Given that 243√3 =3^a, find the value of a

Answer: 0.4255

Step-by-step explanation:

Given:  IQ scores of adults, and those scores are normally distributed

Mean: [tex]\mu=100[/tex]

Standard deviation: [tex]\sigma= 15[/tex]

Let X denotes the IQ of a random adults.

The area between 102 and 130 = [tex]P(102<X<130)=P(\dfrac{102-100}{15}<\dfrac{X-\mu}{\sigma}<\dfrac{130-100}{15})[/tex]

[tex]=P(0.13<Z<2)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<2)-P(Z<0.13)\\\\=0.9772- 0.5517\ [\text{By z-table}]\\\\=0.4255[/tex]

Hence, area between 102 and 130 = 0.4255

Answer:

Time taken by Stephen = 162 seconds

Step-by-step explanation:

Stephan gathered data which fits in the line of best fit,

y = -2.1x + 565.6

Where x represents the age (in months)

And y represents the time (in seconds) taken by Stephen to run two laps on the track.

Time taken to run 2 laps at the age of 192 months,

By substituting x = 192 months,

y = -2.1(192) + 565.6

  = -403.2 + 565.6

  = 162.4 seconds

  ≈ 162 seconds

Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.

Answer:

2 meters

Step-by-step explanation:

The volume is 4.5

​

⋅1.5⋅h⋅3

=2.25h

=h

​

The height of the tent is 2 meters.

Hope this helps :)

Answer:

2 meters

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Anything raised to  0 is 1

Multiply i 1 by  1

Simplify.

Rewrite i2 as −1

Move −1  to the left of i

Rewrite −1 i as −i

Factor out i2

Rewrite i2 as −1

Rewrite i2 as  −1

Rewrite i4 as 1

Multiply −1 by  1

Answer:

Slope = -2

Step-by-step explanation:

You want to get it to the slope intercept form first.

2y = -4x + 3

Divide by 2

y = -2x + 3/2

Parallel means in the new slope intercept form there will still be -2x.

y = -2x + b (enter in points ( 0, 1.5 ) )

1.5 = 0 + b

b = 1.5

y = -2x + 1.5 ( just an example of a line parallel to 4x + 2y = 3 )

Answer:

a)P [ z > 1,38 ] = 0,08379

b) P [ 1,233 < z < 2,43 ]  = 0,1012

c)  P [ z > -2,43 ]  = 0,99245

Step-by-step explanation:

a) P [ z > 1,38 ] = 1 -  P [ z < 1,38 ]

From z-table  P [ z < 1,38 ] = 0,91621

P [ z > 1,38 ] = 1 - 0,91621

P [ z > 1,38 ] = 0,08379

b)  P [ 1,233 - 2,43 ]  must be  P [ 1,233 < z < 2,43 ]

P [ 1,233 < z < 2,43 ]  = P [ z < 2,43 ] - P [ z > 1,233 ]

P [ z < 2,43 ]  = 0,99245

P [ z > 1,233 ] = 0,89125    ( approximated value  without interpolation)

Then

P [ 1,233 < z < 2,43 ]  = 0,99245 - 0,89125

P [ 1,233 < z < 2,43 ]  = 0,1012

c) P [ z > -2,43 ]

Fom z-table

P [ z > -2,43 ] = 1 - P [ z < -2,43 ]

P [ z > -2,43 ] = 1 - 0,00755

P [ z > -2,43 ]  = 0,99245

Answer:

A : A1 = -7, an = an-1 + 3

Step-by-step explanation:

a1=-7, a2=-7+(1)3=-4

a3=-7+(2)3=-1

Answer:

C-(7)

Step-by-step explanation:

Given figure is a trapezoid and 21 - x is the mid segment.

Therefore by mid-segment formula of a trapezoid, we have:

21 - x = 1/2(17 + 11)

21 - x = 1/2 * 28

21 - x = 14

21 - 14 = x

7 = x

x = 7

Answer:

55%

Step-by-step explanation:

Because 11/20= 0.55

0.55=55%

Answer:

we will fail to reject the null hypothesis and conclude that the return rate is less than​ 20%.

Step-by-step explanation:

We are given;

Sample size;n = 6970

Success rate;X = 1334/6970 = 0.1914

Now, we want to test the claim that the return rate is less than p = 0.2, hence the null and alternative hypothesis are respectively;

H0: μ < 0.2

Ha: μ ≥ 0.2

The standard deviation formula is;

σ = √(x(1 - x)/n)

σ = √(0.1914(1 - 0.1914)/6970)

σ = 0.004712

Now for the test statistic, formula is;

z = (x - μ)/σ

z = (0.1914 - 0.2)/0.004712

z = -1.825

From the a-distribution table attached, we have a value of 0.03362.

This p-value gotten from the z-table is more than the significance value of 0.01. Thus, we will fail to reject the null hypothesis and conclude that the return rate is less than​ 20%.

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer:

x = -1

y =2

Step-by-step explanation:

3x+ 5y = 7

9x+ 11y = 13

Multiply the first equation by -3 so we can eliminate x

-3 (3x+ 5y = 7)

-9x -15y = -21

Add this to the second equation

-9x -15y = -21

9x+ 11y = 13

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

   - 4y = -8

Divide by -4

-4y/-4 = -8/-4

y=2

Now solve for x

3x+5y = 7

3x+5(2) = 7

3x+10 = 7

Subtract 10

3x = 7-10

3x = -3

Divide by 3

3x/3 = -3/3

x = -1

Answer:

-1, 2

Step-by-step explanation:

Although you already have the answer, here's another method of doing it that may or may not help you someday. First, we solve the top equation for x. We get:

[tex]x = \frac{7}{3} - \frac{5}{3}y\\9x + 11y = 13[/tex]

Now that we know what x is, we can plug it into the bottom equation to solve for y.

[tex]9(\frac{7}{3} - \frac{5}{3}y) + 11y = 13[/tex]

Simplify everything out, and you'll see that y = 2. We can now plug it into our equation to solve for x.

x = 7/3 - 5/3 x 2; x = -1

Answer:

4 ounces

Step-by-step explanation:

6x2/3= 4

Answer:

5u+8

Step-by-step explanation:

Both of the 4's will cancel out with each other.

5u+8. it works actuallly by taking common nunbers and cancelling them. in this case. 4. leaving it with just 5u+8 :)

Answer: 3

Step-by-step explanation:

7x=21 21/7=3

Answer:

the answer is c

Step-by-step explanation:

because if the surgery has a 92% success rate and the splints have a 72% success rate then surgery would be recommended because it has a higher success rate

Answer:

  C.  10

Step-by-step explanation:

The given information tells you that triangles YZX and YZA are congruent, so ZA = ZX = 10.

Answer:

The variable n represents the number of times in a year in which we compound the interest rate

Step-by-step explanation:

The periodic compound interest formula is given as;

A = P( 1 + r/n)^nt

The variable n represents the number of times in a year in which the interest rate is compounded

Answer:

its D. -3c

Step-by-step explanation:

just took the test

The expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c

[(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)]

[3c(2c + 1)/(-2(2c - 1))] ÷ [(2c + 1)/(2(2c - 1)]

3/2 ÷ 1/5 is the same as; 3/2 × 5/1

Applying this same method to our question gives;

[3c(2c + 1)/(-2(2c - 1))] × [(2(2c - 1)/(2c + 1)]

Read more about simplification of fractions at;https://brainly.com/question/6109670

Answer:

g(x) = [tex]5(2^{2x} )[/tex]

Step-by-step explanation:

If a function f(x) is vertically stretched by a factor of k, the new function we get in the form of k.f(x).

Rule to be followed,

y = k.f(x)

Where k > 1

If the function is vertically compressed then 0 < k < 1

Following the same rule,

A function, f(x) = [tex]2^{2x}[/tex] when vertically stretched by a factor of 5,

Transformed function will be,

g(x) = [tex]5(2^{2x} )[/tex]

Answer:

$435,000

Step-by-step explanation:

$760 per month * 12 months = $9,120

The minimum rent requires an annual rental cost of $9,120.

The annual rent was $20,520.

The excess was $20,520 - $9,120 = $11,400.

The amount of $11,400 of the rent was due to the gross sales in excess of $150,000.

$11,400 is 4% of the amount in excess of $150,000.

Let the amount in excess of $150,000 = x.

$11,400 = 4% of x

0.04x = 11,400

x = 285,000

$285,000 is the amount in excess of $150,000.

Total gross sales volume = $285,000 + $150,000 = $435,000

Answer:

$9.95.

Step-by-step explanation:

Let's say that you are buying a avatars and b bats.

3a + 3b = 29.85

Divide all terms by 3.

a + b = 9.95

You will pay $9.95 if you buy one of each.

Hope this helps!

Answer:

The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:

500 = 4 * b³

125 = b³

b = 5 so the answer is f(x) = 4 · 5ˣ.

Answer:

f(x)=4(5)x

Step-by-step explanation:

An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.

Answer:

x = -1.964636

Step-by-step explanation:

Given equation;

eˣ = 4 - x²

This can be re-written as;

eˣ - 4 + x² = 0

Let

f(x) = eˣ - 4 + x²    -----------(i)

To use Newton's method, we need to get the first derivative of the above equation as follows;

f¹(x) = eˣ - 0 + 2x

f¹(x) = eˣ + 2x         -----------(ii)

The graph of f(x) has been attached to this response.

As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.

Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0

From Newton's method,

[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]

=> When n=0, the equation becomes;

[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]

[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]

Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;

f(-2) = e⁻² - 4 + (-2)²

f(-2) = e⁻² = 0.13533528323

And;

f¹(2) = e⁻² + 2(-2)

f¹(2) = e⁻² - 4 = -3.8646647167

Therefore

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - -0.03501863503[/tex]

[tex]x_{1} = -2 + 0.03501863503[/tex]

[tex]x_{1} = -1.9649813649[/tex]

[tex]x_{1} = -1.96498136[/tex]         [to 8 decimal places]

=> When n=1, the equation becomes;

[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]

[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]

Following the same procedure as above we have

[tex]x_{2} = -1.96463563[/tex]

=> When n=2, the equation becomes;

[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]

[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]

Following the same procedure as above we have

[tex]x_{3} = -1.96463560[/tex]

From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately  -1.964636 to 6 decimal places.

Newton's method of approximation is one of the several ways of estimating values.

The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

The equation is given as:

[tex]\mathbf{e^x = 4 - x^2}[/tex]

Equate to 0

[tex]\mathbf{4 - x^2 = 0}[/tex]

So, we have:

[tex]\mathbf{x^2 = 4}[/tex]

Take square roots of both sides

[tex]\mathbf{ x= \pm 2}[/tex]

So, the negative root is:

[tex]\mathbf{x = -2}[/tex]

[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]

Differentiate

[tex]\mathbf{f'(x) = e^x +2x }[/tex]

Using Newton's method of approximation, we have:

[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]

When x = -2, we have:

[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]

[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]

So, we have:

[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -1.96498136}[/tex]

Repeat the above process for repeated x values.

We have:

[tex]\mathbf{x_{2} = -1.96463563}[/tex]

[tex]\mathbf{x_{3} = -1.96463560}[/tex]

Up till the 6th decimal places,

[tex]\mathbf{x_2 = x_3}[/tex]

Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

Read more about Newton approximation at:

https://brainly.com/question/14279052

Answer:

1.5

Step-by-step explanation:

average rate of change = (f(x2) - f(x1))/(x2 - x1)

f(x) = -2/x^2

f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5

f(x1) = f(1) = -2/1^2 = -2

average rate of change = (-0.5 - (-2))/(2 - 1)

average rate of change = (-0.5 + 2)/1

average rate of change = 1.5

Answer:

PR=8x+4

Step-by-step explanation:

Given:

PQ=3x-2

QR=5x+6

Required:

PR=?

Formula:

PR=PQ+QR

Solution:

PR=PQ+QR

PR=3x-2+5x+6

PR=3x+5x+6-2

PR=8x+4

Hope this helps ;)❤❤❤

Answer:

4(2x + 1)

Step-by-step explanation:

4(2x + 1)

Answer:

$12.10

Step-by-step explanation:

First, you have to set up a proportion to find what 20% of $60.50, or 60.5, is. On one side of the proportion you have 20/100 to represent the percent, anytime you have a percent it will always go over 100. On the other side you'll have x/60.5 because you are trying to find a value out of 60.5. This gives you the proportion 20/100=x/60.5. In order to solve this you have to cross multiply using the equation 20(60.5)=100x. First, you multiply to get 1210=100x, then divide both sides by 100 to get 12.1=x. In order for this to represent money, we add a zero on the end. This means that 20% of $60.50 is $12.10, so $12.10 is the tip.

Answer:

x = c × sin(α)

x = 15 x sin(38)

= 9.23492

=      9.2

Step-by-step explanation:

Answer:

18 1/5

Step-by-step explanation:

Hey there!

Well to multiply them let's make them improper.

13/3 * 21/5

13*21 = 273

3*5 = 15

273/15

Simplified

18 1/5

Hope this helps :)

Answer:

[tex]\huge\boxed{4\dfrac{1}{3}\times4\dfrac{1}{5}=18\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]4\dfrac{1}{3}\times4\dfrac{1}{5}\\\\\bold{STEP\ 1}\\\text{convert the mixed numbers to the improper fractions}\\\\4\dfrac{1}{3}=\dfrac{4\times3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\4\dfrac{1}{5}=\dfrac{4\times5+1}{5}=\dfrac{20+1}{5}=\dfrac{21}{5}\\\\\bold{STEP\ 2}\\\text{simplify fractions}\\\\4\dfrac{1}{3}\times4\dfrac{1}{5}=\dfrac{13}{3}\times\dfrac{21}{5}=\dfrac{13}{1}\times\dfrac{7}{5}\\\\\bold{STEP\ 3}\\\text{multiply numerators and denominators}\\\\=\dfrac{13\times7}{1\times5}=\dfrac{91}{5}[/tex]

[tex]\bold{STEP 4}\\\text{convert the improper fraction to the mixed number}\\\\=\dfrac{91}{5}=\dfrac{90+1}{5}=\dfrac{90}{5}+\dfrac{1}{5}=18\dfrac{1}{5}[/tex]