The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 5 minutes. Find the
probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
Find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes.
(Simplify your answer. Round to three decimal places as needed.)
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Answer:

A

Step-by-step explanation:

for the relationship to be a function, then each value from the input must map to exactly one unique value in the output.

This is the case here si represents a function.

Answer: \(\sqrt[3]{a}\)

Step-by-step explanation:

Just as the square root is \(\sqrt[2]{a}\), the cube root is \(\sqrt[3]{a}\)

Hope it helps <3

Answer:

\(\sqrt[3]{a}\)

Step-by-step explanation:

a cube root of a number x is a number a such that a³ = x.

Answer:

x = 3

Hope this helps!

Step-by-step explanation:

ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6\(\sqrt{2}\) ) can be \(x\sqrt{2}\) while AB and CB are x. Because 6\(\sqrt{2}\) is equal to \(x\sqrt{2}\), you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = \(x\sqrt{3}\). CB is equal to 6 so 2x = 6, x = 3.

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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Answer:

y = 15 , x = 6

Step-by-step explanation:

you can easily find y from first equation

Move y to the other side of the equation and reverse its sign

so (-11) changes to (+11) and now we have this equation

y = 15

now you must replace 15 instead of y in second equation ,then we have this equation

15 = 2x + 3

now we have to find x

move (+3) to other side of equation and reverse its sign

(+3) changes to (-3)

we have this equation now

15 - 3 = 2x

12 = 2x

x = 12 ÷ 2 = 6

The volume of the clay brick is 2.25 cubic inches and the weight of the clay brick is 0.1575 pounds

The volume of the clay brick, we need to use the dimensions provided. The length of the brick is 1 inch and the width is 2 \(\frac{1}{4}\) inches. We can assume the height of the brick is also 1 inch since it is not specified.

The formula for the volume of a rectangular object is

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

Using the given dimensions, we can calculate the volume of the brick:

V = (1 inch) x (2 \(\frac{1}{4}\) inches) x (1 inch)

V = (1 inch) x (2.25 inches) x (1 inch)

V = 2.25 cubic inches

V = 2.25 inches³

Since the density of the clay is given as 0.07 pounds per cubic inch, we can find the weight of the brick using the formula:

Weight = Volume x Density

Weight = 2.25 inches³ x 0.07 pounds/inches³

Weight = 0.1575 pounds

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Answer:

√3.14,-√3.14

Step-by-step explanation:

9514 1404 393

Answer:

  $23,600

Step-by-step explanation:

Total pay is the sum of base pay and commission.

  $22000 +1600 = $23,600

__

Additional comment

We can't really answer the take-home pay question unless we know the time period involved and the deductions due to taxes (and other things). With the information given here, we can only assume that the given amounts apply to the time period of interest, and that there are no deductions.

Answer:

23600

Step-by-step explanation:

Add both numbers together!

Answer:

44 feet per second

Step-by-step explanation:

(already a unit rate, because it is at its lowest form with 1 second in the equation) BIG BRAIN

44 feet per second is written as 44ft/sec when expressed in unit rate.

To rapidly determine the unit rate of quantities, use the unit rate calculator. The calculator, for instance, will simplify the fraction and output the result as a unit rate if two values and their units are entered.

Unit rates include things like km/h, m/sec, cost/litre, etc. The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.

The kilometre per hour (km/hour), price per litre, profit per item, etc. are a few instances of unit rates.

Divide the numerator by the denominator, setting the denominator equal to 1, to determine the unit rate.

The ratio of how many units of the first type of quantity to one unit of the second type of quantity is known as the unit rate. The unit rate is used frequently in daily life.

The unit rate is 40 feet/second which can be written as 40ft/sec this means 40ft has been covered per second.

Hence, 44 feet per second is written as 44ft/sec when expressed in unit rate.

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Answer:

Al igual que los cuadrados y los triángulos equiláteros, los hexágonos regulares encajan sin ningún espacio para enlosar el plano (tres hexágonos se encuentran en cada vértice), por lo que son útiles para construir mosaicos.

Answer:

25/16

Step-by-step explanation:

Remember, keep-change-flip

Turn this into a multiplication equation

\(\frac{5}{8} * \frac{5}{2}\)

Multiply to get 25/16

Answer:

solution given;

let

AB=a

AC=b=30ft

AB=c=20ft

<A=115°

By using Cosine rule.

a²=b²+c²-2bc cos angle

a²=30²+20²-2*30*20 Cos 115°

a²=1807.1419

a=√[1807.1419]

a=42.51

Side A is 42.51ft.

