Mathematics College

1.5 4.5 13.5 40.5.... what is the seventh term in the sequence?

Answers

Answer 1

Each term is 3 times the previous one.
The 5th term is 121.5, the 6th is 364.5, the 7th is 1093.5.

Answer 2

The seventh term in the sequence is 1093.5.

What is Sequence?

A sequence in mathematics is a ordered set od objects or numbers which are related with something.

For example, 1, 3, 5, ..... is a sequence of odd numbers.

Given sequence is,

1.5, 4.5, 13.5, 40.5....

There must be a predictable relation between the numbers in order for them to form in a sequence.

It is clear that,

First term = 1.5

Second term = 3 × 1.5

Third term = 3 × 3 × 1.5 = 1.5 (3)²

............

nth term = 1.5 (3)ⁿ⁻¹

seventh term = 1.5 (3)⁷⁻¹ = 1.5 (3)⁶ = 1093.5

Hence the seventh term is 1093.5.

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Related Questions

Use the chain rule to find dw/dt. w = xey/z, x = t7, y = 4 − t, z = 2 + 9t

Answers

Given

[tex]w = xe^{y/z},\ x = t^7,\ y = 4 - t, \ z = 2 + 9t \\ \\ \frac{dw}{dt} = \frac{dw}{dx} \cdot \frac{dx}{dt} + \frac{dw}{dy} \cdot \frac{dy}{dt} + \frac{dw}{dz} \cdot \frac{dz}{dt} \\ \\ \frac{dw}{dx}=e^{y/z} \\ \\ \frac{dw}{dy}= \frac{x}{z} e^{y/z} \\ \\ \frac{dw}{dz}=- \frac{xy}{z^2} e^{y/z} \\ \\ \frac{dx}{dt}=7t^6 \\ \\ \frac{dy}{dt}=-1 \\ \\ \frac{dz}{dt}=9[/tex]

Thus,

[tex] \frac{dw}{dt}=e^{y/z}\cdot7t^6+\frac{x}{z} e^{y/z}\cdot(-1)+- \frac{xy}{z^2} e^{y/z}\cdot(9) \\ \\ =7t^6e^{y/z}-\frac{x}{z} e^{y/z}-9\frac{xy}{z^2} e^{y/z} \\ \\ =\left(7t^6-\frac{x}{z}-9\frac{xy}{z^2}\right)e^{y/z}[/tex]

The derivative[tex]$ \frac{dw}{dt} $ is $ \frac{7t^6 e^{4-t}}{2+9t} - \frac{t^7 e^{4-t}}{2+9t} - \frac{9t^7 e^{4-t}}{(2+9t)^2} $.[/tex]

To find [tex]$ \frac{dw}{dt} $[/tex] using the chain rule for the given function[tex]$ w = \frac{x e^y}{z} $, where $ x = t^7 $, $ y = 4 - t $, and $ z = 2 + 9t $[/tex], follow these steps:

1. **Express ( w ) in terms of ( t ):**

Substitute ( x ), ( y ), and ( z ) into ( w ):

[tex]\[ w = \frac{x e^y}{z} = \frac{(t^7) e^{(4 - t)}}{2 + 9t} \][/tex]

2. **Apply the chain rule:**

The chain rule states that for a function ( w(t) ) defined implicitly by ( w = f(x(t), y(t), z(t)) ), the derivative [tex]$ \frac{dw}{dt} $[/tex] is given by:

[tex]\[ \frac{dw}{dt} = \frac{\partial w}{\partial x} \cdot \frac{dx}{dt} + \frac{\partial w}{\partial y} \cdot \frac{dy}{dt} + \frac{\partial w}{\partial z} \cdot \frac{dz}{dt} \][/tex]

3. **Compute partial derivatives of ( w ) with respect to ( x ), ( y ), and ( z ):**

[tex]$ \frac{\partial w}{\partial x} = \frac{e^y}{z} $[/tex]

[tex]$ \frac{\partial w}{\partial y} = \frac{x e^y}{z} $[/tex]

[tex]$ \frac{\partial w}{\partial z} = -\frac{x e^y}{z^2} $[/tex]

4. **Compute [tex]$ \frac{dx}{dt} $, $ \frac{dy}{dt} $, and $ \frac{dz}{dt} $:**[/tex]

[tex]$ \frac{dx}{dt} = 7t^6 $[/tex]

[tex]$ \frac{dy}{dt} = -1 $[/tex]

[tex]$ \frac{dz}{dt} = 9 $[/tex]

5. **Substitute these into the chain rule formula:**

[tex]\[ \frac{dw}{dt} = \frac{e^y}{z} \cdot 7t^6 + \frac{x e^y}{z} \cdot (-1) + \left(-\frac{x e^y}{z^2}\right) \cdot 9 \][/tex]

6. **Substitute[tex]$ x = t^7 $, $ y = 4 - t $, $ z = 2 + 9t $[/tex] into the expression:**

[tex]$ e^y = e^{4 - t} $[/tex]

Substitute these values into the formula for [tex]$ \frac{dw}{dt} $:[/tex]

[tex]\[ \frac{dw}{dt} = \frac{e^{4 - t}}{2 + 9t} \cdot 7t^6 - \frac{t^7 \cdot e^{4 - t}}{2 + 9t} - \frac{9t^7 \cdot e^{4 - t}}{(2 + 9t)^2} \][/tex]

Therefore, [tex]$ \frac{dw}{dt} $[/tex] is:

[tex]{\frac{dw}{dt} = \frac{7t^6 e^{4 - t}}{2 + 9t} - \frac{t^7 e^{4 - t}}{2 + 9t} - \frac{9t^7 e^{4 - t}}{(2 + 9t)^2} } \][/tex]

how can I adjust a quotient to solve a division problem

Answers

Ask them to first estimate the quotient and then to find the actual

A submarine dives 300 feet every 2 minutes,and 6750 feet every 45 minutes.Find the constant rate at which he submarine dives.Give your answer in feet per minute and in feet per hour.

Answers

The answer is 150 feet/minutes and 9000 feet/hour

In order to find the constant rate per minute, we just need to divide the diving distance with the time needed to do so.

300/ 2 minutes = 150 feet/ minutes
6750/45 minutes = 150 feet/minutes . . . .proof there is no acceleration

So, the constant rate per hour will be
150x60 = 9000 feet/hour

30 POINTS: The art club had an election to select a president. 25% of the 76 members of the club voted in the election. How many members voted?

Answers

Answer:

19 members voted.

Step-by-step explanation:

Percentage problems can be solved by a rule of three.

25% of the 76 members of the club voted in the election. How many members voted?

So 76 is 100% = 1. How much is 0.25?

76 - 1

x - 0.25

[tex]x = 76*0.25[/tex]

[tex]x = 19[/tex]

19 members voted.

Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(t) = at2 + bt + c, where a, b, and c are to be determined.

Answers

The particular quadratic solution to the ODE is found as follows:

[tex]x=at^2+bt+c[/tex]
[tex]x'=2at+b[/tex]

[tex](2at+b)+2(at^2+bt+c)=t^2+4t+7[/tex]
[tex]2at^2+(2a+2b)t+(b+2c)=t^2+4t+7[/tex]

[tex]\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4[/tex]

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

[tex]x'+2x=0\implies r+2=0\implies r=-2[/tex]

so that [tex]x_c=Ce^{-2t}[/tex] is a characteristic solution to the ODE, and the general solution would be

[tex]x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4[/tex]

To find a, b, c for the solution:

Let's start by writing down the expression for the function x(t) and its derivative:

We have:

x(t) = at² + bt + c
and
x'(t) = 2at + b

Using x' and x into the differential equation x′ + 2x = t² + 4t + 7 gives us:

2at + b + 2*(at² + bt + c) = t² + 4t + 7
Expanding this gives:
2at² + 2bt + b + 4at + 2c = t² + 4t + 7

By equating the coefficients of equivalent powers of t on both sides, we get three equations:

For t² :
2a = 1
So, a = 1/2

For t:
2b + 4a = 4
Substitute a = 1/2 into the equation gives b = 1 - 2 = -1

For the constant term:
b + 2c = 7
Substituting b = -1 gives c = 4.

So the solution is a = 1/2, b = -1, c = 4.

So the specific solution of this differential equation is given by x(t) = (1/2)t² - t + 4.

D is the midpoint of CE.E has coordinates (-3,-2), and D has coordinates (2 1/2, 1). Find the coordinate of C.

Answers

midpoint formula : (x1 + x2) / 2, (y1 + y2) / 2
(-3,-2)....x1 = -3 and y1 = -2
(x,y)......x2 = x and y2 = y
now we sub
(-3 + x) / 2, (-2 + y) / 2

(-3 + x) / 2 = 2 1/2
-3 + x = 5/2 * 2
-3 + x = 5
x = 5 + 3
x = 8

(-2 + y) / 2 = 1
-2 + y = 1 * 2
-2 + y = 2
y = 2 + 2
y = 4

so the coordinates of point C are : (8,4)

The coordinate of point C on line CE will be (8, 4).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

D is the midpoint of CE.

E has coordinates (-3,-2), and D has coordinates (2 1/2, 1).

Now, By the definition of midpoint;

Let the coordinate of point C = (x, y)

Then,

((x + (-3))/2 , (y + (-2))/2) = (2 1/2, 1)

By comparison we get;

x + (-3) / 2= 2 1/2

x - 3 = 2 (5/2)

x - 3 = 5

x = 3 + 5

x = 8

And, (y + (-2))/2 = 1

y - 2 = 2

y = 2 + 2

y = 4

Thus, The coordinate of point C = (x, y) = (8, 4)

So, The coordinate of point C on line CE will be (8, 4).

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write a fraction less than 1 with a denominator of 6 that is greater than 3/4

Answers

The answer would be 5/6.

Hope this helps!

Answer:= 5/6

Step-by-step explanation:hope this helps

Given sina=6/7 and cosb=-1/6, where a is in quadrant ii and b is in quadrant iii , find sin(a+b) , cos(a-b) and tan(a+b)

Answers

[tex]\bf sin(a)=\cfrac{\stackrel{opposite}{6}}{\stackrel{hypotenuse}{7}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{7^2-6^2}=a\implies \pm\sqrt{13}=a \\\\\\ \textit{now, angle "a" is in the II quadrant, where the adjacent is negative} \\\\\\ -\sqrt{13}=a\qquad \qquad \boxed{cos(a)=\cfrac{-\sqrt{13}}{7}}[/tex]

now, keep in mind that, the hypotenuse is just a radius unit, and thus is never negative, so if a fraction with it is negative, is the other unit. A good example of that is the second fraction here, -1/6, where the hypotenuse is 6, therefore the adjacent side is -1. Anyhow, let's find the opposite side to get the sin(b).

[tex]\bf cos(b)=\cfrac{\stackrel{adjacent}{-1}}{\stackrel{hypotenuse}{6}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a \\\\\\ \textit{now, angle "b" is in the III quadrant, where the opposite is negative} \\\\\\ -\sqrt{35}=b\qquad \qquad \boxed{sin(b)=\cfrac{-\sqrt{35}}{6}}[/tex]

now

[tex]\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ [/tex]

[tex]\bf tan({{ \alpha}} + {{ \beta}}) = \cfrac{tan({{ \alpha}})+ tan({{ \beta}})}{1- tan({{ \alpha}})tan({{ \beta}})}\qquad tan({{ \alpha}} - {{ \beta}}) = \cfrac{tan({{ \alpha}})- tan({{ \beta}})}{1+ tan({{ \alpha}})tan({{ \beta}})}[/tex]

[tex]\bf sin(a+b)=\cfrac{6}{7}\cdot \cfrac{-1}{6}+\cfrac{-\sqrt{13}}{7}\cdot \cfrac{-\sqrt{35}}{6}\implies \cfrac{-1}{7}+\cfrac{\sqrt{455}}{42} \\\\\\ \cfrac{-6+\sqrt{455}}{42}\\\\ -------------------------------\\\\ cos(a-b)=\cfrac{-\sqrt{13}}{7}\cdot \cfrac{-1}{6}+\cfrac{6}{7}\cdot \cfrac{-\sqrt{35}}{6}\implies \cfrac{\sqrt{13}}{42}-\cfrac{\sqrt{35}}{7} \\\\\\ \cfrac{\sqrt{13}-6\sqrt{35}}{42}[/tex]

[tex]\bf -------------------------------\\\\ tan(a)=\cfrac{\frac{6}{7}}{-\frac{\sqrt{13}}{7}}\implies -\cfrac{6}{\sqrt{13}}\implies -\cfrac{6\sqrt{13}}{13} \\\\\\ tan(b)=\cfrac{\frac{-\sqrt{35}}{6}}{\frac{-1}{6}}\implies -\sqrt{35}\\\\ -------------------------------\\\\[/tex]

[tex]\bf tan(a+b)=\cfrac{-\frac{6}{\sqrt{13}}-\sqrt{35}}{1-\left( -\frac{6}{\sqrt{13}} \right)\left( -\sqrt{35} \right)}\implies \cfrac{\frac{-6-\sqrt{455}}{\sqrt{13}}}{1-\frac{6\sqrt{35}}{\sqrt{13}}} \\\\\\ \cfrac{\frac{-6-\sqrt{455}}{\sqrt{13}}}{\frac{\sqrt{13}-6\sqrt{35}}{\sqrt{13}}}\implies \cfrac{-6-\sqrt{455}}{\sqrt{13}-6\sqrt{35}}[/tex]

and now, let's rationalize the denominator of that one, hmmm let's see

[tex]\bf \cfrac{-6-\sqrt{455}}{\sqrt{13}-6\sqrt{35}}\cdot \cfrac{\sqrt{13}+6\sqrt{35}}{\sqrt{13}+6\sqrt{35}} \\\\\\ \cfrac{-6\sqrt{13}-36\sqrt{35}-\sqrt{5915}-6\sqrt{15925}}{({\sqrt{13}-6\sqrt{35}})({\sqrt{13}+6\sqrt{35}})} \\\\\\ \cfrac{-6\sqrt{13}-36\sqrt{35}-13\sqrt{35}-210\sqrt{13}}{(\sqrt{13})^2-(6\sqrt{35})^2} \\\\\\ \cfrac{-216\sqrt{13}-49\sqrt{35}}{13-210}\implies \cfrac{-216\sqrt{13}-49\sqrt{35}}{-197} \\\\\\ \cfrac{216\sqrt{13}+49\sqrt{35}}{197}[/tex]

sin(a+b) = -1/7 +√455/42 = 0.8721804464845457

cos(a-b) = √13/42 - √35/7 = -0.7761476987942811

tan(a+b )= (6√13/13 + √35) / (1 - 6√455/13) = -0.525

Given sin(a) = 6/7 and cos(b) = -1/6, with a in quadrant II and b in quadrant III, we need to utilize trigonometric identities to find sin(a+b), cos(a-b), and tan(a+b).

Firstly, since a is in quadrant II, cos(a) is negative. We use the identity sin²(a) + cos²(a)=1 to find cos(a):

cos(a) = -√(1 - sin²(a)) = -√(1 - (6/7)²) = -√(1 - 36/49) = -√(13/49) = -√13/7

Similarly, since b is in quadrant III, sin(b) is also negative. We use the identity sin²(b) + cos²(b)=1 to find sin(b):

sin(b) = -√(1 - cos²(b)) = -√(1 - (-1/6)²) = -√(1 - 1/36) = -√(35/36) = -√35/6

Now we can use the angle addition and subtraction formulas:

1. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

sin(a + b) = (6/7)(-1/6) + (-√13/7)(-√35/6) = -1/7 + √(13×35)/(7×6) = -1/7 + √455/42 = -1/7 +√455/42

2. cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

cos(a - b) = (-√13/7)(-1/6) + (6/7)(-√35/6) = √13/(7×6) - (6√35)/(7×6) = √13/42 - √35/7

3. tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

Using tan(a) = -sin(a)/cos(a) = -(6/7)/(-√13/7) = 6/√13 and tan(b) = sin(b)/cos(b) = (-√35/6)/(-1/6) = √35:tan(a + b) = (6/√13 + √35) / (1 - (6/√13)(√35)) = (6√13/13 + √35) / (1 - 6√455/13)

Round 5836197 to the nearest hundred

Answers

5838200 is to the nearest hundred.

Answer:

5836200.

Step-by-step explanation:

Given : 5836197 .

To find : Round 5836197 to the nearest hundred.

Solution : We have given 5836197

Step 1 : First, we look for the rounding place which is the hundreds place.

Step 2 : Rounding place is 97.

Step 3 : 97 is greater than 50 then it would be rounded up mean next number to 97 would be increase to 1 and 97 become 00.

Step 4 : 5836200.

