Cecilia simplified an expression. Her work is shown below.

Where did Cecilia make her first mistake?

Answer:

C is the correct option

Step-by-step explanation:

To find the probability of P(a or b) we will use  the formula:

P(a or b)= P(a)+ P(b) - P(a-b)

Now put the given values in the formula:

P(a or b)= 0.60+0.25-0.15

P(a or b)=0.85 - 0.15

P(a or b)= 0.70

Thus the correct option is C....

Answer: Option C

[tex]P (A\ or\ B) = 0.70[/tex]

Step-by-step explanation:

If A and B are events that are not mutually exciting, then it is true that:

[tex]P (A\ or\ B) = P (A) + P (B) - P (A\ and\ B)[/tex]

In this case we know [tex]P(A)[/tex], [tex]P(B)[/tex] and we also know [tex]P (A\ and\ B)[/tex]

[tex]P(A)=0.60[/tex]

[tex]P(B) = 0.25[/tex]

[tex]P(A\ and\ B)=0.15[/tex]

Therefore we have that:

[tex]P (A\ or\ B) = 0.60 + 0.25 - 0.15[/tex]

[tex]P (A\ or\ B) = 0.60 + 0.1[/tex]

[tex]P (A\ or\ B) = 0.70[/tex]

The ":" is actually a division, a fraction.

So part a is therefore,

[tex]\dfrac{w}{100}=\dfrac{12}{25}[/tex]

Here we use cross multiplication,

[tex]\dfrac{a}{b}=\dfrac{c}{d}\Longleftrightarrow ad=bc[/tex]

And we have,

[tex]

25w=12\cdot100 \\

w=\dfrac{12\cdot100}{25}=\dfrac{1200}{25}=\boxed{48}

[/tex]

Now part b.

First convert 2m to cm. 1m = 100cm therefore 2m is 200cm.

Now we have simplified to,

[tex]\dfrac{180}{200}=\dfrac{1.8}{2}=\dfrac{\dfrac{18}{10}}{2}=\dfrac{\dfrac{9}{5}}{2}=\boxed{\dfrac{9}{10}=9:10}

[/tex]

Hope this helps.

r3t40

first, lets solve by factoring:

Let's solve your equation step-by-step.

2x2+14x−4=−x2+3x

Step 1: Subtract -x^2+3x from both sides.

2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)

3x2+11x−4=0

Step 2: Factor left side of equation.

(3x−1)(x+4)=0

Step 3: Set factors equal to 0.

3x−1=0 or x+4=0

x=

1

3

or x=−4

we can also solve using the quadratic formula:

2x2+14x−4=−x2+3x

Step 1: Subtract -x^2+3x from both sides.

2x2+14x−4−(−x2+3x)=−x2+3x−(−x2+3x)

3x2+11x−4=0

Step 2: Use quadratic formula with a=3, b=11, c=-4.

x=

−b±√b2−4ac

2a

x=

−(11)±√(11)2−4(3)(−4)

2(3)

x=

−11±√169

6

x=

1

3

or x=−4

lastly, we can complete the square.

2x2+14x−4=−x2+3x

Step 1: Add x^2 to both sides.

2x2+14x−4+x2=−x2+3x+x2

3x2+14x−4=3x

Step 2: Subtract 3x from both sides.

3x2+14x−4−3x=3x−3x

3x2+11x−4=0

Step 3: Add 4 to both sides.

3x2+11x−4+4=0+4

3x2+11x=4

Step 4: Since the coefficient of 3x^2 is 3, divide both sides by 3.

3x2+11x

3

=

4

3

x2+

11

3

x=

4

3

Step 5: The coefficient of 11/3x is 11/3. Let b=11/3.

Then we need to add (b/2)^2=121/36 to both sides to complete the square.

Add 121/36 to both sides.

x2+

11

3

x+

121

36

=

4

3

+

121

36

x2+

11

3

x+

121

36

=

169

36

Step 6: Factor left side.

(x+

11

6

)2=

169

36

Step 7: Take square root.

x+

11

6

=±√

169

36

Step 8: Add (-11)/6 to both sides.

x+

11

6

+

−11

6

=

−11

6

±√

169

36

x=

−11

6

±√

169

36

x=

1

3

or x=−4

Answer:

x=

1

3

or x=−4

Final answer:

The equation [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex] is a quadratic equation, which can be solved by standard methods such as factoring, completing the square, or applying the quadratic formula and then validated by substituting the solutions back into the original equation.

