At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f(n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)? f(n)=2.75+4.75+f(n−1),f(0)=2.75 f(n)=4.75+f(n−1),f(0)=2.75 f(n)=2.75+4.75n,n>0 f(n)=(2.75+4.75)n,n>0

The magnetic field using the unit vector notation B = Bx i= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i.

To determine the strength and direction of the magnetic field at the (1 cm, 0 cm, 0 cm) position caused by a moving proton, we can use the formula for the magnetic field produced by a moving charge:

B = (μ₀ / 4π) * (qv × r / r³)

where B is the magnetic field, μ₀ is the permeability of free space (constant), q is the charge of the proton, v is its velocity, × denotes the cross product, r is the position vector, and r³ represents the magnitude cubed of the position vector.

Given information:

u = -1.0 x 10⁷ m/s (velocity of the proton)

Position vector r = 1 cm i

Let's calculate the magnetic field at the given position:

First, we convert the position vector from centimeters to meters:

r = (1 cm, 0 cm, 0 cm) = (0.01 m, 0 m, 0 m)

Next, we substitute the values into the formula and simplify:

B = (μ₀ / 4π) * (qv × r / r³)

= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / (0.01 m)³)

= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 0.000001 m³)

= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) × (0.01 m i) / 10^-18 m³)

= (μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²) i

Now, we can express the magnetic field using the unit vector notation:

B = Bx i

= [(μ₀ / 4π) * (q * (-1.0 x 10⁷ m/s) / 10^-16 m²)] i

where Bx represents the magnitude of the magnetic field in the x-direction.

Please note that the direction of the magnetic field will depend on the orientation of the velocity vector of the proton.

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The required answers are:

(a) GCD = 40        (b) LCM = 36000      (c) GCD = 33        (d) LCM = 1032933

GCD and LCM of the given numbers are:

(a) Prime factors of 360: 2 x 2 x 2 x 3 x 3 x 5.Prime factors of 4000: 2 x 2 x 2 x 2 x 5 x 5 x 5.GCD = 2 x 2 x 2 x 5 = 40.

(b) LCM = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 = 36000.

(c) Prime factors of 627: 3 x 11 x 19.Prime factors of 205143: 3 x 3 x 7 x 7 x 11.GCD = 3 x 11 = 33.

(d) LCM = 3 x 3 x 7 x 7 x 11 x 19 = 1032933.

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Answer: Nicole can spend up to 7 hours in the boat.

Step-by-step explanation:

Based on the information given in the question, the possible number of hours that can be used will be calculated as thus:

(6 × t) - 9 ≤ 33

6t - 9 ≤ 33

Collect like terms

6t ≤ 33 + 9

6t ≤ 42

Divide both side by the coefficient of t

6t/6 ≤ 42/6

t ≤ 7

Nicole can spend up to 7 hours in the boat.

Answer: d. 201.06

Step-by-step explanation:

To find area of a circle we use the equation 2pi(r) or in this case 2*pi(16)= 804.25in^2 but since we are looking for the shaded region which is 1/4 or one-fourth of the circle so divide 804.25/4 to get 201 or specifically 201.06

Answer:

x = 12

z = 101

Step-by-step explanation:

Hello There!

First lets find z

Well the angle that has a measure of 79 degrees and angle z are supplementary angles meaning that the sum of the two is 180

So we can find the missing angle by subtract the given angle (79 in this case) from 180

180 - 79 = 101 so z = 101

Now lets find x

The angle that has a measure of 79 degrees and the angle labeled (6x+7) are vertical angles

If you didn't know vertical angles are congruent

That being said lets create an equation to solve for x

79 = 6x + 7

now we solve for x

step 1 subtract 7 from each side by

7 - 7 cancels out

79 - 7 = 72

now we have 72 = 6x

step 2 divide each side by 6

72/6=12

6x/6=x

we're left with x = 12

Answer:

X axis labels aren't evenly spaces

Y axis has no origin

Missing label

Step-by-step explanation:

Scale of a graph is important when displaying numerical data on a plot.

Based on the bar chart given, it could be seen that the x axis which is labeled days of the week is not adequately spaced. Data on both axis should he a recognizable.

2.)

Taking a look at the graph, it has no origin, the numbering of the vertical axis, number of text messages should start from 0

3.) Also, the x and y axis aren't labeled Hence charts should be well labeled to include x - axis and y-axis.

Answer:

X axis labels aren't evenly spaces

Missing label

there us no scale written starting at 0

Step-by-step explanation:

this will give u 3/3

Answer:

12:2

4:24

6:1

Step-by-step explanation:

those 3 are the correct ones

The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.

