Help is appreciated!! ❤

Simplify the expression (5 + √3)(5 - √3)

Answer:

  105 seconds

Step-by-step explanation:

We can use the relation ...

  distance = speed · time

to write equations for the distance each girl travels as a function of time t since Jillian started.

  Jillian's distance = (6 ft/s)(t)

  Samantha's distance = (7 ft/s)(t -15) . . . . Samantha starts 15 seconds after the clock starts running

These distances are the same when ...

  6t = 7(t -15)

  6t = 7t -105 . . . . eliminate parentheses

  105 = t . . . . . . . . add 105-6t

Jillian had been walking 105 seconds when the two girls met.

Answer:

i dont know how many decimals you need but its 5.56

tell me if u want an explanation

Answer:

5.74456264654

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the characteristic polynomial of the​ matrix, using either a cofactor expansion or the special formula for 3times3 determinants.​ [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row​ operations, because the variable lambda is​ involved.]

[tex]\texttt {let} A = \left[\begin{array}{ccc}4&-4&0\\-4&7&0\\4&6&5\end{array}\right][/tex]

The characteristics polynomial of A is [tex]|A- \lambda I|[/tex]

[tex]\to|A-\lambda I|=\left[\begin{array}{ccc}(4-\lambda)&-4&0\\-4&(7-\lambda)&0\\4&6&(5-\lambda)\end{array}\right][/tex]

[tex]=(4-\lambda)[7-\lambda)(5-\lambda)-0]+4[-4(5-\lambda)-0]+0[-4\time 6-4(7-\lambda)]\\\\=(4-\lambda)[35-7\lambda-5\lambda+\lambda^2]+4[-20+4\lambda]+0\\\\=(4-\lambda)[35-12\lambda+\lambda^2]-80+16\lambda\\\\=140-48\lambda+4\lambda^2-35\lambda+12\lambda^2-\lambda^3-80+16\lambda\\\\=-\lambda^3+16\lambda^2-67\lambda+60[/tex]

Answer:

6w = 30

Step-by-step explanation:

We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.

The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.

This is 2 X (length + width)

From the questions, we can get the dimensions of the rectangle using clues from the various statements made.

From the statement"a rectangular painting length more than twice the width" we can see that the

L = 2w ------------------------- equation 1

substituting this value into the formula for the perimeter of the rectangle we have

30 = 2(2w + w)

30 = 6w

w= 5

from equation 1

L =2 X (5) = 10

Hence, we can set up the equation

6w = 30

However, the closest option to what we have is option D

6w + 6 = 30 - 4

complete question:

Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve

Answer:

D.6w + 6 = 30 = 4

Step-by-step explanation:

perimeter = 30 inches

width = w

length = 2w + 3

perimeter of a rectangle = 2l + 2w

where

w = width

l = length

Therefore,

perimeter of a rectangle = 2(2w + 3) + 2w

perimeter of the rectangle = 4w + 6 + 2w

perimeter = 6w + 6

recall

perimeter = 30 inches

6w + 6 = 30

6w = 24

divide both sides by 6

w = 24/6

w = 4

Answer:

The equation can be y = -7x+11

Step-by-step explanation:

5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus

if 5/6=20

6/6=?

that is 6/6x20 divide by 5/6

=24fruits

Answer:

4-5 12 -13

Step-by-step explanation:

Answer:

a) A sample size of 195 is needed.

b) Smaller

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{1-0.999}{2} = 0.0005[/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]1-0.0005 = 0.9995[/tex], so [tex]z = 3.27[/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.

a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1.

We need a sample size of n.

n is found when [tex]M = 4.1[/tex]

We have that [tex]\sigma = 17.5[/tex]

So

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

[tex]4.1 = 3.27*\frac{17.5}{\sqrt{n}}[/tex]

[tex]4.1\sqrt{n} = 3.27*17.5[/tex]

[tex]\sqrt{n} = \frac{3.27*17.5}{4.1}[/tex]

[tex](\sqrt{n})^{2} = (\frac{3.27*17.5}{4.1})^{2}[/tex]

[tex]n = 194.8[/tex]

Rounding up

A sample size of 195 is needed.

b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?

Same as above for n, the difference is that z would be 1.96 instead of 3.27. So a smaller sample size.

