The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative. show work

Answer:

4x - 8

Step-by-step explanation:

Cost of producing x soccer balls = h(x) = 5x + 6 in thousands of dollars

Revenue generated from x soccer balls = k(x) = 9x - 2 in thousands of dollars

We need to calculate the profit for x soccer balls.

Profit = p (x) = Revenue - Cost

p(x) = (9x - 2) - (5x + 6)

p(x) = 9x -2 - 5x- 6

p(x) = 4x - 8

Thus the profit from x soccer balls in thousands of dollars would be 4x - 8.

Answer:4x-8

Step-by-step explanation:

Answer:

The correct answer option is B. 1/5.

Step-by-step explanation:

We are given four fractions in the answer options and we are to determine whether which one of them has terminating decimal as its decimal expansion.

Terminating decimal means a decimal value which has a finite amount of numbers and has an end to it.

[tex]\frac{1}{3} = 0.333333333[/tex]

[tex]\frac{1}{5} = 0.2[/tex]

[tex]\frac{1}{7} = 0.142357142[/tex]

[tex]\frac{1}{9} = 0.111111111[/tex]

Therefore, the correct answer is 1/5.

Answer:

[tex]4^x-5=6[/tex] gives the solution [tex]x=\frac{\log(11)}{\log(4)}[/tex].

[tex]4^{x-5}=6[/tex] gives the solution [tex]x=\frac{\log(6)}{\log(4)}+5[/tex].

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is [tex]4^{x}-5=6[/tex], then the following is the process:

[tex]4^x-5=6[/tex]

Add 5 on both sides:

[tex]4^x=6+5[/tex]

Simplify:

[tex]4^x=11[/tex]

Now write an equivalent logarithm form:

[tex]\log_4(11)=x[/tex]

[tex]x=\log_4(11)[/tex]

Now using the change of base:

[tex]x=\frac{\log(11)}{\log(4)}[/tex].

If we assume the equation is [tex]4^{x-5}=6[/tex], then we use the following process:

[tex]4^{x-5}=6[/tex]

Write an equivalent logarithm form:

[tex]\log_4(6)=x-5[/tex]

[tex]x-5=\log_4(6)[/tex]

Add 5 on both sides:

[tex]x=\log_4(6)+5[/tex]

Use change of base formula:

[tex]x=\frac{\log(6)}{\log(4)}+5[/tex]

Answer:

6.292

Step-by-step explanation:

I got it right on the test.

Answer:

The correct option is D.

Step-by-step explanation:

Given information:

Total number of teams = 3

Total number of members in each team = 3

A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.

It means the points for 1st, 2nd, 3rd, 4th, and 5th place are 5, 4, 3, 2 and 1 respectively.

Total points that can earned = 5+4+3+2+1=15

There were no ties, disqualifications, or withdrawals.

No team earned more than 6 points.

To minimize the score of a team, we have to maximize the score of the other two teams.

Let two teams earn there maximum score. i.e. 6. So the score of third team is

[tex]15-6-6=3[/tex]

The least possible score a team could have earned is 3. Therefore the correct option is D.

Answer:

  1/250 W/m² or 0.004 W/m² or 4 mW/m²

Step-by-step explanation:

The cargo worker is (50 m)/(1 m) = 50 times the reference distance. The intensity varies as the inverse of the square of the distance, so will be ...

  (1/50)²×(10 W/m²) = 10/2500 W/m² = 1/250 W/m²

This might be more conveniently written as 4 mW/m².

[tex]\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\378=\dfrac{|a\cdot b|}{9}\\\\|a\cdot b|=42\\\\a\cdot b=-42 \vee a\cdot b=42[/tex]

So, the least value is -42

Answer:

The correct option is D.

Step-by-step explanation:

In a data set we have three quartiles and the second quartile is known as median.

First quartile Q₁ divides the data set in 1:3. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to Q₁ and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to Q₁.

