You put $1,000 into a savings account that pays 7% in annual interest. how much money will you have after 7 years if the account pays only simple interest?

In the given triangle ABC right angled at C and [tex]AC = b[/tex] and [tex]CB = a[/tex], the equation using value of b used for solving for a will be [tex]tan(22.6degrees) = \frac{a}{12}[/tex].

According to the question statement, Triangle A B C is shown. Angle A C B is [tex]90[/tex] degrees and angle C A B is [tex]22.6[/tex] degrees. The length of hypotenuse A B is [tex]13[/tex] centimeters, the length of A C is b, and the length of C B is a.

We are supposed to find the equation using value of b used for solving for a.

Solution: Given,

  [tex]AB = 13cm\\AC = b\\BC = a\\Angle BAC = 22.6degrees[/tex]

If hypotenuse is 13cm then value of b is either 5 or 12 as per Pythagorean Triplet. As there is no value such as 5 in the given options we take the value of [tex]b=12 cm[/tex].

[tex]cos(22.6degrees) = \frac{b}{13} =\frac{12}{13} \\sin(22.6degrees) = \frac{a}{13}\\[/tex]

Using the above two equations,

[tex]tan(22.6degrees)=\frac{a}{b} \\b=12\\tan(22.6degrees)=\frac{a}{12}[/tex]

Therefore option three "tan(22.6o) = StartFraction a Over 12 EndFraction" is the correct answer.

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Answer: C tan (22.6)=a/12

Step-by-step explanation: edge 2023

Answer:

I'm pretty sure the answer is D

Step-by-step explanation:

I took the test

The sentence that contains a dangling modifier is D. Searching frantically, the homework was finally found and turned in.

A word or phrase that modifies a term that is not explicitly expressed in the sentence is known as a dangling modifier. A modifier provides a concept's definition, clarification, or more information.

A grammatical modifier that could be mistakenly understood as being connected to a word other than the one intended is known as a hanging modifier. A hanging modifier, which usually refers to a participle, has no subject.

Therefore, the sentence that contains a dangling modifier is Searching frantically, the homework was finally found and turned in.

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Answer:

37.5

Step-by-step explanation:

Answer: 37.5

Step-by-step explanation:

12.5% of 300=37.5

Answer:

x = 18

Step-by-step explanation:

Vertical angles are congruent.

4x + 3 = 75  Subtract 3 from both sides of the equation

4x = 72  Divide both sides by 4

x = 18

Answer:

81, 225, 361

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

this is because If you multiply the denominator by 2 you will get 32

so if you likewise multiply the numerator by 2 you will get 8

Answer:

5x + 3y = 18

Step-by-step explanation:

First find slope.  m = (y2 - y1)/(x2 - x1) = (6 -1)/(-6 --3)  = 5/-3

then. use. y - y1 =. m (x - x1).  which gives. y - 1 = -5/3(x - 3)

then. y - 1 = -5/3x + 5

then y = -5/3 x + 6. or. 5x + 3y = 18

If the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.

Given that the population of pine bluff is 654 and is increasing at the rate of 7 per year.

We are required to find the equation which shows the population and the population after 3 years.

Equation is basically the relationship between two or more variables that are expressed in equal to form and can be solved to find the value of variables. It may be linear equation, quadratic equation, cubic equation and many more depending on the power of the variables that are present in the equation.

Suppose the number of years be x.

The equation which shows the population after x months be:

y=654+7x

To find the population after 3 years, we can use x=3 in the equation.

y=654+7*3

y=654+21

y=675

Hence if the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.

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The probability value indicates that there is statistical significance in 0.0345 option (a) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

As we know,

Statistical significance is commonly defined as a probability value of 0.05 or even less. P-value can be used in replacement of or in addition to preset levels of confidence when testing the claim.

The value 0.0345 < 0.05

The probability value of 0.0345 indicates that there is statistical significance

Thus, the probability value indicates that there is statistical significance in 0.0345 option (a) is correct.

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Answer:  Theorems About Roots of Polynomial Equations

Step-by-step explanation:

Theorems About Roots of Polynomial Equations

In the given case we can conclude that the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]

To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:

A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.

P(x) = [tex]ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g[/tex]

Plugging in the given values, we have:

P(x) = [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5[/tex]

Remember that the degree of a polynomial is determined by the highest exponent of x.

In this case, the degree is 6.

The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.

So, the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]

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The common ratio between successive terms in the sequence is 1. 25

Common ratio is defined as the ratio of each term of a geometric sequence to the term before it.

It is also known as the constant factor between consecutive terms of a geometric sequence.

It is  the number multiplied or divided by at each interval.

Given the sequence;

1.5, 1.2, 0.96, 0.768,

The common ration is;

= 1. 5/ 1. 2

= 1. 25

Thus, the common ratio between successive terms in the sequence is 1. 25

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Answer:

The length of AD is 5 units

Step-by-step explanation:

The acres of vacant land that the county have now will be 144 acres.

Since 36% has been used, the remaining percentage will be:

= 1 - 36%

= 64%

Therefore, the acres of vacant land that the county have now will be:

= 64% × 225

= 64/100 × 225

= 0.64 × 225

= 144

Therefore, the acres of vacant land that the county have now will be 144 acres.

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Answer:

The first and fourth statement.

Step-by-step explanation:

1. - 3 - 12/3 + 5

= - 3 - 4 + 5

= - 7 + 5

= - 2

- 2 < 0

4. 4 - 2 - 3/2

= 2 - 3 / 2

= 1 / 2

1 / 2 > 0

Hope this helped! ^^

Sidenote: If you need me to explain for 2, 3 and 5, comment below this and I'll explain.

Answer:

Step-by-step explanation:

12

Answer:

====================

Total number of outcomes is 16, count of all outcomes.

Number of outcomes with 3 or more tiles is 5:

The probability is:

Correct choice is D.

Answer:

Hello,

Step-by-step explanation:

Let's suppose
t the time of the travel

d1 the distance rided by Cindy in miles

d2 the distance rided by Richard in miles

d1+d2=96

18*t+14*t=96

32*t=96

t=3 (hours)

Equation have infinity solution

Here the equation is 2q-3q =-q.

After solving this we have

                    -q = -q

As Left-hand side is equal to the right-hand side.

Therefore whatever the value we will put for the q, the left and right hand side remains the same.

Therefore this equation has an infinity solution.

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The composite function or combined functions of x(A) and V(x) is V(x(A)) = (√A/6)³ option (C) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

A function relates an input to an output.

x2 (squaring) is a function

x3+1 is also a function

Sine, Cosine, and Tangent are functions used in trigonometry.

Although part of the question is missing the question is The function x(A)= √A/6 can be used to determine the side length, x, of a cube given the surface area of the cube, A. The function V(x)= x³ can be used to find the volume of a cube. how can these functions be combined?

a. x(v(A))= sqrt x^3/6

b. V(x(A)) = sqrt x3/6

c. V(x(A))=(sqrt A/6)^3

d. x(v(A))= (sqrt A/6)^3

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Answer: See attached.

Step-by-step explanation:

         Since this inequality uses < and not ≤, we will be using a dashed line.

         Next, we will shade "below" the line since this inequality uses the < aka less than.

         Lastly, our y-intercept is [tex]\frac{1}{2}[/tex].

The expression c = 9.10 + 0.42(w-5) ; w > 5 will represent the cost c in terms of w, the total weight in pounds of a package weighing over 5 lbs.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Total cost below 5 lbs = base fee

Total cost over 5 lbs = base fee + additional 0.42/pound

Let's say the total cost is c and the total pounds is w

Then,

c = 9.10 + 0.42(w-5) ; w > 5

Here for w = 6 it will gives w - 5 = 6 - 5 = 1 lbs.

Hence "The expression c = 9.10 + 0.42(w) ; w > 5 will represent the cost c in terms of w".

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For the entire independent-measures experiment 24 individuals are participated.

Different participants are utilized in each condition of the independent variable in an experimental design known as an independent measures design, or between-groups. This indicates that a different group of participants is present for each condition of the experiment. A research strategy known as an independent measures design uses numerous experimental groups with subjects only being assigned to one group. Throughout the experiment, each participant is solely exposed to one independent variable condition. A drug trial for a novel medicine would serve as an example. This has the benefit of preventing order effects, which occur when participants behave differently as a result of the order in which conditions are done, often as a result of factors like boredom or exhaustion.

We are given the value  t(22) = 5.30, p < .01

So here degree of freedom (df) is 22 and it is independent so there is two samples,

so df= n₁+n₂-2

⇒ 22 =  n₁+n₂-2

⇒ n₁+n₂ = 24.

Thus for the entire experiment 24 individuals are participated.

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What we answering with these 2 points ?

Where's the question?

well, she really began with "x" total.

then she sold half of that, so hmmm 1/2 of "x" is just x/2 and she's left with half, so she sold x/2 and she was left only with x/2, and then she bought 17 more, we also know that she has 31 now, so

[tex]\stackrel{\textit{leftover}}{\cfrac{1}{2}x}~~ + ~~\stackrel{\textit{more bought}}{17}~~ = ~~\stackrel{\textit{now she has}}{31}\implies \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left(\cfrac{x}{2}~~ + ~~17 \right)~~ = ~~2(31)}\implies x+34=62\implies \LARGE \begin{array}{llll} x=28 \end{array}[/tex]

Step-by-step explanation:

let the larger number=n

then the smaller number=½n

We conclude from the question that

n+½n=75

3/2n=75

3n=150

n=150/3=50

Therefore the larger number=50 and the smaller number=½×50=25

Step-by-step explanation:

Given is a linear equation in t



If we want to simplify we find that 3t gets cancelled and we get



This is an impossible situation.

This implies that original equation has no solution at all

Hence answer is

the given has no solution

Answer:

s=2,−10

Step-by-step explanation:

Find all solutions for s by breaking the absolute value into the positive and negative components.

Answer:

x² + (y + 3)² = 25

Step-by-step explanation:

the centre (C) of the circle is at the midpoint of the diameter.

using the midpoint formula

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )

C = ( [tex]\frac{3-3}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (0, - 3 )

the radius r is the distance from the centre to either P or Q

using the distance formula

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )

r = [tex]\sqrt{(3-0)^2+(1-(-3)^2}[/tex]  

 = [tex]\sqrt{3^2+(1+3)^2}[/tex]

 = [tex]\sqrt{3^2+4^2}[/tex]

 = [tex]\sqrt{9+16}[/tex]

 = [tex]\sqrt{25}[/tex]

 = 5

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (0, - 3 ) and r = 5 , then

(x - 0 )² + (y - (- 3) )² = 5² , that is

x² + (y + 3)² = 25

A function assigns the values. The output(y) of the function y=20x + 38 if the input is -9 is -142.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function y=20x+38, therefore, if the input of the function is -9, then the output can be calculated by substituting the value of x as -9. Therefore, we can write the function as,

y = 20x + 38

y = 20(-9) + 38

y = -180 + 38

y = -142

Hence, the output(y) of the function y=20x + 38 if the input is -9 is -142.

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Answer:

3.64

Step-by-step explanation:

collect like terms

divide both sides by x coefficient

Answer:

x=51/14

Step-by-step explanation:

28x-2=100

+2. +2

28x=98

28x/28=102/28

×=51/14