How do you write the log notation for 3^x = 64?

The value of (3/8+3/4)(1/3+1/6) in its most basic form of fraction is 5/8.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

Here,

(3/8+3/4)−(1/3+1/6)

=3/8+3/4

=(3+6)/8

=9/8

=1/3+1/6

=(2+1)/6

=3/6

=1/2

=9/8-1/2

=(9-4)/8

=5/8

The value of (3/8+3/4)−(1/3+1/6) is 5/8 in the simplest form of fraction.

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All of the given numbers are irrational numbers.  

A real number that can't be stated as a ratio of integers is said to be an irrational number. In simple words, an Irrational number is a number that cannot be represented as p/q where q ≠ 0.  

An irrational number's decimal expansion is neither ending nor recurrent i.e the decimal expansion of an irrational number will be a Non-terminating decimal number.  

Here are some examples of Irrational Numbers

Here we have

[tex]1.7 \overline {3}[/tex] ,  π, ∛90, and √60    

If we observe the given numbers

[tex]1.7 \overline {3}[/tex] = 1.73333333..... is a Non -terminating decimal number  

π is an example of an irrational number

∛90  cannot be represented as a p/q form

√60 = √4 × 15 = 2√15  where √15 is an irrational number

From above information

The given numbers  π, √90, and √60 all are irrational numbers

Therefore,

All of the given numbers are irrational numbers

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Answer:

There are 8! (8 factorial) ways for 8 people to be seated in an 8-passenger van. This is because there are 8 choices for the first person to sit, 7 choices for the second person, 6 choices for the third person, and so on, until there is only 1 choice for the last person. Therefore, the total number of ways for the 8 people to be seated is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!, which is equal to 40,320.

The  missing side length in the given right triangle is d) 23.6cm if the other two sides lengths are 14cm and 19cm respectively. So, correct option is d.

We know very well that if a triangle is a right angled it means that  Pythagorean Theorem is applicable on it.

Pythagorean Theorem states that if a triangle is right angled then the sum of square of two sides which are originating from that angle which is 90 degree is equal to square of third side.

In other words,a²+b²=c² where a and b are two sides originating from 90 degree angle and c is the third side which is opposite of the 90 degree angle.

Now, we have a=14 and b=19cm,we need to find value of c.

So, putting the values, we get

=>14² + 19² =c²

=>c²=361+196

=>c² = 557

=>c=√557

=>c=23.6cm

Hence, missing side length is d)23.6cm

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(Complete question) is:

what is the missing side length in this right triangle if the other two sides length are 14cm and 19cm respectively ? round the answer to the nearest tenth.5.7 cm5.7 cm12.8 cm12.8 cm23.6 cm

Answer:

C,D

Step-by-step explanation:

C and D  are multiplying 250 by  a number greater than one so the result will be greater than 250

 The first two are multiplying 250 by a frction less than one....the result will be less than 250

Answer:

JL = 7.5

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{JL}{AC}[/tex] = [tex]\frac{JK}{AB}[/tex] ( substitute values )

[tex]\frac{JL}{2.5}[/tex] = [tex]\frac{10.5}{3.5}[/tex] ( cross- multiply )

3.5 × JL = 2.5 × 10.5 = 26.25 ( divide both sides by 3.5 )

JL = 7.5

Principal will be $1000

Given values

Simple interest, SI= $800

Interest rate, R=8%

Time, T=10 months

Principle, P= Y

As we know;

[tex]Simple Interest, SI=P×R×T[/tex]

By substituting the values, we get

$800= Y ×8% ×10

$800=0.8Y

$800÷0.8= Y

$1000=Y

Thus the above response is correct.  

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Answer: 96

Step-by-step explanation:

The easy way to do this is to start backward. The last step she did before she got 10.5 as her answer was dividing her answer by 2.

So we can just multiply 10.5 by 2 to reverse the last step.

After doing that we get 21. The step Lara did before dividing by 2 was subtracting 11.

So we can just add 11 to 21 to reverse this step.

After doing that we get 32. The step Lara did before subtracting 11 was dividing by 3.

So we can just multiply 32 by 3 to reverse this step.

After doing that we get 96. So the number that Lara started with is 96.

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.

Equiangular simply implies "equal angles." 2. A triangle with acute angles is one in which each of the three internal angles is smaller than 90 degrees.

A quadrilateral is a rhombus if each of its diagonals bisects the vertex angles through which it travels.

∴Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

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The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).

It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

To find the area under the normal curve at a specific value of z we look into the normal distribution table.

