joe drives a golf cart when he needs to monitor the security of his neighborhood. he can cover the 49 miles of streets in his neighborhood in 2 hours. what unit rate expresses the speed of Joeys golf cart per hour?


A. 10 miles per hour
B. 15 miles per hour
C. 20 miles per hour
D. 30 miles per hour​

Therefore, Morris is traveling at a rate of 70.33 feet per second, which is more accurate than 50 miles per hour.

To determine which measurement is more accurate, we need to convert both rates to the same unit. Since Aneesha's rate is given in miles per hour and Morris's rate is given in feet per second, we need to convert one of them to match the other.

First, let's convert Aneesha's rate to feet per second:

Aneesha's rate = 50 miles per hour

1 mile = 5280 feet

1 hour = 3600 seconds

50 miles per hour = (50 * 5280) feet per (1 * 3600) seconds

= 264,000 feet per 3,600 seconds

= 73.33 feet per second (rounded to two decimal places)

Now let's calculate Morris's rate, which is 3 feet per second less than Aneesha's rate:

Morris's rate = 73.33 feet per second - 3 feet per second

= 70.33 feet per second (rounded to two decimal places)

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The series is given as

3,12,21..........

The first term is 3 .

To determine the common difference, subtract second term frim te

Answer:

A

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

A (- 6, - 12 ) → B (6, - 12 )

Answer:

8

Step-by-step explanation:

4.60=0.2t+0.5f

t=20 cent coins

f=fifty cent coins

t+f=14

multiply the second equation by 0.5 to eliminate the f and subtract one equation from another.

    4.60=0.2t+0.5f

   -(7      =0.5t+0.5f)

-------------------------------

    -2.4= -0.3t

multiply both sides by -0.3 to get 8=t. That's the # of 20 cent coins.

The rest allowance for chopping down a tree is 0.67 hours (rounded to two decimal places) or 40 minutes. In an 8-hour shift, approximately 40 minutes should be allowed for rest.

To calculate the rest allowance, we need to determine the energy expenditure for chopping down a tree and convert it into a time duration.

Given that the energy expenditure associated with chopping down a tree is 8.0 kcal/min, we can calculate the rest allowance using the following formula:

Rest allowance = Energy expenditure (kcal/min) * Time duration (min) / Energy content of food (kcal).

As the rest allowance is typically a fraction of the energy expenditure, we can use the value of 0.25 (25%) as the input for the rest allowance calculation.

Rest allowance = 8.0 kcal/min * Time duration (min) / Energy content of food (kcal) = 0.25.

Solving for the time duration, we find:

Time duration (min) = 0.25 * Energy content of food (kcal) / 8.0 kcal/min.

To determine the time duration in hours, we divide the time duration in minutes by 60:

Time duration (hours) = Time duration (min) / 60.

The specific energy content of food is not provided in the question. Therefore, without knowing the energy content, we cannot calculate the exact time duration for the rest allowance.

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Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

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Let's refer to the chocolate cookies using the variable c, and the oatmeal cookies using the variable o.

Using the information we have, we can set up two equations for the two different transactions.

4c + 9o = 126

8c + 5o = 122

Now, we need to solve for one of the variables in the first equation. I will solve for o.

4c + 9o = 126

9o = 126 - 4c

o = 14 - 4/9c

Next, we'll take this value for o and plug it into the second equation for the variable o. Then we can solve for c.

8c + 5(14 - 4/9c) = 122

8c + 70 - 2 2/9c = 122

5 7/9c + 70 = 122

5 7/9c = 52

c = 9

Finally, we can use the value of c and plug it back into the first equation to solve for o.

o = 14 - 4/9(9)

o = 14 - 4

o = 10

1 dozen chocolate cookies costs $9

1 dozen oatmeal cookies costs $10

Hope this helps!

Answer:

-4/5

Step-by-step explanation:

sin theta = opp/ hyp

sin theta = -3 /5

Using the Pythagorean theorem

opp ^2 + adj ^2 = hyp ^2

(-3) ^2 + adj ^2 = 5^2

9+ adj ^2 = 25

adj ^2 = 25 - 9

adj ^2 = 16

Taking the square root of each side

adj = ±4

Since we are in the 3rd quadrant  sin and cos are both negative so adj must be negative

adj = -4

cos theta = adj / hyp

cos theta = -4/5

Answer: 8/5

Step-by-step explanation:

\((g \circ h)(-3)\) is the same as g(h(-3)).

