Find the balance in Asturos savings account if he deposits $2100 at 3.5% simple interest for 2 years

Answer:

5%

Step-by-step explanation:

Well let’s make a fraction 2/40.

So we have to simplify it to 1/20.

And we do 1 / 20.

So 1 / 20 is .05.

To make this a percent we put the seminal place 2 places to the right.

So the percent is 5%.

Answer:

Step-by-step explanation:

Null hypothesis: u = 9.5hrs

Alternative: u =/ 9.5hrs

Using the t test

t = x-u/sd/√n

Where x is 10hrs, u is 9.5, sd is 1.6 and n is 15

t = 10-9.5 / (1.6/√15)

t = 0.5 / (0.4131)

t = 1.21

In order to make a conclusion, we have to find the p value at a significance level lot 0.1. The p value is 0.2263 which is greater than 0.1. This, we will fail to reject the null hypothesis and conclude that there is not enough statistical evidence to prove that the technique performs differently than the traditional method.

Answer:

576"

Step-by-step explanation:

AL=ph

AL= (4*12)12

AL= 48*12

AL=576"

Answer:

12.04

Step-by-step explanation:

Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,

[tex]a^2 + b^2 = c^2[/tex]

We already have a and b which are 8 and 9 so we plug them in.

[tex](8)^2 + (9)^2 = c^2[/tex]

64 + 81 = c^2

145 = c^2

c = 12.04 rounded to the nearest hundredth.

Thus,

the unknown side is about 12.04.

Hope this helps :)

Answer:

Step-by-step explanation:

w - 3 = 15

Add 3 to both sides to make w stand alone

That's

w - 3 + 3 = 15 + 3

w = 15 + 3

We have the final answer as

w = 18

Hope this helps you

Answer: w = 18

Step-by-step explanation: To solve for w in this equation, we want to get w by itself on the left side of the equation.

Since 3 is being subtracted from w, to get w by itself,

we need to add 3 to the left side of the equation.

If we add 3 to the left side, we must also add 3 to the right side.

Notice that on the left side, -3 and +3 cancel

each other out so were simply left with w.

On the right side, 15 + 3 is 18.

So we have w = 18.

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

x=2

Step-by-step explanation:

3(x-2)-6x=4(x-5)

Distribute

3x -6  -6x = 4x -20

Combine like terms

-3x-6 = 4x-20

Add 3x to each side

-3x-6+3x = 4x-20+3x

-6 = 7x-20

Add 20 to each side

-6+20 = 7x-20+20

14 = 7x

Divide by 7

14/7 =7x/7

2=x

Answer:

Step-by-step explanation:

[tex]3(x - 2) - 6x = 4(x - 5)[/tex]

Distribute 3 through the parentheses

[tex]3x - 6 - 6x = 4(x - 5)[/tex]

Distribute 4 through the parentheses

[tex]3x - 6 - 6x = 4x - 20[/tex]

Collect like terms

[tex] - 3x - 6 = 4x - 20[/tex]

Move variable to L.H.S and change it's sign

[tex] - 3x - 4x - 6 = - 20[/tex]

Move constant to RHS and change it's sign

[tex] - 3x - 4x = - 20 + 6[/tex]

Collect like terms

[tex] - 7x = - 20 + 6[/tex]

Calculate

[tex] - 7x = - 14[/tex]

Divide both sides of the equation by -7

[tex] \frac{ - 7x}{ - 7} = \frac{ - 14}{ - 7} [/tex]

Calculate

[tex]x = 2[/tex]

Hope this helps..

Best regards!!

Answer:  2149

Step-by-step explanation:  If the sum of the first two digits is 3, the choices must be 1 and 2 (or 2 and 1)  In order to satisfy the other specifications, "the tens digit is 4 times the hundreds digit." the hundreds digit can't be 2 because that would make the tens dight 8.  and the ones digit would also have to 8 in order to satisfy the "seven more than the thousands digit" which would be a 1. And that violates the condition, "No two digits are equal."

So the only possible combination is 2149

4 is 4 times 1

9 is 7 +2

Answer:

(a) The probability that the sample mean will be more than 61 pounds is 0.0069.

