100 points!

Only 29 and 31

Rewrite each expression eliminating fractions. Simplified answers may be left in terms of any of the six trigonometric functions.

x = -2 - it's a vertical line with undefined slope.

The line parallel to the vertical line is vertical.

Answer:

The probability that exactly 2 of the rolls is a sum of 7 will is 0.296

Step-by-step explanation:

The probability of rolling a sum of 7 when rolling two dice simultaneously is 0.167.

Let us assume that, A be the event that the sum is 7. So,

[tex]P(A)=0.167[/tex]

Binomial probability represents the probability that a binomial experiment results (i.e either success or failure or only two results) in exactly x successes.

[tex]b(x;\ n, p) =\ ^nC_x \cdot p^x \cdot (1-p)^{n - x}[/tex]

So the probability that exactly 2 of the rolls is a sum of 7 will be,

[tex]P(2) =\ ^{12}C_2 \cdot (0.167)^2 \cdot (1-0.167)^{12 - 2}[/tex]

[tex]=\ ^{12}C_2 \cdot (0.167)^2 \cdot (0.833)^{10}[/tex]

[tex]=66 \cdot (0.167)^2 \cdot (0.833)^{10}[/tex]

[tex]=0.296[/tex]

Answer:

Question 1 is A.

Answer: y = 5.5

Step-by-step explanation:

[tex]y=\dfrac{1}{2}x^2+6x+24[/tex]

Step 1: find the vertex

axis of symmetry: [tex]x = \dfrac{-b}{2a} = \dfrac{-6}{2(\frac{1}{2})} =\dfrac{-6}{1} = -6[/tex]

y-coordinate of vertex: [tex]y=\dfrac{1}{2}(-6)^2+6(-6)+24[/tex]

= 18 - 36 + 24

= 6

Vertex: (-6, 6)

Step 2: find p (the distance from the vertex to the focus): [tex]\dfrac{1}{4p} =a[/tex]

[tex]\dfrac{1}{4p} =\dfrac{1}{2}[/tex]

cross multiply to get: 2 = 4p

divide both sides by 4 to get: [tex]p =\dfrac{1}{2}[/tex]

Step 3: find the directrix

Since the parabola opens up, the focus will be above the vertex.

focus: (-6, 6 + [tex]\dfrac{1}{2}[/tex]) = (-6, 6.5)

and the directrix will be below the vertex.

directrix: y = 6 - [tex]\dfrac{1}{2}[/tex] ⇒ y = 5.5

The directrix also gets shiftd toward right.  Then the equation of the directrix of the parabola will be y = 11/2.

The equation of a parabola function is given as,

y² = 4ax

x² = 4ay

Where a is the coordinate of the focus.

The equation of a parabola is given.

y = (1/2) x² + 6x + 24

Simplify the equation, we have

2y = x² + 12x + 48

2y = x² + 12x + 36 + 12

2y = (x + 6)² + 12

Then the equation can be written as,

4(1/2)y = (x + 6)² + 12

Compare with standard equation, we have

a = (-1/2, 0)

The parabola is gets shifted toward right.

Then the directrix also gets shiftd toward right.

Then the equation the directrix will be

y = -1/2 + 6

y = 11/2

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ2

Answer:The years vary

Step-by-step explanation:

If you are them all and divide, it could solve your equation.

I hoped I helped :)

Answer:

76

Step-by-step explanation:

Caroline can make 804 full pastrami sandwiches with 201 1/4 pounds of pastrami, using 3/8 of a pound for each sandwich.

To find out how many pastrami sandwiches Caroline can make with 201 1/4 pounds of pastrami, we first need to determine the total number of sandwiches that can be made from a single pound of pastrami. As each sandwich uses 3/8 of a pound, we can calculate this as follows:

1 pound / (3/8 pound per sandwich) = 8/3 sandwiches per pound.

Next, we multiply the number of sandwiches that can be made per pound by the total pounds of pastrami:

201 1/4 pounds * 8/3 sandwiches/pound = 804 sandwiches + 2/3 of a sandwich.

Since Caroline can't make 2/3 of a sandwich, she can make a total of 804 full sandwiches with the pastrami she has.

Answer:

The store will sell it for $58.50

Step-by-step explanation:

To find this amount, start by multiplying the cost by the mark up percentage.

$45 * 30% = $13.50

Now that we have the markup amount, we can add it to the original cost to get the store price.

$45.00 + $13.50 = $58.50

Answer:

65

Step-by-step explanation:

Hi,

I think you mean red or blue.

Number which are red or blue = 12 + 14

= 26% or 0.26

The number of red and blue = 0.26 * 250

=  65 marbles

Answer:

8 cm

Step-by-step explanation:

We can use ratio's to solve this problem

4 cm = 5 km

We need to know how many cm = 10 km

4 cm             x cm

---------- = --------------

5 km             10 km

Using cross products

4* 10 = 5* x

40 = 5x

Divide each side by 5

40/5 = 5x/5

8=x

On the map it is 8 cm.

G = number of green = 7

S = number of striped = 8

T = number total = 10+7+8 = 25

probability of picking green = P(G) = G/T = 7/25

probability of picking striped = P(S) = S/T = 8/25

P(green and striped) = P(G)*P(S)  ... events are independent

P(green and striped) = (7/25)*(8/25)

P(green and striped) = (7*8)/(25*25)

P(green and striped) = 56/625

P(green and striped) = 0.0896

--------------------------------

In summary, the answer as a fraction is 56/625

In decimal form, the answer is 0.0896

The value 0.0896 can be converted to percent form to get 8.96%

Final answer:

The probability of picking a green marble and then a striped marble from a bag with replacement is the product of the probability of picking a green marble (7/25) and a striped marble (8/25), which is 56/625.

Explanation:

The student is asking about the probability of selecting a green marble followed by a striped marble when drawing from a bag that contains red, green, and striped marbles with replacement. To calculate this probability, we will use the basic principle that the probability of two independent events happening in sequence is the product of their individual probabilities.

First, we determine the probability of choosing a green marble, which we'll call P(G). Since the bag contains 7 green marbles out of a total of 25 (10 + 7 + 8), the probability P(G) is 7/25. Next, since the marble is replaced, the probability of choosing a striped marble, P(S), remains the same at 8/25. Therefore, the probability of choosing a green marble and then a striped marble is P(G and S) = P(G) x P(S) = (7/25) x (8/25).

To find the combined probability, simply multiply the two individual probabilities:

P(G and S) = (7/25) x (8/25) = 56/625.

The probability of drawing a green and then a striped marble is 56/625.

The Synthetic Division form of Given Division Problem is :

✿   [tex]-5\;\arrowvert\overline{\;4\;\;\;\;\;-13\;\;\;\;\;\;8}[/tex]

Option C is the Answer

In synthetic division for [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex], option C (-5 | 4 -13 8) correctly represents the coefficients, showcasing the division process with a remainder of 8.

The synthetic division problem given is [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex]. Synthetic division is a method used to divide polynomials, particularly when dividing by a linear factor of the form (x - c) . The correct representation in synthetic division form would be:

**C.  -------------

 -  5 | 4   - 13  8**

Here's the breakdown of the synthetic division:

1. The divisor x + 5 corresponds to c = -5, so the root is x = -5.

2. Write down the coefficients of the dividend 4x^2 - 13x + 8 in the synthetic division box.

3. Bring down the leading coefficient, which is 4 in this case.

4. Multiply the root (-5) by the leading coefficient (4) and write the result below the second column. Add the result to the second column.

5. Multiply the root by the result from step 4 and write the result below the third column. Add the result to the third column.

The final result in the bottom row represents the coefficients of the quotient, and the last number (8) is the remainder. The synthetic division in option C accurately reflects this process.

Answer:

a

Step-by-step explanation:

Answer: (A) If it is a bib, then it is a bab

Step-by-step explanation:

p: The bib is a bub.

Rewrite it as: If it is a bib, then it is a bub.

q: The bub is a bab.

Rewrite it as: If it is a bub, then it is a bab

The conclusion of p equals the hypothesis of q so the Law of Syllogism can be applied  --> hypothesis of p → conclusion of q

Answer:

(1)

option-B

(2)

f(x) is continuous at a=4

Step-by-step explanation:

(1)

we are given

[tex]\lim_{x \to 0} \frac{sin(2x)}{x}[/tex]

Since, we are suppose to find limit x-->0

so, we always choose value of x that is  close to 0

At x=-0.03:

[tex]\frac{sin(2\times (-0.03))}{(-0.03)}=1.99880[/tex]

At x=-0.02:

[tex]\frac{sin(2\times (-0.02))}{(-0.02)}=1.99947[/tex]

At x=-0.01:

[tex]\frac{sin(2\times (-0.01))}{(-0.01)}=1.99987[/tex]