\(h(-3)=4-(-3)=7\\g(h(-3))=g(7)=\frac{7+1}{7-2}=\boxed{\frac{8}{5}}\)

Given that sentence forms are (pv-q) = (p>~q) and p=(-q~p), we need to use truth tables to determine whether they are logical truths (tautologies), logical falsehoods (contradictions), or contingent.

a. (pv-q) = (p>~q)The truth table for (pv-q) is:| p | q | p v q | ¬q | ¬q → p | p → ¬q | p v q = (p → ¬q) ||---|---|--------|----|-------|-----------|------------------|---|| F | F | F      | T  | T     | T         | F                | T || F | T  | T      | F  | T     | T         | T                | F || T  | F  | T      | T  | F     | F         | T                | F || T  | T  | T      | F  | T     | T         | T                | T |

Since (pv-q) = (p>~q) is true in all four rows, it is a logical truth (tautology).

b. p=(-q~p)The truth table for p=(-q~p) is:| p | q | -q | ~p | -q ∨ ~p | p = (-q ∨ ~p) ||---|---|---|----|--------|-----------------|---|| F | F | T | T  | T      | F               | F || F | T  | F | T  | T      | F               | F || T  | F  | T | F  | T      | F               | F || T  | T  | F | F  | F      | T               | T |Since p=(-q~p) is true in some rows and false in others, it is contingent.

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Therefore, the equation \(+3 + 5(2n - 1)^2 + n^2 + D(n + 2)\) is true for every positive integer n.

To verify the equation for every positive integer n using induction, we'll follow the steps of mathematical induction.

Step 1: Base Case

Let's check if the equation holds true for n = 1.

For n = 1:

\(3 + 5(2(1) - 1)^2 + 1(1) + D(1 + 2)\)

\(3 + 5(1)^2 + 1 + D(3)\)

3 + 5 + 1 + D(3)

9 + D(3)

At this point, we don't have enough information to determine the value of D. However, as long as the equation holds for any arbitrary value of D, we can proceed with the induction.

Step 2: Inductive Hypothesis

Assume that the equation holds true for an arbitrary positive integer k. That is:

\(3 + 5(2k - 1)^2 + k^2 + D(k + 2)\)

Step 3: Inductive Step

We need to prove that the equation also holds true for n = k + 1, based on the assumption in the previous step.

For n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\\3 + 5(2k + 1)^2 + (k + 1)^2 + D(k + 3)\)

Expanding and simplifying:

=\(3 + 5(4k^2 + 4k + 1) + (k^2 + 2k + 1) + D(k + 3)\\3 + 20k^2 + 20k + 5 + k^2 + 2k + 1 + Dk + 3D\)

Combining like terms:

=\(21k^2 + 22k + 9 + Dk + 3D\)

Now, we compare this expression with the equation for n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\)

We can see that the expression obtained in the inductive step matches the equation for n = k + 1, except for the constant terms 9 and 3D.

As long as we choose D in a way that makes 9 + 3D equal to zero, the equation will hold true for n = k + 1 as well. For example, if we set D = -3, then 9 + 3D = 9 - 9 = 0.

Step 4: Conclusion

Since the equation is true for the base case (n = 1) and we have shown that if it holds for an arbitrary positive integer k, it also holds for k + 1, we can conclude that the equation is true for every positive integer n.

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Therefore:P(θ < M) = 1andP(θn = -min(X₁,X₂,...,Xₙ) > M) → 0 as n → ∞This implies that θn converges to θ in probability as n → ∞, and thus the maximum likelihood estimator is consistent.

a) The likelihood function is:L(θ|x₁, x₂, ..., xₙ) = f(x₁;θ) · f(x₂;θ) · ... · f(xₙ;θ) = { θ 1​, 0​if −θ≤x₁≤0 and 0<θ<[infinity], otherwise } · { θ 1​, 0​if −θ≤x₂≤0 and 0<θ<[infinity], otherwise } · ... · { θ 1​, 0​if −θ≤xₙ≤0 and 0<θ<[infinity], otherwise } = θ ⁿ · Πi=1 ⁿI(-θ≤Xi≤0)where I() denotes the indicator function.

b) Let us first write the likelihood function as a function of the θ only: L(θ|x₁, x₂, ..., xₙ) = θ ⁿ · Πi=1 ⁿI(-θ≤Xi≤0)Let us differentiate this function with respect to θ and try to solve for when the derivative is zero:

∂L/∂θ = nθ ⁿ⁻¹ · Πi=1 ⁿI(-θ≤Xi≤0) · (-1) = 0, thus θ ⁿ⁻¹ · Πi=1 ⁿI(-θ≤Xi≤0) = 0.Since the likelihood function is non-negative, we know that the maximum must occur at one of the boundary values of θ, that is at θ = max(-x₁,-x₂,...,-xₙ) = -min(x₁,x₂,...,xₙ).

c) To show that the maximum likelihood estimator of θ is a consistent estimator, we need to show that it converges in probability to the true value of θ. Let us define the estimator for θ as: θn = -min(X₁,X₂,...,Xₙ)Then we need to show that: P(|θn - θ| > ε) → 0 as n → ∞ for any ε > 0.

