Which value is a discontinuity of x^2+7x+1/x^2+2x-15? x=-1 x=-2 x=-5 x=-4

Answers

Answer 1

[tex]\dfrac{x^2+7x+1}{x^2+2x-15}=\dfrac{x^2+7x+1}{(x+5)(x-3)}[/tex]

which is undefined when [tex]x=-5[/tex] or [tex]x=3[/tex]. The answer is then the third choice.

Answer 2

Final answer:

The value of x=-5 is a discontinuity of the function x^2+7x+1 / x^2+2x-15 since it makes the denominator of this function equal to zero.

Explanation:

The subject of this question is the discontinuity of a rational function. In Mathematics, a function f(x) = (p(x))/(q(x)), where p(x) and q(x) are polynomials, is said to be discontinuous at a particular value of x if and only if q(x) = 0 at that value. From the equation in the question; x^2+7x+1/x^2+2x-15, we can determine its discontinuity by finding the values of x that would make the denominator equal to zero. This is done by solving the polynomial equation x^2+2x-15 = 0 for x. The solutions to this equation represent the values at which the function is discontinuous.

By applying the quadratic formula, (-b ± sqrt(b^2 -4ac))/(2a), where a = 1, b = 2, and c = -15, we get that x = -5, and 3. However, the values given in the question are x=-1, x=-2, x=-5, and x=-4. From these options, only x=-5 makes the denominator zero, thus, x = -5 is a point of discontinuity in the function x^2+7x+1 / x^2+2x-15.

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Related Questions

What is the distance between the two points?

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ \frac{1}{8}}}\quad ,&{{-\frac{9}{5}}})\quad % (c,d) &({{ \frac{3}{8}}}\quad ,&{{ -\frac{4}{5}}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]

[tex]\bf d=\sqrt{\left[ \frac{3}{8}-\frac{1}{8} \right]^2+\left[-\frac{4}{5}-\left( -\frac{9}{5} \right) \right]^2}\implies d=\sqrt{\left( \frac{3}{8}-\frac{1}{8} \right)^2+\left(-\frac{4}{5}+\frac{9}{5} \right)^2} \\\\\\ d=\sqrt{\left( \frac{2}{8}\right)^2+\left(\frac{5}{5} \right)^2}\implies d=\sqrt{\left( \frac{1}{4} \right)^2+\left( 1 \right)^2}\implies d=\sqrt{\frac{1^2}{4^2}+1}[/tex]

[tex]\bf d=\sqrt{\frac{1}{16}+1}\implies d=\sqrt{\cfrac{17}{16}}\implies d=\cfrac{\sqrt{17}}{\sqrt{16}}\implies d=\cfrac{\sqrt{17}}{4}[/tex]

If you have 2 pairs such that A(x₁ , y₁) and B(x₂ , y₂). , the distance is:

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

A(1/8 , 9/5) and B(3/8 , - 4/5)

Plug in the related value:

AB = √[(3/8 - 1/8)² + ( - 4/5 - 9/5)²] = √(2729/400) (ALREADY SIMPLIFIED)
AB = distance = 2.61

Convert r =-72/12+6 sin theta to Cartesian form.

Answers

For converting polar to cartesian form we know
[tex]r = \sqrt{x^2 + y^2} [/tex]
[tex]x = rcos \theta , y = rsin \theta[/tex]

Given equation is

[tex]r = \frac{-72}{12} + 6sin \theta [/tex]

We can simplify it as
[tex]r = -6 + 6sin \theta[/tex]

Now we can write it as
[tex]r^2 = -6r + 6rsin \theta[/tex]

Now we can use
[tex]r^2 = x^ 2+ y^2 , rsin \theta = y , r = \sqrt{x^2 + y^2} [/tex]
So equation we can write it as
[tex]x^2 + y^2 = -6 \sqrt{x^2 + y^2} + 6y [/tex]
[tex]x^2 + y^2 - 6y = -6 \sqrt{x^2 + y^2} [/tex]
On squaring both sides
[tex](x^2 + y^2 - 6y)^2 = (-6 \sqrt{x^2 + y^2})^2 [/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3 -12x^2y = 36(x^2 + y^2)[/tex]
[tex]x^4 + y^4 +36y^2 + 2x^2y^2 -12y^3 -12x^2y = 36x^2 + 36y^2[/tex]
[tex]x^4 + y^4 + 36y^2 +2x^2y^2 -12y^3-12x^2y - 36x^2 - 36y^2 = 0[/tex]
[tex]x^4 + y^4 -12y^3 + 2x^2y^2 - 12x^2y - 36x^2 = 0[/tex]

