7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
8) There are 4 large gifts. Inside each large gift are 2 medium-sized gifts and inside each
medium-sized gift are 3 small gifts. How many gifts are there altogether?
9) Mang Cardo has cows and chickens in his farm. If he counted 13 heads and 36 feet,
how many cows and chickens does he have?
10) Alexander travelled at 6:00 a. M. And started driving at an average speed of 70 km per
hour. After two hours of driving, he stopped for 30 minutes for a rest. He continued
driving and reach his hometown at 9:30 a. M. How far did he travel?​

Answer:

you have it correct sir

Step-by-step explanation:

Based on a survey of 400 non-fatal accidents, where 173 involved faulty equipment, the point estimate for the population proportion (p) of accidents that involved faulty equipment is 173/400 = 0.4325.

To calculate the point estimate for the population proportion, we divide the number of accidents involving faulty equipment (173) by the total number of accidents surveyed (400).

This gives us a ratio of 0.4325, which represents the estimated proportion of accidents involving faulty equipment in the population.

A point estimate is a single value that serves as an approximation or best guess for an unknown population parameter.

In this case, the population proportion (p) represents the proportion of all accidents that involved faulty equipment. The point estimate of 0.4325 suggests that approximately 43.25% of non-fatal accidents may involve faulty equipment based on the sample data.

It's important to note that this point estimate is subject to sampling variability and may not perfectly reflect the true population proportion. To obtain a more precise estimate with a measure of uncertainty, one would need to consider confidence intervals or conduct hypothesis testing using statistical methods.

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Given the function f(x) and f(g), the composite result function f(g(x)) is 3x - 16.

Given the functions in the question;

To determine f(g(x)), we set up the result of the function.

f(g(x)) = f( x - 7 )

f(x) = 3x + 5

We replace all occurrence of x with x-7 and simplify

f( x - 7 ) = 3( x - 7 ) + 5

f( x - 7 ) = 3x - 21 + 5

f( x - 7 ) = 3x - 16

Given the function f(x) and f(g), the composite result function f(g(x)) is 3x - 16.

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Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The product of 6 and 2 is twelve and if you divide 24 by 12 the answer is 2

or

6 x 2 = 12  

24 ÷ 12 = 2

answer: 2

Answer:

y=-1/3x+8

Step-by-step explanation:

3x=y+3

y=3x-3

When it is perp find the reciprocal of the coefficient of x and flip the sign.

3x ---> -1/3x

y=-1/3x+b

Then plug in the (-3,9) to x and y

9=1+b

b=8

Substitute in the answers

y=-1/3x+8

There are 55,440 possible 5-permutations of 11 distinct objects.

There are 55 5-permutations of 11 distinct objects.

To find the number of 5-permutations of 11 distinct objects, you need to use the formula for permutations, which is n!/(n-r)!, where n represents the total number of objects and r represents the number of objects to be arranged.

In this case, n = 11 (total number of distinct objects) and r = 5 (number of objects to be arranged).

Calculate (n-r)!
(11-5)! = 6!

Calculate 6!
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Calculate n!
11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800

Divide n! by (n-r)!
39,916,800 ÷ 720 = 55,440

So, there are 55,440 possible 5-permutations of 11 distinct objects.

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Answer:

61.1 milliliters of acid

Step-by-step explanation:

You find the 18.4 percentage of 382

Answer:

In the expression q/3 + 6 + 9q,

q/3 is a term

6 is a constant term

9q is another term

The coefficient is the numerical factor that is being multiplied by a variable in a term. In this expression,

the coefficient of the term q/3 is 1/3, since q/3 can be written as (1/3)q

the coefficient of the term 9q is 9

Note that the constant term 6 does not have a coefficient, since it is not being multiplied by any variable.

So, to summarize:

q/3 is a term with a coefficient of 1/3

6 is a constant term with no coefficient

9q is a term with a coefficient of 9.

Answer:

I can't

Step-by-step explanation:

I don't know, bro sorry

Answer:

175/2.5=70

Step-by-step explanation:

The correlation coefficient is -7.44, which shows a strong negative correlation.

To calculate the correlation coefficient, you can use the following formula:

r = (n Σ(xy) - Σ(x) Σ(y)) / √((n Σ(x²) - (Σ(x))²) (n Σ(y²) - (Σ(y))²))

Where n is the number of data points, x is the variable on the x-axis, y is the variable on the y-axis, Σ(xy) is the sum of the products of x and y, Σ(x) is the sum of x, Σ(y) is the sum of y, Σ(x²) is the sum of the squares of x, and Σ(y²) is the sum of the squares of y.

Plugging in the values from the data, we get:

r = (5 x 198 - 39 x 91) / √((5 x 114 - 39²) x (5 x 187 - 91²))

Simplifying this equation gives us:

r = (-179) / √((-97) x (-6))

r = (-179) / √(582)

r = (-179) / 24.07

r = -7.44

The correlation coefficient is -7.44, which indicates a strong negative correlation. This means that as the value of x increases, the value of y decreases. Conversely, as the value of x decreases, the value of y increases.

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Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Answer:

it means that the roots of the quadratic equation is real and distinct and that means that 40 is a positive value

5(\(x^{2}\) + 10/2\(x\)) + 2

The number in the brackets is b/2a.

So:

5(x + 10/2(5))^2

5(x + 10/10)^2

5(x + 1)^2

Expand the double brackets for (x + 1)^2:

\(x^{2}\) + \(x\) + \(x\) + 1

This simplifies to:

\(x^2\) + 2\(x\) + 1

5(\(x^2\) + 2\(x\) + 1)

5x^2 + 10x + 5

2 - 5 = -3

5(x + 1)^2 - 3

Answer:

5(x + 1)^2 - 3

Answer:

values of x and y is (4, -2), (0, 0) and (2, 10)

Step-by-step explanation:

\( - 5 = > 45 \\ - 4 = > 28 \\ - 3 = > 15 \\ - 2 = > 6 \\ - 1 = > 1 \\ 0 = > 0 \\ 1 = > 3 \\ 2 = > 10 \\ 3 = > 21\)

Answer:

I think it's 22.65 but I'm not for sure

Answer:

24 , 12x12 = 144. , 144/6 =24

the volume occupied by the mixture of N2 and O2 gases at 0.83 atm and 42.7°C is approximately 41.62 liters.

To find the volume occupied by the mixture of gases, we can use the ideal gas law equation:

PV = nRT

Where:

P = pressure of the gases (in atm)

V = volume of the gases (in liters)

n = number of moles of gas

R = ideal gas constant (0.0821 L.atm/mol.K)

T = temperature of the gases (in Kelvin)

First, let's convert the temperature from Celsius to Kelvin:

T(K) = T(C) + 273.15

T(K) = 42.7 + 273.15

T(K) = 315.85 K

Now we can calculate the volume:

For N2:

n(N2) = 0.522 mol

P(N2) = 0.83 atm

T = 315.85 K

For O2:

n(O2) = 0.522 mol

P(O2) = 0.83 atm

T = 315.85 K

Using the ideal gas law for each gas:

V(N2) = (n(N2) * R * T) / P(N2)

V(O2) = (n(O2) * R * T) / P(O2)

Calculating the volumes:

V(N2) = (0.522 * 0.0821 * 315.85) / 0.83

V(N2) ≈ 20.81 L

V(O2) = (0.522 * 0.0821 * 315.85) / 0.83

V(O2) ≈ 20.81 L

Since the number of moles and pressure are the same for both gases, the volumes will also be the same.

To find the total volume occupied by the mixture of gases, we can sum the individual volumes:

V(total) = V(N2) + V(O2)

V(total) = 20.81 + 20.81

V(total) ≈ 41.62 L

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ABCD IS A RECTANGLE OKK THANKS

Answer:

-1

Step-by-step explanation:

the line is written in slope intercept form making it easy to find that the slope is -1

slope intercept form is y= mx+b

That statement is true. When two integers are multiplied together, the result is always an integer. This property is a fundamental characteristic of integers.

Integers are whole numbers that can be positive, negative, or zero. When you multiply any two integers, the result will always be another integer.

For example:

- Multiplying two positive integers: 3 * 4 = 12

- Multiplying a positive and a negative integer: (-5) * 6 = -30

- Multiplying two negative integers: (-2) * (-8) = 16

- Multiplying an integer by zero: 9 * 0 = 0

In each case, the product of the integers is still an integer. This property holds true regardless of the specific values of the integers being multiplied.