(b) The probability that the sample mean will be more than 57 pounds is 0.4522.

(c) The probability that the sample mean will be between 55 and 58 pounds is 0.6112.

(d) The probability that the sample mean will be less than 55 pounds is 0.14686.

(e) The probability that the sample mean will be less than 48 pounds is 0.00001.

Step-by-step explanation:

We are given that the Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year.

A random sample of 51 households is monitored for one year to determine aluminum usage. Also, the population standard deviation of annual usage is 12.2 pounds.

Let [tex]\bar X[/tex] = sample mean

The z-score probability distribution for the sample mean is given by;

                             Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average aluminum used by American = 56.8 pounds

           [tex]\sigma[/tex] = population standard deviation = 12.2 pounds

           n = sample of households = 51

(a) The probability that the sample mean will be more than 61 pounds is given by = P([tex]\bar X[/tex] > 61 pounds)

   P([tex]\bar X[/tex] > 61 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{61-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 2.46) = 1 - P(Z [tex]\leq[/tex] 2.46)

                                                               = 1 - 0.9931 = 0.0069

The above probability is calculated by looking at the value of x = 2.46 in the z table which has an area of 0.9931.

(b) The probability that the sample mean will be more than 57 pounds is given by = P([tex]\bar X[/tex] > 57 pounds)

   P([tex]\bar X[/tex] > 57 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{57-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z > 0.12) = 1 - P(Z [tex]\leq[/tex] 0.12)

                                                               = 1 - 0.5478 = 0.4522

The above probability is calculated by looking at the value of x = 0.12 in the z table which has an area of 0.5478.

(c) The probability that the sample mean will be between 55 and 58 pounds is given by = P(55 pounds < [tex]\bar X[/tex] < 58 pounds)

P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = P([tex]\bar X[/tex] < 58 pounds) - P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds)    

   P([tex]\bar X[/tex] < 58 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{58-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < 0.70) = 0.75804

   P([tex]\bar X[/tex] [tex]\leq[/tex] 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.05) = 1 - P(Z < 1.05)

                                                               = 1 - 0.85314 = 0.14686

The above probability is calculated by looking at the value of x = 0.70 and x = 1.05 in the z table which has an area of 0.75804 and 0.85314.

Therefore, P(55 pounds < [tex]\bar X[/tex] < 58 pounds) = 0.75804 - 0.14686 = 0.6112.

(d) The probability that the sample mean will be less than 55 pounds is given by = P([tex]\bar X[/tex] < 55 pounds)

   P([tex]\bar X[/tex] < 55 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{55-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -1.05) = 1 - P(Z [tex]\leq[/tex] 1.05)

                                                               = 1 - 0.85314 = 0.14686

The above probability is calculated by looking at the value of x = 1.05 in the z table which has an area of 0.85314.

(e) The probability that the sample mean will be less than 48 pounds is given by = P([tex]\bar X[/tex] < 48 pounds)

   P([tex]\bar X[/tex] < 48 pounds) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{48-56.8}{\frac{12.2}{\sqrt{51} } }[/tex] ) = P(Z < -5.15) = 1 - P(Z [tex]\leq[/tex] 5.15)

                                                               = 1 - 0.99999 = 0.00001

The above probability is calculated by looking at the value of x = 5.15 in the z table which has an area of 0.99999.

Answer:

$12.10

Step-by-step explanation:

First, you have to set up a proportion to find what 20% of $60.50, or 60.5, is. On one side of the proportion you have 20/100 to represent the percent, anytime you have a percent it will always go over 100. On the other side you'll have x/60.5 because you are trying to find a value out of 60.5. This gives you the proportion 20/100=x/60.5. In order to solve this you have to cross multiply using the equation 20(60.5)=100x. First, you multiply to get 1210=100x, then divide both sides by 100 to get 12.1=x. In order for this to represent money, we add a zero on the end. This means that 20% of $60.50 is $12.10, so $12.10 is the tip.

Answer:

well if you want my answer even though it could not be right so dont get mad at me if i am wrong but i think that it is all mostly based on how far they are from each other the further it is the more it will roll the closer it is the less it it will roll

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

rolling it shows its circumference and the other pennine has the ame circumference

Answer:

1. a = -31/9

2. -3/4

3. Different degree polynomials

4. Yes, of a degree 2n

5. a. Even-degree variables

b. Odd- degree variables

Step-by-step explanation:

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a?

