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dybincka [34]
2 years ago
13

A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how m

any of each are there?
Mathematics
1 answer:
lord [1]2 years ago
3 0
Let the number of half dollars be x,

number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
= 0.75x + 0.5
0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
= 17

There are 17 quarters and 15 half dollars.
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Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard de
hammer [34]

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

4 0
2 years ago
Solve the inequality. Using a verbal statement, in simplest terms, describe the solution of the inequality. Be sure to include t
rodikova [14]
-2x + 3 > 3(2x - 1)

the inequality sign > means 'greater than'.

First simplify the right side of the equation by distributing the 3 over the parentheses:-

-2x + 3 > 6x - 3

Now add -6x to both sides of the inequality  which gives us
-8x + 3 > -3
Adding -3 to both sides we have
-8x > -6

The next step is to divide  both sides by -8 so x is isolated on the left side and this gives us the solution. However there is a rule with inequalities that if you divide  the variable term by a negative the inequality is flipped. So in this case , greater that (>) becomes  less than (<):-

-8x / -8 < -6/-8

x <  3/4  is your answer.
7 0
2 years ago
For which values of a the system has no solution: x≤5, x≥a
soldi70 [24.7K]

Given:

The system of inequalities is

x\leq 5

x\geq a

To find:

The values of a for which the system has no solution.

Solution:

We have,

x\leq 5        ...(1)

It means the value of x is less than or equal to 5.

x\geq a        ...(2)

It means the value of x is greater than or equal to a

Using (1) and (2), we get

a\leq x\leq 5

But if a is great than 5, then there is no value of which satisfies this inequality.

Therefore, the system has no solution for a>5.

7 0
2 years ago
. The mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days. Suppose that the incubation ti
Paul [167]

Answer:

Step-by-step explanation:

Given that the  mean incubation time for a type of fertilized egg kept at a certain temperature is 25 days.

Let X be the incubation time for a type of fertilized egg kept at a certain temperature is 25 days.

X is N(25, 1)

a) Normal curve is in the attached file

b) the probability that a randomly selected fertilized egg hatches in less than 23 days

=P(X

we convert x into Z score and use std normal distn table to find probability

P(X

i.e. we can say only 2.5% proportion will hatch in less than 23 days.

8 0
1 year ago
1. A magazine advertise its $12 annual subscription price 70% off the newsstand price. What is the number of dollars per year a
ollegr [7]
1.  $17.14

  12   represents    70%
   x    represents    100%

rule of three

Price                 Percentage 
+12                         70-
  -x                          100+

x= \frac{12*100}{70} &#10; \\  \\&#10;x= \frac{12*10}{7} &#10; \\  \\ x=17.14




3 0
1 year ago
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