three coins are flipped
what is the probability of getting no heads ?
What is the probability of getting at least two tails
PLEASE HELP

Answer:

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Step-by-step explanation:

We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:

cos(C) =  a2 + b2 − c22ab

cos(A) =  b2 + c2 − a22bc

cos(B) =  c2 + a2 − b22ca

Answer:

Law of cosines, two sides and the included angle known

Step-by-step explanation:

double check that the question is exactly the same to make sure you get the question correct

"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."

Answer:

a)16      (2*2*2*2= 16)

b)16  (-4*-4-16)(-+-=+)

c)500 (5*5*5=125        125*4=500)

d)0.49  (0.7*07)

e)480  (4^=16     9^=81  121^0=1          16+81 -1 =96     96*5=480)

f)5^2  or 25 (a^m/ a^n=a^m-n)

g) 11^14 (reason same as the f one)

h)8.20

i) 4(-4*16=64)

j)900

The question is not typed properly! Complete question along with answer and step by step explanation is provided below.

Question:

Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .

You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to

a. 118

b. 118/100=1.18

c. 118/√100= 11.8

d. cannot be determined

Answer:

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Step-by-step explanation:

From the given information,  

The population mean SAT critical reading score is

[tex]\mu = 495[/tex]

The population standard deviation is

[tex]\sigma = 118[/tex]

You choose an SRS of 100 students and average their SAT Critical Reading score.

[tex]n = 100[/tex]

Since the sample size is quite large then according to the central limit theorem,

The mean sample will be the same as the population mean  SAT critical reading score.

[tex]\bar{x} = \mu = 495[/tex]

The standard deviation of the sample would be  

[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]

The correct option is (c)

Therefore, the standard deviation of the average scores you get will be close to 11.8

Answer:

X = 275 + 95p

Step-by-step explanation:

Hello,

This question requires us to write an expression to find how much he would've saved over a certain period of time.

Initial deposit = $275

Franklin's monthly deposit = $55

Franklin grandmother's deposit = $40

Let the amount he would've saved over a certain period of time p = x

X = 275 + (55 + 40)p

X = 275 + 95p

Eg, how much would he have saved in 5 months

X = 275 + 95(5)

X = 275 + 475

X = $750

I.e in 5 months, he would've saved $750

Answer:

C

Step-by-step explanation:

Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2 × opp = 21 ( divide both sides by 2 )

opp = [tex]\frac{21}{2}[/tex]

Now consider the right triangle on the right, using the cosine ratio

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C

Hey there! :)

Answer:

6x³ + 14x² + 6x - 12.

Step-by-step explanation:

Given:

(2x² + 6x + 6)(3x - 2)

Multiply each term in the first polynomial by both terms in the second:

3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =

6x³ + 18x² + 18x - 4x² - 12x -12 =

Combine like-terms:

6x³ + 14x² + 6x - 12.

Answer:

-4

Step-by-step explanation:

y = -4x + 6 is the equation and -4 is the slope

Answer: A

Step-by-step explanation:

2x²-2x-9=0

this is a quadratic equation so we will use the quadratic formula .

 Δ= b²-4*a*c

let's calculate Δ to khow how many solutions this equations have .

 Δ= (-2)²-4*2*(-9)

    = 76

 we notice that 76>0

so this equation has two solutions :  (-b-√76)/4 and (-b+√76)/4

the trick here is to notice that :

[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]

      = [tex]\sqrt{19} *\sqrt{4}[/tex]

      = 2[tex]\sqrt{19}[/tex]

Now we will simplify Δ by factoring by 2

so the answer is a .

Answer:

Step-by-step explanation:

Fist let's have a look :

Now the first question : What is the size x ?

The second question : what is the size of y ?

The trick is to khow the situation where we have  corresponding angles

Answer:

He will have 13 packages containing 3 pairs of headphones and 1 music player each.

Step-by-step explanation:

He has 39 pairs of headphones and 13 music players.

He wants to sell both set of items in identical packages.

To do this he has to divide them in such a way that the same number of both set of objects are in every box.

Let us find the ratio of the pairs of headphones to music players:

39 : 13 = 3 : 1

Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.

So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.

Answer:

  -63

Step-by-step explanation:

Compare ...

  f(x) = x^2 -3x +18

to the standard form ...

  f(x) = ax^2 +bx +c

and you will see that ...

  a = 1, b = -3, c = 18.

__

The value of the discriminant is ...

  d = b^2 -4ac

  d = (-3)^2 -4(1)(18) = 9 -72 = -63

The discriminant is -63.

Answer:

JL = 32

Step-by-step explanation:

We are told in the above question that:

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

From the attached diagram, we can see that

JL : JK = JK: JM

Therefore,

JL/ JK = JK /JM

Where JL = Unknown

JK = 24

JM = 18

JL/ 24 = 24/18

Cross Multiply

24 × 24 = JL × 18

Divide both sides by 18

JL = (24 × 24) /18

JL = 576/18

JL = 32

Answer:

its G(2)

Step-by-step explanation:

Gg

Answer: 48

Step-by-step explanation:

The share of sand in the mixture is 3/7

To make 112 kgs. of concrete, he will need

3/7 x 112 = 48 units of sand

Answer:

solution,

Ratio of cement:sand:aggregate

=1:3:3

Total of ratios=1+3+3

=7

Total concrete=112 kg

Amount of sand required:

[tex] \frac{ratio \: of \: sand}{total \: ratio} \times amount \: of \: concrete \\ = \frac{3}{7} \times 112 \\ = 48 \: kg[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer:

g(-5)=-25

Step-by-step explanation:

Answer:

a = 2/27

b = 13/27

Step-by-step explanation:

The given polynomial is presented as follows;

f(x) = a·x³ + b·x² + x + 2/3

Given that x + 3 is a factor, we have;

f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0

-27·a + 9·b - 3 + 2/3 = 0

-27·a + 9·b = 7/3........(1)

Also we have

(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5

Therefore;

a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5

-8·a + 4·b - 2 + 2/3 = 5

-8·a + 4·b = 2 - 2/3 = 4/3........(2)

Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;

-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3

-8·a + 12·a = 8/27

4·a = 8/27

a = 2/27 ≈ 0.0741

imputing the a value in equation (1) gives;

-27×2/27 + 9·b = 7/3

-2 + 9·b = 7/3

9·b = 7/3 + 2 = 13/3

b = 13/27 ≈ 0.481.

Answer:

Uncle is 34. Nephew is 10.

Step-by-step explanation:

Let u equal the age of the uncle, and n equal the age of the nephew.

First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:

[tex](u-2)+(n-2)=40[/tex]

[tex]u+n-4=40[/tex]

[tex]u+n=44[/tex]

Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:

[tex]u+2=3(n+2)[/tex]

We now have a system of equations and can solve accordingly.

First, from the first equation, we can determine that:

[tex]u=44-n[/tex]

We can substitute this into the second equation.

[tex](44-n)+2=3(n+2)[/tex]

[tex]46-n=3n+6[/tex]

[tex]40=4n[/tex]

[tex]n=10[/tex]

Thus, the nephew's age is 10.

And the uncle's age is 44-10 or 34.

Answer:

y ≥ -2/3x +3

Step-by-step explanation:

incline is -2/3

and intercept with y-axis is 3

so the equation of the line is

y = -2/3x +3

Since the intended area in the graph I above the line, we now know enough to find the right one question:

y ≥ -2/3x +3

Answer: y>-2/3x+3 because the line is dotted its >

Answer:

190 Baseballs

Step-by-step explanation:

Since he put 304 baseballs into 8 trash cans with an equal amt. in each,

--> we do 304/8 to find how much baseballs we put in each

=> 304/8 = 38

Now, we takes 5 of these 38 trash cans filled with balls to the field

--> we would do 5 x 38 => 5 x 38 = 190

and Thus, we have our answer of 190 baseballs

Hope this helps!

Answer:

Step-by-step explanation:

[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]

Answer: the answer is A

Step-by-step explanation:

Answer:

JL ≈ 32  

Step-by-step explanation:

The triangle JKL  has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.

Let us find side the angle J first from the  triangle JKM. Angle JMN is 90°(angle on a straight line).

using the cosine ratio

cos J = adjacent/hypotenuse

cos J = 18/24

cos J = 0.75

J = cos⁻¹ 0.75

J = 41.4096221093

J ≈ 41.41°

Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore,  180 - 41.41 - 90 = 48.59

Angle L = 48.59 °.

Using sine ratio

sin 48.59 ° = opposite/hypotenuse

sin 48.59 ° = 24/JL

cross multiply

JL sin 48.59 ° = 24

divide both sides by sin 48.59 °

JL = 24/sin 48.59 °

JL = 24/0.74999563751

JL = 32.0001861339

JL ≈ 32  

Answer:

C, D, and F

Step-by-step explanation:

The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

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]

We have a cubic or third-degree polynomial:

F(x) = x³ - 6x² + 7x - 2

To find the all possible roots of the cubic polynomial

By using the trial and error method:

Plug x = 1

F(1) = 1 - 6 + 7 - 2

F(1) = 8 - 8

F(1) =0

x = 1 is one of the roots of the polynomial.

We can write the cubic polynomial in the factored form:

F(x) = (x - 1)(x² -5x + 2)

We have a quadratic polynomial:

= x² -5x + 2

To find the roots of the quadratic polynomial use the quadratic formula:

a= 1, b = -5, and c =2

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]

After solving:

x = (5+√17)/2

x = (5-√17)/2

Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ5

Answer:

Step-by-step explanation:

graph attached

Answer:

graph y

Step-by-step explanation:

We can solve for the y-intercepts of both f(x) and h(x) by plugging in 0 as x. f(0) = -6(0)-3 = -3

h(0) = -2cos(pi)-1 = -2(-1)-1  = 1

So the y-intercept of f(x) is -3 and of h(x) is 1. We can then conclude that h(x) has a greater y-intercept than f(x) because 1>-3.

Answer:

equilateral

acute

Step-by-step explanation:

equilateral = all equal angles

acute = all angles less than 90

Answer:

D. Equilateral

Step-by-step explanation:

An equilateral triangle is a three sided shape with sides of the same size. Since all the sides in the image are 9cm, it is considered as an equilateral triangle.

Hope this helps

Answer:

ZX = 1.3 in

EG = 3.0 in

M∠X = 48°

M∠G = 25°

Step-by-step explanation:

As we can see in the attached figure that these two triangles are identical i.e their corresponding sides and angles are equal

Therefore if we say that

ZX = EF

So ZX = 1.3 in.  

Now the same is applied for other sides and angles

EG = XY

So, EG = 3.0 in

M∠X = M∠E

hence, M∠X = 48°

For the M∠ G,

The angle is

= 180° - 107° - 48°

= 25°

Hence, the M∠ G is 25°

Answer:

zero residual equals zero mean

A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.

The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.

Answer:

Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.

Answer:

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

Step-by-step explanation: