Which of the following expressions is equivalent to 17?​

The solution of the equation is,

⇒ x = - 2/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 5³ˣ⁻² = 125²ˣ

a) Now, We can solve the expression by using change of base formula:

⇒ [tex]log_{b} y = \frac{log y}{log b}[/tex]

Hence, We get;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

Take log both side we get;

⇒ log 5³ˣ⁻² = log 5⁶ˣ

⇒ (3x - 2) log 5 = 6x log 5

⇒ (3x - 2) = 6x

⇒ - 2 = 6x - 3x

⇒ - 2 = 3x

⇒ x = - 2/3

b) Solve for another method as;

⇒ 5³ˣ⁻² = 125²ˣ

⇒ 5³ˣ⁻² = 5⁶ˣ

By comparing,

⇒ 3x - 2 = 6x

⇒ 3x - 6x = 2

⇒ - 3x = 2

⇒ x = - 2/3

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True, the standard deviation is a resistant measure of spread.

The standard deviation is calculated as the square root of the variance of the data set. Variance is calculated as the average of the squared differences between each data point and the mean of the data set. The standard deviation is the square root of this average.

In mathematical terms, the standard deviation can be calculated using the following formula:

σ = √(1/n ∑(x - μ)²)

Where σ is the standard deviation, n is the number of data points in the data set, x is the value of the i-th data point, and μ is the mean of the data set.

The standard deviation is an important measure because it gives an idea of how much the individual values in a data set differ from the mean.

In summary, the standard deviation is a resistant measure of spread because it gives a robust measure of the spread of the data in a set and is not easily influenced by outliers or extreme values.

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Answer:

Step-by-step explanation:

The area of a rectangle is given by the product of its length and width. Therefore, the area of the rectangle is:

A(x) = L(x) ⋅ W(x) = 2x(8x^2 - 4x + 1)

Simplifying the expression, we get:

A(x) = 16x^3 - 8x^2 + 2x

Therefore, the answer is (D) (L ⋅ W)(x) = 16x3 − 8x2 + 2x.

The measure of the angle formed by 2 secants that have a common point outside a circle is 1/2 the difference of the measure of the further intercepted arc and the closer intercepted arc. That means that half of the the measure of arc ABC - measure of arc XYZ is the measure of angle X. Substituting the given values gives you the equation x = 1/2 (125-45)

Then you can solve.

x = 1/2 (80)

x = 40

The measure of angle X is 40 degrees

Let's call the number of months that it takes Pablo to save $700 as "m". The amount of money Pablo has saved after "m" months can be represented by the equation:

y = 200 + 125m

where y is the total amount of money saved after "m" months.

To find the number of months it will take Pablo to save $700, we can set y equal to $700 and solve for m:

700 = 200 + 125m

500 = 125m

m = 500 / 125 = 4

So it will take Pablo 4 months to save $700.

The equation in slope-intercept form is:

y = 125m + 200

where m is the number of months and y is the total amount of money saved. The slope of the line is 125, which represents the amount added to the savings each month, and the y-intercept is 200, which represents the initial amount of money Pablo received for graduation.

The Cylinder can hold 138, 160 cm³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.

Given:

Height= 1.1 m = 110 cm

Radius= 20 cm

Now, Volume of Cylinder

= πr²h

= 3.14 x 20 x 20 x 110

= 3.14 x 44000

= 138, 160 cm³

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Answer:

Step-by-step explanation:

Divide 20 by 0.50. This gets you 40 meaning she can buy 40 candy bars with her $20 if they are $0.50 each. In order to have $7 left over then she would buy 14 candy bars.

The compound inequality is x < 1 or x >= 3

From the question, we have the following parameters that can be used in our computation:

The number line

From the number line, we have the following readings

x is less than 1 (exclusive of 1)

x is greater than or equal to 3 (inclusive of 3)

Using the above as a guide, we have the following:

x < 1 or x >= 3

Hence, the solution is x < 1 or x >= 3

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The next three terms in the following arithmetic sequence -4, 5, 14, 19 … include the following:

Term 5 = 32.

Term 6 = 41

Term 7 = 50

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 5 - (-4)

Common difference, d = 9

Next, we would determine the next three terms as follows:

a₅ = a₁ + (n - 1)d

a₅ = -4 + (5 - 1)9

a₅ = 32

a₆ = a₁ + (n - 1)d

a₆ = -4 + (6 - 1)9

a₆ = 41

a₇ = a₁ + (n - 1)d

a₇ = -4 + (7 - 1)9

a₇ = 50

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By the help of inequality properties The maximum number of interviews is 644.

