What is the area of the parallelogram shown above?
Hint : The area of a parallelogram is
A = b x h.
Area = [?]ft^2

Answer as a fraction:  x =  27/8

Answer in decimal form: x = 3.375

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

Work Shown:

-11x+21=-3x-6

-11x=-3x-6-21

-11x+3x = -6-21

-8x = -27

x = -27/(-8)

x = 27/8 is the answer as a fraction

x = 3.375 is the answer in decimal form

Explanation:

The idea is to get x by itself. In step 2, I subtracted 21 from both sides. In the third step, I added 3x to both sides. This will mean the x terms are on one side, and the non x terms are on the other. After combining like terms, I divided both sides by -8 to fully isolate x.

Side note: The improper fraction 27/8 is equivalent to the mixed number 3 & 3/8

The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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Answer:

-1/3x + 5 = y

Step-by-step explanation:

Answer:

there is the answer 347.82

The answer to this question is 347.82

Answer:

The answer is A f(x)=-2x + 70

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

An isoline that connects all points of highest mean temperature on a world map is called the highest mean temperature isoline.

An isoline is a line on a map that connects points of equal value for a particular variable. In this case, the isoline connects all points of the highest mean temperature, indicating regions with the highest average temperatures.

Therefore, it is referred to as the "highest mean temperature isoline." The other options mentioned are not specifically related to the concept described.

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The variance of the new dataset can be found using the formula for the variance of a sample with replacement.

In statistics, variance is a measure of the spread or variability of a set of data around its mean. It is the average of the squared differences of each data point from the mean.

The formula for variance (σ²) is:

σ² = Σ(x - μ)² / n

where Σ is the sum of, x is a data point, μ is the mean of the data set, and n is the total number of data points.

One important property of variance is that it is not resistant to outliers. That is, if there are extreme values in the data set, the variance will be disproportionately affected. In such cases, it may be more appropriate to use other measures of spread, such as the interquartile range or the range.

Variance is often used in conjunction with other statistical measures, such as the standard deviation and covariance, to describe the characteristics of a data set or to make inferences about a population based on a sample.

Var(new data) = [n/(n+1)] * [σ^2 + (x - μ)^2/n]

where n is the sample size before the new observation, σ^2 is the original variance, x is the value of the new observation, and μ is the original mean.

Plugging in the given values, we get:

Var(new data) = [25/(25+1)] * [1 + (14 - 10)^2/25]

= 0.961

Therefore, the variance of the new dataset is approximately 0.961

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All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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The correct simplification of the expression is c12 (option c).

The expression (c^4)^3 can be simplified using the exponent rules for powers of a power, which states that when a power is raised to another power, we can multiply the exponents.

Thus, we have:

(c^4)^3 = c^(43) [Using the rule (a^m)^n = a^(mn)]

Simplifying the exponent 4*3, we get:

c^(4*3) = c^12

Therefore, the correct simplification of the expression is c^12.

Option (c) is the correct answer as it correctly represents the simplified form of the given expression. Option (a) c^-1, option (b) c^7, and option (d) c^64 are not correct because they do not follow the exponent rules used to simplify the expression.

In summary, the expression (c^4)^3 simplifies to c^12, which is option (c) in the given options.

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Answer:

600 People

Step-by-step explanation:

25%= 150

25%x4=100%

150x4 = 600

The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

Total possible outcome of the event of picking drinks contained in the crate = 19

Hence, we can compute the following as follows;

(a) The probability they both picked Limca = (4/19)×(3/18)

Limca = 12/342

Limca = 0.04

(b) The probability Ademola only picked pepsi = 6/19

pepsi = 0.32

(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)

=(72+29+12)/342

= 114/342

= 0.33

(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)

The probability they picked different brand = (54+36+54+24+36+24)/342

The probability they picked different brand = 228/332

The probability they picked different brand = 0.67

Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.

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When reading a buret with graduated markings at every 0.1 ml, your recorded volume should read to a) hundredths place.

A burette is a long tube-shaped glass instrument with scale lines like a measuring pipette or measuring cup with the same cross section from top to bottom. At the bottom of this tool is equipped with a faucet as a place for the solution to come out at the mouth of the burette.

The function of the burette is as a tool to measure the solution based on the volume released. The burette size usually has a volume of 25 / 50 ml.

If the burette is being used, it must be supported firmly with a stand equipped with clamps to clamp the burette. Make sure that when clamping the burette in the stand and clamp the position of the burette must be perpendicular so that the scale reading is correct and does not cause paralax errors.

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Answer:

12x + 15y = 9

- 12x - 18y = -6

Step-by-step explanation:

Answer:

x is all real numbers

Step-by-step explanation:

This means that the graph is continuous from negative infinity to positive infinity.

No, the graph of a straight line need not always be a function.

The equation of a straight line is,

y = -mx + c

y = the y coordinate

x = the x coordinate

c = y-intercept of the line

m = slope of the line = tan(Ф)

Since the values of y are dependent on the values of x, the graph is a function. But for a line parallel to x-axis, the equation is,

y=a and x=0

That is, for any value of y, the value of x is 0

and for a line parallel to the y-axis, the equation is,

x=a and y=0

That is, for any value of x, the value of y is 0

The values of x and y don't depend on each other. Hence, the graphs of straight lines need not always be a function.

