Have you ever devised a way to solve a problem? How?

Answer:

100%

Step-by-step explanation:

There is no table, but if there is only a green or red in the bag, then the probability of selecting a green or a red is 100%.

Answer:

below

Step-by-step explanation:

In short, a book report is an essay that contains what you read and learned from reading a book. For example, you would write a book report in the following sequence:

Best of Luck!

Answer:

$35 + $50 = $85 per hour

$85 x 3 = $255

So this company would cost $255 for 3 hours.

Answer:

1:300

Step-by-step explanation:

We conclude that the odds of hitting the ball are 0.158

The odds (like the probability) are given by the quotient between the number of attempts in which you hit the ball and the total number of attempts.

Here we know that out of 19 attempts, in 3 you hit the ball. Then the odds of hitting the ball are:

P = 3/19 = 0.158

We conclude that the odds of hitting the ball are 0.158

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Answer:

31,500

Step-by-step explanation:

Multiply the population density by area to get the total population in an area

Density = 15 per km²

Area = 1500 x 1.4 = 2100 km²

Population in 2100 km² = 15 x 2100 = 31,500

7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B).

b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.

Two expressions with equal sign in between is called as equation.

4. 7^4.3^-6.y

In the given expression, 7 has 4 exponent and 3 has -6 exponent.

This can be written as 7.7.7.7.y/3.3.3.3.3.3.

5. b^10/b^4 is b^10-4=b^6.

6. (p^2+p-8)-(-4p^2-p+3)

=p^2+p-8+4p^2+p-3

=5p^2+2p-5.

Therefore 7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B), b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.

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The probability that the weight will be less than 4504 grams is 0.9713.

We need to standardize the value 4504 using the given mean and variance, and then use the standard normal distribution table to find the corresponding probability.

The standard deviation is the square root of the variance: √391876≈626.05

So, the z-score for a weight of 4504 grams is:

z=(4504−3315)/626.05≈1.8974

Using a standard normal distribution table, we find that the probability of a z-score being less than 1.8974 is approximately 0.9713.

Therefore, the probability that a newborn baby boy born at the local hospital will weigh less than 4504 grams is approximately 0.9713.

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The solution is, Right answer: C) -7 is a solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

We have the equation 2x² +5x -63 = 0

First, let's find the coefficients a, b and c as ax² +bx +c = 0:

• a = 2

• b = 5,

• c = -63

Now, we will use the formula below to solve this equation:

x = -b ±√b²-4ac/2a

Let's replace the coefficients with the values that we already found:

putting the values we get,

x = -5±23/4

Now, let's divide it into two solutions, look:

x1 = 9/2

x2 = -7

Right answer: C) -7 is a solution.

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Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

The area of the shaded part is 45 cm² .

Given figure is divided into two triangles of same bases but of different heights. Calculate the areas of bigger triangle( outer one ) and unshaded triangle.

Area of triangle = 1/2×b×h

b = base of triangle

h = height of triangle

Firstly calculate the area of bigger triangle with dimensions,

b= 18 cm

h= 9 cm

Area of triangle = 1/2×b×h

                          = 1/2×18×9

                          = 81 cm²

Now calculate the area of unshaded triangle with dimensions,

b= 18 cm

h= 4 cm

Area of triangle = 1/2×b×h

                          = 1/2×18×4

                          = 36 cm²

Now to calculate the area of the shaded region,

Area of shaded region = Total area of triangle( bigger triangle ) - Area of unshaded triangle.

Area of shaded region = 81 cm² - 36 cm²

Area of shaded region = 45 cm²

Hence area of shaded part of the figure is 45 cm².

