brine flows into a conical tank at a constant rate of 3 cubic feet per minute. the radius of the cone is 5 feet and its height is 12 feet. how fast is the radius increasing when the radius is 2 feet? group of answer choices

Answer:

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

Given is an AP with:

Use the explicit rule to find the 26th term:

Correct choice is (2).

The probability is  0.00000911843.

The number of terms is 40 because the number selected falls within the range of integers 1 through 40 (inclusive).

Thus; n = 40

The combination formula, which is; gives the probability that 6 integers (r = 6)—the number of possible outcomes—will be obtained without repetition.

C(n, r) = n!/((n - r)!(n - r)!)

C(40, 6) = 40!/(6!(40 - 6)!)

C(40,6) = 3838380

When it comes to selecting a single item, there are several options available.

(1 - 6, 2 - 7, 8 - 13,...e.t.c)

There will be 35 successful results in all.

The likelihood that the winning numbers will be chosen from a set of six consecutive integers is;

P (that six consecutive integers will be chosen at random as the winning numbers) = likelihood of favorable outcomes/probabilities = 35/3838380 = 0.00000911843

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Answer:

22.7551745473%

Step-by-step explanation:

I could be very wrong but to find the percentage of change you have to divide the increase by the original number, and then multiply it by 100.

20851820-16986510=3865310

3865310/16986510=0.22755174547

0.22755174547*100=22.755174547

This answer can then be rounded up to 23%

The time taken to traveled the van and the tornado before they  meet as per the speed of the van and the tornado is equal to 2.6 minutes.

As given in the question,

Speed of the van along the straight road = 94 kilometers per hour

After travelling distance of 7 kilometers

Speed of the tornado along the same road = 69 km/hour

Total relative speed of van and tornado = 94 + 69

                                                                  = 163km/hour

Distance travelled between two different speed = 7km

Time used to traveled before they meet = distance / speed

                                                                   = 7 / 163

                                                                   = 0.043 hours

                                                                   = 2.58minutes

                                                                   = 2.6minutes

Therefore, the time required to traveled the van and the tornado before they   meet is equal to 2.6 minutes.

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The number must multiply each side of the equation to produce the equivalent equation is -5/3.

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

The given equation is -3/5 x= 48

Multiply each side of the equation by -5/3, we get

[tex]\frac{-3x}{5} \times\frac{-5}{3} =48\times(\frac{-5}{3} )[/tex]

x=-80

Therefore, the number must multiply each side of the equation to produce the equivalent equation is -5/3.

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"Your question is incomplete, probably the complete question/missing part is:"

What number must multiply each side of the equation -3/5 x= 48 to produce the equivalent equation x= -80?

This problem can be solved using divide and conquer techniques. An method known as "divide and conquer" works by breaking down a large task into smaller ones.

An algorithmic pattern is known as Divide and Conquer. In algorithmic approaches, the idea is to take a dispute involving a large amount of input, divide the input into smaller pieces, solve the problem on each of the smaller pieces, and then combine the piecewise solutions into a comprehensive solution. The Divide and Conquer is the algorithmic  name of the approach that was used to solve the issue.

The three steps below are used in a dispute utilizing the Divide and Conquer method.

Create a group of subproblems from the main issue.

Conquer: Recursively and individually solve each subproblem.

Combine: Combine the solutions to the individual subproblems to arrive at the overall solution.

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The given letters r, x, b, and q are all (B) consonants.

A speaking sound that is not a vowel is called a consonant.

It also refers to the alphabetic letters that stand in for certain sounds; consonants include Z, B, T, G, and H.

A consonant is a speech sound that is produced by the vocal tract closing completely or partially, according to articulatory phonetics.

Examples include the letters "p" and "b," which are pronounced with the lips, "t" and "d," which are pronounced with the front of the tongue, "k" and "g," which are pronounced with the back of the tongue, "h," which is pronounced in the throat, "f," "v," and "s," which are pronounced by forcing air through a narrow channel, and "m" and "n," which are pronounced with air flowing through the nose (nasals).

Vowels contrast with consonants.

Therefore, the given letters r, x, b, and q are all (B) consonants.

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Correct question:

The letters r, x, b, and q are all __.

a. syllables.

b. consonants.

c. accented.

d. vowels.

Answer:

x= 2.18265833

Step-by-step explanation:

is this for solve for x, because i got decimal if it was solve for x

3^x=4+7

3^x=11

In (3^x)=In (11)

xIn(3)=In (11)

x= In (11)/ In (3) Divide

X= 2.18265833

Since the stages are simply whole values taken one after the other, they should be whole numbers or integers.

What in mathematics is a whole number?

Complete numbers those figures that contain zero and natural integers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number. Whole numbers are made up of all the ordinal numbers and 0.