Answer:

Arc length : In his pizza, Arc length is the outer boundary of pizza and it can be calculated if we know the side length of the pizza and the central angle

Area of sector: since the whole pizza piece is a sector hence to calculate it's area we can use the formula of area of sector

(In degrees) = m/360 (πr²)

(In radians) = 1/2r²∅(theta)

Answer:

a) 92% probability that a randomly selected mortgage will not​ default

b) 47.22% probability that nine randomly selected mortgages will not default

c) 52.78% probability that the derivative from part​ (b) becomes​ worthless

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening

Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default.

This means that [tex]p = 0.08[/tex]

(a) What is the probability that a randomly selected mortgage will not​ default?

Either it defaults, or it does not default. The sum of the probabilities of these outcomes is 1. So

0.08 + p = 1

p = 0.92

92% probability that a randomly selected mortgage will not​ default

(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the​ others?

This is P(X = 0) when n = 9. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]

47.22% probability that nine randomly selected mortgages will not default.

​(c) What is the probability that the derivative from part​ (b) becomes​ worthless? That​ is, at least one of the mortgages defaults

Either none defect, or at least one does. The sum of the probabilities of these events is 100%. So

p + 47.22 = 100

p = 52.78

52.78% probability that the derivative from part​ (b) becomes​ worthless

Answer:

16

Step-by-step explanation:

The midpoint theorem says that if a line bisects the two sides of the triangle , it is parallel to the third side and half of it

Thus the x = 1/2 × 32 = 16

Answer:

9.5 ft

Step-by-step explanation:

The perimeter is equal to

P =2(l+w)

29.6 = 2(5.3+z)

Divide each side by 2

29.6 /2 =2/2(5.3+z)

14.8 = 5.3 +z

Subtract 5.3 from each side

14.8-5.3 = z

9.5 =z

Answer:

Z=9.5

Step-by-step explanation:

Perimeter(of a triangle)=2(5.3+z)

29.6=10.6+2z

2z=29.6-10.6

2z=19(then divide both sides by 2 to find the value of z)

z=19/2

z=9.5 ft

To check your answer

29.6=2(5.3+9.5)

29.6=2(14.8)

29.6=29.6 so your answer is correct.

Answer: it is a right tailed probability

Step-by-step explanation:

Population proportion = 26.9/100 = 0.269

We are dealing with the fact that the probability that the mean bond percent for the sample will be at least 28. This means that the sample proportion is 0.28 or above. This means that it is greater than the population proportion of 0.269

The hypothesis would be

For null hypothesis

p = 0.269

For alternative hypothesis,

p > 0.269

The inequality sign means that it is right tailed.

Answer:

  (a, b, c) = (8, 3, 2)

Step-by-step explanation:

Remove cubes from under the radical. Combine terms.

  [tex]\sqrt[3]{16} +2\sqrt[3]{54} =\sqrt[3]{2^3\cdot 2}+2\sqrt[3]{3^3\cdot 2}\\\\=2\sqrt[3]{2}+2\cdot 3\sqrt[3]{2}=(2+6)\sqrt[3]{2}\\\\=8\sqrt[3]{2}\equiv a\sqrt[b]{c}\ \longrightarrow\ \boxed{(a,b,c)=(8,3,2)}[/tex]

Answer:

(a) True

(b) False

(c) True

(d) False

(e) False

(f) True

(g) False

(h) True

(i) True

(k) True

Step-by-step explanation:

(a) Two lines parallel to a third line are parallel

True

(b) Two lines perpendicular to a third line are parallel

Only for  lines on the same plane

Therefore, false

(c) Two planes parallel to a third plane are parallel

True

(d) Two planes perpendicular to a third plane are parallel

The two planes can be at an angle to each other and so intersect

Therefore, false

(e) Two lines parallel to a plane are parallel

Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect

Therefore, false

(f) Two lines perpendicular to a plane are parallel

True

(g) Two planes parallel to a line are parallel

Where the planes are not parallel to each other, they will intersect

Therefore, false

(h) Two planes perpendicular to a line are parallel

True

(i) Two planes either intersect or are parallel

True

(k) A plane and a line either intersect or are parallel

True.