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Answer:

g(n) = - 19 + (n - 1)*6

Step-by-step explanation:

The way to do this is to try a couple and then see if you can make some sort of equation that follows the rule.

g(1) = - 19

=============

g(2) = g(2 - 1) + 6

g(2) = g(1) + 6

g(2) = -19 + 6

g(2) = -13

=============

g(3) = g(2) + 6

g(3) = -13 + 6

g(3) = - 7

==========

g(4) = g(3) + 6

g(4) = - 7 + 6

g(4) = - 1

==========

g(5) = 5

g(6) =11

===========

Now the hard part. You have to start  with - 19

The nth term is g(n) = - 19 + (n - 1)*6

Now see if it works.

g(7) = - 19 + (7 - 1)*6

g(7) = - 19 + 6 * 6

g(7) = -19 + 36

g(7) = 17

Is that correct?

g(7) = g(n - 1) + 6

g(7) = g(6) + 6

g(7) = 11 + 6

g(7) = 17 Seems to be the same as the explicit formula gives.

By applying direct proportion, the information should be filled in the table are as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented the following equation:

y = kx

Where:

Since the boat carried containers that weigh 4000 pounds each, we would multiply each of containers by 4000 as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

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There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

What is permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.

So, the number of desired cases are,

= \(\frac{7_P_3(24)^4}{2} = 34836480\)

Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

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Answer: It would be 30.5 i hope this helps.

Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

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The dimension of the rectangle is (x + 5) and (x – 2). Then the correct option is B.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The area of the rectangle is x² + 3x – 10.

On factorization, we have

x² + 3x – 10

x² + 5x –2x – 10

x (x + 5) –2 (x + 5)

(x + 5) (x – 2)

We know that the area of a rectangle is given as

Area = Length × Width

x² + 3x – 10 = (x + 5)(x – 2)

On comparing, we have

The dimension of the rectangle is (x + 5) and (x – 2). Then the correct option is B.

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Answer:

see picture

Step-by-step explanation:

Answer:

The greatest possible time taken by Maria is 97.4 seconds.

Step-by-step explanation:

The greatest possible time taken by Maria occurs when she moves at constant rate and is equal to the length of the road divided by the length of the road. That is to say:

\(t = \frac{\Delta s}{v}\)

Where:

\(\Delta s\) - Length of the road, measured in meters.

\(v\) - Average speed, measured in meters per second.

Given that \(\Delta s = 380\,m\) and \(v = 3.9\,\frac{m}{s}\), the greatest possible time is:

\(t = \frac{380\,m}{3.9\,\frac{m}{s} }\)

\(t = 97.4\,s\)

The greatest possible time taken by Maria is 97.4 seconds.

Answer:

-4m-17

Step-by-step explanation:

g(2m+7) = -2*(2m+7) -3

= -4m -14 -3

= -4m -17

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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the standard deviation is not less than 13 hours based on the given sample data.

To calculate the standard deviation of the sample mean, we can use the formula:

Standard deviation of the sample mean = Standard deviation of the population / √(sample size)

Given that the population standard deviation is 180 and the sample size is 345, we can plug in these values:

Standard deviation of the sample mean = 180 / √345 ≈ 9.693

The standard deviation of the sample mean represents the average variability or spread of sample means that could be obtained from repeated sampling. In this case, it indicates how much the sample means would typically vary from the true population mean. A smaller standard deviation of the sample mean suggests that the sample means are closer to the population mean, leading to greater precision and accuracy in estimating the population mean.

Regarding the assumptions for the confidence interval at 95%, they typically include:

1. Random Sample: The sample should be selected randomly from the population to ensure its representativeness.

2. Independence: The observations within the sample should be independent of each other. Each data point should not be influenced by others.

3. Normality or Large Sample Size: The population distribution should be approximately normal, or the sample size should be large enough to satisfy the Central Limit Theorem. The CLT states that for a large sample size, the distribution of the sample mean becomes approximately normal, regardless of the population distribution.

4. Unbiasedness: The sample should be unbiased and free from selection or measurement bias.

As for testing the claim that the standard deviation is at least 13 hours, we can use a one-sample t-test with the null and alternative hypotheses:

Null hypothesis (H0): The standard deviation is less than 13 hours.

