what does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to zero?

Answers

Answer 1

The probability of a success gets closer to zero is 15.

What is behavior of the standard deviation ?

The average squared difference between data points and their mean value is called variance, and it is the variance's square root that is used to calculate standard deviation. The symbol for standard deviation can be seen below.

Both the standard deviation and the variance are indicators of dispersion, but the standard deviation is more explicitly the typical distance between a data point and the mean. The majority of the data will be within one standard deviation of the mean. While the variance is not measured in the same units as the actual data, the standard deviation is

If mean deviation is 12, what is its standard deviation?

Lets look the problem .

Given ,

Mean deviation (MD) =12

Here is the inequality to calculate the standard deviation.

6QD=5MD=4SD ,

Where ,QD stands for the Quartile deviation.

SD stands for the standard deviation.

So,

Standard deviation =(5/4)*MD

=(5/4)*12

=15

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Related Questions

each time you put a dollar in a vending machine you get a snack. your response (putting money in the machine) is reinforced according to which of the following schedules? a. fixed ratio b. variable interval c. fixed interval d. variable ratio

Answers

A fixed ratio schedule is a type of reinforcement schedule in which a response is reinforced after a specific number of responses. In this case, the response of putting money in the machine is reinforced after every 1 response.

If each time you put a dollar in a vending machine you get a snack, then your response is reinforced according to a fixed ratio schedule.

Variable interval, fixed interval, and variable ratio schedules are all different types of reinforcement schedules that are based on different criteria. A variable interval schedule is a type of reinforcement schedule in which a response is reinforced after a random interval of time. A fixed interval schedule is a type of reinforcement schedule in which a response is reinforced after a fixed interval of time. A variable ratio schedule is a type of reinforcement schedule in which a response is reinforced after a random number of responses.

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(PLEASE HELP ASAP TYSM LOTS OF LOVE!<3)
A circle has a radius of 30 ft. Which of these is closest to its area?
A. 50 ft²
B. 100 ft²
C. 190 ft²
D. 705 ft²
E. 2,850 ft²

Answers

Answer:

E. 2,850 ft²

Step-by-step explanation:

Answer:

OptionE)

Step-by-step explanation:

Area of a circle = [tex]\pi r^{2}[/tex]

[tex]3.14X30X30[/tex]

= [tex]2826[/tex]

Hence the closest is 2,850

to obtain a smaller margin of error choose a larger confidence level. choose a smaller confidence level.om/input?i

Answers

To obtain a smaller margin of error, choose a smaller confidence level.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error

z = found by using a z-score table

SD = sample standard deviation

n = sample size

Based on the formula, to reduce the margin of error, the z-score, z, must be small. In order to have a smaller value of z, the probability, p, should also be small. And to obtain a small probability, choose a smaller confidence level.

Hence, to reduce the margin of error, use a lower confidence level.

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Write an equation for the relationship between x and y. Simplify any fractions. (IXL K.5 Seventh Grade Math)

Answers

The equation of the line that represents the graph will be y = x.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the two points are (0, 0) and (1, 1).

The line is passing through the origin that is (0, 0), then we have

0 = m (0) + c

c = 0

Then the equation is given as,

y = mx

The equation also passes through (1, 1), then we have

1 = m (1)

m = 1

Then the equation is written as,

y = x

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Solve using the correct order of
operations.
(3³ – 15) ÷ 4 = [?]
P
E
MD
AS

Answers

(3^3 -15) = 12
12/4 = 3

your friend claims that it is possible to draw an quilateral triangle for which the circumecenter, incenter, centroid, and orthocenter are not all the same point. do you agree?

Answers

No, it is not possible to draw an quilateral triangle for which the circumecenter, incenter, centroid, and orthocenter are not all the same point.

Explain the term equilateral triangle?

An equilateral triangle, which is frequently referred to as a "regular" triangle, is a triangle with three equal-length sides.

For the stated question-

The three out-of-the-way sections were not formed of a situation and were not sketched precisely.The Ortho Center is the point of convergence of the medians, and the in center is the point of convergence of the angle by sectors.All four of these would go to the exact same point in an equilateral triangle.

Thus, the statement given by the friend is incorrect.

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3^4 + 18 ÷ 3 +2 pls what is the =

Answers

The value of the given expression, 3^4 + 18 ÷ 3 +2, is 89

Evaluating an expression

From the question, we are to determine the value of the given expression

The given expression is

3^4 + 18 ÷ 3 +2

First, we will write the expression properly

The given expression written properly is

3⁴ + 18 ÷ 3 +2

Using PEMDAS

P - Parentheses

E - Exponent

M - Multiplication

D - Division

A - Addition

S - Subtraction

Then,

3⁴ + 18 ÷ 3 +2

81 + 18 ÷ 3 + 2

81 + 6 + 2

= 89

Hence, the value is 89

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Let R be the region in the first and second quadrants bounded above by the graph of y=201+x2and below by the horizontal line y=2, how do you find the area?

Answers

37.96 sq units is the area enclosed by the graph [tex]y=\frac{20}{1+x^2}[/tex] and y=2

To calculate the area enclosed by 2 graphs we have to firstly find the intersection point of both graph

to find the intersection point we will equate given equation

=>    [tex]\frac{20}{1+x^2}[/tex] = 2

=>  [tex]1+x^2[/tex] = 10

=> [tex]x^2[/tex] = 9

=> x= 3,-3

so we have to find area of graph from x=-3 and x=3

so the formula for equation is given by:

[tex]\int\limits^b_a {\frac{20}{1+x^2} -2} \, dx[/tex]

where a=-3 and b=3

=>[tex]\int\limits^a_b {\frac{20}{1+x^2} } \, dx - \int\limits^a_b {2} \, dx[/tex]                      

[tex]\int\limits {\frac{1}{1+x^2} } \, dx = tan^-^1x[/tex] +c

=> 20 [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex]  [tex]tan^-^1x[/tex] - [tex]\left \{ {{x=3} \atop {x=-3}} \right.[/tex]  2x

=> 20 (  [tex]tan^-^1 3 - tan^-^1 (-3)[/tex]  - 2*(3+3)

=>40 * 1.249 -12

=> 49.96 -12

=> 37.96

so the area enclosed by the given graphs is 37.96 sq. units

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Andrea knows that she can regroup and rewrite the number sentence so that she won't have to multiply by 12. To do this, she needs to find the total for each kind of oatmeal separately. Let's help her. First we need to find the number of boxes of plain oatmeal

Answers

The number sentence needed to find the number of boxes of plain oatmeal is given as follows:

6 x 7 = 42.

How to obtain the number of boxes of plain oatmeal?

From the image given at the end of the answer, we have that:

Andrea has 6 rows of boxes of plain oatmeal.Each row contains 7 boxes of plain oatmeal.

Then the expression that gives the total number of boxes of plain oatmeal can be given by the addition of six terms seven, as follows:

7 + 7 + 7 + 7 + 7 + 7.

Consecutive additions are nothing more than multiplication expressions, hence the number sentence needed to find the number of boxes of plain oatmeal is given as follows:

6 x 7 = 42.

(this is because the product of 6 and 7 has a result of 42, that is, 7 + 7 + 7 + 7 + 7 + 7 = 42).

Missing Information

The problem is given by the image shown at the end of the answer.

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Find the length of AC

Answers

The length of side AC of the triangle ABC using cosine rule is; 10.252 cm

How to use cosine rule?

The cosine formula to find the side lengths of the triangle is given by:

b = √[a² + c² – 2ac cos B]

Where a, b and c are the sides of the triangle.

The Cosine Rule is useful in any triangle that we are trying to relate all three sides to one angle. Thus, when we want to find the length of a side, we need to know the other two sides and the opposite angle.

Considering triangle ABC, we have;

a = 8cm

c = 11 cm

B = 63°

Thus;

b = √[8² + 11² – 2(8 * 11) cos 63]

b = √(185 - 79.9)

b = 10.252 cm

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3. Jennie and Ada are playing a card game where they score points. After one round the ratio of Jennie's points
to Ada's points is 4 to 7. If Ada has 15 more points than Jennie, how many points does Jennie have?

Answers

Jennie has 20 points.

Explanation:

to Ada's points is 4 to 7. If Ada has 15 more points than Jennie, how many points does Jennie have?

To solve this problem, we can use proportions. We know that the ratio of Jennie's points to Ada's points is 4 to 7, so we can set up the following proportion:

4/7 = Jennie's points / Ada's points

We also know that Ada has 15 more points than Jennie, so we can add 15 to both sides of the proportion to represent this:

4/7 = Jennie's points / (Jennie's points + 15)

Next, we can cross-multiply to solve for Jennie's points:

4 * (Jennie's points + 15) = 7 * Jennie's points

4 * Jennie's points + 60 = 7 * Jennie's points

We can then subtract 4 * Jennie's points from both sides to isolate the variable:

60 = 3 * Jennie's points

Finally, we can divide both sides by 3 to find the value of Jennie's points:

Jennie's points = 60/3 = 20

Thus, Jennie has 20 points.

