Given that A = 60° and B = 30'. evaluate (sin
2 cos A) + cos B. leaving your answer in surd
form

Hello!

The value that is in the middle of the data set will be the mean. (So, there will be three numbers on the left of it, and three to the right).

Let's say the numbers are 7, 9, 3, 6, 2, 1, 5 (Just as an example)

Because the amount of numbers in this data set is seven, it is an odd number. This means to find the median, we simply have to look at the number in the middle of the set. (In this case, that would be six).

Answer:

\(g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}\)

Step-by-step explanation:

The inverse of a function has \(x\) and \(y\) values switched from the original function. Therefore, simply switch \(x\) and \(y\) and isolate \(y\) to get your inverse function:

Original function: \(g(x)=41x^3+a\)

Switching \(x\) and \(y\), then isolating \(y\):

\(x=41y^3+a,\\x-a=41y^3,\\\frac{x-a}{41}=y^3,\\y=\sqrt[3]{\frac{x-a}{41}}\).

Therefore, the inverse of the \(g(x)=41x^3+a\) is:

\(\fbox{$g^{-1}(x)=\sqrt[3]{\frac{x-a}{41}}$}\).

The graph of the compound inequalities with intersection points

(2.21, -0.63) is given below.

Please see the graph attached.

A compound inequality has two inequality statements joined either by the "or" or “and.”

We have,

6x+2y<12 or x-6y>6

We can graph each inequality.

And we also need to see the intersection between the inequalities.

Let,

6x + 2y = 12____(1)

x - 6y = 6_______(2)

From (1)

x = (12 - 2y ) / 6 put in (2)

(12 - 2y) / 6 - 6y = 6

2 - 1/3y - 6y = 6

2 - 6 = (1/3)y + 6y

-4 = 19y / 3

y = -12 / 19

y = - 0.63 put in (1)

6x + 2 x (-0.63) = 12

6x = 12 + 1.26

x = 13.26 / 6

x = 2.21

The point of intersection on the graph is (2.21, -0.63).

Thus the graph of the compound inequalities with intersection points (2.21, -0.63) is given below.

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We have that the  first term of the progression is

b=4

From the Question we are told that

Third terms of a Geometric Progression is 48

Sum of third and fourth terms is 144

Generally the equation for the common ratio  is mathematically given as

 r=3

Therefore

Since

 b=4

Answer:

10/50 = 20/100

Step-by-step explanation:

Another way to represent this formula is:

\(\frac{is}{of} = \frac{percent}{100}\)

Allow me to explain this to you.

What is 20% of 50?

"WHAT IS"

"20% (PERCENT)"

"OF 50"

\(\frac{x}{50} =\frac{20}{100}\)

The variable, x, was used to replace the unknown value, which is 10.

Answer:

=−2x+4y−8

Step-by-step explanation:

Let's simplify step-by-step.

2x+4y−8−4x

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

The dimensions of the poster with the smallest area are; 27.75 cm x 27.75 cm

Let "x" and "y" denote the length and the width of the poster.

We are told that the margin of a poster are 4 cm and the side margins are 4 cm.

The length of the print = x - 2(4) = x - 8

The width of the print = y - 2(4) = y - 8

The area of the print = length * width = (x - 8)(y - 8)

The area of the print is given as 390 square inches. Thus;

(x - 8)(y - 8) = 390

Making y the subject gives;

y = (390/(x - 8)) + 8

The area of the poster is; A = xy

Thus;

A = x[(390/(x - 8)) + 8]

A =  (390x/(x - 8)) + 8x

Minimizing the area gives;

A' = 8 - (3120/(x - 8)²)

Equating to zero gives;

8 - (3120/(x - 8)²) = 0

8(x - 8)² = 3120

(x - 8)² = 3120/8

(x - 8)² = 390

x = 27.75 cm

y = (390/(27.75 - 8)) + 8

y = 27.75 cm

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Answer:

350

Step-by-step explanation:

Answer:

70 days

Step-by-step explanation:

Given that,

→ fresh fruit to last 10 days

→ fresh vegetables for 7 days

→ dried insects for 5 days

Then in how many days will they order all three items on the same day?