Answer:

The answer is b. [tex]4x^2+3y^2-24y-144=0[/tex]

Step-by-step explanation:

The equation is:

[tex]r=\frac{-72}{12+6\sin(\theta)}[/tex]

Cross multiply;:

[tex]r(12+6\sin(\theta)=-72[/tex]

Expand;:

[tex]12r+6r\sin(\theta)=-72[/tex]

Divide through by 6;:

[tex]2r+r\sin(\theta)=-12[/tex]

[tex]2r=-12-r\sin(\theta)[/tex]

Substitute;:

[tex]y=r\sin(\theta), r=\sqrt{x^2+y^2}[/tex]

[tex]2\sqrt{x^2+y^2}=-12-y[/tex]

Square both sides;:

[tex](2\sqrt{x^2+y^2})^2=(-12-y)^2[/tex]

[tex]4(x^2+y^2)=144+24y+y^2[/tex]

[tex]4x^2+4y^2=144+24y+y^2[/tex]

Simplify;:

[tex]4x^2+3y^2-24y-144=0[/tex]

How often is the number of house representatives assigned to states reallocated? every 2 years every 6 years every 10 years never?

Answers

The members of the executive branch are the president, vice president and the cabinet. The president holds all the power for this branch of the government and the other members report to the president. The legislative branch writes up and votes on laws. This is called legislation. The legislative branch also known as congress has two parts: the House of Representatives and the senate. Other powers of the congress include declaring war, confirming presidential appointments for groups like the Supreme Court and the cabinet and investigating power. According to Article 1, Section 2, Clause 1, the House of Representatives shall constitute members every 2 years by the people of the state.

If the slope of a straight line Is 0 and the y-intercept is -2, what is the equation of the line

Answers

it is simply y=-2

hoped I helped :)

Jonathan bought a new computer for $1,728 using the electronics store's finance plan. He will pay $96 a month for 18 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?

Answers

1728 = 96x x=Months of payments

Answer:

[tex]y=1728-96x[/tex]

Step-by-step explanation:

Given : Cost of computer = $1728

He will pay $96 a month for 18 months.

To Find: Which equation can Jonathan use to find out how much money he still owes after each month of the plan?

Solution:

He pays per month = $96

Let the number of months be x

So, He pays in x months = 96x

Since the total Cost of computer is $1728

So, amount left to be paid = [tex]1728-96x[/tex]

Let y be the unpaid amount after x months

So, equation becomes : [tex]y=1728-96x[/tex]

Hence An equation can Jonathan use to find out how much money he still owes after each month of the plan is [tex]y=1728-96x[/tex]

martha and mary had 375 jelly beans in all. after mary ate 24 jelly beans and martha ate 1/7 of her jelly beans, they each had the same number of jelly beans left. how many jelly beans did each girl have at first?

Answers

Start by setting up two equations

Let x = number of beans with Martha
Let y = number of beans with Mary

Since total beans is 375,
x + y = 375

Mary ate 24 beans, after this she must be having x - 24 beans
Similarly after eating 1/7y beans, mary must be having y - y/7 beans
Setting them equal to each other
x - 24 = y - y/7

Solving both equations gives x = 186, y = 189

You invest $9000 with a 6% interest rate compounded semiannually. After 9 yrs, how much money is in your account?

Answers

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$9000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\to &2\\ t=years\to &9 \end{cases} \\\\\\ A=9000\left(1+\frac{0.06}{2}\right)^{2\cdot 9}[/tex]

What is the slope of a trend line that passes through the points (–3, 3) and (18, 26)?

Answers

Use can you slope formula:

[tex] \frac{Y_2 - Y_1 }{X_2 - X_1} [/tex]

Then, substitute values into the formula.

[tex] \frac{26 - 3}{18 - (-3)} [/tex]

Then solve. You get the fraction, [tex] \frac{23}{21} [/tex]. That is your slope.

Answer:

C.) 23/21

Step-by-step explanation:

just took the test on edge

A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?

Answers

if both crews work together, let's say the finish the job in "t" hours.

so.. in 1 hour, they have done 1/t of the whole work.

now, the new crew, working by itself can do the whole job in 12 hours, that means, in 1 hour, they have done only 1/12 of all the work.

the experienced crew, can do the job in 6 hours, that means in 1 hour, they have done 1/6 of all the work.

now, let's add their rates for 1 hour worth, to see what we get.

