Which of the following shows the intersection of the sets? {7, 8, 9, 10} {9, 10, 11, 12}

Answer:

The answer to the equation from question 7 is 14.

Step-by-step explanation:

In question 7, we are given an equation.

2³ + (8 - 5)² - 3

First, subtract 5 from 8 in the parentheses.

2³ + 3² - 3

Next, solve the exponents for 2³ and 3².

8 + 9 - 3

Add 8 to 9.

17 - 3

Subtract 3 from 17.

14

So, the answer to this equation from question 7 is 14.

Answers:

please see the attached picture for full solution..

Hope it helps....

Good luck on your assignment...

Answer:

No

Step-by-step explanation:

Let's check the first statement with an example. 2 and 3 are positive numbers and their sum (5) is also positive so his first statement is true.

To check the second statement let's look at the negative numbers -1 and -8 for example. Their sum (-9) is also negative so his second statement is true.

To check the third statement let's look at the numbers 9 and -5. One is positive and one is negative, but their sum (4) is positive, so his third statement is false. However if we look at the numbers 4 and -7, their sum is negative so the third statement is partially false.

Answer:

[tex]\hat p=\frac{48}{64}= 0.75[/tex] represent the estimated proportion successfull

The standard error for this case is given by this formula:

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

And replacing we got:

[tex] SE= \sqrt{\frac{0.75*(1-0.75)}{64}}= 0.0541[/tex]

Step-by-step explanation:

We have the following info:

[tex] n= 64[/tex] represent the sample size

[tex] X= 48[/tex]  represent the number of people classified as successful

[tex]\hat p=\frac{48}{64}= 0.75[/tex] represent the estimated proportion successfull

The standard error for this case is given by this formula:

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

And replacing we got:

[tex] SE= \sqrt{\frac{0.75*(1-0.75)}{64}}= 0.0541[/tex]

Answer:

See below.

Step-by-step explanation:

There are 3 edges and 3 faces  projecting out from a vertex of a cube.

So the polygon produced would be a triangle.

Answer:

A triangle.

Step-by-step explanation:

As shown above, the plane which slices a corner intersects the polyhedron in [tex] n [/tex] faces which depend on the particular polyhedron.

Here it is a cube, and it intersects three faces. Since the intersection of two planes is a line and there are three planes to intersect with, there are three sides of the polygon.

Hence the polygon is a triangle.

Answer:

1.7 m²

Step-by-step explanation:

Given a ∆ABC with side AB = 8 ft, side AC = 8 ft, and the angle (θ) between both sides = 35°

Thus, we can find the area of ∆ABC using the formula below:

Area of ∆ABC = ½*AB*AC*sin(θ)

Length of AB = AC = 8 ft = 2.4384 m

(Note: you must convert from ft to m since we are told to find the area in m²)

Area = ½*2.4384*2.4384*sin(35)

Area = ½*5.95*0.5736

Area = ½*3.41292

Area = 3.41292/2

Area of ∆ABC = 1.7065

Area of ∆ABC ≈ 1.7 m² (to nearest tenth)

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Step-by-step explanation:

For this problem we know that the lenght of the rectangle is given by:

[tex] L= x[/tex]

And the width for this case is:

[tex] W= 5x^3 +4 -x^2[/tex]

And we know that the perimeter is given by:

[tex] P= 2L +2W[/tex]

And replacing we got:

[tex] P(x) = 2x +2(5x^3 +4 -x^2)= 2x +10x^3 +8 -2x^2[/tex]

And symplifying we got:

[tex] P(x)= 10x^3 -2x^2 +2x+8[/tex]

Answer:

[tex] 5.10 X +9.00 Y = 831.60[/tex]

We also know that for Wedneday we have two times tickets for adults compared to child so we have

[tex] Y =2x[/tex]

And using this condition we have:

[tex] 5.10 X + 18 X = 831.60[/tex]

And solving for X we got:

[tex] X= \frac{831.60}{23.1}=36[/tex]

So then the number of tickets sold for child are 36

Step-by-step explanation:

For this problem we can set upt the following notation

X = number of tickets for child

Y= number of tickets for adults

And we know that the total revenue  for Wednesday was 831.60. So then we can set up the following equation for the total revenue

[tex] 5.10 X +9.00 Y = 831.60[/tex]

We also know that for Wedneday we have two times tickets for adults compared to child so we have

[tex] Y =2x[/tex]

And using this condition we have:

[tex] 5.10 X + 18 X = 831.60[/tex]

And solving for X we got:

[tex] X= \frac{831.60}{23.1}=36[/tex]

So then the number of tickets sold for child are 36

Answer:

16.7%

Step-by-step explanation:

Each of the six faces of a six-faced die shows one of the numbers: 1, 2, 3, 4, 5, 6.

A roll of a die is equally likely to land on any face, so the total number of possible outputs is 6, corresponding to the number of faces on the die.

The desired outcome here is 3, meaning the face that shows the number 3. Only one face has the number 3, so the number of desired outcomes is 1.

p(event) = (number of desired outcomes)/(total number of possible outcomes)

p(3) = 1/6 = 0.16666... = 16.7%

Answer:

A) [tex]\boxed{m<VYW = 47 degrees}[/tex]

B) [tex]\boxed{XY = 77 degrees}[/tex]

Step-by-step explanation:

a) According to Outside Angles theorem:

=> m∠VYW = [tex]\frac{1}{2} (VW-VX)[/tex]

Where mVX = 79, VW = 173

=> m∠VYW = (173-79)/2

=> m<VYW = 94/2

=> m∠VYW = 47 degrees

b) According to Angles of Intersecting Chords Theorem:

=> m∠VZW = [tex]\frac{1}{2} (VW+XY)[/tex]

Where m∠VZW = 64, VW = 51

=> 64 = 1/2(51+XY)

Multiplying both sides by 2

=> 64*2 = 51+XY

=> 128 = 51+XY

=> XY = 128-51

=> XY = 77 degrees

CHECK THE ATTACHMENT FOR COMPLETE QUESTION

Answer:

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 unit(s) Left and a Reflection across the x axis.

