diseases tend to spread according to the exponential growth model. in the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. in 1983, about 1700 people in the u.s. died of aids. if the trend had continued unchecked, how many people would have died from aids in 2005?

Answer: m=4

Step-by-step explanation:

3m−7=5

3m = 12

m= 4

Answer:

m = 4

Step-by-step explanation:

The 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

In the given question, the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities.

The sample variance was found to be 6.62.

We have to find a 95% confidence interval for the population variance in the pounds of impurities.

From the question,

N=20,

s^2=6.62

So, the Standard Deviation(SD) = √s^2

SD = √6.62

SD = 2.573

The confidence interval for the population variance is given by the following formula:

[tex]\frac{(n-1)s^2}{ \chi_{\alpha/2}} \leq\sigma^2\leq \frac{(n-1)s^2}{ \chi_{1-\alpha/2}}[/tex]

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculating the critical values. First we need to calculate the degrees of freedom given by:

df = n-1

df = 20-1

df = 19

Since the Confidence is 0.95 or 95%, the value of α=0.05 and α/2=0.025, and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)".

So for this case the critical values are:

[tex]\chi_{\alpha/2}[/tex] = 32.852

[tex]\chi_{1-\alpha/2}[/tex] = 8.907

Now putting the value in the formula:

[tex]\frac{19\times6.62}{32.852}\leq\sigma^2\leq\frac{19\times6.62}{8.907}[/tex]

3.829≤σ^2≤14.121

So the 95% confidence interval for the variance in the pounds of impurities would be (3.829, 14.121).

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1) The probability of F2 seed chosen at random will be yellow is the same as asking about the probability of forming a yellow seed in that generation. The answer is 3/4 (75%) because 1/4 = 25% GG is homozygous dominant and the rest 2/4 = 50% Gg are heterozygous.

2) In the F2 generation there are two genotypes that will breed true, which is homozygotic genotypes: GG and gg. But of these two, only one of them is yellow. The answer is 1/3 because from all the yellow seeds that resulted (GG, Gg and gG) only one has the genotype for true breeding.

3) The probability of taking out three seeds in which a least one is yellow can be calculated by subtracting the only  probability that doesn't fit the criterion, which is taking out a green seed 3 times:   = 1/64.

Then subtract that to 1  =  63/64

4) there are three possible groupings in which the green is taken once and the yellow seeds taken twice. The first possibility (follow the example) is the green being the first to come out, another possibility is being the second and the last possibility is being taken in the third time.

For example, Green yellow yellow- probability :

= 9/64

This is one possibily, but since there are 3, multiply it by 3 and you obtain the final answer:27/64.

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Answer:

If the elimination produces the equation 0=0, then the two equations are for the same line.

Step-by-step explanation:

This means that there are an infinite number of solutions.

From the question the transformations that non-rigid is dilation. The correct answer is B.

Any transformation of a geometric object that alters the size but not the shape is referred to as a nonrigid transformation. Examples of non-rigid types of transformation include stretching and dilation. Any action taken on a shape is referred to as a metamorphosis.

Rigid transformation is When a figure undergoes a stiff transformation, its size and shape are left unaltered. Because the image is unchanged, stiff transformations include translations, rotations, and reflections.

As a result, a dilation is a non-rigid transformation because the size of the image is changing.

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Answer:

z = 11

Step-by-step explanation:

To find the answer we need to set up an expression with the two values they gave us:

8z = z + 77

This works because side IJ is the same length as side JK. So, all we have to do is solve for z:

8z = z + 77

-z    - z

7z = 77

/7     /7

z = 11

The job paying a flat $20 should be chosen instead of the other two options for periods of at most 5 days.

The daily pay for each job is constant, hence they can be modeled by linear functions, in the slope-intercept format, as follows:

y = mx + b.

The coefficients of the linear functions are given as follows:

Hence the functions for each option are given as follows:

The third option is better when:

Which is why it should be chosen for periods of at most five days.