[tex]\bf \begin{array}{clclcllll} \cfrac{1}{12}&+&\cfrac{1}{6}&=&\cfrac{1}{t}\\ \uparrow &&\uparrow &&\uparrow &&\\ new\ crew&&experienced&&total\\ rate/hr&&rate/hr&&work/hr \end{array}\\\\ -------------------------------\\\\ \textit{let's multiply both sides by \underline{12t}, to toss away the denominators} \\\\\\ t+2t=12[/tex]

and pretty sure you know how much that is.

The table shows the outputs y for different inputs x:

Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
(10 points)

Answers

A. Yes. Each x value has only one y value. No x value has 2 different y values.
B. For the table, y is 8 when x is 11.
Plug in the value to determine the y value for the equation.
f(x)= 5(11)-21
f(x)= 55-21
f(x)= 34
Since 34>8, the value of the equation f(x) is greater when x=11.
C. 99=5x-21
120=5x
x=24
Final answer: 24

Answer:24

Step-by-step explanation:

a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each

Answers

The givens can be expressed as the abscissa and ordinate of two points. The first point is (1.5, 91). The second point would then have the coordinates of (2.25, 58)
We are given with two points so we can derive the equation using the two-point form.
That is,
y – y1 = ((y2 – y1)/(x2 – x1))(x – x1)

We may choose which among our derived coordinates will be 1 and 2. Substituting to the equation,
y – 91 = ((58 – 91)/(2.25 – 1.5))(x – 1.5)
y – 91 = -44(x – 1.5)
Simplifying further,
y – 91 = -44x + 66

y = -44x + 157

Thus, the equation above gives the number of pretzels that can be sold given the price.

To model the number of pretzels sold per day as a function of the price in dollars using a linear equation, calculate the slope of the line using two known points, and then use the slope and one point to find the y-intercept. The resulting linear equation is y = -44x + 157, where y represents the number of pretzels sold and x represents the price in dollars.

To write a linear equation that models the number of pretzels sold per day when the price is x dollars each, we can start with two given points that represent the sales and price data: (1.50, 91) and (2.25, 58).

Using these points, we can first find the slope of the demand line.

The formula for slope (m) is:

m = (y2 - y1) / (x2 - x1)

Plugging in our values, we get:

m = (58 - 91) / (2.25 - 1.50) = (-33) / (0.75) = -44

The slope of the demand function is -44. This means that for each dollar increase in price, 44 fewer pretzels are sold.

Next, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use one of the given points. Let's use (1.50, 91).

91 = (-44)(1.50) + b
b = 91 + 66
b = 157

The y-intercept, b, is 157. Knowing both m and b, we can now write the equation of the line:

y = -44x + 157

This equation models the number of pretzels sold, y, at a price of x dollars each.

Find the volume of this figure to the nearest whole number. Use 3.14 for pi. Please help me!!

Answers

volume of square middle = 12 x 12 x 7 = 1008

if you put the 2 ends together it would be a cylinder so volume for that is:

3.14 x 6^2 x 7 = 791.28

1008 + 791.28 = 1799.28 round it off to 1800 mm^3

So D is the correct answer

Answer:

4th option is correct.

Step-by-step explanation:

Here in the given image, we can see that there can be 2 figures if separated. A cuboid with dimensions 12*12*7 and a cylinder with radius as 6 mm and height as 7 mm.

We will first find the volume of cuboid.

V = [tex]12\times12\times7[/tex] = 1008 cubic mm

Now, volume of cylinder is given as : [tex]\pi r^{2} h[/tex]

[tex]3.14\times6^{2}\times7[/tex] = 791.28 cubic mm

Now adding both the volumes to get the volume of complete figure:

V = [tex]1008+791.28=1799.28[/tex] cubic mm

Now this value is closest to option 4th : 1800 cubic mm.

Therefore, last option is true.

A company that packages cold cuts needs to transport the packaged meat to the supermarket.it will cost $1,200 to rent a truck,and it will cost an additional $100 for every 50 pounds transported.which equation represents the transport cost for every 50 pounds if cold cuts transported? The options are
A) y=1,200-100x
B) y= 1,200+100x
C) y=1,200x +100
D) y=100x-1,200

Answers

it to calculate the cost of $100 for every 50lbs, you would use 100x

then you need to add that to the 1200

so the equation would be y = 1200+100x

B is the correct answer

The difference between the squares of two numbers is 7. four times the square of the first number increased by the square of the second number is 73. find the numbers.

Answers

let a = x^2 and b=y^2
a-b=7
4a+b=73
4(7+b)+b=73 5b=45 b=9
a=7+b = 7+9 = 16
Then
x^2=16, x=+-4
y^2=9, y=+-3

The difference between the squares of two numbers is 7. Four times the square of the first number increased by the square of the second number is 73. By formulating this information into equations, the numbers, thus, obtained are 3 and 4 or -3 and -4.

An equation is a combination of numbers, variables, functions, mathematical operations, etc. in a meaningful way. The equation comprises two or more expressions separated by the equality sign(=), indicating the equivalency.

Let the numbers be x and y, then according to the question,

[tex]x^2 - y^2 = 7[/tex] ...(i)

[tex]4x^2 + y^2 = 73[/tex] ...(ii)

Add both equations,

[tex](x^2 - y^2) + (4x^2 + y^2) = 7 + 73\\(x^2 + 4x^2) + (-y^2 +y^2) = 80\\5x^2 = 80\\x^2 = 16\\x = \pm4[/tex]

Put x = 4 in equation (i),

[tex]4^2 - y^2 = 7\\16 - y^2 = 7\\y^2 = 16-7\\y^2 = 9\\y = \pm3[/tex]

So, the numbers are 3 and 4 or -3 and -4.

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a rectangular floor is 18 feet long and 12 feet wide. what is the area of the floor in square yards

Answers

You need to find the answer in yards
1 yard=3 feet
Divide 18 and 12 by 3
18/3=6
12/3=4
A=bh
A=4*6
A=24 yards ^2
hope this helps:)
please mark thanks and brainliest:)

1 yard = 3 feet

18/3 =6

12/3=4

6*4 = 24 square yards

the primary advantage of a stratified random sample is that it ____.

Answers

The answer is that it "ensures that segments of the population that are important for a statistical survey are reasonably represented".

Explanation:
It is sometimes practical to divide the population being surveyed into subpopulations before applying random sampling.on each subpopulation.
Doing so ensures that no subpopulations are under represented or over represented, thereby removing bias.

A bag contains 6 poker chips, one is red and the other 5 are blue. you and a friend take turns selecting a chip at random from the bag. the first person to get the red chip is the winner. find the probability that you win if you go first and

Answers

the probability of pulling the red chip if you go first is 1/6

first it's 1/6
second = 1/5
Third= 1/4
fourth= 1/3
Fifth = 1/2
And sixth is guaranteed

Final answer:

The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.

Explanation:

The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.

If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:

P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...

This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:

P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.

3/10, 0.222, 3/5, 0.53 in order from greastest to least

Answers

3/10 = 0.3
3/5 = 0.6

order from greatest to least

3/5, 0.53, 3/10 and 0.222

Melissa is making clothes for her dolls. She has 78 yard of fabric. Each style shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls?

Answers

[tex]\bf 78 \div \cfrac{2}{7}\implies \cfrac{78}{1}\div \cfrac{2}{7}\implies \cfrac{78}{1}\cdot \cfrac{7}{2}\implies \cfrac{78\cdot 7}{1\cdot 2}\implies \cfrac{273}{1}\implies 273[/tex]

Calculate M6 for f(x)=4⋅ln(x^2) over [1,2].

Answers

In this we need to approximate definite integral by midpoint formula.
According to this formula if we have to calculate [tex] \int\limits^a_b {f(x)} \, dx [/tex]
then we will divide the interval [a,b] into n subinterval of equal width.
Δx = [tex] \frac{b-a}{n} [/tex]
So we will denote each of interval as follows
[tex][x_0 , x_1] , [x_1, x_2], ................[x_{n-1} , x_n][/tex] where [tex]x_0 = a , x_n = b[/tex]
Then for each interval we will calculate midpoint.
So we can calculate definite integral as
[tex] \int\limits^a_b {f(x)} \, dx = \triangle x f(y_1) + \triangle x f(y_2)+ ...............+ \triangle x f(y_n)[/tex]
where [tex]y_1 , y_2 , ....................y_n [/tex] are midpoint of each interval.

