Question 1 of 10
What is the value of x ?
A. 160°
B. 50°
C. 55°
D. 20°

Answer:

√15

Step-by-step explanation:

Assuming that it is:

\(15^\frac{1}{2}\)

Exponent rule for fractional exponents are:

\(x^\frac{a}{b}=\sqrt[b]{x^a}\)

Apply rule:

\(15^\frac{1}{2}=\sqrt{15}\)

Hope this helps!

Answer:

17 feet 10 inches

Step-by-step explanation:

26 feet 10 inches is cut from a wire that is 44 feet 8 inches

Therefore the length of wire that is left can be calculated as follows

44 feet 8 inches - 26 feet 10 inches

= 17 feet 10 inches

The function f(x) in standard form as described in the task content is; 3x³ + 21x² - 23x + 5.

It follows from the task content that the function, f(x) which is as described is to be determined.

Since the polynomial remainder theorem postulates that;

Polynomial = (quotient × divisor) + remainder.

According to the given task content;

The quotient is; 3x² - 3x + 1.

The divisor is; (x + 8) and the remainder is; -3.

Therefore, the required polynomial is;

f(x) = (3x² - 3x + 1)(x + 8) + (-3)

= 3x³ + 24x² -3x² -24x + x + 8 - 3

= 3x³ + 21x² - 23x + 5.

Therefore, the required function, f(x) is; 3x³ + 21x² - 23x + 5.

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a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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Answer:

Maybe 7?

Sorry if it incorrect

Answer:

90°

-Sum of angles in a triangle= 180°

-angle C is 90°

-therefore angle A + angle B is,

180° - 90° = 90°

The formula for y in terms of x is a cubic equation:

y = 0.25*x³

We know that y is directly proportional to x³, then we can write the equation:

y = k*x³

Where k is the constant of proportionality.

In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:

250 = k*10³

250 = k*1,000

Dividing both sides by 1,000 we get:

250/1,000 = k

0.25 = k

Then the equation is:

y = 0.25*10³

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$9.86, Kendra donates to the charity.

Kendra worked 8 hours and 30 minutes last week

She earns $ 11.60 per hour

She will earn money if she works for 30 minutes = $(11.60/2)

Therefore,

Total amount of money she earns last week = $((11.60×8) + (11.60÷2))

                                                                            = $(92.8+5.80)

                                                                            = $98.6

Kendra donates 1/10th of the total money she earns in a week

Therefore,

Amount she donate last week = total amount she earns last week * 1/10

                                                         = $(98.6× (1÷10))

                                                         =$9.86

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Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

181.46 = A

Step-by-step explanation:

pi X r^2 is the area of a circle

the diameter is already given so you can skip the radius an jump straight into pi X d diameter = (r^2) giving you area pi X diameter

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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The size of the killers feet can be seen as 20 cm

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides..

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is represented as cos(θ) = adjacent/hypotenuse.

Cosine is used in trigonometry to solve problems involving angles and sides of right triangles, and they have many applications in fields such as engineering, physics, and navigation.

We have that;

Cos 12 = 20/x

x = 20/Cos 12

x = 20 cm

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Answer:

300 mg

Step-by-step explanation:

900 mg    spilled   1/3

1/3 * 900 = 900/3 = 300mg lost

Answer:

300 mg

Step-by-step explanation:

900 mg    spilled   1/3

1/3 * 900 = 900/3 = 300mg lost

Answer:

Step-by-step explanation:

Which formula can we use or find the circumference of a circle when we know the radius?

Answer:

\(\pi r^{2} \)

Step-by-step explanation:

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

Answer:

The probability that the proportion of flops in a sample of 701 released films would differ from the population proportion by greater than 7% is 0.00001

Step-by-step explanation:

We are given;

Probability that the films released are flops = 9% = 0.09

Sample size = 701

Formula for standard deviation is;

σ = √(p(1 - p)/n)

σ = √(0.09(1 - 0.09)/701)

σ = √0.0001168331

σ = 0.0108

We want to find the probability that the proportion of flops in a sample of 701 released films would be greater than 7%.

Thus, it means x - μ = 7% = 0.07

Z-score formula here is;

z = (x - μ)/σ

z = 0.07/0.0108

z = 6.4815

From online p-value from z-score calculator attached using; z = 6.4815, Nominal significance level = 0.05, two tailed distribution, we have;

P-value = 0.00001

The inequality that represents the sentence "The stadium held less than 25,000 people" is given as follows:

c < 25,000.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The amount is less than in this problem, hence the symbol is given as follows:

<.