Second quartile Q₂ divides the data set in 1:1. It means [tex]\frac{1}{2}[/tex] of the data values are less than or equal to Q₂ and [tex]\frac{1}{2}[/tex] of the data values are more than or equal to Q₂.

Third quartile Q₃ divides the data set in 3:1. It means [tex]\frac{3}{4}[/tex] of the data values are less than or equal to Q₃ and [tex]\frac{1}{4}[/tex] of the data values are more than or equal to Q₃.

It is given that first quartile of a data set is 2.5. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to 2.5 and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to 2.5.

Therefore the correct option is D.

Answer:

D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solving the density equation for mass, we get ...

  D = m/V

  m = DV . . . . . multiply by volume

Substituting the volume formula gives ...

  m = D(4/3π)r³

Alloy A

Substituting D = 7.5 gives ...

  m = 7.5(4/3)πr³

  m = 10πr³ . . . . . simplify

__

Alloy B

Substituting D = 8.5 gives ...

  m = 8.5(4/3π)r³

  m = (34π/3)r³ . . . . . simplify

Answer:

the coordinates of C' = (2,1)

Step-by-step explanation:

The coordinates of point C can be found by looking at the graph.

Coordinates of C are C= (6,3)

If ABCD is dilated by a factor of 1/3 then the coordinates of C' can be found by multiplying the coordinates of C by 1/3

C = (6,3)

C' =(1/3*6,1/3*3)

C' = (2,1)

So, the coordinates of C' = (2,1)

Answer:

140

Step-by-step explanation:

Rewording the problem will make it easier to write the equation you need to solve this. Think of it in simpler terms: "7 is 5% of how many?". "7" is just a 7; the word "is" means =; "5%" is expressed as its decimal equivalency (.05); the word "of" means to multiply; and "how many" is our unknown (x). Putting that all together in one equation looks like this:

7 = .05x

Solve for x by dividing both sides by .05 to see that

x = 140

Answer:

C and D

Step-by-step explanation:

The quadratic formula is

x= (-b±√b²-4ac)/2a

The formula uses the numerical coefficients in the quadratic equation.

The general quadratic equation is ax²+bx+c where a, b and c are the numerical coefficients

So, lets try and see;

A.

[tex]5x+4=3x^4-2\\\\=3x^4-5x-2-4\\=3x^4-5x-6\\a=3,b=-5,c=-6[/tex]

But due to the fact that  in this equation you have x⁴, the equation is not a quadratic equation thus can not be solved using this formula

B

[tex]-x^2+4x+7=-x^2-9\\\\\\=-x^2+x^2+4x+7+9\\=4x+16[/tex]

C

[tex]9x+3x^2=14+x-1\\\\\\=3x^2+9x-x-14+1\\\\=3x^2+8x-13\\\\\\a=3,b=8,c=-13\\[/tex]

D.

[tex]2x^2+x^2+x=30\\\\\\=3x^2+x-30\\\\\\a=3,b=1,c=-30[/tex]

From the checking above, the equations will be C and D

Answer:

Option C and D

Step-by-step explanation:

To find : After being rearranged and simplified, which of the following equations could  be solved using the quadratic formula? Check all that apply.

Solution :

Quadratic equation is [tex]ax^2+bx+c=0[/tex] with solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

A. [tex]5x+4=3x^4-2[/tex]

Simplifying the equation,

[tex]3x^4-2-5x-4=0[/tex]

[tex]3x^4-5x-6=0[/tex]

It is not a quadratic equation.

B. [tex]-x^2+4x+7=-x^2-9[/tex]

Simplifying the equation,

[tex]-x^2+4x+7+x^2+9=0[/tex]

[tex]4x+16=0[/tex]

It is not a quadratic equation.

C. [tex]9x + 3x^2 = 14 + x-1[/tex]

Simplifying the equation,

[tex]3x^2+9x-x-14+1=0[/tex]

[tex]3x^2+8x-13=0[/tex]

It is a quadratic equation where a=3, b=8 and c=-13.

