Write 792 as a product of its prime
factors.
Show your working clearly.

Answer:

Y is not directly proportional to x because the line does not pass through the Origin.

Answer:

Step-by-step explanation:

• 12a - 2b - 4b - 15a + 2 (a = 0, b = 3)

→ apply the values

• 12x0 - 2x3 - 4x3 - 15x0 + 2

• 0 - 6 -12 - 0 + 2

→ use BODMAS formulae

• 0 - 6 - 12 - 2

= 0 - 6 - 10

→ zero wouldn't be counted so

- 6 - 10

(-) + (-) = (+) so:

= -16

50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

Step-by-step explanation:

we do first the multiplication 3*6=18

-2+18=16

16/5 is your answer or 3.2

To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we can use the Ratio Test. Answer : the series is divergent.

Let's analyze the given series:

4, 7, 4 · 10, 7 · 9, 4 · 10 · 16, 7 · 9 · 11, 4 · 10 · 16 · 22, 7 · 9 · 11 · 13, ...

We will calculate the ratio of consecutive terms:

(7/4), (40/7), (63/40), (352/63), (1386/352), (7722/1386), ...

Now, we will calculate the limit of the absolute value of the ratios:

lim(n->∞) |a(n+1)/a(n)| = lim(n->∞) |(7722/1386) / (1386/352)| = lim(n->∞) |(7722/1386) * (352/1386)| = lim(n->∞) |7722/1386 * 352/1386| = |2039328/1933156| = 1.055...

The limit of the absolute value of the ratios is greater than 1. According to the Ratio Test, if the limit is greater than 1, the series diverges. Therefore, the given series is divergent.

In conclusion, the series is divergent.

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Answer:

about 159 people per square mile

Step-by-step explanation:

The area of the circular region is

\(\pi( {8}^{2}) = 64\pi \)

From this, the population density of this region is

\( \frac{32000}{64\pi} = \frac{500}{\pi} = 159.2\)

The population density in people per square mile is 158.97.

Population density is a measure of the number of individuals living in a particular area, usually expressed as the number of people per unit of land area or per unit of volume.

We have,

The area of a circle with radius r is given by the formula A = πr².

In this case,

The radius is 8 miles, so the area of the circular region is:

A = π(8)² = 64π square miles

The population density is the number of people per square mile, which is found by dividing the total population by the area:

Population density = total population/area

In this case,

The total population is 32,000 people, so the population density is:

Population density = 32,000 / (64π) people per square mile

We can simplify this expression by dividing both the numerator and the denominator by 64:

Population density = 500 / π people per square mile

Rounding to two decimal places, the population density in people per square mile is approximate:

Population density = 158.97 people per square mile

Thus,

The population density in people per square mile is 158.97.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:(-2,2)

Step-by-step explanation:

2x+3(1/2x+3)=2

⇒7/2x=-7

÷7⇒1/2x=-1

×2⇒x=-2

x=-2 into the equation

⇒2×(-2)+3y=2

⇒3y=6

⇒y=2

Answer:

(-2 , 2)

Step-by-step explanation:

2x + 3y = 2 ---------------(I)

y = (1/2)x + 3  --------------(II)

Substitute y value in equation (I)

\(2x + 3*[ \frac{1}{2}x + 3] = 2\\\\2x + 3*\frac{1}{2}x+3*3=2\\\\2x+ \frac{3}{2}x+9=2\\\\2x + \frac{3}{2}x = 2-9\\\\2x + \frac{3}{2}x = -7 \\\)

Multiply the whole equation by 2

\(2*2x + 2* \frac{3}{2}x = -7 *2\\\\4x + 3x = -14\)

        7x = -14

           x = -14/7

x = -2

Plugin x = -2 in equation (I)

2*(-2) + 3y= 2

-4 + 3y = 2

Add 4 to both sides

3y = 2+4

3y = 6

Divide both sides by 3

y = 6/3

y = 2

If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.

To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Mathematically, this can be expressed as:

x + 4 > 6

x + 6 > 4

4 + 6 > x

Simplifying these inequalities, we get:

x > 2

x > -2

x < 10

The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.

This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.

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Answer:

The measure of KJL is 25 degrees

Alt. interior angles

Step-by-step explanation:

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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Answer:

To find the shorter route, we need to calculate the distances for both routes and compare them.

Route through Towns P and Q:

The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.

The distance between Town P and Town Q is 2 units to the right, so it is 2 km.

The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.

Therefore, the total distance for this route is √34 + 2 + 4√2 km.

Route through Town R:

The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.

The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.

Therefore, the total distance for this route is √34 + √74 km.

Comparing the distances, we can see that:

√34 + 2 + 4√2 km ≈ 10.2 km

√34 + √74 km ≈ 12.6 km

Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.

Dan's weight can be any value between 82 kg and 96 kg

Let's call Steve's weight "x".

According to the problem, Dan weighs 14 kg more than Steve, so Dan's weight would be x + 14.

Together, their weight would be the sum of their weights

x + (x + 14) = 2x + 14

We know that their combined weight is less than 178 kg, so the inequality will be

2x + 14 < 178

Subtracting 14 from both sides

2x < 164

Dividing by 2

x < 82

So Steve's weight is less than 82 kg.

To find the possible range of Dan's weight, we can substitute x + 14 for Dan's weight

(x + 14) < (178 - x)

Simplifying

2x < 164

x < 82

x + 14 < 96

So Dan's weight is less than 96 kg.

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Let's call the length of the shorter leg "x". According to the problem, the length of the longer leg is 3 feet more than 3 times the length of the shorter leg. So, the length of the longer leg can be expressed as 3x + 3.

