Find all the missing side lengths for the following triangles.

Multiply both sides of the ODE

[tex]x'+2tx+5t[/tex]

by [tex]e^{t^2}[/tex]:

[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]

Now the left side can be condensed as the derivative of a product:

[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]

Integrate both sides, then solve for x :

[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]

[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]

Given that x(0) = 8, we find

[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]

so that the particular solution to this IVP is

[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]

Answer:

20*19*18 = 6840

UNLESS...............  

he is allowed to ride the same ride again , over and over....  

then it is 20 x 20 x 20 = 8000

Step-by-step explanation:

Answer:

These are vertical transformations because the parent function is being translated up and down which are vertical directions.

Answer:

Total bill = $70.80

Step-by-step explanation:

$60 × 0.18 = $10.80

$60 + $10.80 = $70.80

Hope this helps! :)

Answer:

$70.8

Step-by-step explanation:

Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8

Now we have to add 60+10.8=$70.8

Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.

Answer:

1). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]

2). log(x - 1) + log5x = 2

3). ln(x + 5) = ln(x - 1) + ln(x + 1)

4). [tex]e^{x^2}=e^{4x+5}[/tex]

Step-by-step explanation:

1). ln(x + 5) = ln(x - 1) + ln(x + 1)

   ln(x + 5) = ln(x - 1)(x + 1)  [Since ln(a×b) = ln a + lnb]

   (x + 5) = (x- 1)(x + 1)

   x + 5 = x² - 1

   x² - x - 6 = 0

   x² - 3x + 2x - 6 = 0

   x(x - 3) + 2(x - 3) = 0

   (x + 2)(x - 3 ) = 0

   x = -2, 3

   But x = -2 is an extraneous solution.

  Therefore, x = 3 is the only solution.

2). [tex]e^{x^2}=e^{4x+5}[/tex]

  x² = 4x +5

  x² - 4x - 5 = 0

  x² - 5x + x - 5 = 0

  x(x - 5) + 1(x - 5) = 0

  (x + 1)(x - 5) = 0

  x = -1, 5

  Therefore, solution set is (-1, 5)

3). [tex]\text{log}_4(5x^2+2)=\text{log}_4(x + 8)[/tex]

   5x² + 2 = (x + 8)  

   5x² - x - 6 = 0

   5x² - 6x + 5x - 6 = 0

   x(5x - 6) + 1(5x - 6) = 0

   (x + 1)(5x - 6) = 0

   x = -1, [tex]\frac{6}{5}[/tex]

4). log(x - 1) + log5x = 2

    log(x - 1)(5x) = 2

    5x(x - 1) = 10² [if loga = b, [tex]a=10^{b}[/tex]]

    5x² - 5x - 100 = 0

    x² - x - 20 = 0

    x² - 5x + 4x - 20 = 0

    x(x - 5) + 4(x - 5) =0

    (x - 5)(x + 4) = 0

    x = -4, 5

But x = -4 is an extraneous solution.

Therefore, x = 5 is the only solution.

Full question:

Eighteen of 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

Answer:

16/25

Step-by-step explanation:

Probability is the likelihood of an event happening and it is calculated as the number of favourable outcomes divided by the total number of possible outcomes. From the above we can calculate probability of finding a DVR that is not defective by adding up number of DVRS that are not defective in the DVRS(favourable outcomes) and dividing it by the total number of DVRS(total number of possible outcomes).

Non defective dvrs=total number of dvrs-defective dvrs=50-18=32

So probability here=non defective dvrs/total number of dvrs

=32/50=16/25

Answer: If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.

Step-by-step explanation:

Given: 7+5i is a zero of a polynomial function of degree 5 with coefficients

Here, 7+5i is a complex number.

So, it conjugate ([tex]\overline{7+5i}=7-5i[/tex]) is also a zero of a polynomial function.

Hence, if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.

If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i

The standard form of writing complex numbers with real and imaginary values is expressed as:

z = x + iy

The conjugate of the complex number will be y = x - iy

Given the polynomial 7 + 5i. If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i

Learn more here: https://brainly.com/question/18018849

Answer:

I don't think so

Step-by-step explanation:

Answer:

D. x²/1953²  + y²/ 1466² = 1

Step-by-step explanation:

==>Given:

Radius of spherical moon = 1000km

Distance of satellite from moon surface = 953km to 466km

==>Required:

Derived equation of ellipse

==>Solution:

The formula for driving an equation of ellipse is given as:

x²/a² + y²/b² = 1

Where,

a = length of the semi-major axis, while,

b = length of the semi-major axis

Since we are told that the satellite distance to the surface of the moon varies from 953km to 466km, values of a and b is calculated by summing each length to the radius of the moon as follows:

a = radius of moon + the larger distance of the satellite = 1000+953 = 1,953km

b = radius of moon + the smaller distance of the satellite = 1000+466 = 1,466km

Thus, the equation of the ellipse would be:

x²/1953²  + y²/ 1466² = 1

Answer:

D.

Step-by-step explanation:

To tell whether the domains can include 0, all you need to do is find where x = 0, and whether the y-value is real.

h(x) = sqrt(2x^2 + 5x - 3)

= sqrt(0^2 + 5 * 0 - 3)

= sqrt(-3)

Since this includes the square root of a negative number, h(0) is an imaginary number. That means that we can eliminate choices A and B.

If you look at the graph of w(x), when x = 0, there is a real value for the y-value on the graph. But, if you think about it, if you have 0 workers, there is no way that you can still be producing wrenches. So, the domain cannot contain 0.

Your answer will be D.

Hope this helps!!

Answer:

Result = 9b/25 or 36b/100

Step-by-step explanation:

The number is b

step 1

b is decreased by 40%

value of 40% of b = 40/100 *b = 4b/10

New value after this change = b - 40% decreased value of b = b -4b/10

= (10b-4b)/10 = 6b/10

Step 2 The new value obtained is again decreased by 40%

value of 40%  number found in step 1 =  40% of value found in step 1

value of 40%  number found in step 1 =  40/100 * 6b/10 = 24b/100

This value (24b/100) is subtracted from value found in step 1(6b/10) as given that  value obtained is decreased by 40%

new value found after 40% decrease = 6b/10 - 24b/100

new value found after 40% decrease = 60b/100 - 24b/100= 36b/100

new value found after 40% decrease =  36b/100 = 9b/25

Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25

Answer:

Option A

Step-by-step explanation:

Given function is,

f(x) = x² + 3x + 5

We have to find the value of f(a + h) so we will substitute (a + h) in place of x, and simplify the expression.

f(a + h) = (a + h)² + 3(a + h) + 5

           = a² + 2ah + h² + 3(a + h) + 5 [(a + b)² = a² + 2ab + b²]

           = a² + 2ah + h² + 3a + 3h + 5

Therefore, Option A will be the answer.

Answer: A) 45%

Step-by-step explanation:

The question is incomplete. The complete question is

Carl, Gilda, Conroy, and Kyla are the four candidates in a school election. Carl received 1/5 of the votes, Gilda received 10% of the votes, and Conroy received 1/4 of the votes. If Kyla received all of the remaining votes, what percentage of the votes did she receive? A. 45\% B. 55\% C. 20\% D. 50\%

Solution:

The total percentage of the votes that is spread among the 4 contestants is 100%

Carl received 1/5 of the votes. It means that the percentage of votes that Carl received is

1/5 × 100 = 20%

Gilda received 10% of the votes.

Conroy received 1/4 of the votes. It means that the percentage of the votes that Conroy received is

1/4 × 100 = 25%

Therefore, if Kyla received all of the remaining votes, then the percentage of the votes that she received is

100 - (20 + 10 + 25) = 45%

Answer:

40%

Step-by-step explanation:

Answer:

csc∅ = 25/7

sec∅ = 25/24

cot∅ = 24/7

Step-by-step explanation:

Cosecant (csc) is 1/sin∅ or hypotenuse over opposite

Secant (sec) is 1/cos∅ or hypotenuse over adjacent

Cotangent (cot) is 1/tan∅ or adjacent over opposite

Answer:

The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).

p-value = 0.0473

Step-by-step explanation:

To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).

Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).

