Please help this is a geometry problem

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$10000\\ P=\textit{initial amount}\dotfill &15000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\\ \end{cases}[/tex]

[tex]10000=15000(1 - 0.04)^{t} \implies \cfrac{10000}{15000}=(1 - 0.04)^{t}\implies \cfrac{2}{3}=0.96^t \\\\\\ \log\left( \cfrac{2}{3} \right)=\log(0.96^t)\implies \log\left( \cfrac{2}{3} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left( \frac{2}{3} \right)}{\log(0.96)}=t\implies 9.93\approx t\qquad \textit{about 9 years and 11 months}[/tex]

The value of the 60th term is -721 in given arithmetic progression or we call as AP

What is arithmetic progression?

The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).

It is possible to obtain a formula for the nth term of the AP using this kind of development.

A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term.

The nth term in this series equals 4n-2. You can get the sequence's terms by inserting n=1,2,3,...

Given:

-13, -25, -37, -49,..

a = -13

d = t₂ - t₁

= -25 - (-13)

= -25 + 13

d = -12

tₙ = a +(n-1) d

t₆₀ = -13 + (60-1) (-12)

= -13 + (59) (-12)

= -13 - 708

t₆₀  = -721

Hence, the value of the 60th term is -721 in given arithmetic progression.

complete question is

Find a formula for the

nth term, Tn, of the following arithmetic sequence:−13,−25,−37,−49

,. . . Hence, or otherwise, find the value of the 60th term,

T60

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There are 2,540,160 strings of SALESPERSONS with no consecutive S's.

Explanation:

The number of r-combinations of a set of n distinct objects is C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]

Multiplication principle : If one event can occur in m ways AND a second event can occur in n ways, then the number of ways that the two events can occur in sequence is then mn.

We want to place the 4S's in the string of the other letters such that there are not consecutive. Since there are 9 positions including spaces between two consecutive letters in the 8-letter string and two positions on either side of the string, we need to place 4 of the 9 positions to contain a single S each.

By the definition of combination, there are ⁹C₄ ways to select 4 of the 9 positions to place the S's (as the order of the positions is not important since a different order of the S's leads to the same string).

By the multiplication principle, there are then ⁹C₄. [tex]\frac{8!}{2}[/tex] (divided by 2 since , in remaining 8 characters 2E are identical) possible strings of SALESPERSONS with no consecutive S's.

⁹C₄ . [tex]\frac{8!}{2}[/tex] = [tex]\frac{9!}{4!(9-4)!}[/tex] [tex]\frac{8!}{2}[/tex]

           = [tex]\frac{9!}{4!.5!} . 20,160[/tex]

           = 126.20,160

           = 2,540,160

Thus, there are 2,540,160 strings of SALESPERSONS with no consecutive S's.

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Answer:

Not sure what you are asking, but 6 to the third power = 216 and 6 times 3 = 18. Hopefully one of those is the answer you are looking for.

for every one (1) you have, you have 3 times the first

Ok,

for example for every 1 penny you have, you have 3dollars,

you counted and you have 4 pennies, in order to find out how many dollars you have, you have to times 4 by 3 to get 12

altogether you would have 4 pennies: 12 dollars.

In mathematics, a geometric series is defined as the sum of an infinite number of terms that have a constant ratio say "r" between successive terms.

a) Sum of first infinite geometric series is 49/8640

b) Sum of second infinite geometric series is 68/9.

In general, a geometric series is written as

a+ar+ar²+ar³+... ..

where 'a' is the coefficient of each term and 'r' is the common ratio between adjacent terms.

We have given that

a) 7²/12⁴ + 7³/12⁵ + ......

it is a geometric infinite series with a = 7²/12⁴and r = 7/12

we have find out the sum of series.

Using sum geometric infinite terms formula,

Sₙ= a /(1-r)

where, n = ∞ ; |r| <0

put all known values we get ,

Sₙ = 7²/12⁴ + 7³/12⁵ + ......

=> Sₙ = 7/12( 7/12³ + 7²/12² +---)

=> Sₙ = 7²/12³ ( 1 - 7/12)

=> Sₙ = 7²/12³ × 5/12

=> Sₙ = 49/8640

b) Second series is

16/9 + 4/3 + 1 + 3/4 + 9/16 + ------

= 16/9 + 4/3 +( 1 + 3/4 + 9/16 + ------ )

= 16/9 + 4/3 + ( 1 + 3/4 + (3/4)² + ------ )

= 16/9 + 4/3 + B

B = 1 + 3/4 + (3/4)²+ ------

it is geometric infinite series with a = 1 , r = 3/4

Sₙ = a/(1-r) = 1/(1- 3/4 ) = 1/1/4 = 4

16/9 + 4/3 + 1 + 3/4 + 9/16 + ------ = 16/9 + 4/3 + 4

= (16+16+36)/9 = 68/9

Hence, the sum of first geometric infinite series is

49/8640 and second series is 68/9.

