7. For the piecewise defined function {f(x)=1 x<3
{1/2x+7 x_>3
(1) 7
(2) 10
3x-1 x<3
[//x+7 _x23²)
(3) 17
(4) 27
which of the following is the value of f(6)?

Answer:

t=1.33333 seconds

Step-by-step explanation:

1. We are give the the position function, s(t). We must differentiate s(t) twice in order to find the acceleration function, a(t).

s(t) = t⁶-2t⁵

Taking the power rule to differentiate s(t), we find the velocity function, v(t).

v(t) = d/dt (t⁶-2t⁵)

v(t) = 6t⁵-10t⁴

Differentiate v(t) using the power rule again to find the acceleration function, a(t).

a(t) = d/dt (6t⁵-10t⁴)

a(t) = 30t⁴-40t³

2. To find the other t value where acceleration is equal to zero, we must set a(t) to zero.

a(t) = 30t⁴-40t³ = 0

3. Algebraically solve for t. Factoring out 10t³ from a(t), we have:

10t³(3t-4)=0

Our solutions are t=0 and t=4/3.

The other value of t when acceleration is equal to zero is 4/3, or 1.33333 seconds.

The value of x and y in the similar triangles are 10 and 12 respectively.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In other words, similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other

The triangles ABC and MPN are similar triangles.

Therefore,

∠A = ∠M

∠B = ∠P

∠C = ∠N

Hence, let's find x and y using the proportion as follows:

[tex]\frac{AB}{MP}=\frac{BC}{PN}=\frac{AC}{MN}[/tex]

Hence,

PN = y

MP = x

Therefore, let's find x

[tex]\frac{9}{6}=\frac{15}{x}[/tex]

cross multiply

9x = 90

x = 90 / 9

x = 10

Let's find y

[tex]\frac{9}{6}=\frac{18}{y}[/tex]

cross multiply

9y = 108

y = 108 / 9

y = 12

learn more on similar triangles here: https://brainly.com/question/12757954

#SPJ1

Answer:

5 : (1/4) = 201 = 20

Step-by-step explanation:

Answer: Area of triangle=30 cm²

Step-by-step explanation:

Let's name the triangle ABC.

Assuming these are the 3 sides of the triangle, and naming them a,b,c.

a=5 cm

b=13 cm

c=12 cm

Semi perimeter of the triangle ABC= s = (a+b+c)/2

s=(5+13+12)/2 =30/2=15.

Area of triangle ABC= √(s * (s-a)*(s-b)*(s-c)

                                  =  √(15*(15-5)*(15-13)*(15-12)

                                  =  √15*10*2*3

                                  = √150*6

                                  =√900

                                   =30 cm²

Area of triangle ABC = 30 cm².

The number of different codes available is 4500 unique codes

What is digit?
A positional numeral system uses a single symbol, such as "2," or a combination of symbols, such as "25," to represent numbers. This single symbol is known as a numerical digit. The word "digit" derives from the fact that ten fingers (Latin: digiti) on each hand correspond to the ten numeral symbols used in the base-10 system, or decimal digits (Old Latin: decem, meaning "ten"). The absolute value of the base determines how many different digits are necessary for a given numeral system with just an integer base. For instance, the binary system (base 2) only needs two digits, whereas the decimal system (base 10) necessitates ten digits (0 through 9). (0 and 1).

The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

There are nine options because the first digit cannot be 0. (assuming 1 can be the first digit as well as all others)

There are 10 options for the second digit, third digit, fourth digit, and fifth digit.

4 digits must be odd, giving you 5 options (1,3,5,7,9)

9*10*10*5=4500 unique codes

Hence, there are 4500 unique codes available

To learn more about Combination click on the link

https://brainly.com/question/11732255

#SPJ1

The possible number is 10 which is a product of 2, 5, 10

LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is defined as the least common multiple. It is also known as the Least Common Divisor (LCD). For example, LCM (4, 5) = 20. In this case, the LCM 20 is divisible by both 4 and 5, so 4 and 5 are referred to as the divisors of 20.

Given numbers 2, 5, 10

We have to find the number which is produced by the given numbers

Now we have to find the LCM of these numbers

LCM of 2, 5, 10

2 = 2 x 1

5= 5 x 1  

10 = 2 x 5

= 1x 2 x 5

= 10

The LCM of 2,5,10 is 10

Therefore 10 is the required number which is a product of 2, 5, 10

To learn more about LCM visit

https://brainly.com/question/24510622

#SPJ1

The sub's regular selling price, if it represents a 20% markdown is $3.75

option D.

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability. The precise value that corresponds to the unit price paid is represented by the cost price.

The amount a buyer pays for a good or service is known as the selling price. Depending on the price that consumers are prepared to pay, the seller is willing to take, and how competitive the price is in relation to other companies in the market, it may change.

Given,

ALGEBRA Diego's Subs is offering $0.75 off its foot-long meatball sub.

Then, C.P-S.P= 0.75

S.P-C.P= 0.75

And also given that it represents 20% mark down.

Then,

((C.P-S.P)/C.P)×100=% mark down

((C.P-S.P)/C.P)×100=20%

(0.75×100)/C.P=20

C.P=75/20

C.P=$3.75

Therefore, the sub's regular selling price is $3.75

So, the answer is option D

To know more about cost price and selling price, visit:

https://brainly.com/question/28017453

#SPJ1

The correct answer or scientific notation when 3.185× 10¹⁷ is divided by 9.1×10⁸ is 3.46×10⁸ and multiplying  3.185× 10¹⁷ with 9.1×10⁸  is 2.9×10²⁶.

It is given in the question that 3.185× 10¹⁷ is divided by 9.1×10⁸

we can write 3.185×10×10¹⁶ which equals 31.5×10¹⁶.

Now dividing 31.5×10¹⁶ by 9.1×10⁸ we get 3.46×10⁸.

Now multiplying  3.185× 10¹⁷ with 9.1×10⁸ we get 28.98×10²⁵

Converting 28.98×10²⁵ in scientific notation we get 2.9×10²⁶.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation and known as standard form in the UK .

In scientific notation, a representation of a number that is a power of ten can also be written with equal ease. Additionally, you'll see that the amount of zeros in a regular decimal expression is exactly equal to the power to which 10 is raised.

Any time a number is expressed in words, it must first be written down as a regular decimal number before being converted. "Ten million" becomes "10,000,000" and vice versa.Ten million is written in powers of ten notation because there are seven zeros in all.

To know more about 'scientific notation' related questions

visit- https://brainly.com/question/28876255

#SPJ9

The mean of the number of plants (d) increases by 5.5

From the question, we have the table of values that can be used in our computation:

In the table, we have the following rows

Plants and Number of tomatoes

The mean of the number of plants is calculated as

Mean plant = Total number of tomatoes/Total number of plants

For the four plants, we have

Total number of tomatoes = 31 + 25 + 6 + 28 =  90

Total number of plants = 4

Substitute the known values in the above equation So, we have the following equation

Mean plant = 90/4

Mean plant = 22.5

For the three plants, we have

Total number of tomatoes = 31 + 25 + 28 =  84

Total number of plants = 3

Substitute the known values in the above equation So, we have the following equation

Mean plant = 84/3

Mean plant = 28

See that the difference is an increment of

Increment = 28 - 22.5

Evaluate

Increment = 5.5

Hence, the mean increases by 5.5

Read more about mean at

https://brainly.com/question/14532771

#SPJ1

The number of additional red marbles to be added to the total 24 marbles present in the bag is 16 marbles.

What is Probability?

From the question, it is given that the,

Number of Red marbles = 8

Number of Yellow marbles = 9

Number of Green marbles = 7

So, the total number of marbles = 8 + 9 + 7 = 24

Let [tex]x[/tex] be the additional number of red marbles added to the bag.

The total number of red marbles after the addition of [tex]x[/tex] red marbles into the bag = [tex]8+x[/tex]

The total number of all marbles after the addition of [tex]x[/tex] red marbles into the bag = [tex]24+x[/tex]

The probability of randomly drawing a red marble is given as equal to [tex]\frac{3}{5}[/tex]

We know that, the probability of randomly drawing a red marble is equal to the ratio of the total number of red marbles to the total number of all marbles.

---> P(R) = n(R)/n(T)

Substituting the given values, we get

3/5 = 8+x / 24+x
---> 5(8+x) = 3(24+x)
---> 40 + 5x = 72+3x

Solving, we get

5x - 3x = 72 - 40
---> 2x = 32
---> x = 16

Therefore, the additional number of red marbles to be added to obtain the required probability is equal to 16.

