ABC is a straight line. The length of AB is four times the length of BC. AC = 75cm
Work out the length of AB. Thanks, I'm so bad at math :)

Answer: 4.8

3/4+2 1/4= 3

7.8-3=4.8

Therefore, the vector form of the given equation is y = 2(x - 2)² + 1.

To change the standard form of a quadratic equation, y = ax² + bx + c, to the vertex form, y = a(x - h)² + k, we need to complete the square. The vertex form provides a way to quickly identify the vertex, or the minimum or maximum point, of the parabola.

In the given example, we have the standard form y = 2x² - 8x + 9, and we want to convert it to the vertex form y = a(x - h)² + k.

First, we factor out the coeffi

y = 2x² - 8x + 9

 = 2(x² - 4x) + 9

 = 2(x² - 4x + 4 - 4) + 9  // Add and subtract (b/2a)^2

 = 2((x - 2)² - 4) + 9     // Factor and simplify

 = 2(x - 2)² + 1           // Distribute and simplify

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According to the World Health Organization (WHO), the European and Mediterranean populations over the age of 20 have a high percentage of overweight people. In fact, the WHO estimates that approximately 55% of the population in this region is overweight or obese.

This is a significant percentage, and it is important to note that being overweight or obese can increase the risk of numerous health problems, including cardiovascular disease, diabetes, and certain types of cancer.

There are a number of factors that contribute to the high prevalence of overweight and obesity in this region, including changes in diet, decreased physical activity levels, and cultural factors. For example, many people in these regions consume a diet that is high in calories, fat, and sugar, while also engaging in sedentary behaviors.

Overall, the high percentage of overweight and obese individuals in the European and Mediterranean populations over the age of 20 is a cause for concern. It highlights the need for effective public health interventions to promote healthy lifestyles and prevent chronic disease.

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The reason why the confidence interval for the coefficient of rooms in the multiple regression model can be different from the one in part (b) is that in the multiple regression, we are controlling for the effects of other variables (home size, lot size, and bathrooms) on the dependent variable. This can lead to changes in the null hypothesis and their standard errors compared to a simple linear regression model that only considers one independent variable (rooms).

To calculate the 95% confidence interval for the coefficient of rooms in the multiple regression model, we need to use the t-distribution and the standard error of the estimate. The formula is:

Coefficient of rooms ± t_(α/2,n-k-1) x SE

Where t_(α/2,n-k-1) is the critical value of the t-distribution with n-k-1 degrees of freedom and α/2 significance level (α/2 = 0.025 for a 95% confidence interval), n is the sample size, and k is the number of independent variables in the regression model. SE is the standard error of the estimate, which measures the variability of the data around the regression line.

If the confidence interval does not include zero, we can conclude that the coefficient of rooms is statistically significant at the 0.05 level and has a non-zero effect on the dependent variable (price). If the confidence interval includes zero, we cannot reject the null hypothesis that the population regression coefficient of room is zero, meaning that there is no evidence of a significant relationship between rooms and price.

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Step-by-step explanation:

(8 x 10,000=80,000)

 (5 x 1,000=5,000) 

(3 x 100=300)

(8 x 1=8)

80,000+5,000+300+8

Answer:

85308

Step-by-step explanation:

[tex]8*10000=80000[/tex]

[tex]5*1000=5000[/tex]

[tex]3*100=300[/tex]

[tex]8*1=8[/tex]

[tex]80000+5000+300+8=85308[/tex]

Hope this helps :)

Pls brainliest...

To approximate the mean age of the residents of the town, we need to calculate the midpoint of each age range, multiply it by its frequency, and then divide the sum of these products by the total frequency.

The midpoint of the age range:
(10+19)/2 = 14.5
(20+29)/2 = 24.5
(30+39)/2 = 34.5
(40+49)/2 = 44.5
(50+59)/2 = 54.5
(60+69)/2 = 64.5
(70+79)/2 = 74.5
(80+89)/2 = 84.5

Frequency x Midpoint:
20 x 14.5 = 290
13 x 24.5 = 318.5
22 x 34.5 = 759
18 x 44.5 = 801
57 x 54.5 = 3106.5
46 x 64.5 = 2967
15 x 74.5 = 1117.5
6 x 84.5 = 507

Total frequency = 197

Mean age = (290 + 318.5 + 759 + 801 + 3106.5 + 2967 + 1117.5 + 507) / 197 = 54.4 years

Therefore, the approximate mean age of the residents of the town is 54.4 years.
To approximate the mean of the frequency distribution for the ages of the residents, we will follow these steps:

1. Find the midpoint of each age range.
2. Multiply the midpoint by the frequency of the corresponding age range.
3. Sum the products from step 2.
4. Sum the frequencies.
5. Divide the sum of the products by the sum of the frequencies.

