The ending balance on an investment is $1,620.24. If the principal was invested at 8% for nine years, what was the principal?​

Type I error would be that we conclude to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

We are given that the percentage of households with more than 1 pet is 65%.

Let p = population % of households with more than 1 pet

So, Null Hypothesis,  : p = 65%     {means that the percentage of households with more than 1 pet is equal to 65 %}

Alternate Hypothesis,  : p  65%      {means that the percentage of households with more than 1 pet is different from 65 %}

Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our case, type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our case, type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

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Answer:

(look in the the Step by step)

Step-by-step explanation:

When the diagonals of a quadrilateral are perpendicular, the area of that quadrilateral is half the product of their lengths.

.. A = (1/2)*d₁*d₂

Substituting the given information, this becomes

.. 58 in² = (1/2)*(14.5 in)*d₂

.. 2*58/14.5 in = d₂ = 8 in

The length of diagonal BD is 8 in.

Answer:

BD = 8 in.

Step-by-step explanation:

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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Answer:

x = 33

Step-by-step explanation:

Pls brainliest I knew it because of K12

Answer: A

Step-by-step explanation:

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

(4, 1)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

~Solve by Graphing~

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The answer is  {x,y} = {-52/5,-53/5}

The extreme values of the function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1 are approximately ±0.235

To find the extreme values of the given function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1, we can use the method of Lagrange multipliers.

First, we write down the Lagrangian function L(x, y, λ) as follows:

L(x, y, λ) = xy(2y^2 x^4 − y^4) + λ(x^2 + y^2 − 1)

Then, we take the partial derivatives of L with respect to x, y, and λ and set them equal to zero:

∂L/∂x = y(2y^2 x^4 − y^4) + 2λx = 0

∂L/∂y = x(6y^3 x^4 − 4y^3) + 2λy = 0

∂L/∂λ = x^2 + y^2 − 1 = 0

Simplifying the first two equations, we get:

2y^5 x^4 − y^5 + 2λxy = 0

6y^4 x^4 − 4y^4 + 2λxy = 0

Dividing these equations, we obtain:

3x^4 = 2y^2

Substituting this back into the equation x^2 + y^2 = 1, we get:

3x^4 + x^2 = 1

This is a quartic equation in x^2. We can solve it using numerical methods to get the two possible values of x:

x ≈ ±0.681

y ≈ ±0.732

Plugging these values into the equation 3x^4 = 2y^2, we get:

y ≈ ±0.524

Now we can calculate the corresponding values of the function f(x, y) = xy(2y^2 x^4 − y^4):

f(x, y) ≈ ±0.235

Therefore, the extreme values of the function f(x, y) on the circle x^2 + y^2 = 1 are approximately ±0.235, and they are attained at the points (±0.681, ±0.732) and (±0.732, ±0.681).

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The probability of scanning the items in order of price, given a random order, depends on the number of orderings. The probability that the items are scanned in order of price is 1/n!.

To determine the probability of scanning the items in order of price, we need to consider the number of possible orderings that satisfy the condition and divide it by the total number of possible orderings.

Let's assume there are 'n' items with distinct prices. If the items are scanned in order of price, it means that the lowest-priced item must be scanned first, followed by the second lowest-priced item, and so on.

The total number of possible orderings of 'n' items is given by n!. However, since we want the items to be scanned in a specific order, only one ordering satisfies the condition. Therefore, the number of possible orderings that satisfy the condition is 1.

Thus, the probability of scanning the items in order of price is 1/n!.

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For the value h = -1, the vector y = [4,-1,-1] is in the plane spanned by v1 and v2.

To determine whether y is in the plane spanned by v1 and v2, we need to check if y can be expressed as a linear combination of v1 and v2.

Let's set up an equation using the vectors v1, v2, and y:

y = av1 + bv2,

where a and b are scalar coefficients to be determined.

Substituting the given values of v1, v2, and y, we have:

[4,-1,h] = a[1,2,-1] + b[-2,-1,1].

Expanding the right side of the equation, we get:

[4,-1,h] = [a,2a,-a] + [-2b,-b,b].

Combining like terms, we obtain:

[4,-1,h] = [a-2b,2a-b,-a+b].

Now, we can set up a system of equations by comparing the corresponding components:

a - 2b = 4,     (1)

2a - b = -1,    (2)

-a + b = h.     (3)

We can solve this system to find the values of a, b, and h.

From equation (2), we can solve for a in terms of b:

2a = b - 1,

a = (b - 1)/2.

Substituting this expression for a into equation (1), we have:

(b - 1)/2 - 2b = 4,

b - 1 - 4b = 8,

-3b = 9,

b = -3.

Substituting the value of b = -3 into equation (2), we find:

2a - (-3) = -1,

2a + 3 = -1,

2a = -4,

a = -2.

Finally, substituting the values of a = -2 and b = -3 into equation (3), we get:

-(-2) + (-3) = h,

2 - 3 = h,

h = -1.

Therefore, for h = -1, the vector y = [4,-1,-1] is in the plane spanned by v1 and v2.

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Answer:

n = 18

Step-by-step explanation:

Corresponding parts of similar triangles are in same ratio

\(\frac{FG}{XY}=\frac{HG}{YZ}\\\\\frac{n}{6}=\frac{15}{5}\\\\n=\frac{15}{5}*6\\\\n=3*6\\\\n=18\)

Answer:

\(x_1=\frac{-2+\sqrt{14}}{2}\approx 0.871,x_2=\frac{-2-\sqrt{14}}{2}\approx-2.871\)

Step-by-step explanation:

\(2x^2+4x-5=0\)

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(x=\frac{-4\pm\sqrt{4^2-4(2)(-5)}}{2(2)}\)

\(x=\frac{-4\pm\sqrt{16+40}}{4}\)

\(x=\frac{-4\pm\sqrt{56}}{4}\)

\(x=\frac{-4\pm2\sqrt{14}}{4}\)

\(x=\frac{-2\pm\sqrt{14}}{2}\)

\(x_1=\frac{-2+\sqrt{14}}{2}\approx 0.871,x_2=\frac{-2-\sqrt{14}}{2}\approx-2.871\)

Answer:

there wont be a fraction the sweets are gone

Step-by-step explanation:

she got fat

The potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

The product of the log rule says that the sum of number of logarithm functions is equal to the log function of product of all the numbers, given  that base is same.

The given logarithmic function in the problem is,

\(\log_6x+\log(6x+5)=2\)

Using the product rule of logarithmic function, the above equation can be written as,

\(\log_6(x\times(x+5))=2\\\log_6(x^2+5x))=2\)

Using the equality rule of logarithmic function, the above equation can be written as,

\(x^2+5x=6^2\\x^2+5x=36\)

Take all the terms one side of the equation as,

\(x^2+5x-36=0\)

Find the factors of above equation using the split the middle term method as,

\(x^2+9x-4x-36=0\\x(x+9)-4(x+9)=0\\(x+9)(x-4)=0\)

By equating these factor to the zero one by one, we get the potential solution as -9 and 4.

Thus, the potential solutions of logarithmic function using the logarithmic properties are found as -9 and 4.

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Answer:

-9 and 4

Step-by-step explanation:

Did it on edge :)

Answer:

The difference in price between a small pizza and a medium pizza is $0.81

Step-by-step explanation:

Small pizza

Side = 5inch

Area =  25 sq.in

Cost = $4 +0.04*25

        = 4 + 1.25  = $5.25

Medium pizza

Side = 8inche

Area = 64 sq.in

Cost = 3.50 + 0.04*64 = $6.06

Difference = Medium pizza - small pizza

                  = 6.06 - 5.25

                   = $0.81

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Answer:

-1/5

y=-1/5 x-8

-1/5 is the slope

Step-by-step explanation:

-1/5

Formula-    y=mx+b

The slope-intercept form is

y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Rewrite in slope-intercept form.

Simplify the left side

Simplify each term.

Combine 1/8 and x.

x/9+5y/8=-5

Subtract x/8 from both sides of the equation.

5y/8=-5-x/8

Multiply both sides of the equation by8/5.

8/5.5y/8=8/5(-5-x/8)

Simplify both sides of the equation.

Simplify the left side.

Simplify 8/5.5y/8

y=-x/5-8

y=-1/5 x-8

Step-by-step explanation:

Given equation:

1/8x + 5/8y =-5

Now write it in standard form like ax+by+c=0

1/8x + 5/8y + 5= 0

Now,slope of line (m) = -a/b

here value of a is 1/8 and value of b is 5/8

now by formula..

