A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

Answer:

Angle x= 60°

Step-by-step explanation:

For the triangle HIL, you're going to add 30+90=120

Angles in a triangle add up to 180.

So, therefore,

180-120=60   so angle L must equal 60.

HJ is a straight line and angles in a straight line add up to 180.

180-90=90

Angle JIL is equal to 90.

To find y you add 90+45 which equals 135.

Again, angles in a triangle add up to 180.

180-135=45

So,

y = 45

Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.

To find angle JLK we must add angle L and angle y.

60+45=105

Angles in a straight line add up to 180. So,

180-105=75

75 = Angle JLK

75+45=120

Angles in a triangle add up to 180 so,

180-120= 60

Angle x= 60°

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Answer:9[tex]a^{10}[/tex][tex]b^{-6}[/tex]=[tex]\frac{9a^{10} }{b^6}[/tex]

Step-by-step explanation:

Answer:

9*a^10*(1/(b^6))

Step-by-step explanation:

(-3a^5*b^-3)^2

(-3)^2 * (a^5)^2 * (b^-3)^2

9a^10*b^-6

9*a^10*(1/(b^6))

Answer:

1200 centimeters

Step-by-step explanation:

Hello!

1meter=100centimeters

12meter = ?

[tex]thus \: \frac{12m \times 100cm}{1m} = 1200cm[/tex]

Answer:

1200cm

Step-by-step explanation:

1m=100cm

12m=xcm

by multiplying cris cross

x=12*100

x=1200cm

12m=1200cm

Answer:

0.85

Step-by-step explanation:

1 - 15% = 1 - 0.15 = 0.85

[tex] y = (0.85)^\frac{t}{12} [/tex]

Answer: 0.85

The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.

A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.

Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.

We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.

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Step-by-step explanation:

b + 35° = 180° ( supplementary angle )

b = 180° - 35°

b = 145°

Answer: [tex]\Large\boxed{b=145^\circ}[/tex]

Step-by-step explanation:

Given information

∡1 = 35°

∡b = ?

Total Angle = 180° (Supplementary Angle)

Derived formula from the given information

∡1 + ∡b = Total Angle

Substitute values into the given formula

(35) + b = 180

Subtract 35 on both sides

35 + b - 35 = 180 - 35

[tex]\Large\boxed{b=145^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:(3+3)(1+3) = 24

Step-by-step explanation: There is a 1 and 3 3's. We know that added up, the sum is not 24. So it can't be all addition. But, 3 is a factor of 6 which is a factor of 24. There are 2 3's, so we add them up to get 6. Then, we have a 1 and a 3 left. we add these up to get 4. 6x4= 24.

Based on the random sample of beach lengths taken, the probability of a randomly selected beach having a length of 12 miles is C. 0.

Beach length is considered a continuous variable which takes a numerically positive form because it can have any one of infinite possible values.

As a result, there is no possibility that a beach chosen at random will have a given length of 12 miles which means that the probability is 0.

In conclusion, the probability that a selected beach has a length of 12 miles is 0.

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:

[tex]H_0: \mu = 16[/tex]

At the alternative hypothesis, it is tested if the mean is different, hence:

[tex]H_1: \mu \neq 16[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]

z = -2.1

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.

Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

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well, with the assumption that a year has 365 days, that means one day is really just 1/365th of a year, so then 54 days will be 54/365 of a year.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$17100\\ r=rate\to 9.65\%\to \frac{9.65}{100}\dotfill &0.0965\\ t=years\dotfill &\frac{54}{365} \end{cases} \\\\\\ I = (17100)(0.0965)(\frac{54}{365})\implies \stackrel{\textit{interest owed}}{I\approx 244.13}~\hfill \underset{amount~owed}{\stackrel{17100~~ + ~~244.13}{\approx 17344.13}}[/tex]

Using proportions, it is found that the two cities are 27.5 miles apart.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the given scale, we have that each inch of distance represents 10 miles. Hence the distance in miles for a distance of 2 and 3/4 miles = 2.75 miles is given by:

D = 10 x 2.75 = 27.5 miles.

Hence, the two cities are 27.5 miles apart.

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Answer:

the coordinates of equations

1.4x+y=-7

for x =0

f(0,y)=4(0)+y=-7

y=-7

for y=0

f(x,0)=4x+0=-7

4x=-7

x=-7/4

2.x-y=2

for x=0

f(0,y)=0-y=2

-y=2

y=-2

for y=0

f(x,0)=x-0=2

x=2

graph all of the equations coordinates or you can look the image

so the answers are : {-3,-1}

CMIIW

Part a

The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex]

Part b

The range is the set of y-values, which is [tex](-\infty, -2][/tex]

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

1) The following trigonometric formulae are used to derive the half-angle formulas:

sin² θ / 2 + cos² θ / 2 = 1                      (1)

cos θ = cos² (θ / 2) - sin² (θ / 2)           (2)

First, we derive the formula for the sine of a half angle:

cos θ = 2 · cos² (θ / 2) - 1

cos² (θ / 2) = (1 + cos θ) / 2

cos (θ / 2) = √[(1 + cos θ) / 2]

Second, we derive the formula for the cosine of a half angle:

cos θ = 1 - 2 · sin² (θ / 2)

2 · sin² (θ / 2) = 1 - cos θ

sin² (θ / 2) = (1 - cos θ) / 2

sin (θ / 2) = √[(1 - cos θ) / 2]

Third, we derive the formula for the tangent of a half angle:

tan (θ / 2) = sin (θ / 2) / cos (θ / 2)

tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]

2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:

(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).

3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:

r = √(2² + 3²)

r = √13

θ = atan(3 / 2)

θ ≈ 56.309°

The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).

Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:

(x, y) = (4 · cos 30°, 4 · sin 30°)

(x, y) = (2√3, 2)

The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).

4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ

r · sin θ = 5 · r · cos θ - 8

r · sin θ - 5 · r · cos θ = - 8

r · (sin θ - 5 · cos θ) = - 8

r = - 8 / (sin θ - 5 · cos θ)

The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

To prove two lines parallel, we need to check if the two angles involving the lines acts as some angle pair with defininte property.

In the given figure,

( by Alternate Exterior angle pair )

Hence, the two lines are parallel.

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

1. x = 20

2. x = 3

3. RST = 22 degrees

Step-by-step explanation:

1. Since QR bisects PQS, the measure of the angles PQR and PQS should be equal, so we can set their expressions equal to each other, and then solve.

4x-10 = -3x+130

4x = -3x +140

7x = 140

x = 20

2. Since there is a CAB has a right angle, the measure of angles CAD and BAD should add up to 90 degrees. So we can set the sum of their expressions equal to 90 degrees.

(5x+57) + (x+15) = 90

6x + 72 = 90

6x = 18

x = 3

3. I can't see where the R is but if it is on the empty line then we can find RST by subtracting the measure of angle TSU from angle RSU.

TSU - RSU = RST

91 - 69 = 22 degrees

RST = 22 degrees

Answer:

7.  m∠PQR =70°   m∠PQS = 140°

8.  m∠CAD = 18°    m∠BAD = 72°

9.  m∠RST = 22°

Step-by-step explanation:

Question 7

If QR bisects (divides into two equal parts) ∠PQS then:

⇒ m∠PQR = m∠RQS

⇒ 4x - 10 = -3x + 130

⇒ 4x - 10 + 10 = -3x + 130 + 10

⇒ 4x = -3x + 140

⇒ 4x + 3x = -3x + 140 + 3x

⇒ 7x = 140

⇒ 7x ÷ 7 = 140 ÷ 7

⇒ x = 20

Substitute the found value of x into the expression for m∠PQR:

⇒ m∠PQR = 4(20) - 10 = 70°

As QR bisects ∠PQS:

⇒ m∠PQS = 2m∠PQR = 2 × 70° = 140°

Question 8

From inspection of the given diagram, ∠BAC = 90°.

⇒ m∠CAD + m∠BAD = 90

⇒ x + 15 + 5x + 57 = 90

⇒ 6x + 72 = 90

⇒ 6x + 72 - 72 = 90 - 72

⇒ 6x = 18

⇒ 6x ÷6 = 18 ÷ 6

⇒ x = 3

Substitute the found value of x into the expressions for the two angles:

⇒ m∠CAD = 3 + 15 = 18°

⇒ m∠BAD = 5(3) + 57 = 72°

Question 9

From inspection of the given diagram (and assuming R is on the empty line segment):

   m∠RSU = m∠RST + m∠TSU

⇒ 91° = m∠RST + 69°

⇒ 91° - 69° = m∠RST + 69° - 69°

⇒ 22° = m∠RST

⇒ m∠RST = 22°

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Answer
5/9 is the dividend

Step-by-step explanation:

Answer:

line NM

Step-by-step explanation:

Since planes extend infinitely in all directions, planes intersect at a line, not at a line segment.

a.

Solution Given:

Slope of the line passing through the point is

m= [tex] \frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{-2-2}=\frac{8}{-4}=-2[/tex]

slope=-2

b.

Solution given:

equation is

2x-5y=-10

2x+10=5y

y=2x/5 +10/5

y=2/5 x +3

comparing above equation with y=mx+c

we get

m=2/5

slope=2/5

c.

