Points A and B are 80km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 8 hours, but if they travel in opposite directions, they meet in 1 hour 20 mins. What are their speeds in km/hr?

[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]

Area of the biggest circle:

[tex]\pi r^{2}=\pi \times 6^{2}=\pi \times 36 \ cm^2[/tex].

Area of the rectangle:

[tex]4 \times (2+2+2+2) = 4 \times 8 = 32 \ cm^2[/tex].

Area of the 6 semicircles:

[tex]6 \times \dfrac{1}{2} \times \pi \times r^2 = 3 \times \pi \times 2^2 = \pi \times 12 \ cm^2.[/tex]

Total shaded area:

Biggest circle area - rectangle area - 6 semicircles area

[tex]= \pi \times 36 - 32 - \pi \times 12\\= \pi \times (36-12) - 32\\= \pi \times 24 - 32\\= 3.14 \times 24 - 32\\= 75.36 - 32\\= \boxed{43.36 \ cm^2}[/tex]

Therefore, the shaded part area is [tex]43.36 \ cm^2[/tex].

[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\bold{answered \: by: \: akbarsdtazm}}}[/tex]

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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The values of the variables x and y for the cyclic quadrilateral are 85° and 100° respectively.

The figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°

Thus;

x + 95° = 180° {opposite angles of a cyclic quadrilateral}

x = 180° - 95° {collect like terms}

x = 85°

Also;

y + 80° = 180°

y = 180° - 80°

y = 100°.

Therefore, the values of the variables x and y for the cyclic quadrilateral are 85° and 100° respectively.

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Answer: The student will need to save about 416.66 dollars a month.

Step-by-step explanation:

Step 1. Find out how much the student will need to pay themselves.

20,000 - 10,000 (grandparents) - 5,000 (scholarship) = 5,000

Step 2. Divide the student's cost by the number of months

5,000/12 = about 416.66

The mean number of golf balls ordered by customers is 8.22 (rounded to 2 decimal places).

To find the mean number of golf balls, we need to multiply each possible value of X by its corresponding probability, and then sum up the products. That is:

Mean number of golf balls = E(X) = Σ[X*P(X)] where Σ is the summation symbol.

Using the given probability model, we have:

E(X) = 30.14 + 60.29 + 90.36 + 120.11 + 15*0.10

E(X) = 0.42 + 1.74 + 3.24 + 1.32 + 1.50

E(X) = 8.22

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The correct answer is c. Yes, because the evidence was not strong enough to suggest that average reading and writing scores differ.

In hypothesis testing, we use a significance level to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the alternative hypothesis.

Based on the results of the hypothesis test, if we failed to reject the null hypothesis (which is the case in this question), then we cannot conclude that the average reading and writing scores differ. Therefore, it is reasonable to expect a confidence interval for the average difference between the reading and writing scores to include 0. A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. Since we cannot conclude that the average scores differ, it is possible that the true population parameter is 0, and thus 0 could be included in the confidence interval.

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It took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

To find out how long it took for Amy to run her slowest and fastest mile combined, we need to first determine her slowest and fastest mile times.

From the frequency table, we can see that the slowest mile time recorded is 9 2/4 (which can be simplified to 9 1/2) and it occurred once. The fastest mile time recorded is 8 3/4 and it occurred twice.

To find the total time it took for Amy to run her slowest and fastest miles combined, we need to add these two times together.

9 1/2 + 8 3/4 = 18 1/4

Therefore, it took Amy a total of 18 1/4 minutes (or 18 minutes and 15 seconds) to run her slowest and fastest miles combined, rounded to the nearest 1/4 of a minute.

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Here is the complete question:

Amy ran 8 miles. She recorded how long it took her to run each mile, rounded to the nearest 1/4 of a minute?

TIME                                                  FREQUENCY

8 3/4                                                     2

9                                                            3

9 1/4                                                      2

9 2/4                                                      1

How long did it take army to run her slowest and fastest mile combined?

The perimeter of the triangle with sides 3x + 4, x² and 19 cm is is x² + 3x + 23 centimetres.

The perimeter of the triangle is the sum of the whole sides of the triangle. A triangle have three sides. Therefore, let's sum the sides of the triangle to find the perimeter of the triangle.

Hence,

perimeter of the triangle = x² + 3x + 4 + 19

perimeter of the triangle = x² + 3x + 23

Therefore, the perimeter of the triangle is x² + 3x + 23 centimetres.

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Answer:

2 g

Step-by-step explanation:

She has a total of

5 1/2 + 11 1/4 =

= 5 2/4 + 11 1/4

= 16 3/4

She needs a total of 18 3/4.

She needs an additional

18 3/4 - 16 3/4 = 2

Answer: 2 g

Yes, the Penders are living within their monthly net income.

To determine the monthly living cost, you have to add up the monthly fixed and variable costs. Next, you will subtract these from the monthly net income, if there is a remainder, or none, then they are living within their monthly income.

However, if there is a deficit from the calculation, we can arrive at an answer that shows that the Penders are living above their monthly net income. Subtracting the expenses from the income of $2,600 shows a controlled budget.

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False.

It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.

It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.

This is because if no two columns of A are scalar multiples of each other, then the columns are linearly independent, and the rank of A is at least 3. Similarly, if no two rows of A are scalar multiples of each other, then the rows are linearly independent, and the rank of A is also at least 3. Since A is a 3 by 3 matrix, it follows that the rank of A is at most 3. Therefore, the only way for A to have rank 3 is for A to be invertible.

So, any 3 by 3 matrix A that is not invertible must have either two columns that are scalar multiples of each other, or two rows that are scalar multiples of each other.

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(a) The answer of the question "What is the interval's margin of error (Round your answers to 3 decimal places.)" to part (b) is B = 0.978.

(b) margin of error = 1.96*(10/sqrt(385)) = 0.978

(a) To find the sample size needed to construct a 95% confidence interval with a margin of error of 1, we use the formula:

margin of error = z*(standard deviation/sqrt(sample size))

where z is the critical value from the standard normal distribution for a 95% confidence level, which is approximately 1.96.

Plugging in the given values and solving for the sample size, we get:

[tex]1 = 1.96*(10/sqrt(sample size))[/tex]

[tex]sqrt(sample size) = 1.96*10/1[/tex]

[tex]sample size = (1.96*10)^2 = 384.16[/tex]

Rounding up to the nearest whole number, we need a sample size of 385.

Therefore, the answer to part (a) is 385.

(b) To calculate the 95% confidence interval for the population mean given a sample size of 385 and a sample mean of 295, we use the same formula as above with the values we have:

1 = 1.96*(10/sqrt(385))

Solving for the margin of error, we get:

margin of error = 1.96*(10/sqrt(385)) = 0.978

The 95% confidence interval for the population mean is then:

295 - 0.978 to 295 + 0.978

or

(294.022, 295.978)

Therefore, the answer to part (b) is B = 0.978.

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The side x of the given right angle triangle is: 24.388

The six trigonometric ratios that we have are:

sine (sin)

cosine (cos)

tangent (tan)

cotangent (cot)

cosecant (cosec)

secant (sec).

In geometry, trigonometry is defined as a branch of mathematics that caters for the sides and also the angles of right-angled triangles. Thus, trigonometric ratios are evaluated considering the sides and angles

The three main trigonometric ratios are expressed as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We want to find the side x of the given right angle triangle.

Thus:

16/x = cos 49

x = 16/cos 49

x = 24.388

Thus, we can say that is the value of x

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Answer:

(681) 20.115

I think that's the answer

Based on the mentioned informations, the farmer is calculated to have 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

The farmer starts with 1800 chickens.

He sells 2/5 of the total, which is:

(2/5) x 1800 = 720 chickens.

So he has 1080 chickens left.

He then sells 5/6 of the remaining chickens, which is:

(5/6) x 1080 = 900 chickens.

So he has 180 chickens left.

Unfortunately, 37 chickens die, so the final number of chickens he has left is:

180 - 37 = 143 chickens.

Therefore, the farmer has 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.

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The complete question is :

A farmer has to sell 1800 chickens, first he sells 2/5 of the total, then 5/6 of the rest and if 37 chickens die, how many chickens does he still have left?

The linear function f(x) and g(x) have different intercept and slope.

To find what true or false about the given statements, we need to write out the equations for both functions.

f(x) = x + 9

To find the function g(x), we need to find the slope and y-intercept.

The slope of the function is given as;

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table;

m = 14 - 10 / 3 - 1

m = 4 / 2

m = 2

Using the slope, we can find the y - intercept with any one point;

y = mx + c

10 = 2(1) + c

10 = 2 + c

c = 10 - 2

c = 8

The equation is y = 2x + 8

Now, we can write out the functions again;

f(x) = x + 9

g(x) = 2x + 8

Let's observe each of the given statements;

a. f(x) has a greater y - intercept than g(x) which is true because f(x) has intercept at 9 and g(x) has intercept at 8.

b. f(x) has greater x -intercept than g(x). This is false as f(x) has a lower x-intercept than g(x)

c. f(x) has a greater slope than g(x). This is also false as g(x) has a slope of 2 and f(x) has a slope of 1

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Answer:

Step-by-step explanation:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

There are several methods that can be used to verify the normality conditions for a scenario where a normal model is used to represent the distribution of sample means.

One common method is the visual inspection of a histogram or a normal probability plot. Another method is to use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to assess the normality of the sample data. Additionally, the sample size and the presence of outliers can also impact the normality conditions and should be taken into consideration when verifying normality.
Hi! To verify the normality conditions for the distribution of sample means, you should consider the following criteria:

1. Randomness: The sample data must be collected randomly to ensure independence of observations.
2. Sample size: The sample size should be sufficiently large (typically, n ≥ 30) to allow the Central Limit Theorem to apply.
3. Underlying distribution: If the population distribution is known to be normal, the sample means will also be normally distributed regardless of sample size.

These criteria help ensure the use of a normal model is appropriate in representing the distribution of sample means.

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The kicker's ability to punt the ball any distance from the goal line means that the domain is unlimited in range.

As a transformation of f(x), g(x) carries the same infinity of values within its range as well with a limit up to 25.

Decidedly opening downwards, f(x)'s parabola possesses a vertex located at (30, 25). For playing according to territory: representing the kicker’s goal line, x = 30 houses the vertex of f(x) , so punting happens closer there.

In sum, while f(x) equips football players to strategically understand their field posisioning ranging  across all heights, trajectory of direction & ranges, executing effective plays based on the available resources; along with g(x) which offers a modified visual representation- they both obey the constraints of physics-based rules.

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The requried, (6x10¹) + (9x10¹) in scientific notation is 1.50x10²

To add (6x10^1) + (9x10^1) in scientific notation, we need to first make sure that the exponents of 10 are the same.

Now we can add the two numbers:

6.0x10¹ + 9.0x10¹ = 15.0x10¹

To express the result in scientific notation, we need to write 15.0 as 1.50 and move the decimal point one place to the left, which gives:

1.50x10²

Therefore, (6x10¹) + (9x10¹) in scientific notation is 1.50x10².

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The distance from Point A to Point B is

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (4, 6) and (-5, 5) is calculated by

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

substituting the values

d =√{(4 - (-5))² + (6 - 5)²}

d =√{81 + 1}

d = √82

d = 9.055 units

d = 9.1 units (to the nearest tenths)

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The magnitude of the vector is 435 units.

The direction of the vector is  173.3⁰ .

The magnitude of the vector -3u is calculated as follows;

The new vector - 3u is determined as;

u = 144i - 17j

-3u = -3(144i - 17j )

= -432i + 51j

The magnitude of the vector is calculated as;

|u| = √ (-432² + 51²)

|u| = 435 units

The direction of the vector is calculated as follows;

θ = tan⁻¹ (uy / ux)

θ = tan⁻¹ (-51/432)

θ = -6.7⁰ = 173.3⁰

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61

Why my answer is sixty one Because the Triangle ls the same size Of the other sixty one

Answer:

61

Step-by-step explanation:

Answer:

10h+6b=£48

5h+2b=£19

12h+9b=£60

Step-by-step explanation:

10h+6b=(3h+1b)+(7h+5b)

5h+2b=(7h+5b)-(2h+3b)

12h+9b=(10h+6b)+(2h+3b)

h=handles

b=bolts

The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.

In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.

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A line plot for the data is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 9 because it has the highest frequency of 4.

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The test statistic is z = 2.75. Since the test statistic is greater than 1.96, we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.

To calculate the test statistic, we first need to find the proportion of the sample that favored candidate a:
Proportion = 80/111 = 0.72
Next, we calculate the standard error of the proportion:
SE = sqrt[(0.7)(0.3)/111] = 0.045
Finally, we calculate the test statistic using the formula:
z = (Proportion - Hypothesized Proportion) / SE
z = (0.72 - 0.7) / 0.045 = 2.75
Since the test statistic is greater than 1.96 (the critical value for a two-tailed test at the 5% level of significance), we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.

To determine whether the proportion of the population in favor of candidate A is significantly more than 70%, we'll use the test statistic formula for proportions:
Test statistic = (Sample proportion - Hypothesized proportion) / Standard error
In this case, a random sample of 111 people was taken, and 80 of them favored candidate A. We are interested in finding if the proportion favoring candidate A is more than 70% (0.7).
First, calculate the sample proportion:
Sample proportion = Favored candidate / Total sample
Sample proportion = 80 / 111 ≈ 0.7207
Next, calculate the standard error using the formula:
Standard error = √(p(1-p)/n), where p is the hypothesized proportion and n is the sample size.
Standard error = √(0.7 * (1-0.7) / 111) ≈ 0.0452
Finally, calculate the test statistic:
Test statistic = (0.7207 - 0.7) / 0.0452 ≈ 0.4581
The test statistic for determining whether the proportion of the population in favor of candidate A is significantly more than 70% is approximately 0.4581.

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The number of ordered quadruplets of non-negative integers that satisfy the given condition is:
|A| - |B| = 161,700 - 16,215 = 145,485

To solve this problem, we need to use the Principle of Inclusion-Exclusion (PIE). Let A be the set of all quadruplets (a1,a2,a3,a4) of non-negative integers that satisfy the equation a1+a2+a3+a4=100, and let B be the set of all quadruplets where all four integers are odd. Then the number of quadruplets that satisfy the given condition is given by:
|A| - |B|
To find |A|, we can use stars and bars. If we consider 100 stars and 3 bars, we can partition the stars into 4 groups, corresponding to the four integers. There will be 99 gaps between the stars and bars, and we need to choose 3 of them to place the bars. This gives us:
|A| = (99 choose 3) = 161,700
To find |B|, we can use a similar approach. If all four integers are odd, then they must be of the form 2k+1, where k is a non-negative integer. Substituting this into the equation a1+a2+a3+a4=100, we get:
2k1 + 1 + 2k2 + 1 + 2k3 + 1 + 2k4 + 1 = 100
Simplifying this equation, we get:
k1 + k2 + k3 + k4 = 48
This is now an equation in non-negative integers, which we can solve using stars and bars. We need to partition 48 stars into 4 groups, and there will be 3 bars separating them. This gives us:
|B| = (47 choose 3) = 16,215.

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The volume of the parallelepiped is 80 cubic inches.

To find the volume of the parallelepiped, we need to multiply the area of the base by the height. We are given that two parallel sides of the base are 5 inches long and 2 inches apart, which means that the base is a parallelogram with base length of 5 inches and height of 2 inches. The area of the base is therefore:

Area of base = base length x height = 5 inches x 2 inches = 10 square inches

The height of the parallelepiped is given as 8 inches. Therefore, the volume of the parallelepiped is:

Volume = area of base x height = 10 square inches x 8 inches = 80 cubic inches

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Based on th mentioned iinformations, we would be requiring about 157 pens (rounded up) in order to exceed the weight of 1 kilogram.

There are 1000 grams in a kilogram. To find out how many pens are needed to exceed 1 kilogram, we need to divide 1000 grams by the weight of one pen:

1000 g / 6.4 g = 156.25 pens

Therefore, we would need 157 pens (rounded up) to exceed 1 kilogram.

Dividing 1000 grams by the weight of one pen gives us the number of pens that would weigh 1000 grams or 1 kilogram, which turns out to be 156.25 pens. Since we cannot have a fractional part of a pen, we round up to 157 pens to ensure that their total weight exceeds 1 kilogram.

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The complete question is :

A pen weighs 6.4 g. How many pens do we need to exceed the kilogram?