Step-by-step explanation:

We were given triangles ABC and A'B'C' of which were told are congruents,

Now we can provide the coordinates of A and A' from the given triangles ΔABC and ΔA'B'C' ,if we choose a point of A from ΔABC and A' from ΔA'B'C' we have these coordinates;

A as (8,8) and A' (6,-8) from the two triangles.

If we shift A to A' , we have (8_6) = 2 unit for that of x- axis

If we try the shift on the y-coordinates we will see that there is no translation.

Hence, the only translation that take place is of 2 units left.

It can also be deducted that there is a reflection

by x-axis to form A'B'C' by the ΔABC.

BEST OF LUCK

Answer:

18 and 40

Step-by-step explanation:

Let x be the age of Claire and y the age of her mother

Claire's mother is 4 years more than twice Claire's age

The sum of their ages are is 58

the system is:

[tex]\left \{ {{y=2x-4} \atop {y+x=58}} \right.[/tex]  

Multiply (y+x = 58) by -1 and then add it to (y = 2x+4) to eliminate y

y= 58-18 = 40

so claire's mother is 40 years old and claire is 18

Answer:

Step-by-step explanation:

Write in slope intercept form.

y - 9 = -2(x - 8)

y - 9 = -2x + 16

y = -2x + 16 + 9

y = -2x + 25

y = mx + b

The m is the slope, b is the y-intercept.

y = -2 x + 25

The slope is -2.

Answer:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Step-by-step explanation:

If our random variable of interest for this case is X="the number of teenagers between 12-17 with smartphone" we can model the variable with this distribution:

[tex] X \sim Binom(n=234, p=0.75)[/tex]

And the mean for this case would be:

[tex] E(X) =np = 234*0.75= 175.5[/tex]

And the standard deviation would be given by:

[tex] \sigma =\sqrt{np(1-p)}= \sqrt{234*0.75*(1-0.75)}= 6.624[/tex]

Answer:

a) 0.25

b) 52.76% probability that a person waits for less than 3 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \lambda e^{-\lambda x}[/tex]

In which [tex]\lambda = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this question:

[tex]m = 4[/tex]

a. Find the value of λ.

[tex]\lambda = \frac{1}{m} = \frac{1}{4} = 0.25[/tex]

b. What is the probability that a person waits for less than 3 minutes?

[tex]P(X \leq 3) = 1 - e^{-0.25*3} = 0.5276[/tex]

52.76% probability that a person waits for less than 3 minutes

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Answer:

16$

Step-by-step explanation:

8*2=16

HOPE THIS HELPS :)

Answer: $16

Step-by-step explanation:

As the book was purchased for half its price plus 8 you can create the equation 1/2x + 8 = x.  Then, simplifying the expression you get x = 16.  Thus, the book costs 16 dollars.

Answer:

The pair of numbers is (3,3) while the maximum product is 9

Step-by-step explanation:

The pairs of numbers whose sum is 6 starting from zero is ;

0,6

1,5

2,4

3,3

Kindly note 2,4 is same as 4,2 , so there is no need for repetition

So the maximum product is 3 * 3 = 9 and the pair is 3,3

The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.

Since the sum of the pairs is 6

So, here are the following probabilities

0,6

1,5

2,4

3,3

Now if we multiply 3 and 3 so it comes 9 also it should be large

Therefore, The pair of the numbers where the sum is 6 should be 3 and 3 and the maximum product is 9.

Learn more about numbers here: https://brainly.com/question/13902300

Answer:

  27 years

Step-by-step explanation:

The formula for the number of payments can be used:

  N = -log(1 +0.05(1 -1000000/65000))/log(1.05) +1 = 27.03

There will be a couple thousand dollars left after the 27th payment.

The winnings will last 27 years.

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

The discontinuity occurs when x is either -5 or 3.

That is determined by solving denominator = 0 quadratic equation for x.

Hope this helps.

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

the answer is D

Step-by-step explanation:

Answer:

95°

Step-by-step explanation:

To get the value of n° we must get the values of the traingle angle's sides

and to do that :

Answer:

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{x}[/tex]

Step-by-step explanation:

The double angle formula states that:

[tex]\sin{2a} = 2\sin{a}\cos{a}[/tex]

In this question:

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}}[/tex]

So

[tex]a = \frac{x}{2}[/tex]

Then

[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{\frac{2x}{2}} = \sin{x}[/tex]

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=58.2[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME =1[/tex] represent the margin of error desire

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]

So the answer for this case would be n=22547 rounded up to the nearest integer

Answer:

see below

Step-by-step explanation:

Let x be the original price

x* discount rate = discount

x * 60% = 30

Change to decimal form

x * .60 = 30

Divide each side by .60

x = 30/.60

x =50

The original price was 50 dollars

Answer:

A-30     B-20    C-50

Step-by-step explanation:

Answer:

  $11,991.60

Step-by-step explanation:

An appropriate formula is ...

  A = P(1 +r/n)^(nt)

where r is the annual rate, n is the number of time per year interest is compounded, and t is the number of year. P is the principal invested.

Filling in the given numbers, we have ...

  A = $2000(1 +0.12/12)^(12·15) = $2000(1.01^180) ≈ $11,991.60

The account balance after 15 years will be $11,991.60.