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4 years ago

Solve 1)3x-7=35? 2)22=7-3a 3)-d+7=3 4)2x+23=49 5)-c+2=5

2 answers:

8 0

$1)\\3x-7=35\\3x-7+7=35+7\\3x=42\\3x=3\cdot14\ /:3\\x=14\ \ \ \leftarrow\ \ \ Answer\\\\
2)\\22=7-3a\\22-22+3a=7-3a-22+3a\\3a=-15\\3a=3\cdot(-5)\ /:3\\a=-5\ \ \ \leftarrow\ \ \ Answer\\\\3)\\-d+7=3\\-d+7-7=3-7\\-d=-4\\d\cdot(-1)=4\cdot(-1)\ /:(-1)\\d=4\ \ \ \leftarrow\ \ \ Answer\\\\$

$4)\\2x+23=49\\ 2x+23-23=49-23\\2x=26\\2\cdot x=2\cdot 13\ /:2\\x=13 \ \ \ \leftarrow\ \ \ Answer\\\\ 
5)-c+2=5\\ -c+2-2=5-2\\ -c=3\\ c\cdot(-1)=-3\cdot(-1)\ /:(-1)\\c=-3 \ \ \ \leftarrow\ \ \ Answer$

astra-53 [7]4 years ago

7 0

$1)\ 3x-7=35\ \ \ |add\ 7\ to\ both\ sides\\\\3x=42\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=14}\\-------------------------\\2)\ 22=7-3a\\\\7-3a=22\ \ \ \ |subtract\ 7\ from\ both\ sides\\\\-3a=15\ \ \ \ \ |divide\ both\ sides\ by\ (-3)\\\\\boxed{a=-5}\\--------------------------$

$3)\ -d+7=3\ \ \ \ \ |subtract\ 7\ from\ both\ sides\\\\-d=-4\\\\\boxed{d=4}\\---------------------------\\\\4)\ 2x+23=49\ \ \ \ \ \ |subtract\ 23\ from\ both\ sides\\\\2x=26\ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=13}\\---------------------------\\5)\ -c+2=5\ \ \ \ \ \ |subtract\ 2\ from\ both\ sides\\\\-c=3\\\\\boxed{c=-3}$

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Question 2 of 10

seraphim [82]

Answer:

N(c) = (C - 15)/20.

Step-by-step explanation:

C(n) = 20n + 15

20n = C- 15

N(c) = (C - 15)/20.

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3 years ago

A manufacturer is studying the effects of cooking temperature, cooking time, and type of cooking oilfor making potato chips. Thr

Lera25 [3.4K]

Answer:

(a) The total number of combinations that can be applied for making potato chips is 36.

(b) The number of combinations that will be used for each type of oil is 12.

Step-by-step explanation:

The effects of cooking temperature, cooking time and cooking oil is studied for making potato chips.

The number of different temperatures applied is, n (T) = 3.

The number of different times taken is, n (t) = 4.

The number of different oils used is, n (O) = 3.

If an assignment can be done in n₁ ways and if for this assignment another assignment can be done in n₂ ways then these two assignments can be performed in (n₁ × n₂) ways.

(a)

Compute the total number of combinations that can be applied for making potato chips as follows:

Total number of combinations for making chips = n (T) × n (t) × n (O)

$=3\times4\times 3\\=36$

Thus, the total number of combinations that can be applied for making potato chips is 36.

(b)

To make potato chips 4 different temperatures are used and 3 different oils are used.

Each of the oil type is cooked in 4 different temperatures.

So the number of ways to select each oil type is,

n (T) × n (O) = $4\times3=12$

Thus, the number of combinations that will be used for each type of oil is 12.

(c)

Permutation is the arrangement of objects in a specified order.

Since in this case ordering of the the three effects, i.e. temperature. time and oil type is not important, permutations are not an issue.

8 0

3 years ago

P=$4000.00,A=$5300.00,t=5 years

defon

Answer:

The rate of Simple Interest is 6.5 %

Step-by-step explanation:

Given as :

Principal = $ 4000.00

Amount = $ 5300.00

The time period of loan = 5 years

Let The rate of simple interest = R

Now,

From Simple Interest method

Simple Interest = $\frac{Principal\times Rate\times Time}{100}$

And , Simple Interest = Amount - Principal

So , Simple Interest = $ 5300.00 - $ 4000.00

Or, Simple Interest = $ 1300

Now, Simple Interest = $\frac{Principal\times Rate\times Time}{100}$

So, $ 1300 = $\frac{ 4000\times Rate\times 5}{100}$

Or, $ 1300 × 100 = $ 4000 × Rate × 5

Or, Rate = $\frac{1300\times 100}{4000\times 5}$

Or, Rate = 6.5

Hence The rate of Simple Interest is 6.5 % Answer

3 0

3 years ago

The mean number of words per minute (WPM) read by sixth graders is 84 with a standard deviation of 15 WPM. If 188 sixth graders

Anna007 [38]

Answer:

0.1836 = 18.36% probability that the sample mean would differ from the population mean by greater than 1.46 WPM

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean number of words per minute (WPM) read by sixth graders is 84 with a standard deviation of 15 WPM.

This means that $\mu = 84, \sigma = 15$

Sample of 188

This means that $n = 188, s = \frac{15}{\sqrt{188}}$

What is the probability that the sample mean would differ from the population mean by greater than 1.46 WPM?

Greater than 84 + 1.46 = 85.46 or less than 84 - 1.46 = 82.54. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability is is less than 82.54.

P-value of Z when X = 82.54. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$