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The chance density characteristic of lifetime in months of a transistor in a positive utility is:

[tex]f(x)=0.4cdot e^x > 0f(x)=0.4⋅e −0.4x ;x>0[/tex]

The chance density characteristic shows that the random variable X follows a exponential characteristic with parameter λ = 0.4.

Compute the suggest lifetime as follows:

[tex]mu=frac=2.5μ= λ1 = 0.401 =2.5[/tex]

Thus, the suggest lifetime is months.

Compute the usual deviation of the lifetimes as follows:

[tex]sigma=2.5σ= λ 2 1 = 0.40 2 1 =2.5.[/tex]

Thus, the usual deviation of the lifetimes is 2.5 months.

Compute the sixtieth percentile of the lifetime as follows:

Thus, the sixtieth percentile of the lifetime is 2.3 months.

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Answer:

you remember vertex: h,k in (x-h)²+k..

replace in that. In that graph vertex: (10, -20)

So in that Equation, a(x-10)²-20, a<0 since it is maximum graph.

I cannot find the full Equation but from what I can see you can find h,k and the fact that a<0

The probability of getting 5 face cards when taken without replacement is 0.00030473728.

There are 12 face cards in the deck overall.

When six cards are dealt, 12C5 equals 792.

without a replacement

P (5 face cards) = 12/5

P(5)=792 / 2598960 for five face cards.

P(5)=0.00030473728 for five face cards.

When 6 cards are picked from a deck without replacement, the likelihood of getting 6 face cards (a king, queen, or jack) is therefore 0.00030473728.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood that an event will occur or that a claim is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 indicates the event's impossibility and 1 indicates its certainty.

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Answer:

Step-by-step explanation:

You want the net and total surface area for the triangular prism shown.

The net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.

The net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.

  A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)

  = 144 cm² +24 cm²

  = 168 cm²

The total surface area of the prism is 168 cm².

__

Additional comment

The formulas for the area of a rectangle and triangle are ...

  A = LW . . . . . area of a rectangle of length L and width W

  A = 1/2bh . . . . area of a triangle of base b and height h

From the various triangle proofs below, we have been able to show that; 3A F = AC

A median of a triangle is defined as a line segment from a vertex of the triangle to the midpoint of the side opposite that vertex.

We are given that;

AD is the median of ΔABC.

E is the midpoint of AD

Through D, we draw DG parallel to BF

In ΔADG, E is the midpoint of AD and EF is parallel to DG

By using the converse of midpoint theorem, we have;

F is midpoint of AG and A F = FG     ------(eq 1)

Likewise, In ΔBCF ;

D is the midpoint of BC and DG is parallel to BF  

G is midpoint of CF and FG is congruent to GC (FG ≅ GC) .........(eq 2)

From equations 1 and 2, we will get;

A F = FG = GC     -------(3)

Thus;

A F + FG + GC = AC

A F + A F + A F = AC (from eq 3)

3A F = AC

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The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

The system of equations is a set of one or more equations that intersects at locations called solutions of the system.

The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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A new form of the triple integral [tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx[/tex] as a = 0 b = 1 g2(z) = 1 h2(y,z) = 1.

In other words, we want the integration order to be totally reversed for

[tex]\int\limits^1_0\int\limits^x_0 \int\limits^y_0 f (x,y,z) dz dy dx[/tex]

Keep in mind that this area is quite simple to define. The planes z = y and y = x, as well as the coordinate planes [tex]x=y=z=0[/tex], define our boundaries. We essentially have upper bounds z = y = x = 1 because x ∈[ 0, 1 ]. Therefore, we can alternatively express the region as:-

[tex]0\leq x\leq y\\0\leq y\leq z\\[/tex]

z∈ I0,1I. So

[tex]\int\limits^1_0 \int\limits^x_0 \int\limits^y_0 f(x,y,z)dzdydx = \int\limits^1_0 \int\limits^z_0 \int\limits^y_0 f(x,y,z)dxdydz[/tex]

Remember that a double integral could be set up in two different ways. Our number of alternative orders of integration increases from two to six when we include that third integral. We will rewrite the supplied integral in one of the other five possible orders in this exercise.

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The following equation √ 3x² - 2x + 1/2 = 0 is quadratic

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.

Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."

As the expression √ 3x² - 2x + 1/2 = 0 has square root so it is  a quadratic equation.

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The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

What do you mean by step function?

A piecewise function is one that is broken up into smaller functions, each of which has its own equation. A very particular (and much simpler) type of piecewise function is called a step function (or staircase function), and it has parts that resemble steps or the stairs of a staircase.

The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

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If all sales are made on​ account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.

It is False.

Information available from the question,

In the question:

If all sales are made on​ account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.

The answer in TRUE/FALSE

Now, According to the question:

Accounting for cash transactions:

Daily cash sheet: If cash transactions are a significant part of your business, you should also prepare a daily cash sheet to reconcile your cash received and paid out for the day. If you use a daily cash sheet, you can reconcile your cash receipts with your daily deposit into your bank account.

So, The given statement is False.

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Answer:

JL = 7.5

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{JL}{AC}[/tex] = [tex]\frac{JK}{AB}[/tex] ( substitute values )

[tex]\frac{JL}{2.5}[/tex] = [tex]\frac{10.5}{3.5}[/tex] ( cross- multiply )

3.5 × JL = 2.5 × 10.5 = 26.25 ( divide both sides by 3.5 )

JL = 7.5

The expected value of x for the awarded 3 points for each coin that lands with heads faceup is 27/8.

In this instance, we are informed that:

The probability of each of them is calculated as:

Situation 1: No heads

That implies that all three coins must land on the tail.

Thus, there is only one method to accomplish this. While the whole range of potential outcomes is;

= 2x 2x 2

= 8

via the product rule (because each coin has two alternative outcomes).

The result is:

P(x =0) = 1/8

Situation 2: One head

Single head means three points, or X = three.

Total outcomes possible = 8,

Single head can occur in 3 different ways, as other two needs to be strictly tails.

Thus,

P(x = 3) = 2/8

Situation 3: Two heads

Two heads equals 3+3 = 6.

X = 6

8 outcomes are possible in total.

Single tail means two heads. Three separate scenarios can lead to a single tail.

Therefore,

P(x = 6) = 2/8

Situation 4: Three heads

Three heads signifies that X = 9 or 3+3+3 = 9 points.

8 outcomes are possible in total.

Three heads means there is only one way to do it and no tail.

Thus,

P(x = 9) = 1/8

As a result, the expectation of X is determined as follows:

E(x) = 0. 1/8 + 3. 2/8 + 6. 2/8 + 9. 1/8

E(x) = 27/8

Therefore, 27/8 is the expected value of X.

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The given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5.

(A) x² - 4x + 5 = 0

LHS: x² - 4x + 5

= (2)² - 4(2) + 5

= 4 - 8 + 5

= -4 + 5

= 1

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(B) x² + 3x - 12 = 0

LHS: x² + 3x - 12

= (2)² + 3(2) - 12

= 4 + 6 - 12

= 10 - 12

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(C) 2x² - 7x + 6 = 0

Put x = 2

= 2(2)² - 7(2) + 6

= 8 - 14 + 6

= 14 - 14

= 0

RHS = 0

LHS = RHS

It has 2 roots.

(D) 3x² - 6x - 2 = 0

LHS: 3x² - 6x - 2

= 3(2)² - 6(2) - 2

= 12 - 12 - 2

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

Therefore, the given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

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Answer: y=3/4x

Step-by-step explanation:

1. Find slope using slope formula

2. Find b value by plugging a point to solve for b with

The graph of the linear function y = 36 - 4x that represents this function is given by the image shown at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are listed as follows:

Initially, he has 36 overdue activities, hence the intercept is of:

b = 36.

Each day, he can do 4 activities, hence the number of remaining activities decays by 4, and thus the slope is of:

m = -4.

Thus the function is given as follows:

y = -4x + 36.

