You are building a model sailboat. The plans show that the base of the main sail is 9 cm, the bottom acute angle in the sail is 52°, and the distance between the base of the sail and the deck is 2 cm. What is the height of the mast? a. 12.5 cm b. 11.2 cm c. 13.5 cm d. 11.5 cm

Answer:

We have 20% fruit juice and 70% fruit juice.

We need 60 pints of 35% fruit juice.

We set up 2 equations where t is 20% and s is 70%

t + s = 60 pints

.20t + .70s = (.35 * 60)

We solve for both unknowns

t = 42  s = 18

We need 42 pints of 20% and 18 pints of 70 %

**** DOUBLE CHECK *******************************

42 pints of 20% = 8.40 pints of juice 33.6 pints water

18 pints of 70% = 12.60 pints of juice 5.40 pints water

TOTAL mixture = 21 pints juice 39 pints water = 60 total pints

21 pints juice / 60 = .35 (or 35% fruit juice)

Correct !!!

Step-by-step explanation:

Answer:

y = 4x+48

Step-by-step explanation:

Slope intercept form is y=mx+b. We already know the value for m(4), so we can plug in the x and y coordinates for x and y in the equation. This gives us 12=4(-9)+b. Solve for b to get 48

Answer:

the correct answer is

Step-by-step explanation:

side CD is proportional to side GH.

hope this helps you!!!!!

Answer:  c) GH

Step-by-step explanation:

Since it is stated that ₙABCD ≡ ₙEFGH, their letters are in the same position. What letters are in the same position as CD?

A B C D

E F G H

AB ≅ EF

BC ≅ FG

CD ≅ GH

AC ≅ EG

AD ≅ EH

BD ≅ FH

Answer:

$96

Step-by-step explanation:

Use the answer choices and test each one

If you test $96 for the paycheck, it works

96/4 = 24

96/8 = 12

24 + 12 = 36

36 + 24 = 60

This option is right because she spent $60 total

Answer:

margo's pay was $96 dollars

Step-by-step explanation:

Let 'x' represent the amount of Margo's paycheck.  Since she spent 0.25 on a dress, 1/8 (0.125) on shoes and another $24 on a present for a total of $60, we can set up the following equation:

0.25x + 0.125x + 24 = 60

Combine like terms:  0.375x + 24 = 60

Subtract 24 from both sides: 0.375x + 24 - 24 = 60-24 or 0.375x = 36

Divide by 0.375: 0.375x/0.375 = 36/0.375

Solve for x: x = $96

please mark me brainliest :)

Answer:

m = 3

Step-by-step explanation:

It is given that there are two triangles [tex]\triangle[/tex]ABC and

[tex]\triangle[/tex]ABC ~

Also, the sides are:

AB= 3

BC= 4

DE= 2m

EF= m+5 and

∠B≅∠E

Please have a look at the attached figure for [tex]\triangle[/tex]ABC and

The triangles are similar so as per the property of similar triangles, the ratio of corresponding sides will be same.

i.e.

[tex]\dfrac{AB}{DE} = \dfrac{BC}{EF}\\\Rightarrow \dfrac{3}{2m} = \dfrac{4}{m+5}\\\Rightarrow 3 \times (m+5) = 4 \times 2m\\\Rightarrow 3m +15= 8m \\\Rightarrow 5m=15\\\Rightarrow m = 3[/tex]

So, value of m = 3.

Answer:

C.

Step-by-step explanation:

Any equation is always infinite. You plug in values to receive values, and since there is an unlimited amount of numbers and values, the graph of the equation will show infinite solutions to the equation.

You can test this by trying to zoom out of your graphing calc. Notice that you'll never be able to get a definite max or min.

Answer:

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Step-by-step explanation:

8 cos^2 x + 4 cos x-4 = 0

Divide by 4

2 cos^2 x +  cos x-1 = 0

Let u = cos x

2 u^2 +u -1 =0

Factor

(2u -1) ( u+1) = 0

Using the zero product property

2u-1 =0    u+1 =0

u = 1/2      u = -1

Substitute cosx for u

cos x = 1/2    cos x = -1

Take the inverse cos on each side

cos ^-1(cos x) = cos ^-1(1/2)   cos ^-1( cos x) =cos ^-1( -1)

x = pi/2 + 2 pi n                            x = pi + 2 pi n   where n is an integer

x = 5pi /3 + 2 pi n                      

Answer:

Length= 19cm

Width= 9cm

Step-by-step explanation:

let the length of the rectangle be L cm and its width be W cm.

Perimeter of rectangle= 56cm

2L +2W= 56

L +W= 56 ÷2

L +W= 28

L= 28 -W -----(1)

Area of rectangle= length ×width

LW= 171 -----(2)

Susbt. (1) into (2):

W(28 -W)= 171

28W -W²= 171 (expand)

W² -28W +171= 0 (bring everything to one side)

(W -19)(W-9)= 0 (factorise)

W-19=0 or W-9=0

W= 19 or W= 9

Subst into (1):

L=28 -19 or L= 28 -9

L=9 or L= 19

Since we usually take the longer side of the rectangle to be its length, L= 19 and hence W=9.

Therefore its length is 19cm and its width is 9cm.

(x1+x2)÷2

(_5+8)=3÷2=1.5

(y1+y2)÷2

(9+14)=23÷2=11.5

Answer:

B (1.5, 11.5)

Step-by-step explanation:

Answer:

12 units^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

A = 1/2 ( 6 ) * 4

A = 1/2 (24)

    = 12 units^2

Answer:

third one

Step-by-step explanation:

when

x=0,      y=0

x=1,       y=8

x=2      y=0

and so on.

Answer:

C. f(x)= -2x^3 -2x^2 +12x

Step-by-step explanation:

edge 2020

Answer:

Option C is the correct option.

Solution,

Given that,

[tex]f(x) = (x - 8)(x + 3)[/tex]

put f(x)=y

[tex]y(x - 8)(x + 3) - - > equation \: (i)[/tex]

For finding y- intercept

put x=0

We get,

[tex]y = (0 - 8)(0 + 3) - - > from \: {eq}^{n} \: (i)[/tex]

[tex]y = ( - 8) \times 3 \\ y = - 24 \\ y - intercept = (0 ,- 24)[/tex]

hope this helps...

Good luck on your assignment..

Answer:

  $1,500

Step-by-step explanation:

A 2.5% increase in the $60,000 average family income would be required:

  0.025 × $60,000 = $1,500

Your annual income would have to increase by $1,500.

Answer:

35÷7=5

Step-by-step explanation:

we have 7 small boxes in an oval and there are 5 ovals

All the boxes add up to 35

Answer:

B) 35/7 = 5

Step-by-step explanation:

First, I counted the number of groupings, which is 5. That will be our answer, since they circled them.

Then, I counted how many boxes were in each group. 7. That will represent the divisor or the number that we will be dividing by.

If you multiply the numbers, they will equal 35. 5*7=35    Since they are asking which division problem the diagram represents,  35 is the dividend or the number that we start with.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: height of seaweed.

X~N(μ;σ²)

μ= 10 cm

σ= 2 cm

You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

P(X≤x)= 0.30

P(X≥x)= 0.70

Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.

P(Z≤z)= 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

z= -0.52

Now you have to clear the value of X:

Z= (X-μ)/σ

Z*σ= X-μ

X= (Z*σ)+μ

X= (-0.52*2)+10= 8.96

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm

I hope this helps!

Answer:-0.53 and 9.72

Step-by-step explanation:

Answer:

Step-by-step explanation:y–3=½(x+2)

Multiply through by the denominator (2).

2×y–2×3=½(x+2)×2

2y–6=1(x+2) because the denominator (2) will cancel the other 2 multiplying it

2y–6=x+2

2y=x+2+6

2y=x+8

---. -----

2. 2

•°•y=x+8

-----. Or y=x+4

2

Answer:

C, B, A

Step-by-step explanation:

The angles in order of the smallest to the biggest is,

⇒ ∠c < ∠b < ∠a

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle

Now, We will use simple logic to get this done. Looking at the question, we are told that

side AC = m

side BC = m + 4, which means that side BC is longer than side AC

side AB = m - 2, which means that side AB is shorter than side AB

If so, we can say that side AB < side AC < side BC

and if that is true, this means that ∠C which is opposite side AB is < ∠B which is opposite AC and is also ∠A which is opposite BC

∠c < ∠b < ∠a

Thus, The angles in order of the smallest to the biggest is,

⇒ ∠c < ∠b < ∠a

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ7

Answer: Minerals

Step-by-step explanation:

The Mineral belongs to the geosphere option (3) Mineral is correct.

Different definitions of the geosphere have conflicting uses. It can be used to refer to the atmosphere, lithosphere, hydrosphere, and cryosphere as a whole. Different mass and/or energy flows can be exchanged between the various geosphere collectives.