                       Natural numbers are the term used to describe counting numbers in mathematics. Therefore, the whole number can be described as a combination of all natural numbers and 0. Along with zero, all positive integers are also considered whole numbers.

He is currently on step 5, there are 15 steps total, therefore he is actually 10 steps away from the top of the ladder. If we walk down the ladder with N being negative, he is -5 steps from the ground.

{ N | N ∈ ℤ , -5 ⩽ N ⩽ 10 }

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The maximum amount per month that Inez would spent on rent is $1170 knowing that he could spend no more than 30% of the take home pay.

Here Inez heard that a a general rule, he should pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year.

The term Take-home pay is the net amount of income received after the deduction of taxes, benefits, and voluntary contributions from a paycheck. It is the difference resulting from the subtraction of all deductions from gross income.

Pay = $46,800

Total allowed = 46,800 x 0.30

Total allowed = $14,040

Now since we know that there are 12 months in a year, we need to divide the Total allowed by 12 to find how much Inez can pay in rent per month.

14,040 / 12 = $1,170

Following the rule that he could not spend more than certain of the take home pay he should rent $1170.

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Answer:

The speed in yards per year is 60.8.

Step-by-step explanation:

To convert the speed from inches per day to yards per year, we need to first convert the speed to inches per year and then convert the units to yards per year.

First, we can convert the speed to inches per year by multiplying the speed by the number of days in a year:

Speed (inches/day) * Days per year = Speed (inches/year)

6 inches/day * 365 days/year = 2190 inches/year

Next, we can convert the units to yards per year by dividing the speed in inches per year by the number of inches per yard:

Speed (inches/year) / Inches per yard = Speed (yards/year)

2190 inches/year / 36 inches/yard = 60.8 yards/year

Rounding to the nearest 10th, we have:

60.8 yards/year ≈ 60.8 yards/year

Therefore, the speed in yards per year is 60.8.

Step-by-step explanation:

the angle south-east of x is hard to read.

I assume this is 86 (but could be also 96).

remember, the sum of all angles in a triangle is always 180°.

and the intersection angles between 2 lines are the same in both sides of the lines. the only difference between above and below angles is that they are left-right mirrored.

so,

180 = x + 22 + 86

x = 180 - 22 - 86 = 72°

x and y are intersection angles of 2 lines and are therefore equal (due to the left-right mirroring).

y = x = 72°

180 = w + 33 + 72

w = 180 - 33 - 72 = 75°

remember also that the sum of all angles around a single point on one side of a line is always 180°, because the line can be seen as diameter of a circle with the point being the circle center. and the degrees of a half-circle are 180°.

180 = angle1 + unnamed angle = angle1 + 85

angle1 = 180 - 85 = 95°

180 = angle2 + angle3 + unnamed angle =

= 42 + angle3 + 85

angle3 = 180 - 42 - 85 = 53°

for the third question we don't see a picture of the situation. I assume this is a circle with O being the center of the circle, and Q, N, P are points on the circle arc.

it is not clear, if the angle QOP is part of the angle QON, or if they are separate segments of the circle.

if the angle QOP is part of the angle QON, then the angle PON = 142 - 46 = 96°

if the angle QOP is separate from the angle QON, then the angle PON = 360 - 142 - 46 = 172°

Answer:

27cm

Step-by-step explanation:

[tex]s + s + s = p \\3x + x + x = 45 \\ 5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]

That's the length of one of its legs

The length of the base = 3x

= 3 x 9

= 45cm

The probability of drawing 3 aces and 2 kings is 9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.

5 cards are drawn from a standard deck of 52 cards.

a) Probability that we draw 3 aces and 2 kings

Number of cards = 52

No of aces = 4

No of kings = 4

Number of cards drawn = 5

So, the probability becomes,

Text, letter

Description automatically generated with medium confidence

[tex]4C_{3}4C_{2}[/tex]/[tex]52C_{5}[/tex]

On simplification,

= 24 / 2598960

= 9.23×[tex]10^{-6}[/tex]

So the probability of drawing 3 aces and 2 kings is 9.23 × [tex]10^{-6}[/tex]

b) a “full house” (3 cards of one kind and 2 cards of another kind)

Since there are 13 sets of each type, we have to select any 2 kinds of it.

The probability becomes  

(2×[tex]13 C_{2}[/tex]×[tex]4C_{3}[/tex][tex]4C_{2}[/tex])/[tex]52C_{5}[/tex]

On simplification,

= 3744 / 2598960

= 0.00144

So, The probability of a “full house” is 0.00144.

Therefore, the probability of drawing 3 aces and 2 kings is  

9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.

The possibility is the department of arithmetic concerning numerical descriptions of ways in all likelihood an event is to arise, or how in all likelihood it's miles that a proposition is authentic. The opportunity of an occasion varies between zero and 1, wherein, more, or less speaks to me, 0 suggests the impossibility of the event and 1 shows reality. The better the probability of an event, the much more likely it's far that the event will arise.