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The properties of the functions are

A sinusoidal function is represented as

f(x) = Acos(2π/B(x + C)) + D or

f(x) = Asin(2π/B(x + C)) + D

Where the properties are

Using the above as a guide, we have the following:

4) y = sin 2(x - π/2):

5) y = cos 1/2(x - π):

6) y = 3cos 2(x + π) - 1:

The graphs of the functions are added as attachments

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Answer:

2g + 4h = 43

2g + 2h = 30

Step-by-step explanation:

Answer:

pairs of gloves = x

hats = y

2x + 4y = 43

2x + 2y = 30

hats = $6.50

gloves = $8.50

Step-by-step explanation:

use the elimination method to solve this system.

subtract the first equation by the second.

2x + 4y = 43

- 2x + 2y = 30

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

         2y = 13

y = 6.5

plug in the y value to find x

2x + 4 (6.5) = 43

2x + 26 = 43

2x = 17

x = 8.5

Answer:

the answer would be 217 [degrees]

Step-by-step explanation:

Since m<1 and m<2 are next to each other, they are adjacent. Adjacent angles  must share a common side which is m<W. This means they have to be added.   m<1+m<2= m<XYZ

145+72=217

Answer:

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A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.

Easy

Solution

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Radius of the wheel =r=

2

60

=30 cm

Circumference of the wheel =2πr=2×

7

22

×30=

7

1320

cm

Distance covered in 1 revolution =

7

1320

cm

Distance covered in 140 revolutions =

7

1320

×140=26400 cm=264 m=

1000

264

km

Distance covered in one minute = Distance covered in 140 revolutions =

1000

264

km

Distance covered in 1 hour =

1000

264

×60=15.84 km

Hence, the speed with which the boy is cycling is 15.84km/hr.

The answer to the question is x = 4

Answer:

4

Step-by-step explanation:

3(x - 4) + 2x =8

3x - 12 + 2x =8

5x -12 =8

5x +20

x= 4

Answer:

because a=b and c=d so bisect

The function, which Ladarius could use for the estimation of the replacement of equipment is defined as t(v) = m*v + b.

For an estimate of when Ladarius would need to replace his equipment, we need to define a relation between time and a variable that gives us the condition of the equipment. These are represented by 't' and 'v' respectively.

We can create a function based on the information given.

If Ladarius knows the rate at which the equipment deteriorates, which he measures under the variable v, we can establish a relation between time and v, which goes as follows:

t(v) = m*v + b

where t(v) is the time taken for replacing the equipment, clearly dependent on v.

v, as mentioned before measures the conditions of the equipment.

m is the slope of the graph between t(v) and v, and thus also the rate at which equipment deteriorates.

b is the y-intercept of the above equation on the graph.

To use this equation, Ladarius would need to study the behaviors of the equipment at different and frequent intervals of time. By plotting such data systematically, he can obtain the slope and the y-intercept, which ultimately helps him write the equation.

As a word of caution, it is important to note, that t(v) may not just be linearly dependent on v, and might involve a couple more parameters influencing the process. In both these cases, the equation will change.

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Ladarius can estimate when he would need to replace the equipment based on its current value.

To estimate when Ladarius would need to replace the equipment, we can use a function called t(v). The function t(v) represents the time, in years, that Ladarius would need to replace the equipment based on its value v.

To find the function t(v), we need to consider the lifespan of the equipment and how its value decreases over time. Let's say the equipment has a lifespan of 10 years. We can assume that its value depreciates linearly over those 10 years.

We can start by finding the rate of depreciation per year. Let's say the initial value of the equipment is V0 and its value after 10 years is V10. The rate of depreciation per year can be calculated as (V0 - V10)/10.

Now, we can use this rate of depreciation to find the value of the equipment after any number of years t. The function t(v) can be represented as:

t(v) = (V0 - v)/[(V0 - V10)/10]

In this function, v represents the value of the equipment after t years. Each part of the function represents the following:

- V0: The initial value of the equipment.
- V10: The value of the equipment after 10 years.
- (V0 - V10)/10: The rate of depreciation per year.
- (V0 - v): The difference between the initial value and the value after t years.

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The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

Given data:

X: height of seaweed.

       X~N (μ;σ²)

       μ= 10 cm

       σ= 2 cm

We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

              P(X ≤ x) = 0.30

              P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

        Z = (X - μ)/σ

translates the Z value to the corresponding X value.

           P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                  z= -0.52

Now you have to clear the value of X:

        Z= (X - μ)/σ

        X= (Z * σ) + μ

       X = (-0.52 * 2) + 10

         = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

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Answer:

y is 6.5 because it's kind of a ratio, you just need to find out what number to divide them by or multiply them by in this case, it was 13÷2 =6.5

Answer:

No, it is not correct. You should divide by 21 and 3.

Step-by-step explanation:

3x=21

x=7

Q 1)

3(x + 5) = 36

3x + 15 = 36

3x = 36 - 15

3x = 21

x = 21/3

x = 7

Verification:

3(x + 5) = 36

3(7 + 5) = 36

3(12) = 36

36 = 36

Hence proved that x = 7

Answer:

15, 11, 60

Step-by-step explanation:

Let Joe's amount be x

x + x - 6 + 4x = 96

6x - 6 = 96

6x = 90

x = 15

Joe has 15

Kaitlin has 11

Miguel has 60

that there is no smallest positive rational number is proven below.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have commonly divisible.

Let r be any reasonable number.

We can infer that r/2 is rational because r is a rational number.

There is no smallest rational number so we can assume that r/2 r because r/2 is rational.

Hence, proved that here is no smallest positive rational number.

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