A tap leaks at the rate of 2cm³ per second.How long will it take the tap to fill a container of 45litres capacity.

​

Answer:

Yes

Step-by-step explanation:

The sine rule works on all triangles (not just right-angled triangles) where a side and it's opposit angles are known.

Answer:

We conclude that the population mean is greater than 10.

Step-by-step explanation:

The complete question is: A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3. Using the 0.05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis [tex]H_0= \mu \leq 10[/tex] and [tex]H_A=\mu >10[/tex].

We are given that a random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation was 3.

Let [tex]\mu[/tex] = population mean

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq 10[/tex]    {means that the population mean is less than or equal to 10}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 10    {means that the population mean is greater than 10}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

                             T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 12

             s = sample standard deviation = 3  

            n = sample of observations = 10

So, the test statistics =  [tex]\frac{12-10}{\frac{3}{\sqrt{10} } }[/tex]  ~  [tex]t_9[/tex]

                                    =  2.108  

The value of t-test statistics is 2.108.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is more than the critical value of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean is greater than 10.

Complete question:

The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at

Answer:

27,800

Step-by-step explanation:

We need to obtain the initial population(P0) and constant value (k)

Population function : p(t) = P0e^kt

At t = 0, population = 19,000

19,000 = P0e^(k*0)

19,000 = P0 * e^0

19000 = P0 * 1

19000 = P0

Hence, initial population = 19,000

At t = 3; population = 23,000

23,000 = 19000e^(k*3)

23000 = 19000 * e^3k

e^3k = 23000/ 19000

e^3k = 1.2105263

Take the ln

3k = ln(1.2105263)

k = 0.1910552 / 3

k = 0.0636850

At t = 6

p(t) = P0e^kt

p(6) = 19000 * e^(0.0636850 * 6)

P(6) = 19000 * e^0.3821104

P(6) = 19000 * 1.4653739

P(6) = 27842.104

27,800 ( nearest whole number)

Answer:

Below.

Step-by-step explanation:

(sine) [tex]sin=30=1/2[/tex]

[tex]=cos [90-30][/tex]

Which means cos=60

Same as:

(cosine) [tex]cos=60=1/2[/tex] or [tex]Sin30=Cos 60=1/2[/tex]

Hence, the answer is...

cos 60° = ½....

By:✨ RobloxYt ✨

The value of the trigonometric ratio cos60 is  1 / 2.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the value of sin 30° is 1 over 2. The value of cos(90-30) will be calculated as:-

sin(30) = cos(90-30) = cos60
sin(30) = cos(90-30) = 1 / 2

Hence, the value of the cos60 is 1 / 2.

To know more about Trigonometry follow

https://brainly.com/question/24349828

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Answer: x = ⅓ or 5

Step-by-step explanation:

From the quadratic equation, we are asked to find the root of the equation. Therefore, we may use any of the methods.

Here I am using grouping method.

3x² - 16x + 15 = 0

3x² - 15x -x + 15 = 0, we now factorize

3x( x - 5 ) - ( x - 5 ) = 0, we now collect like terms.

( 3x - 1 )( x - 5 ) = 0

Now to find x, we equate each in brackets to zero and then solve.

3x - 1 = 0

x = ⅓ , and if

x - 5 = 0

x = 5, .

Now , the solution of the equation will be

x = ⅓ or 5

Answer:

x = 9.0

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 39 = 7/x

x cos 39 = 7

x = 7/cos 39

x =9.007316961

x = 9.0

Looks like the equation is

[tex]x^7y+y^7x=7[/tex]

Differentiate both sides with respect to [tex]x[/tex], taking [tex]y[/tex] to be a function of [tex]x[/tex].

[tex]\dfrac{\mathrm d[x^7y+y^7x]}{\mathrm dx}=\dfrac{\mathrm d[7]}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm d[x^7]}{\mathrm dx}y+x^7\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\mathrm d[y^7]}{\mathrm dx}x+y^7\dfrac{\mathrm dx}{\mathrm dx}=0[/tex]

[tex]7x^6y+x^7\dfrac{\mathrm dy}{\mathrm dx}+7y^6x\dfrac{\mathrm dy}{\mathrm dx}+y^7=0[/tex]

Solve for [tex]\frac{\mathrm dy}{\mathrm dx}[/tex]:

[tex](x^7+7y^6)\dfrac{\mathrm dy}{\mathrm dx}=-(7x^6y+y^7)[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{7x^6y+y^7}{x^7+7y^6}[/tex]

Answer:

The piecewise function would be as follows :

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Step-by-step explanation:

This piecewise function is composed of one segment, and a ray. Let's start by identifying the properties of this segment.

Segment : As you can see the segment extends from 0 to 2 on the x - axis. This is at y = 25. Therefore our first expression would be 'C(g) = 25 at {0 < g < 2}.'

Ray : As this is ray, we have C(g) = 10g, as the slope is apparently 10. As you can see the rise is 10, over a run of 1, given the points (2, 25) and (3, 35) lie on the plane. The ray starts at the coordinate (2, 25), leaving us with the inequality g > 2.

So now that we have the expressions 'C(g) = 25 at {0 < g < 2}' and 'C(g) = 10g at {g > 2}' we can combine them to create the following piecewise function,

[tex]\mathrm{C(g) = \left \{ {{25\:if\: 0 < g < 2} \atop {10g\:if\:g>2}} \right. }[/tex]

Answer:

Answer: {4,5}. 13) ∪ . Put the sets together in one large set. {1,2,3,5} ... {2,3,1,5}. There are no duplicates to remove, but I can write this in a nicer order.

Step-by-step explanation:

Answer: y = 4

Step-by-step explanation: If y = x + 2, then the value of y will correspond

to the values that are located in the x-column.

In other words, for the first column, we know that 2 = x.

So if y = x + 2, then y = 2 + 2 or y = 4.

Answer:

4

Step-by-step explanation:

When you convert 160 inches to meters you get 4 meters

Answer:

4.064 Meters

Step-by-step explanation:

Answer:

THE ANSWER IS :

-(1/10)

Answer:

1. There are a total of 19 marbles in the bag. The probability of picking a green marble out of them is 4/19 since there are only 4 green ones. The probability of picking a brown marble after replacing what has been initially picked is 1/19. The final probability is the product of the two probabilities and that is 4/361.

2. ?

3. 60%

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.

Therefore,

∠ABO + ∠BOP = 180° (by interior angle Postulate)

118° + ∠BOP = 180°

∠BOP = 180° - 118°

∠BOP = 62°.... (1)

Since, ∠BOP + ∠POD = ∠BOD

Therefore, 62° + ∠POD = 152°

∠POD = 152° - 62°

∠POD = 90°.....(2)

∠POD + ∠ODC = 180° (by interior angle Postulate)

90° + ∠ODC = 180°

∠ODC = 180° - 90°

[tex] \huge\red {\boxed {m\angle ODC = 90°}} [/tex]

Answer:

[tex] d = \sqrt{113} = 10.63014 [/tex]

Step-by-step explanation:

Distance between the endpoints of the graph, (-3, 3) and (5, -4), can be calculated using distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex].

Where,

[tex] (-3, 3) = (x_1, y_1) [/tex]

[tex] (5, -4) = (x_2, y_2) [/tex]

Thus,

[tex] d = \sqrt{(5 - (-3))^2 + (-4 - 3)^2} [/tex]

[tex] d = \sqrt{(8)^2 + (-7)^2} [/tex]

[tex] d = \sqrt{64 + 49} = \sqrt{113} [/tex]

[tex] d = \sqrt{113} = 10.63014 [/tex]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

  [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

b

[tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

c

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]\mu = 64 \ inches[/tex]

    The standard deviation is  [tex]\sigma = 2 \ inches[/tex]

The probability that a randomly selected woman is taller than 66 inches   is mathematically represented as

    [tex]P(X > 66) = P(\frac{X - \mu }{\sigma } > \frac{ 66 - \mu }{\sigma} )[/tex]

Generally [tex]\frac{ X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So  

      [tex]P(X > 66) = P(Z> \frac{ 66 - 64 }{ 2} )[/tex]

     [tex]P(X > 66) = P(Z> 1 )[/tex]

From the z-table  the value of  [tex]P(Z > 1 ) = 0.15866[/tex]

 So  

       [tex]P(X > 66) = P(Z> 1 ) = 0.15866[/tex]

Considering b

 sample mean is  n  =  4  

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = \frac{2 }{\sqrt{4} }[/tex]

=>    [tex]\sigma _{\= x} = 1[/tex]

The probability that the sample mean height is greater than 66 inches    

     [tex]P(\= X > 66) = P(\frac{X - \mu }{\sigma_{\= x } } > \frac{ 66 - \mu }{\sigma_{\= x }} )[/tex]

=>   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{1} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 2 )[/tex]

From the z-table  the value of  [tex]P(Z > 2 ) = 0.02275[/tex]

=> [tex]P(\= X > 66) = P(Z> 2 ) = 0.02275[/tex]

Considering b

 sample mean is  n  =  100

Generally the standard error of mean is mathematically represented as

        [tex]\sigma _{\= x} = \frac{2 }{\sqrt{100} }[/tex]

=>    [tex]\sigma _{\= x} = 0.2[/tex]

The probability that the sample mean height is greater than 66 inches

   [tex]P(\= X > 66) = P(Z > \frac{ 66 - 64 }{0.2} )[/tex]

=>  [tex]P(\= X > 66) = P(Z> 10 )[/tex]

From the z-table  the value of  [tex]P(Z > 10 ) = 0[/tex]

[tex]P(\= X > 66) = P(Z> 10 ) = 0[/tex]

Answer:

