expand the expression: [tex]-\frac{1}{3}[/tex](-6x+15y) to write an equivalent expression. Use as few terms as possible.

Answer: 160 mg

Step-by-step explanation:

10% of 200 is 20

therefore, every 6 hours, 20 milligrams of medicine filters into your blood.

there are 24 hours in a day, and 48 hours in 2 days.

6 * 4 = 24

20 * 4 = 80

you get 80 mg of medicine every day.

80 * 2 = 160

you get 160 mg of medicine in two days.

The parent function of the quadratic function is

∵ x is added by 7

∴ The graph of the function is translated 7 units to the left

∴ The image of the function will be

∵ The function is added by -4

∴ The graph of the function translated 4 units down

∴ The image of the function will be

The transformation is

Shift 7 units left and shift down 4

The answer is D

Answer:

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

Segment EF with:

Use midpoint equation:

Find unknown coordinates of the point F:

So the point is F = ( - 22, 4)

Answer:

F = (-22, 4)

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ \textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.}[/tex]

Given information:

Define the endpoints of the line segment EF:

Substitute the given information into the formula:

[tex]\implies (x_M,y_M)=\left(\dfrac{x_F+x_E}{2},\dfrac{y_F+y_E}{2}\right)[/tex]

[tex]\implies (-6,-2)=\left(\dfrac{x_F+10}{2},\dfrac{y_F-8}{2}\right)[/tex]

Find the x-coordinate of M:

[tex]\implies \dfrac{x_F+10}{2}=-6[/tex]

[tex]\implies x_F+10=-12[/tex]

[tex]\implies x_F=-22[/tex]

Find the y-coordinate of M:

[tex]\implies \dfrac{y_F-8}{2}=-2[/tex]

[tex]\implies y_F-8=-4[/tex]

[tex]\implies y_F=4[/tex]

Therefore, the coordinates of endpoint F are (-22, 4).

The correct option regarding the ratio is given as follows:

For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.

A ratio of an amount a over a total amount a + b is given as follows:

r = a/(a + b) = a:b.

In the context of this problem, the ratio is given as follows:

r = 3:2.

Hence the number of equal parts is given by:

equal parts = 3 + 2 = 5.

The length of the segment is:

B - A = 6 - (-4) = 10 units.

Hence the length of each equal part is:

length equal part = 10/5 = 2.

The point that is 3/5 of the way from point -4 to point 6 is found as follows:

x - (-4) = 3/5(6 - (-4))

x + 4 = 30/5

x + 4 = 6

x = 2.

Meaning that the correct option is given by the last one.

The coordinates of A and B are missing, and they are given as follows:

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The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.

An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.

From the given box of nails,

The height of 2 boxes of nails = (9× 2) + 39 = 57 In

The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In

The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln

That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.

Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.

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Answer:

Tip- $5.16

Total cost- $33.86

Step-by-step explanation:

To find a 18% tip, turn 18% into 0.18.

Multiply 28.67 by 0.18.

28.67x0.18=

5.16

If you add that to the bill, it would be 33.86

Answer:

2a

Step-by-step explanation:

8a² / 4a

8/4 a²-¹

2a

please rate as brainliest

Answer:

2a

Step-by-step explanation:

8a^2 = 4a x 2a

8a^2 ➗ 4a

= ( 4a x 2a )/4a

= 2a

step 1

Find the slope of the line represented by the table of values

take the points

(-8,13) and (-4,5)

m=(5-13)/(-4+8)

m=-8/4

m=-2

step 2

Write the equation of the line that contains the point (-8,6) and has the same slope as the line represented by the table

y=mx+b

we have

m=-2 -----> the same slope of the given line

point (-8,6)

substitute in the equation of the line in slope intercepot form

6=-2*(-8)+b

solve for b

6=16+b

b=-10

therefore

teh equatiion of the line is

Variable used to write the equation are x,  Number of pennies and y, Number of nickels and the system of equations used is x+y=0.81 and  x+9=y.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Let the variables defined to form the system of equation are as follows:

x= Number of pennies

y= Number of nickels

Total worth of  pennies and nickels is 0.81

mathematically, x+y=0.81

Given condition,  she has 9 more nickels than pennies

mathematically, x+9=y

So, the system of equation which can be used to determine the number of pennies and the number of nickels that Kennedy has are x+y=0.81 and  x+9=y, where variables used are x and y.

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From the given diagram, let's find the length of the park's boundary.

We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.

To find the length of the circular sides, apply the length of arc formula:

Where:

Θ = 120 degrees

π = 3.14

radius, r = 50 yards

Hence, we have:

This means the length of one circular side of the boundary is 104.67 yards.

We have two circular sides of the boundary.

The top and bottom sides form equilateral traingles.

Hence, the length of the top and bottom sides are 50 yards each.

To find the total length of the boundary, we have:

Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards

Rounding off to the nearest yard, the length of the park's boundary is:

309 yards

ANSWER:

D. 309 yards

Answer:

x = 114

Step-by-step explanation:

since the triangles are congruent then corresponding angles are congruent, then

∠ C = ∠ D , that is

x + 18 = 132 ( subtract 18 from both sides )

x = 114

Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.

Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.

Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.

A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.

Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

A size can be determined by using these parameters but is not directly seen in a Box Plot

Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

Yes, the peak of the distribution can be analyzed from Box Plot

Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.

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When a person is 3 feet from a street light, the length of the shadow grows at a rate of 4 feet per second.

See the figure that illustrates the in question statement, attached.

making use of the related triangle theorem;

4/y = 12/x+y

Cross multiply

4(x+y)=12y

4x+4y = 12y

4x=8y

x/y =2

x=2y

Divide the two sides of the equation by t, where dx/dt = 2 dy/dt. The speed at which the person is walking away from the street light is expressed as dx/dt 

The growth rate of the shadow's length is measured by the ratio dy/dt.

Given that dx/dt = 8ft/s

by solving,

dy/dt = 4 ft/s

Hence the rate at which the length of the shadow growing when the person is 3 feet from the street light is 4ft/s

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The correct option regarding the scale and the origin of the graph are as follows:

D.

x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

The scale should be chosen focusing on improving the readability of the data-set by the reader, while the origin should be chosen according to the values assumed by the variables.

In the context of this problem, the values of x, in weeks, are:

2, 3, 4, 5, 6, 7, 8.

They increase by one, hence the scale of x should be of 1 unit = 1 week.

The values of y, in minutes are given as follows:

300, 450, 600, 750, 900, 1050, 1200.

They increase by 150, hence the scale of y should be of 1 unit = 150 minutes, which is the rate of change of the problem.

As the measures are both positive values, the origin should be of (0,0), hence the correct option for the scales and the origin is option D.

The table is:

Weeks Minutes

2 300

3 450

4 600

5 750

6 900

7 1,050

8 1,200

The options are:

A. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 50 minutes

origin: (0 weeks, 0 minutes)

B. x-axis scale: 1 unit = 2 weeks

y-axis scale: 1 unit = 150 minutes

origin: (2 weeks, 300 minutes)

C. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 50 minutes

origin: (2 weeks, 300 minutes)

D. x-axis scale: 1 unit = 1 week

y-axis scale: 1 unit = 150 minutes

origin: (0 weeks, 0 minutes)

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An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.

For example, let's take the first number:

This number is written as a fraction. But, this is also equivalent to:

Since it can also be written without making use of a fraction then this number is an integer.

Also, there are numbers that are written in decimal form. For example:

These types of numbers are not integers.

When the pile is 22 feet high, the height of the pile changes to 20/1089π.

Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?

The volume of cone is V = 1/3 * pi * r ^ 2 * h

d=3h

2r = 3h

r = (3h)/2

V = 1/3 * pi * r ^ 2 * h

= 1/3 * pi * ((3h)/2) ^ 2 * h

= 1/3 * pi((9 * H ^ 2 )/4) * h

= (9pi)/12 * h ^ 3

Differentiate w.r.to t

(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)

(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)

(dV)/(dt)=20, h=22 feet

20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)

(dh)/(dt) = 80/ (9pi * (22^ 2))

h^ t = 20/ 1089 *pi   ft / min

Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π

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Answer:

-4

Step-by-step explanation:

6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4

Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend.

According to the question,

We have the following information:

Devon has $15.

Cost of 1 candy bar = $1

Cost of 1 sports drink = $3

Devon wants to purchase at most 10 items.

It means that the total items should be less than or equal to 10.

Now, we have to spend $15 in such a way that number of items should be less than or equal to 10.

Now, we will look for the number of items for sports drink and change the number of candy bars accordingly.

Let's take 1 sports drink:

$3

We are left with $12. Now, there will be 12 candy bars.

So, this can not satisfy our conditions.

Let's take 2 sports drink:

$6

We are left $9. Now, there will be 9 candy bars. And the number of items is 11.

(This is not satisfying our condition.)

Let's take 3 sports drink:

$9

We are left with $6. Now, there will be 6 candy bars. And the number of items is 9.

This is satisfying all the conditions.

Hence, Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend on snacks.

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A polynomial function of degree 3 with real coefficients and given zeros of -3, -1, and 4 is 4(x - 4)(x + 3)(x + 1) for which f(-2) = 24.

