The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphere of radius 1in is dropped in to the tank. What is the new distance from the water to the top of the tank? How many of these balls can be put into the tank with the tank not overflowing?

For this case we must find an expression equivalent to:

[tex](x ^ {\frac{1}{4}} * y ^ {16}) ^ {\frac {1} {2}}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex](x ^ {\frac {1 * 1} {4 * 2}} * y ^ {\frac {16 * 1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {\frac {16} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {8}[/tex]

Answer:

Option B

The ratios 4/6 and 8/12 are equivalent ratio of 2/3 which we obtain by multiplying or dividing both numerator and denominator by same number.

To find a ratio that is the same as 2/3, we can multiply or divide both the numerator and the denominator by the same non-zero number.

This will result in an equivalent ratio.

If we multiply both the numerator and denominator of 2/3 by 2, we get:

(2 × 2) / (3 × 2)

= 4/6

Therefore, the ratio 4/6 is the same as 2/3.

Similarly, if we multiply both the numerator and denominator of 2/3 by 2, we get:

8/12

So, the ratio 8/12 is also the same as 2/3.

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Answer:

13,92838827718412‬ft

Step-by-step explanation:

a² + b² = c²

a = 13ft

b = 5ft

169 + 25 = 194

c = √194

c = 13,92838827718412‬ft

Answer:

a. [tex]-3x^{5}y^{6}[/tex]

Step-by-step explanation:

We want to multiply and simplify:

[tex]-3x^2y^2\times y^4x^3[/tex]

We rearrange the product to obtain:

[tex]-3x^2\times x^3\times y^2\times y^4[/tex]

Recall that:

[tex]a^m\times a^n=a^{m+n}[/tex]

We apply this property to obtain:

[tex]-3x^{2+3}y^{2+4}[/tex]

We simplify to obtain:

[tex]-3x^{5}y^{6}[/tex]

Answer:

Final answer is c=-7.

Step-by-step explanation:

Given equation is [tex]0=-x^2+4x-7[/tex].

Now question says that Misha wrote the quadratic equation 0=-x2+4x-7 in standard form. Now we need to find about what is the value of c in her equation.

We know that standard form of quadratic equation is given by [tex]ax^2+bx+c=0[/tex].

compare given equation with the standard form, we find that -7 is written in place of +c

so that means +c=-7

or c=-7

Hence final answer is c=-7.

Answer:

The trip will take more than one hour

Step-by-step explanation:

The complete question is

A straight road connects the towns of Winridge and Upper Lansbury. On a map on which each unit represents 10 miles, the coordinates of Winridge are (8,4) and the coordinates of Upper Lansbury are (6,10). If Ty drives from Winridge to Upper Lansbyet at an average speed of 40 miles per hour, will the trip take more than an hour? Explain your reasoning

we know that

The speed is equal to divide the distance by the time

so

s=d/t

Solve for t

t=d/s ----> the time is equal to divide the distance by the speed

step 1

Find the distance

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(8,4), (6,10)

substitute

[tex]d=\sqrt{(10-4)^{2}+(6-8)^{2}}[/tex]

[tex]d=\sqrt{(6)^{2}+(-2)^{2}}[/tex]

[tex]d=\sqrt{40}[/tex]

[tex]d=2\sqrt{10}\ units[/tex]

Convert to miles

[tex]d=2\sqrt{10}*10=20\sqrt{10}\ miles[/tex]

[tex]d=63.2\ miles[/tex]

step 2

Find the time

we have

s=40 miles/hour

d=63.2 miles

t=d/s -----> t=63.2/40=1.58 hours

1.58 hours > 1 hour

therefore

The trip will take more than one hour

Given the low sampling variability, the average annual salary for the other group of the business school graduates is most likely to be close to $96,000. Thus, extreme values, significant higher or lower than $96,000, are less likely.