Plugging in 3 for x:

f(3)= 3^4 - 2*3^3 + a*3^2 + 3 + 3= 81 - 54 + 6 + 9a = 33 + 9a and f(3)= 2

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

2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

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

3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g?

If the sum of monic polynomials f(x) + g(x) is also monic, then f(x) and g(x) are of different degree and their sum only change the one with the lower degree, leaving the higher degree variable unchanged.

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

4. If f(x) is a polynomial, is f(x^2) also a polynomial?

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

5. Consider the polynomial function g(x) = x^4-3x^2+9

a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial?

b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial?

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

[tex]18-\sqrt{-25}[/tex]   Original Question

[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex]   Split

[tex]18-5*(\sqrt{-1} )[/tex]   Solve for square root

[tex]12-\sqrt{-1}[/tex]   Subtract

You can substitute [tex]\sqrt{-1}[/tex] for i

[tex]12-i[/tex]   Substitute

Answer:

18-5i

Step-by-step explanation:

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:

[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]

The value of 86º in radians is:

[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]

[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]

Then, the cosine of 86º is:

[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]

[tex]\cos 86^{\circ} \approx 0.06976[/tex]

The cosine of 86º is approximately 0.06976.

Answer:

The answer is below

Step-by-step explanation:

Given that:

Mean (μ) = 3 ounces. standard deviation (σ) = 0.15, sample size (n) = 13 and confidence (C) = 98%

α = 1 - C = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01.

The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33.

The margin of error (E) is:

[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } = 2.33*\frac{0.15}{\sqrt{13} }=0.1\\[/tex]

The confidence interval = μ ± E = 3 ± 0.1 = (2.9, 3.1)

The confidence interval is between 2.9 ounce and 3.1 ounce

Answer:

y=0.5x+40

Step-by-step explanation:

Copy the  equation.

x-2y=8

Subtract x from both sides.

-2y=-x-8

Divide both sides by -2.

y=0.5x+4

Now we know the slope is 0.5.

Any line with a slope of 0.5 will be perpendiculr to the original line.

One that you can use is y=0.5x+40.

Answer:

B. -3x

Step-by-step explanation:

A term is defined as either a constant or a variable with a coefficient.

-3 is incorrect because there is no constant -3 in the expression.

-3x is correct because there is a -3x in the expression

(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.

-7 is incorrect because it has to be distributed.

Answer:

you need to have values for w and v

but u basically have to do

MOVE V TO THE OTHER SIDE

SO

W/V=P

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

              ✌ -ZYLYNN JADE ARDENNE

Answer:

His overall final score is a 73, which means that that student recieved a letter grade of a C.

Step-by-step explanation:

First, we are finding the mean of the scores to average everything out.

So, start by adding up all the scores given: 60+80+75+78=293.

Then, divide that sum by the number of scores given: 293/5=73.25, or rounded to a whole number is a 73.

In most schools, a 73 is a C, so this students letter grade for this course is a C.

Answer:

18.03 inches

Step-by-step explanation:

The cardboard is cut as shown below.

The line c cuts the rectangle into 2 right angled triangles.

To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:

[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]

=> c = 18.03" = 18.03 inches

The length of c, the diagonal, is 18.03 inches.

Answer:

The zeros are x=-3,-2,1

end behavior is one up one down

Step-by-step explanation:

The zeros are x=-3,-2,1

The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.

Answer:

[tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

Step-by-step explanation:

Hello,

"Find the sum of the following infinite geometric series"

infinite

   We will have to find the limit of something when n tends to [tex]+\infty[/tex]

geometric series

   This is a good clue, meaning that each term of the series follows a geometric sequence. Let's check that.

The sum is something like

           [tex]\displaystyle \sum_{k=0}^{+\infty} a_k[/tex]

First of all, we need to find an expression for [tex]a_k[/tex]

First term is

   [tex]a_0=7[/tex]

Second term is

    [tex]a_1=\dfrac{4}{9}\cdot a_0=7*\boxed{\dfrac{4}{9}}=\dfrac{7*4}{9}=\dfrac{28}{9}[/tex]

Then

   [tex]a_2=\dfrac{4}{9}\cdot a_1=\dfrac{28}{9}*\boxed{\dfrac{4}{9}}=\dfrac{28*4}{9*9}=\dfrac{112}{81}[/tex]

and...

   [tex]a_3=\dfrac{4}{9}\cdot a_2=\dfrac{112}{81}*\boxed{\dfrac{4}{9}}=\dfrac{112*4}{9*81}=\dfrac{448}{729}[/tex]

Ok we are good, we can express any term for k integer

   [tex]a_k=a_0\cdot (\dfrac{4}{9})^k[/tex]

So, for n positive integer

[tex]\displaystyle \sum_{k=0}^{n} a_k=\displaystyle \sum_{k=0}^{n} 7\cdot (\dfrac{4}{9})^k=7\cdot \dfrac{1-(\dfrac{4}{9})^{n+1}}{1-\dfrac{4}{9}}=\dfrac{7*9*[1-(\dfrac{4}{9})^{n+1}]}{9-4}=\dfrac{63}{5}\cdot [1-(\dfrac{4}{9})^{n+1}}][/tex]

And the limit of that expression when n tends to [tex]+\infty[/tex] is

   [tex]\large \boxed{\ \ \dfrac{63}{5} \ \ }[/tex]

as

   [tex]\dfrac{4}{9}<1[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

g(2) =10x+6

Step-by-step explanation:

g(x) =5x+3

g(2)=5x+3

g(2)=10x+6

have a great day

Answer:

60

Step-by-step explanation:

x + 0.30x = 78

1.30x = 78

x = 60

Answer:

The answer is 60.

Step-by-step explanation:

here, let another number be x.

according to the question the number when increased by 30% will be 78. so,

x+ 30% of x =78

now, x+ 30/100×x =78

or, x+0.3x=78

or, 1.3x=78

Therefore the another number is 60.

Hope it helps...

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 13/3, 4 1/3, or 4.3

▹ Step-by-Step Explanation

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 7 - 4 = -10

-3x + 3 = -10

-3x = -10 - 3

-3x = -13

x = 13/3, 4 1/3, or 4.3

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x = 13/3

Step-by-step explanation:

x + 7 - 4(x + 1) = -10

x + 7 - 4x - 4 = -10

-3x + 3 = -10

-3x = -13

x = -13/(-3)

x = 13/3

Answer:

its b i got it right on edge

Step-by-step explanation:

Answer: i honestly dont know this seems very complicated

Step-by-step explanation:

Answer:

3x^3+12x

Step-by-step explanation:

Answer:

0.3110

Step-by-step explanation:

This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.

The general formula for a binomial distribution is:

[tex]P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}[/tex]

Where n is the sample size and k is the desired number of successes.

The probability of k=2 in a sample of n =6 is:

[tex]P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110[/tex]

The probability is 0.3110

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

How long will it take the projectile to hit the ground?

It happens when [tex]h(t) = 0[/tex]

So

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

[tex]-16t^{2} + 32t + 128 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-16t^{2} + 32t + 128 = 0[/tex]

So [tex]a = -16, b = 32, c = 128[/tex]

[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]

[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]

[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

a = 14.56231 cm

b(width) = 9 cm

a+b = 23.56231 cm

A(area) = 343.1215 cm

Sorry if this doesnt help

Answer:

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Step-by-step explanation:

In a golden rectangle, the width is a and the length is a + b.

The proportion of the lengths of the sides is:

(a + b)/a = a/b

Here, the width is 9 cm, so we have a = 9 cm.

(9 + b)/9 = 9/b

(9 + b)b = 81

b^2 + 9b - 81 = 0

b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)

b = (-9 +/- sqrt(81 + 324)/2

b = (-9 +/- sqrt(405)/2

b = -9/2 +/- 9sqrt(5)/2

Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2

Length = a + b = 9/2 +/- 9sqrt(5)/2

Since the length of a side of a rectangle cannot be negative, we discard the negative answer.

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm