Which symbol makes this statement true?

7.1 _____ -7.1

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<
=

Answer:

P(2 or fewer left-handed) = 9/25 = 0.36

Step-by-step explanation:

From Chayton simulations, we can see that in 9 simulations there are 2 or fewer left-handed students in a class of 20 students. He simulated 25 classes of 20 students, then the probability to find 2 or fewer left-handed is: 9/25 = 0.36

Answer:

4+0.08 +0.0016+0.000032+ ....

Step-by-step explanation:

a+ar+ar²+ar³+ar⁴+…

the  geometric series converges if  |r| < 1

The geometric series converges:

4+0.08 +0.0016+0.000032+ ....

0.08=4*0.02

0.0016=4*(0.02)²

0.000032=4*(0.02)³

r=0.02<1

The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.

A geometric series is one where each pair of subsequent terms' ratios is a fixed function of the accumulation index. The ratio is a rational function of the accumulation index in a more comprehensive sense. creates what is known as a hypergeometric sequence.

If the common ratio is the same throughout the series, then the series is known as geometric series.

If the common ratio is less than one, then the series is known as convergence.

Let's check all the options, then we have

A. 0.02+0.02+0.02+0.02+...

Then the common ratio is given as,

r = 0.02 / 2 = 0.02 / 0.02

r = 1 = 1

B. 4+0.08 +0.0016+0.000032+....

Then the common ratio is given as,

r = 0.08 / 4 = 0.0016 / 0.08

r = 0.02 = 0.02

C. 4+80+ 1,600+ 32,000+.....

Then the common ratio is given as,

r = 80 / 4 = 1600 / 80

r = 20 = 20

D. 0.02+0.04+0.08+0.16+......

Then the common ratio is given as,

r = 0.04 / 0.02 = 0.08 / 0.04

r = 2 = 2

The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.

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Answer:

Right now I only have the time to give the answer's.

Part A Answer:There is 1.5 times more lotion in Bottle Y than in Bottle X. 6/4=1.5

Part B Answer: Bottle X is better because it is cheaper and there is not much of a difference.

Part C Answer:It would be better to buy the third bottle because it has the same amount as Bottle Y but at a cheaper price.

Step-by-step explanation:

Your welcome.

Answer:

the mean is the midle one

we can get this by getting the average

add all of it and divide by how many it is

The equation of the graph which shows a hyperbola passing through the point (0, 8) is,

⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]

Given that,

The graph of the equation of the hyperbola is shown.

Now, Take a point on the graph of the hyperbola.

Let the point is, (0, 8), which lies on the graph.

Since the point must satisfy the equation of the graph.

Hence, we can check all the options,

A. Equation of graph is,

⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]

Substitute x = 0, y = 8;

⇒ [tex]\frac{(8 - 1)^2}{49} - \frac{0^2}{81} =1[/tex]

⇒ [tex]\frac{(7)^2}{49} - 0 =1[/tex]

⇒ [tex]\frac{49}{49} = 1[/tex]

⇒ 1 = 1

Which is true.

Therefore, the equation of the hyperbola is,

⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]

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Answer:

Volume of the completes tower = 160 units³

Step-by-step explanation:

Martin is using unit cubes to build a tower in the shape of rectangular prism.

Bottom layer of the prism is in the square shape.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base will measure = √16 = 4 units

Therefore, Length = width = 4 units

On this base, additional layers added on the top = 9

Therefore, height of the tower = (9 + 1) = 10 units (each layer having 16 cubes)

Volume of the tower = Volume of the rectangular prism

                                  = Length × width × height

                                  = 4×4×10

                                  = 160 cubic units.

Volume of the completed tower will be 160 cubic units.

The total volume  in cubic units of the completed tower is 160 units³.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base should be

= √16 = 4 units

Now

Length = width = 4 units

The additional layers added on the top = 9

So, height of the tower = (9 + 1)

= 10 units

Now

Volume of the tower = Volume of the rectangular prism

                                = Length × width × height

                                 = 4×4×10

                                 = 160 cubic units.

hence, The total volume in cubic units of the completed tower is 160 units³.

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Answer: 397.39 cm2

Step-by-step explanation:

Hi, first we have to calculate the area of the circle:

Area of a circle = π x r^2

Replacing with the values:

A(C) =π x 12^2 = 452.39cm2

Now, we have to calculate the rectangle area:

Rectangle area = width x length = 5 x11 = 55cm2

Finally, since the shaded region is the circle and the rectangle is inside of it, we have to subtract the area of the rectangle to the area of the circle:

452.39 -55 = 397.39 cm2

Feel free to ask for more if needed or if you did not understand something.

