T/F : If det A is zero, then two columns of A must be the same, or all of the elements in a row or column of A are zero.

The number of miles in 4 weeks is 20 mules

From the question, we have the following parameters that can be used in our computation:

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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The correct family is option D.

To understand this problem we must be aware of the concept of addition and subtraction and also BODMAS rules which applies in an linear equation.

The numbers given here are 4,2 and 6.

We can see here that on adding 4 and 2 we get 6;

4+2=6

And on subtracting 2 from 6 we get 4;

6-2=4

Also we can see here that on subtracting 4 from 6 we get 2;

6-4=2.

These three relations are true for the given numbers.

And we can see that option D clearly fits the answer.

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Answer:

Step-by-step explanation:

given g(x) where g(x) = 6x+32

g(4) means we're gonna plug in 4 everywhere we see an x,

so g(4) = 6(4) + 32 = 6 * 4 + 32 = 24 + 32 = 56

answer: g(4) = 56

Answer:

X = 0

Y = 3

Step-by-step explanation:

To solve using substitution, you would solve one equation and substitute it into the other to get that x or y value, then you would use that found value on any original equation.

x+y=3 2x+2y=6

Using the first equation, if we subtract x

y = -x+3

Lets put this into the second equation

2x + 2y = 6

2x + 2(-x+3) = 6

2x + 2x + 6 = 6

4x = 0

x = 0

Now that we have X, we can plug it into any original equation. let's do the first cause it's easier

x+y=3

0+y=3

y=3

We can use the other too

2x+2y=6

2(0)+2y=6

0+2y=6

y=3

Answer:

HCF of 60 and 80 is 20.

Step-by-step explanation:

Answer:

6/4

Step-by-step explanation:

Answer:

Question a) radius is 2.36

Question b) radius is 11.89

Question c) radius is 6

Question d) radius is 9

Step-by-step explanation:

Radius= Demeter over 2

Answer:false

Step-by-step explanation:

Answer:

Step-by-step explanation:43₊68=111

The domain of the function (f∘g)(x) is (-∞, ∞)

A domain of a function refers to "all the values" that go into a function. The domain of a function is the set of all possible inputs for the function. The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. The domain of a function is the set of values that we are allowed to plug into our function.

This set is the x values in a function such as f(x).

The range of a function is the set of values that the function assumes. This set is the values

that the function shoots out after we plug an x value in. They are the y values.

Consider this box as a function f(x) = 2x .

Data;

(f∘g)(x) = x + 2

The domain of the function (f∘g)(x) is (-∞, ∞)

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Answer:

Geometric

Step-by-step explanation:

A geometric setting does not have a set number of trials, and the variable in question is the number of trials it takes to get the first success.

The upgrades are independent, and the probability of the customer upgrading is the same each time.

The type of variable NNN is Geometric

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

We are given that Alma wrote a phone app. She has noticed that 3%, percent of the users who download her app upgrade it the same day.

Let N be the number of customers who download Alma's app until one upgrades it on the same day.

A geometric does not have a set number of trials, and the variable in question is the number of trials it takes to get the first success.

The upgrades are independent, and the probability of the customer upgrading is the same every time.

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Answer:

1710

Step-by-step explanation:

GPA = 3,1 +- 0,6

0,6 = 2*STDEV

As it is a normal distribution, the interval (Mean +- 2*STDEV) includes 95% of the students.

1800 * 0,95 = 1710

Answer:

a)x²+16x+48=(x+12)(x+4)

b)x²-3x-40=(x+5)(x-8)

c)m²-16m+63=(m-9)(m-7)

Step-by-step explanation:

a)two number that add to give 16 and multiply to give 48 are 12,4

b)two number that add to give -3 and multiply to give -40 are -8,5

c)two number that add to give -16 and multiply to give 63 are -9,-7

The increase in draft will be 6.28 cm.

Given, the dimensions of the vessel are 100 m × 10 m × 6 m and it is floating upright in salt water on an even keel at 4.5 m draft.

Amidships compartment is 15 m long and contains timber cargo.

The stowage factor of timber is 1.4 m³/tonne and the relative density of timber is 0.8.

The volume of the compartment = Length × Breadth × Depth

= 15 m × 10 m × 6 m

= 900 m³

The weight of the timber = volume × relative density= 900 m³ × 0.8= 720 tonnes

The stowage space required = weight of timber ÷ stowage factor

= 720 tonnes ÷ 1.4 m³/tonne

= 514.29 m³

Due to the damage in the amidship compartment, its volume is reduced by 50% = 900 m³ ÷ 2

= 450 m³

Thus, the stowage space available after the bilging = total volume of the compartment – bilge volume

= 900 m³ – 450 m³

= 450 m³

The available stowage space can accommodate 450 ÷ 1.4= 321.43 tonnes of cargo.

Draft increase = (Loaded displacement - Light displacement) ÷ (Waterplane area × Waterplane coefficient)

The volume of the underwater part of the ship before bilging = 100 m × 10 m × 4.5 m

= 4500 m³

The volume of the underwater part of the ship after bilging = 100 m × 10 m × 4 m

= 4000 m³

The light displacement of the ship = (100 m × 10 m × 6 m × 1025 kg/m³) - 321.43 tonnes

= 6157142.86 kg

The displacement of the ship after loading timber = light displacement + weight of timber

= 6157142.86 kg + 720000 kg

= 6877142.86 kg

The waterplane area = Length × Breadth

= 100 m × 10 m

= 1000 m²

The waterplane coefficient for the given box-shaped vessel is 0.98 (given)

Therefore, the increase in draft of the vessel = (6877142.86 kg - 6157142.86 kg) ÷ (1000 m² × 0.98)

= 6.28 cm (approx.)

Therefore, the increase in draft will be 6.28 cm.

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Answer:

Step-by-step explanation:

45% of ____ = 135

135 : 45 * 100 = 300

Answer:

B

Step-by-step explanation:

We have, 45%  x  x = 135

or, 45/100 x x = 135

Multiplying both sides by 100 and dividing both sides by 45, we have

x = 135 x 100/45

x = 300

If your using a calculator, simply enter 135 x 100 ÷ 45, which will give you the answer.

Hopes this helps have a great day :)

Answer:

35 minutes

Step-by-step explanation:

this requires us to find out how long it took and because both times given to figure this out are within the same hour it is easy to figure out in this case, 50 - 15 = 35. This is not as simple with all problems like this but because of the times given in this problem its much easier.

i. Range (A): The space spanned by the columns of matrix A. It represents all possible linear combinations of the columns of A.

ii. Null (A): The set of all vectors x such that Ax = 0. It represents the solutions to the homogeneous equation Ax = 0.

iii. Row (A): The space spanned by the rows of matrix A. It represents all possible linear combinations of the rows of A.

iv. Null (A): The set of all vectors y such that ATy = 0. It represents the solutions to the homogeneous equation ATy = 0.

The equation Ax = b has a solution only when b is in the Range (A). It has a unique solution only when the Null (A) contains only the zero vector.

The equation ATy = d has a solution only when d is in the Row (A). It has a unique solution only when the Null (A) contains only the zero vector.

Assuming the size of A is m × n:

When Ax = b has a unique solution, the space Null (A) must be equal to Rn. This means there are no non-zero vectors that satisfy Ax = 0, ensuring a unique solution.

When ATy = d has a unique solution, the space Null (AT) must be equal to Rm. This means there are no non-zero vectors that satisfy ATy = 0, ensuring a unique solution.

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Answer: D.

Step-by-step explanation:

Using a 0.05 significance level to test a claim that UFO sightings occur in different seasons with the proportions listed in the table the test statistic x² needed to test the claim is 11.562. The correct option is B.

To test the claim that UFO sightings occur in different seasons with the proportions listed in the table, we can use a chi-square goodness-of-fit test.

The null hypothesis is that the observed frequencies in each season are equal to the expected frequencies based on the proportions listed in the table.

The expected frequency for each season can be calculated by multiplying the total number of sightings by the proportion listed in the table. For example, the expected frequency for spring is:

Expected frequency for spring = Total number of sightings × Proportion for spring

= 420 × 0.25

= 105

Similarly, the expected frequencies for summer, fall, and winter are 126, 210, and 105, respectively.

The chi-square test statistic can be calculated as:

χ² = ∑ [(O - E)² / E]

where O is the observed frequency and E is the expected frequency.

Using the observed frequencies from the table and the expected frequencies calculated above, we get:

χ² = [(150-105)²/105] + [(120-126)²/126] + [(100-210)²/210] + [(50-105)²/105]

   = 11.562

The degrees of freedom for the chi-square test is (number of categories - 1), which in this case is 4 - 1 = 3.

Using a chi-square distribution table with 3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated chi-square value (11.562) is greater than the critical value (7.815), we reject the null hypothesis and conclude that there is evidence of a difference in UFO sightings across seasons. Therefore, the test statistic x² needed to test the claim is 11.562.

The correct answer is (B) 11.562.

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Answer: The answer is ⠀ ⠀ ⠀, hope this helps! :))

Step-by-step explanation:

Answer:

11.75 please give brainliest

Step-by-step explanation:

Answer:cost of one toy is 5

Step-by-step explanation:

divide 75 by 15

Answer:

The answer to your problem is, 5

Step-by-step explanation:

First divide:

17 / 15 =

5.

To answer more problems like these you just need to take the biggest number: 75/? = ? The the next smallest number: 75/5 = ?. Easily divide it:

75 / 5 =

5.

Thus the answer to your problem is, 5

Answer:

The operation in the problem is

Division

The inverse operation is

Multiplication

-14  = x

Step-by-step explanation:

1. Division

2. Multiplication

3. -14

Answer:

$169.69

Step-by-step explanation:

for this equation disregard the first # (48)

add all of the amount of square feet from the bathrooms (30.5 + 30.5 + 40.5) which gets you 71

multiply 71 x 2.39 = 169.69

your answer is therefore $169.69

Answer:

The answer is B. 2/3 because y=mx+b mx us always the slope and b is the y intercept