Money that is collecting interest in a bank account doubles in value every 8
years.
When the account was opened, it had 8, or 23 dollars in it. After 32 years, the
account balance has doubled 4 times, increasing by a factor of 24,
It now has a balance of 23. 24. Expressed as a power, how much money, in
dollars, is in the account after 32 years?
A. 24
d
B. 27
C. 212
D. 47

The area of the blue-shaded region is 19.95 m²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,

Using the Pythagoras theorem,

15.5² = 14²+w² [width]

w² = 240.25-196

w² = 44.25

w = 6.65

Therefore, the width of the rectangle is 6.65 m

That mean, the height of the parallelogram is 6.65 m,

The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,

Area of the remaining region = 14×6.65-11×6.65

= 6.65(14-11) = 6.65×3

= 19.95 m²

Hence, the area of the blue-shaded region is 19.95 m²

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Answer:

290

Step-by-step explanation:

(11*8)*2=176, (11*3)*2=66, (3*8)*2=48, 48+176+66= 290

Answer:

y= -1/3x + -5

Step-by-step explanation:

y= mx + b

b= y-intercept, which is -5. (x-value where the lines goes through the y-axis)

To find the slope, you take the

Change of y/ Change of x

Take two points (I did, (0,-5) and (3, -6) ).     (x,y)

-6 - (-5)= -1

3 - 0= 3

-1/3= m

Answer:

1. veinte (10 * 2 = 20)  

2.  tres ( 12 ÷ 4 = 3)

3. veinte (18 + 2= 20)

4.  diez ( 15 - 5 = 10)

5. once (14 - 3 = 11)

Answer:

19%

Step-by-step explanation:

(107.10 ÷ 90) * 100 = (1.19) * 100

= 119

so, increase in cost is 119 - 100 = 19%

Factorisation:

\(\rightarrow \sf 20mn-15m\)

take 5m as common term

\(\rightarrow \sf 5m\left(4n-3\right)\)

solving/simplifying:

\(\rightarrow \sf \left(\dfrac{5}{6}z\:+\:5\right)+\left(-\dfrac{1}{3}z-4\right)\)

\(\rightarrow \sf \dfrac{5}{6}z+5-\dfrac{1}{3}z-4\)

\(\rightarrow \sf \dfrac{5}{6}z-\dfrac{1}{3}z+5-4\)

\(\rightarrow \sf \dfrac{5}{6}z-\dfrac{1(2)}{6}z+1\)

\(\rightarrow \sf \dfrac{5-2}{6}z+1\)

\(\rightarrow \sf \dfrac{3}{6}z+1\)

\(\rightarrow \sf \dfrac{1}{2}z+1\)

Answer:

\(5m(4n - 3)\)

\(\dfrac12z+1\)

Step-by-step explanation:

Given expression:

\(20mn-15m\)

Rewrite 20 as \(4\cdot 5\)

Rewrite 15 at \(3 \cdot 5\)

Therefore,

\(20mn-15m=4\cdot 5m\cdot n-3 \cdot 5m\)

Factor out common term \(5m\) :

\(\implie 5m(4n-3)\)

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

Given expression:

\(\left(\dfrac56z + 5\right)+\left(-\dfrac13z-4\right)\)

Simplify:

\(\dfrac56z+5-\dfrac13z-4\)

Group like terms:

\(\dfrac56z-\dfrac13z+5-4\)

Combine like terms:

\(\dfrac12z+1\)

Given:

A piecewise function

\(f(x)=\begin{cases}3 &,x<0 \\ x^2+2 &,0\leq x<2 \\ \dfrac{1}{2}x+5 &,x\geq 2 \end{cases}\)

To find:

The range of the function.

Solution:

Range is the set of output values.

For \(x<0\), the function is \(f(x)=3\)       ...(i)

For \(0\leq x<2\), the function is \(f(x)=x^2+2\).

\(0\leq x<2\)

Squaring each side.

\(0^2\leq x^2<2^2\)

Adding 2 on each side.

\(0+2\leq x^2+2<4+2\)

\(2\leq f(x)<6\)               ...(ii)

For \(x\geq 2\), the function is \(f(x)=\dfrac{1}{2}x+5\).

