At the end of the day, a bakery had 6/7 of a pie left over. Louie, Duey and Huey split the pie, with each taking home the same amount of leftover pie. How much pie did Louie take home?

p→r

The law of syllogism, also known as transitivity reasoning, is a legitimate kind of deductive reasoning that adheres to a predetermined pattern. The transitive property of equality states that if a = b and b = c, then a = c. so we can conclude that The law of syllogism is almost  similar to the transitive property.

now if we want to define general case then we can say tha

a→b

and

b→c  => a→c

now according to statements given in the problem

p→q and q→r ⇒ p→r

which completes the syllogism.

hence ,  p→r is the required answer.

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Answer:

Its 280

Step-by-step explanation:

I got it right on A P E X

Therefore , the solution of the given problem of probability comes out to be T distribution, which has 28 degrees of freedom, has the widest distribution.

Probability theory is a branch of mathematics that focuses on calculating the likelihood that an assertion is accurate or that an event will occur. Any quantity above range 0 and 1, with 1 signifying certainty and commonly 0 conveying the probability of occurrence, can be used to indicate a chance.

Here,

Based on standard deviation, the distribution's spread (narrow or wide) is established.

The distribution has a broad spread if the standard deviation is high.

The distribution has a low spread if a standard deviation is minimal.

The standard deviation, often known as the standard error of mean, is uo for the t distribution.

degrees of freedom equal to one.

Standard deviation is high because there are few degrees of freedom (i.e., n is few).

the greater diffusion of t

Standard deviation decreases as freedom degrees increase, or as n increases

tighter t distribution

Consequently, the test statistic takes the value of the normal distribution for very big n. ( z distribution )

The z distribution is therefore the narrowest distribution.

T distribution, which has 28 degrees of freedom, has the widest distribution.

Therefore , the solution of the given problem of probability comes out to be T distribution, which has 28 degrees of freedom, has the widest distribution.

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Answer:

x=-4 or 2

Step-by-step explanation:

x(x+1)=8-x

x^2+x=8-x

x^2+2x-8=0

x^2+4x-2x-8=0

x(x+4)-2(x+4)

(x-2)(x+4)=0

x-2=0

x=2

or

x+4=0

x=-4

The table is attached in the solution.

Given that Maria selling the yogurts and the sandwiches at $3 and $6 respectively,

We need to make a table if she sells 0, 1, 2, 3, 4, 5, or 6 frozen yogurts same for the sandwiches,

Yogurt =

Since one yogurt cost $3 therefore we will multiply the number of yogurts to the unit rate to find the cost of the number of packets given,

Similarly,

Sandwich =

one sandwich cost $6 therefore we will multiply the number of sandwiches to the unit rate to find the cost of the number of packets given,

The table is attached.

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Answer:   \(D. h^{2}+9h+23\)

Step-by-step explanation:

\(f(x)=x^{2} +3x+5\)

1. Input (3+h) instead of x.

\(f(3+h)=(3+h)^{2} +3(3+h)+5\\\)

2. Get rid of parentheses.

\(f(3+h)=9+6h+h^{2} +9+3h+5\\\)

\(f(3+h)=h^{2}+9h+23\)

Therefore, D is the answer.

Answer:

l*b*h is the answer of this question

Answer:

(c)

Step-by-step explanation:

Answer is (c) 2

Its my guess

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

20 + 4 + 40 + 9

Step-by-step explanation:

20 + 4 is 24 and 40 + 9 is 49, so it's pretty much the same thing.

Step-by-step explanation:

length of mall=84m

length of post office=38m

how much longer is the mall than the post office=84-38= 46m

Answer:

1 over 36

Step-by-step explanation:

The correct statement among the given options is "Qualitative data is usually nonnumeric.

Qualitative data is the data that are in the form of non-numerical data, which are usually words, images, or objects.

It refers to data that has a descriptive attribute such as color, smell, shape, or texture.

Qualitative data is collected through methods such as surveys, interviews, observations, and focus groups.

Qualitative data is typically associated with the social sciences such as anthropology, sociology, history, and psychology.

The study of qualitative data is a relatively new field of research that has gained popularity in recent years.

It is used in a variety of disciplines, including marketing research, social science research, and health research.

So, the correct statement is that Qualitative data is usually nonnumeric.