Again

Cos B=\( \frac{a²+c²-b²}{2ac} \)

Cos B=\( \frac{42.51²+20²-30²}{2*42.51*20} \)

Cos B=0.7687

<B=Cos -¹(0.7687)

<B=39.46°

Angle B is 39.46

___________________________________

\(\quad\quad\quad\quad\tt{ \angle{A = 115° }}\)

\( \tt{\overline{A}²=b²+c²-2bc \cos( \angle{a}) }\)

\( \tt{\overline{A}²=(30)²+(20)²-2(30)(20) \cos( \angle{115°}) }\)

\( \tt{\overline{A}²=900+400-2(600) \cos( \angle{115°}) }\)

\( \tt{\overline{A}²=1300-1200 \cos( \angle{115°}) }\)

\( \tt{\overline{A} ²=1807.1419}\)

\( \tt{\overline{A}= \sqrt{ 1807.1419}}\)

\( \pink {\boxed{ \tt{ \overline{A}=42.51}}}\)

\( \tt{ cos\;B = \frac{ {a}^{2} + {c}^{2} - {b}^{2} }{2ac} }\)

\( \tt{ cos\:B = \frac{ {42.51}^{2} + {20}^{2} - {30}^{2} }{2(42.51)(20)} }\)

\( \tt{ cos\:B = 0.7687}\)

\( \tt{ \angle{B} = { \cos}^{ - 1} (0.7687)}\)

\(\pink{\boxed{\tt{ \angle{B} = {39.46°}}}}\)

___________________________________

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✍︎ C.Rose❀

Answer:

2

Step-by-step explanation:

It is the only one that makes sense

Haleema would have approximately £3947.46 in her account after 2 years and 11 months, considering the monthly compounding interest of 5%.

To calculate the amount of money in Haleema's account after 2 years and 11 months, we need to consider the monthly compounding interest on the account.

The interest rate is given as 5% per year, which means the monthly interest rate is (5%/12) = 0.4167%.

Let's calculate the final amount using the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = £3700, r = 0.004167, n = 12 (monthly compounding), and t = 2.917 (2 years and 11 months).

Plugging these values into the formula, we get:

A = £3700(1 + 0.004167/12)^(12*2.917)

A ≈ £3947.46

The amount of money in Haleema's account after 2 years and 11 months would be approximately £3947.46.

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Answer: Triangle C.

Step-by-Step Explanation:

To solve this problem, we need to understand what it means for a triangle to be a translation of another triangle. A translation for a triangle means that it is the same shape and size as the original triangle, but it has shifted (or moved) a specific number of units either up, down, left, or right.

In this problem, we have Triangle P, which has been shifted 5 units to the right and 7 units up to form Triangle C. To determine which triangle is a translation of Triangle P, we can look at the coordinates of the different triangles.

Triangle A: (1, 4), (3, 7), (5, 6)

Triangle B: (2, 3), (4, 6), (6, 5)

Triangle C: (6, 11), (8, 14), (10, 13)

Triangle D: (3, 5), (5, 8), (7, 7)

If we compare the coordinates of each triangle with those of Triangle P, we can see that Triangle C, with coordinates (6, 11), (8, 14) and (10, 13), is the translation of Triangle P because all of the coordinates of Triangle P have been shifted 5 units to the right, and 7 units up. Therefore, the answer is Triangle C.

Therefore, there is a 68.75% chance that Reese will win at least two of his next four games, assuming that each game is independent and has a 50-50 chance of winning.

Assuming that each game is independent and has a probability of winning of 0.5 (since there are two cups and Reese has a 50-50 chance of choosing the correct one), we can model Reese's wins in four games as a binomial distribution with n=4 and p=0.5.

The probability of Reese winning at least two games can be calculated as the sum of the probabilities of winning two, three, or four games. We can use the binomial probability formula or a binomial probability calculator to find these probabilities:

\(P(X=2) = 6/16 = 0.375\)

\(P(X=3) = 4/16 = 0.25\)

\(P(X=4) = 1/16 = 0.0625\)

So, the probability of Reese winning at least two of his next four games is:

\(P(X\geq 2) = P(X=2) + P(X=3) + P(X=4) = 0.375 + 0.25 + 0.0625 = 0.6875\)

Therefore, there is a 68.75% chance that Reese will win at least two of his next four games, assuming that each game is independent and has a 50-50 chance of winning.

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Answer:

(g - h)(3) = -11.

Step-by-step explanation:

To find the expressions for (g • h) (x) and (g + h) (x), we need to use the definitions of function composition and function addition:

(g • h) (x) = g(h(x))

This means we first evaluate h(x), and then use the result as the input for g.

(g + h) (x) = g(x) + h(x)

This means we evaluate g(x) and h(x) separately, and then add their results together.

Using the definitions of g(x) and h(x) given in the problem, we can find:

(g • h) (x) = g(h(x)) = g(3x + 5) = (3x + 5) - 1 = 3x + 4

(g + h) (x) = g(x) + h(x) = (x - 1) + (3x + 5) = 4x + 4

To evaluate (g - h)(3), we need to use the definition of function subtraction:

(g - h)(x) = g(x) - h(x)

This means we evaluate g(x) and h(x) separately, and then subtract their results.

Using the definitions of g(x) and h(x) given in the problem, we can find:

(g - h)(3) = g(3) - h(3) = (3 - 1) - (3(3) + 5) = -11

Therefore, (g - h)(3) = -11.

Answer:

i) 960  ,    ii) 10 cm

Step-by-step explanation:

V of rectangular carton = 80 · 60 · 40 = 192 000

V of a packet of soap = 10 · 5 · 4 = 200

192 000 / 200

1920/2

960

ii)

960 : 1200 = 192 000 : x

x = 192 000 · 1200 / 960

x = 192 000 · 120 / 96

x = 240 000

80 · 60 · x = 240 000

4800 · x = 240 000

x = 240 000/4800

x = 2400/48

x = 200/4

x = 50

50 - 40 = 10

Answer:

i) 960 packets of soap

ii) 10 cm

Step-by-step explanation:

volume of cuboid = l*w*h

volume of carton = 80*60*40 = 192000 cm³

i)

volume of a packet of soap = 10*5*4 = 200 cm³

192000/200 = 960 packets of soaps

ii)

I am assuming the height is 40 cm

volume of carton/volume of a packet of soap = number of soap

x = volume of carton

x/200 = 1200

x = 1200*200 = 240000 cm³

80*60*h = 240000

4800h = 240000

h = 240000/4800 = 50 cm

50cm (desired height) - 40cm (current height) = 10cm

Answer:

the answer will be  

m∠X′Y′Z′ = m∠XYZ

Step-by-step explanation:

i took the test XDStep-by-step explanation:

the answer will be  

m∠X′Y′Z′ = m∠XYZ

Step-by-step explanation:

i took the test XD

Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Answer:

Large box = 50 pounds

Small box = 15 pounds

Step-by-step explanation:

Because there are 50 small boxes, the truck is carrying 50 combined large and small boxes. That means the area of those boxes are 50 * 65 = 3250 pounds. There are 10 large boxes left. 3750-3250 = 500. The weight of 10 large boxes is 500 pounds, which means 1 large box is 500/10 which is 50 pounds.

If a large box is 50 pounds, and the combined weight is 65 pounds, 65-50 = 15 pounds for a small box.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

20 cubic feet.

From feet: length (ft) × width (ft) × height (ft) = cubic feet.

From inches: length (in) × width (in) × height (in) ÷ 1728 = cubic feet.

From yards: length (yd) × width (yd) × height (yd) × 27 = cubic feet.

If you need to convert to cubic feet from inches: divide the final number (i.e. the total you get after multiplying the three dimensions together

The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

En el enunciado tenemos el precio de una impresora para el consumidor, el cual comprende el dinero invertido por vendedor más la ganancia esperada. Este indicador observa la siguiente fórmula:

C' = C · (1 + r/100)     (1)

Donde:

Si sabemos que C' = $ 285.000 y r = 35 %, entonces el coste asumido por el vendedor es:

285.000 = 1,35 · C'

C' ≈ 211.111,11

Excluyendo el componente de ganancia del coste para el consumidor según (1), la impresora tuvo un coste de $ 211.111,11 para el vendedor.

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Answer:

length = 8 width = 2

Step-by-step explanation:

8 X 2 = 16

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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