if the sin 30 = 1/2, then which statement is true?

Answer:

  x = (5 +5d)/(a -3c)

Step-by-step explanation:

Maybe you're to solve for x.

__

This is a typical "3-step" linear equation.

First, you collect terms with the variable x on one side of the equation. You do that by subtracting from both sides the x-term you don't want where it is.

We choose to remove the 3cx term from the right side, so we subtract it from both sides.

  ax -3cx -5d = 3cx -3cx +5 . . . . . . we have combined the constants, too

  x(a -3c) -5d = 5 . . . . . . simplify and factor out x

Second, you remove any terms not containing x from the side of the equation with the x-terms. You do that by adding their opposite to both sides of the equation.

We need to remove the -5d term, so we add 5d to both sides.

  x(a -3c) -5d +5d = 5 +5d

  x(a -3c) = 5 +5d . . . . . . . . . . simplify

Third, we divide by the coefficient of x. We do that to both sides of the equation. We had to put parentheses around the terms on the right, because we're dividing the whole right side of the equation by (a-3c).

  x(a -3c)/(a -3c) = (5 +5d)/(a -3c)

  x = (5 +5d)/(a -3c)

Answer:

[tex]Mean = 53.25[/tex]

Step-by-step explanation:

Given

Low Temperature : 40−44 || 45−49 ||  50−54 || 55−59 || 60−64

Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7

Required

Determine the mean

The first step is to determine the midpoints of the given temperatures

40 - 44:

[tex]Midpoint = \frac{40+44}{2}[/tex]

[tex]Midpoint = \frac{84}{2}[/tex]

[tex]Midpoint = 42[/tex]

45 - 49

[tex]Midpoint = \frac{45+49}{2}[/tex]

[tex]Midpoint = \frac{94}{2}[/tex]

[tex]Midpoint = 47[/tex]

50 - 54:

[tex]Midpoint = \frac{50+54}{2}[/tex]

[tex]Midpoint = \frac{104}{2}[/tex]

[tex]Midpoint = 52[/tex]

55- 59

[tex]Midpoint = \frac{55+59}{2}[/tex]

[tex]Midpoint = \frac{114}{2}[/tex]

[tex]Midpoint = 57[/tex]

60 - 64:

[tex]Midpoint = \frac{60+64}{2}[/tex]

[tex]Midpoint = \frac{124}{2}[/tex]

[tex]Midpoint = 62[/tex]

So, the new frequency table is as thus:

Low Temperature : 42 || 47 ||  52 || 57 || 62

Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7

Next, is to calculate mean by

[tex]Mean = \frac{\sum fx}{\sum x}[/tex]

[tex]Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}[/tex]

[tex]Mean = \frac{1065}{20}[/tex]

[tex]Mean = 53.25[/tex]

The computed mean is greater than the actual mean

Answer:

y=135

x=45

Step-by-step explanation:

x= 45

It is an isosceles so

180-90=90

90/2= 45  

y=135

angles on a straight line add up to 180 so

180-45=135

Hope this helps!

Answer:

Stocks = $15,500

Bonds = $107,250

CD's = $47,250

Step-by-step explanation:

S + B + C = 170000

.0325S + .038B .067C = 7745

60,000 + C = b

S = $15,500

B = $107,250

C = $47,250

Answer:

x = 1/e^-5 - 1

Step-by-step explanation:

–2 ln (x + 1) − 3 = 7

–2 ln (x + 1) = 10

ln (x + 1) = –5

x + 1 = e^-5

x = e^-5 - 1

x = 1/e^-5 - 1

the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:

1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.

2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.

3. Simplify: -2 ln(x + 1) = 10.

4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.

5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.

6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.

7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.

8. Simplify: x ≈ -0.9933.

Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.

Learn more about equation here

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Answer:

see below

Step-by-step explanation:

First we need to find the slope

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

   = (60-64)/( 10-0)

   = -6/10

   = -2/5

The y intercept is (0,64)

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = -2/5 x + 64  where y is in the thousands of feet

m = -2/5 * 1000 = -400 ft / minute

The height decreases since the sign is negative

The height decreases 400 ft per minute

The y intercept is (0,64)

64 is in the thousands of ft

64*1000 = 64,000 ft

When it starts, it is at 64,000 ft

The descent starts at a cruising altitude of 64,000 ft

Answer:

0.14

Step-by-step explanation:

The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:

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

From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14

The area under the curve shaded is 1 to 2 is 0.14

Probabilities are used to determine the chances of an event

The shaded region represents the probability of the z-scores

The shaded region 1 to 2 is represented as:

P(1 < z < 2) =

Using the probability of z-score, we have the formula

P(1 < z < 2) = P(z < 2) - P(z < 1)

From the given standard normal table:

P(z < 2) = 0.9772

P(z < 1) = 0.8413

So, we have:

P(1 < z < 2) = 0.9772 - 0.8413

P(1 < z < 2) = 0.1359

Approximate

P(1 < z < 2) = 0.14

Hence, the area under the curve shaded is 1 to 2 is 0.14

Read more about normal distribution at:

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Answer:

54°

Step-by-step explanation:

Let ∠CYX=x

AB║CD

∠AXE=∠CYX  (corresponding angles)

∠AXE=3∠CYX-108

x=3x-108

3x-x=108

2x=108

x=108/2=54°

∠AXE=∠CYX=x=54°

∠BXY=∠AXE=54° (Vertically opposite angles)

Answer:

12 , 19 , 26 , 33

Here, n+7

12+7=19

19+7=26

So,

26+7=33

Hope you understand ❣

Step-by-step explanation:

12 , 19 , 26 , ?

