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2 years ago

Find the integer a such that a.a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.

1 answer:

8 0

Given that a is an integer from -22 to 0 such that a is equivalent to 43 (mod 23).

Such a can be obtained as follows:

a = 43 (mod 23) - 23 = 20 - 23 = -3.

Therefore, a = -3.

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Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day

AfilCa [17]

Answer:

Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = $5\frac34 \ hrs.$

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

$5\frac34 \ hrs.$ can be Rewritten as $\frac{23}{4}\ hrs$

Number of hours rode on first day = $\frac{23}{4}\ hrs$

Also Given:

Number of hours rode on second day = $6\frac45 \ hrs$

$6\frac45 \ hrs$ can be Rewritten as $\frac{34}{5}\ hrs.$

Number of hours rode on second day = $\frac{34}{5}\ hrs.$

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = $20-\frac{23}{4}-\frac{34}{5}$

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = $\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}$

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day = $\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.$

Hence Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

3 0

2 years ago

The ordered array below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sam

Lapatulllka [165]

Answer:

the third quartile of the customs data is 27

Step-by-step explanation:

For the third quartile, we should first find upper half of the data and then the median of the upper half.

lower half: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23,

median: 23

upper half: 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32

Middle value (median) of the upper half is: 27 since 8 of the values are lower than 27 and 8 of the values are higher than 27.

7 0

2 years ago

A home building company routinely orders standard interior doors with a height of 80 inches. Recently the installers have compla

Helga [31]

Answer: Alternative Hypothesis

Ha : u ≠ 80 inches ( mean not equal to 80 inches)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean.

While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above, the mean door height is 80 inches

H0 : u = 80 inches

Ha : u ≠ 80 inches ( mean not equal to 80 inches)

3 0

2 years ago

Jaxson and his children went into a movie theater and he bought $42.50 worth of drinks and candies. Each drink costs $6 and each

sattari [20]

Answer:

6x + 3.25y = 42.50

x + y = 8

Step-by-step explanation:

x is the amount of drinks, and y represents the amount of candies that are bought. The first equation is used to figure out the amount of candies and drinks needed to be bought to add up to 42.50, and the second equation is used to make sure that the quantity of drinks and candies add up to 8.

4 0

2 years ago

Jody, a statistics major, grows tomatoes in her spare time. She measures the diameters of each tomato. Assume the Normal model

lina2011 [118]

Answer:

Zscore = 0.5

Step-by-step explanation:

If we assume a normal distribution, we mean that the diameters of each tomato follow a normal distribution. This is N~ (0,1).

By that, we mean that the mean (μ) = 0 and variance ( $\sigma^{2}$ ) = 1. Thus, since we are told that one tomato was in the 50th percentile. This implies the median. And is 0.5. And if the distribution is normal, the mean and median and mode should be equal.

Thus:

==> Z score = $\frac{x-\mu}{\sigma}$ = $\frac{0.5 - \mu}{\sigma} = \frac{0.5-0}{1} = 0.5$

8 0

2 years ago