Explanation:

To solve the quadratic equation, [tex]2x^2 + 14x - 4 = -x^2 + 3x[/tex], first combine like terms by getting all terms on one side of the equation, resulting in [tex]3x^2 + 11x - 4[/tex] = 0. This is a standardized quadratic equation [tex]ax^2[/tex] + bx + c = 0. To find the solutions for this equation, you can either factorize it, complete the square or use the quadratic formula, (-b ± √([tex]b^2[/tex] - 4ac)) / (2a). After finding the roots (values for x), verify them by plugging them back into the original equation to ensure they satisfy it.

Answer:

6.68%

Step-by-step explanation:

First find the z-score:

z = (x − μ) / σ

z = (13.30 − 13.00) / 0.2

z = 1.50

Look the value up in a z-score table, or use a calculator.

P(z>1.50) = 1 − 0.9332

P(z>1.50) = 0.0668

6.68% of players on the team run the 100 meter dash in 13.30 seconds or faster.

Answer:

The answer to this question is True

Answer: true

Step-by-step explanation:

Answer:

Option C and D are correct options

Step-by-step explanation:

The correct options are C and D.

We know that i = √-1

i² = -1

i³ = -i

and i^4 = 1

Lets solve the options one by one:

i^6 =1

Break the power:

i² *i ² * i² = (-1)(-1)(-1)

= -1

Therefore A is wrong

B) i^18 = 1

Lets break the power:

i²* i² *i² *i²*i²*i²*i²*i²*i²

put the value of i^2

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)(-1)

= -1

Therefore option B is incorrect.

C) i^7 = -i

= i² * i² *i² *i

=(-1) (-1) (-1) * √-1

= - √-1

We know that √-1 = i

So,

- √-1 = -i

Therefore option C is correct.

D) i^16 = 1

= i² * i² * i² * i² * i² * i² *i² *i²

= (-1) (-1) (-1) (-1) (-1) (-1) (-1) (-1)

= 1

Therefore option D is correct.

Thus option C and D are correct option....

Answer: Option C and Option D

Step-by-step explanation:

Remember that by definition we have to:

[tex]i=\sqrt{-1}[/tex] and [tex]i^2=-1[/tex]

So for the option A we have to:

[tex]i^6=(\sqrt{-1})^2*(\sqrt{-1})^4\\\\i^6=-1*(-1)^2\\\\i^6=-1[/tex]

Option A is false

So for the  option B we have to:

[tex]i^{18}=(i^6)^3[/tex]

We know that [tex]i^6=-1[/tex]

So

[tex]i^{18}=(-1)^3[/tex]

[tex]i^{18}=-1[/tex]

Option B is false

So for the option C we have to:

[tex]i^7=(i)^6*i^1[/tex]

[tex]i^7=-i[/tex]

Option C is true

Finally for the option D we have to:

[tex]i^{16}=(i^4)^4[/tex]

[tex]i^{16}=((-1)^2)^4[/tex]

[tex]i^{16}=(1)^4[/tex]

[tex]i^{16}=1[/tex]

Option D is true

Answer:

(1, 3)

(2, 2)

(3, 1)

Step-by-step explanation:

Substitute x and y with the numbers given

2(1) + 2(3) = 8

2(2) + 2(2) = 8

2(3) + 2(1) = 8

Answer

(1, 3)

(2, 2)

(3, 1)

Answer:

[tex]\frac{1}{x^2y^6}[/tex]

Step-by-step explanation:

We are given [tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex]

First rule I'm going to use is [tex](m^rn^p)^s=m^{r \cdot s}n^{p \cdot s}[/tex].

This gives us:

[tex](xy^3)^2 \cdot (xy^3)^{-4}[/tex] is

[tex](x^2y^6) \cdot (x^{-4}y^{-12})[/tex].

Now pair up the bases that are the same:

[tex](x^2x^{-4}) \cdot (y^6y^{-12})[/tex].

Add the exponents when multiplying if the bases are the same:

[tex]x^{-2} \cdot y^{-6}[/tex]

Now usually teachers don't like negative exponents.

To get rid of the negative exponents just take the reciprocal:

[tex]\frac{1}{x^2} \cdot \frac{1}{y^6}[/tex]

[tex]\frac{1}{x^2y^6}[/tex]

[tex]\huge{\boxed{-\frac{1}{2}}}[/tex]

We can find the slope with [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are both points.

Plug in the values. [tex]\frac{1-(-3)}{-4-4}[/tex]

Simplify. [tex]\frac{1+3}{-4-4}[/tex]

Add/subtract. [tex]\frac{4}{-8}[/tex]

Simplify. [tex]\boxed{-\frac{1}{2}}[/tex]

Answer:

No.

The slope of the line is -1/2.

Step-by-step explanation:

I'll give you a hint, to solve slope of the line use [tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex].

[tex]\displaystyle \frac{1-(-3)}{(-4)-4}=\frac{4}{-8}=\frac{4\div4}{-8\div4}=\frac{1}{-2}=-\frac{1}{2}[/tex]

The slope of the line is -1/2, which is our answer.

I hope this helps!

volume of a cylinder = pi×r^2×h

Answer:

I can increase r and decrease h, or I can decrease r and increase h.

Step-by-step explanation:

answer given in edmentum

Answer:

1. the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. 2x+2.1=7.5

Step-by-step explanation:

Given:

1.

A scalene triangle with sides y, 4y and x

and perimeter,p= 60cm

As per perimeter formula:

p= sum of all sides

Putting values we get

60=x+4y+y

60=x+5y

so correct options are

the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. An isosceles triangle with sides y=2.1, x and x

and perimeter,p = 7.5

As per perimeter formula:

p= sum of all sides

Putting values we get

7.5=2.1 + x +x

7.1=2.1+2x !

Answer:

AB is longer than FD.

Step-by-step explanation:

This is an SAS triangle problem.

According to the law of cosines,

c^2 = a^2 + b^2 - 2abcosC

In triangle ABC, a = BC, b = AC, and c = AB

In triangle FDE, a = DE, b = FE, and c = FD.

The only difference is that C is 72° in one triangle and 65° in the other.

We know that cos0° = 1 and cos 90° = 0, so cos72° < cos65°.

In triangle ABC, cosC is smaller, so you are subtracting a smaller number from a^2 + b^2.

c^2 is larger, so c is larger.

AB is longer than FD.

That makes sense because, as you widen the angle between your outstretched arms, the distance between your hands increases.

The statement which correctly compares AB and FD is AB is longer than FD.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given two triangles, ABC and DEF.

We have to find the relationship between the sides AB and FD.

Given that,

Sides AC and FE are congruent.

Sides BC and DE are congruent.

Included angles, ∠C = 72° and ∠E = 65°

The side opposite to larger angle will be larger.

So AB is longer than FD.

Hence AB is longer than FD.

Learn more about Angles here :

https://brainly.com/question/30381855

#SPJ7

Answer:

This relation is a function.

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have

{(-3, -6), (-1, -6), (5, -6), (8, -6)}

x = -3 → y = -6

x = -1 → y = -6

x = 5 → y = -6

x = 8 → y = -6

YES. This relation is a function.

/each x has one value of y/

Answer: Yes, it is a function

Step-by-step explanation:

Answer:

The equation x+3=9 is true if and only if x=6.

Not enough information.

Step-by-step explanation:

We are looking for a if and only if statement for a bioconditional.

There is only one such choice:

The equation x+3=9 is true if and only if x=6.

We only know information about the triangle's angles, and nothing about their sides.  AAA (angle-angle-angle) is not enough information to conclude congruence.  It is enough for proving it to be similar.  

Out of those 80 counters, 20 counters may have a white dab on them.

Total number of counters in the bag = 200

counters that have a white dab = 50

counters that are now taken out of the bag = 80

Let's first take the ratio of counters that have a white dab to the total number of counters in the bag.

[tex]\rm{=\dfrac{counters\ that\ have\ a\ white\ dab}{Total\ number\ of\ counters\ in\ the\ bag}[/tex]

[tex]=\dfrac{50}{200} = \dfrac{1}{4} = 0.25[/tex]

Therefore, the ratio of counters that have a white dab to the total number of counters in the bag is 0.25.

