Simplify open parentheses x to the two fifths power close parentheses to the 3 sevenths power.

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

-6x^2-18x+1

Step-by-step explanation:

not fully sure but hope this helps!!

The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

We have,

We can use the standard normal distribution to solve this problem by standardizing the height value using the formula:

z = (x - μ) / σ

where:

x = the height value (in inches)

μ = the mean height (in inches)

σ = the standard deviation (in inches)

Substituting the given values, we get:

z = (74 - 68) / 3

z = 2.0

Using a standard normal table or calculator, we can find the probability that a random standard normal variable is greater than 2.0 to be approximately 0.0228.

Therefore,

The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

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By answering the presented question, we may conclude that Therefore, 1  expressions cm on the map corresponds to a real distance of 3.2 km. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Scale 1:

320000 means that 1 unit on the map represents his 320000 units in the real world.

To find the actual distance represented by 1 cm on the map, you need to convert the units to the same scale.

1 kilometer = 100000 cm

So,

1 unit on the map = 320000 units in the real world

1 cm on the map = (1/100000) km in the real world

Multiplying both sides by 1 cm gives:

1 cm on the map = (1/100000) km * 320000

A simplification of this expression:

1 cm on the map = 3.2 km

Therefore, 1 cm on the map corresponds to a real distance of 3.2 km. 

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Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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Answer:

x + 7 and x + 5 are possible dimensions

Step-by-step explanation:

x² + 12x + 35 ← factor the quadratic

consider the product of the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (+ 12)

the factors are + 7 and + 5 , since

7 × 5 = + 35 and 7 + 5 = + 12 , then

x² + 12x + 35 = (x + 7)(x + 5) ← in factored form

now the area A = length × breadth , that is

A = x² + 12x + 35 = (x + 7)(x + 5) , then

length = x + 7 or x + 5

breadth = x + 5 or x + 7

Step-by-step explanation:

please make it a little bit clear

Answer: 63

Step-by-step explanation: we need 6 units of 1/6 to equal 1

6*10=60

6* 1/6=6/6=1

1/2*6=6/2=3

60+3=63

The total length of the pathway with the added tile is 513 and 2/3 yards

or 22 feet.

Feet (ft) is a unit of length or distance commonly used in the United States, United Kingdom, and other countries that have adopted the imperial or US customary systems of measurement.

The problem tells us that the pathway is 513 yards long. However, the length of the tile that is added to the end of the pathway is given in feet. So, we need to convert the 513 yards to feet, which we can do by multiplying 513 by the conversion factor of 3 feet per yard:

513 yards x 3 feet per yard = 1539 feet

This gives us the length of the original pathway in feet. To find the total length of the pathway with the additional tile, we simply add the length of the tile to the original length:

1539 feet + 2 feet = 1541 feet

Now we need to convert this length back to yards. To do this, we divide the total length by 3 (since there are 3 feet in a yard):

1541 feet ÷ 3 feet per yard = 513 and 2/3 yards

So the total length of the pathway with the added tile is 513 and 2/3 yards, which can be simplified to 514 yards (since 2/3 yard is equivalent to 22 and 2/3 feet, which is less than half a yard). Therefore, the answer is D) 22 ft.

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9514 1404 393

Answer:

  1) 135°

  2) 0.77 units

  3) 0.92 units

  4) 6.12 units

  5) 2.83 square units

Step-by-step explanation:

1) The exterior angle at any vertex is 360°/n, where n is the number of sides. For the octagon, the exterior angle is 360°/8 = 45°. The interior angle will be the supplement of this: 180° -45° = 135°.

The measure of each interior angle is 135°.

__

2) Each sector of the octagon is an isosceles triangle with a central angle of 45° (also 360°/8). Since the radius is 1 unit, the length of one side is twice the sine of half the central angle.

  s = 2·sin(45°/2) ≈ 0.765367

The length of one side is about 0.77 units.

__

3) Similarly, the apothem is the cosine of half the central angle:

  a = cos(45°/2) ≈ 0.923880

The apothem is about 0.92 units.

__

4) For an octagon, the perimeter is 8 times the length of one side.

  P = 8s = 8(0.765367) ≈ 6.12293

The perimeter is about 6.12 units.

__

5) The area of one sector (isosceles triangle) is given by the formula ...

  A = (1/2)bh

  A = 1/2sa ≈ 1/2(0.765367)(0.923880) ≈ 0.353553

Then the area of the octagon is 8 times this:

  A = 8(sector area) = 8(0.353553) ≈ 2.82843

The octagon area is about 2.83 square units.

The quantity of each colour beads that are in the necklace include the following:

Purple beads = 56

Purple beads = 56silver beads = 24

A ratio is defined as the mathematical expression that shows the number of times one value is contained in another value.

The number of purple beads = 14

The number of silver beads ,= 6

The total quantity of beads = 80

Therefore the total combination = 14+6 = 20

For purple beads = 14/20 × 80/1

= 1120/20 = 56

For silver beads = 6/20×80/1

= 480/20= 24

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Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Answer:

Answer:00

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.

b=0b=0

3b−5=03b-5=0

Set the first factor equal to 00.

b=0b=0

Step-by-step explanation:

The result can be shown in multiple forms.

Exact Form:

b=0,53b=0,53

Decimal Form:

b=0,1.¯6b=0,1.6‾

Mixed Number Form:

b=0,123b=0,123

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9514 1404 393

Answer:

  a)  12

  b)  y +5 = 12(x +2)

Step-by-step explanation:

The slope of a function is its derivative.

a) The slope of y = x^3 +3 at any point is y' = 3x^2. So, at the point where x=-2, the slope of the curve is ...

  m = 3(-2)^2 = 12 . . . . slope at (-2, -5)

__

b) The equation of the tangent line is most easily written using the point-slope form of the equation of a line.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

  y +5 = 12(x +2) . . . . line with slope 12 through point (-2, -5)

Answer:

x + 3y + 9 = 0

Step-by-step explanation:

y=3x + 2

Coefficient of x = 3

Gradient (m) of line y= 3x + 2 is 3

Since the line passing through point

(3,-4) is perpendicular to line y=3x + 2

hence gradient (m) of the line is -1/3;

And hence it equation is given as;

y - y1 = m(x - x1)

y - (-4) = -1/3(x - 3)

multiplying through by 3;

3 × y + 3 × 4 = 3 × -1/3(x - 3)

3y + 12 = -1(x - 3)

3y + 12 = -x + 3

x + 3y + 12 - 3 = 0

x + 3y + 9 = 0

The required present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

To find the present value of $600 after 4 years at 7% compounded monthly, we can use the formula for compound interest:

Compound Interest =P(1+r/n)^rt

Substituting the given values, we get:

Compound Interest =600 (1+7/n)^4

Simplifying this equation, we get

P = 600 / 1.487

P = 451.73

Therefore, the present value needed now to get $600 after 4 years at 7% compounded monthly is $451.73.

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Answer:

Left side: Bottom

Right side: Top

Step-by-step explanation:

If the angles are congruent AND the sides are proportional, then the two polygons are similar.

The similar pairs of polygons are:-

Left side: Bottom

Right side: Top

A polygon is a plane figure described by a finite number of straight-line segments connected to form a closed polygonal chain in geometry. A polygon is defined as a bounded plane region, a bounding circuit, or both.

If the angles are congruent AND the sides are proportional, then the two polygons are similar.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

The polygons left side bottom  right side top are similar to each other in the given image.

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Answer:

36,552

Step-by-step explanation:

To estimate the product of 481.68 and 76.25 to the nearest whole number, we can round both numbers to the nearest whole number first. 481.68 can be rounded to 482 and 76.25 can be rounded to 76.

Then, we can calculate the product of 482 and 76 to get the estimated result:

482 * 76 = 36,552

Therefore, the estimated product of 481.68 and 76.25 to the nearest whole number is 36,552.

Answer:

36,552

Step-by-step explanation:

To estimate the product of 481.68 and 76.25, you can round each number to the nearest whole number. 481.68 rounds to 482, and 76.25 rounds to 76.

The product of 482 and 76 is approximately 36,552. Therefore, the product of 481.68 and 76.25 is approximately 36,552.

Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

Answer:

Step-by-step explanation:

\(\frac{(3x+4)(2x-6)}{0}\)=

\(6x^{2} -18x+8x-24\)/0

anything divided by zero is not possible so the answer is infinity

Answer:

The percentage rate of decay per year is of 3.25%.

The function showing the mass of the sample remaining after t is \(A(t) = 80(0.9675)^t\)

Step-by-step explanation:

Equation for decay of substance:

The equation that models the amount of a decaying substance after t years is given by:

\(A(t) = A(0)(1-r)^t\)

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Every 21 years, its mass decreases by half.

This means that \(A(21) = 0.5A(0)\). We use this to find r, the percentage rate of decay per year.

\(A(t) = A(0)(1-r)^t\)

\(0.5A(0) = A(0)(1-r)^{21}\)

\((1-r)^{21} = 0.5\)

\(\sqrt[21]{(1-r)^{21}} = \sqrt[21]{0.5}\)

\(1 - r = 0.5^{\frac{1}{21}}\)

\(1 - r = 0.9675\)

\(r = 1 - 0.9675 = 0.0325\)

The percentage rate of decay per year is of 3.25%.

Given that the initial mass of a sample of Element X is 80 grams.

This means that \(A(0) = 80\)

The equation is:

\(A(t) = A(0)(1-r)^t\)

\(A(t) = 80(1-0.0325)^t\)

\(A(t) = 80(0.9675)^t\)

The function showing the mass of the sample remaining after t is \(A(t) = 80(0.9675)^t\)

The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.

The function will be:

F = 2.40 + (0.40 × m)

F = 2.40 + 0.40m

where m = number of miles

F = taxi fare.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

Define ratio?

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From the line plot given, each x sign represents a pound

So that the weight of the dog toy of 1/2 is x + x + x + x, where x = 1 pound

=> 1+1+1+1+1 = 4

Hence the total weight will be 1/2 x 4 = 2 =>option c is correct

Answer:

D and C

Step-by-step explanation:

Good job on the first question!

The range reflects upon the y-axis interval so the value must be greater than equal to 300,000