The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁

The null hypothesis is represented as

H₀: μ = 0 or μ₂ = μ₁

The alternative hypothesis is represented as

Hₐ: μ ≠ 0 or μ₂ ≠ μ₁

So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average productivity level of the East Coast group = 1299 parts shipped

n₁ = sample size of East Coast group surveyed = 35

s₁ = standard deviation of the East Coast group sampled = 350

μ₂ = average productivity level of the Midwest group = 1456 parts shipped

n₂ = sample size of Midwest group surveyed = 35

s₂ = standard deviation of the Midwest group sampled = 297

σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59

We will use the t-distribution as no information on population standard deviation is provided

t = (1456 - 1299) ÷ 77.59

= 2.02

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68

Significance level = 0.01

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = 0.047326

0.047326 > 0.01

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Hope this Helps!!!

Answer:

Every decade, the number of species decays by a factor of 0.0834.

Step-by-step explanation:

Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:

[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]

Every decade, the number of species decays by a factor of 0.0834.

Answer:

28% subtracted

Step-by-step explanation:

khan

192.

2(8+4)÷2(8+8) = 1(4+8)×(8+8)

1×12×16=192.

Answer:

Step-by-step explanation:

[tex]2(4 + 8) \div 2(8 + 8)[/tex]

Any expression divided by itself equals 1

[tex]1(4 +8) \times (8 + 8)[/tex]

Add numbers

[tex]1 \times 12 \times 16[/tex]

Any expression multiplied by 1 remains the same

[tex]12 \times 16[/tex]

Multiply the numbers

[tex]192[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

4

Step-by-step explanation:

I used Desmos

We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).

For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.

So, for the first function:

[tex]f(x) = (1/5)*|x - 15|[/tex]

The y-intercept is:

[tex]f(0) =  (1/5)*|0 - 15| = 15/5 = 3[/tex]

For the second function:

[tex]g(x) = (x - 2)^2[/tex]

The y-intercept is:

[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]

Then we can see that g(x) has a greater y-intercept than f(x).

If you want to learn more about y-intercepts:

https://brainly.com/question/1884491

#SPJ2

Answer:

slope is m=1. y-intercept is -1

Answer:

Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0

Answer: 8 is the anwser

Step-by-step explanation:

Answer:The first one

Step-by-step explanation:

V rectangular prism = Area of the base *5

Answer:

None of the sides can be a triangle.

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

There are 3 numbers fitting the rule, 1, 2, and 6. There is a 3/6 chance rolling one of them or 50%.

Answer:

50%

Step-by-step explanation:

1 value> 5 and 2 values<3, out of total of 6

P (greater than 5 or less than 3) = 3/6= 50%

Answer:

r= 29.82

Step-by-step explanation:

r/7.1=4.2

r= 4.2*7.1

r= 29.82

Answer:

29.82         i did the unit test

Step-by-step explanation:

Answer: 4 wholes and 1/5 is 4.20 and you need something greater than that but less than 4.25 which still has only 2 decimals.

Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100.

So to write 3/7 as a percent, we need to find a fraction

equivalent to 3/7 that has a 100 in the denominator.

We can do this by setting up a proportion.

So we have [tex]\frac{3}{7} = \frac{n}{100}[/tex].

Now, we can use cross-products to find the missing value.

So we have (3)(100) which is 300 is equal to (7)(n) or 7n.

So we have the equation 300 = 7n.

Next, dividing both sides of the equation by 7, we have 42.8571 = n.

So 3/7 is equal to 42.8571/100 or 42.8571%.

If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.

So  [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.

As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: [tex] \\8x^{9}[/tex]

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]

[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]

[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]

[tex] \\8x^{9}[/tex]

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]

[tex] \\ (2*x^{5-2})^{3}[/tex]

[tex] \\ (2*x^{3})^{3}[/tex]

[tex] \\ (2^{3}*x^{3*3})[/tex]

[tex] \\ (8*x^{9})[/tex]

or [tex] \\ 8x^{9}[/tex].

Answer:

56 46 38 2 12

Step-by-step explanation:

Answer:

Six Million Seven Hundred Eighty Two Thousand one hundred sixty three

Step-by-step explanation:

Hope it helps...Pls Mark as Brainliest!!

Answer:

Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.

Step-by-step explanation:

6, 782, 163