[tex]x=\frac{-8\pm\sqrt{8^2-4(3)(-13)}}{2(3)}[/tex]

[tex]x=\frac{-8\pm\sqrt{220}}{6}[/tex]

[tex]x=\frac{-8+\sqrt{220}}{6},\frac{-8-\sqrt{220}}{6}[/tex]

[tex]x=1.13,-3.80[/tex]

D. [tex]2x^2+x^2+x=30[/tex]

Simplifying the equation,

[tex]3x^2+x-30=0[/tex]

It is a quadratic equation where a=3, b=1 and c=-30.

[tex]x=\frac{-1\pm\sqrt{1^2-4(3)(-30)}}{2(3)}[/tex]

[tex]x=\frac{-1\pm\sqrt{361}}{6}[/tex]

[tex]x=\frac{-1+19}{6},\frac{-1-19}{6}[/tex]

[tex]x=3,-3.3[/tex]

Therefore, option C and D are correct.

Answer:

X=5, X=9

Step-by-step explanation:

The first one has two sides that are equal length, so the angles opposite of those sides are equal. This means that there are 2 73 degree angles. A triangle only had 180 degrees, so the last angle is equal to 34 degrees. When you set 6x+4=34, x is equal to 5.

The second triangle is an equilateral triangle, so every angle is equal to 60 degrees. We can set 7x-3=60. Add 3 to isolate x. 7x=63. Divide by 7 to solve for x. x=9.

Answer:

Give Zdomi Brainliest now <3

Step-by-step explanation:

Answer:

On a number line, -4 is located to the right of -5

Step-by-step explanation:

Answer:

On a number line, -4 is located to the right of -5

Step-by-step explanation:

Answer:

1/258 *(t^28)

= t^28 / 4^4

= t^28 4^-4

= (t^-7 * 4)^-4

= (4t^-7)^-4

Step-by-step explanation:

Answer:

so the answer is d

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

It doesn't make sense for either x or y to be negative because we are talking about x representing the number of acres and y representing another number of acres and that they should add up to no more than 400.

So I'm not going to look at A or C.

B looks good 250+150=400

D almost looks good 1+400=401; the problem with this answer is that is more than 400

Option B (250, 150) is the only viable solution as it adheres to the constraints of the problem, summing to exactly 400 acres with both variables being non-negative.

The farmer has set a constraint for planting peas and carrots where the total acres used for planting both cannot exceed 400 acres.

Thus, we are looking for a solution where the sum of x (acres of peas) and y (acres of carrots) must be equal to or less than 400. The solution should also satisfy the requirement that both x and y must be non-negative since you cannot plant crops on a negative amount of land.

Among the options provided, option B (250, 150) is the viable solution. Here's why:

A.) (−125, 500): We cannot have negative acres for crops, so x cannot be negative. Also, y exceeds 400 acres on its own, violating the total area constraint.

B.) (250, 150): This solution sums up to 400 acres exactly, fitting within the constraint and with both x and y being non-negative.

C.) (400, −10): y cannot be negative, representing a nonsensical scenario for planting.

D.) (1, 400): The total acreage here is 401, which exceeds the maximum allowable acreage.

The probability is:

              [tex]\dfrac{9}{38}[/tex]

We need to use the Baye's theorem in order to find the probability .

Jar 1:  has 1 white ball and 4 black balls.

This means that the probability of white ball is: 1/5

( since there are a total of 1+4=5 balls out of which 1 is white)

Jar 2: has 2 white balls and 1 black ball.

This means that the probability of white ball is: 2/3

( since there are a total of 2+1=3 balls out of which 2 are white)

Jar 3 : has 3 white balls and 2 black balls.

This means that the probability of white ball is: 3/5

( since there are a total of 3+2=5 balls out of which 3 are white)

Hence, the probability the ball was drawn from Jar 1​, given that the ball is white is:

Ratio of drawing jar 1 and a white ball from it to the sum of choosing each jar and a white ball from it.

i.e.