We have a statement:

Which part of Earth belongs to the geosphere?

The options are:

As we know, air belongs to the atmosphere.

Plants belong to the biosphere

Water belongs to the hydrosphere

Mineral belongs to the geosphere

The mineral is the part of the earth that belongs to the geosphere.

Thus, the Mineral belongs to the geosphere option (3) Mineral is correct.

Learn more about the geosphere here:

https://brainly.com/question/5137630

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Answer:

Option B

Step-by-step explanation:

Triangle DEF was rotated 90 degrees counter clockwise to create Triangle D'E'F'.

Answer:

it was b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the money earned during fundraising activities =x

Since the World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation.

The amount of money the foundation will receive

=60% of x

= 0.6x

In the bake sale, the club raised $72.

Therefore, the amount the foundation will receive =0.6*72=$43.20

At the end of the year, the World Issues Club mailed a cheque to the foundation for $850.

Therefore:

0.6x=850

x=850/0.6

x=$1416.67

The total amount of money the club raised is $1416.67.

Answer:

V = 6 cm^3

Step-by-step explanation:

To find the volume you multiply the dimensions of the three sides of the box, length times width times height

The length is 1 cm the width is 2 cm and the height is 3 cm

The units for volume will be cm^3 since we are multiplying cm* cm*cm

V = l*w*h

V = 1*2*3

V = 6 cm^3

Answer:

6 cm³

Step-by-step explanation:

The volume of a box or rectangular prism is l×w×h.

length × width × height

The dimensions of the box are 1cm × 2cm × 3cm

1 × 2 × 3

Multiply the numbers.

= 6

The volume of the box is 6 cm³.

Answer:

x= 70

Step-by-step explanation:

Rectangles have four right angles (angles of 90 degrees).

The point of intersection of the diagonals divides each one of them into two equal parts.

Knowing this, we can conclude that:

m\angle c=m\angle b=55\°

Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":

x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°

Step-by-step explanation:

Use Pythagorean

the ans. is just 9cm, 15cm,12cm

shorter sides are 9cm and 12cm

Answer:  6x + 3.5y > 60

Step-by-step explanation:

Popcorn: cost is $6.00, variable is x

Soda: cost is $3.50, variable is y

Total: GREATER than $60

Popcorn + Soda    >    Total

 6x        +   3.5y    >      60

Answer: B

Step-by-step explanation: The pattern is add 1 vertically, then add one horizontally.

Step-by-step explanation:

We are given here for the random variable X:

P( X > 10.282) = 0.08 and P(X < 9.69) = 0.06

From standard normal tables, we have:

P(Z < 1.405) = 0.92. Therefore P(Z > 1.405) = 0.08

Therefore, the z score of 10.282 is 1.405

Therefore, Mean + 1.405*Std Dev = 10.282

Also from standard normal tables, we have:

P(Z < -1.555) = 0.06

Therefore, Mean - 1.555×Std Dev = 9.69

Subtracting the second equation from first, we get here:

Std Dev(1.405 + 1.555) = 10.282 - 9.69

Std Dev = 0.2

Now the mean can be computed as:

Mean = 1.555*Std Dev + 9.69 = 1.555*0.2 + 9.69 = 10.001

Therefore 10.001 is the required mean and 0.2 is the required standard deviation for the distribution here.

Answer:

  [tex]\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}[/tex]

Step-by-step explanation:

[tex]\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}[/tex]

__

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  log(a^b) = b·log(a)

Answer:

A

Step-by-step explanation:

Just did it on edge2020

Answer:

slope: -9

y-int: 13

Step-by-step explanation:

Answer:

Check the attachment below!

Answer:

Step-by-step explanation:

The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.

Let Y the amount I received for playing. So, we want to calculate the expected value of Y.

We can calculate it as follows

[tex]E[Y] = 2 P(X=1)+ 4 P(X=2)+ 8 P(X =3)  + \dots  = \sum_{n=1}^infty 2^n P(X=n)[/tex]

Since X is a geometric random variable, we have that [tex] P(X=n) = (\frac{1}{2})^{n-1}\frac{1}{2}[/tex]

Then,

[tex] E[Y] = \sum_{n=1}^\infty 2^{n} (\frac{1}{2})^{n-1} \frac{1}{2} = \sum_{n=1}^\infty 2^{n-1} \cdot \frac{1}{2^{n-1}} = \sum_{n=1}^\infty 1 = \infty[/tex]

So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.