To learn more about the probability from the given link

https://brainly.com/question/13604758

#SPJ1

Answer: 16

Step-by-step explanation:

To *increase* 24 in the ratio 2:3

To *increase* a quantity in given ratio consider new quantity and old quantity.

Formula: New quantity:old quantity=given ratio solution: let us take the new quantity as x, old quantity as 24(given) and given ratio=2:3(given)

-> x:24=2:3

-> x/24=2/3

-> Multiply with 24 on both sides to get x

-> 24*x/24=2/3*24

-> x=16

So, the *increase* of 24 in the ratio 2:3 is 16

To know more about *increase* of number in given ratio

https://brainly.in/question/20179533?utm_source=android&utm_medium=share&utm_campaign=question

Answer:

Step-by-step explanation:

Find the equation of p(x) using table.

We see it is a proportional relationship, therefore:

Conveyor belt2: p(x) = 62.8x

As we see 157.1 > 62.8 which means conveyor 1 belt is faster.

Answer:

The conveyor belt 1 is faster.

Step-by-step explanation:

Speed of conveyor belt 1,

→ m(x) = 157.1x

Now the speed of conveyor belt 2,

→ p(x) = x

→ p(125.6) = 2x || p(188.4) = 3x

→ x = 125.6/2 || x = 188.4/3

→ [ p(x) = 62.8 ] || [ p(x) = 62.8 ]

Then the fastest conveyor is,

→ m(x) = 157.1x > p(x) = 62.8

→ 157.1x > 62.8

→ Conveyor 1 > Conveyor 2

Hence, the conveyor belt 1 is faster.

86.135 is the IQ score separating the bottom 25% from the top 75%.

The number between a data set's lowest and median is known as the first quartile. We would utilize a Z table to locate it.

As we are looking on the left side of distribution, value of z-score will be negative.

z-score equation for x : [tex]z = \frac{x-M}{S}[/tex]

                                       [tex]x = zS+M[/tex]

where x = value we're looking for

M = Mean

   = 99.2

S = Standard deviation

  = 19.5

z = z-score

  = -0.67

Putting the value in equation,

x = -0.67*19.5 + 99.2

  = -13.065 + 99.2

  = 86.135

Hence, 86.135 is the IQ score separating the bottom 25% from the top 75%.

To learn more about IQ score here:

https://brainly.com/question/13185136

#SPJ1

Answer:

Step-by-step explanation:

divide by R

Answer:

Step-by-step explanation:

4.75 x 32=152

2,456.75+152=2608.75

Answer:

2608.75

Step-by-step explanation:

4.75 x 32 = 152

2456.75 + 152 = 2608.75

The slope-intercept definition of the linear function is given as follows:

y = x + 2.

The slope-intercept representation of a linear function is obtained by the rule presented as follows:

y = mx + b.

The coefficients of the function, along with their meaning, are shown as follows:

For this problem, the values of these coefficients are given as follows:

Hence the slope-intercept rule for the function is:

y = x + 2.

The graph of the linear function is given by the image shown at the end of the answer.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

Domain: (-∞, +∞)

Range: [2, +∞)

Step-by-step explanation:

Domain is the "allowable x-values/inputs"

Range is the "possible y-values/outputs when the x-values in the domain are inputted".

From the graph, notice how each end of it extends infinitely to the left and to the right. This means that the domain is infinite and there are no restrictions. Writing it in interval location would look like this:

(-∞, +∞)

Also, notice how the y-values increase from the vertex but do not go below it. That suggests that the range is "lower-bounded" to the vertex, and increases infinitely. Writing it in interval location would look like this:

[2, +∞)

A equation of line with a slope of -7/16 passes through the point (-16, 7) is y = (-7/16)x

We know that the formula for the slope-point form of equation of line:

(y - y1) = m(x - x1)

Let (x1, y1) = (-16, 7)

and slope m = -7/16

Using above formula,

(y - 7) = (-7/16)(x - (-16))

y - 7 = (-7/16)(x + 16)

y = -7/16x - 7 + 7

y = (-7/16)x

This equation is slope-intercept form (y = mx + c) with slope -7/16 and y-intercept 0.

