2x+3y + 2z=14-3x+2y+z=274x + 5y – 4z = 28

The probability that  a randomly received emergency call is between 5 and 10 min is 77.97%.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation and x is the raw score.

Given that μ = 6.4, σ = 1.7

For x = 5:

z = (5 - 6.4) / 1.7 = -0.83

For x = 10:

z = (10 - 6.4) / 1.7 = 2.12

a) P(5 < x < 10) = P(-0.83 < z < 2.12) = P(z < 2.12) - P(z < -0.83) = 0.9830 - 0.2033 = 0.7797

b)  P( x < 5) = P(z < -0.83) = 0.2033

c)  P(x > 10) =1 - P(z < 2.12) = 1 - 0.9830 - 0.2033 = 0.017

The probability that  a randomly received emergency call is between 5 and 10 min is 77.97%.

Find out more on Z score at: https://brainly.com/question/25638875

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Answer:

Step-by-step explanation:

A. 3x+21=6x-60 -> 3x=81 -> x=27. So false. The value of x=27.

B. True. Alternate interior angles theorem.

C. False. The marked angles are alternate interior angles.

Step-by-step explanation: Notice that the angle diagonal

of the 114° is a vertical angle and vertical <'s are ≅.

Now, notice that we have two parallel lines cut by a transversal.

If two parallel lines are cut by a transversal, then

consecutive interior angles are supplementary.

So we can setup the equation 114 + y + 12 = 180.

Simplifying on the left gives us 126 + y = 180.

Now subtract 126 from both sides to get y = 54.

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

For more such questions on explicit

https://brainly.com/question/30394385

#SPJ8

The value of x is 24 and different angles of hexagon will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

An angle is a geometric shape that is defined as the amount of rotation that occurs between two straight lines or planes. Angles are measured in degrees, with 360° representing a full circle.

We need to apply the inverse tangent function to determine the angle at which the sun strikes the flagpole. We are aware that the triangle's adjacent side is 42 feet long and its opposite side is 25 feet tall (the height of the flagpole) (the length of the shadow).

Given the figure is hexagon,

the sum of angles of a hexagon is 720,

Upon adding the given angles,

mA = (7x-8)°

mB (4x+46)°

mC = (5x)

mD = (6x+12)°

mE = (x+7)°

mF = (5x-9)°

⇒ 7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720

⇒ 28x + 48 = 720

⇒ 28x = 672

⇒ x = 24

Therefore, the angles will be -

A = 160

B = 142

C = 120

D = 156

E = 31

F = 111

To know more about angle click-

https://brainly.com/question/28769265

#SPJ1

Remember the formula for calculating volume is: Volume = Area by height. V = A X h.

For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.

So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h. i hoped this helped sorry if it didnt

Answer:

f(7x−1)=63x−16

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

since f(x) and g(x) are equal, we can make the equation, 9x-7 = 7x - 1

9x = 7x + 6, 2x = 6, x = 3

If the interest is compounded semiannually, you'll have approximately $2,599.20 after 20 years. If it's compounded monthly, you'll have around $2,635.79. For daily compounding, it will be about $2,641.56, and with continuous compounding, the amount will be roughly $2,644.34.

To calculate the amount you'll have in 20 years with different compounding frequencies, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Given:

P = $1520

r = 3.2% or 0.032 (as a decimal)

t = 20 years

Semiannually:

n = 2 (compounded twice a year)

A = 1520(1 + 0.032/2)^(2*20)

A = 1520(1 + 0.016)^(40)

A = 1520(1.016)^40

A ≈ 2,599.20

Monthly:

n = 12 (compounded twelve times a year)

A = 1520(1 + 0.032/12)^(12*20)

A = 1520(1 + 0.00267)^(240)

A = 1520(1.00267)^240

A ≈ 2,635.79

Daily:

n = 365 (compounded 365 times a year)

A = 1520(1 + 0.032/365)^(365*20)

A = 1520(1 + 0.00008767)^(7300)

A = 1520(1.00008767)^7300

A ≈ 2,641.56

Continuously:

n = infinity (compounded continuously)

A = Pe^(rt)

A = 1520e^(0.032*20)

A = 1520e^(0.64)

A ≈ 2,644.34

For more such question on interest. visit :

https://brainly.com/question/25720319

#SPJ8

Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

Learn more about graph of the function at: https://brainly.com/question/28643733

#SPJ1

The distance AB between the two points is 5.7 units

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

A = (2, 2) and B =(-2, -2)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (2, 2) and (-2, -2)

Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(2 + 2)² + (2 + 2)²]

Evaluate

distance = 5.7

Hence, the distance is 5.7 units

Read more about distance at

brainly.com/question/7243416

#SPJ1

Answer:

-2/3 = -4/6 = -6/9 = -8/12

= -10/15 = -12/18 = -14/21 = -16/24

= -18/27 = -20/30 = -22/33 = -24/36

= -26/39 = -28/42 = -30/45 = -32/48

= -34/51 = -36/54 = -38/57 = -40/60

= -42/63 = -44/66 = -46/69 = -48/72

= -50/75 = -52/78 = -54/81 = -56/84

= -58/87 = -60/90 = -62/93 = -64/96

= -66/99 = -68/102 = -70/105 = -72/108

= -74/111 = -76/114 = -78/117 = -80/120

= -82/123 = -84/126 = -86/129 = -88/132

= -90/135 = -92/138 = -94/141 = -96/144

= -98/147 = -100/150 = -102/153 = -104/156

= -106/159 = -108/162 = -110/165 = -112/168

= -114/171 = -116/174 = -118/177 = -120/180

= -122/183 = -124/186 = -126/189 = -128/192

= -130/195 = -132/198 = -134/201 = -136/204

= -138/207 = -140/210 = -142/213 = -144/216

= -146/219 = -148/222 = -150/225 = -152/228

= -154/231 = -156/234 = -158/237 = -160/240

= -162/243 = -164/246 = -166/249 = -168/252

= -170/255 = -172/258 = -174/261 = -176/264

= -178/267 = -180/270 = -182/273 = -184/276

= -186/279 = -188/282 = -190/285 = -192/288

= -194/291 = -196/294 = -198/297 = -200/300

Step-by-step explanation:

Answer:

The expression for the number of parents is  

p = 25 -c

Step-by-step explanation:

Answer:

c-9

Step-by-step explanation:

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

Read more about probability,

https://brainly.com/question/30390037

Cost of the health insurance is $11657.14

What is cost?

A cost is the worth of money that has been used up to create something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting. In business, the cost might be one of acquisition, in which case the money spent to obtain it is recognized as cost. In this situation, money is the input that is used to purchase the item. This acquisition cost might be the total of the original producer's production expenses and the acquirer's additional transaction costs over and above the amount paid to the producer. Typically, the price includes a profit margin above the cost of manufacture.

14% of x = 68

x = 68 x 100/14

  = $485.71

Total cost = $485.71 x 24 months = $11657.14

To know more about cost, click on the link

https://brainly.com/question/24353331

#SPJ10

The gas bill exceeded $87 from last month to this month.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, The Haddad expected the automatic withdrawal of their gas bill to

be more than last month's bill of $215.85 but did not know by how much.

Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.

∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.

Haddads' present balance is $555.82,

∴ The gas bill is $(858.69 - 555.82) = $302.87.

So the gas bill s exceeded by $(302.87 - 215.85) = $87.

learn more about simple interests here :

https://brainly.com/question/11564235

#SPJ1

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

The gradient of the blue line as shown in the graph is 0.25

The gradient of any line or curve tells us the rate of change of one variable with respect to another.

To calculate the gradient of the blue line, we use the formula below.

Formula:

Where:

From the graph,

Given:

Substitute these values into equation 1

Hence, the gradient of the blue line is 0.25.

Learn more about gradient here: https://brainly.com/question/21727173

#SPJ1

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

Answer:

C

Step-by-step explanation:

Choose C. 2,2,5

semoga membantu

The requried value of the sides of the triangle DEF is DE = 2, DF = 2, and EF = 5.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,

Since Triangle ABC is similar to Triangle DEF,
And  ABC = 1/5 DEF

So,
DE = 1/5 AB ;  DF = 1/5 AC ;  EF = 1/5BC

Put the values in the above expression we get:
DE = 2; DF = 2; EF = 5

Thus, the requried value of the sides of the triangle DEF is DE = 2, DF = 2, and EF = 5.

Learn more about similar triangles here:

brainly.com/question/25882965

#SPJ5

The point is given (6,14) and equation parallel to the equation passes through the point is given Y=4/3X-4.

To determine the equation of line that passes through the point (6,14)

Use the general equation of line.

Substitute the values.

Now the slope of the line will be same as the slope of the equation of line which is parallel .

Because when two lines are parallel the slope of the lines are equal.

Then the equation formed is

Hence the equation of line formed is

Answer: y=3/5x+3

Step-by-step explanation:

I put both points into a graphing calculator (-5,0) (0,3) and found the difference between both and calculated slope using y2-y1/x2-x1 and plugged in each value.

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

<95141404393>

To determine the total number of cyclists who prefer a Wooded Path, we can complete the contingency table and calculate the sum for the Wooded Path category.

The given incomplete contingency table is:

\(\begin{array}{|c|c|c|c|}\hline &\text{Lake Path} & \text{Hilly Path} & \text{Wooded Path} & \text{Total} \\ \hline \text{Female} & 45 & & & \\ \hline \text{Male} & 52 & & & \\ \hline\text{Total} & 71 & 90 & & 200 \\ \hline \end{array}\\\)

We need to fill in the missing values in the contingency table.

To find the total number of cyclists who prefer a Wooded Path, we need to calculate the sum for the Wooded Path category.

The sum for the Wooded Path category can be obtained by subtracting the sum of the other two paths (Lake Path and Hilly Path) from the total count of cyclists:

\(\sf\:\text{Wooded Path} = \text{Total} - (\text{Lake Path} + \text{Hilly Path})\\\)

Substituting the given values:

\(\sf\:\text{Wooded Path} = 200 - (71 + 90)\\\)

Calculating:

\(\sf\:\text{Wooded Path} = 200 - 161\\\)

\(\sf\:\text{Wooded Path} = 39 \\\)

Therefore, the total number of cyclists who prefer a Wooded Path is 39.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

it will be choice 3

Step-by-step explanation:

as if you bend each shape of each of them the only choice that will give you a pyramide with a omitted side

the counting number just before C5F16 is 3,072.

Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³

\(\frac{m}{4.2} =7\\m = 4.2 * 7 = 29.4\)

Hope that helps!

Answer:

m = 29.4

Step-by-step explanation:

\(\frac{m}{4.2}=7\)

\(\mathrm{Multiply\:both\:sides\:by\:}4.2\)

\(\frac{4.2m}{4.2}=7\cdot \:4.2\)

\(\mathrm{Simplify}\)

\(m=29.4\)

Check Answer;

\(\frac{29.4}{4.2}\)

\(\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:10\)

\(\frac{294}{42}\)

\(\mathrm{Write\:the\:problem\:in\:long\:division\:format}\)

\(42\overline{|\smallspace294}\)

\(\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\\ 42\overline{|\smallspace294}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace2\emptyspace9\emptyspace4}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}\)

Hence, m = 29.4

~learn with Lenvy~

The increased number of tickets will be 220.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number of tickets is increased by a factor of 1.1. The increased amount will be calculated as:-

Amount = 200 x 1.1

Amount = 220

Hence, the increased number of tickets will be 220.

To know more about an expression follow

https://brainly.com/question/21106737

#SPJ1