What is the average of 127 and 46?

Answers

Answer:

86.5

We add them together, which is 173, and since there are two terms, divide by 2

173/2=86.5

Answer:

86.5

127 + 46 / 2 = 86.5

I could be wrong but I believe this is correct.

What is the exact value of sin(x/2), cos(x/2) and tan(x/2) if cos(x/6)=3/5
+explaination

Answers

Step-by-step explanation:

x/2 = 3×x/6

sin(x/2) = sin(3x/6)

cos(x/2) = cos(3x/6)

tan(x/2) = tan(3x/6) = sin(3x/6)/cos(3x/6)

looking up triple angle identities for trigonometric functions we find :

cos(3x) = 4cos³(x) - 3cos(x)

so,

cos(x/2) =

cos(3x/6) = 4cos³(x/6) - 3cos(x/6) = 4(3/5)³ - 3×3/5 =

= 4×27/125 - 9/5 = 108/125 - 9×25/125 =

= 108/125 - 225/125 = -117/125 =

= -0.936

sin(3x) = 3×sin(x) - 4×sin³(x)

so,

sin(x/2) =

sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6)

also remember,

sin²(x) + cos²(x) = 1

therefore,

sin²(x/6) + cos²(x/6) = 1

sin(x/6) = sqrt(1 - cos²(x/6)) = sqrt(1 - (3/5)²) =

= sqrt(1 - 9/25) = sqrt(25/25 - 9/25) =

= sqrt(16/25) = 4/5 = 0.8

so, again

sin(x/2) =

sin(3×x/6) = 3×sin(x/6) - 4×sin³(x/6) =

= 3×4/5 - 4×(4/5)³ =

= 12/5 - 4×64/125 = 12×25/125 - 256/125 =

= 300/125 - 256/125 = 44/125 =

= 3×0.8 - 4×0.8³ = 0.352

tan(x/2) = sin(x/2)/cos(x/2) =

= 44/125 / -117/125 = -44/117 =

= 0.352 / -0.936 =

= -0.376068376...

La señora Rosa junta ropa usada para venderla en el mercado por cajas de 5 kg. La semana pasada logró juntar media tonelada de ropa

1. -¿Cuántos kilos de ropa equivalen media tonelada?

2. -¿cuantas cajas logró con esa media tonelada de ropa?

3. -si en una semana ha vendido 1/4 de la media tonelada ¿Cuántos kilos ha vendido?

4. -con los kilos que ha vendido en la semana ¿a cuantas cajas equivale?

5. -¿Cuántos kilos le faltan por vender?


Ayuda es para hoy mismo

Doy coronita al que responda bien ​

Answers

Media tonelada son 500kg, con esa cantidad Rosa logra hacer 100 cajas de 5kg. En una semana ha vendido 125 kilos, es decir 25 cajas. Aún le quedan 375kg.

¿Cómo calcular cuántos kilos de ropa tiene Rosa?

Para calcular los kilos de ropa que tiene Rosa debemos tener en cuenta que una tonelada equivale a 1000kg. De acuerdo con esto, media tonelada sería equivalente a 500kg.

1000kg / 2 = 500kg

¿Cuántas cajas de 5kg alcanza a hacer con media tonelada?

Para saber cuántas cajas de 5kg hace con media tonelada debemos realizar la siguiente operación:

500 / 5 = 100

Sí en una semana ha vendido 1/4 de la media tonelada ¿Cuántos kilos ha vendido?

Para identificar cuántos kilos ha vendido Rosa, debemos identificar a cuántos kilos equivale 1/4 de media tonelada, para ello realizamos la siguiente operación.

500kg / 4 = 125kg

Con los kilo que ha vendido en la semana ¿a cuánta cajas equivale?

Para identificar a cuántas cajas equivale lo vendido por Rosa, debemos realizar la siguiente operación:

125kg / 5kg = 25 cajas

¿Cuántos kilos le faltan por vender?

Para identificar cuántos kilos le faltan por vender, debemos realizar la siguiente operación:

500kg - 125kg = 375kg.

