The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem

dN/dt = N(1 − 0.0008N), N(0) = 1.

Required:
Predict how many supermarkets are expected to adopt the new procedure over a long period of time?

Answer:

The first three terms in the geometric sequence are 18, 24, 32.

Step-by-step explanation:

A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]

Given

[tex]x = 1, y = 7, z = 15[/tex]

We know

[tex]\alpha _1 = 1+t[/tex]

[tex]\alpha _2 = 7+t[/tex]

[tex]\alpha _3 = 15+t[/tex]

Recall that a geometric sequence is in the form

[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]

Therefore, once  [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,

[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]

To find the ratio, for

[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]

we know

[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]

Therefore,

[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]

[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]

The ratio is therefore

[tex]r=\dfrac{4}{3}[/tex]

Therefore, the first three terms in the geometric sequence are 18, 24, 32.

Answer:

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

Step-by-step explanation:

For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.

To find the probability of damage on a parachute, the normal distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability of a parachute having damage.

The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]

Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of  Z when X = 100. So

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

[tex]Z = \frac{100 - 185}{32}[/tex]

[tex]Z = -2.66[/tex]

[tex]Z = -2.66[/tex] has a p-value of 0.0039.

What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?

0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]

5 parachutes, which means that [tex]n = 5[/tex]

This probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]

0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.

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Answer:

  (x, y) = (0, -2)

Step-by-step explanation:

When solving by substitution, you usually want to find an expression for one of the variables in terms of the other. So, the first thing you look for is an equation that has a coefficient of 1 or -1 on one of the variables. Recognizing that the second equation's terms all have a common factor of 3, you basically have two choices.

Using equation 1, you can write an expression for y:

  y = 5x -2 . . . . . . add 5x to both sides

Then substituting this into the original equation 2, you have ...

  -3x +6(5x -2) = -12

  27x -12 = -12 . . . . . . . simplify

  27x = 0 . . . . . . . . . add 12

  x = 0 . . . . . . . . .  divide by 27

  y = 5(0) -2 = -2 . . . . find y using the expression for substitution

The solution is (x, y) = (0, -2).

__

If you decide you'd rather substitute for x, you can solve the second equation easily for x.

  -3x +6y = -12

  x -2y = 4 . . . . . . divide by -3

  x = 2y +4 . . . . . . add 2y

Substituting for x in the first equation gives ...

  -5(2y +4) +y = -2 . . . . substitute for x

  -9y -20 = -2 . . . . . . . simplify

  -9y = 18 . . . . . . . . .  add 20

  y = -2 . . . . . . . . . . . divide by -9

  x = 2(-2) +4 = 0 . . . . find x using the expression for substitution

The solution is (x, y) = (0, -2).

_____

Additional comment

In some cases, there are no variables that have a coefficient of ±1, so you just need to "bite the bullet" and deal with the resulting fractions.

Example:

  solve for y: -5x +2y = -2

     2y = 5x -2

     y = 5/2x -1 . . . . expression used to substitute for y

Of course, you can multiply the equation after substitution by 2 to eliminate fractions, or just work the problem as is. The point of looking for coefficients of ±1 is to avoid having to do arithmetic with fractions. It can help avoid errors to work with integers, but ultimately the method is the same regardless of the form of the numbers.

__

You don't always have to substitute for the "bare" variable. Sometimes it can save steps to substitute for expressions instead of variables. If our system of equations were ...

You can substitute into the second equation for (2y). In that case, the second equation becomes ...

  -3x +3(2y) = -12

  -3x +3(5x-2) = -12 . . . . . . where 2y = 5x -2

Answer:

Shawn earns $11 per hour.

Step-by-step explanation:

When looking at the x axis (hours), and find where 1 hour intersects with the y axis It intersects with the point labeled at $11. This means after working for 1 hour, Shawn earned $11.

Answer:

The slope of a line that goes through both [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex] would be [tex](-3)[/tex].

Step-by-step explanation:

The slope of a line is the ratio between rise and run between these two points.

The rise between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex](-5) - 7 = (-12)[/tex] (subtract the first [tex]y\![/tex]-coordinate from the second.)

The run between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex]2 - (-2) = 4[/tex] (likewise, subtract the first [tex]x[/tex]-coordinate from the second.)

Hence, the slope of this line would be:

[tex]\begin{aligned} \frac{\text{rise}}{\text{run}} &= \frac{-12}{4} = -3\end{aligned}[/tex].

Answer:

[tex]\displaystyle m = \frac{3}{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify points from graph.

Point (4, 0)

Point (0, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  y = 2x +4

Step-by-step explanation:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (12 -(-6))/(4 -(-5)) = 18/9 = 2

The y-intercept can be found from ...

  b = y -mx

  b = 12 -(2)(4) = 4

Then the slope-intercept equation for the line is ...

  y = mx +b

  y = 2x +4

Answer:

y=2x+4

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the points (-5, -6) and (4, 12)

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The formula for the slope calculated from two points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where ([tex]x_1[/tex], [tex]y_1[/tex]) and ([tex]x_2[/tex], [tex]y_2[/tex]) are points

We have everything needed to calculate the slope, but let's label the values of the points to avoid any confusion

[tex]x_1[/tex]=-5

[tex]y_1[/tex]=-6

[tex]x_2[/tex]=4

[tex]y_2[/tex]=12

Now substitute into the formula (remember: the formula has SUBTRACTION in it)

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{12--6}{4--5}[/tex]

Simplify

m=[tex]\frac{12+6}{4+5}[/tex]

Add

m=[tex]\frac{18}{9}[/tex]

Divide

m=2

So the slope of the line is 2

Here is the equation so far:

y=2x+b

We need to find b

As the line will pass through both (-5, -6) and (4, 12), we can use the values of either one to solve for b

Let's take (4, 12) for instance

Substitute 4 as x and 12 as y

12=2(4)+b

Multiply

12=8+b

Subtract 8 from both sides

4=b

Substitute 4 as b in the equation

y=2x+4

Hope this helps!

Answer:

∠ SPQ = 75°

Step-by-step explanation:

The sum of the 4 angles in a quadrilateral = 360°

Subtract the sum of the 3 angles from 360 for ∠ SPQ

∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°

9514 1404 393

Answer:

  D, C

Step-by-step explanation:

The only two rational expressions that have appropriate denominators are ...

  1/(x² +6x) . . . contributes a factor of x to the denominator

  (x+2)/(x² -36) . . . contributes a factor of (x -6) to the denominator

The proper order in the expression is ...

  [tex]\displaystyle\dfrac{x+2}{x^2-36}-\dfrac{1}{x^2+6x}=\dfrac{x^2+x+6}{x(x-6)(x+6)}[/tex]

Answer:

(x+2/x^2-36) - (1/x^2+6x) = (x^2+x+6/x(x-6)(x+6))

Step-by-step explanation:

I hope that helps

4. Percent increase

Because Original Value < New Value

5. Percent

6. Whole

Because it's asking what number that means total.

Thanks :)

Answer:

the last two answers are the only correct ones

Answer:

[tex] \sin(θ) = \frac{19}{41} \\ θ = 27.6 \\ θ = 28[/tex]

Answer:

0.5

0.25

Step-by-step explanation:

The equation for the exponential function is f(x) = 0.5(0.25)ˣ after applying the concept of the function.

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ

where a is a constant and a>1

It is given that:

A 2-column table has 2 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 8, 2, 0.5, 0.125, and 0.03125.

x     f(x)

-2     8

-1      2

0      0.5

1       0.125

2       0.03125

Let the function is:

f(x) = a(b)ˣ

Plug x = 0 and f(x) = 0.5

0.5 = a

Plug x = -1 and f(x) = 2

2 = 0.5(1/b)

b = 0.5/2 = 0.25

f(x) = 0.5(0.25)ˣ

Thus, the equation for the exponential function is f(x) = 0.5(0.25)ˣ after applying the concept of the function.

Learn more about the exponential function here:

brainly.com/question/11487261

#SPJ2

Answer:

y =6

Step-by-step explanation:

We can write a ratio to solve

3           y

----- = ----------

4            8

Using cross products

3*8 = 4y

24 = 4y

Divide by 4

24/4 = 4y/4

6 = y

Answer:

x = 20

y = 10

Answered by Gauthmat

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

Answer:

4% and 5% respectively

Step-by-step explanation:

Let the intrest rate be x in the first account at x% and (x+1)% in the second account.

ATQ, 100=(x)*1500/100+(x+1)*800/100

x=4.

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Answer:

  θ = 1.5 radians ≈ 85.9°

Step-by-step explanation:

The arc length in terms of central angle and radius is ...

  s = rθ

where θ is the central angle in radians. Here, we want to find θ, so we have ...

  θ = s/r . . . . divide by r

For the given numbers, ...

  θ = (6 cm)/(4 cm) = 3/2 = 1.5 . . . radians

I radian is 180°/π, so 3/2 radians is ...

  (3/2)(180°/π) = 270°/π ≈ 85.9°

Answer:

A. Use the​ two-sample t-methods when a sample was taken from each of two populations​ (i.e. two groups being​ compared) and the population standard deviations are not known.

Step-by-step explanation:

T-distribution:

When the population standard deviation is not known, the t-distribution is used.

If a sample was taken from one population, we use the one-sample method, while if there is a comparison of two populations, the two-sample method is used, and thus, the correct answer is given by option A.

Step-by-step explanation:

2 x y + x + 2 y is equal to 3 x y + 2 y final answer is 5xy

Answer:

The expected number of offspring is 2

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]

Required

The expected number of offspring

This implies that we calculate the expected value of the function.

So, we have:

[tex]E(x) = \sum x * P(x)[/tex]

Substitute known values

[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]

Using a calculator, we have:

[tex]E(x) = 1.74[/tex]

[tex]E(x) = 2[/tex] --- approximated

Answer:

<5

Step-by-step explanation:

exterior angles + the corresponding interior angle of the triangle = 180º or a straight angle

the only exterior angle shown in the diagram is <5, which corresponds to the interior <2

hope this helps!

Answer:

<5

Step-by-step explanation:

everything else is matched up perfectly so it has to be <5

Answer:

11.2

Step-by-step explanation:

yz = 11.2

since the corresponding arc of yz and xy are same, their measures will ba same too

Answered by GAUTHMATH

Answer:

11.2

Step-by-step explanation:

good luck!

Answer:

the graph would cut the y-axis 11 units below y=f(x)

Answer:

5

Step-by-step explanation:

4.5*10^-8/ 9*10^-9

1) Reduce the fraction, express 9 as a product of multiplying 4.5*2

4.5*10^-8/4.5*2*10^-9

2) Then notice the common factor of numerator and denominator( 4.5) , get rid of it in both numerator and dnominator

3) 10^-8/ 2*10^-9= 1/2*(10^-8/10^-9)= 0.5* (10^-8/10^-9)

10^-8/10^-9= 10^(-8-(-9))= 10^1=10.

so 0.5*10=5 (it is the answer written in scientific form)

Answer:

χ² = 19

Pvalue = 0.0008 ( 4 decimal places)

WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries

Step-by-step explanation:

H0 : probability of complaint is the same for the 5 industries.

H1: probability of complaint is not the same for the 5 industries.

Category ____ observed frequency

Bank _______ 26

Cable _______44

Car _________42

Cell _________60

Collection ____ 28

Total ________200

The test statistic ;

χ² = (O - E)² / E

O = Observed Frequency ; E = Expected Frequency

Expected Frequency, E = (1 / n) * total

n = number of industries = 5

Expected frequency, E = (1/5)*200 = 40

Expected frequency is the same for all, thus E for all 5 industries = 40

χ² = Σ(O - E)² / E;

χ² = (26-40)² / 40 + (44-40)² / 40 + (42-40)² / 40 + (60-40)² / 40 + (28-40)² / 40

χ² = 19

At α = 0.05 ; df = n-1 = 4 ; χ²critical = 0.000786

Since Pvalue < α ; WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries.

Answer:

12*(3)^x

Step-by-step explanation:

Let the exponential function be y=a*b^x. Given y(0)=12, a=12. Next y(2)=36, b=3

Answer:

Your answer is f(x)=4(3)x

Step-by-step explanation:

Mark me brainliest :)

Answer:

$54

Step-by-step explanation:

10% of $60 is $6

$60-$6=$54