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Answer:x < 3/14

Step-by-step explanation:

-14x > -3

x < 3/14

Answer: x<3/14

Step-by-step explanation:

The result of the multiplication operation yields 7 7/12

From the question, we are to multiply the given fractions. The given fractions are

1 3/4 and 4 2/6

First, we will convert the fractions to improper fractions

Converting 1 3/4 to an improper fraction

1 3/4 = 7/4

Converting 4 2/6 to an improper fraction

4 2/6 = 26/6

Thus,

The multiplication operation becomes

7/4 × 26/6

= 7/4 × 13/3

= 91/12

= 7 7/12

Hence, the product of the given numbers is 7 1/12

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Riya wants to have enough saved to live off of 80% of her current annual gross wage, which is $81,000.00 * 80/100 = $64,800.00.

She wants to withdraw 4% of her retirement savings the first year, which means she will need to have $64,800.00 / .04 = $1,620,000.00 saved.

So the answer is $1,620,000 (Second to last one)

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

Step-by-step explanation:

Given

Use formula

The question is incomplete. Here is the complete question.

(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?

(b) How many of these are odd numbers?

(c) How many are greater than 330?

Answer: (a) 180

              (b) 75

               (c) 105

Step-by-step explanation:

(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:

For the hundreds position, there are 6 choices.

For the tens position, since the digit can be used only once, there are 6 choices.

For the unit position, there are 5 choices.

The total three-digit number formed is: 6*6*5 = 180

(b) To form an odd number, the unit position must be an odd digit, then:

unit position has 3 choices;

hundreds position has 5 choices;

tens position has 5 remaining choices.

The total three-digit odd number is: 3*5*5 = 75

(c) The number formed must be greater than 330, so:

If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.

Total number is: 3*5 = 15

Another possibility is the number starts with a digit bigger than 3 and so,  there are 3 choices.

Tens position has 6 choices;

Unit position has 5 choices;

Total possibilities are: 3*6*5 = 90

The total number of ways a three-digit number is greater than 330 is:

90 + 15 = 105

Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

Step-by-step explanation:

Simple interest is

I=Prt

I=11500(0.10)(60/360)

I=$191.67

The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

220mi

Step-by-step explanation:

Annie's dad drove a total of 490 miles before heading home. The correct option is D.

Distance is defined as the product of speed and time.

We can use the formula distance = rate x time to calculate the distance for each day.

On Monday, he drove for 4 hours at 55 mph, so the distance he traveled was:

distance = 55 mph x 4 hours = 220 miles

On Tuesday, he drove for 3 hours at 50 mph, so the distance he traveled was:

distance = 50 mph x 3 hours = 150 miles

On Wednesday, he drove for 2 hours at 60 mph, so the distance he traveled was:

distance = 60 mph x 2 hours = 120 miles

To find the total distance, we can add up the distances for each day:

220 miles + 150 miles + 120 miles = 490 miles

Therefore, Annie's dad drove a total of 490 miles before heading home.

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Answer:

The probability that x is larger than 12 when df = 19 = 0.100

Step-by-step explanation:

We are supposed to find the probability value at x>12 at degree of freedom equals to 19.

P(x>12)

By looking at the chi square table we can see, at df = 19 and x>12, P(x>12) is equal to 0.100

because at df = 19, the least x values is 27.2036 for which (Px=27.2036) or (Px>12) = 0.100

The true statement about the side lengths of quadrilateral MNOP is (d) MP = OP = 11.25 cm because the scale factor for dilating quadrilateral EFGH is 1.25.

The side lengths of EFGH are given as:

\(EF = 12\ cm\)

\(FG = 6\ cm\)

\(GH = 9\ cm\)

\(EH = 9\ cm\)

Length NO is also given as:

\(NO = 7.5\ cm\)

Because both quadrilaterals are similar, then side NO corresponds to side FG.

The scale factor (k) from EFGH to MNOP is then calculated as:

\(k = \frac{NO}{FG}\)

\(k = \frac{7.5}{6}\)

\(k = 1.25\)

The side lengths of MNOP are then calculated using:

\(MN = 12cm \times 1.25\)

\(MN = 15\ cm\)

\(OP = 9cm \times 1.25\)

\(O P = 11. 25 cm\)

Also,

\(MP = 11. 25 cm\)

So, the true statement is (d)

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Answer:  C. The width of the bar representing dogs is more than the widths of the other bars.

Step-by-step explanation: The following statements describes how this Bar Chart misrepresents the data.

Answer:

-4

Step-by-step explanation:

G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. preconditions: x

x(x + 1)/2 = O(x^2)

The pseudocode segment given has two nested for loops. The outer loop is iterating over the variable x, while the inner loop is iterating over variable i. G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. Each loop iteration is increasing the variable z by 1. In total, this will result in x*(x+1) / 2 operations being performed. This is equal to O(x^2), which is the worst-case number of operations.

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According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The weight of the coalition P1, P2, P3 is 36

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

weighted voting system [20: 9,7,5,3,1]

The variable P1, P2 and P3 are the first three values

So, we have

P1 = 20

P2 = 9

P3 = 7

The weight of the coalition P1, P2, P3 is the sum of the points

So, we have

Coalition = 20 + 9 + 7

Coalition = 36

Hence, the weight coalition is 36

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Answer:

x would be equal to 6

Step-by-step explanation:

24 would be divided by 4 because it's 4x

Answer:

x = 24 ÷ 4 or 24/4

Step-by-step explanation:

In order to isolate the variable, you multiply both sides by the reciprocal of 4, which is 1/4.

Answer:

It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.

Step-by-step explanation:

I listed all of the possible combinations below

GGGGGGGGG           BGGGGGGGG

BBGGGGGGG           BBBGGGGGG

BBBBGGGGG           BBBBBGGGG

BBBBBBGGG            BBBBBBBGG

BBBBBBBBG             BBBBBBBBB

Total number of combinations with at least one boy is 9/10

This is a very high percentage, which means the couple is very likely to have at least one boy.

In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:

9, 12, 15

Step-by-step explanation:

Using the recursive formula and T₁ = 6 , then

T₂ = T₁ + 3 = 6 + 3 = 9

T₃ = T₂ + 3 = 9 + 3 = 12

T₄ = T₃ + 3 = 12 + 3 = 15

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

$3.24

Step-by-step explanation:

Cost for the coffee + Cost for the bagel

$1.39 + $1.85

$3.24

The system of equations with the solution are 2x + y - z = 5, 5x - 3y + 4z = 7 and -6x -7y + 2z = -19.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Solution to this system will give us the solution to the considered equation.

Solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.

The system of equations with the solution (2, 1, 0) is;

2x + y - z = 5

The system of equations with the solution (5, -3, 4) is;

5x - 3y + 4z = 7

The system of equations with the solution(-6 , -7, 2) is;

-6x -7y + 2z = -19

The complete question is

"Write a system of equations with the solution (2, 1, 0) is 5, (5, -3, 4) is 7 and (-6 , -7, 2) is -19."

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