Consider a single spin of the spinner. Which events are mutually exclusive? Choose all that apply. a)landing on a shaded sector and landing on a number greater than 3
b)landing on a shaded sector and landing on a 3
c)landing on a shaded sector and landing on an even number
d)landing on an unshaded sector and landing on a number less than 2
e)landing on an unshaded portion and landing on an odd number

Answer:

see below

Step-by-step explanation:

y=x^2-4x-12

Set equal to 0 to find the zeros

0 =x^2-4x-12

Factor.  What 2 numbers multiply to -12 and add to -4

-6*2 = -12  

-6+2 = -4

0= (x-6) (x+2)

Using the zero product property

0=x-6         0 = x+2

x=6            x = -2

zeros: -2,6

Vertex

h = -b/2a = - (-4)/ 2(1) = 4/2 = 2

OR  Average the roots  (-2+6)/2 = 4/2 =2

The y coordinate is found by substituting into the equation

y = (2)^2 -4(2) -12

y = 4-8-12

y =-16

vertex : (2, -16)

Answer:

x = -2, 6

Vertex: (2,-16)

Step-by-step explanation:

x² - 4x - 12

x² - 6x + 2x - 12

x(x - 6) + 2(x - 6)

(x - 6)(x + 2) = 0

x = -2, 6

h = -(-4)/2

h = 4/2

h = 2

k = 2² - 4(2) - 12

k = 4 - 8 - 12

k = -16

Vertex: (2,-16)

Answer:

C = 12 pi

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

36 pi = pi r^2

Divide each side by pi

36 = r^2

Take the square root of each side

sqrt(36) = sqrt (r^2)

6 =r

We can find the circumference

C = 2 * pi *r

C = 2* pi *6

C = 12 pi

Answer:

first option

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Since the 3's are the same on either side, you need to find a number that, when multiplied by 9, yields 18. The only number that satisfies that is 2, which is the answer. Hope this helps!

A set of data will not always have a mode.

A mode is defined as the value that appears the most often in a set.

For instance, a set of 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6 would have a mode of 4, as it appears more often than any other number in the set.

However, a set of 1, 2, 3, 4, 5, 6 has no mode as there is no number that appears more than other numbers in the set.

Answer:

sin 70= x/8

Step-by-step explanation:

Opposite of 70 degrees is x and the hypotenuse is 8.

Sin is opposite over hypotenuse

Therefore, sin 70=x/8

Answer:

Step-by-step explanation:

because you go with you first answer bc its going to be right

Answer:

+30 + -25

Savings is positive

Buying is negative

Step-by-step explanation:

We save 30 dollars

+30

We buy a game for 25

-25

+30 -25

Savings is positive

Buying is negative

Answer:

C) 4 (5+3)

Step-by-step explanation:

Answer:

(x + y)(x² - xy + y²)(x + 1)

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + xy³ + x³ + y³ ( factor out x from the first 2 terms )

= x(x³ + y³) + 1(x³ + y³) ← factor out (x³ + y³) from each term

= (x³ + y³)(x + 1)

x³ + y³ is a sum of cubes and factors as (x + y)(x² - xy + y²)

Thus

[tex]x^{4}[/tex] + xy³ + x³ + y³ = (x + y)(x² - xy + y²)(x + 1)

Answer:

the hotel is four blocks west from the bus; the bus is four blocks east from the hotel.

The bus is 4 blocks east of the hotel.

Since a sightseeing bus picks up a group of tourists at a hotel, and it then travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, to determine where the bus is in relation to the hotel, the following calculation must be carried out:

Therefore, the bus is 4 blocks east of the hotel.

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Answer:

b = 9

Step-by-step explanation:

A= 30°      a = 3[tex]\sqrt{3x}[/tex]

B =            b =

C = 90°     c =

find B first

90 + 30 = 120

180 - 120 = 60

B = 60°

Now, let's find b

use the Law of Sines

[tex]\frac{sin A}{a} = \frac{sin B}{b} \\\frac{sin 30}{3\sqrt{3} } = \frac{sin 60}{b}\\b = \frac{3\sqrt{3} sin 60 }{sin 30}\\b = 9[/tex]

Answer:

Length of the other side of the backyard is 80.4 feet.

Step-by-step explanation:

Let the dimensions of the Liam's rectangular backyard = 85 feet × a feet

Diagonal of the rectangle, AD = 117 feet

When we apply Pythagoras theorem in ΔABD,

AD² = AB² + BD²

(117)² = (85)² + BD²

a² = 13689 - 7225

a = √6464

  = 80.399 feet

a ≈ 80.4 feet

Therefore, length of the other side of the backyard is 80.4 feet.

Answer:

the answer is C

Step-by-step explanation:

Answer:

1,000,000,000 as a power of 10, is: 10^12

Step-by-step Solution:

We can expand 1,000,000,000, and write this number as a multiplication sentence using only the number 10. By doing this, we can count the number of tens needed to be multiplied to get to his answer:

1,000,000,000 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10  

Since 10 is multiplied by itself 12 times, we can therefore say that 10^12 is equal to 1,000,000,000

Answer:

10^12 (10 to the 12th power)

Step-by-step explanation:

10 to the twelth power would basically be 10x10x10x10x10x10x10x10x10x10x10x10

This equals 1,000,000,000,000, which is one trillion.

Answer:

Area =  

b1 + b2  ×h

2

=  

10 + 10  × 10

2

=  100 feet2

Step-by-step explanation:

Final answer:

The percent increase in the price of iceberg lettuce is 140%.

Explanation:

To find the percent increase, we need to calculate the difference between the price at which iceberg lettuce is grown and shipped and the price at which consumers purchase it, and then divide that difference by the original price and multiply by 100.

Let's start by finding the difference:

Difference = Consumer price - Production price

Difference = 120 cents - 50 cents = 70 cents

Now, let's calculate the percent increase:

Percent Increase = (Difference / Production price) * 100

Percent Increase = (70 cents / 50 cents) * 100 = 140%

Answer:

Option D

Step-by-step explanation:

Given: set of inequalities

To find: Points which do not satisfy all the inequalities

Solution:

For point [tex](15,0)[/tex]:

[tex]15\leq 30-3(0)=30\\15\geq 15-0=15\\15\leq 25-0=25\\15\geq 0\\0\geq 0[/tex]

So, (15, 0) satisfies all the inequalities

For point [tex](7.5,7.5)[/tex]:

[tex]7.5\leq 30-3(7.5)=30-22.5=7.5\\7.5\geq 15-7.5=7.5\\7.5\leq 25-7.5=17.5\\7.5\geq 0\\7.5\geq 0[/tex]

So, (7.5, 7.5) satisfies all the inequalities

For point (22.5,2.5):

[tex]22.5\leq 30-3(2.5)=30-7.5=22.5\\22.5\geq 15-2.5=12.5\\22.5\leq 25-2.5=22.5\\22.5\geq 0\\2.5\geq 0\\[/tex]

So, (22.5,2.5) satisfies all the inequalities

For point (7.5 ,0):

Put s = 7.5 and t = 0 in [tex]s\geq 15-t[/tex]

[tex]7.5\geq 15-0=15[/tex] which is false

So, [tex](s,t)\neq (7.5,0)[/tex]

Answer:

D.

Step-by-step explanation:

Answer:

I think its -120m

Step-by-step explanation:

Coz negatives are less than positives

Answer:

See below in bold.

Step-by-step explanation:

(x - 1)(x^2 + 1)

= x(x^2 + 1) - 1(x^2 + 1)

= x^3 + x - x^2 - 1

= x^3 - x^2 - x - 1.

Leading coefficient = 1.

Constant term = -1.

Degree = 3.   (because of the x^3).

If the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,

(x - 1)(x² + 1)

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

=(x - 1)(x²+ 1)

= x(x² + 1) - 1(x² + 1)

= x³ + x - x² - 1

= x³ - x² - x - 1.

From the expression the obtained result is,

Leading coefficient = 1

Constant term: -1

Degree: 3

Thus, if the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.

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Answer:

[tex]x=7[/tex]

[tex]y=3[/tex]

Step-by-step explanation:

Considering the system of equations:

[tex]$\left \{ {{-2x + 3y = -5} \atop {2x + 4y = 26}} \right. $[/tex]

[tex]$\left \{ {{ 3y = -5} \atop {4y = 26}} \right. $[/tex]

[tex]7y=21\\y=3[/tex]

[tex]2x + 4(3) = 26\\2x + 12 = 26\\2x=14\\x=7[/tex]

Answer:

80%

Step-by-step explanation:

75% + 20% - 15% = 80%

The probability is 80%

The probability that he or she buys a shirt or a pair of pants is 80%.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that in a clothing store, 75% of the customers buy a shirt, 20% of the customers buy a pair of pants, and 15% of the customers buy both the shirt and a pair of pants.

