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Elanso [62]
3 years ago
5

Rita has 6 cups of frosting. She plans to use 2/3 of it to decorate cakes. How many cups of frosting will rita use to decorate c

ake?
Mathematics
1 answer:
DENIUS [597]3 years ago
6 0
She's going to use 2/3 of the frosting(6 cups) to decorate cakes. 'of' means multiplication. So we can multiply to figure it out:

\sf\dfrac{2}{3}\times 6

\sf\dfrac{12}{3}

\sf\boxed{\sf 4}

So Rita will use 4 cups of frosting to decorate cakes.
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The number line represents −4 1/2+3 1/4. What is the sum?
rjkz [21]

Answer:

C

Step-by-step explanation:

Rbrberbrb

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3 years ago
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A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hu
castortr0y [4]

<em>Answer: h = 120 ft;    w = 80 ft </em>

<em></em>

<em>A = 9600 ft^2</em>

<em />

<em>Step-by-step explanation: Let h and w be the dimensions of the playground. The area is given by:</em>

<em></em>

<em>A = h*w   (eq1)</em>

<em></em>

<em>The total amount of fence used is:</em>

<em></em>

<em>L = 2*h + 2*w + w    (eq2)    (an extra distance w beacuse of the division)</em>

<em></em>

<em>Solving for w:</em>

<em></em>

<em>w = L - 2/3*h = 480 - 2/3*h   (eq3)  Replacing this into the area eq:</em>

<em></em>

<em></em>

<em></em>

<em>We derive this and equal zero to find its maximum:</em>

<em></em>

<em>   Solving for h:</em>

<em></em>

<em>h = 120 ft.  Replacing this into eq3:</em>

<em></em>

<em>w = 80ft</em>

<em></em>

<em>Therefore the maximum area is:</em>

<em></em>

<em>A = 9600 ft^2</em>

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5 0
3 years ago
If you multiply me by 5 and subtract 6 from me you get 14. what number am I.<br>​
damaskus [11]

Answer:

tje answer is 4

Step-by-step explanation:

4x5=20

20-6=14

5 0
4 years ago
Use the given information to answer the following questions. center (3, -9, 3), radius 5 (a) Find an equation of the sphere with
lianna [129]

Answer: The equation of the sphere with the center and radius

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

Step-by-step explanation:

a) The equation of the sphere having center (h,k,l) and radius r is

(x-h)^{2} +(y-k)^2+(z-l)^2 = r^2

Given center of the sphere  (3, -9, 3) and radius 5

(x-3)^{2}+(y+9)^2+(z-3)^2 = 5^2

on simplification , we get solution

x^{2} -6 x+9+y^{2} +18 y+81+z^{2}-6 z+9=25

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

Final answer :-

x^{2} +y^{2} +z^{2}-6 x+18 y-6 z+74=0

b) The intersection of this sphere with the y z-plane the x- co-ordinate

is zero(i.e., x = 0 )

y^{2} +z^{2}+18 y-6 z+74=0

7 0
3 years ago
A center for medical services reported that there were 295,000 appeals for hospitalization and other services. For this group, 4
pshichka [43]

Answer:

a) 0.0025 = 0.25% probability that none of the appeals will be successful.

b) 0.0207 = 2.07% probability that exactly one of the appeals will be successful.

c) 0.9768 = 97.68% probability that at least two of the appeals will be successful

Step-by-step explanation:

For each appeal, there are only two possible outcomes. Either it is succesful, or it is not. The probability of an appeal being succesful is independent of other appeals, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

45% of first-round appeals were successful.

This means that p = 0.45

Suppose 10 first-round appeals have just been received by a Medicare appeals office.

This means that n = 10

(a) Compute the probability that none of the appeals will be successful.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.45)^{0}.(0.55)^{10} = 0.0025

0.0025 = 0.25% probability that none of the appeals will be successful.

(b) Compute the probability that exactly one of the appeals will be successful.

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{10,1}.(0.45)^{1}.(0.55)^{9} = 0.0207

0.0207 = 2.07% probability that exactly one of the appeals will be successful.

(c) What is the probability that at least two of the appeals will be successful

This is P(X \geq 2)

Either less than two appeals are succesful, or at least two are. The sum of the probabilities of these events is decimal 1. So

P(X < 2) + P(X \geq 2) = 1

P(X < 2) = P(X = 0) + P(X = 1) = 0.0025 + 0.0207 = 0.0232

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0232 = 0.9768

0.9768 = 97.68% probability that at least two of the appeals will be successful

6 0
3 years ago
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