To make 7 bowls of punch, you need 5 bottles of soda. How many bottles do you need to make 12 bowls of punch?

Answer:

As per the given condition:  Rodrigo has a ladder that is 13 ft long. The ladder is leaned against a vertical wall. The top of the ladder is 10.8 ft above the ground.

The Orientation of the ladder with the wall forms a right triangle.  

The ladder length is the hypotenuse of the triangle,

the distance between the ladder at ground level and the base of the wall is the horizontal leg of the triangle,

and the height of the ladder is the vertical leg of the triangle.

⇒ Height of the ladder = 10.8 ft and hypotenuse = 13 ft

Using sine ratio formula;

[tex]\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse side}}[/tex]

Opposite side = height of the ladder = 10.8 ft and

Hypotenuse side = 13 ft.

then;

[tex]\sin \theta = \frac{10.8}{13} =0.830769230769[/tex]

or

[tex]\theta = \sin^{-1}(0.830769230769)[/tex]

Simplify:

[tex]\theta = 56.2^{\circ}[/tex] (nearest to tenth place)

Since, it is given that the angle the ladder makes with the ground needs to be 60 degree or less for safety purposes.

(a)

Yes, this ladder in a safe position.

as [tex]\theta = 56.2^{\circ} < 60^{\circ}[/tex]

(b)

You can see the diagram as shown below in the attachment.

The new dimensions are 6.75 inches by 9 inches

The dimensions of the new photo if, Sandra has a photo that is 9 inches by 12 inches, and The scale factor is 3 / 4, is 6.75 inches by 9 inches.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.

Given:

Sandra has a photo that is 9 inches by 12 inches,

The scale factor is, s = 3 / 4

Calculate the dimensions of the new photo as shown below,

The length = 9 × 3 / 4

The length = 27 / 4

The length = 6.75 inches,

The width of photo = 12 × 3 / 4

The width of the photo = 36 / 4

The width of the photo = 9 inches

Thus, the dimensions of the new photo will be 6.75 inches by 9 inches.

To know more about scale factors:

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The fromula of a slope:

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

We have A(4, 3) and m = 3.

(0, 3)

[tex]\dfrac{3-3}{0-4}=0\neq3[/tex]

(5, 0)

[tex]\dfrac{0-3}{5-4}=\dfrac{-3}{1}=-3\neq3[/tex]

(3, 0)

[tex]\dfrac{0-3}{3-4}=\dfrac{-3}{-1}=3\qquad CORRECT[/tex]

(0, 0)

[tex]\dfrac{0-3}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}\neq3[/tex]

Vertical angles are opposite each other when two lines intersect and are equal. Linear pairs of angles are adjacent angles that form a straight line and their sum is always 180 degrees. The difference lies both in their position and their angle sum.

So, in sum, the difference lies in their positioning (vertical angles are opposite, linear pair angles are adjacent) and in their sum (vertical angles are equal, linear pair angles sum to 180 degrees).

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In order to better find the points on this graph, we need to convert it from standard form to slope-intercept.

We can do that by solving for y.

-7y + 8 = 21x - 6

Subtract 8 from both sides.

-7y = 21x - 14

Divide both sides by -7

y = -3x + 2

Now that the equation is in slope-intercept, we can find two points on the line.

We know that (0, 2) will be the first point, because 2 is the y-intercept.

We can plug 1 into the x value of the equation to find the corresponding y value.

y = -3(1) + 2

y = -3 + 2

y = -1

The second point is (1, -1)

It's the linear function.

The slope-intercept form: y = mx + b.

-7y + 8 = 21x - 6      subtract 8 from both sides

-7y = 21x - 14     divide both sides by (-7)

y = -3x + 2

We need only two points:

for x = 0 → y = -3(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = 2 → y = -3(2) + 2 = -6 + 2 = -4 → (2, -4)

Problem 13

10p+10q factors to 10(p+q). If we apply the distributive property, we can distribute the 10 to each term inside (p and q) to get

10(p+q) = (10 times p)+(10 times q) = 10*p + 10*q = 10p+10q

so we get the original expression again. Here 10 is the GCF of the two terms.

--------------------------------------------------------------

Plug p = 1 and q = 2 into the factored form

10*(p+q) = 10*(1+2) = 10*(3) = 30

As a check, let's plug those p,q values into the original expression

10*p+10*q = 10*1+10*2 = 10+20 = 30

We get the same output of 30

Answer:

12 total picks, 4 green and 8 orange

Step-by-step explanation:

green(g)=4

orange(O)=2g

since g=4,

O=2(4)

O=8

8+4=12

note that +(-) is equivalent to -

thus the equation can be written as

n - 11 = 24 ( add 11 to both sides )

n = 24 + 11 = 35

"More" means you're adding. So the problem would look like this...

3t + 4

I hope this is what you're looking for. :)

positive correlation

plz rate me

Answer:

Hello! I believe that this will help you find the line best fit.  

Step-by-step explanation:

Remember, for it to be a line best fit, you must find the two points that you think will be on the "line best fit".

Answer: D

Step-by-step explanation:

   y = x² - 8x + 5

  -5                -5

y - 5 = x² - 8x           complete the square by adding [tex](\frac{-8}{2})^{2}[/tex] to both sides

y - 5 + 16 =  x² - 8x + 16      the right side is a perfect square:  (x - 4)²

y + 11 = (x - 4)²

    -11            -11

y        = (x - 4)² - 11

Answer:

The solution in the attached figure

Step-by-step explanation:

we have

[tex]50q+43 > -11q+70[/tex]

Solve for q

Adds 11 q both sides

[tex]50q+43 +11q > 70[/tex]

[tex]61q+43 > 70[/tex]

Subtract 43 both sides

[tex]61q > 70-43[/tex]

[tex]61q > 27[/tex]

Divide by 61 both sides

[tex]q > \frac{27}{61}[/tex]

The solution is the interval ------> (27/61,∞)

All real numbers greater than 27/61

In a number line the solution is the shaded area at right of 27/61 (open circle)

Answer:

Her commission on that sale is $3,498

Step-by-step explanation:

1. You have the following information given in the problem above:

- She sells the house for $159,000.

- Her rate of commission is 2.2% (0.022).

2. Therefore, to solve this problem you only need to multiply $159,000 by 2.2% (0.022), as following:

[tex](159,000)(0.022)=3,498[/tex] dollars

2 1/9 divided 2/3 = 19/6 OR 3 1/6

3/5 divided 1 1/4 = 12/25

7 9/16 divided 2 3/4 = 11/4 OR 2 3/4

Answer:

2 1/9 divided 2/3 = 19/6 OR 3 1/6

3/5 divided 1 1/4 = 12/25

7 9/16 divided 2 3/4 = 11/4 OR 2 3/4

Step-by-step explanation:

Set the polynomial equal to each other.

x2 - 2x - 5 = x3 - 2x2 - 5x - 9

Move all the terms to the right side of the equation to make the left side equal to zero.

0 = x3 - 3x2 - 3x - 4

Now we use synthetic division to factor.

4 |  1       -3        -3           -4

                4         4             4

___________________________

       1       1          1            0

0 = (x - 4)(x2 + x + 1)

Now you can set the factors equal to zero and solve for x.   Since the quadratic factor has no real solutions, we ignore and focus on the linear factor. x = 4

Evaluate any of the function when x=4 to get the y-coordinate of the intersection point.

Answer:

The answer is 0.8 so A

Step-by-step explanation:

To find the time it takes for the area to be at least 5 times its original size, we need to solve an equation involving the rates of increase for the length and width of the rectangle. The original area is 32 km² and the rates of increase are both 3 km/sec. By substituting these values into the equation and solving for time, we can determine the answer.

To determine how long it takes for the area A to be at least 5 times its original size, we first need to find the original area and then solve for the time it takes for the area to reach 5 times that value.

The original area is equal to the length multiplied by the width, so it is A = 4 km * 8 km = 32 km².

Let's denote the rate at which the length and width increase as dl/dt and dw/dt respectively. We know that dl/dt = dw/dt = 3 km/sec.

To find the time it takes for the area to be 5 times its original size, we need to solve the equation 32 + 3l(t) * 3w(t) = 5 * 32, where l(t) and w(t) are the length and width at time t.

Simplifying the equation, we get 9lw - 160 = 0.

Since we're given the rates at which l and w increase, we can substitute l and w with their formulas: l(t) = 4 + 3t and w(t) = 8 + 3t.

Substituting these formulas into the equation, we get 9(4 + 3t)(8 + 3t) - 160 = 0.

Solving this equation will give us the value of t, which represents the time it takes for the area to be at least 5 times its original size.

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Step 1.  Subtract 4y from both sides

5y + 18 - 4y = -3.2

Step 2. Simplify 5y + 1.8 -4y to y + 1.8

y + 1.8 = -3.2

Step 3. Subtract 1.8 from both sides

y = -3.2 - 1.8

Step 4. Simplify -3.2 - 1.8 to -5

y = -5

Your answer is A.

[tex]5y+1.8=4y-3.2\qquad|\text{subtract 1.8 from both sides}\\\\5y=4y-5\qquad|\text{subtract 4y from both sides}\\\\\boxed{y=-5}\to\boxed{a.}[/tex]

C. 26 degrees Celsius

Answer:

The temperature on the thermometer is 26°C

Step-by-step explanation:

The image is very clear.

To answer this question you need to know the scale of the thermometer.

As between 20 and 30 there are 5 "spaces" (four lines) , we should divide

10 (the difference between 30 and 20) by 5.

10/5= 2

So each line means 2 °C

As there are 3 lines painted in red after 20, the answer is:

20+3*2= 26°C

The truth value for the following conditional i.e., conjunction statement P is false and Q is true is False.

Answer:

Step-by-step explanation:

This conditional statement:

Has a truth value of true if:

And has a truth value of false, if

Then, for this statements:

As both p and q are true, then, this statement is true.

As p is true and q is false, this statement is false.

As p is false, this statement is true, no matter the truth value of q.

∼p its the negation of p. if p is true, then ∼p is false. And this statement is true, no matter the truth value of q.

The volume of the cone can be calculated using fofmula

[tex]V=\dfrac{1}{3}\cdot b\cdot h,[/tex] wher b is the area of the base and h is the hieght.

Multiply the whole equation by 3:

[tex]3V=b\cdot h.[/tex]

Divide this equation by b:

[tex]h=\dfrac{3V}{b}.[/tex]

Answer: [tex]h=\dfrac{3V}{b}.[/tex]

We rearranged the equation v=1/3bh to solve for h, the height of the cone, by first multiplying by 3 to cancel the 1/3 and then dividing by b, resulting in h=3v/b.

The question is asking to Solving for Variable for h in the formula v=1/3bh, where v is the volume of a cone, b is the base area, and h is the height.

To find h, we need to rearrange the equation by first multiplying both sides by 3 to cancel out the 1/3 in front of bh.

So, it becomes 3v=bh.

Then, we divide both sides by b to isolate h, which gives us h=3v/b.

So the height of the cone is h=3v/b.

Learn more about Solving for Variable here:

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we know that

distributive property of multiplication over addition:

[tex]a \times (b+c)=a \times b + a \times c[/tex]

now, we will verify each options

option-A:

3 × (4 + 5) = (3 × 4) + (3 × 5)

We can see that both sides match with property

so, this is TRUE

option-B:

3 × (4 + 5) = (3 + 4) × (3 + 5)

We can see that right side does not match with property

so, this is FALSE

option-C:

3 × (4 + 5) = (3 × 4) + 5

We can see that right side does not match with property

so, this is FALSE

In the binomial development, the main problem is calculation of binomial coefficients.

If we want to get term a∧8*b∧2 we see that this is the third member in binomial development (n 2) a∧n-2*b∧2

The given binomial  is ((1/3)a∧2 - 3b)∧6, the first element is (1/3)a∧2, the second element is (-3b) and n=6 when we replace this in the formula we get

(6 2) * ((1/3)a∧2)∧(6-2) * (-3b)2 = (6*5)/2 * ((1/3)a∧2)∧4 *9b∧2= 15*(1/81)*9 *(a∧8b∧2) =

= 15*9* a∧8b∧2 = 135*a∧8b∧2

We finally get numerical coefficient 135

Good luck!!!

The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] is -45/16.

The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] can be found using the binomial theorem, which states that [tex](x+y)^n = \sum (n choose k) x^(^n^-^k^) y^k[/tex] where the sum is from k=0 to n. Here, x = [tex](1/3)a^2[/tex], y = -3b, and n = 6.

In the term [tex]a^8*b^2, a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power. Hence, we are looking for the coefficient in the term in the binomial expansion where [tex](1/3)a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power.

This can be calculated by multiplying together the coefficient '6 choose 4', the 4th power of [tex](1/3)a^2[/tex], and the 2nd power of -3b.

That leads to coefficient =[tex](6 choose 4)*((1/3)^4)*(-3)^2 * a^8 * b^2[/tex]. After calculation this simplifies to -45/16.

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A=wl

32 times 28=  896

i converted the feet and inches into just inches btw

Answer:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Step-by-step explanation:

Let's rewrite the table:

Time (seconds) Height (feet)

0 0

0.5 16

1 24

1.25 25

1.5 24

2 16

2.5 0

By simply looking at the table, we can see that the following statements are all correct:

- Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet

- The ball rises by 16 in the first half second, but only 8 feet over the next one

- After it reaches 25 feet in the air, the ball drops

- The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

y=7 and x=-3c

Tell me if i got it wrong!