Given

___________

a1= 12

a2= 19

a3 = 26

d= ?

a4 = ?

––——————

we can solve this by using formula from Ap .

But for this we have to find d

As we know that

common difference(d) = a2-a1 = 19 -12

= 7

so difference after every no is 7 so

a4 = a3 + d

= 26 +7

= 33

So 33 is ur answer mate

Hope it helps

Answer:

5 and 3/32 of an inch.

Answer:is the first answer 15.875 and the second answer 17 x 28 ÷5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

[tex]x = 5 + In (t)[/tex]

[tex]y = t^2+2[/tex]

At point (5,3)

To find an equation of the tangent to the curve at the given point,

By without eliminating the parameter

[tex]\dfrac{dx}{dt}= \dfrac{1}{t}[/tex]

[tex]\dfrac{dy}{dt}= 2t[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ \dfrac{dy}{dt} }{\dfrac{dx}{dt} }[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{ 2t }{\dfrac{1}{t} }[/tex]

[tex]\dfrac{dy}{dx}= 2t^2[/tex]

[tex]\dfrac{dy}{dx}_{ (5,3)}= 2t^2_{ (5,3)}[/tex]

t²  + 5 = 4

t² = 4 - 5

t² = - 1

Then;

[tex]\dfrac{dy}{dx}_{ (5,3)}= -2[/tex]

The equation of the tangent  is:

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

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

By eliminating the parameter

x = 5 + In(t)

In(t)  = 5 - x

[tex]t =e^{x-5}[/tex]

[tex]y = (e^{x-5})^2+5[/tex][tex]y = (e^{2x-10})+5[/tex]

[tex]\dfrac{dy}{dx} = 2e^{2x-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2e^{10-10}[/tex]

[tex]\dfrac{dy}{dx}_{(5,3)} = 2[/tex]

The equation of the tangent  is:

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

[tex](y-3 )= -2(x - 5)[/tex]

y - 3 = -2x +10

y = -2x + 7

y = 2x - 7

Answer:

Example: solve √(2x−5) − √(x−1) = 1

isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...

expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...

isolate the square root:√(x−1) = (x−5)/2. ...

Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...

Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.

Answer:

Step-by-step explanation:

ewrerewrwrwerrwer

Answer:

2. 20 oranges

3. 18 yellow tulips

4. 23 students

Answer:

Step-by-step explanation:

To find the ratio first find the diameter of the larger circle

Diameter of first circle = 6 inches

Diameter of second circle = 4 × diameter of the first circle

Which is

Diameter of second circle

= 4 × 6 = 24 inches

Area of a circle = πr²

r is the radius

Area of smaller circle

Diameter = 6 inches

Radius = 6 / 2 = 3 inches

Area = (3)² π = 9π in²

Area of larger circle

Diameter = 24 inches

Radius = 24 / 2 = 12 inches

Area = (12)²π = 144π in²

The ratio of the smaller circle to the larger circle is

[tex] \frac{9\pi}{144\pi} [/tex]

Reduce the fraction by 9π

That's

[tex] \frac{1}{16} [/tex]

We have the final answer as

Hope this helps you

Answer:

C. 1:16

Step-by-step explanation:

Area of a circle is:

[tex]\pi \times {r}^{2} [/tex]

Small circle Area:

radius = diameter/2

radius = 6/2 = 3

[tex]area \: of \: a \: circle \: = \pi {3}^{2} [/tex]

a = 28.27

Large circle 4 times larger diameter

6*4 = 24

diameter = 24

r = 24/2

r = 12

[tex]a \: = \pi {12}^{2} [/tex]

a = 452.39

area of large circle/ area of small circle

452.39/28.27 = 16.00

ratio is 1:16

Answer:

Its commutative property..

Step-by-step explanation:

Commutative property says A×B=B×A

Explanation is attached below.

Answer:

They will need 160 cans to make 5 lbs

32 cans for 1 lbs

Step-by-step explanation:

We can use ratios to solve

8 cans             x cans

--------------- = ---------------

1/4 lbs             5 lbs

Using cross products

8 * 5 = 1/4x

40 = 1/4 x

Multiply each side by 4

4 * 40 = 1/4 x * 4

160 =x

They will need 160 cans to make 5 lbs

8 cans             x cans

--------------- = ---------------

1/4 lbs             1 lbs

Using cross products

8 * 1 = 1/4x

Multiply each side by 4

8*4 = x

32 cans for 1 lbs

Answer:

32 cans per pound of aluminum

160 cans per 5 pounds of aluminum

Step-by-step explanation:

will make it short and simple.

