Rewrite 2 ^ x = 128as a logarithmic equation !???

Answer:

2

Step-by-step explanation:do it on a piese of parer them it will make more sence

Answer:

x  =  25    Total worked hours by welder winning 34 $ /h

y  =  21    Total worked hours by welder winning 39 $ /h

Step-by-step explanation:

Let call

"x" numbers of hours worked by welder winning 34 $/h

"y" numbers of hours worked by welder winning 39 $/h

Then according to problem statement

x  +  y  = 46      ⇒     y  = 46  -  x

1669  =  34*x  +  39*y     ⇒  

We got a two equation system, solving

1669  =  34*x  +  39* ( 46  -  x )  ⇒   1669   =  34*x  + 1794 - 39*x

1669 - 1794  = - 5*x      ⇒  -125 = - 5*x

x = 125/5   ⇒  x = 25

And as         y = 46 - x       y  =  46  -  25   ⇒  y  = 21  

Answer:

It's D.

Step-by-step explanation:

Final answer:

The function f(x) = 3x⁴+5x²+1 is an even function because f(-x) equals f(x) for any value of x, confirming the student's statement as true.

Explanation:

The function f(x) = 3x4+5x2+1 is indeed an even function. This can be determined by checking if f(-x) = f(x) for any value of x. An even function is symmetrical about the y-axis and does not change when x is replaced with -x. Applying this to the given function:

f(-x) = 3(-x)4+5(-x)2+1 = 3x4+5x2+1

f(x) = 3x4+5x2+1

Since f(-x) and f(x) are indeed equal, the function is even. Therefore, the correct answer to the student's statement that the function is even is: 4) The student's claim is true, because for any input of x, f(x) = f(-x).

Answer:

There are a total number of 1656 students in the school.

Step-by-step explanation:

Let's set up this word problem in mathematical terms.

We can call the number of Left Handed Students as X,

and we can call the number of Right Handed Students as Y.

Since there are 276 more right handed pupils than left handed, we have the following equation:

X + 276 = Y   -Equation 1

Also, since there are 5/12 ratio of left handed students and 7/12 right handed students, we get:

Total Students = T

(5/12) T = X                  -Equation 2

(7/12) T = Y                  -Equation 3

Substituting equations 2 and 3 into equation 1 we get:

[tex]\frac{5}{12} T+276=\frac{7}{12} T[/tex]

Solving for Total number of students (T) we get:

T = 1656

Answer:

radius = 6

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² - 12x + y² + 4y = - 4

Using the method of completing the square on the x and y terms

add (half the coefficient of the x/y term )² to both sides

x² + 2(- 6)x + 36 + y² + 2(2)y + 4 = - 4 + 36 + 4, that is

(x - 6)² + (y + 2)² = 36 ← in standard form

with r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6

Answer:

6

Step-by-step explanation:

h = -12/-2 = 6

k = 4/-2 = -2

h² + k² - r² = 4

6² + (-2)² - 4 = r²

r² = 36

r = sqrt(36) = 6

Answer:

a)  ¬p : I didn't buy a lottery ticket this week.

b) p ∨ q: I bought a lottery ticket this week or I won the million dollar jackpot.

c) p → q: If I didn't buy a lottery ticket this week, then I won the million dollar jackpot.

d) p ∧ q:  I bought a lottery ticket this week and I won the million dollar jackpot.

e) p ↔ q: I bought a lottery ticket this week if and only if I won the million dollar jackpot.

f ) ¬p → ¬q: If I didn't buy a lottery ticket this week, then I didn't win the million dollar jackpot.

g) ¬p ∧ ¬q: I didn't buy a lottery ticket this week and I didn't win the million dollar jackpot.

h) ¬p ∨ (p ∧ q): I didn't buy a lottery ticket this week or I bought a lottery ticket this week and I won the million dollar jackpot.

Step-by-step explanation:

In logic, a word or group of words that joins two or more propositions together to form a connective proposition it's called connective, also called sentential connective, or propositional connective

1. Negation: the symbol is ¬, or ~. It is use for saying that the proposition is false. This connective proposition only affects one statement.

2. Disjunction ("or"): the symbol is ∨. It is use for saying that at least one of the propositions are true.

3. Conjunction ("and"): the symbol is ∧. It is use for saying that both of the propositions, at the same time are true.

4. Conditional (“if . . . then”): the symbor is →. In this structure the first proposition it's called antecedent and the second one consecuent. For this connective the only case when it's not true is when the antecendent is true and the consecuent is false.

5. Biconditional ("if and only if"): the symbol is  ↔. This structure is a double conditional. And the proposition is true when antecent and consecuent are both true or both false.

Final answer:

The student's question involves translating logical propositions into English sentences. These include negation, disjunction, conjunction, conditional, and bi-conditional statements based on the scenarios presented.

Explanation:

The student wants to express each proposition as an English sentence. The propositions include notations for negation (¬), disjunction (∨), conjunction (∧), and implication (→), as well as bi-conditional (↔).

Each sentence corresponds to different logical statements found in propositional logic.

Answer:

600

Step-by-step explanation:

Answer:

One cubic foot of the stone weigh 10 tons.

Step-by-step explanation:

There is a mistake in the question, thus it is corrected:

A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?

Now, to find the volume of average stone and how much one cubic foot of stone weigh.

Dimension of rectangular prism:

Length = 5 feet.

Height = 5 feet.

Width = 6 feet.

Now, to get the volume of stone which was a rectangular prism we put formula:

[tex]Volume=length\times width\times height[/tex]

[tex]Volume=5\times 6\times 5[/tex]

[tex]Volume=150\ cubic\ feet.[/tex]

The volume of the average stone was = 150 cubic feet.

Weight of stone = 15 tons.

Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:

The volume of the average stone ÷ weight of stone

[tex]150\div 15[/tex]

[tex]=10\ tons.[/tex]

Therefore, one cubic foot of the stone weigh 10 tons.

Answer:

Investments in order by least risk to greatest risk: A, C, E, D, F, B.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are to find 62×1000

We can write in standard form

62×10³

6.2×10×10³

Using indices

a^m × a^n = a^(m+n)

Therefore,

6.2×10¹+³

6.2×10⁴

Using the normal multiplication

................1000

...............×. .62

...…......-------------

....., ... ..2 0 0 0

.......+.6 0 0 0

-------------------

..........6 2 0 0 0

----------------------

Answer:

a. E(F)=0.875

b. 99.9976%

c. P(X=2)=0.1683

Step-by-step explanation:

a. We notice that this is a binomial distribution with the probability of success;

[tex]p=\frac{5}{40}=0.125[/tex]

#We are given the sample size, n=7. The Expected value is calculated as:

[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]

Hence the expectation, E(F)=0.875

b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;

[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]

Hence, the range of F is 99.9976%

c. The probability that F=2 is calculated  using the binomial distribution function as:

[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]

Hence, the probability of F=2 is 0.1683

Using the hypergeometric distribution, it is found that:

a) E(F) = 0.875

b) The range is {0, 1, 2, 3, 4, 5}

c) 0.1741 = 17.41% probability that F = 2.

The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

The expected value of the hypergeometric distribution is:

[tex]E(F) =  \frac{nk}{N}[/tex]

Hence:

[tex]E(F) = \frac{35}{40} = 0.875[/tex]

Item b:

The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.

Item c:

The probability is P(X = 2), applying the hypergeometric distribution.

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]

0.1741 = 17.41% probability that F = 2.

You can learn more about the hypergeometric distribution at https://brainly.com/question/25303388

Answer:

Velocity of the 24.6 g marble is 31 cm/s.

Step-by-step explanation:

Given:

Marble 1:

Mass of the marble [tex](m_1)[/tex] = 12.3 gm

Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s

Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s

Marble 2:

Mass of the marble [tex](m_2)[/tex] = 24.6 gm

Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s

Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?

