While playing a game of chance, Mei rolled a regular six-sided die 100 times and noticed that it landed on the number 4 exactly 48 times. What could Mei conclude about the die?

We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.398 and 0.562. Since this includes 0.5, the die appears to be fair.
We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.398 and 0.562. Since this is much greater than 1 out of 6, the die appears to be unfair.
We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.382 and 0.578. Since this is much greater than 1 out of 6, the die appears to be unfair.
We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.382 and 0.578. Since this includes 0.5, the die appears to be fair.

A general formula to describe is F = 1.6×d² will be correct answer.

A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.

Finding the general formula we obtain:

F=kd²

40=k×5²

k=1.6

so, F =1.6×d².

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The actual dimensions of the figure is 3.9 x 2.1

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

For the first dimension of 7.8 cm, we can set up a proportion using the scale factor:

2 cm : 1 m = 7.8 cm : x

where x is the actual length we want to find.

Solving for x, we get:

x = (7.8 cm x 1 m) / 2 cm

x = 3.9 m

Therefore, the first actual dimension is 3.9 meters.

For the second dimension of 4.2 cm, we can use the same method:

2 cm : 1 m = 4.2 cm : y

where y is the actual width we want to find. Solving for y, we get:

y = (4.2 cm x 1 m) / 2 cm

y = 2.1 m

Therefore, the second actual dimension is 2.1 meters.

So the actual dimensions of the figure are 3.9 meters by 2.1 meters.

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Answer: 1.08g

Step-by-step explanation:

Concentration = Moles/ Volume

Moles = Concentration x Volume

Moles = 0.048 x 250/1000

Moles= 0.012

Moles= Mass / Relative Formula Mass

Mass = Moles x Relative Formula Mass

Mass = 0.012 x 90

= 1.08g

The statement that correctly compares the two functions is

They have the same x-intercept and the same end behavior as x approaches ∞.

A function's final behaviour is represented by the value of f(x) as x approaches infinity. Both functions in this scenario have the same final behaviour because they both have unbounded growth, or they both go to positive infinity.

To find y-intercept of a function we have to put x= 0

So, The y-intercept of f(x) is y = -3.

and, The y-intercept of g(x) is y = -4.

To  find x -intercept of a function put y = 0

So, The x-intercept of f(x) is x = 1.

and, The x-intercept of g(x) is x = 1.

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Answer: 5/12

Step-by-step explanation:

2/3 - 1/4 = 5/12

Answer:

1.75

Step-by-step explanation:

Answer: look at the image for the solution and the answer

Step-by-step explanation:

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

To check if a curve represents a function, draw vertical lines all over the graph intersecting the curve at different regions.

Now, check how many times a line cuts the curve, if all the vertical lines cuts the curve at a single point then it represents a function, and if the vertical line cuts the curve at more than one point, then its not a function.

By keeping the above instructions in mind, conclusion can be made that :

Functions : (i), (ii), (iii), (iv) and (vi)

Non function : (v) and (vii)

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Jane would take 5 hours painting the window so both of them could end up charging the same amount

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Let y represent the total charge for working x hours.

Suzie has quoted a flat rate of $250 for the job. For Suzie:

y = 250

Jane's quote is $40 per hour, plus $50 to cover the cost of materials. For Jane:

y = 40x + 50

For the two to charge the same amount:

250 = 40x + 50

40x = 200

x = 5 hours

Jane would spend 5 hours painting the window.

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Answer: The answer is x²+2x-8

Step-by-step explanation:

The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

Let 'x' be the number of weeks and 'y' be the total test. Then the equations are given as,

y = 4 + 3x           ...1

y = 8 + x            ...2

From equations 1 and 2, then we have

4 + 3x = 8 + x

3x - x = 8 - 4

2x = 4

x = 2

The number of weeks when Sofia will catch up to Jacob will be 2 weeks.

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Answer:

Step-by-step explanation: A congruence statement expresses that two figures have the same size and shape. Here's how you can write a congruence statement step by step:

Write the two figures you want to compare. For example, you could write "Triangle ABC" and "Triangle DEF".

Use the symbol "≅" to indicate congruence. Place the symbol between the two figures, like this: "Triangle ABC ≅ Triangle DEF".

Label the corresponding parts of the two figures to show that they are congruent. For example, you could write "AB = DE", "BC = EF", and "AC = DF".

The final congruence statement would look like this: "Triangle ABC ≅ Triangle DEF, with AB = DE, BC = EF, and AC = DF". This statement says that Triangle ABC is congruent to Triangle DEF, and that the lengths of their corresponding sides are equal.

The speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

What is meant by the speed of an object?

The size of a change in an object's position over time is measured by its speed. The rate at which an object travels a distance can be thought of as its speed. A fast-moving object travels at a high speed and completes a significant distance in a brief period of time. This is in contrast to an object travelling slowly, which travels a relatively short distance in the same length of time. It is a scalar value.

