Select all expressions that equal the distance between the points on the number line

| 3 | + | -2 |
| -2 + 3 |
| -3 - 2 |
3 - ( -2 )
| 3 - ( -2 ) |

Kevin's typing speed is 20 words/min

An hour has 60 minutes.

Using cross multiplication you can calculate how many words he types per hour:

1 min ______20 words

60 min _____x words

Kevin will type 1200words/hour

To solve inequalities with fractions and variables in the denominator, multiply both sides of the inequality by the least common multiple (LCM) of the denominators and solve the resulting equation.

To solve inequalities with fractions and variables in the denominator, follow these steps:

1. Clear the denominator: Multiply both sides of the inequality by the least common multiple (LCM) of the denominators to eliminate the fractions. This step helps in simplifying the inequality.

2. Simplify and combine terms: Distribute and simplify any terms resulting from multiplying through by the LCM. Combine like terms if necessary.

3. Solve as a regular inequality: Treat the resulting inequality as a regular inequality without fractions. Use algebraic techniques to isolate the variable on one side of the inequality sign.

4. Determine the direction of the inequality: Determine the direction of the inequality by considering the signs of any coefficients or variables in the simplified inequality. If the coefficient of the variable is positive, the direction of the inequality remains the same. If the coefficient is negative, the direction of the inequality is reversed.

5. Express the solution: Write the solution as an inequality or as an interval, depending on the context of the problem.

It's important to note that when multiplying both sides of an inequality by a negative number, the direction of the inequality needs to be reversed.

Example: Solve the inequality (3/x) - (2/5) ≥ 1

1. Clear the denominator: Multiply both sides by 5x, which is the LCM of the denominators:

5x * [(3/x) - (2/5)] ≥ 5x * 1

Simplifying, we get:

15 - (2x) ≥ 5x

2. Simplify and combine terms:

15 - 2x ≥ 5x

3. Solve as a regular inequality:

Add 2x to both sides to isolate the variable:

15 ≥ 7x

4. Determine the direction of the inequality:

Since the coefficient of x is positive (7), the direction remains the same.

5. Express the solution:

Divide both sides by 7 to solve for x:

15/7 ≥ x

The solution is x ≤ 15/7.

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Answer: Option 4

Step-by-step explanation:

Answer: 69.12

Step-by-step explanation: circumference=2*pi*radius

Answer:

The circumference of the circle is 69.12 m

Step-by-step explanation:

Circumference of a Circle

Given a circle of radius r, the circumference or perimeter of the circle is calculated by the formula:

\(C=2\pi\ r\)

The circle shown in the image has a radius of r=11 m, thus the circumference is:

\(C=2\pi\ *11\)

\(C=22\pi\)

Calculating:

C = 69.12 m

Answer:

what is the question tho you didn't post it

have a good day :)

Step-by-step explanation:

Answer:

4 ft

Step-by-step explanation:

Volume of a cube = \(x^{3}\) (where x equals the side/edge length)

V = \(x^{3}\)

64 = \(x^{3}\)

64 divided by 3 = 4 ft

The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.

The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:

Standard Error = Standard Deviation / sqrt(sample size)

Let's determine the likelihoods for sample sizes of n = 100 and n = 400:

For n = 100:

Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6

We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 1.6

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 1.6

Upper Bound z-score = 4 / 1.6

Upper Bound z-score = 2.5

We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.

For n = 400:

Standard Error = 16/√400

Standard Error = 16/20

Standard Error = 0.8

We determine the z-scores by following the same procedure as above:

Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error

Lower Bound z-score = (100 - 100) / 0.8

Lower Bound z-score = 0

Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error

Upper Bound z-score = (104 - 100) / 0.8

Upper Bound z-score = 4 / 0.8

Upper Bound z-score = 5

Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.

A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.

As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.

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Answer: 16m+8

Step-by-step explanation: 8 (2m + 1)

16m+8

Answer:

t = -9

Step-by-step explanation:

y2-y1 over x2 - x1 = t+10 / 10

-9 + 10 = 1

1/10 is the slope

For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

We are given the system of equations as:

4 x+2 y = 4    … (1)

6 x+2 y = 8    … (2)

We need to solve it to find the value of x and y.