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The probability that a person selected at random to have the test until (s)he passes the test is, 0.03125

Given, a test occurred 5 times in a class.

we have to find that how many times a person selected at random to have the test until (s)he passes it.

the probability of getting pass in the exam be, 1/2

and similarly the probability of getting fail in the exam also be, 1/2

so, the probability that a person selected at random to have the test until (s)he passes the test is,

(1/2)^5

= 1/32

= 0.03125

Hence, the probability that a person selected at random to have the test until (s)he passes the test is, 0.03125

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The required set of 5 positive integers is 3, 3, 4, 4, 16.

The mean is the mathematical average of a group of integers.

Given, to find a set of 5 positive integers such that their mode is 3 and 4, the median is 4, and the mean is 6.

Since the median is 4, the middle number or the number at the 3rd position will be 4.

Since the mode of the data set is 3 and 4, the frequency of 3 and 4 must be 2.

Now, the numbers found so far are 3,3,4,4.

Let the fifth number be x.

The mean of the data set is given by:

mean = (3 + 3 + 4 + 4 + x)/5

Given that mean is 6, therefore,

(3 + 3 + 4 + 4 + x)/5 = 6

14 + x = 30

x = 30 -14

x = 16

Hence, the required set of 5 positive integers is 3, 3, 4, 4, 16.

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In multiple regression, a large value of the test statistic f indicates that most of the variation in the response is unexplained by the regression equation and a small value of f indicates that most of the variation in the response is explained by the regression equation. False.

Multiple regression refers to a statistical technique utilized to evaluate the relationship between a single dependent variable and several independent variables. The main goal of the analysis is to use the independent variables with known values to predict the value of the single dependent value. Test statistic f refers to a statistical measure used to test the significance of regression coefficients in linear regression models. In testing the validity of a multiple regression model, a large value of the F-test statistic indicates that most of the variation in y is explained by the regression equation, hence most of the variation in the response is explained by the regression equation.

Note: The question is incomplete as it is missing options which are a) True. b) False.

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The probability of rolling a number greater than 2 is 2/3

Given that a six sided die with sides labelled with numbers 1,2,3,4,5 and 6 is rolled once.

Since die is said to be equally likely for each number, die is unbiased

P(1) = P(2)=...=P(6) = 1/6

For a number greater than 2, we must not include 2 and hence numbers can be 3 or 4 or 5 or 6

Probability of rolling a number >2 = Probability of rolling 3 or 4 or 5 or 6

= P(3)+P(4)+P(5)+P(6)

= 1/6+1/6+1/6+1/6

=4/6

=2/3

Therefore, the probability of rolling a number greater than 2 is 2/3

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c is a constant of the function y = ax² + bx + c is -3

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

y = ax² + bx + c

At point (5, 32)

32 = a(5²) + 5b + c   (1)

At point (6,45)

45 = a(6²) + 6b + c   (2)

At point (4, 21)

21 = a(4²) + 4b + c   (3)

Hence:

a = 1, b = 2 and c = -3

The value of c which is a constant of the function y = ax² + bx + c, is -3.

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Answer:

The number is 0.

Step-by-step explanation:

Let's say the number is "n"

5(-5+n)=-25

rearrange:

5(n-5)=-25

Simplify:

5n-25=-25

rearrange:

5n=-25+25

simplify:

5n=0

n=0

if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

How do you know if a triangle is HL congruent?

Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. Using words: In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.

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Four different symmetry types are translation symmetry, rotational symmetry, reflection symmetry, and glide symmetry can be seen in a variety of contexts.

A balanced and proportionate likeness between two sides of an item is referred to as symmetry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that may be used to fold a figure into symmetrical halves.

If an object exhibits translational symmetry, it indicates that no matter how it is translated, the thing remains unchanged. The translations for a particular object that fall under this constitute the object's symmetry group or, if the object has other types of symmetry, a subgroup of the symmetry group.

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The equation which describes the problem statement would be 250x = 750.

What is the equation in one variable?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable.

The rent for staying one night is $250.

and if a couple stays in the standard room for x night and their total rent was $750 then this can be expressed as

             250x = 750

Hence, the equation which describes the problem statement would be 250x = 750.

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Four  electrons are required for the reduction of one molecule of oxygen to water in the mitochondria

Reduction means that a reaction in which electrons are added to a compound or molecule; the compound or molecule that gains electrons is said to be reduced

Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria

Therefore, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria

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ANSWER

13.5

EXPLANATION

It was given that, y varies directly as x.

Therefore, the variation equation is of the form:

If y is 4.5 when x is 3, then we can substitute to find the constant of variation.

Divide both sides by 3;

Hence the equation becomes:

When x=9,

The examples of ASA congruence in its only form, ASA is calculated via way of means of: ASA = Total Wait Time for Answered Calls/Total # of Answered Calls.

The concept at the back of ASA is to get a top level view of trendy performance.any angles and the aspect covered among the angles of 1 triangle are equal to the corresponding angles and aspect covered among the angles of the second one triangle, then the 2 triangles are stated to be congruent via way of means of ASA rule.

Examples on ASA Congruence RuleExample 1: For Δ ABC, display that AB = AC and Δ ABC is isosceles if the bisector AD of ∠ A is perpendicular to aspect BC. Also, this situation satisfies the homes of the isosceles triangles, thus, Δ ABC is an isosceles triangle. Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.

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The estimated probability of the occupation of firefighters is 0.62

A recent Harris Poll survey of 1010 U.S. adults selected at random showed that 627 consider the occupation of firefighter to have very great prestige. i.e. The sample size of U.S. adults : n= 1010

The number of U.S. adults consider the occupation of firefighter to have very great prestige: x= 627

Now we see, the probability that a U.S adult selected at random thinks the occupation of firefighters has very great prestige will be:

p = x/n

 = 627/ 1010 = 0.62 [ To the nearest hundredth]

        Therefore, the estimated probability that a U.S adult selected at random thinks the occupation of firefighters has very great prestige = 0.62

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The value of the side EC for the given triangle is 28.75 .

A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.

In the given triangle,

Side AD = 12, BD = 20 and AC = 56,

Also, the side BC is parallel to side DE.

Let the side EC is x,

Then side AE = 56-x

Since, lines BC and DE are parallel

Therefore, by triangle proportionality theorem,

AD/BD = AE/EC

12/20 = 56-x/x

3/5 = 56-x/x

3x = 230 - 5x

8x = 230

x = 230/8

x = 28.75

The required side EC is 28.75.

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0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).

What is real numbers?

A real number in mathematics is a number that can be used to represent a continuous one-dimensional quantity, such as a length of time, temperature, or distance. In this context, continuous denotes that values may vary by arbitrary little amounts. An endless decimal expansion allows for a nearly universal representation of every real number.

The given equation is,

[tex]log_xa+log_ya=4log_x_ya[/tex]

Using the log rule: [tex]log_ab = \frac{ln b}{lna}[/tex]

⇒ [tex]\frac{lna}{lnx}+\frac{lna}{lny} = \frac{4lna}{lnxy}[/tex]

Multiply both sides by, [tex]\frac{lnxy}{lna}[/tex]

⇒  [tex]\frac{lnxy}{lnx}+\frac{lnxy}{lny} = 4[/tex],  a ≠ e

Using log rule: [tex]ln(ab) = lna + lnb[/tex]

⇒

[tex]\frac{lnx+lny}{lnx} +\frac{lnx+lny}{lny} = 4\\ \frac{lnx}{lnx}+\frac{lny}{lnx}+ \frac{lnx}{lny}+\frac{lny}{lny} = 4\\1+\frac{lny}{lnx}+ \frac{lnx}{lny} +1=4\\\frac{lny}{lnx}+\frac{lnx}{lny}=2[/tex]

[tex]\frac{(lnx)^2+(lny)^2}{lnx(lny)} =2\\(lnx)^2+(lny)^2 = 2 lnx ln y\\(lnx)^2 - 2lnxlny+(lny)^2=0\\(lnx - lny)^2 = 0\\lnx - ln y = 0\\x = y[/tex]

Hence, 0 is the minimum (and maximum) of x−y for x, y ∈ (0, 1).

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A number c divided by 8 is greater than or equal to 26:

c/8 ≥ 26

b) h = [tex]tan \theta[/tex]  x 17 is the required equation.

c) The height of the streetlight is 20.4 ft.

The height of the person is 6 ft.

The distance at which the person is standing from the streetlight = 12 ft.

The distance at which the person's shadow appears = 5ft.

a) Hence, we can make the following diagram.

The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.

b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.

from the below diagram, we can say that,

[tex]tan \theta[/tex] = h/base

base= 12+5=17

hence we have, [tex]tan \theta[/tex] = h/17

h = [tex]tan \theta[/tex]  x 17 is the required equation.

c) Now we have to find the height of the streetlight.

firstly let's find the value of [tex]\theta[/tex],

[tex]\theta[/tex] = tan 6/5.

[tex]tan^{-1}[/tex](6/5) = 50.2°

hence, tan 50.2 = h/17

                   1.20 = h/17

                         h= 1.20 x 17

                         h= 20.4 ft.

Hence, the height of the streetlight is 20.4 ft.

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andi $8,$8,0xFF is the instructions that clears all the bits in register $8 except for the low order byte, which is unchanged.

The byte with the least amount of the value would be the low-order byte. For instance, a 16-bit int with the value 5,243 might be represented in hex as 0x147B. The low-order byte is 0x7B, whereas the high-order byte is 0x14. A word's bits are numbered 0 through 15, with bit 0 being the least important. The word's low byte, which contains bit 0, and high byte, which contains bit 15, are referred to as such. Byte ordering comes in two flavors. Big-endian format places the byte with the most important bit in the first memory location, followed by bytes whose importance decreases.

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=Answer:   x+2

Step-by-step explanation:

A sample of 50 provided a mean of 28.4. The population standard deviation is 6. the value of test statistic is 1.65

The following hypothesis test:

H₀ : μ ≤ 27

Ha: μ 27

A sample of 50 provided a mean of 28.4. The population standard deviation is 6.

We need to find the value of test statistics

test statistic  = (28.4 - 27)/(6/√50)

test statistic= 1.4/0.848

test statistic = 1.65

Therefore, a sample of 50 provided a mean of 28.4. The population standard deviation is 6. The value of test statistic is 1.65.

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Five to the seven thirds power is the correct answer. This expression can be rewritten as the cube root of five to the seventh power, which is equal to five to the seven-thirds power.

When a term is multiplied by itself several times, it is said to have "power" or exponents in mathematics. An exponent, which is expressed as a little number above and to the right of the base number, serves as a representation for this. For instance, the number 2 to the power of 3 (23) is represented as 222 and equals 8.Power can alternatively be written as xy, in which x is the base number and y is the exponent. The equation 23 is represented as 23 in this notation, and it still equals 8.Power, in addition to representing repeated multiplication, may also be used to indicate a number's root.

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The air conditioner can circulate 16.2963 cubic yards of air per minute.

The air conditioner circulates 440 cubic feet of air per minute.

We know that 3 feet =  1 yard

Therefore cubic feet when converted to yard we have to divide the data by 27.

Therefore 440 cubic feet = 440 / 27 = 16.2963 cubic yards.

Therefore the air conditioner can circulate  16.2963 cubic yards of air per minute.

A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. It can also be essential to round the numbers and select the right number of significant digits. Different units of metric conversion are used to measure different parameters.

Unit conversion is a multi-step procedure that involves adding, subtracting, or multiplying by a number. There are many ways to measure weight, distance, volume and temperature.

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The probability of winning is 30/59.

What is a probability simple definition?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                 Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

probability = wanted outcomes / total outcomes

odds = wanted outcomes / unwanted outcomes

odds of 29/30 losing means 29 losing outcomes and 30 winning outcomes.

The total outcomes is 59

The probability of losing is 29/30. Yet we want the probability of winning.

Provability of winning is 1 - probability of losing.

1 - 29/59 = 30/59

The probability of winning is 30/59.

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Answer:

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

Mia has 5 bottles of water, it gives her:

Within this 10 miles Mia can eat a snack twice and this will limit her further run.

The items Mia has allow her to run 10 miles maximum.

Answer:

12 miles

Step-by-step explanation:

Given information:

Mia drinks water after every 2 miles she runs.  Therefore, if Mia has packed 5 bottles of water she can run:

⇒ 2 + 5 × 2 = 12 miles

Mia eats a snack after every 4 miles she runs.  Therefore, if Mia has packed 2 snacks she can run:

⇒ 4 + 2 × 4 = 12 miles

Therefore, Mia can run 12 miles with the items she has packed.

0 miles: Begins running.

2 miles: Drinks bottle 1.

4 miles: Drinks bottle 2 and eats snack 1.

6 miles: Drinks bottle 3

8 miles: Drinks bottle 4 and eats snack 2.

10 miles: Drinks bottle 5.

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

12 miles: Drinks another bottle.

Remember that Mia drinks a bottle of water after she has run 2 miles, and eats a snack after she has run 4 miles.

Therefore, drinking a bottle of water allows Mia to run for 2 further miles, and eating a snack allows her to run for 4 further miles.

So when she drinks her last bottle of water at 10 miles, she can only continue running for a further 2 miles before she needs to drink again.  As she doesn't have a 6th bottle of water, she will have to stop running at 12 miles.