An easy example is the tossing of a fair (unbiased) coin. for the reason that coin is fair, the 2 effects ("heads" and "tails") are each equally probable; the opportunity of "heads" equals the possibility of "tails"; and considering no other outcomes are viable, the opportunity of either "heads" or "tails" is half off (which can additionally be written as 0.5 or 50%).

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Answer: 2.1

Step-by-step explanation:

Calculator

The length of the curve [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex] is 13.

The given curve is defined by the parametric equation [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex].

The length of a curve is given by the formula

⇒  [tex]|| r(t) || = \int\limits^a_b {\sqrt{{(x')^{2}} + (y')^{2} + (z')^{2} } } \, dt[/tex]

where the variables x', y', z' are defined as

[tex]x' = \frac{d(4t)}{dt} = 4 \\y' = \frac{d(8t^{3/2})}{dt} = 12t^{1/2} \\x' = \frac{d(9t^{2})}{dt} = 18t\\[/tex]

Hence, substituting the values in the formula for the length

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{(4)^{2}} + (12t^{1/2})^{2} + (18t)^{2} } } \, dt[/tex]

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]

The given definite integral is in the form of

[tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \int\limits^a_b {\sqrt{{ax^{2} + bx + c}} } \, dx[/tex]

where P(x) is a polynomial of degree 2.

Writing the polynomial P(x) as

⇒ [tex]\sqrt{P(x)} = \sqrt{a}\sqrt{{(x + b_1)^{2} + c_1}} dx[/tex]

⇒ [tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \sqrt{a}\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx[/tex]

where [tex]b_1, c_1[/tex] are defined as

⇒ [tex]b_1= \frac{a}{2b} \\c1 = \frac{c}{a} - b_1^{2}[/tex]

Therefore, the solution will be

⇒ [tex]\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx = \frac{(b_1 + x)\sqrt{P(x)} + c_1log{(b_1 + x + \sqrt{P(x)}}}{2}[/tex]

Hence, solving the integral

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]

we get the value as 13.

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Answer:

-3.5

Step-by-step explanation:

To find the slope of line n, we need to find the slope of line m first. The slope of a line is calculated by dividing the difference in the y-coordinates of two points on the line by the difference in the x-coordinates of the same two points. In this case, we can use the two points (7, 6) and (5, 13) to calculate the slope of line m. The difference in the y-coordinates of these two points is 13 - 6 = 7, and the difference in the x-coordinates is 5 - 7 = -2. Dividing the difference in the y-coordinates by the difference in the x-coordinates yields 7 / -2 = -3.5.

A line is perpendicular to another line if the product of their slopes is -1. Since the slope of line m is -3.5, the slope of line n, which is perpendicular to line m, is -1 / -3.5 = 1/3.5 = <<-1/-3.5=1/3.5>>1/3.5.

Answer:

Slope of a line equation.

Formula for slope of line n is m= rise/run. y2-y1/x2-x1

(7,6) is (x1, y1) and (5,13) is (x2,y2). Simply plug these values in to the equation and solve.

Step-by-step explanation:

(13)-(6) = 7.

(5)-(7) = -2.

7/-2 = - 7/2

- 7/2 = -3.5.

Perpendicular just means that the 1. answer changes sign (pos/neg). This answer is negative, so it becomes a positive. 2. the denominator number switches places with the numerator number. so 7/2 becomes 2/7. Decimal version is 3.5/1 becomes 1/3.5

Final Answer: 1/3.5 or 2/7

For the absolute value function g(x) = |x + 2| + 1, h must be negative and k must be positive.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know the coordination of the vertex of an absolute value function

g(x) = |x - h| + k is, (h, k).

Given, An absolute value function has vertex coordinate (- 2, 1).

Therfore the absolue value function g(x) = |x - (-2)| + 1.

g(x) = |x + 2| + 1, The graph is shifted horizontally left by 2 units and up vertically by 1 unit so h must be negative and k must be positive.

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The formula for the area A of a trapezoid [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex], the formula for the height of the trapezoid is [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] , and the height of the given trapezoid is 6cm.

(a) let us find the formula for the area A of a trapezoid as follows-

As b₁, b₂ being the lengths of the bases and 'h' is the height.

So, the formula for the area A of a trapezoid is given by-

[tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]

(b) Let us solve for the formula for the height h of the trapezoid as follows-

As the formula for the area A of a trapezoid is [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]

So, the formula for height h of the trapezoid can be given by -

[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]

(c) Let us find the new formula to find the height h of the trapezoid as follows-

Using, [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] to find the height h of the trapezoid.

So,

[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]  

[tex]h= \frac{2(72)} {16 +8}[/tex]   --------(substituting the values of b₁ = 16, b₂ = 8, A = 72cm²)

h = 144/24

h = 6 cm

Hence, the height of the trapezoid is 6cm.

