Given a_4=135\;and\;a_6=1215a
4
​
=135anda
6
​
=1215, find the explicit rule for the geometric sequence, given that the common ratio is positive.

Answer:

5 and a 250,000

Step-by-step explanation:

A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000

Answer:

It is: 5,250,000

Answer:

it will increase the production

Step-by-step explanation:

Answer:

sin(cos^-1(-15/17))=8/17

Step-by-step explanation:

I apologize for the bad writing, I hope you can read it

Answer:

x=100/7

Step-by-step explanation:

The interior angles will sum to 360 so 72+89+99+7x=360

260+7x=360

7x=100

x=100/7

The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.

A function is a law that defines relation between two variables.

The function given in the question is

f(x) = 8x² +2

h(x) = -8x²-2

The graph is plotted and the similarities or differences are studied ,

It can be seen from the graph that

f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).

Therefore Option D is the right answer.

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Answer:

A. y = 600x, the jet travels 12,000 miles in 20 hours

Explanation:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Take two points: (2, 1200), (4, 2400)

[tex]\sf slope : \dfrac{2400-1200}{4-2 } = 600[/tex]

Equation:

y - 1200 = 600(x - 2)

y - 1200 = 600x - 1200

y = 600x

Miles the Jet travels at 20 hours:

Miles the Jet travels at 22 hours:

Answer:

y = 600x, the jet travels 12,000 miles in 20 hours

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]y = mx + b[/tex]

where:

To find the slope, define two points on the line and use the slope formula to find the slope:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1200-0}{2-0}=600[/tex]

From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0).  Therefore, the equation of the line is:

y = 600x

y is defined as the distance (in miles).  Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:

[tex]\sf \implies 600x=12000[/tex]

[tex]\sf \implies x=\dfrac{12000}{600}[/tex]

[tex]\sf \implies x=\dfrac{120}{6}[/tex]

[tex]\implies \sf x=20[/tex]

Therefore, it takes the jet 20 hours to travel 12,000 miles.

Part 1: Finding slope

The slope is [tex]\frac{-3-15}{5-(-10)}=\frac{-18}{15}=\boxed{-\frac{6}{5}}[/tex]

Part 2: Finding the equation

Using the point (-10, 15) to substitute into point-slope form,

[tex]y-15=-\frac{6}{5}(x+10)\\\\y-15=-\frac{6}{5}x-12\\\\\boxed{y=-\frac{6}{5}x+3}[/tex]

Answer:

Using the given points we find that the slope is -1.2 and using the slope-point form we find that the equation of line is y+1.2x = 3.

Step-by-step explanation:

In the question, two points are given, (5,-3) and (-10,15). Using them we can find the slope using the formula, (y2 - y1) / (x2 - x1). So, the slope is

(-3-15) / (5+10) = -18 / 15 = -1.2

Now, we have to find the equation of line. We have two points and a slope. Using any one point and the slope, we can find the equation of line using slope-point form of line. Let us take (5,-3).

(y+3) / (x-5) = -1.2

y+3 = -1.2(x-5)

y+3 = -1.2x + 6

y+1.2x = 3

So, the slope of line is -1.2 and the equation of line is y+1.2x = 3.

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Answer:

graph A

Step-by-step explanation:

When looking at a graph, there are two different axes. The vertical values--marked by the center up/down line--are "y-values"; and this is called the "y-axis"

The horizontal values--marked by the left/right line--are "x-values"; and this is called the "x-axis"

For the x-axis, values to the left side of the origin (the place where the y-axis and x-axis intercept) are smaller than 0--they are all negative values.

Values to the right side of the origin are positive--greater than 0.

For the y-axis, positive numbers are on the top half [once again, the midpoint / 0 is where the two lines are both = to 0; the origin] and negative numbers are on the bottom half.

Ordered pairs (points) are written as (x,y)

(x-value, y-value)

We are looking for a graph that decreases (along the y-axis), hits a point below the origin, and goes flat/stays constant.

When a graph is decreasing (note: we read graphs from left to right), the line of the graph is slanted downwards (it looks like a line going down).

So, if we look at the graphs, we can see Graph A descending, crossing the y-axis {crossing the middle line /vertical line / y-axis} at a value of -7, and then staying constant (it is no longer increasing or decreasing because the y-values stay the same)

hope this helps!!

Answer:

-51

Step-by-step explanation:

If the limits are reversed, then place a negative sign in front of the integral.

[tex]\int\limits^a_bf ({x}) \, dx =-\int\limits^b_a f({x}) \, dx[/tex]

[tex]\int\limits^a_3 f({x}) \, dx = 51\\[/tex] where [tex]\alpha =10\\[/tex]

[tex]\int\limits^3_\alpha f( {x}) \, dx =-51[/tex]  where[tex]\alpha =10[/tex]

Answer:

$27,500.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6%/100 = 0.06 per year.