[tex]=\dfrac{\dfrac{1}{2}\times \dfrac{1}{5}}{\dfrac{1}{2}\times \dfrac{1}{5}+\dfrac{1}{3}\times \dfrac{2}{3}+\dfrac{1}{6}\times \dfrac{3}{5}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{1}{10}+\dfrac{2}{9}+\dfrac{1}{10}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{2}{10}+\dfrac{2}{9}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{38}{90}}\\\\\\=\dfrac{9}{38}[/tex]

The probability that a drawn white ball came from Jar 1, given the stated conditions, is approximately 0.286 or 28.6%.

This problem can be solved using the concept of conditional probability. Let's define the events as follows:

The question requires us to find P(J1|W), that is, the probability that the ball came from Jar 1 given that it is white. Using Bayes' theorem, we can write this as:

P(J1|W) = [P(W|J1) * P(J1)] / P(W). Here, P(W|J1) is the probability of drawing a white ball from Jar 1, P(J1) is the probability of choosing Jar 1, and P(W) is the total probability of drawing a white ball.

We can find these probabilities as:

Substituting these values into the Bayes' theorem, we find P(J1|W) = [(1/5) * (1/2)] / 0.35 = 0.286 approximately. Therefore, there is approximately a 28.6% chance that the drawn white ball came from Jar 1.

https://brainly.com/question/10567654

#SPJ3

Answer:

128/3 cubic inches

Step-by-step explanation:

The formula for pyramid volume is (1/3)lwh. Using this we can calculate that the volume of each shape is 320/3 cubic inches and 192/3 inches. When these are subtracted, it reads 128/3 cubic inches.

Answer:

The answer is 42.67 cubic inches.

Step-by-step explanation:

Both the models are in the shape of a square pyramid.

The length of the sides of the base for both the models is 8 inches.

Amy’s model is 5 inches tall and Alex’s model is 3 inches tall.

The volume is given by :

[tex]a^{2}\frac{h}{3}[/tex]

So, Amy's figure volume is :

[tex]8^{2}\times \frac{5}{3}[/tex] = 106.67 cubic inches

And Alex's figure volume is:

[tex]8^{2}\times \frac{3}{3}[/tex] = 64 cubic inches

So, the difference between volumes is = [tex]106.66-64=42.67[/tex] cubic inches.

The answer is 42.67 cubic inches.

Answer:

  D.  1/10

Step-by-step explanation:

The trial results (# who watched TV) are ...

  4 4 3 4 4 4 4 3 3 2

Of the 10 trials, only 1 resulted in 2 in the group of 4 watching TV.

Your probability is 1/10.

Answer:

10 windows are on the 8th floor

Step-by-step explanation:

1 = 52

2 = 46

3 = 40

4 = 34

5 = 28

6 = 22

7 = 16

8 = 10

The price per pound of apples and cherries can be calculated using a system of linear equations. This is based on the given information about how much Frederick and Wilhelmina spent on these fruits at the farmers' market.

In order to find the price per pound of apples and cherries at the farmers' market, we will use a system of linear equations. We can assume the price per pound of apples is A and the price per pound of cherries is C. Frederick's purchases can be represented as 4A + 15C = 36.93 and Wilhelmina's purchases can be represented as 12A + 9C = 30.51. By using these equations, we can solve for A and C using any method you are comfortable with, such as substitution or elimination.

Note: The information regarding fruit consumption in 2001 and the cost calculation methodology is not directly relevant to the main question, but it provides a context of fun facts.

https://brainly.com/question/34783456

#SPJ2

Answer:

My proof is in the explanation.  

Step-by-step explanation:

This is a two-column proof.

One column for statements and the other for the reason for that statement.

Hopefully it shows up well on your screen. Let me know if it doesn't.

Statement                                          |        Reason

1) CD is the perpendicular                   1) Given

bisector of AB

2) AD=DB                                              2) Definition of bisector

3) CD=CD                                              3) Reflexive property

4) mAngleCDA=90                               4) Definition of perpendicular

5) mAngleCDB=90                               5) Definition of perpendicular

6) mAngleCDA=mAngleCDB               6) Substitution property

7) Corresponding parts of each           7)  SAS

triangle are congruent                                (side-angle-side)

8) AC=CB                                               8) The two triangles are ............................................................................congruent so

                                                                   the corresponding parts ............................................................................are

                                                                   congruent.

Answer:

2.04 seconds

Step-by-step explanation:

Falling objects near the surface of the earth have an acceleration of -9.81 m/s².

Acceleration is the change in velocity over change in time:

a = (v − v₀) / t

-9.81 = (-30.0 − (-10.0)) / t

-9.81 = -20.0 / t

t = 2.04

It takes 2.04 seconds.

Answer:

Arc length is  [tex]\frac{14\pi}{3}[/tex] ,  or,  14.7

Step-by-step explanation:

AB is an arc intercepted by 140 degree angle. The formula for length of an arc is given by

[tex]AL=\frac{\theta}{360}*2\pi r[/tex]

Where

AL is the arc length

[tex]\theta[/tex]  is the angle (in our case, 140)

r is the radius of the circle (which is 6)

Substituting, we get:

[tex]AL=\frac{\theta}{360}*2\pi r\\AL=\frac{140}{360}*2\pi (6)\\AL=\frac{7}{18}*12\pi\\AL=\frac{14\pi}{3}[/tex]

In decimal (rounded to tenths) -  14.7

Answer:

[tex]t=0.444\ seconds [/tex]

Step-by-step explanation:

Let

x -----> the number of objects

t ----> the time in seconds

we have

[tex]t=0.003x^{2}+0.001x[/tex]

For x=12 objects

substitute in the formula and solve for t

[tex]t=0.003(12)^{2}+0.001(12)[/tex]

[tex]t=0.444\ seconds [/tex]

To find the time to sort 12 objects, we plug x = 12 into the equation t=0.003x^2 + 0.001x to get t = 0.444 seconds.

The student has asked for the time it will take for a computer to sort 12 objects, according to the function t=0.003x^2 + 0.001x.

Step 1: Plug in the value

The first step is to plug the value x = 12 into the given equation.

t = 0.003(12)^2 + 0.001(12)

Step 2: Calculate squares and products

We calculate (12)^2 which is 144, then multiply it by 0.003, which equals 0.432.

Next, we calculate 0.001 times 12, which equals 0.012.

Step 3: Solve for t

Finally, we sum the two products: t = 0.432 + 0.012, resulting in t = 0.444 seconds.

Answer:

The loan will cost you 2000 dollars more.

Step-by-step explanation:

If you pay 200 per month for 60 months, then you are paying 200(60) after the 60 months.

200(60)=12000.

So the loan will cost you 12000.

The difference between paying 12000 and 10000 is 2000.

The loan will cost you 2000 dollars more.

For this case we have that by definition, if two lines are parallel their slopes are equal.

The line given for the following points:

(0,3) and (3, -1). Then the slope is:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}[/tex]

Then, the requested line will be of the form:

[tex]y = - \frac {4} {3} x + b[/tex]

To find "b" we substitute the given point:

[tex]2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2[/tex]

Finally, the line is:

[tex]y = - \frac {4} {3} x-2[/tex]

By manipulating algebraically we have:

[tex]y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6[/tex]

Answer:

Option D

Answer: last option.

Step-by-step explanation:

 The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:

[tex]m=\frac{-1-3}{3-0}=-\frac{4}{3}[/tex]

Since the other line is parallel to this line, its slope must  be equal:

 [tex]m=-\frac{4}{3}[/tex]

Substitute the slope and the point (-3, 2) into [tex]y=mx+b[/tex] and solve for "b":

 [tex]2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2[/tex]

Then, the equation of the other line in Slope-Intercept form is:

[tex]y=-\frac{4}{3}x-2[/tex]

Rewriting it in Standard form, you get:

[tex]y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6[/tex]

Answer:

1/15 or 6.67%.

