3) Solve the trigonometric equation 2 sin² 0 - 5sin0 + 3 = 0 on the interval 0 ≤ 0 ≤ 2π. Show each step to justify your solutions. [DOK 3: 4 marks] 4) Write at least a paragraph justifying your

Answer:

1. \(x^2-6x+8=0\)

2. \((x-4)(x-2)=0\)

3. \(x=4 \text{ and } x=2\)

4. \(x=4 \text{ and } x=2\)

Step-by-step explanation:

1. When using substitution all we do would be is substituse the y for a 3.

This leaves us with the equation:

\(3=-x^2+6x-5\)

Rewriting it we get:
\(0=-x^2+6x-8\)

or if we shift the 0 to the other side:

\(x^2-6x+8=0\)

2. In order to factor the equation we can use the butterfly method:

\(\left[\begin{array}{ccc}1&-4\\1&-2\end{array}\right]\)
So it factors out to:

\((x-4)(x-2)=0\)
You can also use the quadratic formula.

3. To find the solutions we just set each factor to 0
\(x-4=0\\\text{and}\\x-2=0\)
So the x-values would be:
\(x=4 \text{ and } x=2\)

4. To find the solution to the system we just plug in the values and it turns out to be the same numbers as before.

Answer:

20 ÷ (4x +2y) is your answer

Answer:

What is the greatest number of binders Eula can buy? Answer=5

What is the greatest number of notebooks Eula can buy? Answer=10

If Eula buys 7 notebooks, what is the greatest number of binders she can buy? Answer=1

Step-by-step explanation:

EDGE. 2022

Answer:

\((2, \frac{7}{2} )\)

Step-by-step explanation:

The midpoint between two points is:

\((\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\) when the given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the points (1,6) and (3,1)

\(= (\frac{1+3}{2} , \frac{6+1}{2} )\\= (\frac{4}{2} , \frac{7}{2} )\\= (2, \frac{7}{2} )\)

Therefore, the midpoint between (1,6) and (3,1) is \((2, \frac{7}{2} )\).

I hope this helps!

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

Answer:

113 + 22 = 135

113.5 + 22.41 = 135.91

The answer would be 135.91

Step-by-step explanation:

Answer:

100,300

Step-by-step explanation:

The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

To know more about fraction here

https://brainly.com/question/10354322

#SPJ4

Answer:

the first plotting was correct.

Step-by-step explanation:

the values will be arranged in an ascending order from their roots which are the first digit

(A) There is a 0.62 percent probability that the present is upstairs.

(B) The probability that dad hid it is 0.526.

Let P denote the probability of a present being hidden by mom (M)

Let P denote the probability of the father concealing the present (F)

Let P denote the probability of a gift being concealed upstairs by mother (Um)

Let P denote the probability of a gift being concealed downstairs by the mother (Dm)

Let P denote the probability of a gift being concealed upstairs by father (Uf)

Let P denote the probability of a gift being concealed downstairs by the father (Df)

P(M)=0.6, P(F)=0.4, P(Um)=0.7, P(Dm)=0.3, P(Uf)=0.5, P(Df)=0.5

a) Mother concealed and hid upstairs P(M) x P(Um)  

= 0.6 x 0.7

= 0.42

Or

Father concealed and hiding upstairs = P(F) x P(Uf)

= 0.4 x 0.5

= 0.2

Final answer = 0.42 + 0.2

= 0.62

b) It is a conditional probability issue.

The probability of concealed presence downstairs is one minus the probability of hidden presence above.

= 1 – 0.62  

= 0.38

probability of father hiding gift downstairs = P(F) x P(Df)

= 0.4 x 0.5

= 0.2

Conditional Probability Equation P(F|Downstairs) = Father's Chance of Hiding Present Downstairs / Chance of Father Hiding Present Downstairs

P(F|Downstairs) = 0.2 ÷ 0.38

P(F|Downstairs) = 0.526 (correct to 3 decimal places)

Read more about probability at

https://brainly.com/question/14720996?referrer=searchResults

#SPJ4

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

Read more about p-value at; https://brainly.com/question/4621112

#SPJ1

Answer:

x =62

Step-by-step explanation:

The two angles form a straight line so they add to 180

x+118 = 180

Subtract 118 from each side

x = 180-118

x =62

Answer:

x = 62°

Step-by-step explanation:

These both angles are located at straight line.

So, the sum of both angles is 180 °.

x + 118 ° = 180 °

Subtract 118 ° from 180 °

x = 180 ° - 118 °

x = 62 °

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

Analytics is often described as the study of historical data to extract insights and make informed decisions. It involves the collection, processing, and analysis of data to discover patterns, identify trends, and gain insights into business operations. By examining data sets, analytics can help businesses identify areas of improvement, optimize performance, and increase efficiency. Analytics tools and techniques can be used across many different fields, including finance, marketing, healthcare, and sports. In finance, analytics can be used to analyze market trends and predict future outcomes. In marketing, analytics can help businesses identify customer behavior patterns and optimize marketing campaigns. In healthcare, analytics can help identify patterns in patient data and improve healthcare outcomes. In sports, analytics can be used to analyze player performance and predict game outcomes.

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

To know more about statement visit :

https://brainly.com/question/27839142

#SPJ11

Given the the following equations, find the unknown value, ?, that makes the equations true

.\(? - 4 - 2p + 5 = 6p + 17d - 4 + 3 - 2d = ? - 112c - 8 - 2c + 10 - 4 = 10c -?\)

Starting with the equation, \(? - 4 - 2p + 5 = 6p + 1\)

Start with the side that is more complex, \(?-4-2p+5\). Simplify it as best you can by combining all like terms.

\(?-4-2p+5\)

=>\((?)+(-2p)+(-4+5)\)

=> \(?-2p+1\)

Now look at the R.H.S (\(6p+1\)), notice how we have the +1 in the simplified expression above. So what value would we put in for "?" to get 6p? That value would be 8p.

Now we have, \((8p)-2p+1=6p+1\)

=> \(6p+1=6p+1\)

The equation matches making it true. I will now do the rest without a long explanation. If you need an explanation or have any questions, please leave a comment.

Now for, \(7d - 4 + 3 - 2d = ? - 1\)

Simplifying L.H.S, we get...

=> \(5d-1\)

To match it with the R.H.S, "?" would have to be 5d.

Lastly, \(12c - 8 - 2c + 10 - 4 = 10c -?\)

Simplifying L.H.S, we get...

=> \(10c-2\)

To match it with the R.H.S, "?" would have to be 2.

Answers:

8p, 5d, & 2

The statement that truly represent the diagram is

y = w and Δ ABC ~ Δ CDE

The two triangles depicted are similar triangles and similar triangle is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure shows that pair of congruent angles are

angle  y = angle  w (alternate angles)

angle D = angle B (right triangle)

angle x = angle z (alternate angles)

similar triangles is represented by ~ and only the first option match the description

Learn more about similar triangles here:

https://brainly.com/question/29333623

#SPJ1

In a right-angled triangle, the Pythagoras theorem is used to find the hypotenuse. Then the hypotenuse is 32.2 inches.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

A right triangle has legs measuring 16 inches And 28 inches.

We know the Pythagoras theorem

\(\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\)

Then the hypotenuse will be.

\(\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\\\\\rm Hypotenuse ^2 = 16^2 + 28^2\\\\ \rm Hypotenuse ^2 = 256 + 784\\\\\rm Hypotenuse ^2 = 1040\\\\\rm Hypotenuse \ = 32.2\)

Thus, the hypotenuse is 32.2 inches.

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

https://brainly.com/question/3770177

Answer:

 8k + 9

 ———————

 10k + 9

Step-by-step explanation:

uhh i tried

\(\\ \sf\longmapsto tan(270+\theta)=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto \dfrac{sin(270+\theta)}{cos(270+\theta)}=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto \dfrac{-cos\theta}{sin\theta}=1-\dfrac{sin\theta}{cos\theta}\)

\(\\ \sf\longmapsto\dfrac{sin\theta}{cos\theta} \dfrac{-cos\theta}{sin\theta}=1\)

\(\\ \sf\longmapsto \dfrac{sin^2\theta-cos^2\theta}{-cos\theta sin\theta}=1\)

\(\\ \sf\longmapsto \dfrac{-2cos\theta}{-cos\theta sin\theta}\)

\(\\ \sf\longmapsto \dfrac{2}{sin\theta}=1\)

\(\\ \sf\longmapsto 2cosec\theta=1\)

\(\\ \sf\longmapsto cosec\theta=\dfrac{1}{2}\)

\(\\ \sf\longmapsto \theta=cosec^{-1}\left(\dfrac{1}{2}\right)\)

The remote interior angles of the exterior angle ∠1 are ∠5 and ∠6.

The remote interior angles of the exterior angle ∠3 are ∠5 and ∠4.

The remote interior angles of the exterior angle ∠1 are ∠4 and ∠6.

A triangle is a polygon that has three sides. The sum of angles in a triangle

is 180 degrees. The exterior angle theorem can be used to find the interior

angles of a triangle.

The exterior angle theorem states that the measure of an exterior angle is

equal to the sum of the measures of the two remote interior angles of the

triangle.

Therefore,

learn more on triangle here: https://brainly.com/question/2125016

#SPJ1

There are 1,320 possibilities for the win, place, and show positions in a horse race with 12 horses where all orders of finish are possible.

The number of possibilities for the win, place, and show positions in a horse race with 12 horses where all orders of finish are possible can be calculated using permutations.

The number of possibilities for the win position is 12, as any of the 12 horses can win.

After the winner is determined, there are 11 horses left that can potentially take the second position. Therefore, the number of possibilities for the place position is 11.

Similarly, there are 10 horses left for the third position, so the number of possibilities for the show position is 10.

To find the total number of possibilities, we multiply the number of possibilities for each position

Total number of possibilities = number of possibilities for win position × number of possibilities for place position × number of possibilities for show position

= 12 × 11 × 10

= 1,320

Learn more about possibilities here

brainly.com/question/21366488

#SPJ4

The given question is incomplete, the complete question is:

Consider a horse race with 12 horses with possibilities win, place, and show (First, Second, and third) positions.

The objective is to find how many possibilities are there for the win, place, and show (First, Second, and third) positions if all orders of finish are possible

Positive correlation means that both variables tend to increase (or decrease) together. Thus, Option A is the answer.

Positive correlation refers to a relationship between two variables in which an increase in one variable is associated with an increase in the other variable. Negative correlation, on the other hand, refers to a relationship in which an increase in one variable is associated with a decrease in the other variable. No correlation means that there is no relationship between the two variables.

To determine the strength of a correlation, we can use a statistical measure called the correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, a correlation coefficient of -1 indicates a perfect negative correlation, and a correlation coefficient of 0 indicates no correlation.

Learn more about Positive correlation:

https://brainly.com/question/28898177

#SPJ4

Check the picture below.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill\)

\(\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}\)

A factor is the product of one number multiplied by another number. When you multiply two or more numbers together, the original numbers are called factors.

Consider the following example: Factor pairs are two numbers that, when multiplied together, produce a specific product. The factor pairs of 12 are:1 x 12 = 122 x 6 = 123 x 4 = 12A factor is a number that divides into another number evenly. A factor is a divisor. Every number has at least two factors: one and itself.

A factor of a number is any number that divides into it evenly, leaving no remainder. Therefore, the correct answer to the given blank is A. Factor.

Factors are numbers that are multiplied to obtain a result, and they are commonly used in mathematics. They're an important component of problem-solving. In factoring, you'll break down an equation into smaller parts to make it more manageable, and then combine those smaller parts to solve the problem.

Factorization is the process of writing a number as a product of two or more factors. For example, the factorization of 12 is 2 × 2 × 3. The prime factorization of a number is the factorization in which all factors are prime.

Learn more about factor from the given link

https://brainly.com/question/14549998

#SPJ11

Step-by-step explanation:

6x+21=-9

6x=-9-21

x=-30/6

x= -5

Answer:

\(3(2x + 7) = - 23 + 14 \\ 6x + 21 = - 9 \\ 6x = - 30 \\ x = \frac{ - 30}{6} \\ x = 5 \\ thnk \: you\)

Answer:

The function rule is f(x)=2x+3. It cut the three out.

Step-by-step explanation: cut the three out

The variance for the sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores is 5.

The formula for the variance of a sample is:

\(s^2\) = SS / (n - 1)

where SS is the sum of squared deviation scores, n is the sample size, and \(s^2\) is the variance.

In this case, SS = 20 and n = 5, so we can substitute these values into the formula:

\(s^2\) = 20 / (5 - 1)

\(s^2\) = 5

Therefore, the variance for this sample is 5.

Learn more about variance:

https://brainly.com/question/29505178

#SPJ4

the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

What is Origin?

Origin is the beginning, middle, or beginning of something, or where one comes from. An example of origin is when an idea comes to you while you are sleeping. An example of an origin is the soil where oil comes from. An example of ancestry is your ethnicity.

To find the point on the plane 7x - y + 7z = 70 nearest to the origin, we can use the concept of perpendicular distance. The point on the plane closest to the origin will lie along the line perpendicular to the plane that passes through the origin.

The equation of the plane is 7x - y + 7z = 70. We can rewrite it in the form Ax + By + Cz + D = 0, where A, B, C are the coefficients of x, y, z respectively, and D is a constant.

In this case, A = 7, B = -1, C = 7, and D = -70.

The direction ratios of the line perpendicular to the plane are equal to the coefficients of x, y, z in the plane equation. Therefore, the direction ratios are (7, -1, 7).

Let's assume the coordinates of the point closest to the origin on the plane are (x, y, z).

The line passing through the origin and perpendicular to the plane can be parametrically represented as:

x = 7t

y = -t

z = 7t

Substituting these values into the equation of the plane, we get:

7(7t) - (-t) + 7(7t) = 70

49t + t + 49t = 70

99t = 70

t = 70/99

Substituting the value of t back into the parametric equations, we get:

x = 7(70/99) = 490/99

y = -(70/99) = -70/99

z = 7(70/99) = 490/99

Therefore, the point on the plane 7x - y + 7z = 70 nearest to the origin is (x, y, z) = (490/99, -70/99, 490/99).

To learn more about Origin from the given link

https://brainly.com/question/24594125

#SPJ4