8 empty cans can make 1/4 pound of aluminum.

therefore... 8 x 4 = 32 cans per pound of aluminum.

Number of cans to make 5 pounds of aluminum = 32 x 5

= 160 cans per 5 pounds of aluminum

Answer:

The correct option is (B).

Step-by-step explanation:

It is provided that, in a game of roulette the  wheel consists of slots numbered​ 00, 0,​ 1, 2,​ ..., 33.

The sample space of an experiment, is the set of all the possible outcomes of the random trials.

There are a total of 35 slots on the roulette wheel where the ball can land.

So, there are a total of 35 outcomes for one rotation of the wheel.

Then the sample space consists of all the 35 outcomes, i.e.

S = {00, 0, 1, 2, 3, ..., 33}

Thus, the correct option is (B).

Answer:

a. True

b. true

c. false

d. false

e. false

Step-by-step explanation:

a. true

polutation = 25% = 0.25

sample = n= 12

n x p

= 12 x o. 25 = 3 and 3 is less than 10

12(1 - p)

= 12 x 0.75

= 9 and is less than 10

b. True

the sample distribution of the population is normal when

sample size x population > or equal to 10

40 x 0.75

= 30 and 30 is greater than 10

c. false

50 x 0.25 = 12.5

50 x 0.20 = 10

z = 10 - 12.5/sqrt(12.5)

= -2.5/3.54

= -0.70

H0: Young american family who delayed

H1: young american family who did not delay

p(z = -0.70)

0.2420>0.005

therefore we accept the null hypothesis

d. false

150 x 0.20 = 30

150 x 0.75 = 37.5

z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22

p(z = -1.22) = 0.1112 > 0.05

therefore we do not reject the null hypothesis

e. false

se1 = sqrt(p(1-p)/n

se2 = sqrt(p(1-p)/3n

se2 = 1/sqrt(3)se2

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

Answer:

The equation to be solved is missing in the question.

I will explain power series and ways to find the radius and interval of convergence of a powers series in the attached image.

Step-by-step explanation:

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

Answer:

Step-by-step explanation:

The answer is b

120.01 grams

[tex]\sf{\implies Range = Highest \: - lowest }[/tex]

→ Range of Lewistown = 74 - 64

→ Range of Lewistown = 10 .

→ Range of Hamersville = 71 - 55

→ Range of Hamersville = 16 .

☆ Range of Hamersville - Range of Lewistown

→ 16 - 10

→ 6

Answer → The range for Hamersville is 6 more than the range for Lewistown .

Answer:

f(x)= 3x-5

f(2) = 3(2)-5 = 6-5= 1

f(-1)= 3(-1)-5= -3-5= -8

Hope this helps

if u have question let me know in comments ^°^

Step-by-step explanation:

a. The mean can be found using the AVERAGE() function.

x = 272.7

b. The standard deviation can be found with the STDEV() function.

s = 39.9

c. The t-score can be found with the T.INV.2T() function.  The confidence level is 0.04, and the degrees of freedom is 26.

t = 2.162

d. Find the lower and upper ends of the confidence interval.

Lower = 272.7 − 2.162 × 39.9 = 186.5

Upper = 272.7 + 2.162 × 39.9 = 358.9

Answer:

-3x - 7y = 36

Step-by-step explanation:

The given line -3x - 7y = 10 has an infinite number of parallel lines, all of the form -3x - 7y = C.

If we want the equation of a line parallel to -3x - 7y = 10 that passes through (-5, -3), we substitute -5 for x in -3x - 7y = 10 and substitute -3 for y in -3x - 7y = 10:

-3(-5) - 7(-3) = C, or

15  + 21 = C, or C = 36

Then the desired equation is -3x - 7y = 36.

Answer:

97290

Step-by-step explanation:

47 different people can win first

47

Now there are only 46 people left

46 different people can win second

46

45 different people can win third

47*46*45

97290

Answer:

because this is equal to the given matrix, the given matrix is symmetric.

Step-by-step explanation:

A symmetric matrix is a square matrix which has same number of rows and columns. Square matrix is equal to transpose. Equal matrices have equal dimensions. The given matrix is symmetric because the rows and columns are equally distributed.

Answer:

(a) Minimum red blood cells 5.744 million cells per micro liter

(b) Maximum red blood cells 5.068 million cells per micro liter.

Step-by-step explanation:

Z-score formula is = [tex]\frac{x-u}{Standard deviation}[/tex]

Z-score = [tex]\frac{x-5.5}{0.4}[/tex]

The value of z-score is 0.61 so then x will be;

x = 5.744

The minimum red blood cells count that can in top is 27% of count which is 5.744 million cells per micro liter.

Z-score = [tex]\frac{x-5.5}{0.4}[/tex]

The value of z-score is 0.14 so then x will be;

x = 5.068

The maximum red blood cells count that can be in top is 14% of count which is 5.068 million cells per micro liter.