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Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

volume : 7.5 cm²

\(\hookrightarrow \sf Length \ * Width \ * \ Height\)

\(\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3\)

\(\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3\)

\(\hookrightarrow \sf \dfrac{15}{2}\)

\(\hookrightarrow \sf 7.5 \ cm^2\)

Answer:

\(\sf volume=7 \frac12 \ cm^3\)

Step-by-step explanation:

Formula

volume of cuboid = length × width × height

Given dimensions of the ice cube:

Substituting the given values into the formula:

\(\sf \implies volume=2\times 1 \frac14 \times 3\)

Converting to improper fractions:

\(\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31\)

                  \(\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}\)

                  \(\sf =\dfrac{30}{4}\)

Dividing the numerator and denominator by the highest common factor:

\(\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}\)

                  \(\sf =\dfrac{15}{2}\)

Converting the improper fraction into a mixed number:

\(\sf \implies volume=7 \frac12 \ cm^3\)

The bearing from pt 1 to pt2 is in northwest (NW) quadrant.

To determine the quadrant in which the bearing from Point 1 (pt1) to Point 2 (pt2) lies, we need to compare the latitudes and longitudes of both points.

Latitude of pt1 = 12° 53.5' N

Longitude of pt1 = 42° 33' E

Latitude of pt2 = 12° 0.5' N

Longitude of pt2 = 37° 25' E

We can see that the latitude of both points is in the northern hemisphere, which means the bearing will be either NE or NW.

The longitude of pt2 is less than that of pt1, which means the bearing will be towards the west. Therefore, the bearing will be in the northwest (NW) quadrant.

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The acceleration of the particle at t = 36 seconds is 11/8 meters/s2

Here.

a)

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt

Using the second derivative of a and to find the time at 36 seconds is

a(36)=v'(36)

= v(40) - v(32)/40 - 32

= 7 - (-4)/8

a(36) = 11/8 meters/s²

b)

The Trapezoidal Rule:

This is a rule that defines the area under the curves by dividing the total area into smaller trapezoids rather than using rectangles.

The formula for the trapezoidal rule:

T n = 1 2 Δ x ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + ⋯ + 2 f ( x n − 1 ) + f ( x n ) )

∫v(t) dt is the particle’s change in position in meters from time

t = 20 seconds to time 40 t = seconds.

∫v(t) dt = [v(20) + v(25)/2] * 5  + [v(25) + v(32)/2] *7 + [v(32) + v(40)/2] * 8

= [-90/2] + [-84/2] + [24/2]

= -75

c)

For 0 ≤t≤40, must the particle change direction in any of the subintervals indicated by the data in the table

since v(t) is differentiable, v(t) is continuous.

Particle changes direction is v(t) changes sign.

The particle must change direction in (8,20) and (32,40)

v(8)=5>0 and v(20)=-10<0

∴ v(t) changes sign for same C for 8<C<20.

v(32)=-4<0 and v(4)=7>0

∴ v(t) changes sign for some d for 32<d<40

The above is true due to the Intermediate Value theorem.

Since v(t) changes sign in (8,20) and in (32,40) .

The particle changes sign in (8,20) and in (32,40) .

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To find all x ∈ zp such that x^2 ≡ 1 (mod p), we can use the fact that (−1)^2 ≡ 1 (mod p) and (1)^2 ≡ 1 (mod p). Therefore, x ≡ 1 (mod p) and x ≡ −1 (mod p) are the only solutions.

If p = 2, then zp = {0, 1} and we can check that 1^2 ≡ 1 (mod 2) and (−1)^2 ≡ 1 (mod 2), which means that the same solutions as above apply. However, in this case, −1 ≡ 1 (mod 2), so the two solutions collapse into a single solution x ≡ 1 (mod 2). This is the special property of p = 2.


Given that p is prime, we want to find all x ∈ Zp such that x^2 ≡ 1 (mod p).

By definition, x^2 ≡ 1 (mod p) if and only if p divides (x^2 - 1). Now, we can rewrite x^2 - 1 as (x - 1)(x + 1). Since p is prime, it must either divide (x - 1) or (x + 1).

Case 1: p divides (x - 1)
In this case, x ≡ 1 (mod p).

Case 2: p divides (x + 1)
In this case, x ≡ -1 (mod p).

So, the possible values for x are 1 and -1 (mod p). For any prime p, these are the only two solutions.

For the special case when p = 2, we have x^2 ≡ 1 (mod 2). The solutions are x ≡ 1 (mod 2) and x ≡ -1 (mod 2). Since -1 is congruent to 1 (mod 2), there is only one unique solution for x in this case, which is x ≡ 1 (mod 2).

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There are 90 ways to arrange 6 beads of distinct colors in a 2*3 grid if reflections and rotations are considered the same.

In order to reach this result, we may use Burnside's Lemma, which states that the average number of arrangements of a symmetric object's symmetric parts, is taken throughout the set of all possible symmetry operations of the object.

You may fix one element and position the rest around it because of the rotation. You now have a total of 90 configurations available.

Thus, If reflections and rotations are treated equally, there are 90 ways to arrange 6 beads of different colors on a 2*3 grid.