At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.

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The chance of a difference this large (or larger) happening by chance would be 6.03%

In this question, we have been given a die is rolled 1,000 times. the total number of spots is 3,711 instead of the expected 3,500

We need to find the chance of a difference this large (or larger) happening by chance.

The total number of spots is 3,711 instead of the expected 3,500.

So, the difference is:

3711 - 3500 = 211

So, the chance of a difference:

211/3500

= 0.0603

= 6.03%

Therefore, the chance of a difference this large happening by chance = 6.03%

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There are 144 ways to place 4 pairs of shoes per shelf in the store.

What is a permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

This question can be solved using basic logic . One can also solve this by using permutations.
Since 12 different models arrive and 4 pairs of shoes should be placed per shelf , the answer can be sort by

4!×3! = [ 4×3×2×1] × [3×2×1] = 24×6 = 144.

( Because 4 pairs of shoes can be interchanged among themselves , therefore 4! , and 12/4=3 , so the 12 pair of shoes can be organised amongst 3 shelves , and hence 3!)
Therefore , none of the options is correct. The correct answer is 144 ways.
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The valid converse of the statement is, Yes. If x + 4 is even, then x is even. If x is even, then x + 4 is even.

A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The converse statement is known as p⇒ q in geometry. In logic and mathematics, the reverse of a categorical or implicational statement is the outcome of reversing its two constituent statements, and it is denoted by the symbol q⇒ p. The opposite of the implication P ⇒ Q is Q P. The inverse of the categorical assertion All S are P is that All P are S.

Given,

If x is even, then x + 4 is even.

The valid converse of the statement is,

Yes. If x + 4 is even, then x is even.

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There are 3 dimes and 12 nickels

Two or more expressions with an Equal sign is called as Equation.

Given,

let x = the number of dimes

then  4x = the number of nickels =y

0.05(4x) = the value of the nickels

0.10x = the value of the dimes

Since the total value of the coins is $0.90 we can write the equation:

0.05(4x) + 0.1x = 0.90

0.2x + 0.1x = 0.90

0.3x = 0.90

Divide both sides by 0.3

x = 3

Hence, there are 3 dimes and 12 nickels

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The answer is false because the answer will be 0.04863%

To find the periodic interest rate we have to know about the following terms:-

Interest Rate (R)

It is the nominal interest rate or "stated rate" in percent. r = R/100

Compounding Periods (m)

It is the number of times compounding will occur during a period.

Periodic Interest Rate (P)

This is the rate per compounding period, such as per month when your period is year and compounding is 12 times per year.

R ={  (1 + i/m) to the power m/n - 1 }

Where,

i = nominal annual rate

n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.

m = number of compounding periods per year

The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.

So, R = 0.04863%

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Answer:

£12000

Step-by-step explanation:

1 year = 1.5%

4 years = 6%

6% = 0.06

200000 times 0.06 = £12000

So, Katy will get £12000 interest rate at the end of 4 years.

If you can, please give me a Brainliest; thank you, and have a good day!

Answer:

£3,137

Step-by-step explanation:

First year: £200000 x 1.5% = £3,000

Second year: £203,000 x 1.5% = £3,045

Third year: £206,045 (because of 203,000+3,045) x 1.5% = £3,090.675

Last year: £209,135.675 x 1.5% = approximately £3,137

Answer:

49

Step-by-step explanation:

10 weeks = 70 days

0.7 : 1 = x : 70

x = 0.7 * 70

x = 49

Any value x not explicitly associated with a positive probability is taken as P(X=x) = 0. The function pX(x)= P(X=x) for any x in the range of X is given as a probability. It is often called the probability mass function of a discrete random variable X.

Binomial Distribution:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own It has a Boolean result: success (for probability p) or failure (for probability q = 1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.

The binomial distribution is commonly used to model the number of successes in a sample of size n drawn from a population of size N with replacement. If sampling is performed without replacement, the resulting distribution is hypergeometric rather than binomial because the plots are not independent. However, for N much larger than n, the binomial distribution remains a good approximation and is widely used.

In the binomial distribution, the trials to be investigated must have the same probability of success. For example, if you toss a coin, the probability of flipping the coin is 1/2. 0.5 for each trial because there are only two possibilities.

Binomial Random Variable:

This is a special kind of discrete random variable. A binomial random variable counts the number of times a particular event occurs over a fixed number of trials or trials.

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Answer:

The lowest common denominator is 8

Step-by-step explanation:

To find the lowest common denominator, we look at the multiples

Multiples of 4: 4,8,12,16,20

Multiples of 8: 8,16,24

The 1st common multiple is 8

The lowest common denominator is 8

Answer:

Step-by-step explanation:

Answer:

X =  1

X = -4/5

Hope this helps!

The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.

The Remainder is the extra part of a number that restricts the number to be divided completely.

a)

(19² mod 41) mod 9

Let us determine 361 mod 41

a=361 = 328+33= 8*41+33 =8d+33

The remainder is the constant in the final expression: 361 mod 41=33

33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)

b)

(32³ mod 13)² mod 11

Let us determine 32 mod 13

a=32=26+6=2*13+6+2d+6

The remainder is the constant in the final expression: 32 mod 13=6

[tex](6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11[/tex]

Let us determine 216 mod 13

a= 216= 208+8=16*13+8 = 16d+8

The remainder is the constant in the final expression: 216 mod 13=8

[tex]8^{2} mod 11\\64 mod 11[/tex] = 9 (since, 64= 55+9= 11*5+6= 11d+6)

c)

(7³ mod 23)² mod 31

[tex](343mod23)^{2} mod 31\\[/tex]

Let us determine 343 mod 23

a=343=322+21=14*23+21=14d+21

The remainder is the constant in the final expression: 343 mod 23= 21

[tex]21^{2} mod 31 = 441 mod 31=7[/tex] (since a = 441=434+7=14*31+7=14d+7)

d)

(21² mod 15)³ mod 22

[tex](441mod15)^{3} mod 22[/tex]

Let us determine 441 mod 15

a=441 = 435+6= 29*15+6= 29d+6

The remainder is the constant in the final expression: 441 mod 15= 6

[tex]6^{2} mod 22=36mod22= 14[/tex] (since a = 36= 22+14= 1*22+14= d+14)

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The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.

What means binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.

For each random variable X, the binomial distribution formula is given by;

P(x:n,p) = nCx px (q)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment = 1 – p

formula for finding standard deviation of a binomial distribution is npq. f.

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The equation (A) x² - 4x + 3√2 = 0 has no real roots.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

(A) x² - 4x + 3√2 = 0

b² - 4ac = (-4)² - 4(1)(3√2)

= 16 - 12√2

= 16 - 12(1.414)

= 16 - 16.968

= -0.968 < 0

There are no true roots to the equation.

(B) x² + 4x - 3√2 = 0

b² - 4ac = (4)² - 4(1)(-3√2)

= 16 + 12√2 > 0

There are 2 different real roots in the equation.

(C) x² - 4x - 3√2 = 0

b² - 4ac = (-4)² - 4(1)(-3√2)

= 16 + 12√2 > 0

There are 2 different real roots in the equation.

(D) 3x² + 4√3x + 4 = 0

b² - 4ac = (4√3)² - 4(3)(4)

= 48 - 48

= 0

The equation contains two equal roots.

Therefore, the equation (A) x² - 4x + 3√2 = 0 has no real roots.

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Answer: 22 = a - 295

Step-by-step explanation:

"equals" means equals or the solution and can be shown with the equal sign.

"reduced by" also means subtracted by and can be shown as the minus sign.

I hope this helps :)

Answer:

62.625

Step-by-step explanation:

First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35

8.35*7=58.45+(8.35*(1/2))= 62.625

Therefore, your answer is 62.625

I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.

please give brainliest! Thanks! Hope this helped.

Answer:

62.625 lb

Step-by-step explanation:

Define the variable:

Set up a ratio of weight to number of gallons:

[tex]\implies x:7.5=33.4 :4[/tex]

Solve for x:

[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]

Cross multiply:

[tex]\implies 4x=33.4 \cdot 7.5[/tex]

[tex]\implies 4x=250.5[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]

[tex]\implies x=62.625[/tex]

Therefore, the weight of 7.5 gallons of water is 62.625 lb.

The two points that represent Justine‘s function for the yards left to hike in terms of the hours she spent hiking are; (0, 320) and (4, 0)

From the table in the attached file, we see that;

Justine started when Michael was 320 yards from the top.

This coordinate is expressed as (0,320)

where;

0 represents the time Justine started

320 represents the number of yards left.

Now, it is clear that every minute, Justine covers 80 yards.

Thus;

After 1 minute, Justine will have:

(320 - 80) yards left

After 2 minutes, Justine will have:

(320 - 80 - 80) yards left

After 3 minutes, Justine will have:

(320 - 80 - 80 - 80) yards left

After n minutes, Justine will have;

(320 - 80n) yards left

Thus, the possible coordinates are:

(0, 320), (1, 240), (2, 160), (3, 80), (4, 0)

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Proportional functions are used to express direct variation in graphs.