Then the LCM of 10, 7 & 5 is,

→ 2 × 5 × 7

→ 10 × 7 = 70

Hence, the answer is 70 days.

Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Answer:

Dan eat 2 2/3 of a pizza

Step-by-step explanation:

the answer is above

Let

x-----> amount of pizza Jay ate

y-----> amount of pizza Dan ate

we know that

----> equation A

-----> equation B

substitute equation A in the equation B and solve for y

Convert to mixed number

Answer:

(1) The between groups degrees of freedom is 2.

(2) TRUE.

(3) The correct option is (a).

Step-by-step explanation:

(1)

The between groups degrees of freedom for the study is:

\(\text{df}_{B}=k-1\\=3-1\\=2\)

Thus, the between groups degrees of freedom is 2.

(2)

The hypothesis for he one-way ANOVA is:

H₀: All the means are equal.

Hₐ: At least one of the mean is not equal.

The output of the ANOVA test is attached below.

The p-value of the test is 0.00005.

p-value = 0.00005 < α = 0.05

Thus, the result is statistically significant.

The statement is TRUE.

(3)

As the p-value of the test is less than the significance level, the researcher should make the decision to reject the null hypothesis.

The correct option is (a).

Hi there!

\(\large\boxed{y = \pm \sqrt{x - 16}}\)

To solve for the inverse, swap the x and y variables:

x = y² + 16

Isolate for y by subtracting both sides by 16:

x - 16 = y²

Square root both sides:

√(x - 16) = y

Add the plus/minus sign:

y = ±√(x - 16)

Answer:

c

Step-by-step explanation:

Each game should cost us roughly 8 cents.This game's expected value is negative, thus playing it is not a good idea because you will most likely lose money in the long run.

Given problem describes that there can be 4 unique ball colour combinations as :

Provided that each colour contains two balls in the respective boxes, each combination has a probability of happening of 2/4 * 1/3 = 1/6. The likelihood that the payoff will be zero is thus 4 * 1/6 = 2/3.

Red balls make two different combinations as: (red, red) in left box and (red, red) in  right box. Due to the fact that each box contains just one red ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. The likelihood that the dividend will be $0.50 is thus 2 * 1/12, or 1/6

Blue balls makes two different combinations as: blue and blue in the left box and (blue, blue) in the right box. Due to the fact that each box contains just one blue ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. Hence, the likelihood that the payoff will be $1 is 2 * 1/12, or 1/6.

In the left box, there is only one conceivable pair of balls that are both green: (green, green). Given that there is only one green ball in the left box, this combination has a probability of happening of 1/4 * 1/3, or 1/12. Hence, there is a 1/12 chance that the payment will be $16.

\(Payout\; |\;Probability\\ \ $0 \qquad \qquad 2/3\\$0.50 \quad \qquad 1/6\\$1 \qquad \qquad 1/6\\$16 \qquad \qquad 1/12\)

By multiplying each payout by the associated probability and adding them together, the anticipated value is determined. The predicted outcome in this situation is:

\(\$ 0 * 2/3 + \$0.50 * 1/6 + \$1 * 1/6 + \$16 * 1/12 - \$1 = -\$0.0833\)

The anticipated value of playing this game, according to the revised figures above, is \(-\$0.0833\), which indicates that you should anticipate losing on average roughly $0.08 every game. Thus, it is unprofitable game to play if played on regular basis.

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Answer:0

Step-by-step explanation:

The value of angle x in the triangle is 15°

Given: the triangle ABC with equal sides of 9 units.

Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).

Thus, <A = <B = < C =  4x°

Since the sum of angles in a triangle is 180°. We have:

<A + <B + < C = 180°

4x + 4x + 4x = 180°

12x = 180

x = 180/12

x = 15°

Therefore, the value of x is 15°

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Answer: 56x

Step-by-step explanation: Multiply -8 by -7. Be sure to add your x at the end. VERY important.

I hope this helps you out! ♥

Answer:

\(56x\)

Step-by-step explanation:

\(-7x(-8)\)

The one and only thing you have to do in this question is to simplify.

\(-7x)(-8)\)

This equals

\(56x\)

Now you got your answer!

Hope this helps!

Answer:

-0.91 = strong, as it is close to -1 and if it's close to -1 that means it is linear.

0.82 = strong. Again, it's approaching 1 and is, therefore, approaching linearity.

-0.49 = moderate

0.26= weak

0.54 = moderate

-0.18 = weak

Step-by-step explanation:

Answer:

C (lower left corner)

Step-by-step explanation:

Lower extreme: 67

Upper extreme: 75

Median: 70

Upper quartile: 73

Lower quatile: 69

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Step-by-step explanation:

Answer:

y = \(-\frac{5}{2}\)x - 1

Step-by-step explanation:

5x + 2y = 12

2y = -5x + 12

y = \(-\frac{5}{2}\)x + 6

y = mx + b

4 = \(-\frac{5}{2}\) ( -2 ) + b

4 = 5 + b

b = -1

y = \(-\frac{5}{2}\)x - 1

Answer:

Step-by-step explanation:

m (slope) =  rise    =    y    =  y₁ - y₁

                   run           x        x₁ - x₁

to get y = mx

therefore, the answer to the question is :

A. The slope m is rise over run, so y over x =m.

    Solve for y to get y=mx.

When three college students are randomly selected, the probability that ALL three buy their textbooks online is 0.227

The probability that at least one purchases their textbooks online is 1.

As per the question the probability of students purchase their textbooks online 61%.

\(=\frac{61}{100}\)

p = 0.61.

So, failure = 1 - 0.61 = 0.39

q = 0.39

When 3 students are selected(n = 3)

We know that, \($$p(x)={ }^n c_x p^x q^{n-x}$$\)

So, probability that all of them to purchase

\($$\begin{aligned}&(x=3) \\& p(3)={ }^3 c_3(0.61)^3(0.39)^{3-3} \\& p(3)=0.22698\end{aligned}$$\)

When 5 students are selected (n = 5)

And probability that at least one purchases books online

\(=P(x=1)+P(x=2)+P(x=3)$ $+P(x=4)+P(x=5)$\)

Now we know that probability of all equal to 1.

\(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1\)

So, we can simply write

\($$\begin{aligned}P & =1-p(x=0)+p(x=1) \\& =1-\left[{ }^5 C_0(0.61)(0.35)^{50}+{ }^5 C_1(0.61)^1(0.39)^{5-1}\right] \\& =1-0.00902-0.07056 \\P& =0.92042\end{aligned}$$\)

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Answer:

There were 5928 entries

Step-by-step explanation:

You multiply 14% by 5200, which is 0.14 in decimal form, and you get 728. Then you add 5200 and 728 together, since 14% of 5200 is 728

Answer:

Step-by-step explanation:

To find the slope of the line, you have to use a slope formula.

Slope formula:

\(\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }\)

⇒ y2=(-15)

⇒ y1=1

⇒ x2=1

⇒ x1=(-1)

Rewrite the whole problem down.

\(\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}\)

I hope this helps you! Let me know if my answer is wrong or not.

A frequency polygon for the times taken by 18 people to complete a puzzle is shown in the image attached below.

In order to draw a frequency polygon for the given data, we would construct a frequency table as follows:

Time, t minutes                                      Frequency

0 < t ≤ 10                                                         5

10 < t ≤ 20                                                       5

20 < t ≤ 30                                                      7

30 < t ≤ 40                                                      1

Next, we would determine the midpoint of the data set:

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There are two elements in A' ∩ B.

The given sets are: U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, B = {1, 3, 5, 7}To find the number of elements in A' ∩ B, we first need to find the complement of A,

which is the set of all elements that are not in A.Complement of A: A' = {3, 6, 7}

Now, we need to find the intersection of A' and B.Intersection of A' and B: A' ∩ B = {3, 7}

Therefore, there are two elements in A' ∩ B, which are 3 and 7.

To summarize, we have U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 4, 5}, and B = {1, 3, 5, 7}. The complement of A is A' = {3, 6, 7}.

The intersection of A' and B is A' ∩ B = {3, 7}.

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