Answer:

397.39

Step-by-step explanation:

extras...

The given triangle is an acute scalene triangle.

A triangle is a closed polygon with three sides and angles.

Obtuse triangle - the triangle with angle greater than 90°;

Acute triangle - the triangle with all interior angles under 90°;

Isosceles triangle - the triangle with a pair of equal sides;

Scalene triangle - the triangle with all three sides (or angles) of different measure.

We have,

All sides are different and all angles are under 90°.

Hence the given triangle is an acute scalene triangle.

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Answer: Cos A  = 0.96, Tan A = 0.29 and Sin A = 0.28

Step-by-step explanation: The right angled triangle can be solved by applying the trigonometric ratios given a follows;

Sin A = opposite/hypotenuse

Cos A = adjacent/hypotenuse

Tan A = opposite/adjacent

In the triangle ABC, the side AB (25) is the hypotenuse [facing the right angle], the side CB (7) is the opposite [facing the reference angle A°] while the side AC (24) is the adjacent [line between the reference angle and the right angle].

Therefore, using angle A as the reference angle;

(a) Cos A = adjacent/hypotenuse

Cos A = AC/AB

Cos A = 24/25

Cos A = 0.96

(b) Tan A = opposite/adjacent

Tan A= CB/AC

Tan A = 7/24

Tan A = 0.29

(c) Sin A = opposite/hypotenuse

Sin A = CB/AB

Sin A  = 7/25

Sin A = 0.28

Answer:22.5

Step-by-step explanation: just saying that is no the actual answer you still have to estimate it

The equation n² =45 is solved step by step. The nearest perfect squares, 36 and 49, are identified. Using a calculator, the square root of 45 is found to be approximately 6.708, satisfying the equation.

let's go through the steps to solve n² = 45 in detail:

Step 1: Find the Perfect Squares

The closest perfect squares to 45 are 6² = 36 and

7² = 49.

Since 45 is between 6² and 7², we'll use these values as reference.

Calculate the Square Root

We'll use a calculator to find the square root of 45.

√45 ≈ 6.708203932499369

So, the square root of 45 is approximately 6.708203932499369.

Step 3: Solve for n

Since we're looking for n² = 45, we have √n = 45.

Plugging in the calculated square root:

√n = 45

n ≈ 6.708203932499369

Thus, the approximate value of n that satisfies the equation n² = 45 is n ≈ 6.708.

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Answer:

What shapes can be cross sections of the rectangular pyramid?

A slice parallel to the base will take the shape of a

✔ rectangle

.

A slice perpendicular to the base and through the top vertex will take the shape of a

✔ triangle

.

A slice perpendicular to the base and not through the top vertex will take the shape of a

✔ trapezoid

.

A slice parallel to the base will take the shape of the rectangle. A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

A slice perpendicular to the base and through the top vertex will take the shape of a .

A slice perpendicular to the base and not through the top vertex will take the shape of a .

Take a rectangle and the base. Now take four triangles such that each of them is connected to one-one side of the base rectangle and when they are taken together, they form a closed object.

That shape is called a rectangular pyramid.

A slice parallel to the base will take the shape of a "rectangle"

A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".

A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

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Answer:

$1.50

Step-by-step explanation:

12÷8=3/2 or 1.50

Answer: the answer would be 1$ and 50 cents

Step-by-step explanation:

Step-by-step explanation:

2X alla seconda meno 3

Answer:

The vertex is (6, -4)

Step-by-step explanation:

f(x) =(х – 8)(х – 4)

First find the zeros

0 = (х – 8)(х – 4)

0 = x-8      0 =x-4

x=8          x=4

The zeros are x=8 and x=4

The vertex is 1/2 way between the zeros

(8+4)/2 = 12/2 =6

To find the y value, substitute 6 into the function

f(6) = (6-8) (6-4)

     =  -2 (2) = -4

The vertex is (6, -4)

Answer:

Area is Base multipled by your height, so fro that particular section, it's quite a simple equation! :D

Step-by-step explanation:

Let's identify our sides. 39ft6in is our HEIGHT, and 5ft3in is our BASE.

- 39ft and 6in is a total of: 472 inches. 472 inches is 39.3ft

- 5ft and 3in is a total of: 63 inches. 63 inches is 5.3ft

Now that we know this, we can plug it in depending on the unit you need to find! Let's assume it's feet?

The Equation Completed: 5.3 × 39.3 = 208.29, which rounds to 208.3!

FINAL ANSWER: 208.3ft

Answer:

l=(3w-5) Inches

Step-by-step explanation:

Let the width of the rectangle =w inches

The length of a rectangle is five inches less than triple the width.

Let us break the statement down into parts.

Therefore, the length of the rectangle, l= (3w-5) Inches

Question:

Felicia makes ½ gallon of fruit punch. She pours an equal amount into 8 glasses.

What fraction of a gallon fruit punch is in each glass?

Answer:

The fraction of a gallon fruit punch is in each glass is 1/16

Step-by-step explanation:

Given

Size of fruit punch = ½ gallon

Number of glass = 8

Required

Fraction of a gallon fruit punch is in each glass?

To solve this question, the following assumption has to be made.

- The 8 glass cups are of equal sizes.

Having said that;

The interpretation of the question is that, the fruit is evenly distributed into the 8 glass cups.

Mathematically, the size of the fruit punch will be divided by the number of glass cups.

So, we have

Fraction = ½ ÷ 8 (convert ÷ to *)

Fraction = ½ * ⅛

Fraction = 1/16

Hence, the fraction of a gallon fruit punch is in each glass is 1/16

Final answer:

To find the fraction of a gallon of fruit punch in each glass, divide 1/2 gallon by 8. This results in each glass containing 1/16 of a gallon of fruit punch.

Explanation:

The student asked how to find the fraction of a gallon of fruit punch in each glass if Felicia makes ½ gallon of fruit punch and pours an equal amount into 8 glasses. To answer this question, you need to perform a division of the total amount by the number of glasses. Given that Felicia has ½ gallon, which is the same as 2/4, we can divide this by 8 to find the amount in each glass.

Step-by-step solution:

Start with the fraction of a gallon Felicia has: ½ gallon.

Convert ½ to fourths to make the division easier: ½ = 2/4 gallons.

Since there are 8 glasses, divide 2/4 by 8. This is done by multiplying the denominator by 8:
(2/4) × (1/8) = 2/32.

Simplify the fraction by dividing numerator and denominator by the common factor of 2: 2/32 = 1/16.

Therefore, each glass contains 1/16 of a gallon of fruit punch.

Answer:

0.75 g/cm^3 to 2 decimal places.

Step-by-step explanation:

Density = mass / volume

= 140 / 182

= 0.7487 g/cm^3.

The density of the cheese is 0.75 [tex]g/cm^3[/tex].

The student has asked to calculate the density of a block of cheese with a given volume and mass. Density is defined as mass per unit volume and is calculated using the formula:

Density = Mass / Volume

To find the density of cheese:

Use the given mass of the cheese, which is 140 grams.

Divide the mass by the given volume of the cheese, which is 187  [tex]g/cm^3[/tex].

Perform the division to get the density in grams per cubic centimeter ( [tex]g/cm^3[/tex].)

The calculation is as follows:

Density = 140 g / 187  [tex]g/cm^3[/tex]= 0.7487 [tex]g/cm^3[/tex].

After rounding to two decimal places, the density of the cheese is 0.75  [tex]g/cm^3[/tex].

Answer:

The value of DC is 66.34.

Step-by-step explanation:

The triangles ABC and DCA are right angled triangles.

The straight line AC is a bisector for angles C and A.

The measure of ∠C is 30°.

Then the measure of angles BCA and ACD will be 15° each.

The measure of angle DAB is 150°.

Then the measure of angles DAC and BAC will be 75° each.

Now consider the right angled triangle ABC.

The measure of side AC is:

[tex]AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}[/tex]

Consider the right angled triangle DCA.

The angle DAC measure 75°.

Using the trigonometric identities compute the value of Perpendicular DC as follows:

[tex]tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34[/tex]

Thus, the value of DC is 66.34.

Answer:

You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line,  square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.

Step-by-step explanation:

Answer:

15625

Step-by-step explanation:

25^3

The base is 25 and the power is 3

That means we multiply 25 together 3 times

 = 25*25*25 =15625

Answer:

15,625

Step-by-step explanation:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(20+5)³

20³ + 3(20²)(5) + 3(20)(5²) + 5³

8000 + 6000 + 1500 + 125

15625

No, the relation isn't a function. Though positive and balanced, one input has two outputs, violating the "one input, one output" rule.

No, the relation depicted in the image is not a function. While the relation does have the same number of x values as y values, and all the values are positive, a key characteristic of a function is missing.

For a relation to be a function, each input (represented by the x -value) must correspond to exactly one output (represented by the y -value).

In the image, we see that the input value 1 has two corresponding output values, 7 and 11. Since an input value cannot have multiple outputs, this relation is not a function.

So the answer is D. No, because two points with the same x -value have different y values.

Answer:

72

Step-by-step explanation:

You need to add the two middle numbers then divide them by two.

Hope this helps.

Answer: 72

Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.

Notice that our data set is already written from least to greatest so all we have to do now is find the number that appears in the middle.

Notice however that there are two numbers in the middle.

When this happens, take the sum of the two numbers in the middle or add them together and then divide the sum of the numbers by 2.

So if we add 71 + 73, we get 144.

Now just divide 144 by 2 to get 72.

So the median of the data set shown here is 72.

Answer:

C. The vertex of the function doesn't change.

Answer:

A) h = 40

Step-by-step explanation:

Because 40/2 = 20

Which is greater than 16 and makes the equation true

Answer:

2.9

Step-by-step explanation:

The mean is the average of the date It is surprisingly easy to calculate: add up all the data, then divide by how many data points there are.

Becker's data added up is 28. Kayla's data added up is 30. The total amount is 58.

The amount of data points are 20.

58/20 = 2.9

Hope this helps!

The mean number of games chess team members play per day is 2.9

Becker = 5,2,4,1,1,4,5,3,2,1

= (5 + 2 + 4 + 1 + 1 + 4 + 5 + 3 + 2 + 1) / 10

Mean average = 28 / 10

= 2.8

Kayla = 2,3,1,1,4,1,5,3,5,5

= (2 + 3 + 1 + 1 + 4 + 1 + 5 + 3 + 5 + 5) / 10

= 30 / 10

= 3

Total = Becker + Kayla

= 2.8 + 3

= 5.8

Mean average = 5.8 / 2

= 2.9

Therefore, the mean number of games chess team members play per day is 2.9

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Answer:

5th term is -12

Step-by-step explanation:

First term is 8, which means 0th term is 13.

You can use the equation to find the nth term: y = -5(x) + 13

y = -5(5) + 13

y = -25 +13

y= -12

The fifth term in the sequence is -12.

It is a sequence where the difference between each consecutive term is the same.

We have,

First term = 8

Common difference = -5

We can consider the sequence to be an arithmetic sequence.

Now,

a = 8

Second term.

= a + (n - 1)d

= 8 + (2 - 1)(-5)

= 8 - 5

= 3

Third term.

= 8 + (3 - 1) (-5)

= 8 + 2 x -5

= 8 - 10

= -2

Fourth term.

= 8 + (4 - 1) x -5

= 8 + 3 x -5

= 8 - 15

= -7

Fifth term.

= 8 + (5 - 1) x -5

= 8 + 4 x -5

= 8 - 20

= -12

Thus,

The fifth term of the sequence is -12.

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Answer:

1) x/8+ x/16= 3/4    2) 4 miles

Step-by-step explanation:

The table is an illustration of distance, rates (speed) and time.

From the question, we have:

[tex]t =45\ mins[/tex] --- total time spent

Convert to hours

[tex]t =\frac{45}{60}hr[/tex]

Reduce fraction

[tex]t =\frac{3}{4}hr[/tex]

The times spent to school and back home are given as:

[tex]t_1 = \frac x8[/tex]

[tex]t_2 = \frac x{16}[/tex]

So, we have:

[tex]t_1 + t_2 = t[/tex]

This gives:

[tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Take LCM

[tex]\frac{2x + x}{16} = \frac 34[/tex]

[tex]\frac{3x}{16} = \frac 34[/tex]

Multiply through by 16

[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]

[tex]3x = 12[/tex]

Divide both sides by 3

[tex]x = 4[/tex]

The distance to school and back home are given as:

[tex]d_1 = d_2 = x[/tex]

So, we have:

[tex]d_1 = d_2 = 4[/tex]

This means that Gerry lives 4 miles from school

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