Step-by-step explanation:

Empirical Probability =  number of red haired people  in the last 60 people  / 60.

= 4/60

= 1/15.

The empirical probability of the next customer at the department store having red hair is approximately 0.0667 or 6.67%, based on the hair color distribution of the previous 60 customers.

The student is asking to determine the empirical probability that the next person to come to the cash register has red hair. Empirical probability is based on actual experiment results and calculated by the number of successful trials divided by the total number of trials.

In this case, the total number of people who went to the cash register is 60. Out of these, 4 people had red hair. Hence, the empirical probability of the next customer having red hair would be 4 out of 60 or 0.0667 when rounded to four decimal places. So, there's approximately a 6.67% chance that the next person to visit the cash register will have red hair assuming that the hair color distribution remains consistent.

https://brainly.com/question/31525380

#SPJ2

Answer:

The length of this altitude is 5 cm.

Step-by-step explanation:

The length of the altitude = ?

Given the diagonal forms the altitude of the parallelogram. The figure is shown in image.

Given

The perimeter of the parallelogram = 50 cm

The length of one side is 1 cm longer than the length of the other.

Thus,

Let one side (a) is x cm, The other side (b) be (x + 1) cm

Perimeter of parallelogram = 2(a + b) = 2(x +(x + 1)) = 4x + 2 = 50 cm

Thus,

x = AB = CD = 12 cm

x + 1 = BC = AD = 13 cm

Using Pythagorean theorem to find the length of the altitude as:

ΔABC is a right angle triangle.

AB² + AC² = BC²

AC² = 13² - 12² = 5 cm

The length of this altitude is 5 cm.

Answer:

The correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

The correct option is missing from the given options:

Option A states that a reflection across the line y = x followed by a reflection across the line yaxis

These transformation map triangle ABC to triangle A'B'C' . So this option is in correct.

Option B states that a reflection across the x-axis followed by a reflection across the y-axis

This option is also incorrect because these transformation map triangle ABC to triangle A'B'C'.

Thus the correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x ....

Answer:

A

Step-by-step explanation:

To solve the problem we will substitute the value of x and C in the given function.

Given to us

The cost​ C, in​ dollars, of renting a moving truck for a day C(x)=0.20x+45,

To find the cost if a person drives x=160 ​miles, simply substitute the value of x in the function of cost c,

[tex]C(x)=0.20x+45\\\\C(160)=0.20(160)+45\\\\C(160)=77[/tex]

Hence, the cost of the moving truck if a person drives x=160 ​miles is $77.

To solve the problem substitute the value of C as 120 in the given function,

[tex]C(x)=0.20x+45\\\\120 = 0.20x+45\\\\x = 375\rm\ miles[/tex]

Hence, If the cost of renting the moving truck is ​$120​, the person​ drives 375 miles.

To solve the problem substitute the value of C as 200 in the given function,

[tex]C(x)=0.20x+45\\\\200 = 0.20x+45\\\\x = 775\rm\ miles[/tex]

Hence, if a person wants the cost to be no more than ​$200. The maximum number of miles a person can​ drive is 775.

Implied Domain is the value of C for which it is defined, since even if the truck is not moving a single mile it will still be costing $45, to a person, therefore, the domain of C is [45, +∞].

If we look at the function it is a function of line therefore, the comparing the two equations,

[tex]y = mx+c\\C=0.20x+45[/tex]

we know that m is the slope of the function,

m = 0.20

therefore, the slope of the function is 0.20.

We know that the intercept of y is the value of y at which it intersect the y axis.

when we put the value of x=0, we get the value of y as 45, therefore, the intercept of y is 45.

Hence, the intercept of y is 45.

Learn more about Line:

https://brainly.com/question/2696693