\(x\geq 2\)

Divide both sides by 2.

\(\dfrac{1}{2}x\geq 1\)

Adding 5 on each side.

\(\dfrac{1}{2}x+5\geq 1+5\)

\(f(x)\geq 6\)                 ...(iii)

From (i), (ii) and (iii), it is clear that the values of f(x) lies in the interval [2,∞).

So, the range of the given function is [2,∞).

Therefore, the correct option is b.

correct answer is B

Life is a high way i wan to drive it all night long.

The equations that can be used to determine the length of the room are:

y(y + 5) = 750

y²– 5y = 750

(y - 30) (y + 25) = 0

A rectangle is a two-dimensional object that has four sides and four right angles. The sides of a rectangle are known as the width and the length.  A rectangle has two diagonals of equal length which bisect each other at right angles.

Area of a rectangle = length x width

750 = y x (y - 5)

750 = y² - 5y

y² - 5y - 750 = 0

The factors of -750y² that add up to -5y are 25y and -30

(y² + 25y)(-30y - 750) = 0

y(y + 25) = 0

-30(y + 25) = 0

(y - 30) (y + 25) = 0

Here is the complete question:

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

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Answer:

Step-by-step explanation:

25.65 ≈ 25.7, 13.23 ≈ 13.2, 6.35 ≈ 6.4

Correct choice is b.

Answer:

the year is 2016

Step-by-step explanation:

The computation is shown below:

Given that

The population in 2009 is 45.1 million

And it would be increased 2.3% each year

So,

In the year 2010 it is = 45.1 million × (1 + 0.023) = $46.14 million

In the year 2011, it is = $46.14 million × (1 + 0.023) =$47.20 million

In the year 2012, it is = $47.20 million × (1 + 0.023) = $48.29 million

In the year 2013, it is = $48.29 million × (1 + 0.023) = $49.40 million

In the year 2014, it is = $49.40 million × (1 + 0.023) = $50.54 million

In the year 2015, it is = $50.54 million × (1 + 0.023) = $51.70 million

In the year 2016, it is = $51.70 million × (1 + 0.023) = $52.89 million

Hence, the year is 2016

Answer:

0=4×4−4×4

Step-by-step explanation:

Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

1 = 4 ÷ 4

2 = (4 + 4) ÷ 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 - 4

5 = (4 × 4 + 4) ÷ 4

6 = (4 + 4) - (4 ÷ 4) - (4 ÷ 4)

7 = (4 + 4) - (4 ÷ 4)

8 = 4 + 4

9 = (4 + 4) + (4 ÷ 4)

10 = (4 + 4) + (4 ÷ 4) + (4 ÷ 4)

Answer:

94 stickers

Step-by-step explanation:

X/2 + 50 = 238

X/2 = 238-50

X= 188/2

X = 94

Answer:

1

Step-by-step explanation:

13 x 4 = 52

53 - 52 = 1

Answer:

1 ballon

Step-by-step explanation:

if we take 53 divided by 4, we get 13 so each child get 13 ballons leaving one behind

There are a total of 4 combinations of 3 digit combinations using only 4 digits

The number of 3 digit combinations of any group of numbers is calculated using:

Combination = \(^nC_r\)

Where:

n = the available digits

r = 3 i.e. the digits to combine

When the value of n is 4, the equation becomes

Combination = \(^4C_3\)

Apply the combination formula

Combination = 4

The lowest and the highest number depend on the value of each digit to be combined

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All values of t for which the rocket's height is 92 feet are;

t= 0.55 or 10.89 seconds  

Given that model rocket is launched with an initial upward velocity of 164 ft/s.

The rocket's height h (in feet) after t seconds :

To Find:  

Find all values of t for which the rocket's height is 92 feet.

h=164t – 16t²

92 = 164t – 16t²

-164t + 16t² + 92 = 0

Solve with the quadratic formula:

t = [ -(-164) ± √((-164)² − 4(16)(92)) ] / 2(16)

t = (164± √27409) / 32

t = (164± √27409) / 32

t ≈ 0.55 or 10.89

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Answer:

Step-by-step explanation:

what is 12/21 + 18/21 + 14/21

(12 + 18 + 14)/21 =

44/21

The angular acceleration of the propeller can be determined from the slope of the velocity-time graph, which represents the rate of change of the propeller's angular velocity with time.

In the first motion graph, we see that the angular position of the propeller is increasing with time, which means that the propeller is rotating in a clockwise direction.

In the second motion graph, we see that the angular velocity of the propeller is increasing with time, which means that the propeller is accelerating in its rotational motion.

acceleration = change in velocity / change in time

In mathematical terms, we can express the angular acceleration of the propeller as:

α = Δω / Δt

Where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the change in time. We can determine the angular acceleration of the propeller at a specific time by finding the slope of the tangent line to the velocity-time graph at that time.

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the counting number just before C5F16 is 3,072.

The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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Answer: 0.655

Step-by-step explanation:

Let X be a random variable that represents percent of fat calories that a person in America consumes each day.

As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).

Sample size : n= 16

The probability that the average percent of fat calories consumed is more than 35:

\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)

Hence, Required probability =0.655

Answer:

144

Step-by-step explanation:

Surface Area is the area of every side.

Top and bottom:  6*8/2=24 (area of a triangle)

small side: 6*4=24

medium side: 4*8=32

large side: 4*10=40

So answer 24+24+24+32+40=144

Have a Great Day! (This is my first answer)

Answer:

x=2 or x=-2

Step-by-step explanation:

Answer: correct answer is A! -2 and 2

Step-by-step explanation:

Answer:

A: 12.5 per week B= 12.75

Step-by-step explanation:

1/2 times 7 (days in a week) is 3.5. So A is 8+3.5=12.5. 7 times 5/4 is 8.75. So B is 4+8.75=12.75

Answer:

Step-by-step explanation:

Given equation:

Solve:

The sοlutiοn οf the system οf equatiοn is x = 0 and y = 7/3.

If there is nο sοlutiοn tο a system οf equatiοns, it is incοnsistent system; οtherwise, there must be at least οne sοlutiοn. If a set οf equatiοns has infinitely many sοlutiοns, it is dependent.

Every οne οf the equatiοns in a system οf equatiοns must have a sοlutiοn in οrder fοr the system tο be cοnsistent. This demοnstrates that a set οf values fοr the variables may simultaneοusly satisfy all οf the system's equatiοns and shοw that they are nοt mutually exclusive.

There is nο sοlutiοn tο an equatiοn system that satisfies all οf the equatiοns in the system. This indicates that nο cοmbinatiοn οf values fοr the variables can cοncurrently satisfy all οf the system's equatiοns since they are incοmpatible.

The given equatiοns are:

y = 2/3x + 7/3

-4x+6y=14

Substituting the value of y in the second equation:

-4x + 6y = 14

-4x + 6(2/3x + 7/3) = 14

-2x + 4x + 14 = 14

2x = 0

x = 0

Substitute the value of x = 0 we have:

y = 2/3(0) + 7/3

y = 7/3

Hence, the solution of the system of equation is x = 0 and y = 7/3.

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Complete question:

Given system of equations y = 2/3x + 7/3 and -4x + 6y = 14

Find the value of x and y.

No, it is impossible to construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm as the dimensions defy the triangle inequality theorem.

It follows from the triangle inequality theorem that the sum of any two side lengths of a triangle must be greater than the third side length and also, the difference of two side lengths of a triangle must be less than the third side lengths.

However, in this case, since QR + PR = PQ, it can be inferred that the two side lengths cannot possibly be used to construct a triangle.

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Answer:

d 0.5282

Step-by-step explanation:

Given the following :

Probability of getting to the bus on time = 70% = P = probability of success = 0.7

(1 - p) = probability of failure = 0.3

Number of trials(n) = 5 days

Number of sucesses (r) = atleast 4 days : >= 4

This is a binomial probability problem

P(r) = nCr × P^r × (1 - P)^(n - r)

P(X >=4) = P(4) + P(5)

P(4) = 5C4 × (0.7)^4 × (0.3)^1 = 0.36015

P(5) = 5C5 × (0.7)^5 × (0.3)^0 = 0.16807

P(4) + P(5) = 0.36015 + 0.16807 = 0.52822

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