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If x = 3, y = 6, then cosO is equal to:
3√5.
√5/5
9.
15.

Answers

The answer is in the photo(√5/5)

The ticket wheel at the arcade has the following potential outcomes:

Ticket

Value

10

Ticket Wheel Outcomes Table

2

15

25

2

Spots on

the

Wheel

What is the expected number of tickets won from one spin?

30

2

40

2

6

100

3

500

1

Answers

The product of the value of each outcome and the likelihood that it will occur results in the expected value. The likelihood of each outcome occuring for the ticket wheel is inversely correlated to the number of points on the wheel for that outcome.

When N is the number of slots on the wheel for 15 tickets, for instance, the probability of winning 15 tickets is N/20.

So, the following is the expected value of the number of tickets won:

[tex](15 × \frac{N}{20} ) + (25 × \frac{N}{20} ) + (30 × \frac{N}{20} ) + (40 × \frac{N}{20} ) + (10 × \frac{2}{20} ) + (100 × \frac{6}{20} ) + (500 \times \frac{3}{20} )[/tex]

Simplifying this expression, we get:

[tex] \frac{(15N + 25N + 30N + 40N + 20 + 600 + 1500)}{20} [/tex]

Further simplifying, we get:

[tex]\frac{(100N + 2120)}{20} [/tex]

This expression can be further simplified by dividing the numerator and denominator by 5 to get:

[tex] \frac{(20N + 424) }{4} [/tex]

The response to the first query is that this expression is equal to the expected value of the quantity of tickets won. Therefore, (d) 102 tickets is the right response.

The percentage of data that falls within two standard deviations of the mean for all normal curves is what is being questioned in the second question. The correct response is (b) 95% because this is roughly 95% according to the Empirical Rule.

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Type the correct answer in the box. use numerals instead of words. enter the number of the topic sentence.Consider this expression. underroot x4-y2When r = 3 and y = -6, the value of the expression is____.

Answers

When the variables r = 3 and y = -6, the value of the expression is -27.

What is an expression?

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables, parameters, and numerical quantities (number).

Based on the information provided, the mathematical expression is given by;

Mathematical expression = √x⁴ - y²

Substituting the given parameters into the mathematical expression, we have;

Mathematical expression = √(3)⁴ - (-6)²

Mathematical expression = √81 - 36

Mathematical expression = 9 - 36

Mathematical expression = -27.

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Complete Question:

Type the correct answer in the box. use numerals instead of words. Enter the number of the topic sentence.

Consider this expression. √x⁴ - y². When r = 3 and y = -6, the value of the expression is____.

Select the graph of the solution. Click until the correct graph appears.

|x| + 3 > 7

Answers

Answer:

graph B

Step-by-step explanation:

if x ≥ 0

x + 3 > 7

x > 7 - 3

x >4


if x < 0

-x + 3 > 7

-x > 7-3

-x > 4

x < -4


final solution

x < -4 ∨ x > 4

Solve for x. Round to the nearest tenth if necessary.
20
X
25
X type your answer.

Answers

The value of the side x for the given similar triangle will be 12 units.

What is a triangle?

The three-sided shape known as a triangle is sometimes used to allude to it. Every triangle has three sides and three angles, some of which might be the same.

The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.

As per the given both triangle,

The one angle of both triangles is 90° and one angle is the common angle.

Since the two angles are the same thus the third angle will be the same thus by the AAA postulate both triangles will be similar.

By a similar triangle rule,

20/x = 25/(√(25² - 20²))

x = 20/25 (15)

x = 12

Hence "The value of side x will be 12 units by AAA postulate".

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Type the correct answer in the box.
Find the length of SU in the isosceles trapezoid.
SW = 1.7
VW = 3
SV = 1.5
TU= 1.5
SU=
W
T
U

Answers

The value of SU is 4.7 units

What is an isosceles trapezoid?

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.

Given is an isosceles trapezoid,

In an isosceles trapezoid, the triangles Δ SWV and Δ TWU must be congruent. Then, the corresponding sides are congruent too:

TW ≅ SW

UW ≅ VW

From the given information,

UW = 3

SU = SW+UW

Finally, using the values of SW and UW:

SU = 1.7+3 = 4.7

Hence, the value of SU is 4.7 units.

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Answer:

4.7

Step-by-step explanation:

Which function is increasing on the interval (-∞, ∞)?

O A. g(x) = -4(2^x)
O B. f(x) = -3x + 7
O c. h(x) = 2^x - 1
O D. j(x) = x² + 8x + 1


Answers

Which function is growing on the (-, ) interval? O A. g(x) = "-4(2^x)" O B. f(x)= "-3x"+7 O C. h(x)= 2x—1 O D. j(x)= x2 + 8x+1

Try searching for Which function is rising on the range (-, ) instead. O A. g(x) = -4(2^x) O B. f(x) = -3x + 7, O c. h(x) = 2x - 1, and O D. j(x) = x2 + 8x + 1.

Which function is increasing on the interval (- ∞ ∞?

Image result for Which function is increasing on the interval (-∞, ∞)? O A. g(x) = -4(2^x) O B. f(x) = -3x + 7 O c. h(x) = 2^x - 1 O D. j(x) = x² + 8x + 1

Since, x and y are arbitrary values, therefore, f (x) < f (y) whenever x < y. Therefore, the interval (-∞, ∞) is a strictly increasing interval for f(x) = 3x + 5

The interval is increasing if the value of the function f(x) increases with an increase in the value of x and it is decreasing if f(x) decreases with a decrease in x.

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Line u passes through points (7, 2) and (10, 10). Line v passes through points (10, 8) and
(2, 11). Are line u and line v parallel or perpendicular?

Answers

Line u and line v are perpendicular lines by the relation of their slopes.

What is Slope?

Slope of a line is the ratio of the difference of the y coordinates of two points to the x coordinates of those points. Slope is commonly denoted by the letter 'm'.

If a line passes through the points (x₁, y₁) and (x₂, y₂), then slope of the line,

m = (y₂ - y₁) / (x₂ - x₁)

Slopes of two lines, m₁ and m₂, are equal if they are parallel ⇒ m₁ = m₂.

Slopes of two lines, if the lines are perpendicular have the relation,

m₁ × m₂ = -1.

First let's find the slopes of the given lines.

Let m₁ be the slope of line u and m₂ be the slope of line v.

Line u passes through (7, 2) and (10, 10).

m₁ = (10 - 2) / (10 - 7) = 8/3

Line v passes through (10, 8) and (2, 11).

m₂ = (11 - 8) / (2 - 10) = 3/(-8)

Slopes are not equal, so they are not parallel.

m₁ × m₂ = [tex]\frac{8}{3}[/tex] × [tex]\frac{3}{-8}[/tex] = -1.

So the lines are perpendicular.

Hence the given lines u and v are perpendicular.

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Multiply the binomial (8p-2)(6p+2)

Answers

Answer:

48p²+4p-4

Step-by-step explanation:

(8p-2)(6p+2)

=48p²+16p-12p-4

=48p²+4p-4

Please Help!! 25 points!!!

Find the value of X​

Answers

18.) 360+4x=540-360
4x=180/4

X=45

Answer: x = 0.1396263404

Step-by-step explanation:

The expression x+16 = 4x-15

(3 x (-1)) * degrees =-0.0523598776

6 x degrees) + (5 x degrees) =0.191986218

For #1

The diameter of a penny is 19 mm. How far from your eye must it be held so that it has the same apparent size as the moon?

Answers

For a penny of diameter 19mm to be of the same apparent size as the moon it should be held at a distance of about 2.1m away from the eye.

Therefore, the answer is 2.1m.

Distance of moon from earth is 384,400km, that is 384,400,000m. Also 3,474.8km that is 3,474,800m.

For penny to have same apparent size as the moon, it should subtend equal angle as moon to the viewer. See the attached figure for reference. Thus ΔABC is similar to ΔEDB by AA criterion as ∠A is common and ∠BAC = ∠DEB as they are corresponding angles.

Let distance between penny and observer be x. Then

x/ ED = 384,400,000m/ AB

x/ 19mm = 384,400,000m/ 3,474,800m

x/ 19mm = 961000/ 8687

x = 961000/ 8687 × 19

x ≈ 2101.88mm

x = 2.1m

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Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.

Answers

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8[/tex]

[tex]\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r[/tex]

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02[/tex]

Is (22, 11) a solution to the following
system of equations: y 5 2x 2 5,
y 5 4x 2 3? Explain.

Answers

Answer:

Step-by-step explanation:

Yes, (22, 11) is a solution to the given system of equations. To check if a given point is a solution to a system of equations, we can substitute the values of the point into the equations and see if they are satisfied. For example, we can substitute 22 for x and 11 for y in both equations and see if they hold true. For the first equation, we get:

11 = 5 * 2 * 22 + 2 * 5

11 = 110 + 10

11 = 120

Since 11 does indeed equal 120, the first equation is satisfied. Similarly, for the second equation, we get:

11 = 5 * 4 * 22 + 2 * 3

11 = 440 + 6

11 = 446

11 does indeed equal 446, so the second equation is also satisfied. Since both equations are satisfied, we can conclude that (22, 11) is a solution to the given system of equations.

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Factor X^3-2x^2-8x???

Answers

Answer:Cannot be factored

Step-by-step explanation:

Answer:

[tex]x(x+2)(x-4)[/tex]

Step-by-step explanation:

Given:

[tex]x^3-2x^2-8x[/tex]

Factor out the common term x:

[tex]\implies x(x^2-2x-8)[/tex]

Factor (x² - 2x - 8) by rewriting -2x as (-4x + 2x):

[tex]\implies x \left[ x^2-4x+2x-8 \right][/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x \left[x(x-4)+2(x-4) \right][/tex]

Factor out the common term (x - 4):

[tex]\implies x \left[ (x+2)(x-4) \right][/tex]

Therefore:

[tex]x^3-2x^2-8x=x(x+2)(x-4)[/tex]

In the triangles below, Angle AOI is congruent to Angle IEA. Find each missing measure.

Answers

The values of the variables and the measures of the angles, found using the congruency of ΔAOI and ΔIEA are;

w = 2        [tex]{}[/tex]   ∠EAI = 45°

x = 4   [tex]{}[/tex]         ∠AOI = 128°

y = 7 [tex]{}[/tex]           ∠OIA = 45°

z = 20 [tex]{}[/tex]        ∠IEA = 128°

What are congruent triangles?

Two triangles are congruent if two angles and a non included side of one triangle are congruent to two angles and a non included side of another triangle.

The relationship between the triangles ΔAOI and ΔIEA is ΔAOI ≅ ΔIEA

Therefore; ∠IEA is congruent to ∠AOI, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

∠IEA ≅ ∠AOI

Therefore; ∠IEA = ∠AOI by the definition of congruency

(6·z + 8)° = (7·z - 12)°

7·z - 6·z = (8 + 12)° = 20°

z = 20°

∠AOI = (7·z - 12)°

Therefore;

∠AOI = (7 × 20 - 12)° = 128°

∠IEA = 128°

Similarly; AO ≅ EI by CPCTC

AO = EI definition of congruency

5·w - 6 = 2·w

5·w - 2·w = 6

3·w = 6

w = 6 ÷ 3 = 2

w = 2

∠OIA ≅ ∠EAI by CPCTC

Therefore; ∠OIA = ∠EAI definition of congruency

(7·x + 17)° = 3·(4·x - 1)° substitution property

(7·x + 17)° = 3·(4·x - 1)° = (12·x - 3)°

12·x - 7·x = 17° + 3° = 20°

5·x = 20°

x = 20° ÷ 5 = 4°

x = 4°

∠EAI = 3·(4·x - 1)°

∠OIA = (7·x + 17)°

Therefore;

∠EAI = 3·(4×4 - 1)° = 45°

∠OIA = (7×4 + 17)° = 45°

y° + (7·z - 12)° + 3·(4·x - 1)° = 180° (angle sum property of a triangle)

∠AOI = (7·z - 12)° = 128°

∠EAI = 3·(4·x - 1)° = 45°

Therefore;

y° + 128° + 45° = 180°

y° = 180° - (128° + 45°) = 7°

y° = 7°

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Work out how many triangles can be drawn between the labelled points in the diagram below

Answers

The triangles that are congruent to (a) ΔCDE, and (b) ΔCDF include ΔBFG, ΔADG, ΔBDE, and  ΔABH, ΔBHCΔ, ΔGHE respectively

How to find congruent triangles?

We should know that when two or more objects in geometry have the same shape and size, or if one has the same shape and size as the mirror image of the other, they are congruent.

From the object drawn the congruent triangles to ΔCDE include the following

ΔBDF

ΔABG

ΔBDE

ΔABI

ΔACH

ΔBCJ

ΔIHJ

All the triangle has side, side, right angle

The triangles that are congruent to ΔCDF include the following

ΔABG

ΔBHC

HGE

These triangles have SIDE, SIDE, SIDE (SSS)

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