Alternative hypothesis (Ha): The standard deviation is at least 13 hours.

Using the sample data, we can calculate the test statistic:

t = (sample standard deviation - claimed standard deviation) / (standard deviation of the sample mean / √sample size)

t = (10.4 - 13) / (10.4 / √32) ≈ -2.035

Next, we determine the critical value at a significance level (α) of 0.05 for a one-tailed test with degrees of freedom (df) = sample size - 1 = 32 - 1 = 31. Checking a t-distribution table or using a statistical calculator, we find the critical value to be approximately -1.697.

Since the calculated t-value (-2.035) is less than the critical value (-1.697), we have evidence to reject the null hypothesis. Therefore, we can conclude that the standard deviation is not less than 13 hours based on the given sample data.

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Answer:

D) 4

Step-by-step explanation:

By remote interior angle property if a triangle, we have:

19x° + (18x - 4)° = 144°

(18x - 4 + 19x)° = 144°

(37x - 4)° = 144°

37x - 4 = 144

37x = 144 + 4

37x = 148

x = 148/37

x = 4

The probability that the number drawn is even or a multiple of 9 is 14/25, which simplifies to 0.56 or 56%.

To find the probability that the number drawn is even or a multiple of 9, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

There are a total of 25 balls numbered from 1 through 25 in the container.

Even numbers: Out of the 25 balls, half of them are even numbers (2, 4, 6, ..., 24). So there are 25/2 = 12.5 even numbers, but since we cannot have a fraction of a ball, we consider it as 12 even numbers. Multiples of 9: Out of the 25 balls, the multiples of 9 are 9, 18, and 27 (which is not in the container). So there are 2 multiples of 9.

Now we sum up the favorable outcomes: 12 even numbers + 2 multiples of 9 = 14 favorable outcomes. The total number of possible outcomes is 25 (since there are 25 balls in total).

Therefore, the probability that the number drawn is even or a multiple of 9 is 14/25, which simplifies to 0.56 or 56%.

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The parameters needed to calculate a confidence interval at the 99% confidence level are the sample mean ($\overline{x}$), the population standard deviation ($\sigma$), the sample size ($n$), and the confidence level ($1-\alpha$).

In this case, we are given that $\sigma = 8$ minutes, $n=25$, and $1-\alpha = 0.99$. We also know that the sample mean is $\overline{x} = 58$ minutes.

To find the confidence interval, we first need to find the critical value for a 99% confidence level. Using a t-distribution with $n-1=24$ degrees of freedom, we can find this value using a t-table or a calculator. For a 99% confidence level, the critical value is approximately 2.797.

Next, we can use the formula for a confidence interval for a population mean:

$\overline{x} \pm t_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Plugging in our values, we get:

$58 \pm 2.797\cdot \frac{8}{\sqrt{25}}$

Simplifying this expression, we get:

$58 \pm 5.58$

So the confidence interval is:

$(52.42, 63.58)$

Rounded to two decimal places, the confidence interval is:

$(52.42, 63.58)$
To calculate the 99% confidence interval for the time it takes to edit a successful resume, we'll need the following parameters:

1. Sample mean (x) = 58 minutes
2. Population standard deviation (σ) = 8 minutes
3. Sample size (n) = 25 resume editors
4. Confidence level (CL) = 99%

Now, we need to find the critical value (z*) for a 99% confidence level. Using a standard normal (z) table or calculator, we find that z* ≈ 2.576.

Next, we'll use the formula for the confidence interval:

CI =x ± z*(σ/√n)

CI = 58 ± 2.576*(8/√25)

CI = 58 ± 4.12

So, the 99% confidence interval is (53.88, 62.12). This means we can be 99% confident that the true population mean for the time it takes to edit a successful resume lies between 53.88 and 62.12 minutes.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

The x value is directly proportional to the y value such as in the equation y = kx.

Answer:

Think its 275

Step-by-step explanation:

Answer:

Step-by-step explanation: