Simplify (5^3x5^)^5 checking again,

6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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Answer:

  12x³y²

Step-by-step explanation:

You want the product -2x (-3x²y)(2y).

An exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:

  x² = x·x

When the same factor appears a number of times in a product, an exponent can be used to represent that number.

  (-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)

The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...

  12x³y²

Step-by-step explanation:

1. a) q=4+0.8(7)

q=4+5.6

q=9.6

b) q=4+0.8(100)

q=4+80

q= 84

2. a) 12=4+0.8p

-4 -4

8=0.8p

0.8 0.8

10=p

b) 60=4+0.8p

-4 -4

56=0.8p

0.8 0.8

70=p

Answer:

Q1. a) q= 9.6

b) q= 84

Q2. a) p= 10

b) p= 70

Step-by-step explanation:

Substitute the equation with the given value and solve the equation to arrive at the answer.

Q1. a) q= 4 +0.8p

When p= 7,

q= 4 +0.8(7)

q= 4 +5.6

q= 9.6

b) q= 4 +0.8p

When p= 100,

q= 4 +0.8(100)

q= 4 +80

q= 84

Q2. a) q= 4 +0.8p

When q= 12,

12= 4 +0.8p

0.8p= 12 -4 (-4 on both sides)

0.8p= 8

p= 8 ÷0.8 (÷0.8 on both sides)

p= 10

b) q= 4 +0.8p

When q= 60,

60= 4 +0.8p

0.8p= 60 -4 (-4 on both sides)

0.8p= 56

p= 56 ÷0.8 (÷0.8 on both sides)

p= 70

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

Answer:2, 7, 7, 6

Step-by-step explanation:

Answer:

1) 8/4 = 2

2) 21/3 = 7

3) 56/8 = 7

4) 48/8 = 6

Step-by-step explanation:

To convert a fraction into a whole number: Divide the numerator by the denominator.

What's a numerator?:

A numerator is the part of a fraction above the line. So, 8 in 8/4 is the numerator.

What's a denominator?:

A denominator is the  bottom number in a fraction. So, 4 in 8/4 is the denominator.

1) 8/4 = 8 divided by 4 = 2.

2) 21/3 = 21 divided by 3 = 7

3)56/ 8 = 56 divided by 8 = 7

4) 48 / 8 = 48 divided by 8 = 6

We can show that every proper subspace U of \($\mathbb{R}^2$\) is a line through the origin, as desired.

Let U be a proper subspace of \($ \mathbb{R}^ 2 $\), which means U is a subset of \($ \mathbb{R}^ 2 $\) that is closed under vector addition and scalar multiplication, but does not equal \($ \mathbb{R}^ 2 $\) itself. We need to show that U is a line through the origin.

Given a nonzero vector d in U, we define L = Rd as the line with direction vector d. Since d is nonzero, L is not degenerate and passes through the origin (0,0) since Rd always contains the zero vector (0,0).

Now, let u be a vector in U but not in L. Since u is in U, and U is a subspace, u must be closed under scalar multiplication. Thus, for any scalar r in \($ \mathbb{R} $\), \(r_u\) must also be in U.

Consider any vector v in \($ \mathbb{R}^ 2 $\). We want to show that v can be expressed as a linear combination of u and d.

Since u is not in L, u and d must be linearly independent, as any nonzero vector on the line L = Rd is a scalar multiple of d. This means that u and d do not lie on the same line through the origin.

Geometrically, this implies that u and d span the entire plane \($ \mathbb{R}^ 2 $\), as they do not lie on the same line and any vector in \($ \mathbb{R}^ 2 $\) can be expressed as a linear combination of u and d.

Thus, for any vector v in \($ \mathbb{R}^ 2 $\), v can be expressed as a linear combination of u and d.

Specifically, we can write \(v = c_1u + c_2d\), where \(c_1\) and \(c_2\) are scalars.

Since U is closed under scalar multiplication, \(c_1u\) and \(c_2d\) must also be in U for any scalar \(c_1\) and \(c_2\). Therefore, U contains all possible linear combinations of u and d, and U must be a subspace that spans the entire plane \($ \mathbb{R}^ 2 $\).

However, since U is a proper subspace, it cannot span the entire plane \($ \mathbb{R}^ 2 $\). The only way for U to span the entire plane \($ \mathbb{R}^ 2 $\) while still being a proper subspace is if U is a line through the origin.

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Answer:

\(n = \frac{7}{m + 2} \)

Step-by-step explanation:

\(m + 2 = \frac{7}{n} \)

To make n as the subject , we need to isolate it.

■ Lets multiply n on both the sides in order to shift n to the L.H.S.

