Given this unit circle what is the value of x? HELP PLEASE

Answer:

Step-by-step explanation:

You want solutions to the equation 4sin(θ)² -7sin(θ) -4 = 0 on the interval [0, 2π].

A graph of the left-side expression shows it has a value of 0 at ...

  θ ≈ 3.61 or 5.81.

Using a calculator to check the offered answer choices, we find the values of θ that best satisfy the equation are θ = 3.61 or 5.81. (For this purpose, ±0.02 ≈ 0.)

We can let x = sin(θ). Then the equation is ...

  4x² -7x -4 = 0

  x² -7/4x = 1

  (x -7/8)² = 1 +(7/8)² = 113/64

  x = (7 ±√113)/8

The value (7+√113)/8 is greater than 1, so the only value of x that is useful here is x = (7-√113)/8. The angles in the desired range are ...

  {π - arcsin((7 -√113)/8), 2π +arcsin((7 -√113)/8)} ≈ {3.61, 5.81} . . . radians

The probability that exactly 128 flights are on time is 0.0950.

The probability that at least 128 flights are on time is 0.5079.

The probability that fewer than 124 flights are on time is 0.2147.

It should be noted that exactly 128 means P(X=128) = P(127.5 < X < 128.5) (By using continues correlation )

At X = 127.5

Z =(127.5-127.6) / 3.91305 = -0.02

At X = 128.5

Z =(128.5-127.6) / 3.91305 = 0.22

P(127.5 < X < 128.5) = P(-0.02 < Z < 0.22)

P(127.5 < X < 128.5) = P(Z < 0.22) - P(Z < -0.02)

P(127.5 < X < 128.5) =0.58706 - 0.49202

P(127.5 < X < 128.5) =0.0950

(b) at least 128 flights are on time.

P(X > 128) = P(X > 127.5) (by using continues correction)

P(X > 127.5) = P(Z > (127.5-127.6)/3.91305)

P(X > 127.5) = P( Z > -0.02)

P(X > 127.5) = 1- P( Z< -0.02)

P(X > 127.5) = 1- 0.49202

P(X > 127.5) = 0.5079

(c) fewer than 124 flights are on time.

P(X < 124 ) =P(X<124.5) (by using continouse correction)

P(X<124.5) = P(Z < (124.5-127.6)/3.91305)

P(X<124.5) = P(Z < -0.79)

P(X<124.5) = 0.2147

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The option that best describes the change in viewers the network is experiencing is B. Each year, the total number of viewers increases to approximately 120% of the previous year's total.

When 't' surpasses 1/ln(5) at 3.5, the expression yields a negative result; connoting the network is witnessing a dwindling viewership.

Consequently, the network initially experiences an intensifying viewership ratio which then fades; in accordance with Option B, "Each year, the total number of viewers increases to roughly 120% of the preceding year's sum". Clearly, this demarcation reveals itself as the accurate answer.

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

Answer:

2/3

Step-by-step explanation:

since a is 5 and b is 9.

so, 5+1( according to the expression given)/9

5+1/9 equals 6/9 and taking them down to the lowest terms that makes the answer 2/3

Answer:

C

Step-by-step explanation:

It does not belong because like the other ones it is not side ways, as well as it's common sense.

The probability that the total team time in the 400-meter freestyle relay is less than 215 seconds is: 0.8345

From the table given the mean and standard deviation, we can say that:

Total time spent = 54.2 + 57 + 55.3 + 53.7

Total time spent = 220.2 secs

The total standard deviation is:

2.8 + 3 + 2.4 + 2.5 = 10.7 secs

Formula for z-score here is:

z = (x' - μ)/(σ/√n)

where:

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

Thus:

z = (220.2 - 215)/(10.7/√4)

z = 0.972

From online p-value from z-score calculator, we have:

p(x < 0.972) = 0.8345

Read more about Probability from Z-score at: https://brainly.com/question/25638875

#SPJ1

Answer: b

Step-by-step explanation: cause i just did it

Based on my experiment, My appropriate conclusion based on the results  is option A: The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.

This conclusion is based on the truth that the experiment  conducted in California found that 85% of the respondents matches with the view,  one that is diverse from the extent of Modern York inhabitants (88%) who concurred with the same conclusion .

The "strong evidence" based on the experiment shows that the findings are statistically significant and the conclusion will thus be that the extent of California inhabitants who agree is "essentially wide" from the extent of other York inhabitants, showing some differences between the two populaces.

Learn more about survey  from

https://brainly.com/question/14610641

#SPJ1

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex] (option H).

The lengths of the woods are expressed as mixed numbers. Mixed numbers are non-integers that consists of a whole number and a proper fraction. For example, [tex]3\frac{1}{4}[/tex] is a mixed number. 3 is the whole number and [tex]\frac{1}{4}[/tex] is the proper fraction.

In order to arrange the lengths of the woods from shortest to the longest, convert the mixed numbers to decimals for easy comparison.

[tex]3\frac{1}{4}[/tex] becomes 3.25

[tex]2\frac{7}{8}[/tex] becomes 2.875

[tex]3\frac{5}{6}[/tex] becomes 3.833

[tex]4\frac{2}{3}[/tex] becomes 4.667

[tex]3\frac{1}{2}[/tex] becomes 3.5

The lengths arranged from shortest to longest is [tex]2\frac{7}{8}[/tex],  [tex]3\frac{1}{4}[/tex], [tex]3\frac{1}{2}[/tex] , [tex]3\frac{5}{6}[/tex], [tex]4\frac{2}{3}[/tex]

To learn more about fractions, please check: https://brainly.com/question/25779356

#SPJ1

The solution is, : the area of the rectangle is 4000 sq inches.

Here, we have,

A rectangle is given with sides 82 and 48 inches

We have to round off these dimensions to the nearest 10.

82 inches ~80 inches

since 2 <5, we make it 0

Similarly 48 inches ~50 inches since 8>5

Now area

= length x width

=80(50)

=4000 square inches

Hence, the area of the rectangle is 4000 sq inches is correct answer.

To learn more on Area click:

brainly.com/question/20693059

#SPJ1

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]

Answer:

n₁ = 198,610

P₁ = 27/198,610

n₂ = 196,877

P₂ = 104/196,877

q₁ = 1 - P₁

q₂ = 1 - P₂

Step-by-step explanation:

Answer:

85.84

Step-by-step explanation:

6x4 is the area of 1 rectangle

There r 3 rectangles

6x4 =24

24x3 =72

That’s the area if all the rectangles

There r 2 triangles

(4x3.46)/2 is the area of 1 triangle

=6.92

6.92x2 =13.84

total surface area is all the areas added up

72+13.84

=85.84

The box plot that has the smallest interquartile range would be the fourth box plot.

The bar graph that shows Ellen's steps would be B. Second bar graph.

The interquartile range on a box plot can be found by subtracting the figure where the box starts at, from the figure where the box plot stops.

This means that the figure with the least interquartile range is the fourth box plot with an interquartile range of :

= 8 - 4

= 4

The bar graph that would show Ellen's steps would be the one that has the most steps on the graph, closest to the mean of 10, 000 steps. Only Graph B has steps in the number of days, which are closest to 10, 000 steps consistently so this is the correct graph.

Find out more on bar graphs at https://brainly.com/question/30243333

#SPJ1

Answer: B: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The figure indicates this is a right triangle. As such, we can use the pythagorean theorem:

a^2 + b^2 = c^2

16 + 49 = x^2

sqrt(65) = x

.: x = [tex]\sqrt{65}[/tex]

Answer:

19cm

Step-by-step explanation:

I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC

25 - 15 = 10cm

9 + 10 = 19cm

Hope this helped :)

The median number of students who checked books out of the library in a 10-day period is 50.

We have,

To find the median of the list, we need to first put the numbers in order from least to greatest:

32, 35, 40, 40, 48, 52, 63, 68, 75, 83

The median is the middle value in the list.

If there is an odd number of values, the median is the middle value.

If there is an even number of values, the median is the average of the two middle values.

There are 10 values, which is an even number.

The middle values are 48 and 52.

Median = (48 + 52) / 2

Median = 50

So the median number of students who checked books out of the library in a 10-day period is 50.

Interpretation:

The median represents the middle value in the list, which in this case is 50.

This means that half of the values in the list are greater than 50, and half of the values are less than 50.

In terms of the number of students checking out books, this means that 50 is the typical number of students who checked books out of the library during the 10-day period.

Thus,

The median number of students who checked books out of the library in a 10-day period is 50.

Learn more about the median here:

https://brainly.com/question/28060453

#SPJ1

Answer:

5/36

Step-by-step explanation:

hope this helps

The predicted amount of debt for a financial education time of 34 hours is $26,350.

The predicted amount of debt for a financial education time of 24 hours is $31,550.

For the given information, we need to know the regression equation that relates financial education time and amount of debt to predict the amount of debt for different time durations.

Assuming a linear relationship between financial education time and amount of debt, we can estimate the regression equation as:

where a and b are the intercept and slope of the regression line, respectively, and Error is the random error term.

Using the given data points, we can estimate the regression line as:

(a) For a financial education time of 34 hours:

Therefore, the predicted amount of debt for a financial education time of 34 hours is $26,350.

(b) For a financial education time of 24 hours:

Therefore, the predicted amount of debt for a financial education time of 24 hours is $31,550.

To learn more about financial education time, here

https://brainly.com/question/31108935

#SPJ1

Sebastian can choose between 4,320 different sweaters.

to find the total number of different sweaters, we need to take the product between the numbers of options for each of the given selections, we have the numbers:

Color = 10 options.

Pattern = 4 options.

Letter type = 12 options.

Image = 9 options.

Then the total number of different options is:

D = 10*4*12*9 = 4,320

Learn more about combinations at:

https://brainly.com/question/11732255

#SPJ1

The mass per running metre of a copper bar with a uniform cross-section in the form of a triangle as shown in the figure when the density of copper is 8 850 kg/m³ is 3.

Mass per running meter = density x area x length

Substituting the values for density, area, and length, you get:

Mass per running meter = 8,850 x [(b x h) / 2] x length

Simplifying the equation, you get:

Mass per running meter = 4,425 x b x h x length

Mass = 8850 / 4425

Mass = 2

Learn more about mass on

https://brainly.com/question/86444

#SPJ1

The volume of a cylinder can be found using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

For Container A, the radius is half the diameter, or 16 feet. So the volume of Container A is:

V_A = π(16 ft)^2(16 ft) = 8,192π cubic feet

For Container B, the radius is half the diameter, or 15 feet. So the volume of Container B is:

V_B = π(15 ft)^2(18 ft) = 12,735π cubic feet

To find the volume of water that was transferred from Container A to Container B, we can subtract the volume of Container A from the volume of both containers combined:

V_water = V_A + V_B - V_A = V_B

V_water = 12,735π cubic feet

To find the volume of water remaining in Container A, we can subtract the volume of water that was transferred from the volume of Container A:

V_remaining = V_A - V_water

V_remaining = 8,192π - 12,735π

V_remaining ≈ -3,543.7 cubic feet

However, a negative volume doesn't make sense in this context, so we know that there must be no water remaining in Container A after the transfer. Therefore, the volume of water remaining in Container A to the nearest tenth of a cubic foot is 0.

The equation of proportion will be x/4 = 36/x. Then the value of 'x' will be 12 units.

According to the hypotenuse-leg (HL) principle, a right triangle is harmonious if each of its third side and legs are congruent with its equivalent hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are identical.

The equation is given as,

x/4 = 36/x

Simplify the equation, then we have

x/4 = 36/x

x² = 2² × 6²

x = 2 × 6

x = 12

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ1

a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.

b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate for this problem are given as follows:

[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]

The lower bound of the interval is given as follows:

0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.

The upper bound of the interval is given as follows:

0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

The degree of overlap between the two data sets is said to be high degree of overlap

Data overlap is a statistical term that analyzes the extent to which data points or distributions intersect.

It is often employed when comparing two or more datasets, determining how similar or dissimilar they are from each other.

A high degree of overlapping indicates an extensive similarity among shared values between multiple sets of data or distributions. Conversely, if there is a low level of overlapping observed between two datasets, it suggests complete distinctness and no sharing of common quantitative baseline measurements or metrics.

The domain of the overlap according to the plot is [55 85]

Learn more about degree of overlap at

https://brainly.com/question/31447794

#SPJ1

Answer:6

Step-by-step explanation: It’s 6 because it’s only greater than, not greater than or equal to

Answer:

Step-by-step explanation:

Answer:

28.27 CM ^2

Step-by-step explanation:

The formula for area of a circle is pi * r^2 where r = the radius.

Plugging the radius into the formula we get pi3^2, which equals 28.274 cm ^2 (and change)

Work Shown:

(A'C')/(AC) = 12/5 = 2.4

or you could say

(B'C')/(BC) = 16.8/7 = 2.4

or

(A'B')/(AB) = 9.6/4 = 2.4

The sides of triangle A'B'C' are 2.4 times longer compared to the corresponding sides of triangle ABC.