A principal of $1700 is invested at 6% interest, compounded annually. How much will the investment be worth after 13 years?

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

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

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

This is a graph of the function h. from that its clear that h(x) =-1 occurs at 0 and the value of h(0) is 3.

A sentence, rule, or piece of law in mathematics that demonstrates the relationship between an independent variable and a dependent variable (the dependent variable).. In mathematics, functions exist everywhere

given that :h (x)=-1 .

h(x) =-1 occurs at 0 and the value of h(0) is 3.

We must first notice the y coordinates for a certain value of the x coordinate in this scenario.

We have h (x) = -1. It is evident from the graph that this occurs when x = 0.        

On the other hand, we have to find  h(0). Which occurs at 3.

Thus,  h(x) =-1 occurs at 0 and the value of h(0) is 3.

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Answer:

first you choose one of the varibles to solve for so im going to start with s you would add them up and subtract them that way there on the other side of the = sighs so you equation would be 8+2d+3=-7s then you add the 8 and the 3 and you would get 11+2d=-7s i dont know what you do after this i think this is the answer.

Answer:

the other guy is right trust him

Answer:

 y = 4.87x + 2.28 Is the answer

Step-by-step explanation:

( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )

using a:

THE ULTIMATE LINEAR REGRESSION CACLAULTOR

yes it is the epic i get:

y = 4.87x + 2.28

Nothing more noting less ikr

y = 4.87x + 2.28 Being the answer

Answer:

52 pounds

Step-by-step explanation:

2 x 26= 52

Answer:

Here's a table showing the possible numbers of positive real, negative real, and complex zeros of the given polynomial function:

Number of Positive Real Zeros Number of Negative Real Zeros Number of Complex Zeros

0 3 2

In this case, the polynomial function f(x) = -7x^4 - 12x^3 + 9x^2 - 17x + 3 has no positive real zeros, three negative real zeros, and two complex zeros.

Step-by-step explanation:

GIVE ME BRAINLIEST PLS

By the product rule,

\((fg)'=f'g+fg'\)

so that

\((fg)'(7)=f'(7)g(7)+f(7)g'(7)=10\cdot(-1)+4\cdot8=22\)

By the quotient rule,

\(\left(\dfrac fg\right)'=\dfrac{f'g-fg'}{g^2}\)

so that

\(\left(\dfrac fg\right)'(7)=\dfrac{f'(7)g(7)-f(7)g'(7)}{g(7)^2}=\dfrac{10\cdot(-1)-4\cdot8}{(-1)^2}=-42\)

Answer:

A) Yes. At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.

B) P-value = 0.001

C) The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean water temperature is significantly below 100 °F.

Then, the null and alternative hypothesis are:

\(H_0: \mu=100\\\\H_a:\mu< 100\)

The significance level is 0.05.

The sample has a size n=9.

The sample mean is M=98.

The standard deviation of the population is known and has a value of σ=2.

We can calculate the standard error as:

\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{2}{\sqrt{9}}=0.667\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{98-100}{0.667}=\dfrac{-2}{0.667}=-3\)

This test is a left-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=P(z<-3)=0.001\)

As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the mean water temperature is significantly below 100 °F.

The critical value for this left-tailed test is zc=-1.645.

The null hypothesis would be accepted if the test statistic is higher than zc=-1.645. For a normal distribution with the parameters of the null hypothesis (μ=100, σ=2), this would correspond to a value of:

\(X=\mu+z\sigma/\sqrt{n}=100+(-1.645)\cdot 2/\sqrt{9}=100-1.1=98.9\)

This means that if we get a sample of size n=9 and mean bigger than 98.9, we will failed to reject the null hypothesis.

If the true mean is 104 °F, the probability of getting a sample mean over 98.9 for this sample size can be calculated as:

\(z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{98.9-104}{2/\sqrt{9}}=\dfrac{-5.1}{0.6667}=-7.65\\\\\\P(M>98.9)=P(z>-7.65)=1\)

The probability of not rejecting the null hypothesis at α = 0.05 if the true mean is 104 °F is P(M>98.9)=1. This means that is almost impossible to reject the null hypothesis μ≤100 given that the true mean is 104.

\(sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(80^o)-tan^2(80^o)\implies \cfrac{1}{cos^2(80^o)}-\cfrac{sin^2(80^o)}{cos^2(80^o)} \\\\\\ \cfrac{1-sin^2(80^o)}{\underset{\textit{using this LCD}}{cos^2(80^o)}}\implies \cfrac{cos^2(80^o)}{cos^2(80^o)}\implies 1\)

To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

How to determine the appropriate graph?

