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To round the nearest hundred the digit in the hundred column and test digit in the tens column.

To round the nearest hundred the digit in the hundred column is rounding digit and the digit in the tens column is test digit.

We find the rounding digit in hundred column is 3. Then we look out the test digit 2 to the right of the 3 in the tens column. Because 2<5 we round down and leave the 3 in the hundred column. Then replace the two rightmost digits with 0's.

The 9,321 rounded to the nearest hundred is 9,300.

start expanding the squared expression using the square of a binomial,

then,

replace in the original function

apply distributive and simplify

Answer:

Given:

There are given that the expression:

Explanation:

Multiply -9b into the value of bracket.

So,

Final answer:

Hence, the equation is shown below:

Equation: S = $70·W + $550

Amount of manoey after 18 weeks: $1810

To solve this, we have two variables, the amount of weeks (W) and savings (S)

Each week, $70 dolars are added to the account. Then we can write this as: $70·W.

Now there is an initial amount of $550. Then we must add that mount to the previous calculation: $70·W + $550

This give us the savings on each week. THen THe complete equation is S = $70·W + $550

Now, to know the savings after 18 weeks, we can replace W = 18 and solve:

Thus, the savings after 18 weeks is $1810

ANSWER

EXPLANATION

We want to divide the given complex fraction:

To do this, we have to rationalize the denominator of the fraction by multiplying the given fraction by another fraction made up of the conjugate of the denominator of the given fraction:

Simplifying this, we have:

That is the solution of the division.

Answer:

  (d)  b = 7

Step-by-step explanation:

You want the solution to b³ = 343.

The equation can be written in standard form and factored according to the factoring of the difference of cubes:

  b³ -343 = 0

  (b -7)(b² +7b +49) = 0

The solutions to this are the values of b that make the factors 0.

  b -7 = 0   ⇒   b = 7

  b² +7b +49 = 0   ⇒   b = -3.5 ± i√36.75 . . . . . complex solutions

The one real solution to the equation is b = 7.

__

Additional comment

Every cubic has 3 solutions. Here, two of them are complex. When the only terms in the equation are the cubic term and the constant, there will always be only one real root.

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The equation b^3 = 343 has two valid real solutions: b = 7 and b = -7. Both values satisfy the equation and meet the given condition. Option B.

To determine the value of b, we can solve the equation b^3 = 343.

Taking the cube root of both sides, we get:

b = ∛343

The cube root of 343 is 7, since 7 * 7 * 7 = 343. Therefore, one solution to the equation is b = 7.

However, it's important to note that the cube root function has a real and complex solution. In this case, b = 7 is the real solution, but there are two additional complex solutions.

Using complex numbers, we can express the other two solutions as follows:

b = -∛343

b = -7

So the complete set of solutions for b is b = 7, -7.

In summary, the equation b^3 = 343 has two real solutions: b = 7 and b = -7. These solutions satisfy the equation and fulfill the condition. So Option B is correct.

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None of the operations with radicals are correct, as two radical terms can only be added or subtracted if they have the same radical and the same exponent.

Terms with radicals can only be added or subtracted if they have the same radical and same exponent, for example:

[tex]3\sqrt{2} + 2\sqrt{2} = 5\sqrt{2}[/tex]

In the above example, they have the same radical, of 2, and same exponent, also of 2.

The first example is given by:

[tex]7\sqrt{3} + 4\sqrt{2} = 11\sqrt{5}[/tex]

The mistake is that the two terms cannot be added, as they have different radicals, of 3 and 2.

The second example is given as follows:

[tex]3\sqrt[3]{k} - 6\sqrt{k} = -3\sqrt{k}[/tex]

The terms have the same radical, of k, but they have different exponents, of 3 and 2, hence they cannot be subtracted.

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The given expression is:

Therefore, the value of the expression is:

3 7/8

.

Answer:

1/36

Explanation:

In a single die, the total number of outcomes = 6

• The probability of rolling a 6 the first time = 1/6

• The probability of rolling a 1 the second time = 1/6

Thus, the probability of rolling a 6 the first time and a 1 the second time is:

The sum of all two-digit numbers which are not divisible by 3 is 2240.

What is Arithmetic progression?

An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.

The sum of two-digit number in AP is Sn = n/2[2a+(n-1)d]

First, sum of  two digit number 10, 11.....99 is

n = 90, a = 10 an= 99

Sn = n/2[2a+(n-1)d]

Sn = 90/2[2(10)+(90-1)1]

Sn = 45[20+89]

Sn= 4905

Now, the sum of two digit number divisible by 3 =

12, 15,...99

a = 12, n = 30, d = 3

Sn = n/2[2a+(n-1)d]

Sn=30/2[2(12)+(30-1)3]

Sn= 1665

Hence, sum of two digit number not divisible by 3 are 4905-1665

=2240

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Answer:

To find the perimeter of the triangle, you would add p + m + n. To find the area of the triangle you would use (p x m) /2. To find a missing side of the triangle, given that it is a right triangle, you would use p^2 + m^2 = n^2

Given:

The amount to spend on books, T=$20.

The cost of a handcoverbook, m=$5.

The cost of a paperback, n=$2.

Let x be the number of handcover books and y be the number of paperback books.

It is said that the complete amount of $20 cannot be spend.

So, the inequality to determine x and y can be written as,

So, the inequality is 20>5x+2y.

Hello! To find the number of liters of water, we have to calculate the volume of the parallelepiped:

The formula of the volume is:

Now that we know the volume, we have to convert cm³ to liters.

For this, we must remember:

1cm³ = 0.001 liter

Multiplying by rule of three, we will obtain:

Answer with explanation: To find the values of x where the f(x) is discontinuous, we have to set the denominator equal to zero, doing this gives:

The f(x) is discontinuous at x = 9, following graph confirms it:

In conclusion, discontinuity is non-removable.​

Find out the difference

so

(4.65-2.83)=$1.82

therefore

The most appropriate choice for profit will be given by-

Profit percent after selling a bag of garri is 25%

What is profit?

If the selling price of an article is more than the cost price of the article, then the difference between selling price and the cost price of the article gives the profit

Profit = SP - CP

Here,

Cost price of a bag of Garri = N320

Selling price of a bag of Garri = N400

Profit = N(400 - 320)

         = N80

Profit Percent = [tex]\frac{80}{320} \times 100[/tex]

                       = 25%

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Answer:

f(x) = (-1/4)x - 5

Step-by-step explanation:

(-8, -3), (-12, -2)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁         -2 - (-3)       -2 + 3          1           -1

m = ------------ = ------------- = ----------- = --------- = -------

       x₂ - x₁          -12 - (-8)     -12 + 8        -4           4

y - y₁ = m(x - x₁)

y - (-3) = (-1/4)(x - (-8)

y + 3 = (-1/4)(x + 8)

y + 3 = (-1/4)x - 2

   -3                 -3

-------------------------------

y = (-1/4)x - 5

I hope this helps!

The percent of change is​ computed as follows:

Substituting with data:

According to Double identities

The most appropriate choice for linear equation will be given by -

w = -8 is the required answer

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here

[tex]4(3w - 2) = 8(2w+3)\\12w - 8 = 16w+24\\16w - 12w = -8-24\\4w = -32\\w = -\frac{32}{4}\\w = -8[/tex]

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Let:

Mp = Marked price = $310

r = Rate of discount = 20% = 0.2

D = Discount

Sp = Sale price

The discount will be given by:

And the sale price will be:

Answer

The least likely to occur is Event C

Explanation

A.

P(spade card) = 13/52

P(queen) = 4/51 Note: Without replacement

⇒ 13/52 x 4/51

= 52/2652

= 0.0196

B.

P(a spade) = 13/52

P( another spade) = 12/51 Note: Without replacement

⇒ 13/52 x 12/51

= 156/2652

= 0.0588

C.

P(an ace) = 4/52

P(king) = 4/51

⇒ 4/52 x 4/51

= 16/2652

= 0.006

∴ The least likely to occur is Event C

To find the scale factor use the next formula:

Use dimension of corresponding sides AB and ED:

_____________

Area of the base = 10 x 3 = 30 in^2

Area of the lateral walls = 10 x 2.5 x 2 = 50 in^2

Area of the triangles = 3 x 2 /2 x 2 = 6 in^2

Total area = 30 + 50 + 6

= 86 in^2

Given:

To find:

The value of n.

Explanation:

The nth term formula for the arithmetic sequence is,

Substituting the given values we get,

Thus, -24 is the 4th term of the sequence.

Final answer:

The term -24 is the 4th term of the sequence.

From the question, we can derive the following:

Micheal earns 2x³ + 3x

His wife earns 3x² + 6

If x represents the number of days they work, in a month, we are asked to find the total earnings in a month.

So we will have:

(2x³ + 3x) + (3x² + 6)

Adding up the two earnings:

2x³ + 3x² + 3x + 6

So, (2x³ + 3x² + 3x + 6) is the total earnings in a month.

So the correct answer is the second option wich is (2x³ + 3x² + 3x + 6).

Answer:

A, C, E

Step-by-step explanation:

4^10 = 1048576

A: (4^5)^2 = 1048576

C: 4^20 / 4^10 = 1048576

E: (4^2 x 4^3)^2 = 1048576

Answer

The drug cannot be completely eliminated from one's system.

This is because the kidney removes 25% of the drug, leaving 75% at any time; the 75% of any number will give a smaller number, but never zero.

So, the amount of the drug in the body system can become extremely low, but it can never be 0.

The mathematical proof is shown under explanation.

Explanation

We are told that the kidney filters off 25% of the drug out of the system every 4 hours.

This means that 75% of the dosage of the drug remains in the person's system every 4 hours.

If one starts with A₀ of the drug and classify every 4 hour time period as n

At n = 1,

A₁ = 0.75 (A₀)

A₂ = 0.75 (A₁) = 0.75² (A₀)

Aₙ = 0.75ⁿ (A₀)

For this question, we start wit 1000 mg

A₀ = 1000 mg

We are then asked to calculate if Aₙ, the amount of drug in the system after n time periods, can ever be 0

Aₙ = 0.75ⁿ (A₀)

0 = 0.75ⁿ (1000)

To solve for n, if there's an n for when the value of Aₙ = 0, we first divide both sides by 1000

0 = 0.75ⁿ (1000)

0 = 0.75ⁿ

We then take the natural logarithms of both sides

In 0 = In (0.75ⁿ)

In (0.75ⁿ) = In 0

n (In 0.75) = In 0

But, since In 0 does not exist, it shows that there is no value of n that can make the value of Aₙ go to 0.

Hope this Helps!!!

Given:

The coordinates of the triangle are A(-3,4), B(-1,2), and C(-5,0).

Required:

We need to translate the given triangle to <4,2> 4 units right and 2 units up.

Explanation:

The image of the point can be written as follows.

Consider point A(-3,4).

Consider point B(-1,2).

Consider point C(-5,0).

Final answer:

A'(1, 6), B'(3, 4) and C'(-1, 2).

Given that 150 is increased to 861

The absolute change formula is

Where

The new value = 861

The old value = 150

The absolute change is

Hence, the absolute change is 711

The formula for percentage is

Substitute the values into the percentage change formula

Hence, the percentage change is 474% increase