Jaquelyn wants to start getting to school on time more often. She is looking at some of her habits.
On Monday, she is late twenty percent of the time.

When she is late on Monday, she is late on Tuesday 60% of the time.

When she is not late on Monday, she is late on Tuesday 20% of the time.

What is the approximate probability that Jaquelyn will be late on Tuesday, given she was late to school on Monday?

Answer:

17 / 4

Step-by-step explanation:

To find the right sum, you need to....

Step #1: Find Δx

Step #2: Find [tex]x_k[/tex]

Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx

Step #4: Solve the right-hand sum equation

Answer:

Step-by-step explanation:

If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.

34= 18+x

I hope this helps!

The Total surface area of the rectangular prism = 168 in.²

The Volume of the rectangular prism = 108 in.³

The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:

w = width of the rectangular prism

h = height of the rectangular prism

l = length of the rectangular prism

The volume of a rectangular prism = l × w × h

Find the Total surface area of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²

Find the volume of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Volume of the rectangular prism = l × w × h = 9 × 2 × 6

Volume of the rectangular prism = 108 in.³

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Answer:

5%

Step-by-step explanation:

price after discount :

9 600 - 9 600×40%

= 5760

Original price (price without profit) :

let x be the original price of the device.

x + x × 20% = 5760

Then

x = (5 760×100)÷120

  = 4 800

Original price increased by 30% :

4 800 + 4 800×30%

= 6 240

the discount needed to increase the profit by 10% :

[(9 600-6 240)÷9 600]×100

= 35%

Then

to increase the profit by 10% ,we have to reduce

the percent of discount to :

40% - 35%

= 5%

Answer:

We note that,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

now we can use binomial series on (1+x²)²ᐟ³

(1+x²)²ᐟ³ = ( 1+2x²/3+((2/3)*(2/3 -1)/2) x⁴ + ((2/3)*(2/3 -1)(2/3–2)/6) x⁶ +o(x⁶) =

= 1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶)

The last step is to differentiate,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

= (3/4) d/dx (1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶) )

= (3/4) ( 0 + (4/3)x - 4/9 x³ + 24x⁵/81 + o(x⁵))

= x - x³/3 + 2x⁵/9 + o(x⁵)

The complete Question is- How do I find the Maclaurin series using binomial series in the function f(x) = x/³√1+x^2?

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Part a

[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]

Part C

[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]

The equation that represents the function is y = -x - 1

The complete question is added as an attachment

From the table of values, we have the following points

(x, y) = (-1,0) and (0,-1)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-1 -0)/(0 + 1)

Evaluate the exponent

m = -1

The equation is then calculated as:

y = mx + c

This gives

y = -x + c

Using the point (0,-1), we have:

0 = 1 + c

Solve for c

c = -1

So, we have

y = -x - 1

Hence, the equation that represents the function is y = -x - 1

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Answer:

  (a)  x = -1.10 and x = 1.10

Step-by-step explanation:

A straightforward square root will give the value of x.

Divide by the coefficient of x^2:

  x^2 -30/25 = 0

  x^2 -1.20 = 0

Add 1.20, and take the square root.

  x^2 = 1.20

  x = ±√1.20 ≈ ±1.0954

  x ≈ -1.10 and 1.10 . . . . . round to hundredths

__

Additional comment

For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.

For a circle k(O) with diameter AB and CD ⊥ AB, it is proved that AD·CB=AC·CD, using similarity of triangles.

Given:

circle k(O) with diameter AB

CD ⊥ AB

To Prove: AD·CB=AC·CD

Proof:

In ΔADC and ΔCDB,

∠ADC = ∠CDB = 90°  

[∵Both are right angle triangles]

CB = CB [Common side]

⇒ AC / CB = CD / DB

Thus, ΔACD is similar to ΔCDB by RHS similarity.

Therefore, we can write,

AD/CD = AC/CB [Since corresponding sides of similar triangles are proportional]

⇒ AD·CB = AC·CD

Hence proved.

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Answer:

$700

Step-by-step explanation:

If he made a loss of 15%, then it means that selling price is 85% of the cost price.

If the cost price is x, then we have;

0.85x = 595

x = 595/0.85

x = $700

Answer:

ummation of n=1 to n=7 (-2)^n

Step-by-step explanation:

summation of n=1 to n=7 (-2)^n

Answer: x = 3.5

Step-by-Step Solution:

Let us first label the figure.

Let the Triangle be ABC with a line DE || BC.