The graphs that complete the question are added as an attachment

From the attached graph, we have the following highlights:

The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....

The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....

The above means that graph B is a misleading graph

Hence, Benjamin should use graph A for his report

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Answer:

count the number of places it is. The 5 in 458,039 is in the 10,000 place and the 5 in 271,145 is in the ones place so the 5 in 458,039 is 10,000 times greater

The system of measurement is most commonly used in the United States is Metric system.

Answer: metric system hope this help a had this problem

Answer:

Step-by-step explanation:

it is -12 because -6 plus -6 is also like 6 plus 6

and then you have to add the negative Sign.

pls brainliest me

-6 - 6 = - 12

Happy to help! Please mark as the brainliest!

Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

15

Step-by-step explanation:

Joyce reserved number 1 for herself

Of all  the possible combinations,

1 and  15 is a perfect match for a perfect square

So,Joyce dinner partner was number 15.

Given :-

5 years ago, Ram's mother was five times his age

Ram's Mother is now thrice as old as him.

To find :-

Present age of Ram

Present age of Ram's mother

Solution :-

Let the present age of Ram be x years

Let the present age of Ram's mother be y years.

As per the first condition,

5 years ago, Ram's mother was five times his age

5 years ago,

Ram's age = x - 5

Mother's age = y - 5

Let's represent the first condition mathematically to get our first equation.

y - 5 = 5 ( x - 5)

y - 5 = 5x - 25

5x - 25 = y - 5

5x - y = - 5 + 25

5x - y = 20 -----> 1

As per the second condition,

If his mother is now thrice as old as him

Ram's age = 3x

Mother's age = y

Let's represent this too mathematically. Here we will get just the value of one of the variables, either x or y.

y = 3x

Substitute, y = 3x in equation 1,

5x - y = 20 ----> 1

Plug in the value of y,

5x - 3x = 20

2x = 20

x = \(\frac{20}2}\)

x = 10

Present age of Ram = x = 10 years

Substitute, x = 10 in equation 1,

5x - y = 20 ---> 1

5 ( 10 ) - y = 20

50 - y = 20

- y = 20 - 50

- y = - 30

[canceling minus from both sides]

y = 30

Present age of Mother = y = 30 years

•°• Present age of Ram = 10 years.

For first case :-

5 years ago, Ram's mother was five times his age

Present age of Ram = 10 years

5 years ago,

Ram's age = 10 - 5 = 5 years

Present age of Mother = 30 years

5 years ago,

Mother's age = 30 - 5 = 25 years

Let's check if the ages satisfies the first condition,

Mother's age = 5 ( Ram's age )

25 = 5 ( 5 )

25 = 25

LHS = RHS.

For second case :-

His mother is now thrice as old as him

Mother's age = 30 years

Ram's age = 10 years

Let's check whether the second condition is satisfied or not.

Mother = 3 ( Ram's age)

30 = 3 ( 10)

30 = 30

LHS = RHS.

Hence the answer is verified.

The equation that best describes the relation is y = -x+1 ( optionD)

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Taking x(0,1) and y ( 1,0)

therefore the slope of the line

= 0-1/1-0

= -1/1 = -1

the equation a line is given as

y-y1 = m(x-x1)

= y-1 = -1( x - 0)

= y-1 = -x

y = -x +1

therefore the equation that describe relation is y = 1-x or y = -x+1

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Answer:

A: 12.5

B: 36

C: 40

D: 88

Step-by-step explanation:

those are the answers

Answer:

56

Step-by-step explanation:

Step 1: Order the data

43,49,55,58,64,67

Step 2: Count all numbers and add them up

43+49+55+58+64+67=336 and we have 6 numbers in total so... 336 ÷ 6

Step 3: Divide!

336 ÷ 6 = 56

Hope this helps you!

Answer:

I think its C

Step-by-step explanation:

we have

Multiply in cross

square root both sides

see the attached figure to better understand the problem

the solution is the interval {-6,6}

the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)

Step-by-step explanation:

4 is the base of the exponent.

hope it helps.. please mark brainliest

Answer:

\(x^2+2x+1\)

Step-by-step explanation:

Note that \((a+b)^2=a^2+2ab+b^2\).

Let \(a=x\) and \(b=1\).

\((x+1)^2=x^2+2(x)(1)+1^2=x^2+2x+1\)

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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