Here are some integers where a a
b
C
d
d
d
The mode of the integers is 9
The median of the integers is 8
The range of the integers is 4
Work out the value of a, the value of b, the value of c and the value of d

The  three equivalent numerical expressions are; Options M, R and S

To determine the expressions, we need to take note that index forms are described as forms that are used for the representation of numbers or variables that are too large or small to be written.

Some rules of index forms are;

From the information given, we have that;

(2^-3)(2^5)/2^7)

add the exponents of the numerator

2⁻³⁺⁵/2⁷

Add the values

2²/2⁷

Subtract the exponents

2⁻⁵

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The missing number in the ratios of numbers are 16:10     8:20 and 0:30

Ratios are quantitative relationships between two numbers that describe how many times one value can contain another

the given parameters are

Forks         16          8              ----

Spoons       10         ---            30

The numbers are written in ascending order of magnitude

Using AP,

for forks: a = 16, 2nd term = 8

common difference = 8-16 - -8

For spoons a = 10, 3rd term = a + 2d = 30

30 = 10 + 2d

30 -10 = 2d

d= 20/2 = 10

Therefore the 2nd term = 10+10=20

The table reappears as follows

Forks         16          8             0

Spoons       10        20          30

Therefore the equivalent ratios are 16:10     8:20 and 0:30

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The volume of the sphere with a diameter of 6cm is 108 cm³.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi

Given the data in the question:

Diameter d = 6cm

Radius is half of diameter

Radius r - 6cm/2

Radius r = 3cm

Also, π = 3

Plug the given values into the above formula.

Volume =  (4/3)πr³

Volume =  (4/3)π3³

Volume =  (4/3)(3)(27)

Volume =  108 cm³

Therefore, the volume is 108 cm³.

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The temperature of Srinagar on Wednesday was -3°C.

If the temperature was -5°C on Monday and dropped by 2°C on Tuesday, we can subtract 2 from -5 to get:

-5°C - 2°C = -7°C

So the temperature of Srinagar on Tuesday was -7°C.

If the temperature on Wednesday rose by 4°C from the temperature on Tuesday, we can add 4 to -7°C to get:

-7°C + 4°C = -3°C

So the temperature of Srinagar on Wednesday was -3°C.

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The complete question:

At Srinagar temperature was -5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

Here cuz:

Frank got more cuz you see Graham has 1/3  and 3/4 and frank got 3/5 and 1/2 so he got more.

Hope This Helps Cuz!

1) The decay constant is  0.0385

2) The amount after ten years is  27.2 mg

3) The time taken for 10 mg to remain is  36 years.

We know that;

P = Poe^-kt

Given that the half life is 18 years;

20=40e^-18k

20/40=e^-18k

0.5 =e^-18k

ln0.5 = -18k

k = -0.693/-18k

k = 0.0385

After 10 years we have;

P = 40e^-10(0.0385)

P = 27.2 mg

10 mg will remain when;

10 = 40e^-0.0385t

10/40 =e^-0.0385t

0.25 = e^-0.0385t

ln0.25 = -0.0385t

t = -1.386/-0.0385

t = 36 years

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Answer: Its high

Step-by-step explanation: It just is

The probability that Brent draws mismatched socks is 32/153.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since Brent is drawing two socks without replacement, there are 18 choices for the first sock and 17 choices for the second sock.

Therefore, there are 18 x 17 = 306 possible ways Brent could draw two socks.

For Brent to have mismatched socks, he needs to draw a white sock first and a black sock second, or a black sock first and a white sock second.

Let's consider the first case.

There are 16 white socks and 2 black socks, so there are 16 x 2 = 32 ways Brent could draw a white sock first and a black sock second.

For the second case, there are 2 black socks and 16 white socks, so there are 2 x 16 = 32 ways Brent could draw a black sock first and a white sock second.

Therefore, the probability of Brent drawing mismatched socks is:

= (32 + 32) / 306

= 64 / 306

= 32 / 153

Thus, the probability that Brent draws mismatched socks is 32/153.

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Answer:

Step-by-step explanation:

Answer:

$68,796.57

Step-by-step explanation:

approx $68,796.57 at 18 years

The volume of the pyramid is determined as 433.33 mm³.

The volume of the right square pyramid is calculated by applying the following formula.

V = ¹/₃a²h

where;

The volume of the pyramid is calculated as follows;

V = ¹/₃ (10 mm)² x ( 13 mm )

V = 433.33 mm³

Thus, the volume of the pyramid is calculated from the formula stated.

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Answer: C

Step-by-step explanation:

Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

Answer:

z=199.68

Step-by-step explanation:

The new surface area of the hemisphere-shaped mole would be = 102mm².

A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.

Since the surface area of one hemisphere has been given, the second hemisphere can be determined.

To calculate the new surface area of the hemisphere-shaped moles the following is carried out;

Radius of the initial mole = 5.7/2 = 2.85 mm

If 2.85mm radius = 51 mm²

2(2.85mm) radius = x

Make X the subject of formula;

X = 2×2.85 × 51/2.85

= 102 mm²

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The volume of the oblique cylinder can be calculated as:

833π cm³

The formula that would be used to find the volume of any given oblique cylinder can be expressed as:

Volume = πr²h, where:

radius of the cylinder = r

height of the cylinder = h

π is a constant

We are given the values for the cylinder as:

r = 14/2 = 7 cm

h = 17 cm

Volume of the oblique cylinder =  πr²h =  π × 7² ×  17

Volume of the oblique cylinder = 833π cm³

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The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

It should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.

The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.

After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

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Answer:

The slope is [tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

the slope is the number before the x.

Helping in the name of Jesus.

A = s^2, where A is the area and s is the length of one side of the square gives the area of a square base. The correct option is true

If s^2 = 144, then s = √144 = 12 feet. The correct option is false

A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex.

Therefore, s^2 = 144 is a valid equation to find the length of one side of the base. The correct option is true

Therefore, one side of the pyramid's base is 12 feet, not 72 feet.

The correct option is false

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The system of equations are t = 22.28 years , number of nickles and dimes are solved

Given data ,

a)

Let the number of years be represented as t

For truck A, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck A = 20345 + 1230t

For truck B, the total cost (including the initial cost and average yearly repair cost) after "t" years can be represented as:

Total cost for truck B = 16000 + 1425t

when the total costs are equal , we get

20345 + 1230t = 16000 + 1425t

On simplifying , we get

195t = 4,345

t = 22.28 years

b)

Let the number of nickels be n and number of dimes be d

The total value of nickels is 0.05n (since the value of one nickel is $0.05) and the total value of dimes is 0.10d (since the value of one dime is $0.10)

The total value of the coins = $ 2.05

And , the total number of coins = 56

0.05n + 0.10d = 2.05

And , n + d = 56

Hence , the system of equations are solved

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The fourth term in the expanded form of (x - 1)⁶ is  -20x³.

The fourth term in the expanded form of (x - 1)⁶  using the binomial theorem is calculated as follows;

The expanded form of (x - 1)⁶ using the binomial theorem is;

(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1

(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1

To find the fourth term, we look for the fourth term from the left side to right side, which is  -20x³.

Therefore, the fourth term in the expanded form of (x - 1)⁶ is  -20x³.

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The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.

The graph of the solution set of -48 < -8t is shown below.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Next, we would determine the solution to the given inequality as follows;

2.5x ≥ 20

x ≥ 20/2.5

x ≥ 8 (Sebastian was wrong)

-48 < -8t

-48/-8 < -8t/-8

6 < t

t > 8

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The coordinates of the new point  is (-6, -2)

From the question, we have the following parameters that can be used in our computation:

Point = (6, 2)

Rule: 180 degrees rotation

The rule of 180 degrees rotation is

(x, y) = (-x -y)

Substitute the known values in the above equation, so, we have the following representation

image = (-6, -2)

Hence, the image is (-6, -2)

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All city residents who support the arts. Therefore, the option C is the correct answer.

As the city official would lie to know that if public support for increased funding of arts programs. By collecting data the officials show the survey after every 25 persons and ask for their opinion.

They also tend to raise a fund that states the population in the scenario of a city resident that supports the arts.

The population in this scenario is the people surveyed by the city official. The city official is conducting a survey outside a concert hall after a show, which means they are targeting people who have just attended a show. Since the city official is asking every 25th person to exit their opinion about raising funds for the arts, these are the people who are included in the population being surveyed.

Therefore, the option C is the correct answer.

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The length of each rope if all the ropes had the same length is 3 ft

From the question, we have the following parameters that can be used in our computation:

The dot plot

From the dot plot, we can see that the data are normally distributed

This means that the length of each rope is the mean, the median and the mode

Given that the data on the dot plot is normally distributed, we have the following values

So, we can conclude that the length is 3 ft

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The value of x rounded to 1 decimal place is 15.9 cm.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

First of all, we would determine length of sides or side lengths of the opposite side of the ight-angled triangle as follows;

12.5² + y² = 19.5²

156.25 + y² = 380.25

y² = 224 cm.

y = √224 cm

Now, we can determine value of x;

x² = (√224)² + (5.5)²

x² = 224 + 30.25

x = 15.9 cm.

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Missing information:

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

The planes that are parallel in the cube shown would be C. NOR and LMP.

Two planes that are located on a cube and are always opposite and never intersect; they remain continuously at the same distance from each other. A cube consists of three pairs of parallel planes in correspondence with its triplet of opposing faces.

From the given options, the only parallel planes would be NOR and LMP. One of the reasons for this, is that these planes have no point of intersection unlike the planes in the other options.

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The average rate of change of the height of the rocket is 11.25/(a - 1)

From the question, we have the following parameters that can be used in our computation:

h(1) = 23 meters and h(a) = 34.25 meters.

The average rate of change of the height of the rocket is

Rate = Change in height /Time

So, we have

Rate = (34.25 - 23)/(a - 1)

Evaluate

Rate = 11.25/(a - 1)

Hence, the rate = 11.25/(a - 1)

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Complete question

Melissa launches a rocket from a 3-meter-tall platform. The height, h, of the rocket, in meters, can be modeled by the given graph.

Melissa knows that h(1) = 23 meters and h(a) = 34.25 meters.

What is a reasonable estimate of the average rate of change of the height of the rocket, in meters per second

The formula for the variable r is r = √A/π

The subject of formula can be defined as the variable that is allowed to alone in an equation.

The variables is made to be written on one end of the equality sign.

It is also described as the variable that is worked out in an equation.

From the information given, we have that;

the formula for the area of the circular pool is;

A = πr²

Such that;

We then have;

r = √A/π

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