Simplify the following expression. 7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}

The equation of  this parallel line is y = 4x - 22.  Railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, an eraser, and other real-world objects are instances of parallel lines.

Since there is no "b" in the conventional equation y = mx + b, the line y = 4x has a slope of 4 and an intercept of 0. Any parallel line will have the same slope as the slope (m = 4) in this case. The slope of all parallel lines will be the same.

So let's return to the conventional format and replace the m with a "4".

y = 4x + b

Now that the values have been entered into the equation, let's solve for "b" using the point that sits on the line.

-6 = 4(4) + b

-6 - 16 = b

b = -22

The equation of  this parallel line is y = 4x - 22

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The sample variance of the given data 13,11,15,2,9,14 is 356.6.

Sample variance can be defined as the expectation of the squared difference of data points from the mean of the data set. It is an absolute measure of dispersion and is used to check the deviation of data points with respect to the data's average.

we have data 13, 11, 5, 2, 9, 14, and we have to determine the sample variance of given data.

Sample variance is given by,

[tex]S^2=\frac{\sum^n_1(X_i-X')^2}{(n-1)}[/tex]

where X' is the sample mean,

the mean of given data is,

[tex]X'=\frac{(13+11+5+2+9+14)}{6} \\\\X'=\frac{54}{6} \\\\X'=9[/tex]

now the sample variance is given by,

[tex]S^2=\frac{(13+9)^2+(11+9)^2+(5+9)^2+(9+9)^2+(14+9)^2}{6-1} \\\\S^2=\frac{(484+400+289+81+529)}{5} \\\\S^2=356.6[/tex]

Hence the sample variance is 356.6.

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The correct answer is open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket, as it is the vector u.

The projection of vector u onto vector v is given by the formula:

projv(u) = (u . v/||v||^2) * v

where u . v is the dot product of vectors u and v,and ||v|| is the magnitude of vector v

Given that u = <-10, -3> and v = <4, 8>, we can substitute these values into the formula and find projv(u)

projv(u) = ( (-10)(4) + (-3)(8) )/ (4^2 + 8^2) * <4,8>

projv(u) = ((-40 - 24)/ (16 + 64))* <4,8>

projv(u) = (-64/80) * <4,8>

projv(u) = (-4/5) * <4,8>

projv(u) = <-16/5,-32/5>

The vector u is already parallel to the vector v, that's why the projection of vector u on vector v is equal to vector u itself.

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When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

What is division?

A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.

We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Here given that,

We have to divide 87/7,

By dividing,

we know that 8/7 gives reminder 1, and a quotient of 1.

Then divide 14 by 7,

which gives reminder 0 and quotient 2.

So by dividing 84 / 7 we get reminder 0 with a quotient of 12.

Therefore the correct option is option A. With a quotient of 12.

Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

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The distance traveled during the given time interval be 2024 m.

An object's rate of change in velocity is referred to as its acceleration. The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.

By integrating the velocity v in terms of time t, v = gt, we can determine acceleration, which is the rate of change of velocity with respect to time.

Let the function be a(t) = t + 4

time = 11

substitute the value of t in the above equation, we get

a(11) = 11 + 6 = 17 m/s²

a = v/t, so v = at

finally v = (17 m/s²) (11s)

v = 187 m/s

b) Find the distance traveled during the given time interval

[tex]$$V_{total} = V_{final} - V_{ initial[/tex]

V final = 187 m/s, Vinitial = 3 m/s

V total = 187 - 3 = 184 m/s

Let the equation of velocity be

Velocity = distance/time

distance = velocity × time

distance = 184 m/s × 11 s

distance = 2024 m

Therefore, the distance traveled during the given time interval be 2024 m.

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The value of c according to the given equation as described is; -14.

The other root of the equation in discuss is; 7.

