Suppose that 11,000 is invested in a bond fund and the account grows to 14,539.95 in 5 yr.

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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The matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

To represent the profit from the sales of book A for each store, we can use a matrix where the rows correspond to the stores (X, Y, Z) and the columns correspond to the book A.

The matrix representing the profit from the sales of book A for each store is as follows:

Store Book A

X $4

Y $4

Z $4

Therefore, the matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

Each element in the matrix represents the profit from the sales of book A in a specific store, which is $4 for all stores (X, Y, Z).

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Answer:

Step-by-step explanation:

Let the speed in the morning be s, then in the evening it is s - 4

The distance is equal both directions:

Time in hours:

Multiply all terms by 12 to clear fraction:

The distance is:

Answer:

the answer is 8.4

Step-by-step explanation:

hope it helps. even I'm stuck so I went on brainly and the guy who helped you is a god ls mark the other person brainliest he deserves it with all the clean work and all

Answer:

x = 21

Step-by-step explanation:

As stated in the hint: When angles form a linear pair, their sum is 180° in other words, these are supplementary angles:

3x + 18 + 4x + 15 = 180 add like terms

7x + 33 = 180 subtract 33 from both sides

7x = 147 divide both sides by 7

x = 21

Answer:

price = 4.1

cost = 12.3

Step-by-step explanation:

price = 0.8+1.2+1.5+0.6 = p4.1

cost = 2.40+3.60+4.50+1.80 = $12.3

"Let x be any vector in \(C^n\), let q = \(x^T\)Ax, and let A be an n-by-n real matrix with the characteristic that \(A^T\) = A. By confirming that q = q, the equalities below demonstrate that q is a real number.

Let A be n x n real matrix with the property that. \(A^T = A\).

if Ax = λx.

(Ax) = λx

\(xA^T=\) λx

xA = λx( and therefore dλ are real, A =\(A^{T}\) = and dλ = λ).

x(A-λL) = 0

Therefore, A-λL is a real matrix.

Assume that A is a n by n matrix with a characteristic polynomial defined by det(λI−A). The number of times an eigenvalue of A appears as a root of that distinctive polynomial is known as its multiplicity.

and x (λI-A) = 0

Therefore, x(λL-A) is also real.

X1 is real.

Therefore, since is one of A's eigenvalues, there exists a nonzero vector X\(C^n\) such that AX=X

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The amount of the down payment and the fixed rate mortgage is $35000 and $9625.

According to the statement

We have given that the

Thomas osler is buying a house selling for $175,000 And we have to find the amount of the down payment and the monthly payment.

So, The down payment is :

percentage of the down payment is 20%

So,

Amount = 20/100*175000

Amount = 35,000$

And the percentage of the fixed rate mortgage with 5.5%

So,

Amount = 5.5/100*175000

Amount = $9625.

This the amount of the down payment with the given percentage and with the fixed rate mortgage.

So, The amount of the down payment and the fixed rate mortgage is $35000 and $9625.

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Answer:

  36 +12y

Step-by-step explanation:

The factor outside parentheses multiplies each term inside parentheses:

  12(3 +y)

  = (12)(3) +(12)(y)

  = 36 +12y

Answer:

Let

\(\displaystyle f(x) = \sum_{n=1}^\infty (-1)^{n-1} \frac{x^{2n-1}}{(2n-1)! (2n+1)}\)

The exponent is indeed \(2n-1\) - not a typo!

Take the antiderivative of \(f\), denoted by \(F\). This recovers a factor of \(2n\) in the denominator, which lets us condense it to a single factorial.

\(\displaystyle F(x) = \int f(x) \, dx = C + \sum_{n=1}^\infty (-1)^{n-1} \frac{x^{2n}}{(2n+1)!}\)

Recall the series expansion of sine,

\(\displaystyle \sin(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{(2n+1)!}\)

Then with a little algebraic manipulation, we get

\(\displaystyle F(x) = \int f(x) \, dx = C + 1 - \frac{\sin(x)}x\)

Differentiate to recover \(f\).

\(f(x) = \dfrac{\sin(x) - x\cos(x)}{x^2}\)

Finally, \(f(\pi) = \frac1\pi\), so our sum is

\(\displaystyle \pi^2 f(\pi) = \sum_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n+1}}{(2n-1)! (2n+1)} = \boxed{\pi}\)

Answer:

Answer:00

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.

b=0b=0

3b−5=03b-5=0

Set the first factor equal to 00.

b=0b=0

Step-by-step explanation:

The result can be shown in multiple forms.

Exact Form:

b=0,53b=0,53

Decimal Form:

b=0,1.¯6b=0,1.6‾

Mixed Number Form:

b=0,123b=0,123

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Answer:

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

Solve each parenthesis and then divide:

Answer:

The answer is -6.

