Solve for x and find the measure of

Answer:

1). sin 30°=5/x

1/2=5/x

x=10

2)sin 30°=y/18

1/2=y/18

y=9°

cos 30°=x/18

√3/2=x/18

x=9√3

3) option D is correct

because cosine ratio is base / hypotenuse.

4) option c is correct.

x=1 or x= 12

Step-by-step explanation:

x²-13x+12=0

x²-12x-x+12=0

x(x-12)-1(x-12)=0

(x-1)(x-12)=0

x-1=0 or x-12=0

x=1 or x=12

Answer:

The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.

Step-by-step explanation:

The statement is incomplete: The size of a cylinder changes with time. If r increases at the rate of 2 cm/min and h decreases at the rate of 7 cm/min. ¿At what rate is the volume changing at the instant when r = 1 cm and h = 7 cm?

The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is expressed by the following formula:

[tex]V = \frac{\pi}{4}\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, measured in centimeters.

[tex]h[/tex] - Height, measured in centimeters.

The rate of change of the volume ([tex]\frac{dV}{dt}[/tex]), measured in cubic centimeters is obtained by deriving (1) in time:

[tex]\frac{dV}{dt} = \frac{\pi}{2} \cdot r\cdot h\cdot \frac{dr}{dt} + \frac{\pi}{4}\cdot r^{2}\cdot \frac{dh}{dt}[/tex] (2)

Where:

[tex]\frac{dr}{dt}[/tex] - Rate of change of the radius, measured in centimeters per minute.

[tex]\frac{dh}{dt}[/tex] - Rate of change of the height, measured in centimeters per minute.

If we know that [tex]r = 1\,cm[/tex], [tex]h = 7\,cm[/tex], [tex]\frac{dr}{dt} = 2\,\frac{cm}{min}[/tex] and [tex]\frac{dh}{dt} = -7\,\frac{cm}{min}[/tex], then the rate of change of the volume is:

[tex]\frac{dV}{dt} = \frac{\pi}{2}\cdot (1\,cm)\cdot (7\,cm)\cdot \left(2\,\frac{cm}{min} \right) + \frac{\pi}{4}\cdot (1\,cm)^{2}\cdot \left(-7\,\frac{cm}{min} \right)[/tex]

[tex]\frac{dV}{dt} \approx 16.493\,\frac{cm^{3}}{min}[/tex]

The volume of the cylinder with time is increasing approximately at a rate of 16.493 cubic centimeters per minute.

Answer:

[tex]\approx 13^\circ[/tex]

Step-by-step explanation:

Given two lines with the equations:

[tex]9x - y = 4\\ 8x + y = 6[/tex]

First of all, let us learn the formula for finding the angle between the two lines with given equations:

[tex]tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]

[tex]m_1, m_2[/tex] are the slopes of the two lines respectively.

Let us convert the given equation to point intercept form.

Point intercept form of a line is given as:

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

[tex]y = 9x-4\\y =-8x+6[/tex]

Comparing with slope intercept form, we get:

[tex]m_1 = 9\\m_2 = -8[/tex]

Using the above formula:

[tex]tan\theta =\dfrac{9 -(-8)}{1+9(-8)}\\\Rightarrow tan\theta = -\dfrac{17}{71}\\\Rightarrow \theta = -13.46^\circ\\[/tex]

Therefore, the acute angle between the two lines is [tex]\approx 13^\circ[/tex]

The acute angles between the equations is 13.46 degree.

To find the acute angles between the two equation, let's write out the individual slope of each equation.

Given Data

The given equations can be rearranged into equation of line.

[tex]9x-y=4\\ y=9x-4\\ slope=m_1=9[/tex]

The second equation can also be rearranged as and solving for the slope

[tex]8x+y=6\\ y=6-8x\\ y=-8x+6\\ slope = m_2 = -8[/tex]

Since we have the slopes of the two equation, we can now find the acute angle between them.

θ = [tex]tan^-^1[\frac{m_1-m_2}{1+m_1m_2}]\\ [/tex]

substituting the values and solving for the angle

[tex]x = tan^-^1[\frac{9-(-8)}{1+(9*-8)}]\\ x = tan^-^1[17/-71]\\ x=-13.46 = 13.46^0[/tex]

The acute angle between the equations is 13.46 degree

Learn more about acute angle in equations here;

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Answer:

I'm not sure I understand this. elaborate a bit more and I can help tho :)

Answer:

x[tex]\geq[/tex]2

Step-by-step explanation:

You add 2 to both sides. Then you divide everything by 6. Hope this helps!

Answer:

RS and PT

Step-by-step explanation:

Judging by looks, RS and PT are going the exact same direction, and look like they don't touch. Also, if RSTP is a square, then those two are definitely parallel.

Total area of shaded region in trapezoid is 54.4in²

A trapezoid is a four-sided, quadrilateral shape with two parallel sides, which are called the bases, and two non-parallel sides, which are called the legs.

here, we have,

The formula for the area of a trapezoid is:

Area = (1/2) × (sum of the bases) × (height)

The Shaded region in trapezoid form right angled triangle.

Area of 1st shaded region=area of right triangle

=1/2×b×h

=1/2×6.8×7.4

=25.16in²

Area of 2nd shaded region=area of right triangle

=1/2×b×h

=1/2×6.8×8.6

=29.24in²

Hence, total area of shaded region in trapezoid is 54.4in²

To know more about trapezoid, visit:

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Answer:

0.2364

Step-by-step explanation:

We will take

Lyme = L

HGE = H

P(L) = 16% = 0.16

P(H) = 10% = 0.10

P(L ∩ H) = 0.10 x p(L U H)

Using the addition theorem

P(L U H) = p(L) + P(H) - P(L ∩ H)

P(L U H) = 0.16 + 0.10 - 0.10 * p(L u H)

P(L U H) = 0.26 - 0.10p(L u H)

We collect like terms

P(L U H) + 0.10P(L U H) = 0.26

This can be rewritten as:

P(L U H)[1 +0.1] = 0.26

Then we have,

1.1p(L U H) = 0.26

We divide through by 1.1

P(L U H) = 0.26/1.1

= 0.2364

Therefore

P(L ∩ H) = 0.10 x 0.2364

The probability of tick also carrying lyme disease

P(L|H) = p(L ∩ H)/P(H)

= 0.1x0.2364/0.1

= 0.2364

Answer:

A Parallelogram.

Step-by-step explanation:

Hope this helps! :)

Answer:

the answer is 5,087 or 5,086.8

Answer:

5086.8

Step-by-step explanation:

Answer:

the exponent is 10 ^ 3 and the word form is ten times ten times ten

Step-by-step explanation:

if you need more help just ask

Answer:

7.0m

Step-by-step explanation:

=2h ×2w

=2(1.5m)+2(2.0m)

=7.0m

Answer:

We are given that The valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch.

We are also given that the valve was designed to produce a mean pressure of 7.6 lbs/square inch

So,  

Null hypothesis:  

Alternate hypothesis :  

Since n > 30 and population standard deviation is given

So, We will use z test

Formula :  

Substitute the values

refer the z table for p value

so, p value is 0.9927

Since it is a two tailed test So, p = 2(1-  0.9927) = 0.0146

α = 0.1

p value< α

So, we reject null hypothesis

Hence There is  sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Step-by-step explanation:

No, there is insufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Step-by-step explanation:

We are given that an engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 7.5 pounds/square inch (psi). Assume the population variance is 0.36 and the valve was designed to produce a mean pressure of 7.4 psi.

We have to test if there sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Let, NULL HYPOTHESIS, H_0H

0

: \muμ = 7.4 psi {means that the valve perform to the specifications}

ALTERNATE HYPOTHESIS, H_1H

1

: \mu\neqμ



= 7.4 psi {means that the valve does not perform to the specifications}

The test statistics that will be used here is One-sample z-test;

T.S. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }

n

σ

X

ˉ

−μ

~ N(0,1)

where, \bar X

X

ˉ

= sample mean pressure = 7.5 psi

\sigmaσ = population standard deviation = \sqrt{Variance}

Variance

= \sqrt{0.36}

0.36

= 0.6

n = sample of engines = 170

So, test statistics = \frac{7.5-7.4}{\frac{0.6}{\sqrt{170} } }

170

0.6

7.5−7.4

= 2.173

Now, at 0.02 significance level z table gives critical value of 2.3263. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the valve perform to the specifications and there is not sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Answer:

10 1/2

Step-by-step explanation:

Answer:

21+4

Step-by-step explanation:

3 times 7=21

3 times4=12

21d+4e

Answer:

21d+12e

Step-by-step explanation:

I'm pretty sure thats it if its expanding.

Answer:

The answer is 59

Step-by-step explanation:

5(8+2)+3(6-3)

5*8=40

5*2=10

3*6=18

3*-3=-9

(40+10)+(18-9)

50+9=59

Answer:

8/12 + 3/12

Step-by-step explanation: multiply 2 and 3 by 4 to add these two fractions correctly.

The answer would be -3 4/3

Step-by-step explanation:

ok ok ok ok I'm very sorry if i get it wrong at least I tried on this app most of the people don't even do the homework they do it to cheat.

Answer:

Dan and Paul share some money in the ratio 13:5.

Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.

How much did Paul originally have

Answer:

pq = st and qu = tr

the last option

The area of the triangle is 126 square units. Then the correct option is D.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The height of the triangle will be 12 units and the base of the triangle will be 21 units. Then the area of the triangle is calculated as,

A = 1/2 x 21 x 12

A = 21 x 6

A = 126 square units

Thus, the correct option is D.

More about the area of the triangle link is given below.

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Answer:

3937.01 Inch are in 100 meter

Answer:

The area of the yard is 4.34.

Step-by-step explanation:

a = l x w

a = 3.1 x 1.4

a = 4.34

Answer:

26 if we not adding then -12

Step-by-step explanation:

Answer:

701 cm

Step-by-step explanation:

cm =m * 100.0000

cm =7.1 * 100.0000

cm =710.0000

Using the function definition, it is found that the correct option is:

C. No, because a vertical line can be drawn that intersects the graph more than once.

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

A similar problem is given at https://brainly.com/question/12463448

Answer:

Option B

Step-by-step explanation:

log x=2

x = 10^2

Therefore, the exponential form is the one in option B

Answer:

B

Step-by-step explanation:

Convert to Exponential Form log of x=-2. log(x)=−2 log ( x ) = - 2. For logarithmic equations, logb(x)=y log b ( x ) = y is equivalent to by=x b y = x such that x>0 x

Answer:

y = -3/4x - 4

Step-by-step explanation:

-8y -6x = 32

-8y = 32 + 6x -- isolate the y variable.

(-1) -8y = 32 + 6x (-1) -- the y has to be a positive number so multiply every single number by -1

8y/8 = -32/8 - 6x/8 -- divide both sides by 8

y = - 4 - 6/8x

y = -3/4x -4 - simplify the fraction and that is your answer