The height in meters of a projectile can be modeled by h=-4.91² + vt+s where is the time (in seconds) the
object has been in the air, v is the initial velocity (in meters per seconds) and s is the initial height (in meters). A
soccer ball is kicked upward from the ground and flies through the air with an initial vertical velocity of 4.9
meters per second. Approximately, after how many seconds does it land?

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

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

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

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

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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The height of the smaller pyramid is 0.01875 miles.

The height of the smaller pyramid is obtained applying the proportions in the context of the problem.

The ratio between the volumes is given as follows:

20000/10240 = 1.953125.

The heights are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:

h/0.015 = cubic root of 1.953125

h/0.015 = 1.25

h = 1.25 x 0.015

h = 0.01875 miles.

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Answer: (D): The mean would decrease in value to about 23.3

Step-by-step explanation:

Step 1: Find the Original Mean

Mean = Sum/# of Numbers

Mean = 17 + 17 + 18 + 19 + 22 + 23 + 25 + 27 + 32 + 38/ 10 numbers

Mean = 238/10
Mean = About 23.8

Step 2: Add 18 to the original sum, divide that by 11 numbers

Mean = 238 + 18/11 numbers

Mean = 256/11

Mean = About 23.3

And so, Answer Choice (D) is correct

Answer:

Step-by-step explanation:

You are helping your little brother pick up his toy blocks.  The blocks are cubes and each side measures 5 in.  The toy chest that you have to put them in measures 12 1/3  in by 10 and 3/4  in by 12in.  Your brother has 10 blocks to put away, will they all fit in the toy chest?

Since you have 10 blocks to put away, what is the volume of all 10 blocks

Answer:

85

Step-by-step explanation:

check the lower answer

Answer:

the height of the cylinder is 6 cm.

Step-by-step explanation:

Let's start by using the formulas for the volume of a cylinder and a cone:

Volume of a cylinder = πr^2h

Volume of a cone = (1/3)πr^2h

Given that the cylinder and cone have the same radius and volume, we can set their volume equations equal to each other:

πr^2h = (1/3)πr^2(18)

Simplifying this equation by canceling out πr^2 on both sides, we get:

h = (1/3) * 18

h = 6

Therefore, the height of the cylinder is 6 cm.2

1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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The $28.50 amount Jamie and Dana has to spend and the items that they bought expressed as an equation indicates;

An equation is a mathematical statement that indicates equivalence between two expression.

The amount Jamie and Dana takes to the concert = $28.50

The cost of hot dogs = $1.25

Cost of soft pretzels = $2.50

Cost of a water bottle = 50 cents
Let x represent the number of hot dogs and let y represent the number of soft pretzels Jamie and Dana bought together

The cost of the two water bottles they buy (one each) = 2 × 50 cents = $1

The equation that determines the number of hot dogs and soft pretzels they buy is therefore; 1.25·x + 2.50·y + 1 = 28.50

The graph of the equation can be found by making y the subject of the formula as follows;

1.25·x + 2.50·y = 27.50

2.50·y = 28.50 - 1 - 1.25·x

y = (27.50 - 1.25·x) ÷ 2.50 = 11 - 0.5·x

y = 11 - 0.5·x

The above equation is a linear function

The points on the graph are;

(0, 11), (2, 10), (4, 9), (6, 8), (8, 7), (10, 6), (12, 5), (14, 4), (16, 3), (18, 2), (20, 1), (22, 0)

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Rousseau believed that society corrupted the individual.

Rousseau believed that civilization or society corrupted the individual. He believed that in the state of nature, humans were essentially good and free, but that society imposed unnatural and harmful restrictions on them, leading to corruption and degeneration. According to Rousseau, institutions like private property, government, and social hierarchies were responsible for this corruption, as they encouraged competition, selfishness, and inequality, and forced people to conform to arbitrary standards and norms.

He believed that true freedom and happiness could only be found in a society that valued equality, solidarity, and the common good, and that emphasized the development of the individual's natural capacities and talents.