In the domain of statistics, when the sampling variability is low, it means that most of the samples drawn from a population will have averages (means) that are close to the population mean. The data from the samples will be clustered around a single value.

In this context, given that the average salary of one group was $96,000, the salaries of the other groups are also likely to be around this value given the low sampling variability. Therefore, an average annual salary that is significantly higher or lower than $96,000 for another group would be least likely.

By using the concept of sampling variability, we could reasonably predict that extremes, such as $40,000 or $150,000, would be highly unlikely as average salaries for the other groups if the business school graduates' salaries are distributed normally and the sampling variability is indeed low.

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Answer:

b.-1/3

Step-by-step explanation:

Is means equals and of means multiply

W =5/9 * (-3/5)

W = -3/9

W = -1/3

Answer:

The slope of this line is 1/5

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer:

A : x^2 = -12y

Step-by-step explanation:

TO ALL MY EDGE PEOPLE

Answer:

a) x^2=-12y

Step-by-step explanation:

Answer:

A = 13 cm^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh  where b is the length of the base and h is the height

A = 1/2 (6.5) * 4

A = 13 cm^2

ANSWER

B. 10

EXPLANATION

We need to find the value of x first.

It was given that the perimeter of triangle XYZ is 24.

This means that:

XY+YZ+XZ=24

we substitute the expression in terms of x to get;

[tex](5x - 1) + (13 - x) = 24[/tex]

This implies that

[tex]5x - x = 24 - 13 + 1[/tex]

[tex]4x = 12[/tex]

Divide both sides by 4 to get;

[tex]x = 3[/tex]

|WY|=|ZX|=13-3=10

Answer:

WY = 10 units

Step-by-step explanation:

From the figure we can see a rectangle WXYZ.

Diagonals of rectangle are equal.

It is given that, Perimeter of triangle XYZ = 24

XY + YZ = 5x - 1 and XZ = 13 - x

To find the value of x

Perimeter of ΔXYZ = XY + YZ + XZ

24 = 5x - 1 + 13 - x

4x + 12 = 24

4x = 12

x = 12/4 = 3

x = 3

To find the value of WY

We have WY = XZ

XZ = 13 - x

 = 13 - 3 = 10

Therefore WY = XZ = 10 units

Step 1: Convert [tex]\frac{5\pi }{12}[/tex], which is in radians into degrees. To convert it multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{5\pi }{12} =\frac{180}{\pi }[/tex]

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = [tex]\frac{\sqrt{2} }{2}[/tex]

cos30 =[tex]\frac{\sqrt{3} }{2}[/tex]

Step 3: Add the cos45 and cos30 to get cos5pi/12

[tex]\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}[/tex]

Hope this helped!

Answer:

The correct answers are:

Question 4: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: step 4 could be n ln 2 equals ln 86

Question 6: the exact solution is x=ln(7)

Step-by-step explanation:

Ok,

Question 4: the equation that shows the first step Keisha should take is:

[tex]7^{x}=9[/tex]

[tex]log(7^{x} )=log(9)[/tex]

[tex]x(log(7))=log(9)[/tex] (applying the properties of logarithms)

[tex]x=\frac{log(9)}{log(7)} =1.129[/tex]

Solution: the first step Keisha should take is: log to the power of x equals log 9.

Question 5: Her first three steps are:

[tex]2^{n}-3=83[/tex]

[tex]2^{n}-3+3=83+3[/tex] (adding 3 to both sides)

[tex]2^{n}=86[/tex]

[tex]2^{n}-3+3=83+3[/tex]

[tex]nln(2)=ln(86)[/tex]

Solution: step 4 is: [tex]nln(2)=ln(86)[/tex] (applying the properties of logarithms)

Question 6: The exact solution of 2 e to the power of x equals 14 is:

[tex]2e^{x}=14[/tex]

[tex]\frac{2e^{x} }{2} =\frac{14}{2}[/tex] (dividing both sides by 2)

[tex]e^{x}=7[/tex]

[tex]xln(e)=ln7[/tex] (ln(e)=1)

[tex]x=ln(7)[/tex]

Solution: [tex]x=ln(7)[/tex]

For Keisha's equation, the first step involves taking the logarithm of both sides, and for Mary's equation, the fourth step involves taking the natural logarithm. The exact solution for the third equation is x = ln 7.

Question 4:

Keisha is solving the equation [tex]\(7^x = 9\)[/tex]. The correct first step is:

[tex]\[ \log(7^x) = \log(9) \][/tex]

So the correct option is:

[tex]\[ \text{log } 7^x = \text{log } 9 \][/tex]

Question 5:

For Mary's equation [tex]\(2^n - 3 = 83\)[/tex], Step 4 involves taking the natural logarithm:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

So the correct option is:

[tex]\[ n \ln 2 = \ln 86 \][/tex]

Question 6:

The equation [tex]\(2e^x = 14\)[/tex] can be solved by taking the natural logarithm:

[tex]\[ x = \ln \left(\frac{14}{2}\right) \][/tex]

Simplifying this gives:

[tex]\[ x = \ln 7 \][/tex]

So the correct option is:

[tex]\[ \ln 7 \][/tex]

Answer:

The correct answer option is D. 0.42.

Step-by-step explanation:

We are given the results of a survey in which people were asked if they prefer reading books or e-books.

We are to find the marginal frequency of the number of people who prefer to read books.

For that, we will divide the total number of people who prefer reading books by the total number of people surveyed.

Marginal frequency = 105/250 = 0.42

Answer:

y = 9 + 19x

Step-by-step explanation:

To find the equation matching a set of data, you simply try a few values for x and see if by solving that side of the equation you get the value of y.  If you do, you found your equation.

You have a big advantage here... since you have the value of y when x = 0.

When x = 0, y = 9, that's a very important data to have to simplify your research.

Let's try the value of 0 for x in each of the given equations:

y = 18 + 10 (0) = 18  --- NO

y = 9 + 19 (0) = 9 --- YES!  We can confirm with another value of x:

y = 9 + 19 (1) = 28 --- YES! Confirmed!

y = 9 + 19x is your answer!

Let's simplify step-by-step.

2(11(a−2)+12)−(2(5a−3)+a)

Distribute the Negative Sign:

=2(11(a−2)+12)+−1(2(5a−3)+a)

=2(11(a−2)+12)+−1(2(5a−3))+−1a

=2(11(a−2)+12)+−10a+6+−a

Distribute:

=(2)(11(a−2))+(2)(12)+−10a+6+−a

=22a+−44+24+−10a+6+−a

Combine Like Terms:

=22a+−44+24+−10a+6+−a

=(22a+−10a+−a)+(−44+24+6)

=11a+−14

Answer:

=11a−14

[tex]\cos(15^\circ) = \cos(45^{\circ}-30^{\circ}) = \cos(45^{\circ})\cos(30^{\circ})+\sin(45^{\circ})\sin(30^{\circ}) = \\ \\ =\dfrac{\sqrt 2}{2}\cdot \dfrac{\sqrt 3}{2}+\dfrac{\sqrt 2}{2}\cdot \dfrac{1}{2} = \dfrac{\sqrt 6 +\sqrt 2}{4}[/tex]

Answer:

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Step-by-step explanation:

We want to find the exact value of

[tex]\cos 15\degree[/tex]

We rewrite this expression using compound angles  

[tex]\cos (45\degree-30\degree)[/tex]

Recall that:

[tex]\cos (A-B)=\cos A\cos B+\sin A\sin B[/tex]

We apply this property to obtain:

[tex]\cos (45-30)=\cos 45\cos 30+\sin 45\sin 30[/tex]

[tex]\cos (15)=\frac{\sqrt{2}}{2} \times \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2} \times \frac{1}{2}[/tex]

[tex]\cos (15)=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]

Answer:

A

Step-by-step explanation:the lines do not cross therefor the two equations do not share a solution.

Answer:

A

Step-by-step explanation:

Answer:

$0.75 tax

Step-by-step explanation:

1. Find total cost of meal: $10.50 + $1.50 + $0.50 = $12.50

2. Find tax of meal: $12.50 * 6% = 12.5 * 0.06 = $0.75

Let Poly = X

Andy gets twice as much as Poly so Andy = 2X

Pheobe gets three times as much as Andy, so she is 3(2x) = 6X

Now add them together to equal 270:

X + 2X + 6X = 270

Simplify:

9X = 270

Divide both sides by 9:

X =  270 /9

X = 30

Poly = X = 30

Andy = 2X = 2(30) = 60

Pheobe = 6X = 6(30) = 180

Answer:

see explanation

Step-by-step explanation:

The rule (x + 3, y + 2) means add 3 to the original x- coordinate and add 2 to the original y- coordinate, that is

A(- 2, 2) → A'(- 2 + 3, 2 + 2) → A'(1, 4)

B(- 2, 4) → B'(- 2 + 3, 4 + 2) → B'(1, 6)

C(0, 0) → C'(0 + 3, 0 + 2) → C'(3, 2)

Answer:

25.5%

Step-by-step explanation:

% error = | estimate - actual | / actual × 100%

% error = | 59 - 47 | / 47 × 100%

% error ≈ 25.5%

Answer:

20.3%

Step-by-step explanation:

The formula for percent error is the experimental value minus the theoretical value divided by the theoretical value all times 100.

Experimental - Theoretical

------------------------------------------ x 100

         Theoretical

−12

------- ×100

59

=−0.20339×100

=−20.339

=20.339%

=20.3% error

Hello! The interquartile range would be 5°

You must subtract Quartile one from quartile 3 to find iqr

The conjugate of the complex number 2 - 8i is 2 + 8i, found by changing the sign of the imaginary part from negative to positive.

The conjugate of a complex number is found by changing the sign of the imaginary part.

For a complex number with a real part of 2 and an imaginary part of -8i, the complex number is represented as 2 - 8i. To find its conjugate, we change the sign of the imaginary part, resulting in 2 + 8i.

The general form of a complex number is a + bi, where a is the real part and bi is the imaginary part.

The conjugate is then written as a - bi. Therefore, if we have the complex number z = 2 - 8i, the conjugate, denoted as [tex]\( \overline{z} \)[/tex], is 2 + 8i.

The complement of A would be the elements in U that are not in A.

A is 2, 4, 6, 8

Remove those numbers from U for the complement.

The complement would be {1, 3, 5, 7, 9, 10}

Answer: The complement is 1, 3, 5, 7, 9, 10

I hope that this helps! :3

Answer:

C. 48,5 cm²

Step-by-step explanation:

The area is 8×4 + 3×3 + 5×3/2 = 32+9+15/2 = 41+7,5 = 48,5 cm²

James will have $32,270.13 after 6 years

Answer:

[tex]y=20000(1.083)^6[/tex]

Step-by-step explanation:

Let y represents the amount James have after 6 years,

Given,

Principal amount, P = $ 20,000,

Compound rate of interest per year, r = 8.3 %,

Thus, the amount after x years would be,

[tex]A=P(1+\frac{r}{100})^x[/tex]

[tex]=20,000(1+\frac{8.3}{100})^x[/tex]

[tex]=20000(1.083)^x[/tex]

Therefore, the amount after 6 years would be,

[tex]y=20000(1.083)^6[/tex]

Which is the correct equation that represents the amount, James will have after 6 years.

Answer:

It would be 7.66 and 7.19 because you can not round downward although I am a little confused on how 7.19 is able to round upwards But I am positive 7.66 rounds up to 8

Step-by-step explanation: