Let a = (-4, 3) and 5 = (1, – 4). Find the angle between the vectors (in degrees) rounded to 2 decimal places.

Answer:

x ≈ 73.3

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos39° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{57}{x}\) ( multiply both sides by x )

x × cos39° = 57 ( divide both sides by cos39° )

x = \(\frac{57}{cos39}\) ≈ 73.3 ( to the nearest tenth )

Answer:

 \(\Large \text{$ \frac{1}{w^2} $}\)

Step-by-step explanation:

Given the exponential expression, \(\displaytext\mathsf{w^3\:\times\:w^{-5}}\), where it involves the multiplication of the same base, w, with varying powers.  

Using the Product Rule of Exponents, where it states that, \(\displaystyle\mathsf{a^{m}\:\times\:a^{n}\:=\:a^{(m\:+\:n)}}\).

Hence, we simply need to add the exponents:  

\(\displaytext\mathsf{w^3\:\times\:w^{-5}\:=\:w\:^{[3\:+\:(-5)]}\:=\:w^{-2}}\)

Next, apply the Negative Exponent Rule, where it states that: \(\displaystyle\mathsf{a^{-n}\:=\:\frac{1}{a^n}}\).

Transforming the negative exponent of  \(\displaytext\mathsf{w^{-2}}\)  becomes a positive exponent by using the Negative Exponent Rule.

  \(\displaytext\mathsf{w^{-2}\:=\:\frac{1}{w^2}}\)

Answer:

592 people must be surveyed

Answer:

The slope is 1 1/3.

Step-by-step explanation:

\(m=\frac{y2-y1}{x2-x1} \\m=\frac{-1-(-13)}{3-(-6)}\\m=\frac{12}{9}\\m=\frac{4}{3}\\m=1\frac{1}{3}\)

The sample means are Mean(Y) = 61.4 and Mean(X) = 15, the sample variances are Variance(Y) ≈ 1124.89 and Variance(X) ≈ 2.67, the sample standard deviations are Standard deviation(Y) ≈ 33.56 and Standard deviation(X) ≈ 1.63, the sample covariance is Covariance(X, Y) ≈ -131.69, and the sample correlation is Correlation(X, Y) ≈ -0.77.

a. To find the sample means, variances, and standard deviation, we can use the following formulas:

Sample mean of income (Y):

Mean(Y) = (100 + 65 + 47 + 112 + 34 + 85 + 92 + 83 + 67 + 29) / 10 = 614 / 10 = 61.4

Sample mean of education (X):

Mean(X) = (18 + 14 + 14 + 16 + 12 + 16 + 18 + 14 + 16 + 12) / 10 = 150 / 10 = 15

Sample variance of income (Y):

Variance(Y) = [(100 - 61.4)^2 + (65 - 61.4)^2 + (47 - 61.4)^2 + (112 - 61.4)^2 + (34 - 61.4)^2 + (85 - 61.4)^2 + (92 - 61.4)^2 + (83 - 61.4)^2 + (67 - 61.4)^2 + (29 - 61.4)^2] / 9 ≈ 1124.89

Sample variance of education (X):

Variance(X) = [(18 - 15)^2 + (14 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2 + (16 - 15)^2 + (18 - 15)^2 + (14 - 15)^2 + (16 - 15)^2 + (12 - 15)^2] / 9 ≈ 2.67

Sample standard deviation of income (Y):

Standard deviation(Y) = √Variance(Y) ≈ √1124.89 ≈ 33.56

Sample standard deviation of education (X):

Standard deviation(X) = √Variance(X) ≈ √2.67 ≈ 1.63

b. To find the sample covariance and correlation, we can use the following formulas:

Sample covariance:

Covariance(X, Y) = [(18 - 15)(100 - 61.4) + (14 - 15)(65 - 61.4) + (14 - 15)(47 - 61.4) + (16 - 15)(112 - 61.4) + (12 - 15)(34 - 61.4) + (16 - 15)(85 - 61.4) + (18 - 15)(92 - 61.4) + (14 - 15)(83 - 61.4) + (16 - 15)(67 - 61.4) + (12 - 15)(29 - 61.4)] / 9 ≈ -131.69

Sample correlation:

Correlation(X, Y) = Covariance(X, Y) / (Standard deviation(X) * Standard deviation(Y)) ≈ -131.69 / (1.63 * 33.56) ≈ -0.77

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Correct question-

Consider the following random sample of income and education: Income(Y) Education(X) 100 18 65 14 47 14 112 16 34 12 85 16 92 18 83 14 67 16 29 12 a. Find sample means, variances and standard deviation. b. Find sample covariance and correlation.

The probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

To calculate the probability of randomly selecting a homeowner and a renter from a small village of 300 residents with 190 homeowners and 110 renters in a sample of 20 residents, follow these steps:
1. Calculate the probability of selecting a homeowner (P(homeowner)).
P(homeowner) = Number of homeowners / Total number of residents = 190 / 300
2. Calculate the probability of selecting a renter (P(renter)).
P(renter) = Number of renters / Total number of residents = 110 / 300
3. Calculate the number of ways to choose 19 homeowners and 1 renter from the sample (Combination).
C(190,19) × C(110,1) = (190! / (19! × (190-19)!)) × (110! / (1! × (110-1)!))
4. Calculate the number of ways to select a random sample of 20 residents (Combination).
C(300,20) = 300! / (20! × (300-20)!)
5. Calculate the probability of selecting 19 homeowners and 1 renter from the random sample of 20 residents.
Probability = (C(190,19) × C(110,1)) / C(300,20)
By calculating these values, you will find the probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

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Answer:

9

Step-by-step explanation:

2(x=3)+3

6+3

9

It is nine

let the value be a

2x+3=a

2(3)+3=a

6+3=a

9=a

Answer:

it may be 9

..................

Answer:

11.05882 I think

Step-by-step explanation:

Reasoning:

g(x) = 4*ln(x)

g(x) = 2*2ln(x)

g(x) = 2*f(x)

Whatever the output f(x) is, it is doubled to get g(x). Recall that y = f(x), so we're really doubling the y values to visually stretch it vertically by a factor of 2. In short, g(x) is twice as tall compared to f(x).

Answer:

C. g(x) stretches f(x) vertically by a factor of 2.

Step-by-step explanation:

a p e x

Answer:

2/5, 8/25, 3/20, 37/100, 24/25

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that percentages are fractions of 100, we can convert these percentages:

Simplifying these fractions:

Therefore, the percentages as simplified fractions are listed above.

Answer:

y = 11

Step-by-step explanation:

It is just an equation with one variable ( 'y') which you can solve

-7y + 2 = - 75     subtract 2 from both sides of the equation

-7y = -77             divide both sides by -7

y = 11  

Answer:

-7y+2=-75

-7y=-75-2

-7y=-77

y=11

Hey there! :)

Answer:

15° Celsius.

Step-by-step explanation:

Begin by deriving an equation to represent the values in the table. Use the slope formula:

\(m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

Plug in values from the table into the formula:

\(m = \frac{27.0 - 22.2}{15-9}\)

Simplify:

\(m = \frac{4.8}{6}\)

Reduces to:

m = 0.8. This is the slope of the equation.

Use a point from the table and plug it into the equation y = mx + b, along with the slope to calculate the y-intercept:

27 = 0.8(15) + b

27 = 12 + b

27 - 12 = b

b = 15. This represents the value when x = 0, therefore:

The engine's temperature at rest is 15° Celsius.

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

i would say c

Answer:

C

Step-by-step explanation:

reason: notice that it says constant rate on a graph a constant rate is a straight line!! i really hope this helps!!

Answer:

36 cm³

Step-by-step explanation:

0.09 m × 100 cm / m = 9 cm

20 mm × 1 cm / 10 mm = 2 cm

V = LWH

V = 2 cm × 9 cm × 2 cm

V = 36 cm³

Answer:

the ture was

0.6 • 25 = x

6/10=x/25

x/25=60/100

the fault

6.0 • 25 = x

x • 1.6 = 25

60/100=25/x

The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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Using the slope concept, it is found that the base of the left field wall is 361 feet from a point on level ground directly below the top row.

In this problem:

Hence:

\(\tan{14^{\circ}} = \frac{90}{x}\)

\(0.249328 = \frac{90}{x}\)

\(0.249328x = 90\)

\(x = \frac{90}{0.249328}\)

\(x = 361\)

Hence, the base of the left field wall is 361 feet from a point on level ground directly below the top row.

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Answer:

1

Step-by-step explanation:

8-(+7)

8-7

answer is equal to 1

Answer:

She deposits $17.00 each week

Step-by-step explanation:

You multiply 85 times 0.2 which gives you 17.

Answer:

It would take 15 years

Step-by-step explanation:

The length of time it takes to reach $1,000 savings can be determined from the future value formula given below:

FV=PV*(1+r/4)^n*4

FV is the target savings of $1,000

PV is the amount invested which is $600

r is the rate of interest of 3.4%

n is the unknown

1000=600*(1+3.4%/4)^4n

1000=600*(1+0.0085 )^4n

1000=600*(1.0085)^4n

1000/600=1.0085^4n

1.666666667 =1.0085^4n

take log of both sides

ln 1.666666667 =4n ln 1.0085

4n=ln 1.666666667/ln 1.0085

4n=0.510825624 /0.008464078

4n=60.35218768

n=60.35218768 /4

n= 15.09  

The probability that only one phone call passes through a given minute, provided that the relay follows a Poisson distribution with a mean of 5 is 0.033689.

Here it is given that the number of phone calls that pass through a particular cell phone relay system follows a Poisson distribution. The time interval given here is of a minute.

For any Poisson distribution

P(X = x) = λˣ X e^(-λ) / x!

where λ = mean of the distribution.

x = the no. of times the event occurs in the time interval.

It is given that

λ = 5 calls per minute.

We need to find the probability that only n a given minute, the relay receives only one phone call.

Hence, x = 1

Therefore, the probability that only one phone call passes through in a given minute is

P(X = 1) = 5¹ X e^(-5) / 1!

= 0.033689

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The mean number of bedrooms per house is 2.83

From the question, we have the following parameters that can be used in our computation:

The table of values

The mean number in the housing estate is calculated as

Mean = Sum/Count

Using the above as a guide, we have the following:

Mean = (1.9 + 3.1 + 3.5)/3

Evaluate

Mean = 2.83

Hence, the mean is 2.83

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(a)If log₄​x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆​x = 8 the base is 6 and the logarithm is 8  then x = 1679616.

(a) In the equation log₄​x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.

(b) In the equation log₆​x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.

In both cases, we used the property of logarithms that states: if logₐ​x = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.

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Answer: 7 inches

Step-by-step explanation:

From the question, we are informed that the ratio of the side length of a square to the square's perimeter is always 1 to 4.

We are further told that Peter drew a square with a perimeter of 28 inches. The side length of the square Peter drew will be gotten by dividing 28 inches by 4. This will be:

= 28/4

= 7 inches

Therefore, the side length or the square is 7 inches.

The unit of measure that represents a metric unit dosage of strength is the gram (a).

In the metric system, the gram is the standard unit for measuring mass or weight. It is commonly used in the healthcare field to quantify the amount or dosage of medication or drug strength.

Medications are often prescribed and administered in specific gram amounts, indicating the quantity of the active ingredient in the medication. For example, a doctor may prescribe a medication dosage of 500 milligrams (mg), which is equivalent to 0.5 grams.

On the other hand, grains (b), ounces (c), and tablespoons (d) are not typically used as metric units of measure for medication dosage strength. Grains are more commonly used in the imperial system, especially in the United States, to measure the weight of medications. Ounces and tablespoons are used to measure volume or liquid medications rather than dosage strength.

In the context of metric unit dosage strength, the gram is the most appropriate and commonly used unit of measure.

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The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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According to the Question predicts that there are 24 highway signs throughout the journey.

Length can indeed be measured in a variety of ways, including handspan, foot span, meters, inches, and millimeters. There are two categories of length measurement units: There are conventional units for measuring length and nonstandard ones.

Division will help us resolve this issue. We may calculate of highway signs by dividing the overall driving time, 19.2 hours, by the 0.8-hour includes an aspect interval.

\(\sf \dfrac{19.2 \ hours}{0.8 \ hours/sign} =24\)

Therefore, there will be 24 highway signs on the road trip.

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