The length of the hypotenuse is 4 feet more than 3 times the length of the shorter leg, which can be expressed as 3x + 4. Now we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

So we have:  x^2 + (3x+3)^2 = (3x+4)^2 , Expanding and simplifying: x^2 + 9x^2 + 18x + 9 = 9x^2 + 24x + 16
Combining like terms: 10x^2 - 6x - 7 = 0 , Using the quadratic formula: x = (6 ± sqrt(6^2 - 4(10)(-7))) / (2(10)) x = (6 ± sqrt(316)) / 20 , x ≈ 0.554 or x ≈ -1.271 . We can't have a negative length, so we'll use x ≈ 0.554.

Now we can find the other side lengths: Longer leg = 3x + 3 ≈ 4.662 , Hypotenuse = 3x + 4 ≈ 5.662 ,So the side lengths of the triangle are approximately: Shorter leg ≈ 0.554 ft , Longer leg ≈ 4.662 ft .Hypotenuse ≈ 5.662 ft.

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Answer:

3

Step-by-step explanation:

I think 3 is the answer

32 or 2

Step-by-step explanation:

4×4×4×4= 256

2×2×2====8

Then 256÷8=32 or 32/1

(a) The function f(x) = ||x||² is not linear.

(b) The function f(x) = cᵀ x + bᵀ ax is linear.

To determine if the given functions are linear, we need to check if they satisfy the linearity property:

For any function f: ℝⁿ → ℝ to be linear, it must satisfy the condition:

f(αx + βy) = αf(x) + βf(y)

Let's analyze each function separately:

(a) f(x) = ||x||²

Here, ||x|| represents the Euclidean norm of vector x.

To test for linearity, we need to check if the function satisfies the given condition:

f(αx + βy) = αf(x) + βf(y)

Let's substitute αx + βy into the function:

f(αx + βy) = ||αx + βy||²

Expanding the squared norm, we have:

f(αx + βy) = (αx + βy) · (αx + βy)

= α²(x · x) + 2αβ(x · y) + β²(y · y)

On the other side, we have:

αf(x) + βf(y) = α||x||² + β||y||²

The two expressions are not equal since the cross term 2αβ(x · y) is missing from αf(x) + βf(y). Therefore, function (a) is not linear.

(b) f(x) = cᵀ x + bᵀ ax

To test for linearity, we apply the linearity condition:

f(αx + βy) = αf(x) + βf(y)

Substituting αx + βy into the function, we have:

f(αx + βy) = cᵀ(αx + βy) + bᵀ a(αx + βy)

= α(cᵀ x + bᵀ ax) + β(cᵀ y + bᵀ ay)

On the other side, we have:

αf(x) + βf(y) = α(cᵀ x + bᵀ ax) + β(cᵀ y + bᵀ ay)

The two expressions are equal since they have the same terms. Therefore, function (b) is linear.

In conclusion:

(a) The function f(x) = ||x||² is not linear.

(b) The function f(x) = cᵀ x + bᵀ ax is linear.

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the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Answer:

0.56 is less than 4/5

Step-by-step explanation:

Could I get brainliest please?

Answer:

Step-by-step explanation:4/5 is greater you can use a calculator

When Nautica is making a scaled copy of a square using a scale factor of 2, the option that isn't true is D. The corresponding angles in each figure are equivalent.

It should be noted that based on the information given, we've to multiply the given figures by 2

Therefore, each angle is multiplied by 2, the corresponding side lengths are multiplied by 2, and the perimeter is multiplied by 2

Therefore, the correct option is D.

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Answer:

im not completley sure but i think its B

Step-by-step explanation:

Answer:

Pa: list A Pb: 0.18 Pc: orange

Step-by-step explanation:

When A was added, it made 142

When B was added, it made 131

142 > 131

So part one is A

since it's theoretical, it would be 1/6

1/6 = 0.18

So part 2 is 0.18

I know it is orange bc orange was 24

So part 3 is orange

Answer:

897  3/4 m^3

Step-by-step explanation:

V = l*w*h

V = 19 * 13 1/2 * 3 1/2

Change the mixed number to improper fractions

V = 19 * 27/2 * 7/2

V =3591/4

Now change the improper fraction back to a mixed number

V = 897  3/4 m^3

Answer:-5 to -10 to 10 to 1

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The number of cans of soup purchased and the number of frozen dinners purchased can be found using the system of equations,

x - 2y = 0 and 7x + 10y = 96.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x and y be the number of cans of soup purchased and the number of frozen dinners purchased respectively.

Amount of sodium in one can of soup = 350 mg

Amount of sodium in x can of soup = 350x

Similarly,

Amount of sodium in one frozen dinner = 500 mg

Amount of sodium in y frozen dinner = 500y

Given that, Julia purchased twice as many cans of soup as frozen dinners.

x = 2y

⇒ x - 2y = 0

They all collectively contain 4800 mg of sodium.

350x + 500y = 4800

⇒ 7x + 10y = 96

Hence the system of equations are x - 2y = 0 and 7x + 10y = 96.

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Answer:

d= -1/8

Step-by-step explanation:

8d+d+3d+2+4d= 16d+2

16d= -2

d= -1/8

The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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Answer:

A function can have atmost two different horazontal  asymptotes.

Step-by-step explanation:

Answer: is 48 eggs .

Step-by-step explanation:

3 hens gives 3 eggs in 3 days

Therefore , 1 gives 1 egg in 3 days

So

3days = 1egg

After that 12 days\/3 times = 4 eggs (in 12 times )

So 1 hen offers 4 eggs in 12 days after that

12 hens x 4 eggs = 48 eggs (in 12 days by 12 hens)