Any modifying value connected to a variable through multiplication is referred to as a "coefficient." Any non-imaginary number is a "real" number

How do you locate a degree 3 polynomial with real coefficients?

A polynomial of degree 3 must take the form a(xr1)(xr2)(xr3) since it has three roots. We are provided with the roots 3, 1, and 4. So, all we have to do is change these to r1, r2, and r3. We now get a(x+3)(x+1)(x4).

We must first factor the provided polynomial equation into a linear and quadratic equation in order to obtain the roots of the three-degree polynomial. The zeros of the three-degree polynomial can then be easily found.

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Answer:

Step-by-step explanation:

y>3x+1

y≤-2x-4

The interval is from 0.9330 to 0.9350

For given condition;

mean = 0.9340

standard deviation = 0.0030

z-score at 98% = 2.33

n = size of sample = 47

Step 1: calculate the standard error of the mean

standard error of mean  =  z-score * standard deviation/sqrt(n)

                                        =  2.33 * 0.0030/[tex]\sqrt{47}[/tex]

                                        = 0.0010

step 2: upper limit  =  mean + standard error

                                =  0.9340 + 0.0010

                                = 0.9350

           lower limit  =  mean - standard error

                              =  0.9340 - 0.0010

                              = 0.9330

Hence, the interval is from 0.9330 to 0.9350

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180°

Answer:

$8303.75

Step-by-step explanation:

(6000x1.025^2)+2000=8303.75

Answer:

The area is 196π, or 615.752160 when evaluated to 6 decimal places.

Step-by-step explanation:

There is an equation for the area of a circle:

A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:

A=π([tex]14^{2}[/tex])

A=196π

If we write out π and evaluate with an (un)reasonable amount of decimal places:

π≅3.1415926536

A=196×(3.1415926536)

A≅615.752160

Answer:

A = [tex]\pi ^{2}[/tex]

Step-by-step explanation:

A≈615.75

Answer:

5/42 or 0.1190

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The room numbers of two adjacent classrooms are 359 and 361.

What is consecutive odd numbers?

Consecutive odd numbers are odd integers that are separated by 2 and come after one another.

Suppose the first odd number is x, then the another consecutive odd number is x + 2.

The sum of these two numbers is 720.

So,

x + (x + 2) = 720

2x + 2 = 720

2x = 718

x = 359

Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.

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The faster driving rate of Goldie is 20 miles/hour.

Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours  and Distance = 50 mile.

Now, Distance = Speed × Time

Let the faster driving rate be x.

50 = x × 2.5

⇒ x = 50/2.5

⇒ x = 20 miles/hour

Therefore, the faster driving rate of Goldie is 20 miles/hour.

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Answer:

Step-by-step explanation:

I don't agree with the other answer.

You need to you systems of equations

So

d=50     t=t-2.5       x=r+10

d=rt

50=(r+10)(t-2.5) (faster equation)

50=rt (slower equation)

t=[tex]\frac{50}{r}[/tex]   (substitute into faster equation)

50 = (r+10)(50/r -2.5)                mult both sides by r to get rid of fraction

50r = (r+10)(50-2.5r)                 FOIL

50r = 50r -2.5r² + 500 -25r     Simplify

2.5r²+25r-500=0                      divide all by 2.5

r²+10r-200                                 factor

(r-20)(r+10)                                 eliminate negative answer

r=20

x=r+10  =20+10 =30 mph

The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min

= 6π rad/min

tan θ = x/6

[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]

[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]

[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]

At x=1 km; tan θ= x/6 = 1/6

[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]

[tex]sec^2 \theta = \frac{10}{9}[/tex]

[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

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The least number of distinct values that can occur in the list is 225.

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.

The mode appears 10 times. That leaves 2008 numbers.

The least number of distinct values will occur if all but one of the remaining values appears 9 times

= 2008/9

=223 1/9.

So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.

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Answer

Check Explanation

Explanation

a ≡ b (mod n)

This means a and b have the same remainder when they are divided by n

So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.

1) 67 × 73 ≡ 1 × 3 (mod 5)

4891 ≡ 3 (mod 5)

So, to check,

(4891/5) = 978 remainder 1

(3/5) = 0 remainder 3

The remainders are different.

So, this equation is wrong and does not work.

This equation is false.

2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

Noting that it is the units digit that determines the remainder

3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer

5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer

So, using these numbers,

83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

81 ≡ 625 (mod 17)

(81/17) = 4 remainder 13

(625/17) = 36 remainder 13

The remainders are the same.

So, this equation is correct and it works.

This equation is true.

Hope this Helps!!!