As evident in the task content; if -2 is the root of a quadratic equation x²-5x+c=0, then x = -2 holds true for the equation; therefore, we have;

a). (-2)² - 5 (-2) + c = 0

4 + 10 + c = 0

c = -14

Hence, the value of c is; -14.

b). By substituting into the equation; we have;

x² - 5x - 14 = 0

(x - 7) (x + 2) = 0

x = 7 OR x = -2.

Therefore, the other root of the equation is; 7.

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Answer:

[tex]\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex]

Step-by-step explanation:

I assume your problem is [tex]\displaystyle \int\limits^{5}_{-5} {\sqrt{5^2-x^2}} \, dx[/tex]. Recognize that [tex]\sqrt{5^2-x^2}=\sqrt{25-x^2}[/tex] is a semi-circle directly above the x-axis with a radius of 5. The bounds cover the whole area of the semicircle, so its area is just half the area of a circle with a radius of 5. You probably know that the area of a circle is [tex]A=\pi r^2[/tex], so the area of a semicircle would be [tex]A=\frac{\pi r^2}{2}[/tex]. Thus, the area using geometry is [tex]A=\frac{\pi (5)^2}{2}=\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex].

After examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

What is Number line ?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

What is Symbol?

A mark, sign, or term that denotes, denotes, or is taken to denote an idea, an item, or a relationship is known as a symbol. By connecting seemingly unrelated ideas and events, symbols help people look beyond the known and the visible.

In the question given some relation between the real number which are

a) -2/4 < -1/4 because negative number has the property that the those numbers which is smaller is always greater.

b) 3/4 > 2/4 both numbers are positive so clearly it 3/4 comes after 2/4 so it is greater.

c)  -1/4 < 0 zero is always greater than the negative numbers

So, after examine the number line,and then the correct symbol to complete each statement is -2/4<-1/4; 3/4>2/4;-1/4<0.

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Answer:

10th term = 94

Step-by-step explanation:

Given equation,

→ Tn = n² - n + 4

Now the 10th term will be,

→ Tn = n² - n + 4

→ T10 = (10)² - 10 + 4

→ T10 = 100 - 6

→ [ T10 = 94 ]

Hence, the answer is 94.

[tex]Answer:\ \boxed{96\pi }\ cm^2[/tex]

Step-by-step explanation:

[tex]R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?[/tex]

[tex]V_c=\pi R^2H\\[/tex]

[tex]72\pi =\pi 6^2H\\\\72=36H\\[/tex]

Divide both parts of the equation by 36:

[tex]2=H\\\\Thus,\ H=2\ cm[/tex]

[tex]S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2[/tex]

$75668.4 is the interest earned in 6 months.

percentage, a relative value indicating hundredth parts of any quantity.

Tom has $84,076 in a savings account that earns 15% annually.

The interest is not compounded.

We have to find the interest he earned in 6 months.

Use the formula i = prt,

where i is the interest earned,

p is the principal (starting amount),

r is the interest rate expressed as a decimal,

and t is the time in years.

i=84076×15/100×6

=84076×0.15×6

=$75668

Hence, $75668.4 is the interest earned in 6 months.

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Answer: 11/1000 o 1.1%

Step-by-step explanation:

11 ÷ 1000

0.011

11/1000 o 1.1%

The area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².

Any closed curve that consists entirely of connected line segments (sides) without any intersections is known as a polygon in geometry. The three simplest polygons are pentagons, triangles with three sides, and quadrilaterals with four sides (five sides). The two types are concave and convex polygons.

Convex polygons are those without any extended sides crossing over them. Equilateral refers to a polygon with equal sides. Interior angles of equiangular shapes are equal. Every equilateral and equiangular polygon is a regular polygon (e.g., an equilateral triangle or a square).

As all sides are equal, all diagonals are equal too, and the angle of adjacent diagonals are 90° with vertical opposite angle.

Therefore,

Each side = [tex]\sqrt{\text {diagonal}^2+ \text {diagonal}^2}[/tex]

Each side = [tex]\sqrt{(6\sqrt{2} )^2+(6\sqrt{2} )^2}[/tex]

Each side = [tex]\sqrt{(36\times 2+36\times 2}[/tex]

Each side = [tex]\sqrt{144}[/tex]

Each side = 12 inch

Area =  12 × 12

         = 144.0 in²

Thus, the area the polygon in the diagram with, a length from the center to the vertex 6√2 in is 144.0 in².

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The $31.309 money was spent on a pass and lunch for each student

Two or more expressions with an Equal sign is called as Equation.

School spends on a pass for each student,885.69/39

$22.97

School spends on a lunch for each student,

325.23/39

$8.339

Therefore, total money spent on a pass and lunch for each student

= 22.97 + 8.339

= $31.309

Hence, the $31.309 money was spent on a pass and lunch for each student

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The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.

Volume of a solid plain:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.

Given in the question:

y = 2 - 1/2x

y = 0 , x = 1 and x = 2

As we know that:

We can write 19π / 12 as

(19× 22/7 )÷ 12

=  209/ 42

= 4.97 ≈ 5 cm³

Therefore, the volume is 5 cm³

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The probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.

What is the Central Limit Theorem?

The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables is approximately Normally distributed.

(a) The reason why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds is that the weight of passengers is not Normally distributed.

The Normal distribution is a symmetric bell-shaped distribution that is defined by its mean and standard deviation.

The weight of passengers is not symmetric and it may not follow a bell shape.

Therefore, we cannot use the Normal distribution to calculate the probability of a weight greater than 200 pounds.

(b) To calculate the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the Central Limit Theorem.

Since we don't know the exact distribution of the weight of the passengers, we can use the Central Limit Theorem to approximate the total weight of the passengers on a full flight.

The mean weight of a passenger is 190 pounds, and the standard deviation is 35 pounds. Since a full flight carries 30 passengers, the mean weight of the passengers on a full flight is 19030 = 5700 pounds and the standard deviation is 35sqrt(30) = 175 pounds.

To find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the standard normal distribution table.

z = (6000 - 5700) / 175 = 2.2857

Probability P(X > 6000) = P(Z > 2.2857) = 1 - P(Z < 2.2857) = 1 - 0.9853 = 0.0147

Hence, the probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.

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The average speed of the body in the given interval is 32 + 2z ft/s.

The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.

In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.

Therefore, the average speed v of the body in this interval is:

v = (32z + 2z^ 2 ) ft / zs

v = 32 + 2z ft/s

Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.

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The probability of picking a 2 and then picking a 1 would be = 1/2

Probability is definitely as the expression that to represents the number of outcomes of an event.

The number of cards such as 1,2,3,4 = 4 cards.

The cards picked at random = a 1 and a 2

Therefore, the probability = 2/4 = 1/2

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The Riemann sum formula is ∫(1,5) 2x = 24

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

f(x) = 2x over the interval [1, 5]

The Riemann sum for f(x) = 2x over the interval [1,5] using the right-hand endpoint for each subinterval is given by the formula:

(Δx/2) * (2c1 + 2c2 + ... + 2cn) where c1, c2, ..., cn are the right-hand endpoints of the subintervals and Δx = (b - a)/n.

As a general rule:

As n approaches infinity, the width of the subintervals approaches zero,

Also, we have the Riemann sum approaches the definite integral of f(x) = 2x over the interval [1,5], which is x² evaluated at the interval's endpoints.

So, the formula becomes

∫(1,5) 2x = x²

Substitute the intervals

∫(1,5) 2x = 5² - 1²

Evaluate

∫(1,5) 2x = 24

Hence, the formula is ∫(1,5) 2x = 24

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Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]

Step-by-step explanation:

[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]

Answer:

Rs. 94

Step-by-step explanation:

We will denote the almirahs as A1 and A2 for ease of explanation. I am omitting currency until the final answer

For the following computations note that x% = x/100 in decimal so
15% = 15/100 = 0.15
13 1/3% = 13 1/3 ÷ 100 = 40/3 ÷ 100 = 40/300

Cost of A1 = 4800

A1 was sold for a loss of 15%

Loss = 15% of 3640 = 0.15 x 3640  = Rs 546

A2 bought at 4800 was sold at a gain of 13 1/3%

Gain from sale = 13 1/3% of 4800 = 40/300 x 4800 =Rs 640

We have to treat gain as positive and loss as negative to arrive at the answer

Net gain/loss = 640  - 546 = Rs. 94

The distance from G to the nearest point on the circle is going to be 5.61 cm.

The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.

For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).

In the right triangle AOG, radius AO is the side opposite angle AGO-

= Tangent = Perpendicular / Base

= tan(24) = r / 12

= r = 12tan(24)            (i)

For OG -

= cos(24) = Base / Hypotenuse = 12 / OG

= OG = 12cos(24)        (ii)

Now, we subtract (i) and (ii) -

= 12tan(24) - 12cos(24)    

= 5.61 cm

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Comparibg the probabilities and interpreting the likelihood, the true statement is that:

A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

Player 1 = six tenths = 0.6

Player 2 = five ninths = 0.56

Player 3 four sevenths = 0.57

This shows that player 2 has the highest probability. The correct option is A.

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The sums of the measures of the interior angles of a polygon is three times the sum of its exterior angles then it has 8 sides .

What is Polygon?

A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Here are some illustrations of polygons.

What is interior angles?

Interior angles are those that are located within the confines of two parallel lines that are intersected by a transversal.

What is exterior angles?

The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's external angle.

We know that sum of interior angle of regular polygon is ;

(n-2) x 180°

Where n = no. of sides

We also know that sum of exterior angle of regular polygon is 360°.

The fact that the sum of a polygon's internal angles is three times the sum of its outside angles is now a given;

Therefore;

sum of interior angles of a regular polygon = 3 x sum of exterior angle

⇒ (n-2) x 180°

⇒3 x 360°

Simplify the equation we have above by:

⇒(n-2) = 3 x 360°/180° = 6

⇒ n = 6+2 = 8

Therefore the sides of the regular polygon  is 8.

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Using simultaneous equations, each small candle costs $1.00 and each large candle costs $5.00.

Simultaneous equations are two or more equations solved concurrently.

Simultaneous equations are also known as a system of equations.

                 Small Candle   Large Candle   Total Cost

You buy             4                       2                    $14

A friend buys    5                       3                   $20

Let the cost of the small candle each = s and the cost of the large candle each = l

Equation 1: 4s + 2l = 14

Equation 2: 5s + 3l = 20

Multiply Equation 1 by 1.5:

Equation 3: 6s + 3l = 21

Subtract Equation 2 from Equation 3:

6s + 3l = 21

-

5s + 3l = 20

s = 1

= $1

From Equation 1:

4s + 2l = 14

4 + 2l = 14

2l = 10

l = 5

= $5

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The 5 different colorings are possible.

The rectangle is partitioned into 5 regions.

The objective is to find the different of color.

There are 5 rectangle and 5 colors

Each region is to be painted a solid color-red. orange, yellow, blue, or green

Need to color 5 rectangles by using given five colors.

Then, we need to use 5! colors.

The factorial of a whole number is the function that multiplies the number by every natural number below it. Symbolically, a factorial can be represented by using the symbol "!". So, "n factorial" is the product of the first n natural numbers and is represented as n!

The formula for n factorial is:

=5×4×3×2×1

=120

Therefore, the possible colorings are 5.

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Answer:ts line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.

Step-by-step explanation:

Answer:

9x + 21

Step-by-step explanation:

An equilateral triangle is a triangle with three equal sides. If we know the length of one side, we can find the perimeter by multiplying by three.

3(3x + 7) = 9x + 21

Answer:

is $27.50 per each teacket

Answer:

Give the degree of the polynomial.

6x5+5x4−3x2+x7

Answers:

18

5

6

9

7

Hope it helps :)