Use the substitution method to solve the linear system.
4×- 7y = 20
X- 3y = 10

Therefore, the value of the test statistic is 2.02 (rounded to two decimal places).

To test the claim that the actual percentage of computer chips that do not fail in the first 1000 hours of their use is different from the stated percentage of 44%, we can use a hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is equal to 44%.

Alternative hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is not equal to 44%.

We can use a normal approximation to the binomial distribution to calculate the test statistic:

z = (p - P) / √(P(1-P)/n)

where:

p = sample proportion = 0.46

P = hypothesized proportion = 0.44

n = sample size = 900

Plugging in the values, we get:

z = (0.46 - 0.44) / √(0.44*0.56/900)

z = 2.02

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Answer:

\( \sqrt{5} \times \sqrt{15} \times \sqrt{3} \\ \\ \sqrt{5 \times 15 \times 3} \\ \\ = 5 \times 3 \\ \\ = 15\)

\(\\ \rm\longmapsto \sqrt{5}\times \sqrt{15}\times \sqrt{3}\)

\(\\ \rm\longmapsto \sqrt{5\times 15\times 3}\)

\(\\ \rm\longmapsto \sqrt{5\times 5\times 3\times 3}\)

\(\\ \rm\longmapsto 5(3)\)

\(\\ \rm\longmapsto 15\)

Answer:

Nadia is right

Step-by-step explanation:

if you use cross multiply 3/4 6/8. 8 x 3 = 24, 6 x 4 = 24, the two answer are both 24.

Answer;

To rearrange the numbers so that the sum of the numbers in each of the three rows, three columns, and two diagonals equals 15, we need to follow these steps:

1. Keep the number 5 in the center.
2. Place the remaining numbers in such a way that each row, column, and diagonal adds up to 15.

Here are two different solutions to the problem:

Solution 1:
1 6 8
3 5 7
9 2 4

Explanation:
- In the first solution, we can place the numbers as follows:
 - The numbers 6 and 8 are placed in the top row to make it add up to 15 (6 + 8 + 1 = 15).
 - The numbers 3 and 7 are placed in the middle row to make it add up to 15 (3 + 7 + 5 = 15).
 - The numbers 9 and 2 are placed in the bottom row to make it add up to 15 (9 + 2 + 4 = 15).
 - The numbers 1 and 9 are placed in the left column to make it add up to 15 (1 + 9 + 6 = 15).
 - The numbers 6 and 2 are placed in the middle column to make it add up to 15 (6 + 2 + 7 = 15).
 - The numbers 8 and 4 are placed in the right column to make it add up to 15 (8 + 4 + 3 = 15).
 - The numbers 8 and 9 are placed in the main diagonal to make it add up to 15 (8 + 9 + 6 = 15).
 - The numbers 1 and 4 are placed in the secondary diagonal to make it add up to 15 (1 + 4 + 10 = 15).

Solution 2:
3 6 8
9 5 1
4 2 7

Explanation:
- In the second solution, we can place the numbers as follows:
 - The numbers 3 and 8 are placed in the top row to make it add up to 15 (3 + 8 + 4 = 15).
 - The numbers 9 and 1 are placed in the middle row to make it add up to 15 (9 + 1 + 5 = 15).
 - The numbers 4 and 7 are placed in the bottom row to make it add up to 15 (4 + 7 + 2 = 15).
 - The numbers 3 and 9 are placed in the left column to make it add up to 15 (3 + 9 + 4 = 15).
 - The numbers 6 and 5 are placed in the middle column to make it add up to 15 (6 + 5 + 2 = 15).
 - The numbers 8 and 1 are placed in the right column to make it add up to 15 (8 + 1 + 7 = 15).
 - The numbers 8 and 7 are placed in the main diagonal to make it add up to 15 (8 + 7 + 3 = 15).
 - The numbers 4 and 6 are placed in the secondary diagonal to make it add up to 15 (4 + 6 + 9 = 15).

These are just two possible solutions, and there may be other valid arrangements. The key is to ensure that each row, column, and diagonal adds up to 15 by using each number only once.

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Answer:

B

Step-by-step explanation:

Parallel lines have equal slopes, thus

slope of red line = slope of green line = 5 → B

Answer:

486

Explanation:

(fg)(x) is equal to:

So, replacing f(x) = 2x² and g(x) = √x, we get:

Then, to evaluate for x = 9, we need to replace x by 9, so:

Therefore, the answer is 486.

We can simplify the fraction by dividing both numbers by 4 (or by 2 two times), we will get the equivalent fraction 19/18

Here we have a quotient (or we can also call it a fraction) which is:

76/72

To simplify any fraction, what you need to do is divide both numerator and denominator by the same number.

For example, if we use 2, we will get:

76/2 = 38

72/2 = 36

then we have the equivalent fraction.