Given,

Time at which Joe starts jogging  = 7 am

Time at which Ken starts jogging = 7.10 am

Speed of Joe = 6mi/h

Let Speed of Ken required to overtake Joe = x mi/h

Since Ken has to overtake Joe by 7.30, both will have travelled the same distance by 7.30.

Time taken by Ken to cover the distance = 7.30 - 7.10  20 minutes = 20/60=1/3 h

Time taken by Joe to cover the distance = 7.30 - 7 = 30 minutes = 1/2 h

Distance = speed * time

Both cover the same distance.

6 * 1/2 = x * 1/3

x = 9 mi/h

Therefore the speed at which Ken should run to overtake Joe by 7.30 is 9mi/h.

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Just multiply each side by side

Step-by-step explanation:1.Times one side by another

2. Times your answer by the third side

Answer:

Step-by-step explanation:

(227-127)/4=x

"/" means divide.

The formula possible formula for the trigonometric function whose values are in the following table is  y = 6 x sin(π/2 * x) - 4.

Trigonometric functions are described as the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

The formula for a trigonometric function is typically written as :

y = a sin (bx + c) + d

where a, b, c, and d are constants which tells us  the amplitude, frequency, phase shift, and vertical shift of the function, respectively.

From the above table,  the amplitude = 6,

the frequency is 2π/4 = π/2

the phase shift = 0, and

the vertical shift = -4.

Therefore, we can write  the formula for the function as Y = 6 * sin(π/2 * x) - 4.

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The correct option is B, the system of equations has infinitely many solutions.

When we graph a system of equations, the points where the graphs of the equations intercept are the solutions.

In this case we can see a single line graphed, which only can happen when both equations of the system represent the exact same line.

Then the graphs intercept at infinite points, thus, the system of equatios has infininitely many solutions.

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Answer:

22ft

Step-by-step explanation:

Always good to try and draw out the scenario, it can make it more easily understandable.

Have a look at the pic.

Hope its clear.

The marked-up price of the discounted tablet computer is $298.35.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, During a sale, a store offered a 35% discount.

So, The discounted price of the computer tablet is,

= [(100 - 35)/100]×340.

= (65/100)×340.

= $221.

Now, The price is marked up by 35% which is,

= [(100 = 35)/100]×221.

= (135/100)×221.

= $298.35.

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Answer:

hope this helps!!! That’s the answer!

Step-by-step explanation:

Answer:

9.43 units.

Step-by-step explanation:

To find the distance between two points in a 2D plane, you can use the Pythagorean theorem. The formula for finding the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for W and Z:

d = √((8 - 3)^2 + (-2 - 6)^2)

d = √(5^2 + (-8)^2)

d = √(25 + 64)

d = √89

The distance between the points W and Z is approximately 9.43 units.

If you were to  graph a sine function from the data listed in the table the days since Jan 8 is an independent variable and amount of moon visible is dependent variable

Given that, we have to graph a sine function from the data listed in the table

From the table we can see that there a two types of variables, The days since the Jan 8 and the amount of moon visible

The independent variable is defined as the variables that does not depends on any other variables

The dependent variable is defined as the variables that depends on other variables

Here the days since the Jan 8 does not depends on any other variables, so it is an independent variable. similarly the amount of moon visible depends on the days since Jan 8 value, so it is a dependent variable

Therefore, the days since Jan 8 is an independent variable and amount of moon light visible is dependent variable

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The given question is incomplete, the complete question is :

if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?

Answer:

13 or 17

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

Given numbers:

Put them in the ascending order:

Let the possible number to be added be x.

Since x is the median, it should be between 13 and 17:

Also x is the mode. As we see all 6 number are unique, x should be repeat of 13 or 17 in order to be a mode. Therefore the possible number that can be written on the blank card is either 13 or 17.

Answer:

x = 20

Step-by-step explanation:

since the 3 sides of the triangle are congruent then it is equilateral with 3 congruent angles, each of 60° , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer:

20

Step-by-step explanation:

We know that sum of corner of a triangle is 180° and if the triangle is equilateral, the corners are same

180:3=3x

60=3x

x=20

Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Hence, the complete equation according to this theorem is given above.

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The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.

The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:

P(Medical Assistance) = 0.67

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability

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a. The projectile will be at a height of 576 ft above the ground after 1.43 seconds and after 5.56 seconds.

b. The projectile will crash on the ground after 9.84 seconds.

The solution has been obtained by solving the equation.

What is an equation?

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.

We are given an equation as h = -16t² + v₀t + 448

Also v₀ is given as 112.

a. In order to find the time (t) the projectile will be at a height of 576 ft above the ground, we need to substitute h = 576 and v₀ = 112.

On substitution, we get

⇒h = -16t² + v₀t + 448

⇒576 = -16t² + 112t + 448

⇒36 = -t² + 7t + 28                (On dividing both sides by 16)

⇒0 = -t² + 7t - 8  

⇒t² - 7t + 8 = 0  

On solving the equation using the quadratic equation formula, we get

t = (7 ± √49 - 32)/2

t = 1.43 or 5.56

So, it will be at height 576 ft after 1.43 seconds and after 5.56 seconds.

b. Similarly, now we will put h = 0 and v₀ = 112.

Now, we get

⇒0 = -16t² + 112t + 448

⇒t² - 7t - 28 = 0                (On dividing both sides by 16)

On solving the equation using the quadratic equation formula, we get

t = (7 ± √49 + 112)/2

t = 9.84 or -2.84

Since, time cannot be negative, so it will crash after 9.84 seconds.

Hence, the projectile will be at 576 ft after 1.43 seconds and after 5.56 seconds and will crash on the ground after 9.84 seconds.

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Answer:

The average rate of change of a function over an interval is a measure of how the function's value changes over that interval, given by the ratio of the change in the function's value to the change in the independent variable. To find the average rate of change of a function over an interval, we need to know the function's values at two points in the interval.

In the case of the function f(x) = x^2, the interval is -4 ≤ x ≤ 0. To find the average rate of change, we need to find the difference in the function's value between two points in this interval, and divide that by the difference in the x-values.

For example, if we compare the values of the function at x = -4 and x = 0, we have:

f(-4) = (-4)^2 = 16

f(0) = 0^2 = 0

The difference in the function's value is f(0) - f(-4) = 0 - 16 = -16.

The difference in the x-values is x2 - x1 = 0 - (-4) = 4.

So the average rate of change over this interval is the difference in the function's value divided by the difference in the x-values, or -16 / 4 = -4.

In other words, the average rate of change of the function f(x) = x^2 over the interval -4 ≤ x ≤ 0 is -4, meaning that for every 4 units of change in x, the function value decreases by 16 units.

Step-by-step explanation:

Answer:

The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is  Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M  (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50  (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.

Step-by-step explanation:

.

The two-column table that can be used to prove the congruence relationships between the segments of the triangles are presented as follows;

             Statement    [tex]{}[/tex]                                   Reasons

1. [tex]\overline{KN}[/tex] ≅ [tex]\overline{MN}[/tex]                     [tex]{}[/tex]                            Given

 [tex]\overline{NL}[/tex] bisects ∠KNM           [tex]{}[/tex]                          

2. ∠KNL ≅ ∠MNL [tex]{}[/tex]                                        Definition of bisected angle

3. [tex]\overline{NL}[/tex] ≅ [tex]\overline{NL}[/tex]                   [tex]{}[/tex]                               Reflexive property

4. ΔKNL ≅ ΔMNL [tex]{}[/tex]                                         SAS congruence rule

5. [tex]\overline{KL}[/tex] ≅ [tex]\overline{ML}[/tex]         [tex]{}[/tex]                                        CPCTC

6. KL = ML [tex]{}[/tex]                                                    Definition of congruence

C.  

[tex]{}[/tex]               Statement [tex]{}[/tex]                                   Reasons

1.  [tex]\overline{BE}[/tex] ≅ [tex]\overline{CE}[/tex], [tex]\overline{AE}[/tex] ≅ [tex]\overline{DE}[/tex]                               Given

2. ∠AEB ≅ ∠CED [tex]{}[/tex]                                        Vertical angles theorem

3. ΔABE ≅ ΔCED [tex]{}[/tex]                                        SAS congruence rule

4. [tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]                                         [tex]{}[/tex]        CPCTC

Congruent segments are segments that have the same lengths.

The details of the reasons used to prove the equivalence of sides KL and ML and the congruence of the segments [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are presented as follows;

Definition of bisected angles

Bisected angles are angles that are split in two angles of the same measure by a segment passing through their vertex.

Reflexive property

The reflexive property of congruence states that a segment is congruent to itself.

SAS congruence rule

The SAS, Side-Angle-Side congruence rule states that if two sides and an included angle of a triangle are congruent to two sides and an included angle in another triangle, then the two triangles are congruent.

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

Definition of congruence

Geometric figures, such as segment, angles and shapes are congruent when their sizes and measurements are the same.

Vertical angles theorem

The vertical angles theorem states that vertical angles formed by the intersection of two lines are congruent

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The cost of one ounce of chocolate cream at Philadelphia according to the cost in pound will be $0.47.

We are aware of the fact that 1 pound is equal to 16 ounces. So, the cost of one pound will be the cost of 16 ounces. Representing this information in ounces and expression -

Cost of 1 pound = 7.52

Rewriting the equation according to ounce

Cost of 16 ounces = 7.52

So, cost of 1 ounce = 7.52/16

Performing division on Right Hand Side of the equation

The cost of one ounce = 0.47

Therefore, the cost of one ounce will be $0.47.

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