It is important to note that this property does not apply to all real numbers. When multiplying real numbers, the result may not always be an integer. However, when specifically dealing with integers, their multiplication will always yield an integer result.

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An integer multiplied by an integer is an integer. True or False?

The period of the given trigonometric function is: 20.

The distance between the repetition of any function is called the period of the function. For a trigonometric function, the length of one complete cycle is called a period.

Sine and cosine functions start repeating the same pattern of y-axis values after every 2(pi). The period is defined as just the distance on the x-axis before the pattern repeats.

Now, looking at the trigonometric graph, we see that the x-interval for which the graph repeats itself is 20

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1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.

2. The line which divides an angle into two different angles is known as a bisector.

4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.

5. Given, Both are situated in the same plan so QA≅QA

6.ΔQXA≅ΔQYA, by the AAS Postulate.

8. Definition of equidistant. XA=XY.

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ΔRST ~ ΔVUT holds true because of the ASA similarity condition. Hence, option (B) 3ST = UT is the answer.

The additional information that can be used to prove that ΔRST ~ ΔVUT is 3ST = UT.

Triangles RST and VUT are connected at point T.

We need to prove that ΔRST ~ ΔVUT.

As we know that both triangles share the common side RT, then the remaining two sides of triangles RST and VUT are

RS and ST and VU and UT, respectively.

ΔRST ~ ΔVUT will only hold true if the remaining two sides of triangles RST and VUT are proportional.

Now, we have to look for the additional information provided in the question which can be used to prove that these

triangles are similar.

3ST = UT is given in the question, which is also known as the angle-side-angle (ASA) similarity condition.

It states that if two triangles have two corresponding angles that are equal and the ratio of the lengths of the sides

between the angles is the same, then the triangles are similar.

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Answer:

b

Step-by-step explanation:

did it on edge 2023

Main Answer:

a)det (3A^−1B^2A^T) is equal to 1728

b)det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] is equal to -3.

Supporting Question and Answer:

How can we calculate the determinant of a matrix?

To calculate the determinant of a matrix, we can use various methods such as cofactor expansion, row reduction, or properties of determinants.

Body of the Solution:

(a) To calculate det (3A^−1B^2A^T), we can use the properties of determinants:

det (3A^−1B^2A^T) = 3^3 * det (A^−1) * det (B^2) * det (A^T)

Since det (A^−1) is the reciprocal of det (A) and det (A^T) is equal to det (A), we can simplify further:

det (3A^−1B^2A^T) = 3^3 * (1/det (A)) * det (B^2) * det (A)

We are given that det (A) = 1 and det (B) = -4, so we substitute these values:

det (3A^−1B^2A^T) = 3^3 * (1/1) * (-4)^2 * 1

det (3A^−1B^2A^T) = 3^3 * 4 * 16

det (3A^−1B^2A^T) = 1728

Therefore, det (3A^−1B^2A^T) is equal to 1728.

(b) To calculate det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c], we can expand the determinant using the properties of determinants:

det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = (a + 3d)(3h - 2b)(-c) + (b + 3e)(3g - 2a)(-c) + (c + 3f)(3g - 2a)(-b)

Expanding and simplifying further:

= -abc - 3bcd - 3acf + 2bcd + 6cdh + 6afh - 2bgh - 6agh - 6a^2c - 2bci - 6afi - 6efg

Combining like terms:

= -abc - 3aci - 2bci - 6a^2c + 6cdh - 6afg - 2bgh - 6agh - 6efg

= -abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg

We are given that det [a b c d e f g h i] = -3, so we can set the expanded expression equal to -3:

-abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg = -3

Therefore, we have determined the expression for det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] in terms of the given variables and the constant -3.

Final Answer:Thus, det (3A^−1B^2A^T) is equal to 1728 and det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = -3.

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a) Determinant  (3A^−1B^2A^T) is equal to 1728

b)det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] is equal to -3.

To calculate the determinant of a matrix, we can use various methods such as cofactor expansion, row reduction, or properties of determinants.