So in given question we need to calculate [tex]M_6[/tex] . So we will divide our interval in 6 equal parts.
Given interval is [1,2]
[tex]\triangle x = \frac{2-1}{6} = \frac{1}{6} [/tex]

So we will denote 6 interval as follows
[tex][1 , \frac{7}{6}] , [ \frac{7}{6} , \frac{8}{6} ] , [ \frac{8}{6} , \frac{9}{6} ] , [ \frac{9}{6} , \frac{10}{6} ] , [ \frac{10}{6} , \frac{11}{6} ] , [ \frac{11}{6} , 2 ] [/tex]
Now midpoint of each interval is
[tex]y_1 = \frac{1+ \frac{7}{6} }{2} = \frac{13}{12} = 1.084[/tex]
[tex]y_2 = \frac{ \frac{7}{6} + \frac{8}{6} }{2} = \frac{15}{12} = 1.25[/tex]
[tex]y_3 = \frac{ \frac{8}{6} + \frac{9}{6} }{2} = \frac{17}{12} = 1.417[/tex]
[tex]y_4 = \frac{ \frac{9}{6} + \frac{10}{6} }{2} = \frac{19}{12} = 1.584[/tex]
[tex]y_5 = \frac{ \frac{10}{6} + \frac{11}{6} }{2} = \frac{21}{12} = 1.75[/tex]
[tex]y_6 = \frac{ \frac{11}{6} + \frac{12}{6} }{2} = \frac{23}{12} = 1.917[/tex]

So [tex]M_6[/tex] for the given function is

[tex]M_6 = \triangle x [f(y_1) + f(y_2) + f(y_3) + f(y_4) + f(y_5) + f(y_6) ][/tex]
[tex]= \frac{1}{6}[0.6452+1.7851+2.7883+3.6796+4.4769+5.4243][/tex]
[tex]= \frac{1}{6} * 18.7994 = 3.1333 [/tex]
So [tex]M_6 value for function is 3.1333[/tex]

Final answer:

To calculate M6 for f(x)=4⋅ln(x^2) over [1,2], differentiate the function to find f'(x). Integrate f'(x) over the given interval to find the area under the curve. Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.

Explanation:

To calculate M6 for the function f(x) = 4⋅ln(x^2) over the interval [1,2], follow these steps:

Differentiate the function to find f'(x).Integrate f'(x) over the given interval to find the area under the curve.Subtract the value of the integral at the lower limit from the value at the upper limit to get M6.

In this case, since f(x) = 4⋅ln(x^2), we have f'(x) = 8/x. Integrate f'(x) from 1 to 2 to get M6.

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Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°

Answers

Given |u| = 1 and a = 45, you can determine the component form of u.
[tex]u = \ \textless \ cos(45),sin(45)\ \textgreater \ [/tex]

In same way you can find component form of u+v
[tex]u+v = \ \textless \ 2cos(90), 2sin(90)\ \textgreater \ [/tex]

By property of vector subtraction:
v = (u+v) - u

[tex]v = \ \textless \ 2cos(90) - cos(45), 2sin(90) - sin(45)\ \textgreater \ [/tex]
[tex]v = \ \textless \ -\frac{\sqrt{2}}{2}, 2-\frac{\sqrt{2}}{2} \ \textgreater \ [/tex]

Which one of the following pairs of terms is composed of like terms? A. 2a, 2b B. –3x, +3y C. abc, cab D. 4mn, 3my

Answers

C. abc, cab...keep in mind the commutative property...u can move things around and it will not change the end result....abc = cab = bca = bac = cba...

Answer:

Option C

Step-by-step explanation:

We have to find the pair of terms composed of like terms.

(A) 2a, 2b Unlike terms

(B) -3x, +3y Unlike terms

As we know cumulative property of multiplication shows a×(b×c) = (a×b)c

Therefore, both the terms abc and cab are similar.

(D) 4mn, 3my Unlike terms

Option C is the answer.

I need help badly please help !!

Answers

Probability of green die being even: 3/6, which simplifies to 1/2 (2, 4, 6 are even and 1, 3, 5 are odd)

Probability of blue die being even: 3/6, which simplifies to 1/2.

Compound probability:
1/2* 1/2= 1/4

Final answer: 1/4

Amy is doing a science experiment on how a certain bacterium reacts to an antibiotic. She has 3 dishes of identical bacterium samples with 17 bacteria in each dish. She gives an antibiotic to all of the bacteria in one dish. All of the treated bacteria died, and the bacteria in the other two dishes survived. Is there a sampling bias in the situation above? A. There is not enough information. B. Yes. The antibiotic may not work on the other bacteria. C. Yes. The bacteria in the other 2 dishes are different than the treated bacteria. D. No. All 3 dishes are filled with the same number of identical bacteria.