Here's the calculation using the given data:

Age Range  Frequency  Midpoint  Product
10-19        20         14.5     290
20-29        13         24.5     318.5
30-39        22         34.5     759
40-49        18         44.5     801
50-59        57         54.5     3103.5
60-69        46         64.5     2967
70-79        15         74.5     1117.5
80-89         6         84.5     507

Sum of products = 290 + 318.5 + 759 + 801 + 3103.5 + 2967 + 1117.5 + 507 = 8863.5
Sum of frequencies = 20 + 13 + 22 + 18 + 57 + 46 + 15 + 6 = 197

Mean = Sum of products / Sum of frequencies = 8863.5 / 197 ≈ 44.9 years

The approximate mean age is 44.9 years (rounded to one decimal place).

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Answer:   B, C, E

Step-by-step explanation:

When multiplying or dividing - and + numbers, rules are as follows:

If the signs are the same, equals +

So for division

[tex]\frac{+}{+} =+[/tex]     and       [tex]\frac{-}{-} =+[/tex]

If signs are different, equals -

[tex]\frac{-}{+}=-[/tex]     and     [tex]\frac{+}{-} = -[/tex]

Question [tex]-(\frac{8}{2} )[/tex]    the number is negative

A. not the same because   [tex]\frac{-}{-} =+[/tex]    and your question is -

B. yes it is the same because   [tex]\frac{+}{-} = -[/tex] and your question is also -

C. yes it is the same because the parenthesis are ok to remove and it doesn't change your answer

D. not the same [tex]\frac{+}{+} =+[/tex]  and your question is -

E. yes it is the same because [tex]\frac{-}{+}=-[/tex]  and your answer is also -

it would take the bee 15 seconds to travel 375 meters at a speed of 25 meters/second.

using the distance formula:

distance = speed x time

Finding the unit rate, which is the distance the bee travels per second:

unit rate = distance / time = 50 / 2 = 25 meters/second

Now we can use the unit rate to find the time it takes for the bee to travel 375 meters:

time = distance / unit rate = 375 / 25 = 15 seconds

Therefore, it would take the bee 15 seconds to travel 375 meters at a speed of 25 meters/second.

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f = h - 6 and 5f = 8h + 7 are the system of equations to find f and h

We have to form a system of equations

Let F be no of pages in each science fiction comic book

Let h h be the no of pages in each super hero comic

To find f,

5f = 8h + 7

this is because no of pages in all science fiction is 7 times more than total in super hero bopks

Then f = h - 6

this is because  the science fiction has fewer pages than 6 compared to supoer heroes

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The equations of the graph from the figure are y = 4 and y = -2

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

The graph

On the graph, we can see that

We have two horizontal lines that pass through the points y = 4 and y = -2

This means that the equations represented on the graph are y = 4 and y = -2

So, we can conclude that none of the options are true from the options

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The area of this triangle has 5 significant figures. With the following formula, we can determine a triangle's area:

Area equals (1/2) x base x height.

When we enter the values we have:

(1/2) x 2.218 mm x 1.86 mm is the area.

= 2.0586 mm2 in size

With a fixed base of 2.218 mm and a height of 1.86 mm, the area of the triangle is 2.06 mm2 (rounded to the nearest hundredth).

The number of important figures in the obtained area will next be determined. Every digit is important in decimal numbers greater than or equal to 1, so we may infer that there are five significant figures in this case:

2,0,6,7, and 4 due to the fact that the number 2.06274 is greater than 1

Therefore, the area of this triangle has 5 significant figures.

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Answer:

Step-by-step explanation:

m = 32g

An argument is considered valid if the conclusion logically follows from the premises, meaning that the truth of the premises guarantees the truth of the conclusion.

An argument is considered valid if the conclusion logically follows from the premises, meaning that the truth of the premises guarantees the truth of the conclusion. In other words, an argument is valid if it is impossible for the premises to be true and the conclusion to be false at the same time.