(a) To calculate det (3A^−1B^2A^T), we can use the properties of determinants:

det (3A^−1B^2A^T) = 3^3 * det (A^−1) * det (B^2) * det (A^T)

Since det (A^−1) is the reciprocal of det (A) and det (A^T) is equal to det (A), we can simplify further:

det (3A^−1B^2A^T) = 3^3 * (1/det (A)) * det (B^2) * det (A)

We are given that det (A) = 1 and det (B) = -4, so we substitute these values:

det (3A^−1B^2A^T) = 3^3 * (1/1) * (-4)^2 * 1

det (3A^−1B^2A^T) = 3^3 * 4 * 16

det (3A^−1B^2A^T) = 1728

Therefore, det (3A^−1B^2A^T) is equal to 1728.

(b) To calculate det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c], we can expand the determinant using the properties of determinants:

det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = (a + 3d)(3h - 2b)(-c) + (b + 3e)(3g - 2a)(-c) + (c + 3f)(3g - 2a)(-b)

Expanding and simplifying further:

= -abc - 3bcd - 3acf + 2bcd + 6cdh + 6afh - 2bgh - 6agh - 6a^2c - 2bci - 6afi - 6efg

Combining like terms:

= -abc - 3aci - 2bci - 6a^2c + 6cdh - 6afg - 2bgh - 6agh - 6efg

= -abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg

We are given that det [a b c d e f g h i] = -3, so we can set the expanded expression equal to -3:

-abc - (3a + 2b + 6a^2 + 6af)ci + (6cd - 6ag - 2bg - 6ef)h - 6efg = -3

Therefore, we have determined the expression for det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] in terms of the given variables and the constant -3.

Thus, det (3A^−1B^2A^T) is equal to 1728 and det [a + 3d b + 3e c + 3f ; 3g − 2a 3h − 2b 3i − 2c; −a − b − c] = -3.

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The value of height h is 1/3. Therefore, option (b) is correct.

To solve for the height, h, we need to use the formula for a uniform continuous probability distribution:
f(x) = 1/w for a ≤ x ≤ b
where a is the lower limit of the range of outcomes, b is the upper limit of the range of outcomes, and w is the width of the range of outcomes (b - a).

From the given information, we have:
a = 4
b = 7
w = 3

Substituting these values into the formula, we get:
f(x) = 1/3 for 4 ≤ x ≤ 7.

To find the height, h, we need to find the maximum value of f(x), which occurs at the midpoint of the range of outcomes:
midpoint = (a + b)/2 = (4 + 7)/2 = 5.5

So, we need to evaluate f(5.5):
f(5.5) = 1/3

Therefore, the height, h, is equal to 1/3 which corresponds to option (b).

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The true annual interest rate fοr this lοan is 4.8% (tο the nearest tenth).

Tο calculate the true annual interest rate using the given infοrmatiοn and the fοrmula, we first need tο determine the tοtal amοunt paid οver the life οf the lοan:

Tοtal amοunt paid = Mοnthly payment x Number οf payments

Number οf payments = 5 years x 12 mοnths/year = 60 payments

Tοtal amοunt paid = $170.50 x 60 = $10,230

Next, we can use the fοrmula fοr calculating the true annual interest rate:

Tοtal amοunt paid = Lοan amοunt x (1 + Interest rate)n

where:

Lοan amοunt = $8,500

Interest rate = the annual interest rate expressed as a decimal

n = the number οf years

Substituting the given values, we have:

$10,230 = $8,500 x (1 + Interest rate)5

Dividing bοth sides by $8,500 and taking the fifth rοοt, we get:

(1 + Interest rate) = (10,230 / 8,500)^(1/5)

(1 + Interest rate) = 1.048

Subtracting 1 frοm bοth sides, we get:

Interest rate = 0.048 = 4.8%

Therefοre, the true annual interest rate fοr this lοan is 4.8% (tο the nearest tenth).

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Answer:

47°

Step-by-step explanation:

The given angle and its complement sum to 90°, thus

complement = 90° - 43° = 47°

Answer:

x = 48

Step-by-step explanation:

\(\log_{10}(2x+4)=2\)

\(\implies 10^{\log_{10}(2x+4)}=10^2\)

\(\implies 2x+4=100\)

\(\implies 2x=96\)

\(\implies x=48\)