Solving our equation:

A = 11000(1 + (0.06 × 25)) = 27500

A = $27,500.00

The total amount accrued, principal plus interest, from simple interest on a principal of $11,000.00 at a rate of 6% per year for 25 years is $27,500.00.

Answer:

5 < x ≤ 100

(this is inequality form)

{x| 5 < x ≤ 100}

(this is set notation form)

(options B and C)

Step-by-step explanation:

In interval notation,

(  or   ) : does not include value

[ or ]  : does include value

{and remember:

< or > : does not include value

≤ or ≥ : does include value}

when we write something in interval notation, the range of values is from (lowest value, highest value)

for this equation, we know that we are looking for : (5, 100]

which means that the range of numbers goes from

5 (does not include 5) to 100 [does include 100]

so, x > 5 (not equal to); x ≤ 100

we can combine these two concepts: 5 < x ≤ 100

(inequality form)

{when {x | ...} is present, it means the same thing as without it, so

{x| 5 < x ≤ 100} is also correct

(set notation)

hope this helps!!

Answer:

B and C

Step-by-step explanation:

from interval notation we are including 100 but not 5,

x > 5 and x ≤ 100

so B and C are correct

The confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41 where the lower limit is 97.59 and the upper limit is 102.41

We have:

Mean = 100

Sample size = 80

Standard deviation = 11

At 95% confidence interval, the critical z value is:

z = 1.96

The confidence interval is then calculated as:

[tex]CI = \bar x \pm z \frac{\sigma}{\sqrt n}[/tex]

So, we have:

[tex]CI = 100 \pm 1.96 \frac{11}{\sqrt {80}}[/tex]

Evaluate the product

[tex]CI = 100 \pm \frac{21.56}{\sqrt {80}}[/tex]

Divide

[tex]CI = 100 \pm 2.41[/tex]

Split

CI  = (100 - 2.41,100 + 2.41)

Evaluate

CI  = (97.59,102.41)

Hence, the confidence interval for the true mean diastolic blood pressure of all people is 100 ± 2.41

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Step-by-step explanation:

Using dimensional analysis, let convert km to cm.

[tex] \frac{4cm}{1km} \times \frac{km}{100000 \: cm} [/tex]

Cancel out the km

[tex] \frac{4cm}{100000 \: cm} [/tex]

[tex] \frac{1}{25000 } [/tex]

So n= 25000

iii.

Dimensional Analysis

[tex] \frac{3 \: cm}{1 } \times \frac{km}{100000 \: cm} [/tex]

[tex] \frac{3 \: km}{100000} [/tex]

Or

[tex]0.00003 \: km[/tex]

To calculate the distance between two points we use this formula:

[tex] \boxed{ \boxed{{d \: = \: \sqrt{(x_2 \: - \: x_1)^{2} \: + \: (y_2 \: - \: y_1)^{2} } }}}[/tex]

______________________

We apply the values already obtained to the formula to get the distance:

[tex]d \: = \: \sqrt{( - 3 \: - \:( - 5))^{2} \: + \: (0 \: - \: 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: - \: ( - 5))^{2} \: + \: ( - 8)^{2} }[/tex]

[tex]d \: = \: \sqrt{( - 3 \: + \: 5) ^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{ {2}^{2} \: + \: 64 } [/tex]

[tex]d \: = \: \sqrt{4 \: + \: 64} [/tex]

[tex]d \: = \: \sqrt{68} [/tex]

[tex]d \: = \boxed{ \bold{ \: 2 \sqrt{17} \: units}}[/tex]

[tex] \huge{\boxed{ \bold{2 \sqrt{17} \: units }}}[/tex]

Answer:

errrrrr a not too sure but try

Step-by-step explanation:

i did the test got a 90

Divide number in honor society by total students:

191/2000 = 0.0955

Multiply by 100 to get percent:

0.0955 x 100 = 9.55%

Answer is C. 9.55%

The base case of [tex]n=1[/tex] is trivially true, since

[tex]\displaystyle P\left(\bigcup_{i=1}^1 E_i\right) = P(E_1) = \sum_{i=1}^1 P(E_i)[/tex]

but I think the case of [tex]n=2[/tex] may be a bit more convincing in this role. We have by the inclusion/exclusion principle

[tex]\displaystyle P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1 \cup E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le P(E_1) + P(E_2) \\\\ P\left(\bigcup_{i=1}^2 E_i\right) \le \sum_{i=1}^2 P(E_i)[/tex]

with equality if [tex]E_1\cap E_2=\emptyset[/tex].