The y-intercept is given by the following point:

(0, 36).

The x-intercept is given by the following point:

(9,0).

As:

-4x + 36 = 0

4x = 36

x = 9.

Then a line is traced connecting the intercepts.

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With 99% certainty, the population proportion of adults who say they have started paying bills online in the last year is between the given confidence interval's endpoints.

We have the following confidence interval of proportions in a sample of n people surveyed with a success probability of π and a confidence level of 1 - α.

Confidence interval = [tex]\pi[/tex] ± z [tex]\sqrt{\(\pi (1 - \pi ))/n}[/tex]

z = 1 - α/2

Here given, According to a survey of 3102adults, 1443 have begun paying bills online in the last year.

That is, n = 3102 and x = 1443

p = x / n

  = 1443 / 3102

  = 0.465

significance level = α

= 1 - confidence

= 1 - 0.99

= 0.01

zα/2 = z0.01 / 2 = 2.58

By substituting in confidence interval formula,

The lower limit is :

0.465 - 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]

= -0.01894056008

The upper limit is:

0.465 + 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]  

= 0.02722425658

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The lower limit is 0.456 and upper limit is 0.474

What is confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

As confidence interval (C) = π ± z√[π(1-π)/n]

In the above expression, z = 1 - α/2, where α is the significance level.

Given in the question, n=3102 as the survey was conducted on 3102 adults. Also, x=1443, as 1443 people have started paying bills online in last year.

π = x/n

Substituting the values, we get,

π = 1443/3102

⇒ π = 0.465

Confidence level(α) = 1 - confidence

= 1 - 0.99

= 0.01

Since, z = 1 - α/2

⇒ z = 1 - 0.01/2

⇒ z = 1 - 0.005

⇒ z = 0.995

By substituting in confidence interval formula,

The lower limit is = 0.465 - 0.995√[(0.465*0.535)/3102]

= 0.456

The upper limit is = 0.465 + 0.995√[(0.465*0.535)/3102]

= 0.474

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Answer:

its about the degrees.

Step-by-step explanation:

In a right triangle, the sum of the interior angles will always be 180°. Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest.

The expression that shows a way to factor 16 + 72 is 8(2 + 9)

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

16 + 72

Express the terms of the expression as products

So, we have the following representation

16 + 72 = 8 * 2 + 8 * 9

Factor out 8 from the expression

This gives

16 + 72 = 8 * (2 +  9)

Hence, the factored expression of 16 + 72 is 8 * (2 +  9)

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The percent of the kids scored a 90% is 82%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, some kids scored a 70% on a test and some scored a 90%.

Let x percent of the kids scored a 90%.

Now, x% of 76%=90%

0.01x×0.76=0.9

0.01x=0.9/0.76

0.01x=1.184

x=1.184/0.01

x=118%

So, 100-18=82%

Therefore, the percent of the kids scored a 90% is 82%.

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By using  Pythagorean theorem ,148  is the length of the side of the slab in inches .

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                    This is written as a2 + b2 = c2 in the usual algebraic notation.

12 inches = 1 feet  

 feet measurment = 407/12  = 33.91 feet

In triangle ABC

Using PYTHAOREAN THEOREM

               l² + b² = h²

             l = √h²  -  b²

            l =  √407² - 379²

            l = √165649 - 143641

            l = √22008

           l = 148.35

           l ≈ 148

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The probability that the flight is less than 71 minutes is 0.1471

Let the distribution of the time to fly between New York City and Chicago be X

X~U(66,100)

where,

66 = minimum

100 = maximum

We need to find P(X<71)

We know that in the case of uniform distribution,

P(X<x) = (x - a) / b -a

where,

a = min value

b = max value.

Hence P(X<71)

= (71 - 66) / (100 - 66)

= 5/34

= 0.1471

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Answer: 8x

Step-by-step explanation: We will start by writing out our equation which is 10x2y-2x2y. Next we will subtract using only like terms

10x - 2x = 8x

2y-2y=0

8x plus 0 = 8x.