Find the perimeter and area of a triangle with a base of 9 cm, height of 9.3 cm, and sides of 12 cm and 19 cm.

Option III "E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃, where x₁ = 1 if treatment B, x₁ = 0, otherwise; x₂ = 1 if treatment C, x₂ = 0, otherwise; x₃ = 1 if treatment D, x₃ = 0, otherwise." is a correct multiple regression equation that can be used to analyze these data. So the option III is correct.

Randomized design involving four treatments: A, B, C, and D.

So total number of treatments = 4(A, B, C, D)

So the number of dummy variable is required = 4 - 1

The number of dummy variable is required = 3

The three variables would be x₁ x₂ and x₃ and the fourth treatment scenario would be represented if all three were zero.

So the option III is correct because this is a correct multiple regression equation because it contains all the necessary components to define a linear regression model.

Specifically, it contains a dependent variable (y), a constant (B₀), and three independent variables (x₁, x₂, x₃). Additionally, each of the independent variables is either assigned a value of 1 or 0 depending on the treatment, which is how a linear regression model is typically constructed.

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The complete question is:

Consider a completely randomized design involving four treatments: A, B, C, and D. Select a correct multiple regression equation that can be used to analyze these data. Define all variables.

I. E(y) = B₀ + B₁ x₁ x₂ x₃ x₄, where x₁ = 1 if treatment A, x₁ = 0, otherwise; x₂ = 1 if treatment B, x₂ = 0, otherwise; x₃ = 1 if treatment C, x₃ = 0, otherwise; x₄ = 1 if treatment D, x₄ = 0, otherwise.

II. E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃ + B₄x₄, where x₁ = 1 if treatment A, x₁ = 0, otherwise; x₂ = 1 if treatment B, x₂ = 0, otherwise; x₃ = 1 if treatment C, x₃ = 0, otherwise; x₄ = 1 if treatment D, x₄ = 0, otherwise.

III. E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃, where x₁ = 1 if treatment B, x₁ = 0, otherwise; x₂ = 1 if treatment C, x₂ = 0, otherwise; x₃ = 1 if treatment D, x₃ = 0, otherwise.

Answer:

3-8x 34= -5x 34 = -170

Step-by-step explanation:

Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

3.14

Step-by-step explanation:

Given that:

Mean weight (m) = 79 ounces

Population standard deviation (s) = 13.1

Sample size = 47

Maximal margin of error associated with 90% confidence interval.

The margin of error is given by:

Zcritical * (standard deviation / sqrt(sample size)

Z critical at 90% confidence interval = 1.645

Hence,

Zcritical * (standard deviation / sqrt(sample size)

1.645 * 13.1 / sqrt(47)

1.645 * (13.1 / 6.8556546)

1.645 * 1.9108313

Hence, the margin of error is :

3.1433174885

= 3.14

Answer:

Amadi: 20 years old

Chima : 4 years old

Answer:

7 or 6^7

Step-by-step explanation:

Answer:

2(10^.5)

Step-by-step explanation:

d = ((x2 - x1)^2 + (y2 - y1)^2)^0.5

Answer:

65.54% (nearest hundredth)

Step-by-step explanation:

Given:

\(\sf X \sim N(\mu, \sigma^2)\implies X \sim N(9000,1000^2)\)

P(X > 8600) = 1 - P(X ≤ 8600)

                    = 1 - 0.3445782584

                    = 0.6554217416

                    = 65.54%

Answer:

Add all the digits of the number, then check if that sum is divisible by 9. If yes, we know the number is divisible by 9.

The object needs 10.58 minutes to travel 1 4/5 if the object is traveling at a steady speed of 10 1/5 mi​/h.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

An object is traveling at a steady speed of 10 1/5 mi​/h.

u = 10 1/5 min/h

u = 51/5 min/h

As we know, the speed-distance relationship:

time = distance/speed

distance = 1 4/5 = 9/5

time = (9/5)/(51/5)

time = 9/51 hours

time = (9/51)60

time = 10.58 minutes

Thus, the object needs 10.58 minutes to travel 1 4/5 if the object is traveling at a steady speed of 10 1/5 mi​/h.

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Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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Answer:

1/2 (one over two)

Step-by-step explanation:

when you are finding an a slope, or inequality as you wrote here, you are using formula: y/x ( y over x )

the graph dotes show how they are moving 2 to the right(x) and 1 up(y), so it’s 1/2!

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

yes

Step-by-step explanation:

hey can both be expressed as the quotient of two integers

Answer:

Equity of taxation means each citizen pays an amount of tax equal to their income and ability to pay the tax.

Answer:

C) The tax is paid equally by everyone

Step-by-step explanation:

The range and domain of the graph shown is

domain -4 ≤ x < ∞

range ∞ ≤ x < 3

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a graph is every value in the graph, from left to right.

Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as

-4 ≤ x < ∞

The graph's entire range, from lower to higher numbers, in the vertical line represents the range.

Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as

∞ ≤ x < 3

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Answer:

97

Step-by-step explanation:

This question is about piecewise-defined function whereby the statements given are defined by two or more equations.

We need to translate the statement given in the question into inequality equations.

Piecewise-defined function for C(x) are;

C(x) = $25 {if 0 ≤ x ≥ 250}

C(x) = $25 + $0.20x {if x > 250}

We are told that the phone company offers a monthly plan that costs $25 and that this plan includes a maximum of 250 minutes.

Since the piece wise function for the cost is C(x), where x is the number of minutes in a month, then;

C(x) = $25 {if 0 ≤ x ≥ 250}

Also, we are told that there are charges of $0.20 per minute above 250 minutes.

Thus, we can write;

C(x) = $25 + $0.20x {if x > 250}

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The symbol < means “less than”, and the symbol > means “greater than”. These symbols are inequality symbols. So, the true statement 3 < 8 is read as “3 is less than 8” and the statement 5 > 3 is read as “5 is greater than 3”.

When given two or more fractions, it is often useful to know which fraction is greater than or less than the other. For example, if the discount in one store is 1/3 off the original price and the discount in another store is 1/4 off the original price, which store is offering a better deal? To answer this question, and others like it, you can compare fractions.

To determine which fraction is greater, you need to find a common denominator. You can then compare the fractions directly. Since 3 and 4 are both factors of 12, you will divide the whole into 12 parts, create equivalent fractions for  1/3 and 1/4, and then compare.

Now you see that 1/3 contains 4 parts of 12, and 1/4 contains 3 parts of 12. So, 1/3 is greater than 1/4.

As long as the denominators are the same, the fraction with the greater numerator is the greater fraction, as it contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction as it contains fewer parts of the whole.

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The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Answer:

266.65

Step-by-step explanation:

65% of 60 = 39 sandwiches sold

85% of 40 = 34 baguettes sold

all Jacket potatoes sold 3.25 x 25

34 x 2.70

39 x 2.40

add the total and comes to 266.65

Answer:

approximately 21.05 mg.

Step-by-step explanation:

The mass of a radioactive particle at any given time can be calculated using the following formula:

m(t) = m(0) * (1/2)^(t/T)

where:

m(t) = mass of the particle at time t

m(0) = initial mass of the particle

t = time elapsed since the start of the decay process

T = half-life of the particle

Using this formula, we can solve the given problem as follows:

a. The mass at t=0:

Since we are given the initial mass of the particle, we can simply state that:

m(0) = 50 mg

b. Its mass after 40 minutes:

We can use the formula above to calculate the mass of the particle after 40 minutes:

m(40) = m(0) * (1/2)^(40/30)

m(40) = 50 * (1/2)^(4/3)

m(40) = 50 * 0.421

m(40) = 21.05 mg (rounded to two decimal places)

Therefore, the mass of the particle after 40 minutes is approximately 21.05 mg.

Answer:

X=8

Step-by-step explanation:

2x-13=3     first, add 13 to both sides

2x=16         second, divide by 2 on both sides

x=8             This is the right answer

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Interval notation is a way of writing the subsets of the real number line.

There are 2 types of brackets used to represent two types of intervals on the number line.

A closed interval is one that includes its endpoints. Closed brackets, [ ], are used to write out the intervals. For example, the interval 0 ≤ x ≤ 3 is represented as:

An open interval is one that does not include its endpoints. Open brackets, ( ), are used in this case. For example, the interval 0 < x < 3 is represented as:

The interval in the question is given to be:

This means that the interval contains all real numbers less than or equal to 1:

ANSWER: The answer is "less than or equal to".

Answer:

We can use the distance formula to find the distance between the center of the circle (2, -3) and the point (-1, -6), which should be equal to the radius of the circle.

Step-by-step explanation:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Distance = √[(-1 - 2)² + (-6 - (-3))²]

Distance = √[(-3)² + (-3)²]

Distance = √(18)

So the radius of the circle is equal to √(18) or approximately 4.24.

Answer:

C

Step-by-step explanation:

You are looking at the domain which is on the K axis. It starts at 6 and ends at 11. The range J is 80 to 120