Answers

I think C or A is the answer

A Square has sides that are the same length as the radius of a circle. If the circle has an area of 36π square units how many units long is the perimeter of the square?

Answers

ok so...... the correct answer is ......113.04

πr²= 36π or, r=6 units
now side of a square (l)=radius (r)=6
perimeter of square=4l=6×4=24 units ans

An electronic product contains 40 integrated circuits. the probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. the product operates only if there are no defective integrated circuits. what is the probability that the product operates?

Answers

Final answer:

The probability that the product operates is 0.6706 or 67.06%.

Explanation:

To find the probability that the product operates, we need to find the probability that all 40 integrated circuits are not defective. Since the probability of any integrated circuit being defective is 0.01, the probability that a circuit is not defective is 1 - 0.01 = 0.99. Since the integrated circuits are independent, we can multiply the probabilities together:

P(product operates) = (0.99)⁴⁰ = 0.6706

Therefore, the probability that the product operates is 0.6706 or 67.06%.

Quadrilateral STWR is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary. Circle Q is shown with an inscribed quadrilateral labeled RSTW.

Answers

Consider the figure attached.

Let m(R)=α degrees and m(T)=β degrees.

1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,

so m(arc WTS) = 2α degrees.

2.
Similarly,

Angle T, is an inscribed angle, intercepting the arc WRS. So

m(arc WRS) = 2β degrees.

3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.

thus

2α+2β=360°

divide by 2:

α+β=180°

this means T and R are supplementary angles.

Answer:

Step-by-step explanation:

Arc STR measures twice the measure of angle R, and arc WRS measures twice the measure of angle T.

STR = 2 x ∠R and WRS = 2 x ∠T --- This is because of the Inscribed Angle Theorem

If the measure of arcs STR and WRS are added together, the total would be 360° since a full circle is made up of 360°.

So mSTR + mWRS = 360°

Substituting the angle measures of R and T in for the arcs, the equation becomes:

2 • ∠R + 2 • ∠T = 360°

Simplifying further:

2 • [∠R + ∠T] = 360°

∠R + ∠T = 360° / 2

∠R + ∠T = 180° - This proves that opposite angles of a quadrilateral inscribed in a circle are supplementary.

Mix 20ml per 500 ml of water what is ratio of the amount of insecticide to the amount of water

Answers

Answer:

1 : 25

Step-by-step explanation:

Mix 20 ml per 500 ml. of water the ratio is = 20 : 500

Or [tex]\frac{20}{500}[/tex] = [tex]\frac{1}{25}[/tex] = 1 : 25

1 ml insecticide per 25 ml of water.

The ratio of the amount of insecticide to the amount of water is 1 : 25

Fractions are written as the ratio of two integers. The ratio of the amount of insecticide to the amount of water is 1:25

Ratio and proportions

Fractions are written as the ratio of two integers

From the given question, we have the following measurement:

20ml per 500 ml of water

Required

The ratio of the amount of insecticide to the amount of water

Ratio = 20ml/500ml
Ratio = 1/25 = 1:25

Hence the ratio of the amount of insecticide to the amount of water is 1:25

Learn more on ratio here: https://brainly.com/question/2328454

At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?

Answers

let's say in 2006, year 0, there were "I" amount of customers, and we dunno what "I" is.

now, 4 years later in 2010, t = 4, there are 900 skaters, and the rate of decrease is 5%.

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\to &900\\ I=\textit{initial amount}\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ t=\textit{elapsed time}\to &4\\ \end{cases} \\\\\\ 900=I(1-0.05)^4\implies 900=I(0.95)^4\implies \cfrac{900}{0.95^4}=I \\\\\\ 1105\approx I\qquad thus\qquad \boxed{A=1105(0.95)^t}[/tex]

[tex]\bf \\\\ -------------------------------\\\\ \textit{now in 2006, 4 years earlier, year 0, t = 0} \\\\\\ A=1105(0.95)^0\implies A=1105\cdot 1\implies A=1105[/tex]

In the diagram AB and AC are tangent to the circle. Find the length of the radius D.C.

Answers

If D is the centre of the circle, then DC is perpendicular to AC and DC equals to the radius of the circle.
Otherwise, you need to give more information.

Answer:

D. 6 on e2020

Step-by-step explanation:

just took test

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