Solve the simultaneous equation.
7a+3b=46
4a+5b=69

Answer:

P(X<1) = .216         P(X</=1) = .648

Step-by-step explanation:

its right

The amount of possible paths to success is known as probability. the total number of outcomes that can occur.

For question 1:

Х \(\sim\) Binomial (n, p):

\(\to P(x) =^n C_x \ p^x g^{n-x}\)

n=3

p=0.40

\(\to P(x=3) =^{3} C_3 \ (0.40)^3\ (0.60)^0 = 0.064\)

For question 2:

\(\to P(x \geq 1) = 1 -p(x=0) \\\\\)

                   \(= 1- [^{3} C_0 (0.40)^0 (0.60)^3]\\\\ =0.784\)

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Answer:

you can give x a value, just make sure that the answer of the equation |x+3| is less than or equal to 4

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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The Net Present Value (NPV) of the new refrigeration system is approximately $101,358.94.

To calculate the Net Present Value (NPV) of the new refrigeration system, we need to calculate the cash flows for each year and discount them to the present value. The NPV is the sum of the present values of the cash flows.

Here are the calculations for each year:

Year 0:

Initial investment: -$700,000

Working capital investment: -$70,000

Year 1:

Depreciation expense: $700,000 * 20% = $140,000

Taxable income: $250,000 - $140,000 = $110,000

Tax savings (35% of taxable income): $38,500

After-tax cash flow: $250,000 - $38,500 = $211,500

Years 2-5:

Depreciation expense: $700,000 * 20% = $140,000

Taxable income: $250,000 - $140,000 = $110,000

Tax savings (35% of taxable income): $38,500

After-tax cash flow: $250,000 - $38,500 = $211,500

Year 5:

Salvage value: $90,000

Taxable gain/loss: $90,000 - $140,000 = -$50,000

Tax savings (35% of taxable gain/loss): -$17,500

After-tax cash flow: $90,000 - (-$17,500) = $107,500

Now, let's calculate the present value of each cash flow using the discount rate of 10%:

Year 0:

Present value: -$700,000 - $70,000 = -$770,000

Year 1:

Present value: $211,500 / (1 + 10%)^1 = $192,272.73

Years 2-5:

Present value: $211,500 / (1 + 10%)^2 + $211,500 / (1 + 10%)^3 + $211,500 / (1 + 10%)^4 + $211,500 / (1 + 10%)^5

           = $174,790.08 + $158,900.07 + $144,454.61 + $131,322.37

           = $609,466.13

Year 5:

Present value: $107,500 / (1 + 10%)^5 = $69,620.08

Finally, let's calculate the NPV by summing up the present values of the cash flows:

NPV = Present value of Year 0 + Present value of Year 1 + Present value of Years 2-5 + Present value of Year 5

   = -$770,000 + $192,272.73 + $609,466.13 + $69,620.08

   = $101,358.94

Therefore, the new refrigeration system's Net Present Value (NPV) is roughly $101,358.94.

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Answer:

See below.

Step-by-step explanation:

A measurement could be a distance or a length, or a weight, or a volume. All those quantities are expressed as positive numbers.

For example, what is the distance from New York to Los Angeles?

Answer: 2,800 miles

What is the length of a book?

Answer: 8 inches

How much does John weigh?

Answer: 150 lb

All those numbers are positive.

There is one measurement that is often a negative number. That is a temperature.

Calculated using unit rates, Steven's birthday party will cost him $ 708 if he were to invite 59 guests.

If the party will cost him $168 for him to invite 14 guests, then we will need to calculate the cost for each guest using unit rates.

if 14 guests = $168,

1 guest = 168/14 = $12

so it will cost him $12 per guest he invites

Knowing that each guest will cost him $12, then if Steven wants to invite 59 guests to his birthday party, he will be spending:

59 × $12 = $708

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Assuming the sample sizes are large enough, a two-sample z-test can be used with a significance level of 0.05.

To determine whether the proportion of individuals who developed heart problems differs between the experimental medication group and the placebo group, a hypothesis test can be performed.

Let p1 be the proportion of individuals who developed heart problems in the experimental medication group, and p₂ be the proportion in the placebo group. The null hypothesis is that the difference in proportions is equal to zero (i.e., p₁ - p₂ = 0), and the alternative hypothesis is that the difference in proportions is not equal to zero (i.e., p₁ - p₂ ≠ 0).

Using the given information, we can calculate the sample proportions, denoted by p₁ and p₂. Let x₁ be the number of individuals who developed heart problems in the experimental medication group, and x₂ be the number in the placebo group. Then:

p₁ = x₁/n₁

p₂ = x₂/n₂

where n₁ and n₂ are the sample sizes in the experimental medication and placebo groups, respectively.

Assuming the null hypothesis is true, the test statistic can be calculated using:

z = (p₁ - p₂) / √(p(1 - p) * (1 / n₁ + 1 / n₂))

where p is the pooled sample proportion, calculated as:

p = (x₁ + x₂) / (n₁ + n₂)

Using a standard normal distribution, the critical value for a two-tailed test with a significance level of 0.05 is ±1.96.

If the calculated test statistic falls outside the critical region (i.e., less than -1.96 or greater than 1.96), then we reject the null hypothesis and conclude that there is a significant difference between the two proportions. Otherwise, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in proportions.

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Answer:

Step-by-step explanation:

first you get 2 then you count 2 more which will add up to a sum of 4 becuase two after two is four.

The comparison between A and B is as follows:A < B.

We are given that:120 % of A is equal to 150 => (120/100)A = 150

Divide both sides by 120/100: A = 150 × 100/120 = 125

And, 105 % of B is equal to 165 => (105/100)B = 165

Divide both sides by 105/100: B = 165 × 100/105 = 157.14

Therefore, A = 125 and B = 157.14

Compare A and B:It can be seen that B is greater than A. Therefore, B > A. Hence, the comparison between A and B is as follows:A < B.

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Answer:

2.2

Step-by-step explanation:

To find a, you use a formula called the law of cosines:

The law of cosines tells us:

a^2 = b^2 + c^2 - 2bc cosA

So lets plug in the values:

a^2 =  4^2 + 3^2 -2(4)(3)cos(32)

a^2 = 25-24cos32

a^2 is roughly equal to 4.97

therefore a roughly equal to 2.2

Answer: The answer is A. 2.2. Hoped this helps! :)

Step-by-step explanation:

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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Answer:

the answer is b

Step-by-step explanation:

hoped that helped

Answer:

28.26cm²

Step-by-step explanation:

Formula for area of circle is πr²

So π is also 3. 14

Which means 3.14(3²) and you will get 28.26cm²

Step-by-step explanation:

x² + 2x - 63 = 0

(x+9)(x-7)=0

x=-9 x=7

The total amount of money that the employee made was $400.58

What is the hourly rate?

The amount that is paid per hour of work is known as an hourly rate.

The hourly rate can be calculated by:

The total amount of pay = hours worked * hourly rate of pay

Given, the rate per hour = ​$9.94

Total work duration = 40.3 hours

Now,

The total amount that the employee​ makes = ​$9.94*40.3 = ​$400.58

Hence, the employee​ made $400.58.

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In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

To show that the equation x^(1/lnx) = 2 has no solution, we can analyze the properties of the function f(x) = x^(1/lnx) and examine its behavior.

Let's consider the domain of the function f(x). Since we have a logarithm in the denominator, we need to ensure that x is positive and not equal to 1, so x > 0 and x ≠ 1.

Now, let's investigate the behavior of f(x) as x approaches 0 from the positive side (x → 0+). In this case, ln(x) approaches negative infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 0 as x approaches 0+.

Next, let's examine the behavior of f(x) as x approaches positive infinity (x → ∞). In this case, ln(x) approaches infinity, and the exponent 1/ln(x) approaches 0. Therefore, f(x) approaches 1 as x approaches ∞.

Considering the behavior of the function, we see that it is always positive (since x^(1/lnx) is positive for positive x) and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞.

Now, let's consider the equation x^(1/lnx) = 2. If such an x exists as a solution, it would mean that there is a point where the function f(x) equals 2. However, based on the behavior of the function described above, we can see that f(x) can never equal 2. Therefore, the equation x^(1/lnx) = 2 has no solution.

In conclusion, the function f(x) = x^(1/lnx) is always positive and approaches 0 as x approaches 0+ and approaches 1 as x approaches ∞. The equation x^(1/lnx) = 2 has no solution.

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1. The chance that all 23 people have different birthdays is about 0.493 or 49.3%.

2. The chance that two people in the room have the same birthday is about 0.507 or 50.7%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

(1) The probability that all 23 people have different birthdays can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there are 364 possible birthdays left to choose from (since one has already been taken).

For the third person, there are 363 possible birthdays left to choose from, and so on.

So the probability that all 23 people have different birthdays is:

P(all different) = 365/365 * 364/365 * 363/365 * ... * 344/365

                 = 0.493

Therefore, the chance that all 23 people have different birthdays is about 0.493 or 49.3%.

(2) The probability that two people in the room have the same birthday can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there is a 1/365 chance that they have the same birthday as the first person.

For the third person, there is a 2/365 chance that they have the same birthday as one of the first two people, and so on.

So the probability that at least two people in the room have the same birthday is:

P(at least 2 people share a birthday) = 1 - P(all different)

                                     = 1 - 0.493

                                     = 0.507

Therefore, the chance that two people in the room have the same birthday is about 0.507 or 50.7%.

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Answer:

Line B

Step-by-step explanation:

The line B has a proportionality of one which you can tell because of the equation Y=1X. Simplified, this equation means that for every increase in X value, there is an equal increase in Y value. This equation can be used to find the proportionality rate of other lines such as how A is Y=2X and C is Y=1/2X.

Answer: To find the number of stamps on each page, we can divide the total number of stamps by the number of pages:

263 stamps ÷ 9 pages = 29.22 stamps per page (rounded to two decimal places)

Since we want to place the same number of stamps on each page with as few left over as possible, we can round down to the nearest whole number:

29 stamps per page

To find out how many stamps were left to put in an envelope, we can multiply the number of pages by the number of stamps per page, and then subtract from the total number of stamps:

263 stamps - (29 stamps per page x 9 pages) = 8 stamps left over to put in an envelope

Therefore, the completed sentences are:

29 stamps were placed on each page.

8 stamps were put in an envelope.

Step-by-step explanation:

The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?

The  volume of the largest right circular cone that can be inscribed in a sphere of radius r is  8/27 (volume of sphere)

Let r serve as the foundation. the volume of the area, and radius x is the separation between the base and the sphere's center. Height h of the cone = R + x

∴    V= 1/3πr² h= π/ 3 (R² −x²)(R + x)

       = π/3​ (R² + R² x − Rx² −x² )

∴   dV/ dx​ = π​ /3 [R²−2Rx−3x² ]

  d²V/ dx²​ = π/3​ [−2R−6x]

For max or min V dV/dx​ =0

∴   R² −2Rx−3x² =0

⇒(R + x)(x−3x)=0    

2) x=−R, x​/3 but x = −R

When x= R/3 d² V/dx² <0  V is max only when x= R/3

​∴   Max V= 1/3π(R² − R²/9 )(R+ R/3 )

= 32πR³/81

= 8/27 ( 4/3 πR³)

= 8/27 (volume of sphere)

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The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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The linear function for the data in the table are,  

y = f(x) = -2.5x + 6.5,

y = f(x) = -2.5x + 4

y = f(x) = -2.5x + 6

Based on the given function is,

x         0              1                 2             3

f(x)      4              1.5             -1              -3.5

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

From the given table points on linear function,

points are, (0,4) and (1,1.5)

y - \(y_{1}\) = \(\frac{y_{1}- y_{1} }{x_{2} -x_{1} }\) (x-\(x_{1}\))           (Equation-1)

\(x_{1}\) = 0

\(y_{1}\) = 4

\(x_{2}\) = 1

\(y_{2}\) = 1.5

We can substitute values in equation-1,

y - 4 = \(\frac{1.5-4}{1-0}\) (x-1)

y - 4 = -2.5/1 (x-1)

y -4 = -2.5 (x - 1)

y - 4 = -2.5x + 2.5

y = -2.5x + 2.5 + 4

y = -2.5x + 6.5

y = f(x) = -2.5x + 6.5

points are, (1,1.5) and (2,-1)

y - \(y_{1}\) = \(\frac{y_{1}- y_{1} }{x_{2} -x_{1} }\) (x-\(x_{1}\))           (Equation-1)

\(x_{1}\) = 1

\(y_{1}\) = 1.5

\(x_{2}\) = 2

\(y_{2}\) = -1

We can substitute values in equation-1,

y - 1.5 = \(\frac{-1-1.5}{2-1}\) (x-1)

y - 1.5 = -2.5/1 (x-1)

y - 1.5 = -2.5 (x - 1)

y - 1.5 = -2.5x + 2.5

y = -2.5x + 2.5 + 1.5

y = -2.5x + 4

y = f(x) = -2.5x + 4

points are, (2,-1) and (3,-3.5)

y - \(y_{1}\) = \(\frac{y_{1}- y_{1} }{x_{2} -x_{1} }\) (x-\(x_{1}\))           (Equation-1)

\(x_{1}\) = 2

\(y_{1}\) = -1

\(x_{2}\) = 3

\(y_{2}\) = -3.5

We can substitute values in equation-1,

y - (-1) = \(\frac{-3.5-(-1)}{3-2}\) (x-2)

y + 1 = -2.5/1 (x-2)

y + 1 = -2.5 (x - 2)

y + 1 = -2.5x + 5

y = -2.5x + 5 + 1

y = -2.5x + 6

y = f(x) = -2.5x + 6

Therefore,

The linear function for the data in the table are,  

y = f(x) = -2.5x + 6.5,

y = f(x) = -2.5x + 4

y = f(x) = -2.5x + 6

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Step-by-step explanation:

We have 2x + 6y = 22.

When x = 5,

=> 2(5) + 6y = 22

=> 10 + 6y = 22

=> 6y = 12

=> y = 2.

Hence y = 2 when x = 5.

We will have the following:

*We can see that 2 is part of the set and 2 is not greater than 2, so option A is not the solution.

*We can see that 5 and 10 are divisible by 5, so option B is not the solution.

*We can see that the numbers 2, 4, 6, 8 & 10 are even but the others are odd. The remaining are less than 12, thus option C is the solution.

Answer:2024

Step-by-step explanation:

Answer:

No, it is not a function because if you drew any vertical line it would intersect the points (lines) more than once. Basically, the points plotted intersect themselves if you connect all of them on a graph

Step-by-step explanation:

To show your work and understand it more type in Desmos graphing calculator on Google and type in the points and they will then appear on the graph. Hope this helps

Answer:

The solutions to the graph are (-1,1) and (4,6).

Step-by-step explanation:

Where the line and parabola intersect, or meet, are the solutions.

Therefore, Marcy would run 1.5 miles in one hour if she continues at this rate. Answer: 1.5 miles.

Distance is the overall distance that something has traveled. as one example. If a car travels 5 km east, then turns and travels 8 km further north, it will have covered a distance of 13 km overall.

We can begin by finding how far Marcy runs in one second:

4.4 feet / 2 seconds = 2.2 feet per second

To find how many feet she runs in one hour, we can multiply her speed by the number of seconds in an hour:

2.2 feet per second x 3600 seconds per hour = 7,920 feet per hour

Finally, we can convert this distance to miles by dividing by the number of feet in a mile:

7,920 feet per hour / 5,280 feet per mile = 1.5 miles per hour

Therefore, Marcy would run 1.5 miles in one hour if she continues at this rate. Answer: 1.5 miles.
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