To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:

A = P * [tex]e^{(rt)[/tex],

where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:

0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,

Simplifying the equation, we have:

[tex]e^{(0.5)[/tex] = k / 6600.

Now, we can solve for k by multiplying both sides of the equation by 6600:

k = 6600 * [tex]e^{(0.5)[/tex],

Using a calculator or software, we find that k is approximately $943.57 per year.

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Answer:

14

Step-by-step explanation:

√196

Calculate the square root of 196 and get 14.

14

Answer:

= 5/9 + 1/3

=5/9 + 3/9

= 5+3/9

=8/9

The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)

Let's denote p as the proportion of orders that are not accurate.

The sample proportion of orders that are not accurate is given by:

p(bar) = 70 / (239 + 70)

= 70 / 309

≈ 0.226

The standard error of the proportion is calculated as:

SE = √[(p(bar)(1 - p(bar))) / n]

= √[(0.226(1 - 0.226)) / 309]

≈ √(0.1785 / 309)

≈ 0.0267

To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.

Margin of error = 1.96 × SE

≈ 1.96 × 0.0267

≈ 0.0523

Now we can construct the confidence interval:

Lower limit = p(bar) - Margin of error

= 0.226 - 0.0523

≈ 0.1737

Upper limit = p(bar) + Margin of error

= 0.226 + 0.0523

≈ 0.2783

Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).

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Answer: jet travels a total of 2000 km in total

Step-by-step explanation:

If utility function is given then we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.

(a) To find the probabilities p1 and p2, we set up the equation U(45) = p1 * U(20) + (1 - p1) * U(150) and solve for p1. Similarly, we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.

(b) The selling price of a lottery is the amount at which an individual is willing to sell the lottery. We compare the expected utility of the lottery to the utility of the certain amount. The risk premium is the difference between the selling price and the expected value of the lottery.

(c) The buying price is the amount an individual is willing to pay for a lottery. We set up the equation U(45) = p * U(150) + (1 - p) * U(45) and solve for p to find the buying price.

Note: The specific calculations for parts (a), (b), and (c) require the values of U(X) for each corresponding X value in the utility function.

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30 x 30 = 900

This is the surface area of one side

900 x 6

Multiply by 6 to get the surface area of all 6 sides of the cube

900 x 6 = 5400

Complete question :

Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. H : Pi - P2 - Select your answer HA : P1 P2 - Select your answer - b. What is the sample proportion indicating that their financial security was more than fair in 2012? Round your answer to two decimal places. In 2010?

Answer:

H0 : p1 - p2 = 0

H1 : p1 - p2 ≠ 0

Phat 2010 = 0.35

Phat 2012 = 0.41

Step-by-step explanation:

The null and alternative hypothesis :

H0 : p1 - p2 = 0

H1 : p1 - p2 ≠ 0

The null means there is no difference in proportion for the two years while the alternative claims that there is difference in proportion for the two years.

Sample proportion for 2010:

Phat = x / n

x = 315 ; n = 900

Phat = 315 / 900

Phat = 0.35

Sample proportion for 2012 :

Phat = x / n

x = 410 ; n = 1000

Phat = 410 / 1000

Phat = 0.41

Answer:

x=50 degrees

Step-by-step explanation:

I'm not sure but hope this helps and have a  wonderful day!!!!

Answer:

x = 48

Step-by-step explanation:

2x + 10 + x + 26 = 180

3x + 36 = 180

3x = 180 - 36

3x = 144

x = 48

Answer:

2) $1797

3) $152

4) $5,378

Answer:

Cosec <F = 73/55

Step-by-step explanation:

In ΔEFG, the measure of ∠G=90°, GF = 48, EG = 55, and FE = 73. What ratio represents the cosecant of ∠F?

First you must know that;

Cosecant <F = 1/sin<F

Given

∠G=90°, GF = 48, EG = 55, and FE = 73.

ED ,= hyp = 73

EG = opp = 55*side facing <F

Using DOH CAH TOA

Sin theta = opp/hyp

Sin <F= 55/73

Reciprocate both sides

1/sinF = 73/55

Cosec <F = 73/55

Answer:

W is either less than or( less than or equal to)

Step-by-step explanation:

I do not know what shows if something is equal to so the best answer I can think if is less than -2 as it looks like W is everything lower or equal to -2

We have:

[tex]2x \cdot (5^2)[/tex]

[tex]= 2x \cdot 25[/tex]

[tex]= \boxed{50x}[/tex]

The final result of the given expression is 49.4.