\( = > n(m + 2) = \frac{7}{n} \times n\)

\( = > n(m + 2) = 7\)

■ Lets now divide (m + 2) on both the sides in order to isolate n in L.H.S

\( = > \frac{n(m + 2)}{( m+ 2)} = \frac{7}{(m + 2)} \)

\( = > n = \frac{7}{m + 2} \)

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer: 11x - 9y - 3

Step-by-step explanation:

Collect like terms - start with x

9x - 8y +2x - 6 - y + 3

11x - 8y - 6 - y + 3

Collect all y terms

11x - 9y - 6 +3

Collect all integers

11x - 9y - 3 - final answer

Answer:

d) division property of =

Step-by-step explanation:

by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Answer:

3200 of 768 is 416.67%

Step-by-step explanation:

There's your answer hope this helps.

Answer: 162%.

Step-by-step explanation:

To find the percentage increase in points, we need to calculate the difference between the two values, divide it by the original value, and then multiply by 100 to get the percentage.

The difference between Patrick's old score and his new score is:

328 - 125 = 203

The percentage increase is:

203/125 x 100% = 162.4%

Rounded to the nearest whole number, the percentage increase is 162%.

选项 (d)

option (d)

!!!!!!!!!

Using Pythagorean's theorem we can see that the variables are:

t = 13.86

w = 12.81

Remember that for any right triangle, Pythagorean's theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, where the hypotenuse is the side opposite to the 90° angle.

Then for the first triangle we can write:

t² + 8² = 16²

Solving for t:

t = √(16² - 8²) = 13.86

For the second triangle we have:

10² + 8² = w²

Solving for w:

w = √(10² + 8²)

w = 12.81

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Applying the slope formula, the value of t is calculated as: t = -6.

The slope of a line, m, is the ratio of the change in y to the change in x, and it is expressed as m = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Given the following:

Substitute the values into the slope formula and find the value of t:

1 = (t - (-5)) / (4 - 5)

1 = (t + 5) / -1

1(-1) = t + 5

-1 = t + 5

-1 - 5 = t + 5 - 5

-6 = t

t = -6

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The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

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

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

0.52 units³

Step-by-step explanation:

volume = 4/3 × 22/7 × (½)³ =

88/21 × 1/8 = 11/21= 0.52 units³

Answer:

The force of gravity experienced by the shuttle would be 1.6675×10^N

Answer:

81 days

Step-by-step explanation:

Formula to solve this type of equation \(t=\frac{k}{p}\)

t is time

k is a constant

p is people

We must substitute the values into the equation

\(54=\frac{k}{9}\)

\(k=486\)

Now we must substitute it to find the time

\(t=\frac{486}{6}\)

you get 81

It would take \(6\) builders  \(36\) days to complete the same house.

Builders are those person whose job is to build or repair houses and other buildings.

We have,

\(9\) builders take \(54\) days to complete a house.

So,

\(1\)  builder will take  \((\frac{54}{9})\)  days to complete a house,

In the same way,

\(6\)  builder will take  \((\frac{54}{9}*6)\)  days to complete a house,

i.e.

\(6\)  builder   \(=(\frac{54}{9}*6)= 36\) days.

Hence, we can say that it would take \(6\) builders  \(36\) days to complete the same house.

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Answer:

Step-by-step explanation:

x + x + 1 + x + 2 = 219

→ 3x + 3 = 219

→ 3x = 219 - 3

→ 3x = 216

→ x =  

→ x = 72

∴ 1st natural number → x

→ 72

∴ 2nd natural number → x + 1

→ 72 + 1

→ 73

∴ 3rd natural number → x + 2

→ 72 + 2

→ 74

Answer:

Solve \((x) + (x + 1) + (x + 2) = 219\) to get \(x = 72\). Therefore, the numbers are 72, 73 and 74.

The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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The expression above can be resolved to become; (5a + b)³

According to the question:

To resolve the expression given;

However; the expression above can be factorised to become;

Upon expansion; (5a + b)³ yields the expression gotten earlier;

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Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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Answer:

1 5/8

Step-by-step explanation:

Answer:

1 and 5/8

Step-by-step explanation:

hdhdbfhfhfvvfvfvfhd

Answer: 4

Step-by-step explanation: The correct answer is 4. Find each number, then subtract. 7).

Answer:

D is the answer

Step-by-step explanation:

Answer:

15 - 3 ?

Step-by-step explanation:

We will start by doing the equation on the left:

5(x-3)

Since we will substitute X for 6 the updated equation will be:

5(6-3)

We will now solve it using bodmas so it will be 6-3 which is 3. Then 3 multiplied by 5 is 15.

We will start by doing the equation on the right:

x + 13

Since we will substitute X for 6 the updated equation will be:

6 + 13

So now to simplify it all it will be:

15x = 6 + 13

Answer:

Step-by-step explanation: