } -\frac{4}{25}[/tex]

Answer:

  12√2 feet ≈ 16.97 feet

Step-by-step explanation:

For the dimensions shown in the attached diagram, the distance "a" along the ladder from the ground to the fence is ...

  a = (6 ft)/sin(x) = (6 ft)/sin(0.82) ≈ 8.206 ft

The distance along the ladder from the top of the fence to the wall is ...

  b = (6 ft)/cos(x) = (6 ft)/cos(0.82) ≈ 8.795 ft

__

In general, the distance along the ladder from the ground to the wall is ...

  L(x) = a +b

  L(x) = 6/sin(x) +6/cos(x)

This distance will be shortest for the case where the derivative with respect to x is zero.

  L'(x) = 6(-cos(x)/sin(x)² +sin(x)/cos(x)²) = 6(sin(x)³ -cos(x)³)/(sin(x)²cos(x²))

This will be zero when the numerator is zero:

  0 = 6(sin(x) -cos(x))(1 -sin(x)cos(x))

The last factor is always positive, so the solution here is ...

  sin(x) = cos(x)   ⇒   x = π/4

And the length of the shortest ladder is ...

  L(π/4) = 6√2 + 6√2

  L(π/4) = 12√2 . . . . feet

_____

The ladder length for the "trial" angle of 0.82 radians was ...

  8.206 +8.795 = 17.001 . . . ft

The actual shortest ladder is ...

  12√2 = 16.971 . . . feet

Answer:

(1) Given

(2) Definition of midpoint

(3) Transitivity

(4) PWP (Parts Whole Postulate)

Answer:

Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.

Step-by-step explanation:

The initial value of a function f(x) is f(0), that is, the value of f when x = 0.

Format:

[tex]f(x) = ab^{x}[/tex]

The initial value is f(0). So

[tex]f(x) = ab^{x}[/tex]

[tex]f(0) = ab^{0}[/tex]

Any non-zero value elevated to the zero is 1.

So

[tex]f(0) = ab^{0} = a*1 = a[/tex]

Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.

Answer:

SAmple Answer Edge 2020-2021

Step-by-step explanation:

When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.

Answer:

C (the third graph)

Step-by-step explanation:

This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.

Answer:

see below

Step-by-step explanation:

This graph has an asymptote at y = 0 and x=0

This excludes these values

The domain excludes x =0

The range excludes y=0

Answer:

5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.

Step-by-step explanation:

Answer:

126

Step-by-step explanation:

0.1x=12.6

126

Answer:

1 - 4x

Step-by-step explanation:

First, do multiplication

4 times x is 4x

Then subtract 4x from 1

1 - 4x

Answer:

24

Step-by-step explanation:

Since you are given almost everything, you just simply divide by 5=>

120/5 = 24

Hope this helps

Answer:

The mode would decrease by 3

Step-by-step explanation:

The mode right now is 6, as there are 4 6's. However, closely behind it is 3, with 3 3's. If we replaced a 6 with a 3, we would have 4 3's and 3 6's. Find the difference between 6 and 3 and you answer should be 3.

Answer:

a.1.90 years

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]n = 25, \sigma = 3.8[/tex]

So

[tex]M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90[/tex]

So the correct answer is:

a.1.90 years

Answer:

A

Step-by-step explanation:

The area of a kite is half of the product of the length of the diagonals, or in this case 16*12/2=96 square feet. Hope this helps!

Answer:

a. 96 ft^2

Step-by-step explanation:

You can cut the kite into 2 equal triangle halves vertically.

Then you can use the triangle area formula and multiply it by 2 since there are 2 triangles.

[tex]\frac{1}{2} *12*8*2=\\6*8*2=\\48*2=\\96ft^2[/tex]

The kite's area is a. 96 ft^2.

Answer:

2x - y - 3 = 0

Step-by-step explanation:

Find slope-intercept form first: y = mx + b

Step 1: Pick out 2 points

In this case, I picked out (2, 1) and (0, -3) from the graph

Step 2: Using slope formula y2 - y1/x2 - x1 to find slope

-3 - 1/0 - 2

m = 2

Step 3: Place slope formula results into point-slope form

y = 2x + b

Step 4: Plug in a point to find b

-3 = 2(0) + b

b = -3

Step 5: Write slope-intercept form

y = 2x - 3

Step 6: Move all variables and constants to one side

0 = 2x - 3 - y

Step 7: Rearrange

2x - y - 3 = 0 is your answer

Answer:

x=1

Step-by-step explanation:

sqrt(x+3) = sqrt(5x-1)

Square each side

x+3 = 5x-1

Subtract x from each side

3 = 4x-1

Add 1 to each side

4 =4x

Divide by 4

x=1

Answer:

x= 1

Step-by-step explanation:

[tex]\sqrt{x+3}=\sqrt{5x-1}[/tex]

Square both sides.

x + 3 = 5x - 1

Subtract 3 and 5x on both sides.

x - 5x = -1 - 3

-4x = -4

Divide -4 into both sides.

-4x/-4 = -4/-4

x = 1

Answer: height = 13.24 m

Step-by-step explanation:

Draw a picture (see image below), then set up the proportions to find the length of QB.  Then input QB into either of the equations to find h.

Given: PQ = 10

          ∠TPB = 23°

          ∠TQB = 32°

[tex]\tan P=\dfrac{opposite}{adjacent}\qquad \qquad \tan Q=\dfrac{opposite}{adjacent}\\\\\\\tan 23^o=\dfrac{h}{10+x}\qquad \qquad \tan 32^o=\dfrac{h}{x}\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x[/tex]

[tex]\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}[/tex]

Answer:

21

Step-by-step explanation:

so this is the way i learned it

compare side to side so CA is 12 and LM is 9 so its 4/3

CB is 8 LN is 6 so its 4/3

so AB is 8 so MN would have to be 4/3 which would made MN 6 so MNL would be 21

Answer:

21

Step-by-step explanation:

ΔLMN ≅ ΔABC with a scale factor of 0.75

If Line AB is similar to Line MN, then Line MN is 6.

Perimeter of ΔLMN

9+6+6=

15+6=

21

Answer:

A) 0.028

Step-by-step explanation:

Given:

Sample size, n = 115

Population parameter, p = 0.1

The X-Bin(n=155, p=0.1)

Required:

Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.

To find the standard deviation, use the formula below:

[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

Substitute figures in the equation:

[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]

[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]

[tex] \sigma = 0.028 [/tex]

The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028

Answer:

P(X=2) = 0.302

Step-by-step explanation:

With the conditions mentioned in the question, we can model this variable as a binomial random variable, with parameters n=9 and p=0.2.

The probability of having k defective items in the sample of nine chips is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{9}{k} 0.2^{k} 0.8^{9-k}\\\\\\[/tex]

Then, the probability of having 2 defective chips in the sample is:

[tex]P(x=2) = \dbinom{9}{2} p^{2}(1-p)^{7}=36*0.04*0.2097=0.302\\\\\\[/tex]

Answer: x = -5

Step-by-step explanation:

If you factor each denominator, you can find the LCM.

[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x  + 8 =       3

x        =      -5

4x

Step-by-step explanation:

I think x(5 - 1) is ur answer

X(5-1)

=X(4)

=4x

Hope this helps

Answer:

95% of the data falls between 0.64 and 3.92

Step-by-step explanation:

Using the Empirical Rule, 95% of the data will fall 2 standard deviations above and below the mean. Therefore, from the mean of 2.28, the lower change will be 2.28 - 2(0.82)= 0.64 and the upper change will be 2.28 + 2(0.82)= 3.92‬

Answer:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Step-by-step explanation:

We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).

The values in the form of ([tex]x,y,z[/tex]) are:

[tex]x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5[/tex]

[tex]$\vec{PQ}$[/tex] can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.

[tex]\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>[/tex]

[tex]\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>[/tex]

The equation of line in vector form can be written as:

[tex]\vec{r} (t) = <1,-6,7> + t<-10,16,-12>[/tex]

The standard parametric equation can be written as:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Answer:

$20 of credit left on the card

Step-by-step explanation:

If we say that the prepaid phone card has 25 minutes on it since Maya paid 25 dollars for it. We can multiply 25 times 4 which equals 1 dollar per 4 minutes. Then, we can divide 20 by 4 to get 5 which means that she used 5 dollars of call time. We can now subtract 25-5 and we get 20. This tells us that there is 20 dollars left on the card.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

b

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

There are 4 numbers out of 5 that are greater than 3 so the probability will be 4/5 chance or 80%.

Answer:

Well I got 80%

Step-by-step explanation:

Answer:

[tex]1/\sqrt{2}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $2.70

Standard deviation r = $0.93

Number of samples n = 22

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$2.70+/-1.645($0.93/√22)

$2.70+/-1.645($0.198276666210)

$2.70+/-$0.326165115916

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

[tex]Z = \frac{X - \mu}{s}[/tex]

X = 205

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{205 - 200}{5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{195 - 200}{5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{210 - 200}{5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{190 - 200}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

(a): The required probability is [tex]P(195 < \bar{x} < 205)=0.6826[/tex]

(b): The required probability is [tex]P(190 < \bar{x} < 200)=0.9544[/tex]

A numerical measurement that describes a value's relationship to the mean of a group of values.

Given that,

mean=200

Standard deviation=50

[tex]n=100[/tex]

[tex]\mu_{\bar{x}}=200[/tex]

[tex]\sigma{\bar{x}} =\frac{\sigma}{\sqrt{n} } \\=\frac{50}{\sqrt{100} }\\ =5[/tex]

Part(a):

within [tex]5=200\pm 5=195,205[/tex]

[tex]P(195 < \bar{x} < 205)=P(-1 < z < 1)\\=P(z < 1)-P(z < -1)\\=0.8413-0.1587\\=0.6826[/tex]

Part(b):

within [tex]10=200\pm 10=190,200[/tex]

[tex]P(190 < \bar{x} < 200)=P(-1 .98 < z < 1.98)\\=P(z < 2)-P(z < -2)\\=0.9772-0.0228\\=0.9544[/tex]

Learn more about the topic Z-score:

https://brainly.com/question/5512053

Answer:

Step-by-step explanation:

It is given that

[tex]\Delta=\begin{vmatrix}3&0&3\\2 &3&3\\0 &4&-2\end{vmatrix}[/tex]

By cofactor expansion across the first row, we get

[tex]\Delta=a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}[/tex]

[tex]\Delta=3\left[(-1)^{1+1}\begin{vmatrix}3&3\\4&-2\end{vmatrix}\right]+0\left[(-1)^{1+2}\begin{vmatrix}2&3\\0&-2\end{vmatrix}\right]+3\left[(-1)^{1+3}\begin{vmatrix}2&3\\0&4\end{vmatrix}\right][/tex]

[tex]\Delta=3\left[-18\right]+0\left[(-1)(-4)\right]+3\left[8\right][/tex]

[tex]\Delta=-54+0+24[/tex]

[tex]\Delta=-30[/tex]

Therefore, the value of determinant is -30.

By cofactor expansion across the second column, we get

[tex]\Delta=a_{12}C_{12}+a_{22}C_{22}+a_{32}C_{32}[/tex]

[tex]\Delta=0\left[(-1)^{2+1}\begin{vmatrix}2&3\\0&-2\end{vmatrix}\right]+3\left[(-1)^{2+2}\begin{vmatrix}3&3\\0&-2\end{vmatrix}\right]+4\left[(-1)^{3+2}\begin{vmatrix}3&3\\2&3\end{vmatrix}\right][/tex]

[tex]\Delta=0\left[(-1)(-4)\right]+3\left[(-6)\right]+4\left[(-1)3\right][/tex]

[tex]\Delta=-18-12[/tex]

[tex]\Delta=-30[/tex]

Therefore, the value of determinant is -30.

Answer:

Volume of a cone = 1/3πr²h

h = height

r = radius

r = 3cm h = 4cm

Volume = 1/3π(3)²(4)

= 36 × 1/3π

= 12π

= 36.69cm³

= 37cm³ to the nearest tenth

Hope this helps

Answer:

37.7

_______

NOT 37

Step-by-step explanation:

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]3^{2}[/tex] · [tex]4 = 12\pi = 37.69911 =[/tex] 37.7