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The complete question is -

a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the length of the base, and use h for the height. A=

b. Solve the formula for h. H=

c. Use the new formula to find the height h of the trapezoid. The height of the trapezoid in centimeters.

Answer:

Step-by-step explanation:

y = (-x+1)(x-5)

zeroes

(-x+1)(x-5) = 0

-x + 1 = 0

x = 1

(1,0)

x -5 = 0

x = 5

(5,0)

Vertex

y = (-x+1)(x-5)

y = -x²+5x + x - 5

y = -x² + 6x - 5

x coordinate

-6/-2

3

y coordinate

-(3)² + 6(3) - 5

-9 + 18 - 5

- 14 + 18

4

V(3,4)

not ur dad but try looking in asda might find him

Answer:                                                                                                                                                      

Step-by-step explanation:

Answer:

Step-by-step explanation: To solve this problem, we can use the following formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A is the total amount at the end of the period

P is the principal (initial investment)

r is the annual interest rate

n is the number of times the interest is compounded per year

t is the number of years

We can rearrange this formula to solve for r:

r = n * ((A/P)^(1/n*t) - 1)

We can plug in the values for A, P, and t for each year to solve for the annual interest rate:

Year 1:

r = n * ((4240.00/P)^(1/n*1) - 1)

r = 1 * ((4240.00/P)^(1/1) - 1)

r = (4240.00/P) - 1

r = 4240.00/P - 1

r = 4240.00 - P/P

r = 4240.00 - 1

r = 0.08

Year 2:

r = n * ((4494.40/P)^(1/n*2) - 1)

r = 1 * ((4494.40/P)^(1/2) - 1)

r = (4494.40/P)^(1/2) - 1

r = 4494.40/P - 1

r = 4494.40 - P/P

r = 4494.40 - 1

r = 0.08

Year 3:

r = n * ((4764.06/P)^(1/n*3) - 1)

r = 1 * ((4764.06/P)^(1/3) - 1)

r = (4764.06/P)^(1/3) - 1

r = 4764.06/P - 1

r = 4764.06 - P/P

r = 4764.06 - 1

r = 0.08

Since the annual interest rate is consistent at 0.08 for all three years, we can conclude that this is the annual rate of compound interest earned.

To solve for the principal, we can use the formula for compound interest again, this time solving for P:

P = A / (1 + r/n)^(n*t)

Plugging in the values for A, r, and t for each year, we get:

Year 1:

P = 4240.00 / (1 + 0.08/1)^(1*1)

P = 4240.00 / 1.08

P = 3925.93

Year 2:

P = 4494.40 / (1 + 0.08/1)^(1*2)

P = 4494.40 / 1.16

P = 3925.93

Year 3:

P = 4764.06 / (1 + 0.08/1)^(1*3)

P = 4764.06 / 1.24

P = 3925.93

Since the principal is consistent at $3925.93 for all three years, we can conclude that this is the amount Sima invested.

We can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Two-Hypotheses:  

H0: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is not significantly less than the overall mean waiting time of 13 minutes.

Ha: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

Test Statistic:  t = (11 - 13) / (8/√50) = -2.5  and the Critical Value Approach is: The critical value for a one-tailed test at alpha = 0.05 is 1.645. Since the test statistic (-2.5) is less than the critical value (1.645), we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes, and the   P-Value Approach:  The p-value for the one-tailed test is 0.0062. Since this p-value is less than alpha = 0.05, we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.

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59/40

The numerators don't line up. We require a connecting factor. Therefore, we multiply both denominators next. The next step is to multiply each numerator by the denominator of the other term.

As a result, we multiply 3 by 8 to get 24 and multiply  7 by 5 to get 35 and then 5 by 8 to get 40.

3/5=3*8/5*8 and 7/5= 7*5/8*5

We can add the numerators because our denominators are same.

24 + 35 = 59

As a result, we have the sum, which is

59/40

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Answer:

  replacement is 1/3 the volume of the original

Step-by-step explanation:

You want to compare the volumes of a cone with diameter 6 in and height 2 in to one with a diameter of 2 in and height of 6 in.

The volume of a cone is jointly proportional to the height and the square of the diameter:

  V ∝ d²h

The ratio of the volume of the replacement cone to the original is ...

  r = V2/V1 = ((2 in)²(6 in))/((6 in²)(2 in) = 2/6 = 1/3

The replacement cone has 1/3 the volume of the original.

The simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2, so option A is correct.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given equation:

8y = -2x + 4

Divide both sides by 8,

8y / 8 = -2x / 8 + 4 / 8

Simplify the above expression,

y = -1 / 4x + 1 / 2

Therefore, the simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2.

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Answer: -7[tex]\leq[/tex]x[tex]\leq[/tex]6