Angle of elevation from Kim to the satellite launch = 6.654°

Step-by-step explanation:

The distance from Kim to the satellite launch

= 6 miles

Height of the satellite launch

= 0.7 miles

Angle of elevation from Kim to the satellite launch = b

Tan b = height of satellite/distance from Kim

Tan b= 0.7/6

Tan b= 0.1166667

b = tan^-1 (0.1166667)

b= 6.654°

Angle of elevation from Kim to the satellite launch = 6.654°

Answer:  -2

Step-by-step explanation:

We know that the slope of a secant line over a interval [a,b] is given by :-

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

Given f(x) =[tex]-2x^2 + 4[/tex]

Then, the slope of the secant line over the interval [-1, 2] is given by :-

[tex]m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1[/tex]

Hence, the slope of the secant line over the interval [-1, 2] is -2.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{29 \: mm}}}}}[/tex]

Step-by-step explanation:

Let the width of a rectangle be 'w'

Length of a rectangle be 4w - 5

Perimeter of a rectangle = 75 mm

First, finding the width of the rectangle ( w )

[tex] \boxed{ \sf{perimeter \: of \: a \: rectangle = 2(length + width)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(4w - 5 + w)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 2(5w - 5)}}[/tex]

[tex] \dashrightarrow{ \sf{75 = 10w - 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w - 10 = 75}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 75 + 10}}[/tex]

[tex] \dashrightarrow{ \sf{10w = 85}}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{10w}{10} = \frac{85}{10} }}[/tex]

[tex] \dashrightarrow{ \sf{w = 8 .5 \: mm}}[/tex]

Replacing / substituting the value of width of a rectangle in order to find the length of a rectangle

[tex] \sf{length \: of \: a \: rectangle = 4w - 5}[/tex]

[tex] \dashrightarrow{ \sf{4 \times 8.5 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{34 - 5}}[/tex]

[tex] \dashrightarrow{ \sf{29 \: mm}}[/tex]

Length of a rectangle = 29 mm

Hope I helped!

Best regards! :D

Answer:

[tex]-4.2=q[/tex]

Step-by-step explanation:

To do this you would just add 4.8 to both sides to get rid of the -4.8 so then the equation would look like [tex]-4.2=q[/tex] and that would be our answer.

Answer:

q=-4.2

Step-by-step explanation:

-9 = q - 4.8

Add 4.8 to each side

-9+4.8 = q - 4.8+4.8

-4.2 = q

q=-4.2

Answer:

C

Step-by-step explanation:

We know that A is not true because the angle is formed by rays, not line segments. We know this because the ends of the lines are arrowheads, which indicates that they are rays. You might be saying that A is true because BA and BC form the angle but actually, even if you removed points A and C, you would still have the angle. B is not correct because according to the diagram, the vertex is point B, not point A. The vertex of an angle is the common endpoint of the two rays that form the angle, therefore it would be point B. D is not correct because angles can have multiple names, the letters do not have to be in alphabetical order. Therefore, C is correct.

Answer:

62.32%

Step-by-step explanation:

172/276 * 100%

= 62.32%

Answer:

x^2+y

Step-by-step explanation:

simply because you have x squared and a variable y that needs to be added.

Answer:

y = -45

Step-by-step explanation:

Y/9 + 5 = 0

y/9 = -5

y = -45

Answer:

standard form means that the terms are ordered from biggest exponent to

lowest exponent. The leading coefficient is the coefficient of the first term in a

polynomial in standard form . For example, 3x^4 + x^3 - 2x^2 + 7x.

Answer:

512

Step-by-step explanation:

In a geometric sequence, the ratio between the second term and the first term is equal to the ratio between the third term and the second term.

(m² + 4) / m = 16m / (m² + 4)

Solve:

(m² + 4)² = 16m²

m² + 4 = 4m

m² − 4m + 4 = 0

(m − 2)² = 0

m = 2

The first three terms of the geometric sequence are therefore 2, 8, 32.

The common ratio is 4, and the first term is 2.  So the 5th term is:

a = 2 (4)⁵⁻¹

a = 512

Answer:

2 - [tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the addition formula for tangent

tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values

tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then

tan15° = tan(60 - 45)°

tan(60 - 45)°

= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]

= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]

Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.

The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]

= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL

= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]

= [tex]\frac{-4+2\sqrt{3} }{-2}[/tex]

= [tex]\frac{-4}{-2}[/tex] + [tex]\frac{2\sqrt{3} }{-2}[/tex]

= 2 - [tex]\sqrt{3}[/tex]

Answer:

x = 16.08

Step-by-step explanation:

x - 8.9 = 7.18

Add 8.9 to each side

x - 8.9+8.9 = 7.18+8.9

x = 16.08

Answer:

[tex]\huge \boxed{8t + 56}[/tex]

Step-by-step explanation:

[tex]8(7 + t)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]8(7) + 8(t)[/tex]

[tex]56 + 8t[/tex]