Picture is below to the question

The equivalent expression in the context of this problem is given as follows:

A. 5k² - 3k + 1

The expression in the context of this problem is given as follows:

(15k³ - 9k² + 3k)/3k.

The common term in the numerator is given as follows:

3k.

The simplified numerator then is given as follows:

3k(5k² - 3k + 1).

Simplifying the common term 3k to the numerator and to the denominator, the simplified expression is given as follows:

A. 5k² - 3k + 1

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1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area shaded region is 36.625 ft².

We have,

The shaded region.

= The area of the rectangle - The area of the triangle

Now,

Area of the rectangle.

= 8 x 5

= 40 ft²

Area of the triangle.

= 1/2 x 36 x 27
= 18 x 27

= 486 in²

Now,

12 inch = 1 ft

So,

1 inch = (1/12) ft

Now,

486 in² = 486 x (1/12)² = 3.375 ft²

Now,

The area shaded region.

= The area of the rectangle - The area of the triangle

= 40 - 3.375

= 36.625 ft²

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Answer:

109

Step-by-step explanation:

85-77=8

93-85=8

101-93=8

101+8=109

The shape that can tessellate without leaving gaps is the hexagon (option A).

The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).

A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.

On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.

A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.

In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).

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The resultant of the movement of the runner is 290.087 yards

The cosine rule states that if a , b ,c are sides of a triangle and A,B ,C are the opposite angles of the sides, then, c² = a² + b² − 2ab cos(C).

The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.

c² = 250² + 110² -2( 110) (250) cos 100

c² = 62500 + 12100 - 55000(-0.1738)

c² = 74600 + 9570

c² = 84170

c = √ 84170

c = 290.87 yards

Therefore the resultant of the runner pathway is 290.87 yards

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Answer:

[tex](x+3)^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}[/tex]

Step-by-step explanation:

Since the diameter of the circle has endpoints (-4,-4) and (-2,5), then the midpoint of these endpoints is the center of the circle as follows:

[tex](x_{c},y_{c})=\left(\frac{-4+(-2)}{2},\frac{-4+5}{2}\right)=\left(-3,\frac{1}{2}\right)\\[/tex]

Also notice that the radius of the circle is one-half of the distance from the point (-4,-4) to the point (-2,5) as follows:

[tex]r=\frac{1}{2}\sqrt{(-2-(-4))^2+(5-(-4))^2}\\r=\frac{1}{2}\sqrt{4+81}\\r=\frac{1}{2}\sqrt{85}\\\\r^{2}=\frac{85}{4}[/tex]

Then, the equation of the circle would be:

[tex](x-x_{c})^2+(y-y_{c})^2=r^2\\(x-(-3))^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}\\(x+3)^2+\left(y-\frac{1}{2}\right)^2=\frac{85}{4}[/tex]

The value of x is -15

Functions are simply defined as expressions or rules showing the relationship between two variables.

These variables are listed as;

From the information given, we have that;

g(x) =x  -1, if g(x) = -16

Now, we have to equate the two functions, we get;

x - 1 = -16

collect the like terms, we get;

x =-16 + 1

add the values, we have;

x = -15

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The complete question:

Given g(x) =x  -1, if g(x) = -16, find x.

Juan will have more amount money after a year and with a difference of $2048.3.

Compound interest is the interest you earn on interest.

For example if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The total amount in compound interest is expressed as;

A = P( 1+r/n)^{nt}

where p is the principal, r is the rate and n is the interval at which its compounded.

For Jon

P = $7050, r = 5% = 0.05, n = 1/4 of 12 = 3

A = 7050( 1+0.05/3)^{3×1}

A = 7050( 1.017)³

A = 7050 × 1.052

A = $7416.6

Therefore the total amount for Juan after a year is $7416.6

For Sara,

P = $4867, r = 10% = 0.1 , t = 1.,.n = 365

A = 4867( 1+ 0.1/365) ^{365×1)

A = 4867( 1.00027)^365

A = 4867 × 1.103

A = $5368.3

therefore the total amount for Sara after a year is $5368.3

Therefore Juan will have more money after a year and with a difference of $2048.3

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Answer:

0.2356, 0.1444

Step-by-step explanation:

Is 100 points even possible?
Here it states that 62% of them go on vacations. If 2 people are selected, each one ( technically ) has a 62/100 chance of going on a vacation. So the chance that one goes on vacation and one doesn't is .62 * .38 or .2356. The chance that none of them go on vacation is 0.38 * 0.38 or  0.1444.
Hope this helps

Noah earned $160 last month, and his income tax rate is 10%. To calculate how much he earns after tax, we need to subtract the tax amount from his earnings.

The tax amount is equal to 10% of his earnings, which is:

0.1

×

160

=

16

0.1×160=16

Therefore, Noah's earnings after tax is:

160

−

16

=

144

160−16=144

Noah earns $144 after tax.

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

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

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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The triangle that has an angle greater than 90° and two congruent sides is a obtuse isosceles triangle.

An obtuse isosceles triangle is a triangle in which one of the three angles is obtuse (lies between 90 degrees and 180 degrees) and the other two acute angles are equal in measurement.

One example of obtuse isosceles triangle angles is 30°, 30°, and 120°.

An obtuse isosceles triangle can be considered as the triangle that contains the properties of both an isosceles triangle and an obtuse triangle.

Thus, the triangle that has an angle greater than 90° and two congruent sides is a obtuse isosceles triangle.

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The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

[tex]P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n[/tex]

Putting the values:

[tex]$870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13[/tex]

Using the math we find that the percentage is  approximately 14.13%;

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Given,

Two functions f(x) and g(x) are inverses if the composite functions are equal to the identity.

This means that:

f(g(x)) = g(f(x)) = x.

Now,

In this problem, we know that  f(x) and g(x) are inverse functions,

Using the above relation, we know that:

f(g(x)) = x

Hence the equation that satisfies the inverse relation between two functions is f(g(x)) = x

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Step-by-step explanation:

y = 5/x  + 3       change the x's to y's and y's to x's then solve for 'y'

x = 5/y  + 3

x-3  = 5/y

y = 5/ (x-3)      <====== this is the inverse

The volume of the given three dimensional figure is 14352 cubic inches.

From the given three dimensional figure, dimensions in rectangular prism are Length = 23 inches, Breadth = 16 inches and Height = 18 inches.

So, volume of rectangular prism = Length×Breadth×Height

= 23×16×18

= 6624 cubic inches

Volume of triangular prism = Area of base × Height

= (23×16) × Height

= 368 × Height

= 368 × 21

= 7728 cubic inches

Total volume = 6624 + 7728

= 14352 cubic inches

Therefore, the volume of the given three dimensional figure is 14352 cubic inches.

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The angle on the unit circle is calculated as: 50.77°

A unit circle is defined as a circle with a radius measuring 1 unit. The unit circle is generally represented in the cartesian coordinate plane. The unit circle is algebraically represented using the second-degree equation with two variables x and y. The unit circle has applications in trigonometry and is helpful to find the values of the trigonometric ratios sine, cosine, tangent.

Now, the formula to find the angle in the unit circle is:

tan θ = y/x

we are given:

x = (√10)/5

y = (√15)/5

Thus:

tan θ = (√15)/5)/ ((√10)/5)

tan θ =(√15)/(√10)

θ = tan⁻¹(√15)/(√10)

θ =  1.225

θ = 50.77°

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The graph initially increases from point A to point C

Based on the information provided, let's analyze the changes in the graph between point A and point C:

The graph increases from point A to point B: this means that as you move from point A to point B along the x-axis, the corresponding y-values on the graph increase.

The graph is constant between points B and C: this indicates that the y-values on the graph remain the same as you move from point B to point C along the x-axis.

Therefore, between point A and point C, the graph initially increases from point A to point B and then remains constant between points B and C.

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Answer:

b. no

Step-by-step explanation:

This is not a random sample of the soccer players in the league. A random sample would involve selecting players from the entire population of soccer players in the league using a random and unbiased method. In this case, Donald surveyed only his 3 favorite soccer players, which introduces bias and does not represent the entire population of players in the league.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer: 4

Step-by-step explanation:

1 third of 30 is 10 and 2/5s of 10 is 4

Average velocity of Julian = -21.4 km / 0.25 hours= -85.6 km/hour Julian's average velocity is -85.6 km/hour.

Given: Julian sets the simulated biker to a speed of 20km/h. After he rides his bike for 15 minutes, Julian's app reports a position of -21.4 km.

To find: What is Julian's average velocity?

Solution:We know that,velocity = displacement/time or velocity = (final position - initial position) / time.

Since Julian started from 0 km and after 15 minutes he reached at -21.4 km. So,-21.4 km - 0 km = -21.4 km (Final position - Initial position)Also, time = 15 minutes.

Converting minutes into hours, 15 minutes = 15/60 hours = 0.25 hours.

Therefore, average velocity of Julian = -21.4 km / 0.25 hours= -85.6 km/hour Julian's average velocity is -85.6 km/hour.

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The predicted average score for persons taking a 47-hour review course is approximately 681.2

Given data points:

Review time (x1) = 30 hours, Score (y1) = 620

Review time (x2) = 70 hours, Score (y2) = 764

First, let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (764 - 620) / (70 - 30)

m = 144 / 40

m = 3.6

Next, let's calculate the y-intercept (b) using the formula:

b = y - mx

Taking one of the data points (let's use (x1, y1) = (30, 620)):

b = 620 - 3.6 * 30

b = 620 - 108

b = 512

Now we have the slope (m = 3.6) and the y-intercept (b = 512), so the linear equation that fits this data is:

y = 3.6x + 512

To predict the average score for persons taking a 47-hour review course, we can substitute x = 47 into the equation:

y = 3.6 * 47 + 512

y = 169.2 + 512

y ≈ 681.2

Therefore, the predicted average score for persons taking a 47-hour review course is approximately 681.2 (rounded to the nearest tenth).

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The hyperbolas that open horizontally are equations are:

(x-1)²/6² - (2y+6)²/5² = 1

(2y-6)²/3² - (x+6)²/2² = 1

(2y-10)²/10² - (x+3)²/12² = 1

To identify the hyperbolas that open horizontally, we need to look at the equations and determine the orientation of the terms involving x and y.

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Answer:

.

Step-by-step explanation:

The height needed to reach the desired volume is given as follows:

h = 4 ft.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for this problem are given as follows:

V = 168, l = 7, w = 6.

Hence the height of the prism is obtained as follows:

7 x 6 x h = 168

h = 168/42

h = 4 ft.

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Answer:

Therefore, the approximate volume of the sphere is 4.19 x 10^-9 cubic millimeters.

Step-by-step explanation:

To find the approximate volume of a sphere, we can use the formula:

V = (4/3) * π * r^3

Given that the diameter of the sphere is 4 x 10^-3 mm, we can calculate the radius (r) by dividing the diameter by 2:

r = (4 x 10^-3 mm) / 2 = 2 x 10^-3 mm

Now, we can substitute the values into the volume formula:

V = (4/3) * 3.14 * (2 x 10^-3 mm)^3

Simplifying further:

V = (4/3) * 3.14 * (8 x 10^-9 mm^3)

V ≈ 4.19 x 10^-9 mm^3

The answer to all parts is shown below.

a. To combine the two chemicals, we need to add them together. Therefore, the rational expression for C(z) is:

C(z) = C₁(z) + C₂(z)

C₁(z) = z / (z + 1)

C₂(z) = 2 / (z - 3)

Combining the two chemicals, we have:

C(z) = C₁(z) + C₂(z)

= z / (z + 1) + 2 / (z - 3)

b. To find the simplified equation of V(x), we substitute the expressions for C(z) and H(x) into the formula:

V(x) = C(x) + C₂(x) H(x)

= (z / (z + 1) + 2 / (z - 3)) (x³ - x) / x

Simplifying further, we have:

V(x) = (z(x³ - x) + 2x (z - 3)) / ((z + 1) x)

c. To find the volume when a specific number of units are produced, we substitute the value into the equation V(x) and simplify.

Let's calculate the volume for 50, 100, and 1000 units:

For z = 50:

V(x) = (50 (x³ - x) + 2x (50 - 3)) / ((50 + 1) x)

For z = 100:

V(x) = (100 (x³ - x) + 2x (100 - 3)) / ((100 + 1) x)

For z = 1000:

V(x) = (1000 (x³- x) + 2x (1000 - 3)) / ((1000 + 1) x)

d. To find the number of units needed to achieve a volume of 3000 c³, we set V(x) equal to 3000 and solve for x:

3000 = (z (x³ - x) + 2x (z - 3)) / ((z + 1) x)

Solving this equation for x will give us the number of units needed to produce a volume of 3000 c³.

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You would need approximately 225 mL of the 70% alcohol mixture to obtain the desired 55% solution.

To find out how much of the 70% alcohol mixture you need to obtain a 55% solution, we can set up an equation based on the principle of mixing concentrations.

Let's assume you need "x" mL of the 70% alcohol mixture.

First, we'll determine the amount of alcohol in the 10% alcohol mixture:

Alcohol in 10% mixture = 10% of 75 mL

= (10/100) × 75 mL

= 7.5 mL

Next, we'll determine the total amount of alcohol in the desired 55% solution:

Alcohol in 55% solution = 55% of (75 mL + x mL)

We want the amount of alcohol in the 55% solution to be equal to the sum of the alcohol in the 10% mixture and the alcohol in the x mL of the 70% mixture.

Therefore, we can set up the equation:

Alcohol in 55% solution = Alcohol in 10% mixture + Alcohol in 70% mixture

55% of (75 mL + x mL) = 7.5 mL + 0.7x mL

Now, let's solve for "x" to find the amount of the 70% alcohol mixture needed:

0.55 × (75 mL + x mL) = 7.5 mL + 0.7x mL

41.25 mL + 0.55x mL = 7.5 mL + 0.7x mL

0.55x mL - 0.7x mL = 7.5 mL - 41.25 mL

-0.15x mL = -33.75 mL

x mL = (-33.75 mL) / (-0.15)

x mL ≈ 225 mL

Therefore, you would need approximately 225 mL of the 70% alcohol mixture to obtain the desired 55% solution.

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