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Alisiya [41]
3 years ago
15

A frozen yogurt shop offers 10 different flavors of yogurt and 15 different toppings. How many double-dip sundae combinations ca

n be created with 1 topping? One yogurt flavor may be used for both dips.
Mathematics
2 answers:
Radda [10]3 years ago
8 0

Answer:

825

Step-by-step explanation:

To count how many different double-dip sundae combinations exist, we can count first how many combinations exist where the same yogurt flavor is used for both dips, and then count how many combinations exists where different yogurt flavors are used for the two dips, and simply add them together.

Type 1 - Both dips are of the same flavor: In this case we can choose 10 different flavors for our dips flavor, and for EACH of those 10 choices, we have 15 available options for which topping to choose. So the total sundaes of this kind are 10*15=150.

Type 2 - Dips are of the different flavor: In this case we have to choose 2 different flavors for our dips, and we have 10 available flavors for them. So we have to pick 2 flavors out of 10, which can be done in {10 \choose 2}=45 ways. Now, for EACH of those choices, we can pick 15 different toppings, so the total sundaes of this kind are 45*15=675.

Therefore the total number of different sundae combinations that we can choose is 150+675=825.

Aleksandr [31]3 years ago
3 0
25 yogurt dips 
i took this quiz and that was the answer 


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Answer:

30 more bags

Step-by-step explanation:

7 0
3 years ago
HELPPPPPP MEEEEE<br><br> y=6x-1<br><br> and -2x-3y=-2 <br><br><br> USING SUBSTITUTION
bazaltina [42]
Answer:
 x = 4 
y =23 

work:
 plug in the value of Y to -2x-3y=-2. -2x - 3(<span>6x-1) = -2
 
multiply 3 and the numbers in parenthesis. -2x -18x - 3 =-2
combine like terms (-2x -18x). -20x - 3 = -2
subtract 3 from both sides to isolate the variable. -20x = -5 
divide to isolate the variable (-20/-5) x = 4
-
now that we know the value of x, it'll be easy to find Y.
Plug it in to the first equation.
</span><span>y=6(4)-1
</span>y = 24 - 1
y = 23

so x = 4 
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7 0
3 years ago
Help me on these questions
mojhsa [17]

Answer:

a) The equation is (y - 1)² = -8 (x - 4)

b) The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

Step-by-step explanation:

a) Lets revise the standard form of the equation of the parabola with a

   horizontal axis

# (y - k)² = 4p (x - h), (h , k) are the coordinates of its vertex and p ≠ 0

- The focus of it is (h + p , k)

* Lets solve the problem

∵ The focus is (2 , 1)

∵ focus is (h + p , k)

∴ h + p = 2 ⇒ subtract p from both sides

∴ h = 2 - p ⇒ (1)

∴ k = 1

∵ It opens left, then the axis is horizontal and p is negative

∴ Its equation is (y - k)² = 4p (x - h)

∵ k = 1

∴ Its equation is (y - 1)² = 4p (x - h)

- The parabola contains point (2 , 5), substitute the coordinates of the

 point in the equation of the parabola

∴ (5 - 1)² = 4p (2 - h)

∴ (4)² = 4p (2 - h)

∴ 16 = 4p (2 - h) ⇒ divide both sides by 4

∴ 4 = p (2 - h) ⇒ (2)

- Use equation (1) to substitute h in equation (2)

∴ 4 = p (2 - [2 - p]) ⇒ open the inside bracket

∴ 4 = p (2 - 2 + p) ⇒ simplify

∴ 4 = p (p)

∴ 4 = p² ⇒ take √ for both sides

∴ p = ± 2, we will chose p = -2 because the parabola opens left

- Substitute the value of p in (1) to find h

∵ h = 2 - p

∵ p = -2

∴ h = 2 - (-2) = 2 + 2 = 4

∴ The equation of the parabola in standard form is

  (y - 1)² = 4(-2) (x - 4)

∴ The equation is (y - 1)² = -8 (x - 4)

b) Lets revise the equation of the ellipse

- The standard form of the equation of an ellipse with  center (h , k)

 and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1  

- The coordinates of the vertices are (h ± a , k )  

- The coordinates of the foci are (h ± c , k), where c² = a² - b²  

* Now lets solve the problem

∵ Its vertices are (-4 , 4) and (6 , 4)

∵ The coordinates of the vertices are (h + a , k ) and (h - a , k)  

∴ k = 4

∴ h + a = 6 ⇒ (1)

∴ h - a = -4 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 2 ⇒ divide both sides by 2

∴ h = 1

- Substitute the value of h in (1) or (2) to find a

∴ 1 + a = 6 ⇒subtract 1 from both sides

∴ a = 5

∵ The foci at (-2 , 4) and (4 , 4)

∵ The coordinates of the foci are (h + c , k) , (h - c , k)

∴ h + c = 4

∵ h = 1

∴ 1 + c = 4 ⇒ subtract 1 from both sides

∴ c = 3

∵ c² = a² - b²

∴ 3² = 5² - b²

∴ 9 = 25 - b² ⇒ subtract 25 from both sides

∴ -16 = -b² ⇒ multiply both sides by -1

∴ 16 = b²

∵ a² = 25

∵ The equation of the ellipse is (x - h)²/a² + (y - k)²/b² = 1

∴ The equation is (x - 1)²/25 + (y - 4)²/16 = 1

c) How to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

 then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

∵ x² + 4y² - 6x - 7 = 0

∵ The general form of the conic equation is

   Ax² + Bxy + Cy² + Dx + Ey + F = 0  

∴ A = 1 and C = 4

∵ If A and C are nonzero, have the same sign, and are not equal  to

  each other, then the graph is an ellipse.

∵ x² + 4y² - 6x - 7 = 0 ⇒ re-arrange the terms

∴ (x² - 6x ) + 4y² - 7 = 0

- Lets make x² - 6x completing square

∵ 6x ÷ 2 = 3x

∵ 3x = x × 3

- Lets add and subtract 9 to x² - 6x to make the completing square

 x² - 6x + 9 = (x - 3)²

∴ (x² - 6x + 9) - 9 + 4y² - 7 = 0 ⇒ simplify

∴ (x - 3)² + 4y² - 16 = 0 ⇒ add 16 to both sides

∴ (x - 3)² + 4y² = 16 ⇒ divide all terms by 16

∴ (x - 3)²/16 + 4y²/16 = 1 ⇒ simplify

∴ (x - 3)²/16 + y²/4 = 1

∴ The equation of the ellipse is (x - 3)²/16 + y²/4 = 1

5 0
3 years ago
Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.
oksian1 [2.3K]

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

45% chance that the land has oil.

This means that P(A) = 0.45

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that P(B|A) = 0.8

What is the probability that the land has oil and the test predicts it?

This is P(A \cap B). So

P(B|A) = \frac{P(A \cap B)}{P(A)}

P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36

0.36 = 36% probability that the land has oil and the test predicts it

5 0
2 years ago
Rana's computer repair service charges $45/h. Bill's computer repair service charges a flat fee of $25 plus $18/h. Each company
Dmitry [639]

Answer

I not sure but what i would say is b. or if not c.

Step-by-step explanation:

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