The percentage of customers who buy only shirt = 75% - 15% = 60%

The percentage of customers who buy only pant= 20% - 15% = 5%

The percentage of customers who buy both = 15%

Now, the probability that he or she buys a shirt or a pair of pants is,

Probability = 60% + 5% + 15% = 80%

Hence, the probability that he or she buys a shirt or a pair of pants is 80%.

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Answer:

height = 5

Step-by-step explanation:

If area = (1/2)bh, the equation would be 25 = (1/2)10h.

The first step I'd do is multiply both sides by 2 to get rid of the (1/2). So, now the equation is 50 = 10h.

Divide both sides by 10, and you get h = 5! :D

Answer:

Step-by-step explanation:

Given:

A= 25

b=10

Find the height:-

[tex]\sf A=0.5\:bh[/tex]

[tex]\sf 25=0.5(10)h[/tex]

[tex]\sf 25=5h[/tex]

[tex]\sf 5h=25[/tex]

[tex]\sf \cfrac{5h}{5}=\cfrac{25}{5}[/tex]

[tex]\sf h=5[/tex]

Hope it helps!

Answer:

x = -4

Step-by-step explanation:

x - 8 = 3x

First, subtract x from both sides:

x - 8 = 3x

-x        - x

________

-8 = 2x

Then, divide both sides by 2:

-8 = 2x

-4 = x

Answer:

C. 120°

Step-by-step explanation:

There are two paralell lines, one is part of Angle B, and the other of Angle Q. Then there is a diagonal line, coming at the same angle from B all the way to Q, because the other two lines are paralell. It basically means if you were to slide the flat line which is connected to Q up the diagonal line, it would fit perfectly with it's parallel. So the two angles; Angle B and Angle Q; are the exact same.

Hope this helped! Good luck with future math problems :)

Answer:

The answer for this question is 120 degrees

Step-by-step explanation:

Answer:

<ADC = 131

Step-by-step explanation:

< ADC = <ADB + < BDC

The large angle is the sum of the two smaller angles.

<ADC = 89+42

          =131

Answer:

131 degrees

Step-by-step explanation:

The reason for, is since <ADC is equal to < ADB + <BDC and that we already know the values of <ADB and <BDC, we can simply do

89 + 42 = 131.

So, <ADC is 131 degrees.

:)

Answer:

Ok so the way i see it lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40.  If it isn't to much can you give me brainliest? if not a simple thanks will do!!!

~~ Night

Answer: lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40. Brainliest?

Answer:

i think it would be 28.26

Step-by-step explanation:

because C=2 pie r and D=2 r (solving for C=pie d =pie . 9 = 28.27433 then just round and thats how you get 28.27 (sorry if its confusing) (im not good at explaining but i am smart)

Answer:

Ernie has a greater range

The statement "the medians are equal" is true for the given table of data about playing a game by Ernie and Lori. This is obtained by calculating the mean, median, mode, and range of the data elements of each.

Given data sets for Ernie and Lori as follows:

Ernie: {18, 24, 17, 19, 17} and Lori: {16, 22, 18, 14, 18}

The number of elements in both the data sets is equal and it is 5

Calculating Mean:

For Ernie: {18, 24, 17, 19, 17}

Mean=(18+24+17+19+17)/2

        =19

For Lori: {16, 22, 18, 14, 18}

Mean=(16+22+18+14+18)/2

        =17.6

Thus, their "means are not equal". (3rd statement is false)

Calculating Median:

For Ernie: {18, 24, 17, 19, 17}

Re-arranging the data - 17, 17, 18, 19, 24

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

For Lori: {16, 22, 18, 14, 18}

Re-arranging the data - 14, 16, 18, 18, 22

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

Thus, their "medians are equal". (first statement is true)

Calculating Mode:

The most occurring number in Ernie: {18, 24, 17, 19, 17} is 17 and

The most occurring number in Lori: {16, 22, 18, 14, 18} is 18

Thus, their modes are not equal, and "Lori has the greater mode".

(4th statement is false)

Calculating Range:

The range for Ernie's data set is 24 - 17=7

The range for Lori's data set is 22 - 14=8

Thus, their ranges are also not equal but "Lori has the greater range".

(2nd statement is false).

Therefore, 1st statement - " the medians are equal" is true.

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