A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?

Answer:

1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]

Step-by-step explanation:

1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]

[tex]5\cdot x - x = 5\cdot a + a[/tex]

[tex]4\cdot x = 6\cdot a[/tex]

[tex]x = \frac{3}{2}\cdot a[/tex]

b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]

[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]

[tex]x = 5-3\cdot a[/tex]

c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]

[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]

[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]

[tex]-x = a[/tex]

[tex]x = -a[/tex]

d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]

[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]

[tex]2\cdot x = 5\cdot a[/tex]

[tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]

[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]

[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]

[tex]3\cdot x +6 +5\cdot x = 0[/tex]

[tex]8\cdot x = - 6[/tex]

[tex]x = -\frac{3}{4}[/tex]

b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]

[tex]7\cdot x = 5\cdot (x-2)[/tex]

[tex]7\cdot x = 5\cdot x -10[/tex]

[tex]2\cdot x = -10[/tex]

[tex]x = -5[/tex]

c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]

[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]

[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]

[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]

[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]

[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]

[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]

[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]

[tex]-9\cdot x = -27[/tex]

[tex]x = 3[/tex]

Answer:

(x=6) is less than 18 which would give you the cost of the current plan

Step-by-step explanation:

If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.

Answer:

7.5

Step-by-step explanation:

Answer:

y = (9/4)x - 9

Step-by-step explanation:

The x-intercept is (4, 0) and the y-intercept is (0, -9).

As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9.  Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:

y = (9/4)x - 9

Answer:

x-y=12

Step-by-step explanation:

Answer:

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

Step-by-step explanation:

The summary of the given statistics is:

Population Mean = 26,500

Sample Mean = 30,150

Standard deviation = 10560

sample size = 24

The objective is to state the null hypothesis and the alternate hypothesis.

An hypothesis is a claim with  insufficient information which tends to be challenged into  further testing and experimentation in order to determine if such claim is significant or not.

The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.

The alternative hypothesis is the research hypothesis that the  researcher is trying to prove.

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

The test statistic can be  computed as follows:

[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]

[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]

[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]

z = 1.6933

Answer:

Z=9

Step-by-step explanation:

Insert A into A+Z=14

5+z=14

Subtract 5 on both sides, to find Z.

-5     -5

z=9

Answer:

hello your question has some missing parts attached below is a picture of the complete question

Answer : 3.59

Step-by-step explanation:

Calculating the standard deviation, mean and standard error of the hourly wages

Area 1 : mean = 12.75 , std = 4.9497 , std error = 1.75

Area 2 : mean = 18.25, std = 4.3671,  std error = 1.54399

Area 3 : mean = 16.25, std = 2.8660, std error = 1.01330

mean = sum of terms / number of terms

std = [tex]\sqrt{}[/tex] (X − μ)2 / n

std error = std / [tex]\sqrt{n}[/tex]

The value of the test statistic to test for a difference in the areas is

3.59 ( using anova table attached below )

y = a(x  + 1.5)^2 - 12.5

y intercept is (0,-8) so:-

-8 = a(0+1.5)^2 - 12.5

-8 = 2.25a - 12.5

a =  4.5/ 2.25 = 2

so we have  

y  = 2 ( x +1.5)^2 - 12.5

solving for x  when y = 0:-

(x + 1.5)^2 = 12.5/2 = 6.25

taking sqrt's  x + 1.5  = +/- 2.5

x =  -4,   1

so the x intercepts are (-4,0) and (1,0)

Answer:

y = –1∕4(x – 8)^2 – 1

Step-by-step explanation:

I took the exam and  got  it  right.

Answer:

3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4

Step-by-step explanation:

3x^4+(nothing)=3x^4

x^3y+(nothing)=x^3y

-10x^2y^2=2x^2y^2=-8x^2y^2

9xy^3+(nothing)=0

-4y^4-9y^4=-13y^4

Add it all up and write the terms by descending order of exponent value, and u get my answer.

Answer:

B

Step-by-step explanation:

With limits, the first thing one should always try is direct substitution. Therefore, let's try that.

[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) \\= (\frac{(1)^2+1}{(1)+1}+(1)^2+3) \\=\frac{2}{2}+1+3\\ =1+4=5[/tex]

Therefore:

[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) =5[/tex]

Answer:

[tex]\boxed{\sf C. \ 10}[/tex]

Step-by-step explanation:

[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]

[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]

[tex]NH \times HT = MH \times HY[/tex]

[tex](x+20) \times 8=12 \times 20[/tex]

[tex]\sf Expand \ brackets \ and \ multiply.[/tex]

[tex]8x+160=240[/tex]

[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]

[tex]8x+160-160=240-160[/tex]

[tex]8x=80[/tex]

[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]

[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]

[tex]x=10[/tex]

The value of x is 10.

We have a circle and inside it two chords MY and NT intersect at point H.

We have to find the value of x in the figure.

According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then

AO x OB = CO x OD

Applying the chord intersecting theorem to the figure in the question, we get -

MH x HY = NH x HT

12 x 20 = (x+20) x 8

240 = 8x + 160

8x = 80

x = 10

Hence the value of x is 10.

To solve more questions on Circles and chords, visit the link below -

https://brainly.com/question/15568573

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Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

Answer:

a) What is the cost of a chicken shawarma wrap?

$10.99

b) What is the cost of one order of spiced potatoes?

$4.99

c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

Step-by-step explanation:

Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,

Cost of a chicken sharwarma wrap = x

Cost of an order of spiced potatoes = y

Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.

3x + 2y = $42.95 .............Equation 1

Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.

5x + 4y = $74.91 ................Equation 2

Hence, the Equations needed to solve the question is:

3x + 2y = $42.95 .............Equation 1

5x + 4y = $74.91 ................Equation 2

We use Elimination method to solve for this.

Multiply Equation 1 by coefficient of x in Equation 2

Equation 2 by coefficient of x in Equation 1

3x + 2y = $42.95 .............Equation 1 × 5

5x + 4y = $74.91 ................Equation 2 × 3

15x + 10y = 214.75..............Equation 3

15x + 12y = 224.73..............Equation 4

Subtract Equation 3 from Equation 4

2y = 9.98

y = 9.98/2

y = 4.99

Therefore, y = Cost of an order of spiced potatoes = $4.99

Subtitute 4.99 for y in Equation 1

3x + 2y = $42.95 .............Equation 1

3x +2(4.99) = 42.95

3x + 9.98 = 42.95

3x = 42.95 - 9.98

3x = 32.97

x = 32.97/3

x = 10.99

x = Cost of a chicken sharwarma wrap = $10.99

Therefore,

The cost of a chicken sharwarma wrap = $10.99

The cost of an order of spiced potatoes = $4.99

Answer:

The numbers:

-43    and     58

Step-by-step explanation:

a + b = 15

a = b - 101

then:

(b-101) + b = 15

2b = 15+101

2b = 116

b = 116/2

b = 58

a = b - 101

a = 58 - 101

a = -43

Check:

a + b = 15

-43 + 58 = 15

Answer: 0.129

Step-by-step explanation:

Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.

Population mean : [tex]\mu= \text{3316 grams,}[/tex]

Standard deviation: [tex]\text{324 grams}[/tex]

Sample size = 83

Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :

[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]

hence, the required probability =  0.129

Answer:

Option (C)

Step-by-step explanation:

Since angle 'a' is the inscribed angle of the given triangle

Therefore, angle measure of the intercepted arc will be equal to the double of the inscribed angle.

x = 2a ⇒ a = [tex]\frac{x}{2}[/tex]

By the tangent-chord theorem,

"Angle between a chord and tangent measure the half of the angle measure of intercepted minor arc"

[tex]\frac{x}{2}[/tex] = 40°

Therefore, a = [tex]\frac{x}{2}[/tex] = 40°

Option (C) will be the answer.

Answer:

Solution : y = 4x - 8

Step-by-step explanation:

The first thing we want to do is isolate t², rather than t. Why? As you can see when we substitute t² into the second equation, it will be easier than substituting t, as t is present in the form t². So, let's isolate t² in the first equation --- ( 1 )

x = t² + 2,

t² = x - 2

Now let's substitute this value of t² in the second equation --- ( 2 )

y = 4t²,

y = 4(x - 2),

y = 4x - 8 ~ And hence our solution is option c.

Answer:

Parallel lines never intersect, but they must be in the same plane. The definition does not require the undefined term point, but it does require plane. Because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.

Step-by-step explanation:

Answer: approximately 10.8 centimeters

Step-by-step explanation:

We have a square, where each side measures approx. 4.25 in

Now we know that 1in ≈ 2.54 cm

Then, in 4.25 in, we have 4.25 times 1 inch, so we have 4.25 times the length of 2.54 cm

So the approximate measure of the sides in centimeters is:

4.25*(2.54)cm = 10.8 cm

So we have that each side measures approximately 10.8 centimeters

Answer:

28

Step-by-step explanation:

We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]

We know that,

[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]

Here, n = 3

So,

[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]

So,

[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]

So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

2+4+6+8

Step-by-step explanation:

We have the sum of 2n  where n runs from 1 to 4

n=1  2(1) = 2

n=2  2(2) = 4

n=3  2(3) = 6

n=4  2(4) = 8

The sum is add

2+4+6+8

Answer:

Step-by-step explanation:

Given sinα=−2/3, before we can get secα, we need to get the value of α first from  sinα=−2/3.

[tex]sin \alpha = -2/3[/tex]

Taking the arcsin of both sides

[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]

Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;

α = 180°+41.8°

α = 221.8° which is between the range 270°<α<360°

secα = sec 221.8°

secα = 1/cos 221.8

secα = 1.34

Answer:

Hey there!

Using the foil method: (3x+2)(5x-7)

15x^2+10x-21x-14

15x^2-11x-14

Let me know if this helps :)

Answer:

X= 1/2

Step-by-step explanation:

7^2x+3 =2401

7^(2x+3 )=2401

7^(2x+3 )= 7^4

Taking away the base because its equal to 7

Then solving the power as an equation

2x+3= 4

2x= 4-3

2x= 1

X=1/2

Now substituting x into the equation to know if we are correct

7^(2x+3 )=2401

Where x= 1/2

7^(2*(1/2) +3)= 7^4

7^(1+3)= 7^4

7^4= 7^4

7^4= 2401

Answer:

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Step-by-step explanation:

A test for the difference between two population means is to be performed.

As the population variances are known, the z-test will be used.

The hypothesis can be defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂

Assume that the significance level of the test is, α = 0.05.

The critical region can be defined as follows:

The critical value of z for α = 0.05 is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]

Use a z-table.

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Answer:

Hey there!

We can use the midpoint formula to find that the midpoint is (-1, -9).

Let me know if this helps :)

The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.

What is the midpoint of line segment AB?

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (8,−10) and (−10,−8)

x = (8 – 10) / 2

x = –1

y = (– 10 – 8) / 2

y = –9

Then the correct option is A.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

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Answer:

  45, 180, 145

Step-by-step explanation:

Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...

  n + 4n + (n+100) = 370

  6n = 270

  n = 45

  4n = 180

  n+100 = 145

The three numbers are 45, 180, 145.

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x   this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.