Therefore, an argument is considered valid if the conclusion is true whenever the premises are assumed to be true, as stated in the question. This is the fundamental requirement for a valid argument. However, it is important to note that even a valid argument can have false premises, which would make the conclusion false despite the logical validity of the argument.

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The differential equation describing the cell phone sales is [tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex].

Based on the given information, the cell phone sales growth is logistic, with a carrying capacity of 100 thousand units. When 28 thousand cell phones have been sold, the rate of sales increase is 10 thousand units per month.

The logistic growth differential equation is given by:

[tex]\frac{dy}{dt} = k \cdot y(t) \cdot \left(1 - \frac{y(t)}{M}\right)[/tex]

where dy/dt is the rate of change in sales, y(t) is the number of cell phones sold after t months, k is the growth rate, and M is the carrying capacity.

In this case, y(t) = 28, dy/dt = 10, and M = 100. To find k, we can plug these values into the equation:

10 = [tex]$k \cdot 28 \cdot \left(1 - \frac{28}{100}\right)$[/tex]

Solving for k:

k ≈ 0.5357

Therefore, the differential equation describing the cell phone sales is:

[tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex]

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The number of cups of flour must always be 6 times the number of cups of water, under the condition Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water.

In order to make 4 more pizzas without changing the ratio of flour to water, Mitch have to use 12 cups of flour and 2 cups of water.

To evaluate this we need to perform multiplication
Mitch used 3 cups of flour and 1 cup of water for 2 pizzas. So for each pizza, he used 1.5 cups of flour and 0.5 cups of water.
To make 4 more pizzas, he needs to use 6 cups of flour and 2 cups of water (since he needs twice as many pizzas).
Then, for each pizza, he needs to use 1.5 cups of flour and 0.5 cups of water (since he wants to keep the ratio the same).
So for 4 more pizzas, he needs to use 6 x 2 = 12 cups of flour and 2 x 2 = 4 cups of water.
Since he wants to keep the ratio the same, he needs to use 12 cups of flour and 2 cups of water.

Therefore, the number of cups of flour must always be 6 times.
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The complete question is
Mitch made two 10-inch pizzas using a recipe that calls for 3 cups of four and cup of water. Mitch wants to make 4 more pizzas without changing the ratio of flour to water. Enter a number to make the sentence about the ingredients true.
The number of cups of flour must always be___ times the number of cups of water.

The answer is 4.83 inches. In Chillyville, the average yearly snowfall is approximately normally distributed with a mean of 55 inches. Given that 15% of the years have a snowfall exceeding 60 inches, we can find the standard deviation using the z-score formula and the properties of the normal distribution.

A z-score corresponding to the 85th percentile (since 15% of the years exceed 60 inches) can be found in a standard normal table, which is approximately 1.04. The z-score formula is:

z = (X - μ) / σ

Where z is the z-score, X is the value (60 inches), μ is the mean (55 inches), and σ is the standard deviation we want to find.

1.04 = (60 - 55) / σ

Solving for σ:

σ = (60 - 55) / 1.04
σ ≈ 4.81

The standard deviation is closest to 4.83 inches among the given options. Therefore, the standard deviation of yearly snowfall in Charleville is approximately 4.83 inches.

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(a) The maximum speed of the bob can be found using the conservation of energy. At the maximum displacement, all of the potential energy of the system is converted into kinetic energy, so we can write:

mgh = (1/2)mv^2

where m is the mass of the bob, g is the acceleration due to gravity, h is the maximum height reached by the bob, and v is its maximum speed.

We can find h using trigonometry:

h = L(1 - cosθ)

where L is the length of the pendulum and θ is the maximum angle of displacement.

Substituting for h and solving for v, we get:

v = sqrt(2gh) = sqrt(2gL(1-cosθ)) = 0.546 m/s

(b) The maximum angular acceleration can be found using the equation:

α = -ω^2θ

where ω is the angular frequency of the pendulum, given by:

ω = sqrt(g/L)

Substituting for ω and θ, we get:

α = -g/L * sinθ = -1.46 rad/s^2

(c) The maximum restoring force on the bob is given by:

F = -mg sinθ = -0.406 N

(d) Using the simple harmonic motion equation for the displacement of a pendulum, we can find the maximum speed, maximum angular acceleration, and maximum restoring force:

x = A sin(ωt + φ)

where A is the amplitude of the motion, ω is the angular frequency, t is time, and φ is the phase constant.