Step-by-step explanation:

Given problem,

→ ((-20) - (-8)) ÷ ((-6) - (-8))

Let's solve the problem,

→ ((-20) - (-8)) ÷ ((-6) - (-8))

→ ((-20) - (-8))/((-6) - (-8))

→ ((-20) + 8)/((-6) + 8)

→ (-12)/2 = -6

Thus, the answer is -6.

Answer:

Draw 2 squares and spilt it into 5 pieces.

You would get 2/10 or 1/5 in total, meaning that each person would get that much of an item.

Step-by-step explanation:

 Sorry I couldn't explain it too well but I hope this helped and please give me brainliest if you don't mind, thanks and have a great day!!

Answer:

54

Step-by-step explanation:

24* 2.25= 54

(.25 is 1/4 in decimal form)

Answer: 0.28 is the answer i believe

Step-by-step explanation:

I hope this helps! :)

Nearest whole number will be 782318.

Nearest ones whole number is the first digit before the decimal point of a number.

For example nearest ones of 9.6 is equal to 10.

If the tenth digit (first number before decimal point) of the number is greater than or equal to 5 we round up and add 1 to ones of number, If the tenth digit of the number is less than 5 we remove the decimal part. Example:

124.6

The first number of right of decimal point is 6

6 is greater than 5, so we add 1.

Result = 125

Now given number is 782317.772

since the  first digit after decimal is 7 which is greater than 5 thus the nearest whole number will be 782318.

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Answer:210. 2/3

you would have to add all the numbers to get the answer even the fractions

Answer:

230.6 or 692/3

Step-by-step explanation:

365/6 + 326/6 + 356/6 + 337/6 = 1384/6 = 692/3 = 230.6

\(f(x) = 2x is linear.f(x) = 4^x is exponential.\) This is where at each level, each branch extends into 4 branches.

In the first prompt, the number of boxes in each row is increasing by a constant amount, so the function is linear. In the second prompt, the number of branches is increasing by a factor of 4 with each level, so the function is exponential.

A linear function is defined as one where the output increases by a constant amount for each increase in the input. An exponential function is defined as one where the output increases by a constant factor for each increase in the input. The first prompt corresponds to a linear function, while the second prompt corresponds to an exponential function.

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The complete question is-

Is the function f(x) = 4^x, where x is the number of branches at level x in a tree diagram, linear or exponential? Explain your answer.

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The key here is to find out how long it will take Justin to triple his money, and then use that number of years in Hailey's equation. If Justin starts with $940, he will triple his money when he has $2820 (940*3). We need to find out how long it takes him to do this using the equation

\(A(t)=P(1+\frac{r}{n})^{nt}\)where A(t) is the tripled amount of money, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings done per year, and t is the time in years. Filling in and solving for t:

\(2820=940(1+\frac{.07625}{12})^{12t\) which simplifies a bit to

\(2820=940(1+.0063541667)^{12t\) and a bit more to

\(2820=940(1.0063541667)^{12t\) Begin to solve for t by dividing both sides by 940 to get:

\(3=(1.0063541667)^{12t\) and then take the natural log of both sides to get the t alone eventually. Taking the natural log on the right side enables us to move the 12t down in front. So doing all of that at the same time:

\(ln3=12tln1.0063541667\) and divide both sides by ln(1.0063541667):

\(173.4450855=12t\) then finally divide both sides by 12 to get

t = 14.5 years. Now we use that number of years to find out how much Hailey will have.

\(A(t)=940(1+\frac{.0825}{4})^{(4)(14.5)}\) which simplifies a bit to

\(A(t)=940(1+.020625)^{58\) and a bit more to

\(A(t)=940(1.020625)^{58\) and

A(t) = 940(3.26768151) so in 14.5 years, Hailey will have

A(t) = $3071.62

Answer:

ms.howard has $8.05 left per student

Answer:

Two integers are relatively primes if and only if their only common positive integer factor is 1.

Step-by-step explanation:

The prime number is one whose only divisor is 1 and itself.

The prime factors of a whole number are the exact prime divisors of that whole number. In other words, every composite number can be written as a multiplication of two or more prime factors.

So, two integers are relative primes if they have no prime factor in common, or, put another way, if they have no common divisor other than 1.

So, two integers are relatively primes if and only if their only common positive integer factor is 1.

let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C

\(\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)\)

\((\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)\)

Answer:

( 4, 1 )

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

28/7=4

Answer:

3 years: $27691.30

7 years: $23359.70

Step-by-step explanation:

3.5% of 30,940 = 1082.9

for each year there is interest, we multiply it by that amount of years.

equation: 1082.9x

3 years: 3248.7  

7 years: 7580.3

since interest is subtracted, we will subtract the multiplied interests from above.

equation: 30940 - 1082.9x = answer

3 years: $27691.3

7 years: $23359.7

Answer:

Step-by-step explanation:

Answer:

when evaluate the function with the 1, then you get -2

and when evaluate with the 6, then you get 3/4

Step-by-step explanation:

the domain for this function is , [-3, 2) U (2, infinite)

Answer:  450 cm

Step-by-step explanation:

10 x 9 = 90 x 5 = 450