As the amount is less than 25000, the inequality is given as follows:

c < 25,000.

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The cosine value is given as follows:

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

The tangent value is given as follows:

\(\tan{\theta} = -\frac{\sqrt{7}}{4}\)

First we must obtain the secant value, according to the identity presented as follows:

\(\sec^2{\theta} = 1 + \tan^{2}{\theta}\)

Replacing the tangent into the expression, we have that:

\(\sec^2{\theta} = 1 + \frac{7}{16}\)

\(\sec^2{\theta} = \frac{23}{16}\)

\(\sec{\theta} = \frac{\sqrt{23}}{4}\)

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

\(\cos{\theta} = \frac{1}{\sec{\theta}}\)

\(\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}\)

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

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Answer:

Total area of pyramid = 113.57 sq units

Step-by-step explanation:

Given that

Pyramid has a regular hexagonal with side, a = 4 units

Slant height = 6 units

To find: Total Area of pyramid = ?

Solution:

Total area of pyramid = Area of hexagon + Area of each triangular face

Area of hexagon is given as:

\(A = 6 \times \dfrac{\sqrt3}{4}a^2\\\Rightarrow A = 6 \times \dfrac{\sqrt3}{4}4^2\\\\\Rightarrow A = 41.57\ sq\ units\)

There are 6 triangular faces with base = 4 units and height as 6 units.

Area of 6 triangular faces:

\(6 \times \dfrac{1}{2} \times Base\times Height\\\Rightarrow 6 \times \dfrac{1}{2} \times 4\times 6\\\\\Rightarrow 72\ sq\ units\)

Total area of pyramid = 41.57 + 72 = 113.57 sq units

Step-by-step explanation:

the volume of such a regular cylinder is (as for any regular object) :

base area × height

and for a cylinder the base area is a circle, and its area is

pi×r²

so, combined, the volume of our cylinder is

pi×r²×height = pi×9²×26.5 = pi×81×26.5 =

= 6,743.428631... cm³

≈ 6,743 cm³

Answer:

I don't know

Step-by-step explanation:

it depends on your definition and question

The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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The graph of g(x) is represented by the equation g(x) = Root Index 3 Start Root x EndRoot-1.

Hence, the correct option is D) g(x) = RootIndex 3 Start Root x End Root–1

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\(\\ \sf\longmapsto XY+YZ=XZ\)

\(\\ \sf\longmapsto 7a+5a=6a+24\)

\(\\ \sf\longmapsto 12a=6a+24\)

\(\\ \sf\longmapsto 12a-6a=24\)

\(\\ \sf\longmapsto 6a=24\)

\(\\ \sf\longmapsto a=\dfrac{24}{6}\)

\(\\ \sf\longmapsto a=5\)

Value of a is 4 and value of YZ is 20 units

Step-by-step explanation:

Given:

Y is between point X and Z

Value of line XY = 7a

Value of line YZ = 5a

Value of line XZ = 6a + 24

Find:

Value of "a" and line YZ

Computation:

We know that

XY + YZ = XZ

So,

7a + 5a = 6a + 24

12a = 6a + 24

6a = 24

a = 4

Value of a = 4

So,

Value of line YZ = 5a

By putting value of a

Value of line YZ = 5(4)

Value of line YZ = 20 units

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The distance of the straight line is √17 miles and the angle formed is

75.96°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A bus drives 1 mile west and 4 miles north.

Let, The distance the bus travels along the west be adjacent and the distance traveled in the north be the height.

So, By Pythagoras' theorem,

The straight line distance = √(1² + 4²).

= √(1 + 16) miles.

= √17 miles.

Now, We know tan = opposite/adjacent.

tan = 4/1.

tan⁻¹(4/1) = Ф.

Ф = 75.96°.

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Answer:

84$

Step-by-step explanation:

1. 20% of 70  

0.20x70 = 14

2. Markup then add

70 + 14 = 84$

Answer:

6

Step-by-step explanation:

STATISTICS" is the 10 letters word in which "S" appears 3 times, "T" appears 3 times, "A" appears 1 time, "I" appears 2 times and "C" appears 1 times. To arrange this word letter "T" must be first letter so there is only one way to choose first place. Since vowel can not be the last letter there are 6 choices...

Answer:

14

Step-by-step explanation:

To make 166 a supplementary angle you should add 14 because supplementary angles equal 180.

Answer:

14

Step-by-step explanation:

Supplementary angles add to 180 degrees.

Let x be the unknown supplement

x+166 = 180

x+166-166 = 180-166

x =14

The unknown supplement is 14