Subtracting equation (1) form equation (2), we get that:

6 x - 4 x + 2 y - 2 y = 8 - 4

Combining the like terms, we get that:

2 x = 4

x = 4 / 2

x = 2

Now put it in equation (1) to get the value of y

4 (2) + 2 y = 4

8 + 2 y = 4

2 y = - 4

y = - 2

(x, y) = (2, - 2)

Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

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Answer:

Step-by-step explanation:

Given : ∠1 ≅ ∠2

To prove : p║q

Solution :

In the figure attached,

                Statements                 Reasons

1). m∠1 ≅ m∠2                      1). Given

2) m∠1 ≅ m∠3                      2). Vertical angles

3) m∠2 ≅ m∠3                     3). Transitive property of congruence of the                                                     angles

4). Line p║q                         4). Corresponding angles are equal                                                                                     (m∠2 ≅ m∠3)

Answer:

eudora is wrong ^

Step-by-step explanation:

Statements: Reasons:

1). ∠1 = ∠2. 1). given

2). ∠1 and ∠3 are vertical ∠s. 2). def. of vertical ∠s

3). ∠1 = ∠3. 3). vertical angles theorem

4). ∠2 = ∠3. 4). transitive property

5). p ll q. 5). converse of corresponding angles theorem

Answer:

SAS

Step-by-step explanation:

Y is congruent to X and T is congruent to S, the two triangles kiss each other.

Answer:

321 remainder 3

Step-by-step explanation:

The remainder of 7,707 ÷ 24  is 3

When we want to prove some properties of modular arithmetic we often make use of the quotient remainder theorem. It is a simple idea that comes directly from the long division. Given any integer A and a positive integer B, there exist unique integers Q and R such that

A= B * Q + R where 0 ≤ R < B

Given here 7,707 ÷ 24  this can be written as follows:

7707 = 321×24 + 3

Thus comparing with the above equation we get the remainder as 3

Hence the required form is  7707 = 321×24 + 3

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Probability of randomly selecting a tree or an insect = 3/5

Total number of flashcards, n(Total) = 30

Number of insects, n(Insects) = 10

Number of trees, n(Trees) = 8

Probability of randomly selecting a tree, P(tree) = 8/30

Probability of randomly selecting an insect, P(insect) = 10/30

Probability of randomly selecting a tree or an insect = P(tree) + P(insect)

Probability of randomly selecting a tree or an insect = 8/30 + 10/30

Probability of randomly selecting a tree or an insect = 18/30

Probability of randomly selecting a tree or an insect = 3/5

Using Euler's method with a step size of 0.2, the estimate for y(1.4) is 2. When the step size is reduced to 0.1, the estimated value for y(1.4) remains approximately the same.

Euler's method is a numerical approximation technique used to estimate the solution of a first-order ordinary differential equation (ODE) given an initial condition. In this case, we are given the initial-value problem y′ = x - xy, y(1) = 0.1, and we want to estimate the value of y(1.4).

To apply Euler's method, we start with the initial condition y(1) = 0.1. We then divide the interval [1, 1.4] into smaller subintervals based on the chosen step size. With a step size of 0.2, we have two subintervals: [1, 1.2] and [1.2, 1.4]. For each subinterval, we use the formula y(i+1) = y(i) + h * f(x(i), y(i)), where h is the step size, f(x, y) represents the derivative function, and x(i) and y(i) are the values at the current subinterval.

By applying this formula twice, we obtain the estimate y(1.4) ≈ 2. This means that according to Euler's method with a step size of 0.2, the approximate value of y(1.4) is 2.

If we reduce the step size to 0.1, we would have four subintervals: [1, 1.1], [1.1, 1.2], [1.2, 1.3], and [1.3, 1.4]. However, the estimated value for y(1.4) remains approximately the same at around 2. This suggests that decreasing the step size did not significantly impact the approximation.

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Answer:

\(\Huge \boxed{\£55}\)

________________________________________________________

A 17% reduction means that the dress cost 83% (100 - 17) of the original amount.

\(\large \fbox{\begin{minipage}{8.1 cm}83\% of the original price = \£45.65\\\\$\Rightarrow$1\% of the original price = $\frac{45.65}{83}$\\\\$\Rightarrow$1\% of the original price = 0.55\\\\$\Rightarrow$100\% of the original price = 0.55 \times 100\\\\$\Rightarrow$100\% \text{ of the original price = \£55}\end{minipage}}\)

To work out 83% of the original price, you multiply by 0.83. We can do the inverse, which is dividing by 0.83.

                                 ×0.83

Original Price →→→→→→→→→→→→→ Sale Price

        £?           ←←←←←←←←←←←←←     £45.65

                                ÷0.83

\(\large \boxed{\begin{minipage}{7 cm}Original Price = $\frac{\text{Sale Price}}{0.83}$\\\\$\Rightarrow$Original Price = $\frac{45.65}{0.83}$\\\\$\Rightarrow$Original Price = \£55\end{minipage}}\)

Therefore, the original price of the dress is £55.

________________________________________________________

Answer:

1.33%

Step-by-step explanation:

$9.74 - $9.61 = $0.13

(0.13 divided by $9.74) times 100

=1.33%  

Answer:

It should be A

Step-by-step explanation:

The area of the base is 15.4m, and volume=base*height, so v=15.4*15.6, v=240.24, BUT since it's a pyramid, you have to divide by 3, which'll give you 80.08, if you round to the nearest tenth, you'd get 80.1

Answer:

1cm³

Step-by-step explanation:

You do not need a calculator for this.

The formula for the volume of a rectangular prism is:

Length × Width × Height = Volume

If we substitute our numbers in:

5/4 × 4/3 × 3/5 = 1cm³

All you need to do is multiply across.

5 × 4 × 3 = 60

4 × 3 × 5 = 60

The numerator and denominator both equal 60. So the fraction would look like this if you were to keep it as a fraction.

60/60

The terminal point is (4,-14), so we draw a line from the origin to (4,-14) and then draw a vector from the origin to the terminal point of the resultant vector.

We are given two vectors u and v, and we are asked to find u+v, u-v, and 3u-4v, and then sketch each resultant vector.

u = 4,2 and v = 2,5

u+v = (4+2,2+5) = (6,7)

u-v = (4-2,2-5) = (2,-3)

3u-4v = 3(4,2) - 4(2,5) = (12,6) - (8,20) = (4,-14)

To sketch each resultant vector, we plot the initial point at the origin and then draw a line to the terminal point of each vector. Then, we draw a vector from the origin to the terminal point of the resultant vector.

For u+v, the terminal point is (6,7), so we draw a line from the origin to (6,7) and then draw a vector from the origin to the terminal point of the resultant vector.

For u-v, the terminal point is (2,-3), so we draw a line from the origin to (2,-3) and then draw a vector from the origin to the terminal point of the resultant vector.

For 3u-4v, the terminal point is (4,-14), so we draw a line from the origin to (4,-14) and then draw a vector from the origin to the terminal point of the resultant vector.

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Answer:

2.64 km

Step-by-step explanation:

24*110=2640 meters

2640/1000=2.64 km

Answer: Mean≈73.2   Median=78.5   Mode=85    Range=47

Step-by-step explanation:

85+58+72+85+46+93=439.

Let's arrange the series:

46  58  72  85  85  93

\(\displaystyle\\Mean=\frac{46+58+72+85+85+93}{6} \\\\Mean=\frac{439}{6}\\ \\Mean\approx73.2\\\\Median=\frac{72+85}{2} \\\\\Median=\frac{157}{2}\\ \\Median=78.5\\\\Mode=85\\\\Range=93-46\\\\Range=47\)

Answer:

24

Step-by-step explanation:

75 x .32 = 24

Answer:

32 percent of 75 is 24

Answer:

See below

Step-by-step explanation:

y  =  -(x-1)^2 +4       Expand  R side

y = - ( x^2 -2x+1) + 4

y = -x^2 +2x -1  + 4

y = -x^2 + 2x + 3          a = -1     b = 2    c   = 3  

Answer:

there should be no roots

Step-by-step explanation:

If the eluent were above the 1.5 cm line on the chromatographic paper, it would be considered an unexpected observation.

Normally, during chromatography, the eluent is applied below the baseline or reference line on the paper.

If the eluent exceeds the expected limit and goes above the 1.5 cm line, it can have several implications:

Smearing or spreading: The excess eluent can cause the compounds being separated to spread out more than intended. This can lead to a loss of resolution and poor separation of the individual components.

Incomplete separation: The higher eluent level can disrupt the chromatographic process, resulting in incomplete separation of the compounds. This means that the different components may not be adequately resolved into distinct bands or spots.

Longer analysis time: With the eluent above the expected level, it may take longer for the eluent front to reach the desired distance, as it needs to travel a greater distance on the chromatographic paper. This can increase the overall analysis time and potentially affect the accuracy of the results.

Unreliable measurements: If the eluent exceeds the 1.5 cm line, it can make it challenging to accurately measure the migration distances of the separated compounds. This can introduce uncertainty or errors in the calculations or interpretations of the chromatogram.

In summary, if the eluent is observed above the 1.5 cm line on the chromatographic paper, it is an unexpected observation that can lead to compromised separation, longer analysis times, and potential difficulties in accurate measurements and interpretations of the chromatogram.

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