What is the multiplicity of the zero of the polynomial function that represents the volume of a sphere with radius x+5

The value of sin(θ) is - (4/3)√5 when cos(θ) = 1/9 and θ is in the fourth quadrant.

Given the value of cosθ=1/9 and θ is in the 4th quadrant. We have to find the value of sinθ.

Let us try to plot it in the fourth quadrant.

Since the value of cosine is positive in the fourth quadrant, we have drawn an angle making an acute angle with the negative direction of x-axis. Now, we can use Pythagorean identity as:

cos²θ + sin²θ = 1

sin²θ = 1 - cos²θ

sinθ = ±√(1 - cos²θ)

Since the angle is in the fourth quadrant, the value of sinθ is negative. Hence, sinθ = - √(1 - (1/9)²)

Now, simplify it. We get:

sinθ = - √(80/81)

sinθ = - √80/9

sinθ = - (4/3)√5

Thus, the value of sin(θ) is - (4/3)√5 when cos(θ) = 1/9 and θ is in the fourth quadrant.

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The coordinates of point on the x-axis of the line is given as follows:

(2,0).

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

When two lines are parallel, they have the same slope.

The slope of the line AB is given as follows:

m = -3/6 (change in y from A to B divided by change in x).

m = -0.5.

Hence:

y = -0.5x + b

From point C, when x = -2, y = 2, hence the intercept b is obtained as follows:

2 = -0.5(-2) + b

1 + b = 2

b = 1.

Hence the function is given as follows:

y = -0.5x + 1.

The x-intercept is obtained as follows:

-0.5x + 1 = 0

0.5x = 1

x = 1/0.5

x = 2.

Hence the coordinates are given as follows:

(2,0).

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It would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.

To calculate the time it will take to pay off a credit card balance, we need to consider the interest rate, the balance, and the monthly payment. In your question, you mentioned an annual interest rate of 18% and a monthly payment of $55.

First, let's convert the annual interest rate to a monthly interest rate. We divide the annual interest rate by 12 (the number of months in a year) and convert it to a decimal:

Monthly interest rate = (18% / 12) / 100 = 0.015

Next, we can calculate the number of months it will take to pay off the balance. Let's assume there are no additional charges or fees added to the balance:

Balance = $3052.41

Monthly payment = $55

To determine the time in months, we'll use the formula:

Number of months = log((Monthly payment / Monthly interest rate) / (Monthly payment / Monthly interest rate - Balance))

Using this formula, the calculation would be:

Number of months = log((55 / 0.015) / (55 / 0.015 - 3052.41))

Calculating this equation gives us approximately 140.3 months.

Since we want to find the number of years, we divide the number of months by 12:

Number of years = 140.3 months / 12 months/year ≈ 11.7 years

Therefore, it would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.

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Answer:

9 x 10^-3

Step-by-step explanation:

The fraction of recipes she would have tried in the book after 1 year is 13/125.

It is required to find the the fraction of recipes.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Total recipes in the book= 1,000

Recipe tried each week = 2

We have to find the fraction of recipe she would have tried after 1 year.

We know that there are 52 weeks in 1 year.

Total recipe she tried in a year

=total number of  weeks in a year*number of recipe tried each week

=52*2

=104

fraction of recipe she would have tried after 1 year

=104/1000

=13/125

Therefore, the fraction of recipes she would have tried in the book after 1 year is 13/125.

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The given number is

Here we need to use a power property

As you can see, the property allows us to move the position of the power in order to have a positive exponent. Let's do that

The new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

(a) To find the angle that the pilot should turn to head towards Louisville, we first need to find how far off course the pilot has gone in 15 minutes. At an average speed of 220 miles per hour, the pilot would have flown a distance of:

d = rt = 220 mi/hr × (15 min / 60 min/hr) = 55 miles

Since the pilot was 10 degrees off course, they have effectively traveled 10/360 of the circumference of a circle with radius 55 miles. The length of this arc is:

s = rθ = 55 mi × (10/360) = 1.528 mi

To head towards Louisville, the pilot needs to turn to a heading that is 10 degrees in the opposite direction. The angle θ that the pilot needs to turn is given by:

θ = 2arctan(s/2d) = 2arctan(1.528 mi / 2(330 mi)) ≈ 0.266 radians ≈ 15.26 degrees

So the pilot needs to turn approximately 15.26 degrees to head towards Louisville.

(b) Let's call the distance the pilot needs to travel after correcting course "x". We can use the formula for distance to find "x":

x = 330 mi - 2(55 mi) = 220 mi

To complete the trip in a total time of 90 minutes, the pilot must spend 75 minutes flying at the new speed and 15 minutes turning to the correct heading. Therefore, the time spent flying at the new speed is 75 minutes - 15 minutes = 60 minutes. The new speed can be found using the formula for average speed:

average speed = total distance / total time

We want the new speed to cover a distance of 220 miles in 60 minutes:

average speed = 220 mi / (60 min / 60) = 220 mi/hr

So the new average speed that the pilot should maintain to complete the trip in 90 minutes is 220 miles per hour.

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SOLUTION:

Case: Probability

Given:

20% of cars travelling in a certain diamond lane have fewer than three passengers.

Fifty cars are selected at random.

If 20% have less than 3 passengers. p= 0.20

Then 80% have greater than or equal to 3 passengers, q= 0.80

Total sample,

n= 50

sample, x= 15.

The relation r can be defined as follows: for any two elements a and b in set A, (a, b) belongs to relation r if there exists a positive integer n such that a^n = b.

Considering the set A = {2, 4, 8, 10, 16, 64}, let's examine the pairs (a, b) that satisfy the relation r:

- (2, 4): Since 2² = 4, (2, 4) belongs to r.

- (4, 16): As 4² = 16, (4, 16) satisfies the relation.

- (8, 64): Given 8² = 64, (8, 64) is part of r.

- (10, 100): Since 10² = 100, (10, 100) satisfies the relation.

However, there are no pairs (a, b) where a and b have different values and still satisfy the relation r. For example, (2, 8) or (8, 10) are not part of r because there is no positive integer n that satisfies the equation a^n = b.

In summary, the relation r on set A = {2, 4, 8, 10, 16, 64} consists of pairs (a, b) where a and b have the same value and can be related through exponentiation with a positive integer exponent.

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An airline ticket costs $40. The price is increased by 200 percent. The absolute increase is $80.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Cost of airline ticket = $40.

Increase in price = 200% of $40

Absolute increase = \(\frac{200}{100}* 40 = 80\)

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Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given :

A discrete random variable's anticipated value

So, in order to determine the expected value of a discrete random variable,

we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,

where weights are the probability of that outcome.

Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

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ANOVA is a valuable tool for comparing means across multiple groups and determining if there are significant differences among them.

ANOVA (Analysis of Variance) is a statistical procedure used to compare the means of two or more groups to determine if there are statistically significant differences among them. It helps to determine whether the observed differences in group means are due to actual group differences or simply due to random variation.

The ANOVA procedure compares the variation within each group (within-group variability) to the variation between the groups (between-group variability). If the between-group variability is significantly larger than the within-group variability, it suggests that there are true differences in the means of the groups.

By performing hypothesis testing, ANOVA calculates an F-statistic and compares it to a critical value from the F-distribution. If the calculated F-statistic exceeds the critical value, it indicates that there are significant differences in means among the groups, and we reject the null hypothesis that all group means are equal.

ANOVA does not identify which specific group means are different from each other; it only tells us if there is a statistically significant difference among the means. To determine which groups are different, posthoc tests or pairwise comparisons can be conducted.

Overall, ANOVA is a valuable tool for comparing means across multiple groups and determining if there are significant differences among them.

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Answer:

37.8579

This value is approximate and rounded to four decimal places

===============================================

Explanation:

The tangent function is being applied to some unknown angle x. To isolate x, we undo whatever tangent is doing. So we apply the inverse function. Specifically the inverse tangent function. This is also known as "arctangent" and your calculator most likely shows it as a button with a "-1" exponent above the "tan"

So apply the arctangent to both sides to get

tan(x) = 0.7773

arctan(tan(x)) = arctan(0.7773)

x = 37.8579

heres a diagram to help

Answer:

\(< -0.902, 0.431 >\)

Step-by-step explanation:

The unit vector of any vector is the vector that has the same direction as the given vector, but simply with a magnitude of 1. Therefore, if we can find the magnitude of the vector at hand, and then multiply \(\frac{1}{||v||}\), where ||v|| is the magnitude of the vector, then we can find the unit vector.

Remember the magnitude of the vector is nothing but the pythagorean theorem essentially, so it would be \(\sqrt{(-6.9)^{2} +(3.3)^{2} } ,\) which will be \(\sqrt{58.5}\). Now let us multiply the vector by 1 over this value, and rationalize to make your math teacher happy.\(< -6.9, 3.3 > * \frac{1}{\sqrt{58.5}} = < \frac{-6.9\sqrt{58.5} }{58.5} , \frac{3.3\sqrt{58.5}}{58.5} >\)

You can put those values into your calculator to approximate and get

\(< -0.902, 0.431 >\)

You can always check the answer by finding the magnitude of this vector, and see that it is equal to 1.

Hope this helps

=- No way

Step-by-step explanation:

Answer:

its now proved

Step-by-step explanation:

Answer:

using this identies

easy too solve this question

When y = 100, x is approximately equal to 0.04.

If y varies inversely as x^2 and y = 16 when x = 5, we can find the values of x and y when y = 100.

To solve this problem, we can use the inverse variation formula, which states that y = k/x^2, where k is the constant of variation.

Given that y = 16 when x = 5, we can substitute these values into the formula to find the value of k.

16 = k/(5^2)
16 = k/25

To find k, we can cross multiply:
16 * 25 = k
400 = k

Now that we know the value of k, we can use it to find the value of y when x = 100.

y = k/(100^2)
y = 400/(100^2)
y = 400/10000
y = 0.04

Therefore, when y = 100, x is approximately equal to 0.04.

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In a right-skewed distribution, the correct answer is b. the median is less than the mean. In a right-skewed distribution, the data has a longer tail on the right side, indicating that there are more values greater than the mean. This causes the mean to be greater than the median.

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Answer:

Step-by-step explanation:

f(x)=2x-3, for f(x)=9

2(9)-3

18-3=

Answer:

The answer is -285

Step-by-step explanation:

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48

The requried length of the arc MN is evaluated as 6π.

From the figure,
The area of the shaded sector is given as:

A = ∠NLM/360×πr²

27π= ∠NLM/360×π9²
∠NLM = 120

Now,

length MN = 120/360*2πr

                  = 1/3×2π×9
                  = 6π

Thus, the requried length of the arc MN is evaluated as 6π.

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Answer:

3

Step-by-step explanation:

Answer: The answer is 4

Step-by-step explanation:
the x is equal to an exponent. Since 3x4 equals 12, and 12+3 equals 15

Answer:

I'm not sure but I think the second one. 12.5 < x < 18.9

Step-by-step explanation:

Answer:

B. 12.5 < x < 18.9

Step-by-step explanation:

on edge

Sarah and Joshua both use correct trigonometry expressions to find out the height of garage wall.

Sarah and Joshua serving to estimate the height of a parking garage using a 50 yards-long rope.

Joshua is in the floor while Sarah stands on the top of garage. Each holds an end of the rope. Joshua walks away until the rope is completely tense,

making an angle of 30° with the floor and an angle 60° with the top.

Joshua determined the height of the wall is 25 yards with the help of trigonometry expression for Sin, and Sarah determined by Cos.

So, let us examine whose approach is correct,

We have length of rope is 50 yards and the angle with floor is 30 and angle with top is 60°

first examine the approach of Joshua,

according to trigonometry, we have

\(Sin\theta=\frac{perpendicular}{hypotenuse}\)

\(Sin30=\frac{h}{50}\)

\(\frac{1}{2} =\frac{h}{50}\)

thus, h =25 yards,

now come on the approach of Sarah

\(cos\theta=\frac{base}{hypotenuse}\)

\(cos60=\frac{h}{50}\)

thus, h=25 yards.

According to our examination both Joshua and Sarah have corrected approaches.

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Answer:

Sample survey.

Step-by-step explanation:

In this scenario, a company redesigned its website and wishes to collect data so as to see if the website is user friendly. Thus, the best way to collect the data is through a sample survey from some members of the total website users.

A sample survey is a statistical method used for the collection of data from a target population in order to draw an inference and reach a logical conclusion.

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

There are various types of sampling used by researchers and these are;

1. Random sampling.

2. Systematic sampling.

3. Stratified sampling.

4. Cluster sampling.

Answer:

sample survey

Step-by-step explanation:

edgen

Answer:

18

Step-by-step explanation:

the ratio of blue eyed students to non-blue eyed students is 7 to 12,

Total ratio = 7+12=19

Total student= 50 students

Ratio of blue eyes student= 7/19 ×50

=18.4

Hence, there are approximately 18 students with blue eyes.