The graph shows a straight difference.

How to determine the type of graph?

From the graph, we have the following ordered pairs

(x, y) = (0, 0), (2, 4) and (3, 9)

We can rewrite it as:

(x,x^2) = (0,0^2), (2,2^2) and (3,3^2)

The above means that, the equation of the graph is:

y = x²

It means, y varies directly to the square of x

Where, the proportionality constant is equal to 1

Therefore, the graph represents a direct variation

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Answer:

The two equations that can be used are 7.50a + 4.50s = 3150, and

 a + s = 500.

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

a + s = 3,150  NO

7.5a + 4.5s = 3,150 YES

a + s = 500    YES

7.5s + 4.5a = 500  NO

Step-by-step explanation:

We know that a + s = 500.

Total sales would be the product of the number of adult and student tickets times their repsective prices:

Total Sales ($) = $7.50a + $4.50s = $3150

Leaving off the units for the next steps, we have two equations and we can rearrange one of them to substitute into the other.  

1)   Rearrange the first equation to isolate a:  a = 500-s

Now use this definition of a in the second equation:

7.50a + 4.50s = 3150

7.50(500-s) + 4.50s = 3150

3750 - 7.5s + 4.50s = 3150

 -3s = -600

    s = 200  student tickets were sold

Use a+s=500 to find a:  

a+200 = 500

     a=300   300 adult tickets were sold.

================

The two equations we used to find this answer were:

7.50a + 4.50s = 3150, and

 a + s = 500

Answer:

Step-by-step explanation:

Step 1

1 of 5

Graph the three points and connect them to create the mid segments of the triangle:

Use midsegments of triangles in the coordinate plane.

Use the Triangle Midsegment Theorem to fi nd distances.

Using the Midsegment of a Triangle

A midsegment of a triangle is a segment that connects the

midpoints of two sides of the triangle. Every triangle has

three midsegments, which form the midsegment triangle.

The midsegments of △ABC at the right are MP —, MN —,

and NP —. The midsegment triangle is △MNP.

Using Midsegments in the Coordinate Plane

In △JKL, show that midsegment MN — is parallel to JL —

and that MN =

1

—2 JL.

SOLUTION

Step 1 Find the coordinates of M and N by fi nding

the midpoints of JK — and KL —.

M (—

−6 + (−2)

2

, —

1 + 5

2

) = M ( −8 —

2

, 6

—

2

) = M(−4, 3)

N (—

−2 + 2

2

, —

5 + (−1)

2

) = N ( 0

—

2

, 4

—

2

) = N(0, 2)

Step 2 Find and compare the slopes of MN — and JL —.

slope of MN —= —

2 − 3

0 − (−4) = −

1

—

4

slope of JL — = —

−1 − 1

2 − (−6) = −

2

—

8

= −

1

—

4

Because the slopes are the same, MN — is parallel to JL —.

Step 3 Find and compare the lengths of MN — and JL —.

MN = √——

[0 − (−4)]2 + (2 − 3)2 = √—

16 + 1 = √—

17

JL = √———

[2 − (−6)]2 + (−1 − 1)2 = √—

64 + 4 = √—

68 = 2 √—

17

JL = √———

[2 − (−6)]2 + (−1 − 1)2 = √—

64 + 4 = √—

68 = 2 √—

17

Because √—

17 =

1

—2

(2 √—

17 ) , MN =

1

—2 JL.

Monitoring Progress onitoring Progress Help in English and Spanish at BigIdeasMath.com

Use the graph of △ABC.

1. In △ABC, show that midsegment DE — is parallel

to AC — and that DE =

1

—2 AC.

2. Find the coordinates of the endpoints of

midsegment EF —, which is opposite AB —. Show

that EF — is parallel to AB — and that EF =

1

—2 AB.

READING

In the fi gure for Example 1,

midsegment MN — can be

called “the midsegment

opposite JL —.”

midsegment of a triangle,

p. 330

Previous

midpoint

parallel

slope

coordinate proof

Core Vocabulary Core Vocabulary

A C

P

N

M

B

x

y

4

6

−2

−6 −4 −2

M

N

K(−2, 5)

J(−6, 1)

L(2, −1)

x

y

−4

−6

−2 2 4 6

D

E

C(5, 0)

B(−1, 4)

A(