Let x = number of undergraduate students hired, y = number of graduate students hired, z = number of faculty members hired, n = number of interviews

The objective function is:

Maximize n = 30x + 32y + 33z

The constraints are:

x + y + z ≤ 20

100x + 150y + 200z ≤ 3200

x, y, z integers and ≥ 0 The solution is x = 0, y = 16, z = 4, n = 644

0 undergraduate students, 16 graduate students, and 4 faculty members should be hired to maximize the number of interviews. The maximum number of interviews is 644.

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Answer:

1.59

Step-by-step explanation:

Rounding to the hundredths has the same meaning as rounding to the second decimal place. Since the third decimal place is 7, we have to round up the decimal. Therefore the rounded value would be 1.59

I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!

Step-by-step explanation:

What notes are you speaking of?

Answer:

we can't find it by herons formula. but here is your answer.....

Step-by-step explanation:

[tex]\\\sqrt{22}\\\\we can do by long division method \\ the actual value of \sqrt{22} = 4.69041575982343.\\well \sqrt{22} itself is in the simplest form[/tex]

Answer:

q1= n/4

is the formulato fine lower quartile

Answer:

y=-0.25x+3.5

Step-by-step explanation:

Ik this

Answer: easy, the answer is x^6 (look at the image for the solution and make sure to give me brainliest)

Step-by-step explanation:

There are two imaginary roots and one real root of the equation

Generally, In mathematics, the root of an equation is a value that satisfies the equation. In other words, it is the value of the variable for which the equation is true. For example, in the equation x^2 - 4 = 0, the roots are +2 and -2, because when either of these values is substituted for x, the equation becomes true.

There are different methods for finding roots of an equation, depending on the type of equation. For example, some equations can be solved by factoring, while others require the use of more advanced techniques such as the quadratic formula or numerical methods like the Newton-Raphson method.

In general, finding the roots of an equation is an important task in mathematics and has many practical applications in fields such as engineering, physics, and finance.

The roots of the equation  are

x=-2,3+2 i, 3-2 i

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The AB intersects circle P if PA is 7mm and PB is 3mm it must exit the circle, and it has 2 contact points.

PA is longer than the radius of the circle so Point A must be outside of the circle.

Two or more circles intersect at one point. Two circles can be tangent to each other in two different ways.

here, we have,

We have given that,

AB lies in the same plane as circle P, which has a radius of 6 mm.

PB is less than the radius of the circle so Point B must be inside the circle.

Since the ray is going from A to B it is coming inside the circle and continuing in the other direction.

Therefore, it must exit the circle, giving us 2 contact points.

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Answer:

To find the radius of a ball that holds 66 cubic centimeters of air:

1. Substitute the given volume into the equation r= (3v/4π): r = (3*66/4π).

2. Simplify the equation: r = (198/4π).

3. Calculate the value of 4π: 4π = 12.57.

4. Divide 198 by 12.57: r = 15.75.

5. The radius of the ball that holds 66 cubic centimeters of air is 15.75 cm.

Answer:

Step-by-step explanation:

To find the radius of a sphere that holds 66 cubic centimeters of air, we can use the formula provided in the question:

r = (3v/4π)

where v is the volume of the sphere. We are given that the volume of the sphere is 66 cubic centimeters, so we can substitute this value into the formula:

r = (3 x 66) / (4 x π)

Simplifying this expression:

r = 198 / (4π)

Using a calculator to evaluate this expression:

r ≈ 15.8267

Therefore, the radius of the sphere that holds 66 cubic centimeters of air is approximately 15.8267 centimeters.

Answer:

The answer is B.

Step-by-step explanation:

Method #1 use point slope formula to solve for m of slope.

Method #2 Plug in x-values into option A or B to see you get your dots.

The answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2

b) parallelogram ABCD is a rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

a) Given that, the flag of Scotland is a rectangle with white stripes as the diagonals. In rectangle SCOT, SO = 92.4, and CO = 41.

We need to find the measure of CT, OL, ST and LT,

We know that, the diagonals of a rectangle bisects each other and are congruent, and its opposite sides are equal,

Therefore,

OL = SO/2 = 92.4/2 = 46.2

CT = SO = 92.4

ST = CO = 41

LT = OL = 46.2

b) Given are vertices of parallelogram, A(-6, -2), B(-3, 3), C(2, 0), D(-1, -5), we need to verify if this is a rectangle or not,

Since, the diagonals of a rectangle are congruent, so, we will find AC and BD and see if they equal or not if equal then it is a rectangle.

Distance between two points is =

D = [tex]\sqrt{(x_{2}-x_1)^2+(y_2-y_1)^2 }[/tex]

AC = √(2+6)²+(2)² = √68

BD = √(-1+3)²+(-5-3)² = √68

∵ AC = BD, therefore, parallelogram ABCD is a rectangle.

Hence, the answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2

b) parallelogram ABCD is a rectangle.

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Answer:

1. 7 or S

2. 2 or E

3. 5 or A

4. 3 or I

5. 9 or the shaded-in letter

6. 11 or T

7. 20 or E

Step-by-step explanation:

1. 7 times 2 is 14, and 7 times 3 is 21

2. 2 times 5 is 10, and 2 times 6 is 12

3. 5 times 3 is 15, and 5 times 5 is 25

4. 3 times 2 is 6, and 3 times 5 is 15

5. 9 times 4 is 36, and 9 times 3 is 27

6. 11 times 2 is 22, and 11 times 3 is 33

7. 20 times 3 is 60, and 20 times 1 is 20.

Answer:

133

Step-by-step explanation:

All 3 angles of a triangle must equal 180, so let's make these equal to that

[tex](x + 13) + (10x + 13) + (2x - 2) = 180[/tex]

Now let's combine the X's and the regular numbers together.

[tex]13x + 24 = 180[/tex]

Next, subtract 24 to get all the numbers on the right side.

[tex]13x = 156[/tex]

And lastly, we divide by 13 to get X alone

[tex]x = 12[/tex]

Since Q is (10x + 13), we plug that 12 in

[tex]10(12) + 13 = 133[/tex]

Answer:

W > 28

W has to be greater than 28

Answer:5/8

Step-by-step explanation:

Lowest common denominator is 24

15/24 > 8/24

5/8>1/3

The area of the isosceles trapezoid is 72 square units.

A quadrilateral having at least one set of parallel sides and equal length non-parallel sides is called an isosceles trapezium. To put it another way, it is a trapezium whose two non-parallel sides are congruent. The trapezoid's parallel sides are referred to as the bases, and the segments that link the bases are referred to as the legs. The angle between the bases of an isosceles trapezoid determines its height.

Given:

[tex]\[d = 12 \quad \text{(length of one diagonal)}\][/tex]

Let;

[tex]\[h = \text{height of the trapezoid}\][/tex]

[tex]\[a = \text{smaller base of the trapezoid}\][/tex]

[tex]\[b = \text{larger base of the trapezoid}\][/tex]

Using the given information that the height and median are equal, we have:

[tex]Median(m)=\frac{1}{2} {(a+b)}\\\\Height(h)=\frac{1}{2} {(a+b)}\\\\2h=a+b ........(1)[/tex]

[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]

[tex]\[\text{Area} = m \cdot h\] = h^2 ............(2)[/tex] (∵ [tex]Median(m)=\frac{1}{2} {(a+b)}[/tex] and m=h)

Now,

[tex]\[ d = \sqrt{h^2 + \frac{(a+b)^2}{4}} \][/tex] for isosceles trapezoid,

[tex]\[ 12^2 = h^2 + \frac{(a+b)^2}{4}}[/tex]

[tex]\[ 12^2 = h^2 + \frac{(2h)^2}{4}}[/tex]   (∵from eq (1))

[tex]\[ 12^2 = h^2 + {(h)^2}}\\ \\144= 2h^2\\\\h^2=72 ..........(2)[/tex]

Lastly, we may change the values of "a," "b," and "h" in the following formula to find the area as;

[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]

[tex]\[\text{Area} = \frac{1}{2} \cdot (2h) \cdot h\][/tex]

[tex]\[\text{Area} = h \cdot h\] = h^2 = 72 sq units[/tex]

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Answer: Can you help me with the questions that I asked today.

Step-by-step explanation: Please.

Answer:

(To shawnrg

ask me the questions. I'm not promising I'll be able to help

Step-by-step explanation:

Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

The implied value of an asset as of a particular date in the future based on a growth rate assumption is known as the Future Value (FV). This area of mathematics examines how random events happen. The value might be between 0 and 1. The mathematical idea of probability aids in predicting the possibility of specific events. In general, probability relates to how probable something is to happen. The interest rate assumption, or the rate of return on the initial amount of capital invested, or the present value, determines the projected future value (PV).

Calculation of the value:

The initial deposit is $1.200

The rate of interest is 5%

Now the future value be like

 [tex](1200\times\frac{(1+0.05)^9-1}{0.05} )\times(1+0.05)+1,200\\\\\(1200\times(\frac{1.5513-1}{0.05} )\times(1+0.05)+1,200\\\\(1200\times11.0265)\times(1.05)+1,200\\\\13893.4711+1,200\\$15,093.47[/tex]

Through the aid of future value If no withdrawals or new deposits are made, the account's value following the tenth deposit should be $15,093.47.

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Answer:

(108 - (48 x 2)) / 3 = p

Step-by-step explanation:

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