As n → ∞, the smallest value X(i) will converge to 0 in probability due to the law of large numbers, so we get:P(|θn + min(X₁,X₂,...,Xₙ)| > ε) → 0 as n → ∞

However, since θ < infinity, we know that the support of the distribution will eventually include all values greater than some M > 0. Therefore:P(θ < M) = 1andP(θn = -min(X₁,X₂,...,Xₙ) > M) → 0 as n → ∞This implies that θn converges to θ in probability as n → ∞, and thus the maximum likelihood estimator is consistent.

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Answer:

i get    mABC = 270°

This is fairly straight forward once you the right angle symbol for the arc AC.  Also realizing the 148° for mAB is not needed for this question.  The 148° for mAB would be useful if you wanted to calculate arc mBC.

Remember there are 360° in a circle.  

The arc mAC is 90°

The arc mABC is the rest of the circle.       is the arc from  A to B to C

arc ABC + arc AC is the full circle 360°

    mABC + mAC  = 360°           mAC = 90°

    mABC + 90°  = 360°              - 90° from both sides

    mABC = 360° - 90°

     mABC = 270°

Step-by-step explanation:

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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Answer:

8r + 48

Step-by-step explanation:

In order to expand brackets you have to multiply everything inside the brackets by the number on the outside.

Therefore:

8 x r = 8r

8x 6 = 48

Put these together and you end up with 8r + 48.

The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer:

7344 (yo i haven't done this since like 5th grade so i dont know if its right)

Step-by-step explanation:

800 increase by %2 is 816

816 x 9 = 7344

Answer:

sqrt( 3 V / pi h) =r

Step-by-step explanation:

V = 1/3  pi r^2 h

Multiply each side by 3

3 V = 1/3  pi r^2 h*3

3 V =  pi r^2 h

Divide each side by pi h

3 V/ pi h =  pi r^2 h/ pi h

3 V/ pi h =  r^2

Take the square root of each side

sqrt( 3 V / pi h) = sqrt(r^2)

sqrt( 3 V / pi h) =r

\(6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )\) can be expressed in polar form as\(6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )=\underline{\frac{\sqrt{30} }{3} } \ cis\ (\underline{\frac{4\pi}{3}})\) . Therefore the values to be dragged in the box are \(\frac{\sqrt{30} }{3}\)  and \(\frac{4\pi}{3}\).

We have to express in polar form, polar form of complex number:

\(r(cos\theta+isin\theta) \rightarrow rcis\theta\)

where, r = modulus of complex number

\(\theta\) = argument of complex number

The division of two complex number, \(z=\) \(r_{1} cis \theta_{1}\) and \(x=\) \(r_{2} cis \theta_{2}\)

\(\frac{z}{x} = \frac{r_{1} }{r_{2} }\ cis(\theta_{1}- \theta_{2})\)

Similarly, let a = \(6\sqrt{5} \ cis(\frac{11\pi}{6})\)

                    b = \(3\sqrt{6} \ cis(\frac{pi}{2})\)

\(\frac{a}{b}= \frac{6\sqrt{5} }{3\sqrt{6} } \ cis (\frac{11\pi }{6}- \frac{\pi}{2} )\)

 \(= \frac{{\sqrt{2}}\times\sqrt{2}\times\sqrt{5} }{\sqrt{2} \times\sqrt{3} } \ cis(\frac{11\pi-3\pi}{6} )\)

 \(=\sqrt{\frac{10}{3} }\ cis\ \frac{8\pi}{6}\)

\(\frac{a}{b}= \sqrt{\frac{10}{3} } \ cis\ \frac{4\pi}{3}\)

It can also be written as, \(\frac{a}{b}= \frac{\sqrt{30} }{3} \ cis\ \frac{4\pi}{3}\)

⇒ \(6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )= \frac{\sqrt{30} }{3} \ cis\ \frac{4\pi}{3}\)

Comparing it with the question we get:

\(6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )=\underline{\frac{\sqrt{30} }{3} } \ cis\ (\underline{\frac{4\pi}{3}})\)

Therefore, the first blank is \(\frac{\sqrt{30} }{3}\) and the second blank is \(\frac{4\pi}{3}\).

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Answer:

3. 261 ft³

Step-by-step explanation:

Volume of the figure = ½(volume of cylinder) + volume of triangular prism)

✔️Volume of cylinder = πr²h

r = 3 ft

h = 10 ft

Volume of cylinder = π*3²*10 = 282.74 ft³

✔️Volume of right triangular prism = ½*b*h*l

b = 3*2 = 6 ft

h = 4 ft

l = 10 ft

Volume of triangular prism = ½*6*4*10 = 120 ft³

✔️Plug in the values into the equation:

Volume of the figure = ½(282.74) + 120 = 261.37 ≈ 261 ft³

Step-by-step explanation:

step 1. 3(sqr(27) - 16) sqr is the square root

step 2. 3(3sqr3 -16)

step 3. 9sqr3 - 48.

Answer:

Hello! answer: 45 and 45 is a complementary angle and 60 and 30 is a complementary angle

Step-by-step explanation:

Complementary angles are just angles that add up to 90 degrees so... 45 + 45 = 90 60 + 30 = 90 so that is how those are complementary angles.

Hope that helps!

Answer:

angle QRT/angle VRT  and angle SRW/angle WRV

Step-by-step explanation:

QRT and VRT: Both angles are 45 degrees, adding those degrees together gets you 90 degree angles meaning that they are complementary.

SRW and WRV: 60 plus 30 is equal to 90 making them complementary angles as right angles are 90 degrees

Answer:

Row n ---> 27th term is 27.

Row T ---> 27th term is 80.

Step-by-step explanation:

To find the 27th term for the top row, row n, you will use this formula:

an = a1 + f × (n-1)

The first number = 1

The common difference (f) = 1

a27 = 1 + 1 × (27-1)

a27 = 1 + 27 - 1

a27 = 28 - 1

a27 = 27

So, the 27th term is 27.

We will do the same for the row T.

an = a1 + f × (n-1)

The first number = 2

The common difference (f) = 3

a27 = 2 + 3 × (27-1)

a27 = 2 + 81 - 3

a27 = 83 - 3

a27 = 80

So, the 27th term is 80.

Based on the formulas given for PR and QR, the length of PR is 19.8 units.

The shape that is given is an equilateral triangle. What this means is that all the sides of the triangle are equal.

This means that PR and QR are therefore equal:

PR = QR

This can help us to find the value of n by equating both formulas:

2n + 9 = 7n - 18

The value of n can then be found as:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR can then be solved by substituting n into the formula:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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Answer:

  90 cm²

Step-by-step explanation:

You want the area of a figure that can be described as a 12 cm by 9 cm rectangle with a 6 cm by 3 cm rectangle removed from it.

You can figure the area of this a number of ways. One is to look at the rectangle that bounds it, and subtract the portions of that rectangle that are not included in the figure.

Here, the shaded area is the difference between the "bounding" 12 × 9 cm rectangle area and the "missing" 6 × 3 cm rectangle area:

  Area = (12 cm)(9 cm) -(6 cm)(3 cm) = 108 cm² - 18 cm² = 90 cm²

The area of the figure is 90 cm²

__

Additional comment

Lines have been drawn that divide the figure into three smaller shapes: a rectangle that is 12 cm by 6 cm, and two squares that are 3 cm by 3 cm.

The shaded area is the total of these:

  (12 cm)(6 cm) + 2(3 cm)(3 cm) = 72 cm² +2(9 cm²) = (72 +18) cm² = 90 cm²

The area should be (and is) the same, regardless of how you compute it.

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Answer:

I am not good at this but a good app for math is Math

way

~Hope this helps!!Stay safe~

Answer:

270 per year so 6 years is 1620 and add that with 6000=7620

Answer: m= 0 ; b= 16

(5,16) (-10,16)

Step-by-step explanation:

y=16 so dont need to find y cause it already there so (5,16) (-10,16)

m=y^2- y^1 / x^2-x^1

16-16 / -10-5 = 0/-15 = 0. So m= 0

b is y-intercept and we have y=16 so b=16

Answer:

yes for all 4.

Step-by-step explanation:

I am not sure I see the whole information.

but if the question truly is simply, whether a polygon can have an internal angle of 165 or 171 or 75 or 40 degrees, then the answer is a resounding yes to all 4.

the simplest polygon is a triangle.

the sum of all angles in a triangle is always 180 degrees.

so, any angle smaller than 180 degrees is a possible internal angle in a triangle (and therefore in polygons in general), because the difference to 180 can then be split into 2 angles (e.g. half/half).

so, if one angle is 165 degrees, then the other two angles have to have 15 degrees together (e.g. 10 and 5, or 7 and 8, or 2 and 13, or ...). they will be narrow angles, but they are still angles.

similar for 171 degrees. now the other two angles have to have only 9 degrees together. like 5 and 4.

for 75 degrees the other two angles must have 180-75 = 105 degrees together. like 20 and 85.

for 40 degrees the other two angles must have 180-40 = 140 degrees together. like 90 and 50.