Slope of the line passing through the point is

m=[tex] \frac{y_2-y_1}{x_2-x_1}[/tex]

-4=[tex] \frac{1-(-9)}{0-x}[/tex]

-4=10/-x

doing criss cross multiplication

-4*-x=10

4x=10

x=10/4

x=5/2

slope=5/2

d.

we have

equation of line passing through the one point is

[tex] y-y_1=m(x-x_1)[/tex]

y-5=-7(x-(-1))

y=-7(x+1)+5

y=-7x-7+5

y=-7x-2 is a required equation:

Answer:

BC 1

AC 2

AABC 3

Step-by-step explanation:

BC=16

AC = 15

AABC= 15

Answer: C, B, A

Step-by-step explanation: It just is

The table that represents exponential growth is the second table.

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Answer: B

Step-by-step explanation:

The positive square roots of the number 151,321 according to the task content can be determined by means of division as; 389.

It follows from.the task content above that the number given is; 151,321 whose positive square roots is to be determined.

Upon testing different integers as divisor on the number 151,321; it is concluded that the only positive integer by which 151,321 can be divided to result in a whole is; 389.

Hence, the positive square root of the number 151,321 is; 389.

Consequently, it can be concluded that the positive square root of the number, 151,321 as in the task content is; 389 which is itself a prime number as it is only divisible by 1 and itself.

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Answer + Step-by-step explanation:

the probability that a child will not fall on any given day :

= (63 × 64 + 27 × 88) ÷ 100

= 64.08 %

the probability that a child will fall in dry weather :

= (27 × 12) ÷ 100

= 3.24 %

In mathematical notation, the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.

In mathematical notation, we can represent the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.

For example:

-21 is the integer immediately smaller than -20, so it is included in the set.

-22 is the next integer, smaller than -20, so it is also included in the set.

And this pattern continues indefinitely, encompassing all the integers less than -20.

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So, K and L are located at K = -11 or L = -27 or K = -27 or L = -11

Givent that Point J is located at -19. Points K and L are each 8 units away from Point J. This implies that the modulus of K - J or modulus of L - J = 18.

So, |K - J| = 8

⇒ K - J = 8 or -(K - J) = 8

Substituting the value of J = -19 into the equation, we have

⇒ K - J = 8 or -(K - J) = 8

⇒ K - (-19) = 8 or -(K - (-19)) = 8

⇒ K + 19 = 8 or (K - (-19)) = -8

⇒ K + 19 = 8 or K + 19 = -8

⇒ K = 8 - 19 or K = -8 - 19

⇒ K = - 11 or K = -27

Also, |L - J| = 8

⇒ L - J = 8 or -(L - J) = 8

Substituting the value of J = -19 into the equation, we have

⇒ L - J = 8 or -(L - J) = 8

⇒ L - (-19) = 8 or -(L - (-19)) = 8

⇒ L + 19 = 8 or (L - (-19)) = -8

⇒ L + 19 = 8 or L + 19 = -8

⇒ L = 8 - 19 or L = -8 - 19

⇒ L = - 11 or L = -27

So, K and L are located at K = -11 or L = -27 or K = -27 or L = -11

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The number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

Ratio of flour to loaves of bread = 3 cups : 2 loaves

Number of loaves of bread can the baker make with a 10 lb-bag of flour

3 : 2 = 30 : x

3/2 = 30/x

3 × x = 2 × 30

3x = 60

x = 60/3

x = 20 loaves of bread

Therefore, the number of loaves of bread can the baker make with a 10 lb-bag of flour is 20 loaves of bread.

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a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get

[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]

Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.

[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]

[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that

[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]

Then dividing both sides by [tex]x[/tex] gives

[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]

b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then

[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]

[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]

Taking the first few terms from the infinite series, we can approximate

[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]

[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]

which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].

Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]

and

[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]

which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :

[tex]\dfrac89 \approx 0.8889[/tex]

[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]

[tex]\dfrac99 = 1[/tex]

Answer:

A, C

Step-by-step explanation:

See attached image.

Solving the given logarithmic equation, it is found that the horn is 100 times more intense compared to the weakest sound heard to the human ear.

The equation is given by:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

In which:

In this problem, we have that d = 20, and we have to solve the logarithmic equation for p to find how many times more intense the sound is:

[tex]d = 10\log{\frac{p}{p_0}}[/tex]

[tex]20 = 10\log{\frac{p}{p_0}}[/tex]

[tex]\log{\frac{p}{p_0}} = 2[/tex]

The logarithm is inverse of the function [tex]10^x[/tex], hence we apply the function to both sides to find the ratio.

[tex]\frac{p}{p_0} = 10^2[/tex]

[tex]\frac{p}{p_0} = 100[/tex]

Hence, the horn is 100 times more intense compared to the weakest sound heard to the human ear.

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Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105