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Answer: society

Step-by-step explanation:

just did it

The missing value is 1.9096

According to SOH CAH TOA identity:

[tex]\text{sin} \ \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}[/tex]

[tex]\text{sin} \ \theta = \dfrac{\text{O}}{\text{H}}[/tex]

Given the following

Substitute to have:

[tex]0.1736 = \dfrac{\text{O}}{11}[/tex]

[tex]\text{O} = 11 \times 0.1736[/tex]

[tex]\text{O} = 11 \times 1.9096[/tex]

Hence the missing value is 1.9096

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[tex]\begin{array}{ccll} blueprint&actual\\ \cline{1-2} 1 & 40\\ 4& h \end{array} \implies \cfrac{1}{4}~~=~~\cfrac{40}{h} \implies h=160[/tex]

Answer:

160 inches

Step-by-step explanation:

a scale of 1:40 means that any measurement in the blue print is multiplied by 40 to find the actual measurement

so 4*40= 160 inches

Answer:

(2,3)

Step-by-step explanation:

look at where both lines intersect

2x - 1 = 5 - x

Combine like terms

2x + x = 3x

5 + 1 = 6

3x = 6

6 /3 = 2

X = 2

Put into both equation to find y and to make sure it’s true

Y =2x - 1

2(2) - 1

4 - 1 = 3

Y = 3

y = 5 - x

5 - 2 = 3

Y = 3

X=2 and y = 3

(2,3)

To solve a system of equations, we need to find the values of the variables that make both equations true simultaneously. Several methods for solving systems of equations include substitution, elimination, and graphing.

Substitution method:

Elimination method:

Graphing method:

Let's solve this using substitution and then verify with the graphing method:

To solve the system of equations y = 2x - 1 and y = 5 - x, we can substitute the expression 2x - 1 for y in the second equation and solve for x:

y = 5 - x

2x - 1 = 5 - x (substituting y = 2x - 1 for y)

3x = 6

x = 2

Now that we have found x = 2, we can substitute this value into either equation to solve for y:

y = 2x - 1

y = 2(2) - 1

y = 3

We can verify this with the graphing method by looking at where the two lines intersect. Upon inspecting the graph, the lines intersect at (2,3), verifying that the algebraic method was correct. Therefore, the solution to the system of equations is (2,3)

Answer: = -26

Step-by-step explanation:

Option D is correct, y≥3/4x+10  and y≥-1/2x-3  are the system of inequalities of the given graph

Let us find the equations of the lines

y=3/4x+10

and y=-1/2x-3

A relationship between two expressions or values that are not equal to each other is called 'inequality.

As we observe the two lines, the lines are solid

y=-1/2x-3

y=3/4x+10 the shading is outside the origin

y≥3/4x+10

and  y=-1/2x-3 the shading is outside the origin

y≥-1/2x-3

Hence, option D is correct, y≥3/4x+10  and y≥-1/2x-3  are the system of inequalities of the given graph

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The value of x in the line segment is 6.

When lines intersects, angle relationships are formed such as vertically opposite angles, linear angles etc.

Therefore, let's find the angle x using the angle relationships formed as follows:

∠UJX + 90 + 6 = 180(sum of angles on a straight line)

∠UJX  = 180 - 96

∠UJX  = 84 degrees

Therefore,

∠UJX ≅ 14x (vertically opposite angles)

Vertically opposite angles are congruent.

Hence,

84 = 14x

divide both sides by 14

x = 84 / 14

Therefore,

x = 6

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Step-by-step explanation:

4x²+32=4(x²+8)

56x³+7x²=7x²(8x-1)

6x⁴-4x²+14x=2x(3x³-2x+7)

18x³+27x-9=9(2x³+3x-1)

The equation of the parabola in vertex form is y = (1/4)x² - 2.

A parabola is a symmetrical curve with a U- or smile-shaped shape. It is a particular kind of conic section, a shape created by cutting a cone with a plane.

The set of all points in a plane that are equally distant from a fixed point (referred to as the focus) and a fixed line is known as a parabola (called the directrix).

The vertex form of the equation of a parabola with vertex (h,k) is given by:

y = a(x - h)² + k

where "a" is a constant that determines whether the parabola opens up or down (if "a" is positive, the parabola opens up, and if "a" is negative, the parabola opens down).

We are given that the vertex of the parabola is (0,-2), so we have:

h = 0 and k = -2

We are also given that the parabola passes through the point (-8,14). We can use this information to find the value of "a". Substituting the coordinates of the point into the equation, we get:

14 = a(-8 - 0)² - 2

Simplifying:

14 = 64a - 2

16 = 64a

a = 16/64

a = 1/4

Now that we have found the value of "a", we can write the equation of the parabola in vertex form:

y = (1/4)x² - 2

Therefore, the equation of the parabola in vertex form is y = (1/4)x² - 2.

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Answer:

the mass of a dime is 2.268 grams.

Step-by-step explanation:

Given that the mass of a quarter is 5.67 grams, the mass of a dime can be found by multiplying 0.4 to the mass of a quarter.

So,

Mass of a dime = 0.4 × mass of a quarter

= 0.4 × 5.67 grams

= 2.268 grams

Therefore, the mass of a dime is 2.268 grams.

A function that is represented in the table include the following: A. [tex]y = 2(0.5)^x[/tex].

In Mathematics, an exponential function can be represented by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

At data points (0, 2) and (1, 1), we can calculate or determine the value of a and b as follows;

2 = a(b)⁰

a = 2

For the value of b, we have:

1 = 2(b)¹

1 = 2b

b = 1/2 = 0.5

Therefore, the required function is given by;

[tex]y = 2(0.5)^x[/tex]

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We can determine that Gavon sleeps for 3360 minutes this week using the laws of mensuration.

A measurement action is what the word "mensuration" alludes to. Our universe has three dimensions. Both elementary school and high school mathematics depend heavily on the idea of measurement. Additionally, measurement directly affects how we live. When measuring objects, 2D and 3D measurements are practised. Both traditional and non-conventional measurement techniques can be used to determine the size or quantity of something.

According to the query,

Each night, Gavon slept for eight hours.

Gavon slept for eight hours every night for seven days in a row.

Gavon now sleeps for eight hours per night, or eight times sixty.

= 480 minutes.

Gavon now sleeps seven nights a week, thus

7 × 480

= 3360 minutes.

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The complete question is,

Gavon slept 8 hours all 7 nights this week. How many minutes did Gavon sleep this week? Note: 1 hour = 60 minutes​

Answer: 50 years.

Step-by-step explanation:

We can use the formula for simple interest to solve this problem:

I = P * r * t

where I is the interest earned, P is the principal amount, r is the interest rate as a decimal, and t is the time in years.

We can rearrange this formula to solve for t:

t = I / (P * r)

Substituting the given values, we get:

t = (500 - 312.5) / (312.5 * 0.04)

t = 625 / 12.5

t = 50

Therefore, it will take 50 years for an investment of Gh312.50 at 4% simple interest to amount to Gh500.00.

The estimated population after one year is 160 and the estimated population after two years is 256.

we can multiply the initial population by 1.60 (100% + 60%) to account for the 60% growth rate:

Population after one year = 100 x 1.60 = 160

Since the sanctuary can sustain up to 800 deer, the actual population after one year would be the minimum of 160 and 800, which is 160.

To estimate the population after two years, we can repeat the process using the population after one year as the new initial population:

Population after two years = 160 x 1.60 = 256

Again, since the sanctuary can sustain up to 800 deer, the actual population after two years would be the minimum of 256 and 800, which is 256.

Therefore, the estimated population after one year is 160 and the estimated population after two years is 256.

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Answer:

Step-by-step explanation:

     | Male | Female | Total

------|------|--------|-------

Overweight | 15 | 36 | 51

Not Overweight | 85 | 64 | 149

------|------|--------|-------

Total | 100 | 100 | 200

Now, we can test the hypothesis that the two genders are homogeneous with respect to being overweight using a chi-square test. The null hypothesis is that there is no association between gender and overweight status.

The formula for the chi-square test is:

χ² = Σ [(O - E)² / E]

Where:

χ² = chi-square value

O = observed frequency

E = expected frequency

To calculate the expected frequency, we can use the formula:

E = (row total x column total) / grand total

Using this formula, we can calculate the expected frequencies for each cell of the contingency table:

     | Male | Female | Total

------|------|--------|-------

Overweight | 12.75 | 38.25 | 51

Not Overweight | 87.25 | 61.75 | 149

------|------|--------|-------

Total | 100 | 100 | 200

Now we can use the formula for the chi-square test to calculate the chi-square value:

χ² = [(15 - 12.75)² / 12.75] + [(36 - 38.25)² / 38.25] + [(85 - 87.25)² / 87.25] + [(64 - 61.75)² / 61.75]

χ² = 1.06 + 0.76 + 0.68 + 0.56

χ² = 3.06

Next, we need to determine the degrees of freedom (df) for our test. For a contingency table with r rows and c columns, the degrees of freedom are (r-1) x (c-1). In this case, we have 2 rows and 2 columns, so our degrees of freedom are:

df = (2-1) x (2-1) = 1

We can then use a chi-square distribution table or a statistical software program to determine the critical value of chi-square for our chosen level of significance and degrees of freedom. For a significance level of 0.05 and 1 degree of freedom, the critical value of chi-square is 3.84.

Since our calculated chi-square value of 3.06 is less than the critical value of 3.84, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that there is a significant association between gender and overweight status among diabetic patients.

The graph in this problem is not a function, as it contains vertically aligned points.

The domain and the range are given as follows:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

When we trace a vertical line through the circle, it would cross the circle at two points, meaning that the graph contains vertically aligned points, and thus, is not a function.

The domain and the range are defined as follows:

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The  fraction of prism with dimensions length=10cm , width= 5cm and height=5cm , made using two cubes of 5cm sides each filled with sand is  [tex]\frac{3}{5}[/tex]

What is a prism?

A three-dimensional solid shape or figure known as a prism has two ends that are identical or flat. Prisms are made up of equal cross-sections, flat faces, and congruent bases. The remaining faces of prism are parallelograms or rectangles. Another name for the rectangular prism is a cuboid.

Given that prism if formed using two identical cubes of side 5cm each. The prism so formed using two cubes will be a cuboid also known as rectangular prism.

Dinemsions of prism:

Length=5+5   { length of two cubes}

           =10 cm.

width= 5cm    {width of one cube}

height=5 cm   {height of one cube}

Volume of cuboid= Lengthx widthx height

                             =10 . 5 . 5

                             =250 cu. cm

Given that 150 cu. cm volume of prism is filled with sand.

Fraction of volume filled with sand =[tex]\frac{volume of sand}{total volume of prism}[/tex]

                                                         =[tex]\frac{150}{250}[/tex]

                                                         =[tex]\frac{15}{25}[/tex]

                                                         =[tex]\frac{3}{5}[/tex]

Fraction of volume filled with sand    =[tex]\frac{3}{5}[/tex]

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Refer to the attachment for the complete question.

Answer:9th term is 0.078 approx.

Step-by-step explanation: the given sequence is decreasing by a factor of 2 each time.

so we can find 4th term :-

4th term= 5/2=2.5

similarly,we can find the term 5th,6th,7th,8th terms respectively:-

5th = 2.5/2=1.25

6th=1.25/2=0.625

7th=0.625/2=0.3125

8th=0.3125/2=0.15625

so 9th term is equal to 0.078.

To represent vector a + b using the head-tail method, we can draw vector a + b with its tail at the origin (0,0) and its head at the point (3,-5).

The head-tail method is a graphical technique used to add or subtract two vectors by placing the tail of one vector at the head of the other vector.

So, to represent vector a + b using the head-tail method, we start by drawing vector a with its tail at the origin (0,0) and its head at the point (4,-3). Then, we draw vector b with its tail at the head of vector a, which is the point (4,-3), and its head at the point (-1,-2). The resulting vector from the tail of a to the head of b is vector a + b.

To find the coordinates that can be used to draw vector a + b, we add the corresponding components of vectors a and b. So, (a + b) = (4 + (-1), -3 + (-2)) = (3,-5). Therefore, we can draw vector a + b with its tail at the origin (0,0) and its head at the point (3,-5).

See attached graph.

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The solution for the system of linear equations is: x₁ = -1, x₂ = -3, x₃ = 3 and x₄ = -2

To solve this system of linear equations, we can use the Gaussian elimination method. First, let's represent the system as an augmented matrix:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

| -1 -1  1  0 |  1 |

|  0  0  2 -1 |  4 |

Add the first row to the third row to eliminate x₁ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0 -1  3  0 |  6 |

|  0  0  2 -1 |  4 |

Add the second row to the third row to eliminate x₂ in the third row:

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  3 -1 |  5 |

|  0  0  2 -1 |  4 |

Divide the third row by 3

|  1  0  2  0 |  5 |

|  0  1  0 -1 | -1 |

|  0  0  1 -1/3 |  5/3 |

|  0  0  2 -1 |  4 |

Subtract twice the third row from the fourth row to eliminate x₃ in the fourth row

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0 -1/3 |  2/3 |

Multiply the fourth row by -3 to get x₄

|  1  0  2  0  |  5  |

|  0  1  0 -1  | -1  |

|  0  0  1 -1/3 |  5/3 |

|  0  0  0  1  | -2  |

We can use back substitution to find the values of x₁, x₂, and x₃:

x₄ = -2

x₂ - x₄ = -1 which is x₂ = -1 + (-2) = -3

x₃ - (1/3)x₄ = 5/3 therefore; x₃ = 5/3 + (1/3)(-2) = 3

x₁ + 2x₃ = 5 therefore;  x₁ = 5 - 2(3) = -1

The above answer is in response to the full question below;

Solve this system of linear equations

x₁ + 2x₃ = 5

x₂ - x₄ = -1

-x₁ - x₂ + x₃ = 1

2x₃ - x₄ = 4

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