The polygons in each pair are similar. Find the missing side length.

Answer:

this is the chapter of linear equations in one variable?

Answer:

$7800

Step-by-step explanation:

1. Principal x interest x rate

So: $7500 + 4% (0.04) x 1 year = $300

2. Interest + Principal

So: $7500 + $300

Mrs Lee had $7800 in the bank.

Answer:

$9986

Step-by-step explanation:

You got 13*4=52 quarters in 13 years.

Amount = 830*(1+0.049)^52

Amount = 9986.27

Answer:

-2

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals

Take the slope of AB = 1/2

-1/(1/2)

-1 * 2/1

-2

The slope of a line perpendicular is -2

Answer:

-2/3

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 1-3)/(-2 - -5)

   = (1-3)/(-2+5)

    = -2/3

Answer:

0.0667 = 6.67% probability that all seven machines are nondefective.

Step-by-step explanation:

The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this question:

10 machines means that [tex]n = 10[/tex]

2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]

Seven are selected, which means that [tex]n = 7[/tex]

What is the probability that all seven machines are nondefective?

This is P(X = 7). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]

0.0667 = 6.67% probability that all seven machines are nondefective.

Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).

Then the total differential is

[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]

[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]

Answer:

6,561

that's a good number

0 thru 9 is 10 numbers.

Each digit can be 1 of 10 numbers:

Total combinations = 10 x 10 x 10 x 10 = 10,000

Answer: 10,000

Answer:

x²+12x+35

Step-by-step explanation:

in factored form it would just be

(x+7)(x+5)=0

expand this

x²+12x+35=0

Answer:

3/4

Step-by-step explanation:

There are 13 hearts in a 52 deck.

52-13=39

39/52=3/4

The probability that you are not dealt a heart from the deck of cards is 3/4.

Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)

1 - 13/52 = 39/52 =  3/4

To learn more about probability, please check: https://brainly.com/question/13234031

It looks like the integral in polar coordinates is given to be

[tex]\displaystyle\int_{\pi/2}^\pi \int_0^2 r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta[/tex]

Converting back to Cartesian, we take

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

so we can easily recover the integrand in Cartesian:

[tex]r^3\sin(\theta)\cos(\theta)\,\mathrm dr\,\mathrm d\theta = (r\sin(\theta))(r\cos(\theta))(r\,\mathrm dr\,\mathrm d\theta) = xy\,\mathrm dx\,\mathrm dy[/tex]

This leaves us with the limits:

• π/2 ≤ θ ≤ π corresponds to the second quadrant of the (x, y)-plane (that is, where x < 0 and y > 0)

• 0 ≤ r ≤ 2 correspond to the disk of radius 2 centered at the origin

Taken together, we see the region of integration is a quarter-disk of radius 2 in the second quadrant, which we can capture by the set

{(x, y) : -√2 ≤ x ≤ 0 and 0 ≤ y ≤ √(2 - x ²)}

So, in Cartesian coordinates, the integral would be

[tex]\displaystyle \boxed{\int_{-\sqrt2}^0 \int_0^{\sqrt{2-x^2}} xy\,\mathrm dy\,\mathrm dx}[/tex]

Answer:

D

Step-by-step explanation:

9514 1404 393

Answer:

  64.1 ft²

Step-by-step explanation:

The area of the cone is given by ...

  A = πr(r +h) . . . . for radius r and slant height h

  A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²

Answer:

3.5

Step-by-step explanation:

in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :

-b/2a

the 'b' is 112

the 'a' is -16

so :

-112/-32 = 3.5

the answer is B, 3.5

Answer:

answer is A. 127°C

hopes this helps you

Answer:

B) Its final coordinates are (8,-6)

Step-by-step explanation:

1. Translated 1 unit up and 4 units left

(-2,7) becomes (-6, 8)

2. Reflected about the x-axis

(-6,8) becomes (-6, -8)

3. Rotated 90° anticlockwise about the origin

(-6, -8) becomes (8, -6) because when rotating 90 degrees anticlockwise about the origin, point A (x,y) becomes point A' (-y,x). In other words, switch the x and y and make y negative.

Step-by-step explanation:

By the law of exponent :

(a^n)^m=a^n×m

Option C

b^n×m is the correct answer...

hope it helps

Hey there!

2w^2 - 3w + 7

= 2(-2)^2 - 3(-2) + 7

(-2)^2

= (-2)(-2)

= 4

= 2(4) - 3(-2) + 7

2(4) = 8

3(-2) = -6

= 8 - (-6) + 7

= 8 + 6 + 7

8 + 6 = 14

14 + 7

= 21

Answer: 21

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

A perfect correlation is denoted by:

A. +1.0 and -1.0

Answer:

Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.

Step-by-step explanation:

The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

In this question:

12 resistors, which means that [tex]N = 12[/tex]

3 defective, which means that [tex]k = 3[/tex]

4 are selected, which means that [tex]n = 4[/tex]

To find an specific probability, that is, of x defectives:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = x) = h(x,12,4,3) = \frac{C_{3,x}*C_{9,4-x}}{C_{12,4}}[/tex]

Answer:

x = 12.15 oz

Step-by-step explanation:

z = 1.8808

 1.8808 = (x - 12)/.08

Answer:

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.

The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.

The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).

Respuesta:

a = 8

Explicación paso a paso:

Para obtener el valor de a en la ecuación:

40 / a = 35/7

Cruzamos multiplicamos:

40 / a = 35/7

40 * 7 = 35 * a

280 = 35a

Dividir ambos lados por 35

280/35 = 35a / 35

8 = a

a = 8

Answer:

[tex]x = -7[/tex] and [tex]x = 2[/tex]

Step-by-step explanation:

Given

See attachment for graph

Required

Find x, for [tex]f(x)= 1[/tex]

From the graph, we have the following readings

[tex]f(x)= 1[/tex] when:

[tex]x = 2[/tex] and [tex]x = -7[/tex]

Hence, (d) is correct

4/(√x - √(x - 2)) × (√x + √(x - 2))/(√x + √(x - 2))

= 4 (√x + √(x - 2)) / ((√x)² - (√(x - 2))²)

= 4 (√x + √(x - 2)) / (x - (x - 2))

= 4 (√x + √(x - 2)) / (x - x + 2)

= 4 (√x + √(x - 2)) / 2

= 2 (√x + √(x - 2))

9514 1404 393

Answer:

  c. obtuse

Step-by-step explanation:

For an obtuse triangle, the altitudes from the vertices on either side of the obtuse angle will be drawn outside the triangle.

Answer:

1.) scatter plot is attached below.

There is no sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals.

Step-by-step explanation:

Given the data :

Overhead width : 7.2 7.5 9.7 9.3 8.7 8.2

Weight : 119 156 243 200 199 188

The linear correlation Coefficient, R = 0.946

Using the Pvalue calculator for R score ;

Pvalue = 0.0149

Since, Pvalue > Α ; WE fail to reject the Null and conclude that there is no sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals.

Answer:

The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]

Step-by-step explanation:

Incomplete question, so i will suppose this is a sample of 1000.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Of the n respondents, 502 replied that America is doing about the right amount.

Supposing [tex]n = 1000[/tex], so [tex]\pi = \frac{502}{1000} = 0.502[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 - 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.461[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.502 + 2.575\sqrt{\frac{0.502*0.498}{1000}} = 0.543[/tex]

The 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment is (0.461, 0.543), considering [tex]n = 1000[/tex]