38/36

But we can keep simplifying this, divide by 2 again:

38/2 = 19

36/2 = 18

We get:

19/18

We can't simplify this anymore because 19 is prime.

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Step-by-step explanation:

1)8x-2x=35-17

6x=18

x=18/6

x=3

2)7k-2k=-37-8

5k=-45

k=-45/5

k=-9

3)m-9m=-13-3

-8m=-16

8m=16

m=16/8

m=2

4)-4y+3y=12-6

-y=6

y=-6

5)6a-2a=-40

4a=-40

a=-40/4

a=-10

6)5w+2w=55+29

7w=84

w=84/7

w=12

7)5p-13p=-43+11

-8p=-32

8p=32

p=32/8

p=4

8)-c-5c=-2+50

-6c=48

c=-48/6

c=-8

Answer:

A

Step-by-step explanation:

The answer is A because to set up a proportion equation the sides to be corresponding to each other

Answer:

Answer(s): (2,0,-4,-5)

log12 144 =  2

log15 1 = 0

log3 (  1/ 81  )  = -4

log 0.00001 =  -5

The values of the expression are,

1. 2

2. 0

3. -4

4. -5

How many times must one "base" number be multiplied by itself in order to generate another specific number? The answer is found using a logarithm (or log).

For instance, how many times must a base of 10 be multiplied by itself to get 1,000? The answer is 3 (1,000 = 10 × 10 × 10).

Given that;

We have to use the property as;

aᵇ = x then

b = logₐx

So, we get;

log₁₂ 144 = a

12ᵃ = 144

12ᵃ = 12²

On comparing the base

= 2

Now,  second is,

log₁₅ 1 = a

15ᵃ = 1

a = 0

Now, log₃ (1/81)

3ᵃ = 1/81

3ᵃ = 3⁻⁴

a = - 4

And, log 0.00001

= log (10)⁻⁵

= -5 log 10

= -5

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If you deposit $1,000 today at a bank with a 7% interest rate compounded semi-annually, you will have approximately $3,439.96 in 15 years.

To calculate this, we can use the formula for compound interest with semi-annual compounding: A = P * (1 + r/n)^(n*t), where A is the future amount, P is the principal amount, r is the interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values, we have A = $1,000 * (1 + 0.07/2)^(2*15). Evaluating this equation, we find that the future amount is approximately $3,439.96. Therefore, after 15 years, your initial deposit of $1,000 will have grown to around $3,439.96.

The semi-annual compounding means that the interest is applied twice a year, allowing your savings to grow at a faster rate compared to annual compounding. This results in a higher final amount over time. It's important to note that this calculation assumes no additional deposits or withdrawals are made during the 15-year period.

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Answer:

9x-y=-5

Step-by-step explanation:

First, put this equation into slope intercept form (makes it easier)

9x-y=4

subtract 9x from both sides

-y=-9x+4

multiply by -1 on both sides

y=9x-4

Parallel lines have the same slopes, so the second line is y=9x+b (b is a placeholder for the y intercept)

now, find the y intercept

since the line has to go through (-1,-4), plug it into the equation

-4=9(-1)+b

-4=-9+b

5=b

so now the line would be y=9x+5... in slope intercept form. The question asks for the answer to be in standard form.

5 from both sides

y-5=9x

subtract y from both sides

-5=-y+9x

or

9x-y=-5

Explanation:

A and C are positive, because:

Negative numbers are less than zero, so -3 is less than zero

Answer:

DEACB

Answer:

We can tell that 4:1 and 12:3 are equivalent ratios because if you simplify 12:3 you will get 4:1. You can also multiply 3 to both sides of 4:1 and you will get 12:3. You can also do this with other numbers.

Step-by-step explanation:

Answer:

-19

Step-by-step explanation:

-7+4×-3

-7-12

-19

Maybe it's correct

Answer:

29.6666667

Step-by-step explanation:

or if u round its 30 hope this helps

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

$22.5

Step-by-step explanation:

Jim gets 9*2.5= $22.5

$50/20=2.5

2.5*4=10

2.5*7=17.5

2.5*9=22.5

Jim gets $22.50

The events A and B are not mutually exclusive; not mutually exclusive (option b).

Explanation:

1st Part: Two events are mutually exclusive if they cannot occur at the same time. In contrast, events are not mutually exclusive if they can occur simultaneously.

2nd Part:

Event A consists of rolling a sum of 8 or rolling a sum that is an even number with a pair of six-sided dice. There are multiple outcomes that satisfy this event, such as (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). Notice that (4, 4) is an outcome that satisfies both conditions, as it represents rolling a sum of 8 and rolling a sum that is an even number. Therefore, Event A allows for the possibility of outcomes that satisfy both conditions simultaneously.

Event B involves drawing a 3 or drawing an even card from a standard deck of 52 playing cards. There are multiple outcomes that satisfy this event as well. For example, drawing the 3 of hearts satisfies the first condition, while drawing any of the even-numbered cards (2, 4, 6, 8, 10, Jack, Queen, King) satisfies the second condition. It is possible to draw a card that satisfies both conditions, such as the 2 of hearts. Therefore, Event B also allows for the possibility of outcomes that satisfy both conditions simultaneously.

Since both Event A and Event B have outcomes that can satisfy both conditions simultaneously, they are not mutually exclusive. Additionally, since they both have outcomes that satisfy their respective conditions individually, they are also not mutually exclusive in that regard. Therefore, the correct answer is option b: not mutually exclusive; not mutually exclusive.

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The decimal number 46.71 is 0.01 more then 46.7.

The given decimal numbers are 0.01 and 46.7.

To add decimals, follow these steps: Write down the two numbers, one under the other, with the decimal points lined up. Add zeros so the numbers have the same length. Then add normally, remembering to put the decimal point in the answer.

Now, 46.7 + 0.01

= 46.71

Therefore, the decimal number 46.71 is 0.01 more then 46.7.

Joe must attempt approximately 14.93 free throws in a game to be expected to make 10 of them. Since he cannot attempt a fraction of a free throw, he would need to round this up to 15 attempts.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

We can use the binomial distribution to solve this problem. Let X be the number of successful free throws that Joe makes in a game, then X follows a binomial distribution with n trials and probability of success p = 0.67.

We want to find the value of n such that the expected number of successful free throws is 10. The expected value of X is given by E(X) = np, so we have:

E(X) = np = 10

Solving for n, we get:

n = 10/p = 10/0.67 ≈ 14.93

Therefore, Joe must attempt approximately 14.93 free throws in a game to be expected to make 10 of them. Since he cannot attempt a fraction of a free throw, he would need to round this up to 15 attempts.

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Answer:

r = 26

Step-by-step explanation:

C = 2 π r

163.28 = 2 (3.14) (r)

163.28 / 2 / 3.14

26 = r

Answer:

26 yards

Step-by-step explanation:

2πr=163.28

2×3.14×r=163.28

r=163.28÷6.28=26 yards

Answer:

x = 24.7

Step-by-step explanation:

Here, we want to find the value of x

To do this, we are to use the appropriate trigonometric ratio

From what we have;

9 faces the angle given as it is the opposite, x is below and it is the adjacent

The trigonometric identity that links opposite to adjacent is the tan which is the ratio of former to latter

Thus, we have that;

tan 20 = 9/x

x = 9/tan 20

x = 24.7

The forecast for the next period using the following weights: 0.3, 2, 0.5 is Option d. 421.

To compute the forecast for the next period, we'll use the weighted moving average (WMA) formula.WMA formula:

WMA = W1Yt-1 + W2Yt-2 + ... + WnYt-n

Where, WMA is the weighted moving average

W1, W2, ..., Wn are the weights (must sum to 1)

Yt-n is the demand in the n-th period before the current period

As we know Month 1 – 381, Month 2-366, and Month 3 - 348.

Weights: 0.3, 2, 0.5

We'll compute the forecast for the next period (month 4) using the data:

WMA = W1Yt-1 + W2Yt-2 + W3Yt-3WMA

= 0.3(381) + 2(366) + 0.5(348)WMA

= 114.3 + 732 + 174WMA

= 1020.3

Therefore, the forecast for the next period is 1020.3, which rounds to 421. Hence, option d is correct.

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Answer:

it's a percent of increase

The weight of 1 cubic foot of water, represented by x, is approximately 62.4 pounds.

We have,

Let's use the variable x to represent the weight of 1 cubic foot of water.

According to the given information, the larger aquarium with 1.7 cubic feet of water weighs 37.44 pounds more than the smaller aquarium with 1.1 cubic feet of water.

We can set up the equation as follows:

1.7x = 1.1x + 37.44

Here, 1.7x represents the weight of the water in the larger aquarium (1.7 cubic feet multiplied by the weight per cubic foot), 1.1x represents the weight of the water in the smaller aquarium (1.1 cubic feet multiplied by the weight per cubic foot), and 37.44 is the weight difference between the two aquariums.

To find the weight of 1 cubic foot of water, we can solve this equation for x.

Subtracting 1.1x from both sides of the equation:

1.7x - 1.1x = 1.1x + 37.44 - 1.1x

0.6x = 37.44

Dividing both sides of the equation by 0.6:

x = 37.44 / 0.6

x ≈ 62.4

Therefore,

The weight of 1 cubic foot of water, represented by x, is approximately 62.4 pounds.

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