Valerie took out a loan to pay off some bills. She borrowed $1,200 at an annual interest rate of 9%. How much interest did she pay on the loan the first year?

Answer:

24°

Step-by-step explanation:

The sum of the ratios is 30.  We know that the degree measure of a triangle is 180, so if we divide 180 by 3 we get increments of 6°.  That means that 4 parts algebraically can be expressed as 4(6°); 12 parts as 12(6°); 14 parts as 14(6°).  That gives us angles of 24°, 72°, 84°.  If we add those up we do indeed get 180°, so the smallest angle measure in that extended ratio is 24°

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

[tex]\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}[/tex].

[tex]\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}[/tex].

[tex]\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}[/tex].

Note that the inverse sine function here [tex]\sin^{-1}()[/tex] is also known as arcsin.

By the law of cosine,

[tex]c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}[/tex],

where

For triangle ABC:

Therefore, replace C in the equation with A, and the law of cosine will become:

[tex]a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}[/tex].

[tex]\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}[/tex].

For triangle ABC:

Start by finding the cosine of angle B. Apply the law of cosine.

[tex]b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}[/tex].

[tex]\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}[/tex].

[tex]\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree[/tex].

For triangle DEF:

Apply the law of sine:

[tex]\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}[/tex]

[tex]\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9[/tex].

Answer:

The cost of 1 jar of peanut butter is $2.50 ⇒ answer B

Step-by-step explanation:

* Lets change the story problem to equations to solve it

- The cost of a jar of peanut butter is p dollars

- The cost of a jar of jelly is j dollars

- Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50

- Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00

* Lets write the equations

∵ The cost of a jar of peanut butter is p dollars and the cost of a jar

   of jelly is j dollars

∵ Winston purchased 3 jars of peanut butter and 2 jars of jelly for $11.50

∴ 3p + 2j = 11.50 ⇒ (1)

∵ Peter purchased 2 jars of peanut butter and 4 jars of jelly for $13.00

∴ 2p + 4j = 13.00 ⇒ (2)

- Lets solve this system of equation by using elimination method

- Multiply equation (1) by -2

∴ -6p - 4j = - 23 ⇒ (3)

- Add equations (2) and (3)

∴ -4p = -10 ⇒ divide both sides by -4

∴ p = 2.5

∵ p is the cost of 1 jar of peanut butter

* The cost of 1 jar of peanut butter is $2.50

Final answer:

Using a system of equations based on the purchases of Winston and Peter, the price of one jar of peanut butter is calculated to be $2.50.

Explanation:

To determine the cost of one jar of peanut butter, we can set up a system of equations based on the information provided. Let p represent the price of one jar of peanut butter, and j represent the price of one jar of jelly.

The system of equations based on the purchases made by Winston and Peter are:
1) 3p + 2j = 11.50
2) 2p + 4j = 13.00

To solve for p, we can multiply equation 1) by 2 and equation 2) by 3 to eliminate j when we subtract one equation from the other.

2*(1): 6p + 4j = 23.00
3*(2): 6p + 12j = 39.00

Subtracting the first equation from the second, we get:

6p + 12j - (6p + 4j) = 39.00 - 23.00
8j = 16.00
j = 2.00

Now, substitute j = 2.00 into equation 1) to find p:

3p + 2(2.00) = 11.50
3p + 4.00 = 11.50
3p = 7.50
p = 2.50

Therefore, one jar of peanut butter costs $2.50, which corresponds with option B.

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have the following line:

[tex]2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4[/tex]

If the line we wish to find is perpendicular to the one given, then its slope is given by:

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}[/tex]

Then the line is:

[tex]y = - \frac {3} {2} x + b[/tex]

We substitute the point:

[tex]6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9[/tex]

Finally, the equation is:

[tex]y = - \frac {3} {2} x + 9[/tex]

Answer:

[tex]y = - \frac {3} {2} x + 9[/tex]

Answer:

D. x > -4 or x < -8

Step-by-step explanation:

For this case we must indicate the solution of the following inequalities:

[tex]4x> -16[/tex]

We divide both sides of the inequality by 4:

[tex]x> - \frac {16} {4}\\x> -4[/tex]

On the other hand we have:[tex]6x\leq - 48[/tex]

We divide between 6 on both sides of the inequality:

[tex]x\leq - \frac {48} {6}\\x\leq- 8[/tex]

Thus, the solution will be:

[tex]x>-4[/tex] or [tex]x\leq-8[/tex]

ANswer:

Option D

Answer:

[tex]\frac{b+3}{3}[/tex]

Step-by-step explanation:

[tex]\frac{b+3}{b} \div\frac{3}{b}[/tex]

We need to solve the above equation.