Therefore, a equation of line with a slope of -7/16 passes through the point (-16, 7) is y = (-7/16)x

Learn more about equation of line here:

https://brainly.com/question/21511618

#SPJ9

The probabilities in this problem are given as follows:

The probabilities for each strike are given as follows:

The probabilities are independent, meaning that for each trial they are the same.

Thus the probability that your first strike was a critical hit but not your second strike is obtained as follows:

P = 0.33 x 0.67 = 0.2211 = 22%. (rounded).

Damage is caused with two consecutive critical hits, hence:

p = 0.33 x 0.33 = 0.11 = 11%.

The final probability, that your strike was not critical but your next 2 attacks were, is obtained as follows:

p = 0.67 x 0.33 x 0.33 = 0.07 = 7%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

(-6,4)

Step-by-step explanation:

add the equations together to equal

2y=8

y=4

now solve for x

3x+10(4)=22

3x+40=22

3x=-18

x=-6

Answer:

(-6,4)

Step-by-step explanation:

add the equations together to equal

2y=8

y=4

now solve for x

3x+10(4)=22

3x+40=22

3x=-18

x=-6

Answer:

y = 0.25x³

Step-by-step explanation:

Since y is directly proportional to x³, then y = kx³, where k is a constant.

When x = 10, y = 250,

   250 = k(10)³

1000k = 250

    ∴ k = 0.25

∴ y = 0.25x³

The slope is -5/3

From the question, we have

slope, m = change in y/change in x

= (-6+1)/(8-5)

=-5/3

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Slope of a Line :

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.

where "m" represents a line's slope.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

To learn more about slope of a line visit: https://brainly.com/question/16180119

#SPJ1

Answer: (6, 0)

Step-by-step explanation:

Plug each coordinate in and see if the equation holds true.

At (6,0), [tex]4(6)-5(0)=24[/tex].

So (6, 0) is a solution of the equation.

Answer:

1.y=-16

2.y=-10

3.y=-4

4.y=2

hope ut helps!

have a nice night

Jenni wrote the converse statement properly, however the statement is false, hence the correct option with a counter example is:

Yes; two angles that each measure 41°.

A conditional statement is written as follows:

p -> q.

In which the terms of the conditional statement are listed as follows:

In this problem, the statement is:

If angles are right angles, then the angles have the same measure.

Hence the terms is:

For the converse statement, the hypothesis and the conclusion are exchanged, hence:

q -> p.

Thus the converse of Jenni's statement is:

If two angles have the same measure, then they are right angles.

Which means that she wrote the converse statement properly.

However, the angles do not necessarily need to measure 90º, they only need to have the same measure, hence the correct option is:

Yes; two angles that each measure 41°.

The complete problem is:

Jenni wrote a conditional statement and its converse.Conditional: If angles are right angles, then the angles have the same measure.Converse: If angles have the same measurement, then they are right angles.Did Jenni write the converse statement properly? Give a counterexample to dispute the validity of the converse statement.No; two angles that each measure 45°Yes; two angles that each measure 90°Yes; two angles that each measure 41°No; two angles that each measure 82°.

More can be learned about converse statements at https://brainly.com/question/4421013

#SPJ1

Answer: 13500%

Step-by-step explanation:

73+62=135

135 to make a percentage you would multiply 135 times 100=13500%

I think thats right

The correct vocabulary for the definition is Commutative.

Commutative property states that the result remains the same even if the order of the numbers are changed during operation.

For multiplication,

[tex]a*b=b*a[/tex]

Thus, the correct vocabulary for the definition is Commutative.

To learn more about commutative property refer here

https://brainly.com/question/778086

#SPJ9

The probability that the spinner would land on a number that is not between 16 and 25 as required in the task content is; 13 / 15.

It follows from the task content that the probability that the spinner would land on a number that is not between 16 and 25, inclusive be determined.

Since the spinner contains 1 through 75, the number of event in the sample space is; 75 events.

Also, the number of events between 16 and 25, inclusive is; 10.

Therefore, the number of events outside 16 through 25 is; 75 - 10 = 65.

Therefore, the required probability that the spinner would land on a number that is not between 16 and 25 is;

= 65 / 75

= 13 / 15.

Therefore, the required probability is; 13 / 15.

Read more on probability;

https://brainly.com/question/25839839.

#SPJ1

Answer:

Step-by-step explanation: