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nalin [4]
3 years ago
7

When preparing the cheese for their pizzas, the cooks at Brian's pizza restaurant mix 1 kilogram of Parmesan cheese and 9 kilogr

ams of mozzarella. At Jeff's pizza restaurant, the cooks mix 2 kilograms of Parmesan cheese and 16 kilograms of mozzarella. Which restaurant uses a lower ratio of Parmesan to mozzarella?
Brian's restaurant
Jeff's restaurant
neither; the ratios are equivalent
Mathematics
1 answer:
Vilka [71]3 years ago
6 0
Jeff's Restaurant uses less because if you simplify both of the ratios you get 1/9 and 1/8
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Can someone help me.​
cestrela7 [59]

Answer:

X=11

Step-by-step explanation:

To find x-intercept/zero substitute h(x)=0

0=x-11 move the variable to the left hand side and change it's sign

-x=-11 change the signs on both sides of the equation

x=11

4 0
3 years ago
The owner of a bike shop sells unicycle and bicycles and keeps inventory by counting seats and wheels. One day she counts 20 sea
Mashcka [7]
A unicycle has 1 wheel. u unicycles have u wheels.

A bicycle has 2 wheels. b bicycles have 2b wheels.

In u unicycles and b bicycles, there are a total of
u + 2b wheels.

We are told there are 28 wheels, so u + 2b must equal 28.

The answer is choice C. u + 2b = 28
8 0
3 years ago
Read 2 more answers
What is the common point between lines y = ½ x + 4 and y = x – 4?
nirvana33 [79]
1/2X+4=X-4
1/2X+8=X
8=1/2X
16=X

(Pick one of the equations )
y=1/2X+4
y=(1/2)(16)+4
y=12

point: (16,12)
7 0
3 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
The combined math and verbal scores for students taking a national standardized examination for college admission, is normally d
kipiarov [429]

Answer:

The minimum score that such a student can obtain and still qualify for admission at the college = 660.1

Step-by-step explanation:

This is a normal distribution problem, for the combined math and verbal scores for students taking a national standardized examination for college admission, the

Mean = μ = 560

Standard deviation = σ = 260

A college requires a student to be in the top 35 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?

Let the minimum score that such a student can obtain and still qualify for admission at the college be x' and its z-score be z'.

P(x > x') = P(z > z') = 35% = 0.35

P(z > z') = 1 - P(z ≤ z') = 0.35

P(z ≤ z') = 1 - 0.35 = 0.65

Using the normal distribution table,

z' = 0.385

we then convert this z-score back to a combined math and verbal scores.

The z-score for any value is the value minus the mean then divided by the standard deviation.

z' = (x' - μ)/σ

0.385 = (x' - 560)/260

x' = (0.385×260) + 560 = 660.1

Hope this Helps!!!

8 0
3 years ago
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