Answer:

(-1, 3)

Step-by-step explanation:

5x + 3y = 4

2x + y = 1 ⇒ y=1-2x

Answer:

a. Option D

b. H₀ : p₁ = p₂, H₁: p1 ≠ p₂

Step-by-step explanation:

a. A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the proportions of two populations. This test is usually appropriate under the conditions that:

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

b. Null hypothesis: H₀ : p₁ = p₂

   Alternative hypothesis: H₁ : p₁ ≠ p₂

Diameter of round bud is 22.29 m.

Given that,

The circumference of round bud = 70 m

We have to calculate its diameter,

Since we know that,

Its shape is circular,

Since,

The circumference of the circle, also known as the perimeter of the circle, is the measurement of the circle's boundary. The area of a circle, on the other hand, specifies the territory it occupies. If we open a circle and draw a straight line through it, the length of the line equals the circumference.

S,

⇒ Circumference = 2πr

Where r is radius of circle,

⇒ 70 = 2πr

⇒   r = (70/2x3.14)

⇒   r = 11.14

Here we know that,

Diameter = 2r

Hence,

Diameter = 22.29 m

To learn more about circle visit:

https://brainly.com/question/29288238

#SPJ2

Answer:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

101.5 98.7 95.4 92.3 109.8 104.7

We can calculate the mean with the following formula:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]

Answer:

B:

Step-by-step explanation:

P(A or B) = P(A)+P(B)-P(A and B)

0.5 = 0.4 + P(B) -0.2

P(B) = 0.5-0.4+0.2

P(B) = 0.3

Find the probability of each one:

Taffy would be 1/6

Chips would be 1/3

Soda would be 1/3

For the probability of all three multiply them together:

1/6 x 1/3 x 1/3 = 1/54

Answer:

The first graph

Step-by-step explanation:

when x is equal to something it is always up

y = 2 would be #4

Answer:

The first graph

Step-by-step explanation:

Personally, I use the acronym HAY and VAX to remember this rule. This means that horizontal lines always correlate with y and vertical lines always correlate with x. A horizontal equation (y=#) is valid, so to say, whereas vertical (x=#) is undefined. It is undefined because there are multiple values of y for the same value of x. You can remember this with the following scenario: A person will always be able to walk in a straight line without getting injuries, but if a person tries to walk up the wall, they will fall and can break their bones, making their body "undefined"

Answer:

4/r -1      

Step-by-step explanation:

i did khan

but sorry if its pooop

One way to do this is to exploit the Pythagorean identity,

[tex]\cos^2x+\sin^2x=1[/tex]

to rewrite

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

so that

[tex]\displaystyle\int\cos^3(3x)\sin^7(3x)\,\mathrm dx=\int\cos(3x)\left(\sin^7(3x)-\sin^9(3x)\right)\,\mathrm dx[/tex]

Then substitute [tex]u=\sin(3x)[/tex] and [tex]\frac{\mathrm du}3=\cos(3x)\,\mathrm dx[/tex] to get the integral

[tex]\displaystyle\frac13\int u^7-u^9\,\mathrm du=\frac13\left(\frac{u^8}8-\frac{u^{10}}{10}\right)+C[/tex]

[tex]=\boxed{\dfrac{\sin^8(3x)}{24}-\dfrac{\sin^{10}(3x)}{30}+C}[/tex]

which is one correct form of the antiderivative. There's no reason we can't use the identity from before to express the integrand in terms of powers of cos(3x) instead.

Answer:

length = 50 + 50 = 100 yards

width = 50 yards

Step-by-step explanation:

The area of parking lot for the the ice cream stand is given as  5000 yard². The length of the yard is 50 yard longer than its width.

Let

width = a

length = 50 + a

The parking lot is definitely a rectangle .

Area of a rectangle = length × width

area =  (50 + a)a

5000 = (50 + a)a

5000 = 50a + a²

a² + 50a - 5000 = 0

The numbers that can be multiply together to give you -5000 is -50 and 100 and this same number can be added to give 50. Therefore,

a² - 50a + 100a - 5000 = 0

a(a - 50) + 100(a - 50) = 0

(a + 100)(a - 50) = 0

a = -100 or 50

We can't use negative value so we use 50.

length = 50 + 50 = 100 yards

width = 50 yards

Answer:

50%

Step-by-step explanation:

27 to 30 is exactly the "box" of the box plot and that, by definition, contains 50% of the results.

Answer:

50%

Step-by-step explanation:

Hope this will help