From the law of conservation of momentum, we know that momentum before equals the momentum after :

So,

⇒ [tex]P(i)=P(f)[/tex]

⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]

⇒ Plugging the values.

⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]

⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]

⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]

⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25

⇒ [tex]762.6=24.6\times v_2_f[/tex]

⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6

⇒ [tex]31=v_2_f[/tex]

⇒ [tex]v_2_f =31[/tex] cm/s

The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.

Answer:

t=2652

Step-by-step explanation:

Answer: the ship unloaded 1455 tons of cargo at the bahamas.

Step-by-step explanation:

Let x represent number of tons of cargo that the ship unloaded at the bahamas.

The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be

5678 - x

The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be

5678 - x + 3x

= 5678 + 2x

If the ship holds 8588 tons now, it means that

5678 + 2x = 8588

2x = 8588 - 5678

2x = 2910

x = 2910/2

x = 1455 tons of cargo

Answer:

  8

Step-by-step explanation:

The ratio of white paint to blue paint in the mix is ...

  40% : 20% = 2 : 1

We can multiply this ratio by 4 cups to find ...

  white : blue = 8 cups : 4 cups

There are 8 cups of white paint in the mixture.

Answer: the number of cups of white paint are used is 8

Step-by-step explanation:

Let x represent the total number of cups of paint used in the mixture.

40% of the mixture is white paint, this means that the number of cups of white paint used is 0.4x

20% of the mixture is blue paint, this means that the number of cups of blue paint used is 0.2x

If the rest is red, it means that the number of red cups used is

x - (0.2x + 0.4x) = 0.4x

There are 4 cups of blue paint used in a batch of lilac paint. This means that

0.2x = 4

x = 4/0.2 = 20

Therefore, the number of cups of white paint are used is

0.4 × 20 = 8

Answer:

a) 9(t - u)

Step-by-step explanation:

x = 10t + u

y = 10u + t

x - y = 10t + u - 10u - t

= 9t - 9u

= 9(t - u)

Answer:

Amplitude is 17

Period = 12

Vertical shift of 50

Step-by-step explanation:

One complete cycle in 12 months

Mean line is at y = 50, so vertical shift of 50

Amplitude = 67-50 = 17

Or , 50 - 33 = 17

The vertical shift, amplitude, and period of the given equation would be as follows:

Amplitude [tex]= 17[/tex]

Period [tex]= 12[/tex]

Vertical Shift [tex]= 50[/tex]

Given that,

Duration of the cycle [tex]= 12[/tex] months

∵ Period [tex]= 12 months[/tex]

The Mean line lies at [tex]y = 50[/tex]

So,

The vertical shift [tex]= 50[/tex]

Now,

Amplitude [tex]= 67-50[/tex]

[tex]or[/tex]

[tex]50 - 33[/tex]

[tex]= 17[/tex]

Learn more about "Amplitude" here:

brainly.com/question/9351212

Answer:

cluster sampling

Step-by-step explanation:

ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.

The two problems are almost identical: you have to set up a system, and then solve it.

In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.

We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).

So, we have the system

[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]

We can use the first equation to substitute in the second

[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]

And then solve for [tex]g[/tex]:

[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]

For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]

And you can solve it in the very same way we solved the previous one.

Answer:

The measure of each angle is 143 degrees.  

Step-by-step explanation:

We are given the following in the question:

A nonagon in which measure of seven angles are:

138, 154, 145, 132, 128, 147, 130.

Angle sum property of a nonagon:

Let the two equal angle of nonagon be x degrees. Thus, we can write:

[tex]138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143[/tex]

Thus, the measure of two equal angles is 143 degrees.

Final answer:

Using the formula for the sum of interior angles of a polygon and subtracting the sum of the seven given angles from the total, we find that the remaining two equal angles in a nonagon each measure 111 degrees.

Explanation:

The measure of the seven angles in a nonagon are given as 138, 154, 145, 132, 128, 147, and 130 degrees. To find the measure of each of the remaining two equal angles, we first need to calculate the sum of the angles in a nonagon. Using the formula for the sum of interior angles (S = (n-2) × 180 degrees, where n is the number of sides), we find that a nonagon has interior angles that add up to 1260 degrees. We then sum the seven given angles and subtract this total from 1260 to find the total measure of the remaining two angles. Finally, we divide this result by 2 to get the measure of each of the two equal angles. This allows us to determine that the measure of each of the two equal angles in the nonagon is 111 degrees.

Answer:

(A) 0.15625

(B) 0.1875

(C) Can't be computed

Step-by-step explanation:

We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let X = Amount of time taken by student to complete a statistics quiz

So,   X ~ U(32 , 64)

The PDF of uniform distribution is given by;

    f(X) = [tex]\frac{1}{b-a}[/tex] ,  a < X < b      where a = 32 and b = 64

The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]

(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)

   P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625

(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43)  = P(X <= 43) - P(X < 37)

    P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375

    P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625

    P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) Probability that student complete the quiz in exactly 44.74 minutes

     = P(X = 44.74)

The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.

Answer:

This is true

Step-by-step explanation:

10x1 is 10. 10x10 is 100. but if u did 100x10 you would add the amount of zeros total. which would be 1000. so 400x10 is 4000

Answer:

a) [tex]\mu = 24,\sigma = 3.46[/tex]

b) Significantly low:

[tex]x < 17.08[/tex]

Significantly high:

[tex]x > 30.92[/tex]

c) 42 girls are significantly high.                                      

Step-by-step explanation:

We are given the following in the question:

[tex]p = 0.5[/tex]

a) mean and the standard deviation for the numbers of girls in groups of 48 births

[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]

b) Range rule of thumb

Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.

[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]

Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.

[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]

c) Significance of 42 girls

[tex]42 > \mu + 2\sigma[/tex]

Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.

Answer:

a) Water height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1

b) g = 1

H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5

g=2

H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7

g=3

H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5

c) Greatest height

Find the vertex of the parabole

The vertex is at the mid point between the two roots.

To find the roots you can use the quadratic equation

The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2

The middle poin is 5/2 = 2.5

Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3

hope this helps

Answer:

  x^2 -11x +30 = 0

Step-by-step explanation:

If these two integers are solutions of the quadratic, then its factors are ...

  (x -5)(x -6) = 0

Multiplying this out, we get ...

  x^2 -11x +30 = 0

Answer:

SAS

Step-by-step explanation:

Answer:

1.19 revolutions per second.

Step-by-step explanation:

Given:

A rotating object makes 5/6 of a revolution in 7/10 second.

To find:

Find the approximate speed in revolutions per second ?

Solution:

As here given that a rotating object makes 5/6 of a revolution in 7/10 second,

we will have to find that in one second how many revolution does this object make:

By unitary method:

In [tex]\frac{7}{10}[/tex] second, a rotating object makes = [tex]\frac{5}{6}[/tex]  revolution

In 1 second, a rotating object makes = [tex]\frac{5}{6}\div\frac{7}{10}[/tex]

                                                            [tex]=\frac{5}{6}\times\frac{10}{7} = \frac{50}{42}=1.190\ revolution[/tex]

Therefore, the approximate speed of object is 1.19 revolution per second.

We can also find by, [tex]speed = \frac{distance}{time}[/tex]

                                            [tex]=\frac{5}{6} \div\frac{7}{10} \\=\frac{5}{6} \times\frac{10}{7} =\frac{50}{42} = 1.19[/tex]

We can use any one to solve this type of question:

Finally, the approximate speed is 1.19 revolutions per second.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is an = a1 + (n-1)d, and the explicit formula is an = a1 + (n-1)d.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is given by: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. The explicit formula for an arithmetic sequence is given by: an = a1 + (n-1)d. The explicit formula allows you to directly find any term in the sequence without having to find the previous terms.

Answer:

is d

Step-by-step explanation:

The type of Function shown in the graph

Step-by-step explanation:

1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.

2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.

3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.

Answer:

y= 1/2 csc (x)

Step-by-step explanation:

probably