The maximum speed occurs when the displacement is zero, so we can find it by taking the derivative of x with respect to time:

v = ωA cos(ωt + φ)

Substituting for ω and A, we get:

v = sqrt(gL)cos(ωt + φ) = 0.546 m/s

The maximum angular acceleration occurs when the displacement is at its maximum, so we can find it by taking the second derivative of x with respect to time:

α = -ω^2A sin(ωt + φ)

Substituting for ω and A, we get:

α = -g/L sin(ωt + φ) = -1.46 rad/s^2

The maximum restoring force occurs when the displacement is at its maximum, so we can find it using Hooke's law:

F = -kx = -mg sin(ωt + φ) = -0.406 N

where k is the spring constant of the pendulum.

(e) The answers obtained using the two different analysis models are the same, as expected. Both methods are based on the same underlying physical principles and equations, and they provide equivalent descriptions of the motion of the pendulum. However, the simple harmonic motion analysis is more general and can be applied to a wider range of systems, while the particle model is specific to cases where the mass is concentrated at a single point.

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The prove of identity  (sec t - cos t) / sec t = sin² t is shown.

Given that;

The identity is,

⇒ (sec t - cos t) / sec t = sin² t

Now, We can prove as;

LHS;

⇒ (sec t - cos t) / sec t

⇒ 1 - cos t / sec t

⇒ 1 - cos t cos t

⇒ 1 - cos ² t

⇒ sin² t = RHS

Hence, The prove of identity is shown above.

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The values of the probabilities of the events A or B, occurring, P(A or B), based on the relationship between the events are;

(a) P(A or B) = 0.538

(b) P(A or B) = 0.61

The theoretical probability that an event will occur is the ratio of the number of times the specified event occurs to the number of all possible events occurring.

Whereby A and B are two events and P(A) = 0.45, and P(B) = 0.16

(a) The formula for P(A or B) for independent events A and B can be presented as follows;

P(A or B) = P(A) + P(B) - P(A) × P(B)

Which indicates that we get;

P(A or B) = 0.45 + 0.16 - 0.45 × 0.16 = 0.538

(b) The formula for P(A or B) for mutually exclusive events A and B can be presented as follows;

P(A or B) = P(A) + P(B)

Therefore;

P(A or B) = 0.45 + 0.16 = 0.61

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Answer:

0.7 radians

Step-by-step explanation:

The equation for converting radians to degrees is:

X radians * 180/pi = degrees

Plugging in 0.7 radians,

we have 0.7 * 180/pi

= approx 40.1070457 degrees.

40.1070457 > 40 degrees,

so 0.7 radians is greater than 40 degrees

Bread has a final price of RD$ 7.

In this problem we know the current price of bread and the rise percentage, from which we have to compute the final price of the product in mention, whose expression is described below:

C' = C × (1 + r / 100)

Donde:

If we know that C = 5 y r = 40, then the final price of bread is:

C' = 5 · (1 + 40 / 100)

C' = 7

The final price of bread is RD$ 7.

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(a) This statement is false. The probability of getting heads or tails on a fair coin is always 50%, regardless of previous outcomes.  

(b) This statement is true. Drawing a face card and drawing a red card from a full deck of playing cards are mutually exclusive events.

(a) The statement is false. The outcome of each coin toss is independent of the previous tosses. Therefore, the chance of getting heads on the next toss is still 50%, regardless of the outcome of the previous eight tosses.

(b) The events of drawing a face card and drawing a red card are not mutually exclusive events. There are 12 face cards in a deck of playing cards, and 6 of them are red (2 jacks, 2 queens, and 2 kings). Therefore, the probability of drawing a face card and a red card from a full deck of playing cards is:

P(face card and red card) = P(face card) x P(red card|face card)
P(face card and red card) = (12/52) x (6/12)
P(face card and red card) = 3/52 or about 5.77%

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If a merchant sells 1800 bags of oranges at a profit of Rs. 6/bag and 2500 bags of grapes at a loss of Rs. 4/bag, he made a loss of Rs. 800.

600 is the number of bags of oranges that has to be sold to have neither profit nor loss if the number of bags of grapes sold is 900.

A merchant makes a profit of Rs 6/bag of oranges sold and a loss of Rs. 4/bag of grapes.

In the given question,

Number of bags of oranges = 1800

Number of bags of grapes = 2500

Total outcome = Profit of oranges - loss of grapes

Profit of orange = 1800 * 6

= Rs. 10,800

Loss of grapes = 2500 * 4

= Rs. 10,000

Total outcome = 10,000 - 10,800

= - Rs. 800

Thus, he makes a loss of Rs. 800.

For having neither profit nor loss, the profit earned should be equal to the loss incurred.

Therfore, Profit = Loss

Let the number of bags of orange be x

Profit of oranges = 6x

Loss of grapes = 900 * 4

= Rs. 3600

Profit = Loss

6x = 3600

x = 600

Thus, 600 bags of oranges are sold in order to have neither profit nor loss if we sell 900 bags of grapes.

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Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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The radius of the cylinder is approximately 5.077 inches.

The volume of a cylinder is given by the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

81 = πr²(1)

Simplifying this equation, we get:

81 = πr²

Dividing both sides by π and taking the square root, we get:

r = √(81/π)

r ≈ 5.077

Therefore, the radius of the cylinder is approximately 5.077 inches.

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The volume of the given solid enclosed by the paraboloids y = x2 + z2andy = 72 − x2 − z2 is 10368 cubic units.

Using a triple integral, we will integrate over the region of the xz-plane that is enclosed by the paraboloids.

The limits of integration for x and z can be found by solving the two equations for x^2 + z^2:

$x^2 + z^2 = y = x^2 + z^2 + 72 - x^2 - z^2$

$x^2 + z^2 = 36$

Therefore, the limits of integration for x and z are from -6 to 6.

The limits of integration for y are from the equation of the lower paraboloid $y = x^2 + z^2$ to the equation of the upper paraboloid $y = 72 - x^2 - z^2$.

Therefore, the limits of integration for y are from $x^2 + z^2$ to $72 - x^2 - z^2$.

The triple integral for the volume of the solid is:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} \int_{x^2+z^2}^{72-x^2-z^2} dy dz dx$

Integrating with respect to y:

$\int_{x^2+z^2}^{72-x^2-z^2} dy = 72 - 2(x^2 + z^2)$

Substituting this into the triple integral gives:

$\iiint_V dV = \int_{-6}^{6} \int_{-6}^{6} (72 - 2(x^2 + z^2)) dz dx$

Integrate with respect to z:

$\int_{-6}^{6} (72 - 2(x^2 + z^2)) dz = 72(12) - 4x^2(6) = 864 - 24x^2$

Integrate with respect to x:

$\int_{-6}^{6} (864 - 24x^2) dx = 2(864)(6) - 2\int_{0}^{6} (24x^2) dx = 10368$

Therefore, the volume of the solid enclosed by the paraboloids $y = x^2 + z^2$ and $y = 72 - x^2 - z^2$ is 10368 cubic units.

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The statements which are true for both trigonometric equations y = cos (θ) and y = sin (θ) are:

the function is periodic

the function has a value of about 0.71 when θ = π/4

the maximum value is 1.

The given trigonometric equations are,

y = cos (θ) and y = sin (θ)

The maximum value of sin (θ) = 1 which occurs at θ = 90°, not at θ = 0.

Both the functions sine and cosine are periodic since for both,

f(x) = f(x + θ)

Value of sin (π/4) = cos(π/4) = 1/√2 = 0.707 ≈ 0.71

Maximum value of both functions are 1.

Hence the three statements except first are correct for both.

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The complete question is given below.

The value of angle N is  10⁰.

The value of angle N is calculated by applying intersecting chord theorem as shown below;

This theory states that the tangent angle formed at the circumference is half of the arc angles formed by the intersecting chords.

If line NL is the diameter of the circle, then arc angle NL = 180⁰ (half of angle of a circle)

The value of arc LM is calculated as follows;

arc LM = 360 - ( 180 + 160)

arc LM = 20⁰

The value of angle N is calculated as follows;

∠N = ¹/₂ x 20⁰

∠N = 10⁰

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The linear function in this problem is given as follows:

y = -1/4x + 5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

What differentiates a linear function from the other functions is the variable x has an exponent of 1.

2x + 7 = 12 is not a function, as it does not have the y variable, it is an equation.

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