Need help with this one

Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The parameters are:

[tex]\mu = 15, \sigma = 2.5[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 15}{2.5}[/tex]

Z = 2.8.

Item b:

The parameters are:

[tex]\mu = 38.1, \sigma = 6.35[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]

Z = 2.8.

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The pairs of prime numbers (p,q) such that  p^2-p=37q^2-q is (43, 7)

The expression is given as:

p^2 - p=37q^2 - q

The boundary or range of numbers of p and q is not given.

So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)

i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000

Using the above range, we have the following program to determine the pairs of prime numbers (p, q).

for a in range(2,1000000):

  for b in range(2,1000000):

      if ((a* *2) - a) == (37 * (b* *2) - b):

          print(str(a)+","+str(b))

The output of the above program is:

(43, 7)

The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q

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The probability of E and F expressed as P(E and F) equals;0.12

We are given;

P(E) = 0.2

P(F|E) = 0.6

Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)

Thus;

P(E and F) = 0.2 * 0.6

P(E and F) = 0.12

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Answer:

100 pi = about 314.16

Step-by-step explanation:

the surface area of a cylinder: SA = 2πrh+2πr^2

we plug in the values of r and h, and get

SA = 50pi + 50pi = 100 pi, which is approximately 314.16

Answer:4

Step-by-step explanation: 9y-8y+2, when y=2

9(2)-8(2)+2=

18-16+2

=4

Answer:

270 uits

Step-by-step explanation:

There are $2224.12 need to deposit in an account in order to have $3000 in five years.

What is future value?

Future value is the worth of a financial asset or investment on a specific future date. In other words, future value is the amount of money an investment will be worth, assuming a specific rate of return, after a specific amount of time (interest rate).

Given:

Future value = FV = $3000

Number of years = t = 5

Interest rate = r = 6% = 0.06

Compounding period = n = 12

We have to find the present value form given problem.

Consider, the Future value formula,

[tex]FV = PV(1 + \frac{r}{n})^n^*^t[/tex]

Plug the values in the above formula.

[tex]3000 = PV(1+\frac{0.06}{12})^1^2^*^5\\ 3000 = PV(1+0.005)^6^0\\3000 = PV(1.005)^6^0\\PV = 2224.11658[/tex]

PV = $2224.12

Hence, there are $2224.12 need to deposit in an account in order to have $3000 in five years.

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Answer: 22/85

Step-by-step explanation:

Answer:

22/85

Step-by-step explanation:

The measure of arc RT is 156 degree.

Given:

arc TRM=102°

Hence:

arc RST=2×1O2°

arc RST=204°

Measure of arc RT

arc RT= 2(180° - 102°)

arc RT = 2(78°)

arc RT = 156 degrees

Therefore the correct option is B.

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Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

First, we need to define the variables:

We know that we want to produce 60 liters of 65% acid, then we have the system of equations:

x + y = 60

x*0.35 + y*0.80 = 60*0.65

(in the second equation we wrote the percentages in decimal form).

To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:

x = 60 - y

Replacing that in the other equation:

(60 - y)*0.35 + y*0.80 = 60*0.65

y*(0.80 - 0.35) = 60*(0.65 - 0.35)

y*0.45 = 60*0.30

y = 60*0.30/0.45 = 40

So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

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20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115

Answer:

The simplified form of the above expressions solution is -115.

Step-by-step explanation:

The coordinates of point C are (-9, 1)

The points are given as:

A = (-21, -7)

B = (-6, 3)

m : n = 4 : 1

The coordinates of point C is calculated as:

[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]

So, we have:

[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]

This gives

[tex]C = \frac{1}{5} *(-45, 5)[/tex]

This gives

C = (-9, 1)

Hence, the coordinates of point C are (-9, 1)

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Using a system of equations, it is found that her normal week is of €285.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The first equation, considering the first sentence, is given by:

x + 8y = 375.

The second equation, considering the second sentence, is given by:

x + 4y = 330.

Then the system is:

Multiplying the second equation by -2, the system is:

Adding the equations, we have that her normal week is given by:

x = 660 - 375 = €285.

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The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

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Answer

1 possible solution:

(5x7) in the first blank

(-3!) in the second blank

(-1) in the third blank

Step-by-step explanation:

(5x7) + -(3!) + -(1)          3! equals 3x2x1 or 6

35 + (-6) + (-1)

Answer:

B. quadratic function graph

The graph is shown in the attached image.

Answer:

[tex]3(2x + 5)(3x - 1)[/tex]

Step-by-step explanation:

Hello!

We can first factor out the greatest common factor between the coefficients: 3.

Now, let's work with what we have inside the brackets.

Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]

Given our equation: [tex]6x^2 + 13x - 5[/tex]

We need to find two numbers that add up to b (13) and multiply to ac (-30).

The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.

Now, we simply add the other factor, 3, to the final factored form.

Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]

Answer:

Step-by-step explanation:

Answer:

The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.

Step-by-step explanation:

.05x = .02x + 210  Subtract .02x from both sides.

.03x  = 210   Divide both sides by .03

x  = $7,000.

(a) The number of cases on May 1, 2014, was approximately 188.59.

(b) The number of cases on November 24, 2014, was approximately 27107.76.

(c) C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.

(a) In the question, we are asked for the approximate number of cases on May 1, 2014.

Since, the date is May 1, 2014, t = 0.

Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]

Thus, the number of cases on May 1, 2014, was approximately 188.59.

(b) In the question, we are asked for the approximate number of cases on November 24, 2014.

Since, the date is November 24, 2014, t = 207.

Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]

Thus, the number of cases on November 24, 2014, was approximately 27107.76.

(c) We are asked to find C(92).

This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]

Thus, C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

The complete question is:

"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)

a. [3 pts] Approximately how many cases were there on May 1, 2014?

b. [3 pts] How many cases were projected by November 24, 2014?

c. [4 pts] Find C(92) and explain what it means in the context of the problem.

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The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

The given parameters are:

The above means that:

c = 4 and

The semi-major axis, a = 7 i.e 14/2

Calculate b using

[tex]b = \sqrt{c^2 + a^2[/tex]

So, we have:

[tex]b = \sqrt{4^2 + 7^2[/tex]

[tex]b = \sqrt{65[/tex]

Square both sides

[tex]b^2 = 65[/tex]

The standard form of the ellipse is represented as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

This gives

[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]

Evaluate

[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

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Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

     Diameter = 18 cm

                  r = 18÷ 2 = 9 cm

                 h = 12 cm

[tex]\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]

                                    = π * 9 * 9 * 12 cm³

  [tex]\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}[/tex]

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

 [tex]\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12[/tex]

      [tex]\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}[/tex]

Answer:

  x/6

You're welcome! :)

Answer : 7/6

explanation is long

Answer: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.

Step-by-step explanation: