Find the value of 4³

The measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

What is exterior angle theorem?

In Euclid's Elements, Proposition 1.16, known as the exterior angle theorem, states that the measure of a triangle's exterior angle is greater than either of its remote interior angles. Due to the fact that its proof is independent of the parallel postulate, this is a fundamental result in absolute geometry.

Let the triangle CDE is given.

m ∠D = (10y + 4)°,  m ∠C = (4y + 6)°,  m ∠DEF = 108°

We have to find the measure of each angle of triangle.

By using the Exterior angle theorem,

        m ∠C + m ∠D = m ∠DEF

(4y + 6)° + (10y + 4)° = 108°

                 14y + 10° = 108°

                         14y = 98°

                            y = 7°

⇒ m ∠C = 4y + 6 = 4(10) + 6 = 40 + 6 = 46°

 m ∠D = 10y + 4 = 10(10) + 4 = 100 + 4 = 104°

Since, the measure of three angle of triangle is 180°.

⇒ m ∠C + m ∠D + m ∠DEF = 180°

         46° + 104° + m ∠DEF = 180°

                  150° + m ∠DEF = 180°

                             m ∠DEF = 30°

Hence, the measure of each angle of triangle is,

m ∠C  = 46°

m ∠D  = 104°

m ∠DEF = 30°  

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Answer:

  (d)  log(2) +3log(x)

Step-by-step explanation:

You want the logarithm of y when 2x³ = y.

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

The logarithm of y will be ...

  log(2x³) = log(2) +log(x³)

  = log(2) +3·log(x)

Answer:

B, because the equation of kinetic energy is = mv²

We can choose the x-axis, y-axis and line represented by x = y for our transformation.

The line across which the figure is flipped is known as the mirror line or the line of reflection. We can draw the line of reflection by finding the mid-point of the given two points; the line should pass through the midpoint.

We can perform the reflection of a given figure over any axis. The reflection of any given polygon can be of three types:

1) Reflection over x-axis: When we reflect a figure or polygon over the x-axis, then the x-coordinates of all the vertices of the polygon will remain the same while the sign of the y-coordinate will change. The line of reflection will be the x-axis when a figure is reflected across the x-axis.

2) Reflection over y-axis: When we reflect a figure or polygon over the y-axis, then the y-coordinates of all the vertices of the polygon will remain the same while the sign of the x-coordinates will change. The line of reflection is along the y-axis when a figure is rotated over the y-axis.

3) Reflection over the x and y axis: When a point or figure is reflected across the x-axis and the y-axis, we write that the line is reflected over x=y. We write it as a reflection of a function of over x = y. This type of reflection can further be divided into two scenarios: a) y = x and b) y = -x.

Thus, we can choose the x-axis, y-axis and line represented by x = y for our transformation.

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Answer:

the answer is 5.1 killograms

Step-by-step explanation:

hope this helps

A relation 'f' is referred to as a function if each element of a non-empty set X has just one image or range to a non-empty set Y. Here the function is not a simple power function.

Each function and the requested variable are:

y = 5x³

In this function, k = 5 and p = 3.

y = -2\(x^{-1/2}\)

In this function, k = -2 and p = -1/2.

y = 2

This function is a constant function and not a power function. Therefore, neither k nor p can be identified.

y = 4\(\sqrt{x}\)

In this function, k = 4 and p = 1/2.

y = 7/x²

In this function, k = 7 and p = -2.

y = \(3x^4 + 2x^3 - 5x^2 + 6\)

This function is not a simple power function. Therefore, neither k nor p can be identified.

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The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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The likelihood of the agent making 2 sales out of 8 appointments is 0.132.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

The probability of making a sale on any appointment is 1/5, and the probability of not making a sale is 4/5.

We can use the binomial distribution to find the probability of making 2 sales out of 8 appointments

P(2 sales) = (8 choose 2) × (1/5)² × (4/5)⁶

where (8 choose 2) = 28 is the number of ways to choose 2 appointments out of 8.

So, plugging in the values, we get

P(2 sales) = 28 × (1/5)² × (4/5)⁶

= 0.132

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The value of f(12) is 78, which means that the smallest number of trains that can be formed from a double 12 set of dominoes is 78.

The value of $f(12)$, which represents the smallest number of trains that can be formed from a double-12 set of dominoes, can be found using a formula.

In general, for a double-$n$ set of dominoes, the formula to find the minimum number of trains, $f(n)$, is given by:

$f(n) = \frac{n \cdot (n + 1)}{2}$

Substituting $n = 12$ into the formula,

we get:

$f(12) = \frac{12 \cdot (12 + 1)}{2}$

Simplifying the expression, we have:

$f(12) = \frac{12 \cdot 13}{2}$

$f(12) = \frac{156}{2}$

$f(12) = 78$

Therefore, the value of $f(12)$ is 78, which means that the smallest number of trains that can be formed from a double-12 set of dominoes is 78.

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The value of \($f(12)$\), which represents the smallest number of trains that can be formed from a double-\($n$\) set of dominoes, can be determined by using the formula:\($f(n) = \frac{n(n+1)}{4}$.\)

To find f(12), we substitute n with 12 in the formula:
\($f(12) = \frac{12(12+1)}{4} = \frac{12(13)}{4} = \frac{156}{4} = 39$\)

Therefore, \($f(12) = 39$\), meaning that the smallest number of trains that can be formed from a double-12 set of dominoes is 39.

Let's break down the formula to better understand how it works. In a double-n set of dominoes, there are n pairs of numbers from 0 to n-1. Each train consists of a sequence of dominoes, where each domino has two numbers. The goal is to use every domino exactly once in the trains.

The formula \($f(n) = \frac{n(n+1)}{4}$\) calculates the sum of the first n natural numbers, which corresponds to the number of dominoes in the set. Dividing this sum by 4 gives the minimum number of trains that can be formed.

For example, when \($n=6$, $f(6) = \frac{6(6+1)}{4} = \frac{42}{4} = 10.5$\). Since the number of trains must be a whole number, we round up to 11. Therefore, f(6)=11.

In summary, the formula \($f(n) = \frac{n(n+1)}{4}$\) gives the smallest number of trains that can be formed from a double-n set of dominoes. By substituting n with 12, we find that f(12)=39.

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Answer:

Step-by-step explanation:

(x – 4)(x – 4) = 0.

So factor are x-4=0

X=4 (D) is the answer

Answer:

a) 81

b) 2401

c) 100

d) 78125

Step-by-step explanation:

a) \(3^{2}\) x \(3^{2}\)  = \(3^{4}\)  When the bases are the same and you are multiplying powers, you add the exponents.

\(3^{4}\) means 3x3x3x3 or 81

b) 7 x \(7^{4}\) = \(7^{5}\) When the bases are the same and you are multiplying powers, you add the exponents.  When you do not see an exponent like the number 7, the exponent is 1.

7 = \(7^{1}\)

\(7^{4}\) means 7x7x7x7x or 2401

c) \(\frac{10^{9} }{10^{7} }\)  = \(10^{2}\)  When the bases are the same and you are dividing, you subtract the exponents.

\(10^{2}\) means 10x10 = 100

d) \(\frac{5^{8} }{5}\)= \(5^{7}\) When the bases are the same and you are dividing, you subtract the exponents.

\(5^{7}\) means 5x5x5x5x5x5x5 =

Answer:

a) \(\sf 3^4\)

b) \(\sf 7^5\)

c) \(\sf 10^2\)

d) \(\sf 5^7\)

Step-by-step explanation:

a) → → →

\(\sf 3^2 \times 3^2\) (Apply exponent rule)

\(\sf 3^{2+2}\) ( Add numbers)

\(\bf 3^4\)

b) → → →      

\(\sf 7 \times 7^ 4\) (Apply exponent rule)

\(\sf 7^{1+4}\) (Add numbers)

\(\bf 7^5\)

c) → → →

\(\sf 10^9 \div10^7\) (Apply exponent rule)

\(\sf 10^{9-7}\) (Add numbers)

\(\bf 10^2\)

d) → → →

\(\sf 5^8 \div 5\) (Apply exponent rule)

\(\sf 5^{8-1}\) (Add numbers)

\(\bf 5^7\)

____________________

Hope this helps!

Have a great day!

Answer:

30625

Step-by-step explanation:

Answer:

175²

Step-by-step explanation:

7 × 7 × 5 × 5 × 5 × 5

= (7 × 7) × (5 × 5 × 5 × 5)

= 7² × 5⁴

= 49 × 625

= 30.625

\( \sf = \sqrt{30.625} \)

\( \sf = \sqrt{175 \times 175} \)

\( \sf = 175\)

\( \sf = {175}^{2} \)

Conclusion:

Exponential Form of 7 × 7 × 5 × 5 × 5 × 5 adalah 175².

The total number of ways a chairperson, a secretary, and a treasurer can be selected is 990 ways.

What is meant by selection?

A selection principle is a rule in mathematics that states it is possible to choose elements from predetermined sequences of sets in order to generate mathematically important objects. Studying these principles and how they relate to other mathematical features is called the theory of selection principles.

It is said that there are a total of 11 members on a board of directors.

We are asked to find the number of ways a chairperson, a secretary and a treasurer can be selected.

Number of places to be selected for = 3

Number of members = 11

We are assuming the order of selection in the order of importance of the designation.

So first chairperson, second secretary and third treasurer will be selected.

Then the number of ways the chairperson can be selected = 11 ways

When the chairperson is selected, 1 person reduces.

Then the number of ways the secretary is selected = 10

Now the remaining people are 9.

Then the number of ways the treasurer is selected = 9

Therefore the total number of ways a chairperson, a secretary, and a treasurer can be selected is = 11*10*9 = 990 ways.

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Probability of Parnell winning the game is 2/13 and the probability of Parnell losing the game is 11/13.

The two events in question, drawing a queen or drawing a 7 from a standard deck of 52 cards, are mutually exclusive.What is the probability that Parnell wins the game? When Parnell draws a card from a well-shuffled standard deck of 52 cards, he wins the game if the card he draws is either a queen or a 7. The total number of possible outcomes is 52. The total number of possible outcomes that would result in Parnell winning the game is 8 (4 queens and 4 sevens).Thus, the probability of Parnell winning the game is:P(Parnell wins) = number of favourable outcomes/total number of possible outcomes= 8/52= 2/13What is the probability that Parnell loses the game?The probability that Parnell loses the game is simply the complement of the probability of winning, which is:P(Parnell loses) = 1 - P(Parnell wins)= 1 - 2/13= 11/13. Therefore, the probability of Parnell winning the game is 2/13 and the probability of Parnell losing the game is 11/13.

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Answer:

$130

Step-by-step explanation:

Answer:

$130

Step-by-step explanation:

1300×10%

$130

Answer:

SA=2 bi r h+2 bi r squared

Answer:

\(\boxed {\boxed {\sf mean \approx 6.3}}\)

Step-by-step explanation:

We are given this data and asked to find the data.

8, 7, 8, 5, 4, 6

The mean is also called the average. It is found by dividing the sum of the terms by the number of terms.

\(mean= \frac {sum \ of \ terms}{number \ of \ terms}\)

First, we calculate the sum of the terms. Add up all the numbers.

\(mean=\frac{38}{number \ of \ terms}\)

Next, divide by the number of terms. There are 6 terms (also, there are 6 students that reported).

\(mean=\frac{38}{6}\\mean=6.33333333333\)

Let's round to the nearest tenth.

The 3 in the hundredth place tells us to leave the 3 in the tenth place.

\(mean \approx 6.3\)

The mean number of movies the students saw is approximately 6.3

Step-by-step explanation:

Terms are

\( \rm \mapsto \: mean = \frac{sum \: of \: terms}{number \: of \: terms} \\ \rm \mapsto \: \frac{8 + 6 + 8 + 5 + 4 + 6}{6} \\ \rm \mapsto \: \frac{14 + 13 + 10}{6} \\ \rm \mapsto \: \frac{37}{6} \\ \rm \mapsto \: 6.166 \\ \rm \mapsto \: 6.1 \overline{6} \\ \rm \mapsto \: 6.2\)

\(\boxed{\large{\sf Mean\approx 6.2}}\)

\(\sf Knowledge\:booster{\begin{cases}\bf{\dag}\:\:\underline{\textsf{Fraction Rules :}}\\\\\bigstar\:\:\sf\dfrac{A}{C} + \dfrac{B}{C} = \dfrac{A+B}{C} \\\\\bigstar\:\:\sf{\dfrac{A}{C} - \dfrac{B}{C} = \dfrac{A-B}{C}}\\\\\bigstar\:\:\sf\dfrac{A}{B} \times \dfrac{C}{D} = \dfrac{AC}{BD}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{C}{D} = \dfrac{AD}{BD} + \dfrac{BC}{BD} = \dfrac{AD+BC}{BD} \\\\\bigstar\:\:\sf\dfrac{A}{B} - \dfrac{C}{D} = \dfrac{AD}{BD} - \dfrac{BC}{BD} = \dfrac{AD-BC}{BD}\\\\\bigstar \:\:\sf \dfrac{A}{B} \div \dfrac{C}{D} = \dfrac{A}{B} \times \dfrac{D}{C} = \dfrac{AD}{BC}\end{cases}}\)

You would need to add 16 tablespoons of plant food to 1 cup of water based on the given ratio of 1 tablespoon per gallon of water. Then 1/16 tablespoon should be added to 1 cup.

If you need to add 1 tablespoon of plant food per gallon of water, and you want to determine how much plant food you would need to add to 1 cup of water, we can use a conversion factor.

1 gallon is equal to 16 cups. Therefore, to convert from gallons to cups, we can use the conversion factor:

1 gallon / 16 cups.

Since you need to add 1 tablespoon of plant food per gallon, we can set up a proportion to find the amount of plant food needed for 1 cup of water:

1 tablespoon / 1 gallon = x / 1 cup.

To solve this proportion, we can cross-multiply:

1 tablespoon * 1 cup = 1 gallon * x.

x = (1 tablespoon * 1 cup) / 1 gallon.

Using the conversion factor of 1 gallon / 16 cups, we can substitute the value:

x = (1 tablespoon * 1 cup) / (1 gallon / 16 cups).

x = (1 tablespoon * 1 cup) * (16 cups / 1 gallon).

x = 16 tablespoons.

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Answer:

Step-by-step explanation:

open the icon

The price of the coat after a 40% increase in price will be $77.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A store pays $55 for a coat. The store marks up the price by 40%. Then the marked price is calculated as,

P = $55 x (1 + 0.40)

P = $55 x 1.40

P = $77

The price of the coat after a 40% increase in price will be $77.

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The percentage of the students who weigh more than 125 lbs is 50%.

The question asks to find the percentage of female students who weigh more than 125 lbs. As we know, the second quartile is the median, which means half the students weigh less than 125 lbs, and the other half weigh more than 125 lbs.

Therefore, the answer is 50%.

The quartile is a mathematical concept used in statistics that divides an ordered data set into four equal parts.

The first quartile, Q1, divides the lowest 25% of the data from the rest;

The second quartile, Q2, is the median, or the middle value of the data; and

The third quartile, Q3, divides the upper 25% of the data from the rest.

Let’s discuss the given information. The 1st, 2nd, and 3rd quartiles of female students' weight at a major university are 95 lbs., 125 lbs., and 138 lbs. respectively.

Here, the 2nd quartile i.e., 125 is the median value.

Therefore, half of the female students at a major university weigh less than or equal to 125 lbs, and the other half of the female students weigh more than or equal to 125 lbs.

So, the percentage of students who weigh more than 125 lbs is 50%.

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Answer:

E

Step-by-step explanation:

Here, we want to find the area of the shaded portion on the graph.

That would be P(-1.2<z<0.85)

we complete this by checking these values on the standard score table as follows;

P( z< 0.85) - P(z<-1.2) = 0.68727

The rows selected for the predicate "enrol_mark >= 50" by the DBMS will include all rows where the value of the column "enrol_mark" is greater than or equal to 50.

In a DBMS (Database Management System), a predicate is a condition or criteria used to filter and select specific rows from a database table. In this case, the predicate "enrol_mark >= 50" indicates that we are interested in selecting rows where the value of the "enrol_mark" column is greater than or equal to 50.

When the DBMS evaluates this predicate, it will scan the table and compare the value of the "enrol_mark" column for each row. If the value is greater than or equal to 50, the row will be selected and included in the result set. Rows with "enrol_mark" values less than 50 will not be included in the result set.

It's important to note that the actual rows selected by the DBMS will depend on the specific data in the table. If there are rows where the "enrol_mark" column has values greater than or equal to 50, those rows will be selected. If there are no such rows, then the result set will be empty.

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Answer:

-78

Step-by-step explanation:

You get -78 if you substitute x=-3 into the cubic.

Answer:

x = 101

Step-by-step explanation:

We have given that,

\(x\times 11=1111\)

It is required to find the value of x such that the equation becomes true.

For this divide 11 in both sides of the above equation such that,

\(x=\dfrac{1111}{11}\\\\x=101\)

So, when the value of x is 101, the above equation becomes true.

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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Answer:

I would say C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

You can simplify it into 3 and 2.25. This can be averaged into 2. So, 2 feet for every second. :)

I don't know the choices for the bottom questions, but the answer is x>2, meaning any number higher than 2 works, or any number below 2 doesn't work.

The probability p(2) is 0.125e-0.5(e).

Given, Y follows a Poisson distribution, and p(0) = P(1).

The probability mass function of Poisson distribution is given by:

P(Y = y) = (e^(-λ)*λ^y) / y!

Let p(0) = P(1) = a, then using the Poisson distribution's probability mass function, we get:

P(Y=0) = a = (e^(-λ)*λ^0) / 0! => a = e^(-λ)

Also, P(Y=1) = a = (e^(-λ)λ^1) / 1! => a = λe^(-λ)

Solving these two equations, we get λ=1, and hence a = e^(-1).

Now, to find p(2), we can use the Poisson distribution's probability mass function and substitute λ=1:

P(Y=2) = (e^(-1)*1^2) / 2! = 0.125e^(-0.5)

Therefore, p(2) is 0.125e^-0.5(e).

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