At x=0.01:

[tex]\frac{sin(2\times (0.01))}{(0.01)}=1.99987[/tex]

At x=0.02:

[tex]\frac{sin(2\times (0.02))}{(0.02)}=1.99947[/tex]

At x=0.03:

[tex]\frac{sin(2\times (0.03))}{(0.03)}=1.99880[/tex]

(2)

we are given

[tex]f(x)=\frac{x-4}{x+5}[/tex]

Since, we have to check continuity at a=4

So, firstly we will find limit value and then functional value

Limit value:

[tex]\lim_{x \to a}  f(x)=\lim_{x \to a}\frac{x-4}{x+5}[/tex]

now, we can plug a=4

[tex]\lim_{x \to 4}  f(x)=\lim_{x \to 4}\frac{4-4}{4+5}[/tex]

[tex]\lim_{x \to 4}  f(x)=0[/tex]

Functional value:

We can plug x=4 into f(x)

[tex]f(4)=\frac{4-4}{4+5}[/tex]

[tex]f(4)=0[/tex]

So, we can see that

[tex]\lim_{x \to 4}  f(x)=f(4)=0[/tex]

So, limit value is equal to function value

so, f(x) is continuous at a=4.............Answer

[tex]A.\\\\\dfrac{y}{a}-b=\dfrac{y}{b}-a\qquad\text{multiply both sides by }\ ab\neq0\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\qquad\text{distributive}\\\\(b-a)y=ab^2-a^2b\qquad\text{divide both sides by}\ (b-a)\\\\\boxed{y=\dfrac{ab^2-a^2b}{b-a}}\to y=\dfrac{ab(b-a)}{b-a}\to\boxed{y=ab}[/tex]

[tex]B.\\t+\dfrac{b^2}{a}=\dfrac{bt}{a}+a\qquad\text{multiply both sides by}\ a\neq0\\\\at+b^2=bt+a^2\qquad\text{subtract}\ b^2\ \text{from both sides}\\\\at=bt+a^2-b^2\qquad\text{subtract}\ bt\ \text{from both sides}\\\\at-bt=a^2-b^2\qquad\text{distributive}\\\\(a-b)t=a^2-b^2\qquad\text{divide both sides by}\ (a-b)\neq0\\\\\boxed{t=\dfrac{a^2-b^2}{a-b}}\to t=\dfrac{(a-b)(a+b)}{a-b}\to\boxed{t=a+b}[/tex]

Answer:

Where are y and t?

Step-by-step explanation:

Answer:

cos C = 9/41

Step-by-step explanation:

cos C = adjacent side/ hypotenuse

cos C = 9/41

Answer:

cos C = 9/41

Step-by-step explanation:

The given triangle is right angle triangle.

Cos C = Adjacent/Hypotenuse

Here, Adjacent = 9 and Hypotenuse = 41

cos C = 9/41

Thank you.

Answer:  $ 16.96      

Step-by-step explanation:

Here, the present value of the loan, PV = $695.20

Annual Interest rate = 17.9%

⇒ Monthly interest rate = 17.9/12 = 1.41666666667

Thus, the monthly interest rate (decimal ) , r = 0.014167 ( approx)

Monthly payment, P = $ 325

Let the time period of the loan = n.

Since, [tex]P= \frac{r(PV)}{1-(1+r)^{-n}}[/tex]

⇒ [tex]325= \frac{0.014167(695.20)}{1-(1+0.014167)^{-n}}[/tex]

⇒  [tex]1-(1+0.014167)^{-n}= \frac{10.37008984}{325}[/tex]

⇒ [tex]1-(1+0.014167)^{-n}= 0.03190796873 [/tex]

⇒  n = 2.19

Thus, her total payment = 2.19 × 325 =  711.75

⇒ Her total interest = 711.75 - 695.20 = $16.55

Since only 16.96 is near to 16.55

Thus, second option is correct.

We are given the two bases of the trapezium:

[tex] ED = 5,\qquad AB = 9 [/tex]

The formula for the area of the trapezium is

[tex] A = \dfrac{(B+b)h}{2} [/tex]

So, we only need to figure out the length of the height EF.

We know that FA+EF = 11. Also, we're given that the perimeter of ABCF is 28, which means

[tex] 2AB+2FA = 28 \iff 2\cdot 9 + 2FA = 28 \iff 2FA = 10 \iff FA = 5 [/tex]

So, we can deduce

[tex] EF = 11-FA = 11-5=6 [/tex]

And so we're ready to use the solving formula:

[tex] A = \dfrac{(5+9)\cdot 6}{2} = \dfrac{14\cdot 6}{2} = 7\cdot 6 = 42 [/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{1}{2}[/tex] of the pie.

Step-by-step explanation:  

We have been given that Christine baked a pumpkin pie. She ate 1/6 of the pie. Her brother ate 1/3 of it and gave leftovers to his friends.

Let us find out pie given to friends by subtracting amount of pie eaten by Christine and her brother from 1 pie, that will be 6/6.

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{1}{3})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2*1}{2*3})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-(\frac{1}{6}+\frac{2}{6})[/tex]

[tex]\text{The pie given to friends}=\frac{6}{6}-\frac{3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{6-3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{3}{6}[/tex]

[tex]\text{The pie given to friends}=\frac{1}{2}[/tex]

Therefore, he gave [tex]\frac{1}{2}[/tex] of the pie to his friends.

Answer:

Alternative C

Step-by-step explanation:

x² + 10x + 24 = 0

∆ = 10² - 4.1.24

∆ = 100 - 96

∆ = 4

[tex]x' = \frac{- 10 + 2}{2} \\\\\ x' = - 4 \\\ x" = \frac{- 10 - 2}{2} \\\\\ x" = - 6[/tex]

I hope I helped you.

Answer: C

Step-by-step explanation:

x² + 10x + 24 = 0

                ∧

               1 + 24 = 25

               2 + 12 = 14

               3 + 8 = 11

                4 + 6 = 10  ← THIS WORKS!

(x + 4)(x + 6) = 0

x + 4 = 0       x + 6 = 0

 x = -4             x = -6

Answer:

The original price of the  bracelet before tax is $12.

Step-by-step explanation:

Let us assume that the original price of the  bracelet be x.

As given

Casey buys a bracelet.

She pays for the bracelet and pays $0.72 in sales tax .

The sales tax rate is 6% .

6% is written in the decimal form.

[tex]= \frac{6}{100}[/tex]

= 0.06

Than the equation becomes

x × 0.06 = 0.72

0.06x = 0.72

[tex]x = \frac{0.72}{0.06}[/tex]

x = $12

Therefore the original price of the  bracelet before tax is $12.

Answer:

sinB = 8/17

Step-by-step explanation:

sinB = Opposite/Hypotenuse

Here we have to find the opposite side using the Pythagorean theorem.

AB^2 = AC^2 + BC^2

17^2 = AC^2 + 15^2

AC^2 = 17^2 - 15^2

AC^2 = 289-225

AC^2 = 64

Taking the square root on both sides, we get

AC = 8

Opposite side = 8

SinB = 8/17

Answer:

sin B = 8/17

Step-by-step explanation:

sin B can be expressed as the opposite over the hypotenuse in a right triangle.  But we don't know the opposite yet.  We can use the Pythagorean theorem to solve for it

a^2 + b^2 = c^2

15^2 +b^2 = 17^2

225+b^2 = 289

Subtract 225 on each side

225-225 +b^2 = 289-225

b^2 = 64

Take the square root of each side

b=8

The opposite side is 8

sin B = opp/hyp

sin B = 8/17

Answer:

RX = 12 and XU = 6

Step-by-step explanation:

Given :  In ΔTRV , TW ,RU and VS are the medians .

             X is the centroid

To Find : RX and XU

Solution:

Since we know that the centroid divides each median in a ratio of 2:1.

Since X is the centroid so RX : XU = 2:1

So, let RX = 2x and XU = x

And we are given that RU = 18

⇒RX +XU=18

⇒2x+x=18

⇒3x=18

⇒[tex]x=\frac{18}{3}[/tex]

⇒[tex]x=6[/tex]

Thus,  RX = 2x = 2*6 =12

          XU = x =6

Hence length of RX = 12 and XU = 6

Answer:

1

Step-by-step explanation:

Answer:

B.5.6g

Step-by-step explanation: Density of object=mass/volume

Therefore, Mass=density of object X volume

                           =0.7 X 8

                           =5.6g

Answer:

Mass of an object is:

B. 5.6 g

Step-by-step explanation:

Mass of an object= Density × Volume

An object that has a density of 0.7 g/cm³

and a volume of 8 cm³

Mass= 0.7 g/cm³ × 8 cm³

       = 5.6 g

Hence, Correct option is:

B. 5.6 g