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3 years ago

A 270-mile highway has a toll booth at the beginning, a toll booth every 45 miles, and then a final toll booth at the end. A

Mathematics

1 answer:

Vsevolod [243]3 years ago

5 0

Answer:

$8.25

Step-by-step explanation:

270 sectioned out by 45s is 7 toll booths on the highway. That means theres a toll booth at 0 mi, 45, 90, 135, 180, 225 and 270 mi. If Josh exits after 120 mi, he only hits the booth at the beginning and then the last one at 90 mi because he doesn't reach the next one at 135 mi. $2.75 per toll booth and if he passed 3, then 2.75 x 3 = $8.25.

This should be correct, hope it helps. :)

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After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a

lina2011 [118]

Answer:

Step-by-step explanation:

Hello!

The study variable is:

X: number of customers that recognize a new product out of 120.

There are two possible recordable outcomes for this variable, the customer can either "recognize the new product" or " don't recognize the new product". The number of trials is fixed, assuming that each customer is independent of the others and the probability of success is the same for all customers, p= 0.6, then we can say this variable has a binomial distribution.

The sample proportion obtained is:

p'= 54/120= 0.45

Considering that the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: p' ≈ N(p; $\sqrt{\frac{p(1-p)}{n} }$ )

The other conditions for this approximation are also met: (n*p)≥5 and (n*q)≥5

The probability of getting the calculated sample proportion, or lower is:

P(X≤0.45)= P(Z≤ $\frac{0.45-0.6}{\sqrt{\frac{0.6*0.4}{120} } }$ )= P(Z≤-3.35)= 0.000

This type of problem is for the sample proportion.

I hope this helps!

5 0

2 years ago

What is the area of this figure

kobusy [5.1K]

I think 20 hope that helps

5 0

3 years ago

Read 2 more answers

ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12.

Naily [24]

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

$[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z$

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

$[(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5$

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

$A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2$

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

$A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7$

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

$A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy$

Thus, the expression is (x² - 6y² + 3xy).

7 0

3 years ago

What is 39.79949748 rounded to the nearest hundredth?

Rufina [12.5K]

Answer:

$Number = 39.80$

Step-by-step explanation:

Given

$Number = 39.79949748$

Required

Approximate (to the nearest 100th)

This means that, we approximate at the second digit after the decimal.

So:

i.e,

Number = 39.79 [Begin approximation] 949748

The first digit after [Begin approximation] is then approximated using the following rule:

$0 - 4 \approx 0$

$5 - 9 \approx 1\\$

Since 9 falls in $5 - 9 \approx 1\\$ category, the number becomes:

$Number = 39.[79+1]$

$Number = 39.80$

3 0

2 years ago

Please take a look at the question. Please explain and type your explaination. Please make it quick as possible. Thankyou!

Firlakuza [10]

Answer:

Yes, it's true

Step-by-step explanation:

A fraction is a part of a whole number for example 1/2. 1/2 is a half of one whole piece and if you multiply it into any whole number whether it's 2,4,6,8,10...... basically, if you multiply a fraction less than one with a non-zero whole number, it will always be less than the whole number it's being cut into smaller pieces. However, if the fraction is greater than 1, we would technically have an answer greater than the whole number product, just something to remember.

5 0

2 years ago