How can the following expression be written so that no negative exponents appear?
(a5)³a-6
Q-2

Answer:

C

Step-by-step explanation:

The sum of Sonya's 5 initial tests = 89*5 = 445.

445 + 95 = 540 (sum of the 6 tests)

Average = 540/6 = 90

Hence C

Answer:

C.  90.00

Step-by-step explanation:

We find average by adding up all values in a data set and dividing by the total number of values we have

We can say that Sonya got 89 for each test (it doesn't matter what each test score exactly was--you'll see why in a second)

So, we can add up 89 five times (5 tests have occured)

*I say add up, because that's what average is, but you can find this number by multiplying 89 · 5

89 · 5 = 445

(89 + 89 + 89 + 89 + 89 = 445)

Now, we need to add up our new value: 95

445 + 95 = 540

So, we can now divide 540 (sum of all values) by 6 (total number of values)

540 ÷ 6 = 90

So, C (90.00) is her new average

hope this helps! have a lovely day :)

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The correct option is A.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The diagram for the given problem can be made as shown below. Therefore, the other name for angle 2 will be ∠DGE.

Hence, the correct option is A.

Learn more about Angle:

https://brainly.com/question/7116550

#SPJ1

Answer:

a

Step-by-step explanation:

got it right

The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

The expression is given as:

[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]

[tex]x^2 + y^2 + z^2 = 1[/tex]

Rewrite the integral as:

[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]

As a general rule, we have:

[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]

By comparison, we have:

P = 9

Q = 2

R = z

By the divergence theorem, we have:

F = Pi + Qj + Rk

So, we have:

F = 9i + 2j + zk

Differentiate

F' = 0 + 0 + 1

F' = 1

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Where:

r = F' = 1

So, we have:

[tex]V = \frac{4}{3}\pi (1)^3[/tex]

Evaluate

[tex]V = \frac{4}{3}\pi[/tex]

This means that:

[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]

Read more about divergence theorem at:

https://brainly.com/question/17177764

#SPJ1

Since the lines have the same slopes, hence they are parallel lines

We can determine the relations by knowing the slopes of the line

For the line with coordinates (9, –5) and (5, –2)

Slope = -2+5/5-9
Slope = -3/4

For the line with coordinates (–4, –2) and (–8, 1)

Slope = 1+2/-8+4
Slope = -3/4

Since the lines have the same slopes, hence they are parallel lines

Learn more on parallel lines here: https://brainly.com/question/16742265

#SPJ1

The probability that at least one of the calculators is defective is : 0.725

Probability is the likelihood of an event happening or not.

if there is certainty that the event would happen probability is 1.

Analysis:

probability = required outcome/possible outcome

for 33 good calculators and 12 defective calculators, total calculators = 45

4 calculators were chosen, possible outcome = 45C4 = 148995

Required outcome = 33C3 . 12C1 + 33C2 . 12C2 + 33C1 . 12C3 + 33C0 . 12C4

= 65472 + 34848 + 7260 + 495 = 108075

Probability = 108075/148995 = 0.725

Learn more about Probability: brainly.com/question/25870256

#SPJ1

Step-by-step explanation:

the probability is always the number of desired cases over the number of all possible cases.

in our situation we have 15 cards.

that is the total possible cases when a random card is chosen.

how many desired cases do we have ?

a number NOT a multiple of 5.

how many are there ?

it is easier to say how many numbers there are being a multiple of 5 : 5, 10, 15

so, 3 numbers out of the 15 are multiple of 5.

that means

15 - 3 = 12 numbers of the 15 are NOT multiples of 5.

so, the probability to draw a card that is not a multiple of 5 is

12/15 = 4/5 = 0.8

the information about event B and even numbers is irrelevant for the question.

Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Point A is at (0, 0). Using the transformation T: (x, y) (x + 2, y + 1), point A' = (2, 1). Hence:

[tex]AA'=\sqrt{(1-0)^2+(2 - 0)^2}=\sqrt{5}[/tex]

Triangle ABC was translated using the rule (x, y) (x + 2, y + 1) to form congruent triangle A'B'C' with AA' = √5 units

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

[tex](x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x[/tex]

Answer:

a) 24 [cm]; b) 30°.

Step-by-step explanation:

a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];

b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:

m(∠AOB)=360*(1/12)=30°.

Answer:

Graph 3 represents a function

Graph 4 is not a function

Step-by-step explanation:

By definition :

A function is a rule or law which relates all the elements of one set with some UNIQUE element of another set.

Which means that from a given value of the input x, there will be only one value of y in a function f(x) = y

Graphically it would represent that for a given point x , there would only be one value of y corresponding to that x.

In graph 4, we can see that for one x, there exists two values of y.

Example : at x = 5, we have y=5 AND y= -5; which is not possible in case of a function.

Answer: d

Step-by-step explanation:

60*0.6=36

60-36=24

24 are not thoroughbreds

Answer:

system

equations

Step-by-step explanation:

Answer:

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

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

Explanation:

An equation is something like [tex]\text{y} = 2\text{x}+5[/tex] and [tex]\text{y} = 3\text{x}+7[/tex]

When we combine two such equations to form a group (of sorts), we consider this to be a system of equations.

We use a single curly brace to write the system

[tex]\begin{cases}\text{y} = 2\text{x}+5\\\text{y} = 3\text{x}+7\end{cases}[/tex]

Here are the three cases mentioned when it comes to solutions.

Side note:  Any solution is of the form (x,y)

Option B and D would have closed circles when graphed

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.

At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.

∴ Option B and D that are 5.7 ≤ p and [tex]\frac{1}{2}[/tex] ≥ y respectively would have closed circles

Learn more about domain and range here :

https://brainly.com/question/13856645

#SPJ4

Answer:

Area = 1125mi

Step-by-step explanation:

Area of sector =  [tex]r^2 *\frac{\alpha }{2}[/tex]

[tex]r^{2} =5^{2} =25[/tex]

[tex]25*\frac{\alpha}{2}[/tex]

[tex]25*\frac{90}{2} =25*45=1125[/tex]

[tex]\alpha[/tex] = angle

[tex]r[/tex] = radius

radius is 5mi

in this case the angle is 90°

A = 1125mi

you can also solve by using circle area which is [tex]\pi r^{2}[/tex]

then divide by 4 because this is 1/4 of the circle.

Hope this helps

Now A and B are independent

Both connectors must work together to make the parallel circuit work

P(A and B)

Connectors be C1 and C2

We need P(C1.C2)

Note the formula

For independent events

[tex]\boxed{\sf P(AB)=P(A)P(B)}[/tex]

[tex]\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)[/tex]

[tex]\\ \tt{:}\dashrightarrow 0.84(0.72)[/tex]

[tex]\\ \tt{:}\dashrightarrow 0.6[/tex]

Answer:=102.5

Step-by-step explanation:

The measure of <TRS and angle d are 70 and 43degrees respectively

The given triangles are isosceles triangles since they have two equal sides.

14) From he triangle RST

<TRS + 90 + 20 = 180

<TRS + 110. = 180

Subtract 110 from both sides

<TRS = 180 -110

<TRS = 70 degrees

15) For this triangle;

d = 86/2

d = 43 degrees

Hence the measure of <TRS and angle d are 70 and 43degrees respectively

Learn more on angles here: https://brainly.com/question/25770607

#SPJ1

The area of the triangle is 14.1 square meters

The side lengths are given as:

5m, 6m and 9m

Calculate the semi-perimeter (s) using

s = (5 + 6 + 9)/2

Evaluate

s = 10

The area is then calculated as:

[tex]Area = \sqrt{s(s -a)(s-b)(s-c)[/tex]

This gives

[tex]Area = \sqrt{10 * (10 -5)(10-6)(10-9)[/tex]

Evaluate the products

[tex]Area = \sqrt{200[/tex]

Evaluate the exponent

Area = 14.1

Hence, the area of the triangle is 14.1 square meters

Read more about areas at:

https://brainly.com/question/27683633

#SPJ1

Answer:

[tex]x=6, x=-4[/tex]

Step-by-step explanation:

1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.

3) Write [tex]-2x[/tex] as a sum.

[tex]x^2-6x+4x-24=0[/tex]

Now, we can factor them out by grouping.

[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]

Since, [tex]x -6[/tex] is common in both of the factors, we only take one of the [tex]x -6[/tex] along with [tex]x[/tex] and [tex]4[/tex] and all equated to 0.

[tex](x-6)(x+4) = 0[/tex]

Solve for x: [tex]x-6=0[/tex]

[tex]x=0+6\\x=6[/tex]

Solve for x: [tex]x+4=0[/tex]

[tex]x=0-4\\x=-4[/tex]

Therefore, our solutions to this quadratic equation are  [tex]x=6, x=-4[/tex].

The  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

A translation can be explained as the movement of a shape in a direction which could be up, down but the appearance of the figure remain unchanged in any other way.

And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.

Hence,  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

Learn more about transformation from

https://brainly.com/question/3724552

#SPJ1

(a) By the formula for the area of a square, the answer is [tex]16^2 = 256[/tex] square km

(b) By the formula for the area of a circle, the answer is [tex](\pi)\left(\frac{16}{2} \right)^2 =64\pi[/tex] square km

(c) Subtracting areas, we get [tex]256-64\pi[/tex] square km

The amount of money left from 3 months of saving once he pays for his vacation is $942.50

= $7,003.50

Monthly expenses = $1437

Total expenses = 3 × $1437

= $4,311

Cost of vacation = $1750

Total balance = $7,003.50 - ($4,311 + $1750)

= 7,003.50 - 6061

= $942.50

Learn more about savings:

https://brainly.com/question/25787382

#SPJ1

3) We have

[tex]f(x) = \sec\left(\dfrac{\pi x}2\right) = \dfrac1{\cos\left(\frac{\pi x}2\right)}[/tex]

which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for

[tex]\cos\left(\dfrac{\pi x}2\right) = 0[/tex]

[tex]\implies \dfrac{\pi x}2 = \cos^{-1}(0) + 2n\pi \text{ or } \dfrac{\pi x}2 = -\cos^{-1}(0) + 2n\pi[/tex]

(where [tex]n[/tex] is any integer)

[tex]\implies \dfrac{\pi x}2 = \dfrac\pi2 + 2n\pi \text{ or } \dfrac{\pi x}2 = -\dfrac\pi2 + 2n\pi[/tex]

[tex]\implies x = 1 + 4n \text{ or } x = -1 + 4n[/tex]

So the graph of [tex]f(x)[/tex] has vertical asymptotes whenever [tex]x=4n\pm1[/tex] and [tex]n\in\Bbb Z[/tex].

4) Given

[tex]h(t) = \begin{cases} t^3+1 & \text{if } t<1 \\ \frac12 (t+1) & \text{if } t\ge1 \end{cases}[/tex]

we have the one-sided limits

[tex]\displaystyle \lim_{t\to1^-} h(t) = \lim_{t\to1} (t^3+1) = 1^3+1 = 2[/tex]

and

[tex]\displaystyle \lim_{t\to1^+} h(t) = \lim_{h\to1} \frac{t+1}2 = \frac{1+1}2 = 1[/tex]

The one-sided limits don't match, so the two-sided limit [tex]L[/tex] does not exist. In other words, the limit does not exist at [tex]x=1[/tex] because the function approaches different values from the left and right side of [tex]x=1[/tex].

The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%

An equation is an expression that shows the relationship between two or more variables and numbers.

The zscore is given a:

z = (raw score - mean) / standard deviation

mean = 225, standard deviation o = 10.

a) For x = 200:

z = (200 - 225) / 200 = -0.125

For x = 220:

z = (220 - 225) / 200 = -0.025

P(-0.125 < z < -0.025) = P(z < -0.025) - P(z < -0.125) = 0.4880 - 0.4483 = 3.97%

b) For x = 190:

z = (190 - 225) / 200 = -0.175

P(z < -0.025) = P(z < -0.175) = 0.4286

The probability that a randomly selected chocolate bar will have between 200 and 220 calories is 3.97%

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Two

Step-by-step explanation:

Solutions are when the two graphs intersect

The approximate APR for the purchase is 16%

To calculate the annual percentage rate (APR)

We would calculate the interest rate

Add the administrative fees to the interest amount

Divide the loan amount (principal)

Divide by the total number of days in the loan term

Multiply all year

Multiply by 100 to convert to a percentage

Interest= P * R * t

APR= [tex]\frac{\frac{216}{900}}{6 * 4 * 100}[/tex]

APR = 16%

Read more about APR here:

https://brainly.com/question/2772156

#SPJ1

Using the Empirical Rule, it is found that 49 farms in the sample have land and building values per acre between $1100 and $1700.

It states that, for a normally distributed random variable:

Considering the given mean and standard deviation, values between $1100 and $1700 are within 1 standard deviation of the mean, which is a percentage of 68%.

Hence, the number of farms out of 72 is:

0.68 x 72 = 49 farms.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

#SPJ1

[tex]\huge\boxed{3.81\ \text{centimeters}}[/tex]

We simply need to convert 1.5 inches to centimeters.

Use multiplication:

[tex]1.5\cdot2.54=\boxed{3.81}[/tex]

The sign of f on the interval -5/3 is negative

The function is given as:

f(x)=(2x−1)(3x+5)(x+1)

The zeros of the function are

x= -5/3, x= -1 and x= 1/2

Next, we plot the graph of the function

At x = -5/3, the function approaches negative infinity

This means that the sign of f on the interval -5/3 is negative

Read more about function intervals at:

https://brainly.com/question/27831985

#SPJ1