Therefore, 5836200.

What's 24.67 to one significant figure?

Answers

24.67 is just barely before 25.00, so we should be able to round 20.00, which gives us only one significant digit.

Mrs. Milleman looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent.

Answers

First we need to calculate the difference between the original price and the new price:
[tex]2075-1195=880[/tex]
Now we can set up a proportion and solve for x:
[tex] \frac{1195}{100} = \frac{880}{x} [/tex]
[tex]x= \frac{(880)(100)}{1195} [/tex]
[tex]x= 73.64 [/tex] which rounded to the nearest integer is 74%
We now can conclude that the price increased in 74%

Jonathan pays $1.90 per pound for potatoes. He buys 8.3 pounds of potatoes. He determines that he will pay $15.77, before tax, for the potatoes. Which best describes the reasonableness of Jonathan’s solution?

Answers

The equation for this problem would be 15.77=1.90 times 8.3, as Jonathan buys 8.3 pounds of potatoes and one pound is $1.90. To get the entire cost without the tax, you have to include how much the entire quantity of the product costs, not just part of it.

The correct answer is C.

Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.

Hope this helps.

Determine whether the function f : z × z → z is onto if
a.f(m,n)=m+n. b)f(m,n)=m2+n2.
c.f(m,n)=m.
d.f(m,n) = |n|.
e.f(m,n)=m−n.

Answers

a. Yes; [tex]\mathbb Z[/tex] is closed under addition
b. No; [tex]m^2+n^2\ge0[/tex] for any integers [tex]m,n[/tex]
c. Yes; self-evident
d. No; similar to (b), because [tex]|n|\ge0[/tex] for any [tex]n\in\mathbb Z[/tex]
e. Yes; [tex]\mathbb Z[/tex] is closed under subtraction

The function y = –3(x – 2)2 + 6 shows the daily profit (in hundreds of dollars) of a hot dog stand, where x is the price of a hot dog (in dollars). Find and interpret the zeros of this tion

A. Zeros at x = 2 and x = 6
B. Zeros at
C. The zeros are the hot dog prices that give $0.00 profit (no profit).
D. The zeros are the hot dog prices at which they sell 0 hot dogs.

Answers

the zeroes

the serose of the x value is where y=0,
that is where profit=0

the zeroes of the y value is where x=0
that's when the price is 0 dollars

ok
x zeroes
solve for when y=0
[tex]0=-3(x-2)^2+6[/tex]
[tex]-6=-3(x-2)^2[/tex]
[tex]2=(x-2)^2[/tex]
[tex]+/-\sqrt{2}=x-2[/tex]
[tex]2+/-\sqrt{2}=x[/tex]
x zeroes at [tex]x=2+\sqrt{2}[/tex] and [tex]x=2-\sqrt{2}[/tex]

y zeroes
x=0
[tex]y=-3(0-2)^2+6[/tex]
[tex]y=-3(-2)^2+6[/tex]
[tex]y=-3(4)+6[/tex]
[tex]y=-12+6[/tex]
[tex]y=-6[/tex]

the y zeroes are where they sell 0 hot dogs for 0 dollars, it is $-6 profit
the x zereoes are where you make 0 profit, that occurs when you sell [tex]2+\sqrt{2}[/tex] and [tex]2-\sqrt{2}[/tex] hot dogs
not sure which answer you want because it doesn't specify which zeroes we want

A is wrong tho

Final answer:

The zeros of the function y = -3(x - 2)² + 6 are x = 2 + √2 and x = 2 - √2, which represent the hot dog prices at which the hot dog stand makes $0.00 profit.

Explanation:

The zeros of a function are the values of x that make the y-coordinate equal to zero. In this case, the function y = -3(x - 2)² + 6 represents the daily profit, and we need to find the x-values that result in a profit of $0.00. Setting the profit, y, to zero and solving for x, we get:

0 = -3(x - 2)² + 6

Adding 3(x - 2)² to both sides and simplifying the equation gives:

3(x - 2)² = 6

Dividing both sides by 3, we have:

(x - 2)² = 2

Take the square root of both sides, remembering to consider both the positive and negative square roots:

x - 2 = ±√2

Adding 2 to both sides gives us the final solutions:

x = 2 ± √2

So, the zeros of this function are x = 2 + √2 and x = 2 - √2. These are the hot dog prices at which the hot dog stand makes $0.00 profit.

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A, B, and C are mutually exclusive. P(A) = .2, P(B) = .3, P(C) = .3. Find P(A ∪ B ∪ C). P(A ∪ B ∪ C) =

Answers

Events are said to be mutually exclusive if they can not occur at the same time, that is, the probability of those events occurring at the same time is zero.
In the question given above,
P (A) = .2
P (B) = .3
P (C) = .3
P (A U B U C) = .2 + .3 + .3 = .8
Therefore, P (A U B U C) = 0.8.

The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.

Answers

Answer:

Hence, AB=12.

Step-by-step explanation:

We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.

this means that side AE=BE.

Also we could clear;ly observe that

ΔBED≅ΔAED

( since AE=BE, side ED common, ∠BED=∠AED

so by SAS congruency the two triangles are congruent)

Now we are given that:

the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.

i.e. AB+AC+BC=AC+AD+CD+12

AB+BC=AD+CD+12

as AD=BD

this means that AD+CD=BD+CD=BC

AB+BC=BC+12

AB=12

Hence AB=12

Answer:

The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].

Step-by-step explanation:

Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of [tex]\bigtriangleup{ACD}[/tex].

From the figure,

[tex]AE=BE[/tex] .......(1) (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])

Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]

[tex]AE=BE[/tex] ( from equation 1 )

[tex]\angle {BED} =\angle {AED}[/tex] ( Both [tex]90^\circ[/tex] )

[tex]ED=ED[/tex] ( Common side)

[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex] ( by SAS congruence rule)

[tex]BD=AD[/tex] .........(2) (by CPCT)

As per question,

The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.

[tex]AB+BC+AC=AC+CD+AD+12[/tex]

[tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]

[tex]AB=12\rm\;{cm}[/tex]

Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].

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The diagram represents a reduction of a triangle by using a scale factor of 0.8.

What is the height of the reduced triangle?
4.0 inches
4.8 inches
5.2 inches
7.5 inches

Answers

The reduction factor of 0.8 means the lengths in the reduced triangle are 0.8 times those of the original.

Then the original 6 inch length is reduced to 0.8×6 inches = 4.8 inches in the reduced triangle.

Answer:

4.8 inches

Step-by-step explanation:

The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:

6 inches * scale factor

6 inches* 0.8= 4.8 inches

So the resultant triangle will have a height of 4.8 inches.

The five-number summary for scores on a statistics test is 11, 35, 61, 70, 79. in all, 380 students took the test. about how many scored between 35 and 61

Answers

Answer: There are 95 students who scored between 35 and 61.

Step-by-step explanation:

Since we have given that

The following data : 11,35,61,70,79.

So, the median of this data would be = 61

First two data belongs to "First Quartile " i.e. Q₁

and the second quartile is the median i.e. 61.

The last two quartile belongs to "Third Quartile" i.e. Q₃

And we know that each quartile is the 25th percentile.

And we need "Number of students who scored between 35 and 61."

So, between 35 and 61 is 25% of total number of students.

So, Number of students who scored between 35 and 61 is given by

[tex]\dfrac{25}{100}\times 380\\\\=\dfrac{1}{4}\times 380\\\\=95[/tex]

Hence, There are 95 students who scored between 35 and 61.

The number of students who scored between 35 and 61 is 95

The 5 number summary is the value of the ;

Minimum Lower quartile Median Upper quartile and Maximum values of a distribution.

The total Number of students = 380

The lower quartile (Lower 25%) = 35

The median (50%) = 61

The Number of students who scored between 35 and 61 : 50% - 25% = 25%

This means that 25% of the total students scored between 35 and 61.

25% of 380 = 0.25 × 380 = 95

Hence, 95 students scored between 35 and 61.

Learn more : https://brainly.com/question/24582786

Scores on a certain test are normally distributed with a variance of 88. a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 3 units.

Answers

To solve for the problem, the formula is:

n = [z*s/E]^2

where:

z is the z value for the confidence interval

s is the standard deviation

E is the number of units

So plugging that in our equation, will give us:

= [1.96*9.38/3]^2

= (18.3848/3)^2

= 6.1284^2

= 37.5 or 38

What is the unit rate for 822.6 km in 18 hours? Enter your answer, as a decimal, in the box. Please Help

Answers

unit rate = 822.6 / 18 = 45.7

answer
unit rate = 45.7 km per hour

Find the unit rate by dividing 822.6 km by 18 hours:

822.6 km
-------------- = 45.7 km/hr
18 hrs

Note: this is approx 45.7 km/hr 0.625 mile
--------------- * ----------------- = 28.6 mph
1 1 km

4 is to 5 as 10 is to a

A.8
B.12
C.12.5
D.20

Answers

Use a proportion.

4 is to 5 as 10 is to a

4/5 = 10/a

4a = 5 * 10

4a = 50

a = 12.5

Answer: C. 12.5

605 mi in 11 hours at the same rate how many miles would he drive in 13 hours

Answers

First you need to find the unit rate

605/ 11= 55

55*13=715

In 13 hours, 715 miles will be traveled

15 children voted for their favorite color. The votes for red and blue together we're double the votes for green and yellow together. How did the children vote?

Answers

10 for red and blue together and 5 for green and yellow together

10 children voted for red and blue
and 5 voted gor green and yellow

Which fraction is less than 1/2 a.3/8 b.5/8 c.5/7 d.9/16

Answers

3/8 because half of 8 would be 4/8

You would find it much easier to compare these fractions if you'd work with a common denominator. In this problem the common denominator is 16 (actually, the LCD is 16*7, or 112, but let's continue anyway):

Then we'll be working with 8/16: a.6/16 b.10/16 c.5/7 d.9/16, instead of with 1/2 a.3/8 b.5/8 c.5/7 d.9/16.

Which fraction is less than 1/2? Ask yourself: which fraction is less than 8/16? Only (a) satisfies this: 6/16, or 3/8, is smaller than 1/2.

How do you figure out what 1/10 of 1,7000.000 km squared is?

Answers

The first thing you would do is square 17,000, which is 298,000,000. Then you would multiply 298,000,000 by 0.10. (or divide the number by 10)

This would get you 28,900,000.

Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?

Answers

Compute for the total balance:

total balance = $415 + $215 = $630

Then we compute for the total credit limit:

total credit limit = $1,000 + $750 = $1,750

The credit utilization would simply be the percentage ratio of total balance over total credit limit. That is:

credit utilization = ($630 / $1,750) * 100%

credit utilization = 36%

what is the answer of 9X23+3X39-28=n

Answers

9x23+3x39-28=n

n= 296

Answer: n=296

Step-by-step explanation: 9 x 23 + 3 x 39 - 28 + n = 296

Hope this helps! <3

If I have a floor that is 100 3/4 feet by 75 1/2 what is the area

Answers

the area, assuming is a rectangular floor, is their product.

so simply convert the mixed to improper and get their product.

[tex]\bf \stackrel{mixed}{100\frac{3}{4}}\implies \cfrac{100\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{403}{4}} \\\\\\ \stackrel{mixed}{75\frac{1}{2}}\implies \cfrac{75\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{151}{2}}\\\\ -------------------------------\\\\ \cfrac{403}{4}\cdot \cfrac{151}{2}\implies \cfrac{403\cdot 151}{4\cdot 2}\implies \cfrac{60853}{8}\implies 7606\frac{5}{8}~ft^2[/tex]

During her first year of subscribing to a newspaper, Christie paid $48. During each subsequent year, the annual cost was 1.5 times the price paid the previous year. Which of the following equations may be used to calculate the total cost, C, of subscribing to the newspaper after n years?

Answers

Assuming that n = 0 when we focus on the first year, C = $48*1.5^n would represent the cost for the 2nd, 3rd, 4th, .... , years.

Check: $48(1.5)^0 = $48(1) = $48 (correct)
$48(1.5)^1 = $48(1.5) = $72 (correct)
$48(1.5)^2 = $48(2.25) = $108

These results are as expected.

Newton uses a credit card with a 18.6% APR, compounded monthly, to pay for a cruise totaling $1,920.96. He can pay $720 per month on the card. What will the total cost of this purchase be?

Answers

To find out how much Newton would pay you take the cruise cost of $1920.96 and divide by $720 to find out it would take 3 months for Newton to pay off the balance at $720 per month. The cost of the cruise would be $1920.96 + ($1920.96-$720)*0.186+ ($1920-$1440)*0.186)

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