-(1/8)÷(5/8) = m(slope)

-1/8 × 8/5 = m

-1/5 = m

here ia your answer

The number of written in standard form is 9.45 × 10⁵

From the question, we are to write the given number in standard form

The given number is

Nine hundred forty-nine thousand

That is,

945000

To write a number in standard form, we will write the number as a decimal number between 1.0 and 10.0, multiplied by a power of 10.

The number, 945000, written in standard form is

9.45 × 10⁵

Hence, the number of written in standard form is 9.45 × 10⁵

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Answer:

A.dollors

correcte if I wrong

Answer:

x=-5/3

y=-4/3

Step-by-step explanation:

Given:

x+y=-3

y=2x+2

Substitute y into the first equation

x+2x+2=-3

combine like terms

3x+2=-3

subtract 2 from both sides

3x=-5

divide both sides by 3

x=-5/3

Substitute in x for the second equation:

y=2(-5/3)+2

y= -4/3

Hope this helps! :)

The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.

From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.

An expression have at least two terms which have to be related by through an operator.

Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:

2 - (25% × h)

= 2 - 0.25h

h = number of hours.

The expression is 2 - 0.25h.

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Complete question

Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression

I give u the answers of first and second one.

thank you

brainlist please

Answer:

First answer is 9 or 1 . Second answer is 7 or -7.

Step-by-step explanation:

\((x-5)^{2} =16\)

\(x-5 = 4\)  or \(x - 5 =-4\)

so \(x = 9\) or \(x = 1\)

\(2x^{2} = 98\)

\(x^{2} =49\)

\(x=7\) or \(x = -7\)

Solution :

Cost of carpeting per square yard = $ 15.00

For 3 ft by 6 ft

1 yard = 3 feet

∴ 1 feet =  \($\frac{1}{3}$\) yard

So,

Therefore, area of 3 ft by 6 ft is = \($3 \times \frac{1}{3} \times 6 \times \frac{1}{3} $\)

                                                    = 1 x 2

                                                    = 2 square yard

Therefore, cost of carpeting 2 square yard = 2 x 15

                                                                       = $ 30

For 9 ft by 12 ft

1 yard = 3 feet

∴ 1 feet =  \($\frac{1}{3}$\) yard

So,

Therefore, area of 9 ft by 12 ft is = \($9 \times \frac{1}{3} \times 12 \times \frac{1}{3} $\)

                                                    = 3 x 4

                                                    = 12 square yard

Therefore, cost of carpeting 2 square yard = 12 x 15

                                                                       = $ 180

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

\(s(t)=-16t^2+112t+360\), then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

\(s(3.5)=-16(3.5)^2+112(3.5)+360\) and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Answer:

Step-by-step explanation:

Perimeter is all sides added together...

X+3+2x-1+3x+4

Combine like terms

X+2x+3x.. 6x

3-1+4.. 2+4.. 6

Answer:

6x+6

Answer:

The zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

Step-by-step explanation:

To find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15, we can use the Rational Root Theorem and synthetic division.

Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.

Use synthetic division to test each possible zero. We start with x = 1:

1 │ 1 -2 -8 10 15

│ 1 -1 -9 1

└───────────────

1 -1 -9 1 16

x = 1 is not a zero of the polynomial function.

We continue testing the remaining possible zeros:

-1 │ 1 -2 -8 10 15

│ -1 3 5 -15

└───────────────

1 -3 -3 15 0

Since the remainder is zero, we have found a zero of the polynomial function at x = -1.

We can use synthetic division to factor the polynomial function:

(x + 1)(x^3 - 3x^2 - 6x + 15)

Now we can solve for the remaining zeros of the polynomial function by factoring the cubic equation using the Rational Root Theorem and synthetic division:

3 │ 1 -3 -6 15

│ 3 0 -18

└─────────────

1 0 -6 -3

x = 3 is not a zero of the polynomial function.

-3 │ 1 -3 -6 15

│ -3 18 -36

└────────────

1 -6 12 -21

x = -3 is not a zero of the polynomial function.

The only remaining possible rational zeros are ±1/2 and ±5/2, but testing these values using synthetic division does not yield any more zeros.

However, we can see that the polynomial function can be factored as follows:

(x + 1)(x - 3)(x^2 - 3x - 5)

We can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = (3 + √(29))/2 and x = (3 - √(29))/2.

Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

Hopefully this helps, if not I'm sorry! If you need more help, you may ask me! :]