Now, in ∆ABC,

DE || BC (given)

=> AD/DB = AE/EC (by B.P.T)

Substituting the given values,

AD/DB = AE/EC

2/4 = x/7

1/2 = x/7

2x = 7

x = 7/2

=> x = 3.5

Therefore, x = 3.5

The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

The function is given as:

y = -16x^2 + 48x

When the ball hits the ground, we have

y = 0

Substitute the known values in the above equation

-16x^2 + 48x = 0

Factor out -16x

-16x(x - 3) = 0

Divide through by -16x

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

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The number of people that have watched the video is 858 people

A function is a mathematic rule. We know that a function shows the rule that is to  be carried out and is often written in the form of an equation.

Now we have the function shown as; f(x) = 33(1.3)x. Since we know that the term x is referred as the number of days the video has been online.

Thus,  f(x) = 33(1.3)(20) thus we can now say that the number of people who have vied the video in twenty days is 858 people.

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Answer: the answer is B or 858

Step-by-step explanation: The answer is B or 858

Answer:

  A)  (-3, -2)

  B)  (-7, 3) and (-3, -2)

  C)  (4.074, 1.032)

Step-by-step explanation:

An ordered pair is a solution to an equation if it satisfies the equation — makes it true. The given points are solutions to the functions whose graphs pass through those points.

The function p(x) is defined to pass through points (4, 1) and (-3, -2).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

These function definitions have point (-3, -2) in common.

(-3, -2) is the solution to the equation p(x) = f(x).

The function f(x) is defined to pass through points (-7, 3) and (-3, -2).

Two solutions to f(x) are (-7, 3) and (-3, -2).

We could identify other solutions, (1, -7) for example, but there is no need since the problem statement already gives us two solutions.

The solution to the equation p(x) = g(x) can be read from the graph as approximately (4.074, 1.032). This is close to the point (4, 1) that is used to define p(x). With some refinement (iteration), we can show the irrational solution is closer to ...

  (4.07369423957, 1.03158324553)

Answer:

A)  (-3, -2)

B)  (1, -7) and (5, -12)

C)  (4, 1) to the nearest whole number

Step-by-step explanation:

Function g(x):

[tex]g(x)=2(0.85)^x[/tex]

Function f(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-3-(-7)}=-\dfrac{5}{4}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=-\dfrac{5}{4}(x-(-7))[/tex]

[tex]\implies y=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

[tex]\implies f(x)=-\dfrac{5}{4}x-\dfrac{23}{4}[/tex]

Function p(x) (straight line):

Given ordered pairs:

Calculate the slope of the straight line:

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-1}{-3-4}=\dfrac{3}{7}[/tex]

Using the Point-slope form of linear equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=\dfrac{3}{7}(x-4)[/tex]

[tex]\implies y=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

[tex]\implies p(x)=\dfrac{3}{7}x-\dfrac{5}{7}[/tex]

We have been given two ordered pairs for function f(x) and function p(x).

One of those ordered pairs is the same for both functions.  

The solution to a pair of equations is their point(s) of intersection.  

Therefore, as both functions pass through (-3, -2), this is their point of intersection and therefore the solution.

The solutions for f(x) are any points on the line of the function f(x).  

To find any two points, substitute values of x into the found equation for f(x):

[tex]\implies f(1)=-\dfrac{5}{4}(1)-\dfrac{23}{4}=-7[/tex]

[tex]\implies f(5)=-\dfrac{5}{4}(5)-\dfrac{23}{4}=-12[/tex]

Therefore, two solutions are (1, -7) and (5, -12).

Part C

The solution to p(x) = g(x) is where the two graphs intersect.  From inspection of the graphs, p(x) intersects g(x) at approximately (4, 1).  

Therefore, the approximate solution to p(x) = g(x) is (4, 1).

To prove this, substitute x = 4 into the equations for p(x) and g(x):

[tex]\implies p(4)=\dfrac{3}{7}(4)-\dfrac{5}{7}=1[/tex]

[tex]\implies g(4)=2(0.85)^4=1.0440125=1.0\:(\sf nearest\:tenth)[/tex]

The actual solution to p(x) = g(x) is (4.074, 1.032) to three decimal places, which can be found by equating the functions and solving for x using a numerical method such as iteration.

The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.

Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.

The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

So, each term is ⁿCₓaˣbⁿ⁻ˣ.

Comparing (a + b)ⁿ with (2t + s)⁷,

So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ

= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ

So, the coefficient term is ⁷Cₓ(2)ˣ

Now for the term t²s⁵, x = 2.

So, the coeficient term is  ⁷Cₓ(2)ˣ =  ⁷C₂(2)²

= 7!/2!(7 - 2)! × 4

= 7!/2!5! × 4

= 7 × 6 × 5!/(2! × 5!) × 4

= 7 × 6/2 × 4

= 7 × 3 × 4

= 84

So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

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The surface area of the given figure is 288 km²

From the question, we are to determine the surface area of the figure

The given figure is a square-base pyramid

Surface area of the pyramid = (10×10) + 4× 1/2(10×9.4)

Surface area of the pyramid = (100) + 2(94)

Surface area of the pyramid = 100 + 188

Surface area of the pyramid = 288 km²

Hence, the surface area of the given figure is 288 km²

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The circumference of the given circle is 25.1 cm.

According to the statement

we have given that the the radius of circle which is 4cm.

And we have to find the circumference of the circle.

So, For this purpose

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

The formula to calculate it is

C = 2(pi)r

So, substitute the values in it then

Here use pi value is 3.14

C = 2 *3.14*4

C = 25.12.

The circumference of the given circle is according to one decimal place is 25.12 cm.

So, The circumference of the given circle is 25.1 cm.

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The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds

The complete question is added as an attachment

The function is given as:

[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]

Set the height to 3

[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]

Subtract 3 from both sides

[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]

Apply the following quadratic formula

[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]

So, we have:

[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]

This gives

[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]

This gives

[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]

Expand

[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]

This gives

t = 0.054 and t = 2.80

0.054 is less than 2.80

This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds

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Answer: 16482

Step-by-step explanation:

Let's divide the number into three parts:

sixteen thousand | four hundred |eighty-two

A thousand is 1000, so sixteen thousand should be 16000.

A hundred is 100, so four hundred should be 400.

Eighty-two is just 82.

Let's add all of these:

[tex]16000+400+82=16482[/tex]

Answer: Real, equal, rational.

Step-by-step explanation:

[tex]-x^2-8x-16=0\\-(x^2+8x+16)=0\\Multiply \ the\ left \ and\ right \ sides\ of\ the\ equation\ by \ -1:\\x^2+8x+16=0\\x^2+2*x*4+4^2=0\\(x+4)^2=0\\x+4=0\\x=-4.[/tex]

Answer:

Step-by-step explanation:

integer and rational

We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

Given the following data:

Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

In order to calculate the airplane’s ground speed, we would apply the law of cosine:

C² = A² + D² - 2(A)(D)cosθ

Substituting the given parameters into the formula, we have;

C² = 700² + 60² - 2(700)(60)cos45

C² = 434,203.03

C = √434,203.03

C = 658.94 kph.

In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

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Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:

Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:

p = 15/64 = 0.2344.

0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

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Juan's home is about 12 kilometers from Adam's.

In the study of mathematics and science, measurement is the fundamental idea. By quantifying an object's or event's qualities, we can compare them to those of other objects or occurrences. When discussing the division of a quantity, the phrase "measurement" is most frequently employed.

The distance between Adam's and Juan's residences on the map in centimeters is simply multiplied by the number of kilometers that each centimeter on the map represents, which in this case is 6, to determine how far Adam's house is from Juan's.

2 * 6 = 12

Which is our response.

Juan's home is about 12 kilometers from Adam's.

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Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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The groups which would be most representative of the opinions of all employees in the company are: A sample of 5% of randomly selected employees from each office location, Employees who are randomly selected by a computer from a list of all company employees and Employees who have worked for the company for more than 10 years.

Options (A),(C) and (D) are correct.

A sizable business has locations around the nation. The company's facilities director was tasked with asking employees about their office furnishings. Instead of polling every worker at the company, the director chose to select a sample. We are supposed to find the groups which would be most representative of the opinions of all employees in the company.

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The incorrect step in the induction that all people in Canada are the same height is; Step 9

The principle of mathematical induction as follows:

For example, we have a set of natural numbers. Now, suppose that 1 is in the set. Now, we assume that anytime n is in the set, n + 1 is also in the set. Therefore we can say that every natural number is in the set.

The wrong step in the given mathematical Induction is Step 9. This is because;

We might not be to see anyone else in the arbitrary group G other than groups P or Q!

Recall that G is a group of k + 1 people. Thus, provided that k > 1, k + 1 > 2 and that a third person R in G does not exist, then the rest of the proof will work.

The steps above proves that;

S(k) = S(k + 1), for every k > 1.

Thus, we can also say that if S(2) is true, then it equally means S(3) is true and so on till infinity.

From our induction process written so far, we have see that S(1) was true. However, our induction step in the question does not show us that that S(1) = S(2) = true.

So: Thus, from the induction I have done It shows that S(1) not imply S(2) and as a result the proof is fallacious.

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At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.

Given that 78% of the ages are greater than or equal to 18 years. Hence.

18 years will be (100 - 78)th percentile

i.e. 22nd percentile.

Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.

Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.

Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.

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Answer:

19

Step-by-step explanation: (75/5) + 4= p

15+4=p

19=p

The original price for one lunch meal is $19

p = $15 + $4

p = $19