Part A: In  the missing expression should be the result of squaring three and adding four.

This is because the expression in Step 2 states "the quantity of the sum of three squared plus four divided by 0.25.

" Therefore, to continue simplifying the expression, we need to evaluate the value of the sum of three squared plus four.

The quantity of [tex](3^2 + 4)[/tex] divided by 0.25

To solve Step 3, we first evaluate the expression inside the parentheses:

[tex]3^2 + 4 = 9 + 4 = 13[/tex]

So, Step 3 becomes:

The quantity of 13 divided by 0.25

Part B: In the missing expression should be the result of dividing 13 by 0.25.

This is because in Step 4, the expression is "the quotient of the quantity 13 divided by 0.25 end quantity minus 10.4 divided by 4."

To simplify further, we need to calculate the value of 13 divided by 0.25.

13 divided by 0.25

To solve Step 6, we perform the division:

13 ÷ 0.25 = 52

So, it becomes:

52 minus 10.4 ÷ 4

Following the remaining steps:

52 minus (10.4 ÷ 4) = 52 - 2.6 = 49.4

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The correct answers for the given data are (a) b = 6, (b) arg(z - 9) = -π/4, and (c) ||w/w|| = 1.

(a) To determine z/w, we first need to express z and w in terms of their real and imaginary parts. Given 2 = 3 + 6i, we can rewrite it as z = 3 + 6i. Similarly, w = a + bi. Now, let's calculate z/w:

z/w = (3 + 6i)/(a + bi)

To make z/w real, the imaginary part of the denominator should cancel out the imaginary part of the numerator. This means 6/a = 6i/b. Simplifying further, we get ab = 6a + 6bi. Since a and b are real numbers, the only way for the equation to hold is if b = 6 and a = 1. Therefore, b = 6.

(b) To determine arg(z - 9), we need to subtract 9 from z = 3 + 6i:

z - 9 = (3 + 6i) - 9 = -6 + 6i

The argument (or angle) of -6 + 6i can be calculated as:

arg(-6 + 6i) = arctan(6/(-6)) = arctan(-1) = -π/4

(c) To determine ||w/w|| (the magnitude of w divided by the magnitude of w), we need to find the magnitude of w. Given w = a + bi, the magnitude of w is given by:

||w|| = √(a^2 + b^2)

Now, substituting a = 1 and b = 6 (from part a):

||w|| = √(1^2 + 6^2) = √37

Therefore, ||w/w|| = ||w||/||w|| = 1.

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Answer:

A

Step-by-step explanation:

(6,4)

3x-1y=14

-y= 3x-14

y=-2x+16

sub in first equation

3x-14 =-2x+16

3x+2x= 16 +14

5x = 30

x = 6

plug in x

y=-2x+16

y = -2(6)+16

y = 4

(6,4)

Answer:

C

Step-by-step explanation:

The lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.

To find the lengths of the sides of the triangle with vertices A(3, 4, 1), B(0, 6, 2), and C(3, 5, 6), we can use the distance formula.

The distance formula between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in three-dimensional space is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)

Let's calculate the lengths of the sides of the triangle:

Side AB:

d₁ = √((0 - 3)² + (6 - 4)² + (2 - 1)²)

= √((-3)² + 2² + 1²)

= √(9 + 4 + 1)

= √14

Side BC:

d₂ = √((3 - 0)² + (5 - 6)² + (6 - 2)²)

= √(3² + (-1)² + 4²)

= √(9 + 1 + 16)

= √26

Side AC:

d₃ = √((3 - 3)² + (5 - 4)² + (6 - 1)²)

= √(0² + 1² + 5²)

= √(0 + 1 + 25)

= √26

Now, let's analyze the triangle based on the lengths of its sides:

Since all three sides have different lengths (√14, √26, and √26), the triangle is neither an isosceles triangle (which has at least two sides of equal length) nor a right triangle (which satisfies the Pythagorean theorem).

In summary, the lengths of the sides of the triangle ABC are √14, √26, and √26, and the triangle is neither a right triangle nor an isosceles triangle.

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Answer:

area of trapezoid = 1/2×(a+b)×height

area of trapezoid =1/2×(15m+7m)×7m

area of trapezoid =1/2×22m×7

area of trapezoid =77m²

area of trapezoid =1/2×(a+b)×height

area of trapezoid =1/2×(9ft+12ft)×4ft

area of trapezoid =1/2×21ft×4ft

area of trapezoid =42ft²

Answer:

You asked this question like 4 times

Step-by-step explanation:

The answer is

(5,-1)

(-4,0)