Now assume the case of [tex]n=k[/tex] is true, that

[tex]\displaystyle P\left(\bigcup_{i=1}^k E_i\right) \le \sum_{i=1}^k P(E_i)[/tex]

We want to use this to prove the claim for [tex]n=k+1[/tex], that

[tex]\displaystyle P\left(\bigcup_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

The I/EP tells us

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cup E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right)[/tex]

and by the same argument as in the [tex]n=2[/tex] case, this leads to

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) = P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) - P\left(\left(\bigcup\limits_{i=1}^k E_i\right) \cap E_{k+1}\right) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1})[/tex]

By the induction hypothesis, we have an upper bound for the probability of the union of the [tex]E_1[/tex] through [tex]E_k[/tex]. The result follows.

[tex]\displaystyle P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le P\left(\bigcup\limits_{i=1}^k E_i\right) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^k P(E_i) + P(E_{k+1}) \\\\ P\left(\bigcup\limits_{i=1}^{k+1} E_i\right) \le \sum_{i=1}^{k+1} P(E_i)[/tex]

Answer:

option c (19.2, -6.7) is correct

Step-by-step explanation:

Mid point - it is the middle point of a line segment. It is equidistant from both endpoints and it is the centroid both of the segment and of the endpoints.

if ([tex]x,y[/tex]) and ([tex]x_{1},y_1[/tex]) are the end points of a line segment then mid point is

given by :- [tex](x+x1)/2 , (y+y1)/2[/tex]

according to question :

given : end point T(-16.8, 31.7)  and mid point M(1.2, 12.5)

let coordinates of another end point S (a, b)

therefore, using mid point formula

1.2 = (-16.8 + a)/2

2.4= (-16.8 + a)

19.2 = a

and,

12.5 = (31.7 + b)/2

25 = 31.7 + b

-6.7 = b

so the option c (19.2, -6.7) is the correct answer

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Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6

Step-by-step explanation:

Caden needs to grow 4 inches tall enough to ride the Super Slide.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Given that:-

Caden's height = 4 feet

Min height to ride the Super slide is = 52 inches

Caden's height in inches will be:-

1 feet = 12 inches

4 feet = 12 x 4 = 48 inches.

The difference between the height will be given as:-

D = 50 - 48 = 4 inches

So Caden should grow his height by 4 inches to ride the super slide.

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Answer:

a=1.66

b=8368.12

Step-by-step explanation:

hope it helps

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangles ΔEST and ΔEFD are similar triangles, therefore, we can write,

[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}[/tex]

Since S and T are midpoints of EF and ED, the lines will be divided into two equal parts. Therefore,

[tex]\dfrac{ES}{EF} = \dfrac{ET}{ED} = \dfrac{ST}{FD}= \dfrac12[/tex]

Therefore, we can write it as,

[tex]FD = 2 (ST)[/tex]

In ΔEST and ΔTDR

∠T ≅ ∠T {Vertical angles}

ET ≅ TD {T is the midpoint of ED}

∠SET ≅ ∠TDR {Alternate interior angles}

Therefore,  ΔEST ≅ ΔTDR.

Since the two triangles are equal we can write,

ST ≅ TR

Further, it can be written as,

FD = 2(ST)

FD = ST + ST

FD = ST + TR

FD = SR

Hence, FD≅SR.

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The base is 60, the part is 40 and the rate is 150%.

The base is the whole quantity or amount that the problem is about.

The part is referred to as the percentage is the portion of the base. The rate is the number with the percentage.

In this case, the base is 60, the part is 40 and the rate is 150%.

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The triangle is not a right triangle. This is because the sum of the square of the two shorter lengths is not equal to the square of the longest length.

In order to determine if the triangle is a right triangle, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

12 ² + 24²

= 144 + 576 = 720

29² = 841

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Answer:

Domain: (-∞, ∞)
Range: [-2, ∞)

Step-by-step explanation:

The domain of any parabola is (-∞, ∞)
The range of this parabola is [-2, ∞) because the vertex is at (-2, -2).

Answer:

$2,120

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for A:

⇒ A = 2000(1 + 0.06(1))

⇒ A = 2000(1.06)

⇒ A = 2120

Therefore, there will be $2,120 in the account at the end of the 1 year period.

Answer:

6x = 9

Step-by-step explanation:

4x-5y  = 12

2x+5y  = -3

Add the equations together

4x-5y  = 12

2x+5y  = -3

-------------------

6x + 0y = 9

6x = 9

Answer:

B. 6x = 9

Step-by-step explanation:

4x - 5y = 12

+ 2x + 5y = -3

____________

6x + 0 = 9

Hence, option B. 6x = 9 is the correct answer.

Answer:

state Avogadro's hypothesis and prove that molecular weight

Answer:

[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]

Step-by-step explanation:

The difference of squares formula gives us

[tex]a^2 - b^2 = (a+b)(a-b)[/tex]

(you can multiply this out to confirm)

[tex]0.09y^2 = (0.3y)^2[/tex]

and

[tex]0.81 = 0.9^2[/tex]

Thus, by the difference of squares formula

[tex]0.09y^2 - 0.81 = (0.3y+0.9)(0.3y-0.9)[/tex]