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Answer:

4

Step-by-step explanation:

4x + 15 = x - 3

4x - x = 3 - 15

3x = 12

x = 12 : 3

x = 4

The value of x in the algebraic equation 7 / 2x - 2 / x + 1 = 1 / 4  is 7 and -2

let's find the value of x in the algebraic equation.

7 / 2x - 2 / x + 1 = 1 / 4

Therefore, let's solve the left side.

7 / 2x - 2 / x + 1  = 7(x + 1) - 4x / 2x(x + 1) = 7x + 7 - 4x / 2x² + 2x = 3x + 7 / 2x² + 2x

3x + 7 / 2x² + 2x  = 1 / 4

cross multiply

4(3x + 7) = 2x² + 2x

12x + 28 = 2x² + 2x

2x² + 2x  - 12x - 28 = 0

2x² - 10x  - 28 = 0

x² - 5x - 14 = 0

Therefore,

(x + 2)(x - 7)

hence,

x = -2 or x = 7

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Simplifying and expressing each term in standard and polar form are respectively; 49/2 and  -512 - 512i√3

1) We are given the expression;

[7 cos (45)]²

We know that cos (45) in standard form is 1/√2. Thus;

[7 cos (45)]² = (7 * 1/√2)² = 49/2

2) We are given the expression;

(-2 + 2i√3)⁵

Using binomial theorem, we have;

(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵

Simplifying each term gives;

−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3

⇒ -512 - 512i√3

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The value of n is 45°

the angle between a side of a polygon and an extended adjacent side.

it is also an angle formed by a transversal as it cuts one of two lines and situated on the outside of the line.

The sum of all the exterior angles of a polygon is 360°

The exterior angles of the polygon are, n°, n°, n°, n°, 90°, 90°

The sum of all the exterior angles is 360

so that

n + n + n + 90° + 90° = 360

4n +180 = 360°

4n = 360 - 180°

4n = 180°

n = 180/4

n = 45°

In conclusion, the value of n is 45°

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The indefinite integral of x(5x^2 - 5)^9 dx is:

(5x^2 - 5)^8 / 40 + c

We can find the indefinite integral using the following steps:

1. We can write the integral as (5x^2 - 5)^9 * x^1 dx.

2. We can use the power rule of integration, which states that the integral of x^n dx is x^(n + 1) / (n + 1) + c, where c is the constant of integration.

3. We can simplify the result and add the constant of integration.

The following is the step-by-step solution:

```

∫ x(5x^2 - 5)^9 dx = ∫ (5x^2 - 5)^9 * x^1 dx

= (5x^2 - 5)^9 / 9 + c

```

To check the result, we can differentiate the result and see if we get the original integral.

```

d/dx [(5x^2 - 5)^8 / 40 + c] = (5x^2 - 5)^8 * (10x) / 40 + 0 = x(5x^2 - 5)^8 = ∫ x(5x^2 - 5)^9 dx

```

As we can see, we get the original integral back. Therefore, the answer is correct.

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The inverse is y = x/2 - 4

Steps involved are -

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a) The amount you would have at the end of year three with simple interest is $1,160.

b) The amount you would have at the end of year three with compound interest is $1,259.71.

a) With simple interest, the interest earned is calculated only on the principal amount (the initial deposit) and not on any accumulated interest. Therefore, after one year, you would have earned 8% of $1,000, which is $80.

After two years, you would have earned another $80, for a total of $160 in interest. So after three years, you would have $1,000 (the principal) plus $160 (the interest), which equals $1,160.

b) With compound interest, the interest earned is added to the principal at the end of each period, and the interest for the next period is calculated on the new total. Therefore, after one year, you would have $1,000 plus 8% of $1,000, which is $80, for a total of $1,080. After two years, the interest earned would be 8% of $1,080, which is $86.40, for a total of $1,166.40.

After three years, the interest earned would be 8% of $1,166.40, which is $93.31, for a total of $1,259.71. Therefore, you would have $1,259.71 at the end of year three with compound interest.

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The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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The equivalent logarithmic statement is log base 3 of 9 = 2 for the equation 9 = 3².

To convert the exponential statement 9 = 3² into an equivalent logarithmic statement, we can use the logarithm with base 3.

Step 1: Identify the base and exponent in the exponential statement.

In our case, the base is 3 and the exponent is 2.

Step 2: Write the equivalent logarithmic statement.

Using the base 3 logarithm, we have:

log₃(9) = 2

This logarithmic statement can be read as "the logarithm base 3 of 9 is equal to 2."

The logarithm function gives us the exponent or power that the base needs to be raised to in order to obtain the given number. In this case, log₃(9) tells us that 3 raised to the power of 2 equals 9.

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4(3)(2)/2 + 2² = 12 + 4 = 16