We replace the division sign by multiplication and reciprocated the second term

[tex]=\frac{b+3}{b} *\frac{b}{3}[/tex]

Multiplying both fractions:

[tex]=\frac{(b+3)*b}{3b}[/tex]

Cancelling b from numerator and denominator.

[tex]=\frac{(b+3)}{3}[/tex]

So, answer is:

[tex]\frac{b+3}{3}[/tex]

ANSWER

[tex]\frac{b + 3}{3}[/tex]

EXPLANATION

The given expression is

[tex] \frac{b + 3}{b} \div \frac{3}{b} [/tex]

We multiply the first fraction by the multiplicative inverse of the second fraction.

[tex]\frac{b + 3}{b} \times \frac{b}{3}[/tex]

We now cancel out the common factors to get:

[tex]\frac{b + 3}{3} [/tex]

Therefore simplified form is:

[tex]\frac{b + 3}{3} [/tex]

Answer:

j(t)=230600(1.009)^t

Step-by-step explanation:

Increasing at a rate of 0.9\%0.9%0, point, 9, percent means the expected number of jobs keeps its 100\%100%100, percent and adds 0.9\%0.9%0, point, 9, percent more, for a total of 100.9\%100.9%100, point, 9, percent.

So each year, the expected number of jobs is multiplied by 100.9\%100.9%100, point, 9, percent, which is the same as a factor of 1.0091.0091, point, 009.

If we start with the initial number of jobs, 230{,}600230,600230, comma, 600 jobs, and keep multiplying by 1.0091.0091, point, 009, this function gives us expected number of jobs in radiology ttt years from 201420142014:

j(t)=230600(1.009)^t

Answer:

[tex]J(t) =230600(1.009)^t[/tex]

Step-by-step explanation:

Given,

The initial number of jobs ( or jobs on 2014 ), P = 230,600

Also, the rate of increasing per year, r = 0.9% = 0.009,

Thus, the number of jobs after t years since 2014,

[tex]J(t)=P(1+r)^t[/tex]

[tex]=230600(1+0.009)^t[/tex]

[tex]=230600(1.009)^t[/tex]

Which is the required function.

Answer:

B. -9a+2

Step-by-step explanation:

You are given the sequence

[tex]t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_{n-1}-3t_{n-2}+1,\ n\ge 3[/tex]

According to the given rule, find [tex]t_3,\ n=3[/tex]

[tex]t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1[/tex]

and [tex]t_4,\ n=4[/tex]

[tex]t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2[/tex]

C. randomly select from all residents.

Answer:

Sorry if i'm late but i think the answer is C. Randomly select from all of the town residents

im 97% sure

Set up a ratio for the area.

Area is squared so find the square root of the scale

√64/169 = 0.61538

Volume is cubed so cube the scale factor:

0.61538^3 = 0.23304

Multiply that by the volume:

4394 x 0.23304 = 1024

The volume of the smaller figure is 1,024 m^3

Answer:

Step-by-step explanation:

We know:

The ratio of the surface of two similar figures is equal to the square of the similarity scale. The ratio of the volume of two similar figures is equal to the cube of the similarity scale.

Therefore

k - similarity scale

[tex]k^2=\dfrac{64}{169}\to k=\sqrt{\dfrac{64}{169}}=\dfrac{\sqrt{64}}{\sqrt{169}}=\dfrac{8}{13}\\\\\dfrac{V}{4394}=\left(\dfrac{8}{13}\right)^3\\\\\dfrac{V}{4394}=\dfrac{512}{2197}\qquad\text{cross multiply}\\\\2197V=(512)(4394)\qquad\text{divide both sides by 2197}\\\\V=(512)(2)\\\\V=1024\ m^3[/tex]

Answer:

Step-by-step explanation:

answer:   27/159

The experimental probability of rolling a four is [tex]27 \div 159[/tex]

A number cube with the numbers 1 through 6 is rolled 159 times and shows the number four 27 times.

The experimental probability should be [tex]27 \div 159[/tex]

Learn more about the number here: https://brainly.com/question/1812875

Answer:

The sum is equal to 5

Step-by-step explanation:

we know that

The algebraic expression of the phrase "  the sum of negative two squared plus one" is equal to

[tex](-2)^{2}+1\\=4+1\\=5[/tex]

Answer:

5

Step-by-step explanation:

(-2)^2 +1

Since the quantity is squared, it becomes a positive number

4+1

5

Answer:

(x − 4)2 + ( y + 6)2 = 49

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is                                (x − h)2 + (y − k)2 = r2.

Define h, k and r using the given values. So, h = 4, k = −6 and r = 7.

Substitute the values into the equation of a circle:

(x − 4)2 + (y − (−6))2 =72

Simplify.

(x − 4)2 + (y + 6)2 = 49

Therefore, the equation of the circle B with center B(4, -6) and radius 7 is   (x − 4)2 + (y + 6)2 = 49.

The equation of the circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the corrcet option is B.

A circle can be represented as;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

Where h and k are the centers of the circle and r is the radius of the circle.

The equation of circle B with center B(4,−6) and radius 7.

Substitute all the values in the equation

[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-4)^2+(y-(-6))^2=7^2\\\\\rm (x-4)^2+(y+6)^2=49[/tex]

Hence the equation of circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the correct option is B.

Learn more about circle here;

https://brainly.com/question/11833983

#SPJ2

look at the picture not my text lol

Answer:

B

Step-by-step explanation:

Look at the other guys box and whisker plot

Answer:

275 miles

Step-by-step explanation:

Let x be the number of miles Alan has to drive to get the same cost for tha two plans.

1 plan: total cost

[tex]55+0.50x[/tex]

2 plan: total cost

[tex]0.7x[/tex]

Equate them:

[tex]55+0.5x=0.7x\\ \\55=0.2x\\ \\550=2x\\ \\x=275[/tex]

Answer:

275 miles

Step-by-step explanation:

You can express the cost of each plan as follows:

Plan 1: 55+0.50x

Plan 2: 0.70x

x is the amount of miles driven

As you need to find the amount of miles where the two plans cost the same, you can equate them and solve for x:

55+0.50x= 0.70x

55= 0.70x-0.50x

55= 0.2x

x= 55/0.2

x= 275

Alan needs to drive 175 miles for the two plans to cost the same.

Answer:

The answer is (d) ⇒ cscx = √3

Step-by-step explanation:

∵ sinx + (cotx)(cosx) = √3

∵ sinx + (cosx/sinx)(cosx) = √3

∴ sinx + cos²x/sinx = √3

∵ cos²x = 1 - sin²x

∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M

∴ (sin²x + 1 - sin²x)/sinx = √3

∴ 1/sinx = √3

∵ 1/sinx = cscx

∴ cscx = √3

Answer:

d. [tex]\sqrt{3}[/tex]

Step-by-step explanation:

see attachment, it's correct :))

Answer:

your answer is a

Step-by-step explanation:

The correct inequality and number line that model the situation above is:

             10 ≤ weight of boxes ≤ 20

  and the correct graph is:  Graph A

The desired weight of raisins is:  15 ounces.

As the weight of the raisins packed differs by a maximum of 5 ounces.

This means that the weight of the raisins packed could either be less by 5 ounces or more by 5 ounces.

i.e.  Weight of raisins could be minimum= 15-5=10 ounces.

and weight of raisins could be maximum= 15+5=20 ounces.

Hence, the inequality that will hold true is:

               10 ≤ weight of boxes ≤ 20

and the graph that describe this situation is attached to the answer.

Answer:

Correct choice is (C). [tex]4z^5[/tex].

Step-by-step explanation:

Given expression is [tex]-3z^5-\left(-7z^5\right)[/tex].

Now we need to simplify that then select the correct difference value from the given choices.

[tex]-3z^5-\left(-7z^5\right)[/tex]

negative times negative is positive

[tex]=-3z^5+7z^5[/tex]

Combine like terms because variable z has same exponent.

[tex]=(-3+7)z^5[/tex]

[tex]=4z^5[/tex]

Hence correct choice is (C). [tex]4z^5[/tex].

The line of music which shows a translation is b.

Translation means moving.

The Second line of music shows a translation from all the lines.

The translation is defined as the sliding of an object without changing its shape and size.

In this figure, the second option shows the exact translation operation. but the first and third line doesn't represent a translation.

In the first option, the translation does not take place, the music lines are inverted.

In the third option, the music lines are just interchanged which doesn't prove the translation.

Learn more about translation;

brainly.com/question/15487308

Answer:The length is 13/2, while the width is 15/4, after combination. Ratio of length to width is then (13/2)/(15/4) = 26/15.

Answer:

The coordinates for the location of the center of the platform are (-1 , 2)

Step-by-step explanation:

* Lets revise the equation of the circle

- The equation of the circle of center (h , k) and radius r is:

  (x - h)² + (y - k)² = r²

- The center is equidistant from any point lies on the circumference

 of the circle

- There are three points equidistant from the center of the circle

- We have three unknowns in the equation of the circle h , k , r

- We will substitute the coordinates of these point in the equation of

 the circle to find h , k , r

* Lets solve the problem

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ Points D (-2 , -4) , E (1 , 5) , F (2 , 0)

- Substitute the values of x and y b the coordinates of these points

# Point D (-2 , -4)

∵ (-2 - h)² + (-4 - k)² = r² ⇒ (1)

# Point E (1 , 5)

∵ (1 - h)² + (5 - k)² = r² ⇒ (2)

# Point (2 , 0)

∵ (2 - h)² + (0 - k)² = r²

∴ (2 - h)² + k² = r² ⇒ (3)

- To find h , k equate equation (1) , (2) and equation (2) , (3) because

  all of them equal r²

∵ (-2 - h)² + (-4 - k)² = (1 - h)² + (5 - k)² ⇒ (4)

∵ (1 - h)² + (5 - k)² = (2 - h)² + k² ⇒ (5)

- Simplify (4) and (5) by solve the brackets power 2

# (a ± b)² = (a)² ± (2 × a × b) + (b)²

# Equation (4)

∴ [(-2)² - (2 × 2 × h) + (-h)²] + [(-4)² - (2 × 4 × k) + (-k)²] =

  [(1)² - (2 × 1 × h) + (-h)²] + [(5)² - (2 × 5 × k) + (-k)²]

∴ 4 - 4h + h² + 16 - 8k + k² = 1 - 2h + h² + 25 - 10k + k² ⇒ add like terms

∴ 20 - 4h - 8k + h² + k² = 26 - 2h - 10k + h² + k² ⇒ subtract h² and k²

  from both sides

∴ 20 - 4h - 8k = 26 - 2h - 10k ⇒ subtract 20 and add 2h , 10k

  for both sides

∴ -2h + 2k = 6 ⇒ (6)

- Do the same with equation (5)

# Equation (5)

∴ [(1)² - (2 × 1 × h) + (-h)²] + [(5)² - (2 × 5 × k) + (-k)²] =

  [(2)² - (2 × 2 × h) + k²

∴ 1 - 2h + h² + 25 - 10k + k² = 4 - 4h + k²⇒ add like terms

∴ 26 - 2h - 10k + h² + k² = 4 - 4h + k² ⇒ subtract h² and k²

  from both sides

∴ 26 - 2h - 10k = 4 - 4h  ⇒ subtract 26 and add 4h

  for both sides

∴ 2h - 10k = -22 ⇒ (7)

- Add (6) and (7) to eliminate h and find k

∴ - 8k = -16 ⇒ divide both sides by -8

∴ k = 2

- Substitute this value of k in (6) or (7)

∴ 2h - 10(2) = -22

∴ 2h - 20 = -22 ⇒ add 20 to both sides

∴ 2h = -2 ⇒ divide both sides by 2

∴ h = -1

* The coordinates for the location of the center of the platform are (-1 , 2)

Answer:

The coordinates for the location of the center of the platform are (-3.5,1.5)

Step-by-step explanation:

You have 3 points:

D(−2,−4)

E(1,5)

F(2,0)

And you have to find a equidistant point (c) ([tex]x_{c}[/tex],[tex]y_{c}[/tex]) from the three given.

Then, you know that:

[tex]D_{cD}=D_{cE}[/tex]

And:

[tex]D_{cE}=D_{cF}[/tex]

Where:

[tex]D_{cD}[/tex]=Distance between point c to D

[tex]D_{cE}[/tex]=Distance between point c to E

[tex]D_{cF}[/tex]=Distance between point c to D

The equation to calculate distance between two points (A to B) is:

[tex]D_{AB}=\sqrt{(x_{B}-x_{A})^2+(y_{B}-y_{A})^2)}[/tex]

[tex]D_{AB}=\sqrt{(x_{B}^2)-(2*x_{B}*x_{A})+(x_{A}^2)+(y_{B}^2)-(2*y_{B}*x_{A})+(y_{A}^2)}[/tex]

Then you have to calculate:

*[tex]D_{cD}=D_{cE}[/tex]

[tex]D_{cD}=\sqrt{(x_{D}-x_{c})^2+(y_{D}-y_{c})^2}[/tex]

[tex]D_{cD}=\sqrt{(x_{D}^2)-(2*x_{D}*x_{c})+(x_{c}^2)+(y_{D}^2)-(2*y_{D} y_{c})+(y_{c}^2)}[/tex]

[tex]D_{cD}=\sqrt{(-2^2-(2(-2)*x_{c})+x_{c}^2)+(-4^2-(2(-4) y_{c})+y_{c}^2)}[/tex]

[tex]D_{cD}=\sqrt{(4+4x_{c}+x_{c}^2 )+(16+8y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}-x_{c})^2+(y_{E}-y_{c})^2}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}^2)-(2*x_{E}*x_{c})+(x_{c}^2)+(y_{E}^2)-(2y_{E}*y_{c})+(y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1^2-2(1)*x_{c}+x_{c}^2)+(5^2-2(5)+y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)}[/tex]

[tex]D_{cD}=D_{cE}[/tex]

[tex]\sqrt{((4+4x_{c}+x_{c}^2)+(16+8y_{c}+y_{c}^2))}=\sqrt{(1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)}[/tex]

[tex](4+4x_{c}+x_{c}^2)+(16+8y_{c}+y_{c}^2)= (1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2)[/tex]

[tex]x_{c}^2+y_{c}^2+4x_{c}+8y_{c}+20=x_{c}^2+y_{c}^2-2x_{c}-10y_{c}+26[/tex]

[tex]4x_{c}+2x_{c}+8y_{c}+10y_{c}=6[/tex]

[tex]6x_{c}+18y_{c}=6[/tex]

You get equation number 1.

*[tex]D_{cE}=D_{cF}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}-x_{c})^2+(y_{E}-y_{c})^2}[/tex]

[tex]D_{cE}=\sqrt{(x_{E}^2-(2+x_{E}*x_{c})+x_{c}^2)+(y_{E}^2-(2y_{E} *y_{c})+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{((1^2-2(1)+x_{c}+x_{c}^2)+(5^2-2(5)y_{c}+y_{c}^2)}[/tex]

[tex]D_{cE}=\sqrt{(1-2x_{c}+x_{c}^2 )+(25-10y_{c}+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(x_{F}-x_{c})^2+(y_{F}-y_{c})^2}[/tex]

[tex]D_{cF}=\sqrt{(x_{F}^2-(2*x_{F}*x_{c})+x_{c}^2)+(y_{F}^2-(2*y_{F}* y_{c})+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(2^2-(2(2)x_{c})+x_{c}^2)+(0^2-(2(0)y_{c}+y_{c}^2)}[/tex]

[tex]D_{cF}=\sqrt{(4-4x_{c}+x_{c^2})+(0-0+y_{c}^2)}[/tex]

[tex]D_{cE}=D_{cF}[/tex]

[tex]\sqrt{(1-2x_{c}+x_{c}^2 )+(25-10y_{c}+y_{c}^2)}=\sqrt{(4-4x_{c}+x_{c}^2 )+(0-0+y_{c}^2)}[/tex]

[tex](1-2x_{c}+x_{c}^2)+(25-10y_{c}+y_{c}^2 )=(4-4x_{c}+x_{c}^2)+(0-0+y_{c}^2)[/tex]

[tex]x_{c}^2+y_{c}^2-2x_{c}-10y_{c}+26=x_{c}^2+y_{c}^2-4x_{c}+4[/tex]

[tex]-2x_{c}+4x_{c}-10y_{c}=-22[/tex]

[tex]2x_{c}-10y_{c}=-22[/tex]

You get equation number 2.

Now you have to solve this two equations:

[tex]6x_{c}+18y_{c}=6[/tex] (1)

[tex]2x_{c}-10y_{c}=-22[/tex] (2)

From (2)  

[tex]-10y_{c}=-22-2x_{c}[/tex]

[tex]y_{c}=(-22-2x_{c})/(-10)[/tex]

[tex]y_{c}=2.2+0.2x_{c}[/tex]

Replacing [tex]y_{c}[/tex] in (1)

[tex]6x_{c}+18(2.2+0.2x_{c})=6[/tex]

[tex]6x_{c}+39.6+3.6x_{c}=6[/tex]

[tex]9.6x_{c}=6-39.6[/tex]

[tex]x_{c}=6-39.6[/tex]

[tex]x_{c}=-3.5[/tex]

Replacing [tex]x_{c}=-3.5[/tex] in

[tex]y_{c}=2.2+0.2x_{c}[/tex]

[tex]y_{c}=2.2+0.2(-3.5)[/tex]

[tex]y_{c}=2.2+0.2(-3.5)[/tex]

[tex]y_{c}=2.2-0.7[/tex]

[tex]y_{c}=1.5[/tex]

Then the coordinates for the location of the center of the platform are (-3.5,1.5)

Step-by-step explanation:

In the first three, the probability of success (or failure) is constant, so those distributions have binomial distributions.

The problem says nothing about doses, which most likely wouldn't be independent events anyways.

So the answer is indeed the first three.  Good job!

Answer: A . When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

B. When the medicine is tried with six patients, X is the number of patients for whom the medicine does not work.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

Step-by-step explanation:

From all the given options, option A, B and C has trials that have same probability of success for the given event X .

But option D shows event X is the number of doses each patient needs to take which varies depending on the patient.

Hence, the trials do not have same probability of success .

Answer:

  see below

Step-by-step explanation:

21) The law of sines can be used, since you have a side and its opposite angle.

  sin(F)/DE = sin(D)/EF

  F = arcsin(DE/EF·sin(D)) = arcsin(20/31·sin(95°)) ≈ 39.994°

  E = 180° -95° -39.994° ≈ 45.006°

  DF = sin(45.006°)/sin(95°)·31 ≈ 22.006

__

22) The remaining two problems can be solved using the law of cosines:

  c^2 = a^2 + b^2 - 2ab·cos(C)

Of course, c is the square root of the expression on the right.

  EF = √(19^2 +35^2 -2(19)(35)cos(61°)) ≈ √(941.203) ≈ 30.679

Then an angle can be found using the law of sines

  E ≈ arcsin(35/30.679·sin(61°)) ≈ 86.203°

  F ≈ 180° -61° -86.203° ≈ 32.797°

__

23) As in 22 …

  RS = √(20^2 +28^2 -2(20)(28)cos(91°)) ≈ √(1203.547) ≈ 34.692

  R ≈ arcsin(20/34.692·sin(91°)) ≈ 35.199°

  S ≈ 180° -91° -35.199° ≈ 53.801°

Answer:

The Monday ratio was equal to the Tuesday ratio.

The Tuesday ratio was greater than the Wednesday ratio.

The Wednesday ratio was less than the Monday ratio.

Step-by-step explanation:

Using the ratio and Proportion concept, The true statements are:

The Monday ratio was equal to the Tuesday ratio.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.

What is Proportion?

Ratio and fractions are the main bases on which proportion is discussed. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a percentage. In this case, a and b can be any two numbers. Ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics.

So, According to the question:

The ratio on Monday = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]

The ratio on Tuesday = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

The ratio on Wednesday = [tex]\frac{6}{6}[/tex] = [tex]\frac{1}{1}[/tex]

So, from the above fraction, we can easily conclude that The Monday ratio was equal to the Tuesday ratio.

Hence, The Monday ratio was equal to the Tuesday ratio.

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Answer:

2

Step-by-step explanation:

It is not 7, although that looks possible. The 7 is a coefficient (in my day we called it a numerical coefficient).

The constant is not d either.  That is a variable.

The constant is the 2

the answer is.... no solution

An equation is formed of two equal expressions. For the given equation 64³ˣ=512²ˣ⁺¹² no solution for x exists.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The above equation 64³ˣ=512²ˣ⁺¹² can be solved in the following manner as stated below,

64³ˣ = 512²ˣ⁺¹²

(8²)³ˣ=(8³)²ˣ⁺¹²

8⁶ˣ = 8⁽⁶ˣ⁺³⁶⁾

6x = 6x +36

6x - 6x = 36

0 = 36

As the value of x can not be defined, it can be concluded that the equation has no solution.

Hence, for the given equation no solution for x exists.

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Answer:

N⊥M

Step-by-step explanation:

If N║ P and P⊥M then N⊥M

Answer:

2.3744 ft

Step-by-step explanation:

11.54/(2.7*1.8)

Answer:

an exponential function

Step-by-step explanation:

Use a function of the same form as the compound amount formula:

A = P(1+r)^5, where r is the appreciation or depreciation rate and P is the initial value.  This is definitely an exponential function.

The given function could model the value of the car as an exponential function.

We have given that,

Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year.

We have to determine which type of function could model the value of the car.

Use a function of the same form as the compound amount formula

A = P(1+r)^5,

where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.

Therefore the given function could model the value of the car as an exponential function.

Therefore the option A is correct

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