At her birthday party, Sam is serving a slice of cake to each attendee. Of each attendee receives 2 slices, there will be 20 slices left. If 5 attendees do not receive any slices and the rest receive 5 slices each, there will be no cake left. How many attendees were at the party

√6/3 is the value after rationalization of √2/√3

An expression is combination of variables, numbers and operators.

The given expression is √2/√3

Square root two divided by square root three.

We need to rationalize the denominator

To rationalize multiply numerator and denominator by √3

√2/√3×√3/√3

√2×3/3

√6/3

Hence, √6/3 is the value after rationalization of √2/√3

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Answer: 102.4

Given ratio 5:8

Let's assume the answer to be x

5÷8 should be equal to 64÷x

∴ x= (64×8) ÷ 5

=102.4

The number that has the same ratio to 64 as 5:8 is gotten as; 40

How to Calculate Ratio?

We have the ratio 5:8.

Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;

x/64 = 5/8

Cross multiply to get;

x = 64 * 5/8

x = 40

Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

Answer:

A. The ratios are both identical (three fifths and three fifths).

Step-by-step explanation:

ratio means fraction

ratio also means division

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"SOHCAHTOA"

sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent

mathworldwolframcom

sine equals opposite over hypotenuse

sine X equals 3 over 5

cosine equals adjacent over hypotenuse

cosine Y equals adjacent over hypotenuse

cosine Y equals 3 over 5

side thats 3 is adjacent for y but

side thats 3 is also opposite for x

both identical, aka C on their question is right

its the 1st option for flvs

Answer:

60 because their a 2 induivedinal in 1 sock.

Step-by-step explanation:

30 x 2 = 60

A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.

The correct answer is an option (A)

Consider plot A.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 6, 6, 7, 7, 10

Using the formula of mean, the mean of Plot A would be:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10

mean = 57/10

mean = 5.7

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 6)/2

            = 11/2

            = 5.5

Consider plot B.

The data value represented on the dot plot:

3, 4, 4, 5, 5, 5, 6, 6, 6, 7

mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10

mean = 51/10

mean = 5.1

The middle value of the data is: 5, 6

So, the median is:

Median = (5 + 5)/2

            = 5

Hence, both the mean and median are greater for Plot A than for Plot B.

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The complete question is:

Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.

There are three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

Therefore, the three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

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Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

The correct option is option C which states that , less than 80% power to detect the standard deviation is 0.4.

We know that the power is less and the effect size is small therefore we can say that all other things given as equal, it's harder to detect than the larger effect. As a result power is reduced.

Statistical power is a measure of research efficiency that is estimated before the study begins . This is done so as to predict the likelihood of discovering an actual effect rather than receiving a false negative result or, in the worst case scenario, overestimating the effect by identifying noise in the data.

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Jonathan and Oscar will have the same amount of money saved after  2 weeks.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

If they have same amount of money then,

f(x) = g(x)

18x+5 = 8x+25

10x = 20

x = 2 weeks

Therefore, Jonathan and Oscar will have the same amount of money saved after  2 weeks.

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The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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The comparison operator "≥" in logic means that the number is either greater than or equal to a number , the greater than equal to symbol is used to describe the relationship between two terms .

What is a Comparison Operator ?

The Comparison operator in logic is used to compare logic statements ,such as [tex]a > b[/tex] or [tex]a < b[/tex] , by using a , b as variables, the operator compares their values, returns true and false.

The Comparison Operator "≥" , in logic is read as " greater than equal to" , For Example : if the statement is [tex]a \geq b[/tex] , then if the variable is greater than or equal to b , then the operator will return TRUE and if not then it will return FALSE .

The given question is incomplete , the complete question is

What does the comparison  operator "≥"(greater than equal to) mean in logic ?

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The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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Answer:

x = 1

Step-by-step explanation:

Immediately, we will simplify like terms on the left side of the equation. This will give us:

[tex]\sqrt{2x-x-1}[/tex]  = 0

Simplifying gives us:

[tex]\sqrt{x-1}[/tex] = 0

Now, an important thing to note, is that for the square root of a number to be 0, the number has to be 0. Therefore, x - 1 must equal 0. So, x = 1. Checking our work gives us:

[tex]\sqrt{2x - x - 1}[/tex] = 0

[tex]\\\sqrt{2 - 1 - 1}[/tex] = 0

[tex]\sqrt{0}[/tex] = 0

It all checks out.

Hope this helped!

Step-by-step explanation:

so, clearly, the triangles BCF and DCF are congruent.

that makes the line CF a bisector of the kite figure.

and so, both angles are identical halves of the total angle at C.

therefore,

3x + 13 = 13x - 7

13 = 10x - 7

20 = 10x

x = 20/10 = 2

QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.

When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.

In QUAD ABCD, DP equals x + 7 and AC is 4x-13.

4x - 13 is x + 7 + x + 7

4x - 13 = 2x+14

2x-13 = 14.

hence,

The value of x is 13.5.

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Answer:

a)

24 = 2³ × 3

40 = 2³ × 5

b)

LCM = 120

Step-by-step explanation:

a)

                 24                                      40

              /       \                                  /      \

            2         12                           2         20

                      /     \                                   /      \

                    2       6                               2      10

                           /     \                                     /    \

                        2         3                               2       5

24 = 2³ × 3

40 = 2³ × 5

b)

LCM = 2³ × 3 × 5

LCM = 120

Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.

let's try to learn what is multiplicative inverse.

1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

One is obtained when a number is multiplied by its own multiplicative inverse.

When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.

Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.

Given question is incomplete complete question here:

What is the multiplicative inverse of 7/5?

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The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.

Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D

where, A --> amplitude

B--> period in form of pi

C--> phase or horizontal shift

D --> vertical shift

We have, the depth of water in a tank oscillates sinusoidally.

The smallest depth of water in tank = 6.6 feet

The largest depth of water in tank = 9.4 feet

We have to determine the formula of depth of water in tank as a function of time in hours .

For sinusoidal function,

Amplitude , A = average depth

= ( largest depth + smallest depth)/2

= (6.6 + 9.4)/2

= 16.0/2 = 8

Now, The period of 8 hours so, B = 2π/8

=> B = 45° = π/4

Also, upward shift , D is 9.4 - 6.6 = 2.8

Horizontal shift, C = 0

So, required function is D = 2.8 + 8 sin(π t/4) .

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Step-by-step explanation:

y = 2x + 1 -------- (I)

y = 4x + 6 --------(ii)

from eqn (I)

y = 2x + 1

sub y = 2x + 1 in eqn (ii)

2x + 1 = 4x + 6

2x - 4x = 6 - 1

-2x = 5

x = -5/2

sub x = -5/2 in eqn (I)

y = 2(-5/2) + 1

y = -5 + 1

y = -4

Therefore, (x, y) = (-5/2, -4)

The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the function:

y = -(x/3) + 2

At x = -3:

y = -((-3)/3) + 2 = 3

At x = 0:

y = -(0/3) + 2 = 2

At x = 3:

y = -(3/3) + 2 = 1

At x = 6:

y = -(6/3) + 2 = 0

The value of y when x = -3 is 3

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The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.

A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.

This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).

= ($250 - $320)/4

= $40

This will give you a price of for each additional room.

To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.

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