As the bag is given  a good shake to ensure even distribution of the marked counters.

Those 80 counters will follow the same ratio of the bag, so, the number of tokens with white dab will be,

Number of tokens taken out x ratio of the bag

= 80 x 0.25

= 20

Hence, out of those 80 counters, 20 counters may have a white dab on them.

Learn more about ratio:

https://brainly.com/question/1504221

Answer:

p = 650 – v and 4p + 9v = 2,925 , Its B

https://brainly.com/question/3605037

Answer:

b

Step-by-step explanation:

You need a picture deficiencies did that for 20 characters

Step-by-step explanation:

1 1-5 Measuring Segments Find the distance between two points using the Ruler Postulate Determine the length of a segment using the Segment Addition Postulate.

Answer:

26.

Step-by-step explanation:

We are asked to find the distance between -18 and 8  using the ruler postulate.

The ruler postulate states that the distance between two pints on a ruler is the absolute value of the difference between the numbers shown on ruler.

So the distance between -18 and 8 would be [tex]|-18-8|=|-26|=26[/tex].

Therefore, the distance between -18 and 8 is 26.

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

x ≤ a or x < a - the region below the horizontal line x = a

x ≥ a or x > a - the region above the horizontal line x = a

y ≤ a or y < a - the region on the left side of the vertical line y = a

y ≥ a or y > a - the region to the right of the vertical line y = a

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

We have dotted line (<, >).

The vertical line (y).

The region on the left side of the vertical dotted line y = -3

Answer:

36

Step-by-step explanation:

I think it may be 36. I did 6×6, but I'm not fully positive

There are 720 different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster.

To calculate the number of different arrangements in which the 6 friends can sit in the 6 seats of the rollercoaster, we can use the concept of permutations.

Since each friend occupies one seat and no two friends can occupy the same seat, we have 6 choices for the first seat, 5 choices for the second seat, 4 choices for the third seat, and so on until 1 choice for the last seat.

So, the total number of arrangements is the product of these choices:

[tex]\[ 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

Answer:

Domain [-5,3)

Range [0,2]

Step-by-step explanation:

Domain is where the function exists for the x's.

The graph starts at x=-5 and ends at x=3. The graph includes what happened at x=-5 but not at x=3. Since there are no breaks in the graph, the graph exists for x values bigger that or equal to -5 but less than 3.

The domain is [-5,3) in interval notation.

Range is very similar except it is for the y values. So the graph starts at y=0 and stops at y=2. It includes something happening at both and there are no breaks between y=0 and y=2.

The range in interval notation is [0,2].

The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3), therefore, the domain is [-5,0). The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2), therefore, the range is [0,2].

Domain is nothing but the value of x in the equation (y = f(x)) and range is nothing but the value of y in the equation (y = f(x)).

So, from the given graph there are two values of 'x' at which the graph of the function gets started and ends.

The values are (x = -5) and (x = 3). But the graph includes what happened at (x = -5) but not (x = 3). Therefore, the domain of the given graph is:

[tex]x\; \epsilon\;[-5,3)[/tex]

Similarly, there are two values of 'y' at which the graph of the function gets started and ends.

The values are (y = 0) and (y = 2) and the graph includes what happened at (y = 0) and (y = 2). Therefore, the range of the given graph is:

[tex]y\; \epsilon\;[0,2][/tex]

For more information, refer to the link given below:

https://brainly.com/question/2263981

Answer:

HL

SAS

SSS

Step-by-step explanation:

Since these are right triangles, and you have the two hypotenuses are congruent to each other and two legs that are also congruent to each other, then HL can be applied.

For HA to work we must have been given something else about one of those angle (besides the 90 degree one).

Since you have two corresponding sides that are congruent, then the 90 degree angles in both are congruent, and then the sides right after that 90 degree angle are also congruent to each other, so SAS can be applied.

We can't use AAS.  We only know something about one angle per each triangle due to the markers.

LA? Needed another angle besides the 90 degree one.

All three corresponding sides are congruent. The markers tell us this. So we can apply SSS.

Answer:

HL

SAS

SSS

Step-by-step explanation:

Answer:

[tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

To find the slope of a line using two points, employ the use of the slope formula.

[tex]\frac{y_{2}-y_{1}}{x_{2}- x_{1}}[/tex]

Your y1 term is -2, your y2 term is -3.

Your x1 term is -3, your x2 term is 0.

[tex]\frac{-3-(-2)}{0-(-3)} \\\\\\\frac{-3+2}{0+3} \\\\\frac{-1}{3} \\[/tex]

Answer:

"number line with open circles on negative 9 and 5, shading going in the opposite directions."

Step-by-step explanation:

Your inequality doesn't include an equal sign so there will be no closed holes. It will only be open holes.

|u|>14 means that the number u has to be greater than 14 or less than -14.  These numbers I describe just now all have a distance greater than 14 from 0.

So |u|>14 implies u>14 or u<-14.

But we are solving |2x+4|>14 so this implies we have 2x+4>14 or 2x+4<-14.

2x+4>14

Subtract 4 on both sides:

2x    >10

Divide both sides by 2:

x      >5

2x+4<-14

Subtract 4 on both sides:

2x    <-18

Divide both sides by 2:

x      <-9

So our solution is x>5 or x<-9.

Graphing!

~~~~~~~O                                         O~~~~~~~~

-----------(-9)---------------------------------(5)---------------

So we shaded to the right of 5 because our inequality says x is bigger than 5.

We shaded to the left of -9 because our inequality says x is less than -9.

Answer:

1

Step-by-step explanation:

We are to find the value of the following:

[tex] log _ 3 5 \times log _ { 2 5 } 9 [/tex]

[tex] \log _ { 3 } 5 \times \log _ { 2 5 } 9 =\dfrac{1}{\log_{5}3}\times\log_{25}9=\dfrac{1}{\log_{5}3}\times\log_{5^2}9=\dfrac{1}{\log_{5}3}\times\dfrac{1}{2}\log_{5}9[/tex]

[tex] \dfrac { 1 } { \log _ { 5 } 3 } \times \dfrac { 1 } { 2 } \log_ { 5 } 9 = \dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=[/tex] 1

Answer:

The value is: 1

Step-by-step explanation:

Use the Change of base formula. This is:

[tex]log_a(x)=\frac{log_b(x)}{log_b(a)}[/tex]

Using base 10:

[tex]log_3(5)*log_{25}(9)=\frac{log(5)}{log(3)}*\frac{log(9)}{log(25)}[/tex]

We know that:

[tex]9=3^2\\25=5^2[/tex]

And according to the logarithms properties:

[tex]log(x)^n=nlog(x)[/tex]

Then, we can simplify the expression:

[tex]=\frac{log(5)}{log(3)}*\frac{log(3)^2}{log(5)^2}=\frac{log(5)}{log(3)}*\frac{2log(3)}{2log(5)}=\frac{log(5)}{log(3)}*\frac{log(3)}{log(5)}=\frac{log(5)*log(3)}{log(3)*log(5)}=1[/tex]

Answer:

Step-by-step explanation:

The point-slope of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the poinys (-1, -10) and (5, 2). Substitute:

[tex]m=\dfrac{2-(-10)}{5-(-1)}=\dfrac{12}{6}=2[/tex]

Put the value of the slope and the coordinateso f the point (5, 2), to the equation of a line:

[tex]y-2=2(x-5)[/tex]

In the question we have y - 6 = ...

Therefore

[tex]y-2=2(x-5)[/tex]    subtract 4 from both sides

[tex]y-6=2(x-5)-4[/tex]          use the distributive property

[tex]y-6=2x-10-4[/tex]

[tex]y-6=2x-14[/tex]      distributive

[tex]y-6=2(x-7)[/tex]

Answer:

1,440

Step-by-step explanation:

1.5 percent of 96k

Answer:

B. 3x3+6x−2

Step-by-step explanation:

When you divide 3x3+6x−2 by x+1 we get a remainder of -11.

Answer:

Step-by-step explanation:

Josh has to drive at least 6 hours.                 d≥ 6 Answer 2

Amelia walking 35 min or less                       b ≤ 35 Answer 3

Nancy < 35 hours = part time                         y < 35 Answer 1

Sarah at least 6 hours math                           f > 6 Answer 4