Complete the pattern. 1/9, 1/3, 1, ?

The required value of the given function  f(a) = -2a^2 - 5a + 4 at a = -3 is 1

Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.

Function, f(a) = -2a^2 - 5a + 4

To find value of f(-3),

f(a) = -2a^2 - 5a + 4

Put a = -3 in th function

F(-3) = -2(-3)^2-5×-3+4

F(-3) = -18+15+4=1

F(-3) = 1

Thus, required value of f(-3) is 1

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Coorect Question:

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

5/4 times 36 is found as 9.5=45.

By answering the above question, we may state that As a result, the equation antenna's height is roughly 25 metres.

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.  

draw a diagram of the situation

                B

                |

                | h

                |

   A------------C---------

   |          θ2|        θ1

   |            |

   |            | 16 m

   |            |

   D            E

We need to calculate the height h of point B above point A. To begin, we may use the tangent function to get the heights of points C and E:

\(hC = 16 * tan(θ1)\\hE = 16 * tan(θ2)\\DE = hE - hC\\hB = hC + DE * tan(θ2)\\h = hB + 1.5\\θ1 = 41\\θ2 = 49\\DE = 16 * (tan(θ2) - tan(θ1)) ≈ 9.7587 m\\hC = 16 * tan(θ1) ≈ 12.2272 m\\hB = hC + DE * tan(θ2) ≈ 23.7333 m\\h ≈ hB + 1.5 ≈ 25.2333 m\\\)

As a result, the antenna's height is roughly 25 metres.

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Answer:

$115.2

Step-by-step explanation:

Step one:

Given data

A store used to sell an MP3 for $72 and we are told that this 50% of the wholesale price.

Therefore the wholesale price is

72*2= $144

Required:

The special sales cost at 20% discount

Step two:

We are told that the special sale is at a 20% discount on the wholesale

= 20/100*144

=0.2*144

=$28.8

Therefore the special sales price is

= 144-28.8

=$115.2

\(v = \pi \times {r}^{2} \times h\)

\(v = \pi \times 49 \times 18\)

\(v = 2770.88\)

(a) The number of ways of selecting a committee of 8 students = 45.

(b) The number of ways to select a committee with 3 seniors and 2 juniors are 105.

(c) The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the 8 must be selected as chair = 360 ways

What is combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given that 10 students have volunteered for a committee. 7 of them are seniors and 3 are juniors.

a) Need to find the number of ways of selecting a committee of 8 students

The number of ways of selecting a committee of 8 students = \(10_C_8\)

\(10C_8= \frac{10!}{8!(10-8)!}= \frac{10!}{8!(2!)}=45\)

The number of ways of selecting a committee of 8 students = 45.

(b) Need to find the number of ways to select a committee with 3 seniors and 2 juniors

The number of ways to select a committee with 3 seniors and 2 juniors

= \(7_C_3(3_C_2)\)

\(7_C_3*3_C_2 = \frac{7!}{3!*4!} *\frac{3!}{2!*1!} = 35 * 3 = 105\)

The number of ways to select a committee with 3 seniors and 2 juniors are 105.

(c) Need to find the ways to make the select the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair.

Number of ways = \(10_C_8*8_C_1\)

\(10_C_8*8_C_1 = \frac{10!}{8!*2!} *\frac{8!}{7!*1!} = 45*8 = 360\)

The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the five must be selected as chair = 360 ways.

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The balance in the account at the end of 4 years if the deposit is $2000, the interest rate is 2.5% and it is compounded daily will be $2,251.65.

Let us calculate the interest on the deposit for the first year:

The principal amount, P = $2000

Interest rate, R = 2.5%

Time period, t = 1 year

Number of times the interest is compounded per year, n = 365

Since the interest is compounded daily, the number of times the interest is compounded in a year is 365.

We can calculate the interest for the first year using the formula below:

A = P(1 + r/n)^ntA = 2000(1 + 0.025/365)^(365 * 1)A = $2050.42

The total balance in the account at the end of the first year is $2,050.42.

Let us calculate the interest on the deposit for the second year:

Since the interest is compounded daily, the number of times the interest is compounded in a year is 365.We can calculate the interest for the second year using the formula below:

A = P(1 + r/n)^ntA = 2050.42(1 + 0.025/365)^(365 * 1)A = $2101.84The total balance in the account at the end of the second year is $2,101.84.

Let us calculate the interest on the deposit for the third year:

Since the interest is compounded daily, the number of times the interest is compounded in a year is 365.

We can calculate the interest for the third year using the formula below:A = P(1 + r/n)^ntA = 2101.84(1 + 0.025/365)^(365 * 1)A = $2153.34

The total balance in the account at the end of the third year is $2,153.34.

Let us calculate the interest on the deposit for the fourth year:

Since the interest is compounded daily, the number of times the interest is compounded in a year is 365.We can calculate the interest for the fourth year using the formula below:

A = P(1 + r/n)^ntA = 2153.34(1 + 0.025/365)^(365 * 1)A = $2,251.65

Therefore, the balance in the account at the end of 4 years if the deposit is $2000, the interest rate is 2.5% and it is compounded daily will be $2,251.65.

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Answer:

x = {0, 4y}

Step-by-step explanation:

Simplifying

3x(x + -4y) = 0

(x * 3x + -4y * 3x) = 0

Reorder the terms:

(-12xy + 3x2) = 0

(-12xy + 3x2) = 0

Solving

-12xy + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.

3x(-4y + x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(-4y + x)' equal to zero and attempt to solve:

Simplifying

-4y + x = 0

Reorder the terms:

x + -4y = 0

Solving

x + -4y = 0

Move all terms containing x to the left, all other terms to the right.

Add '4y' to each side of the equation.

x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0

x + 0 = 0 + 4y

x = 0 + 4y

Remove the zero:

x = 4y

Simplifying

x = 4y

Solution

x = {0, 4y}

The simplified form of the given expression a)3x×4y and 2p×3q×5r will be 12xy and 30pqr respectively.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,

a)3x × 4y

b)2p × 3q ×5r

When you simplify an expression, your goal is to make it as simple as you can. There shouldn't be any further multiplication, dividing, adding, or removing to be done at the conclusion. We can apply all the arithmetic operations in order to simplify the expression.

The expression can be simplified by multiplying the variable and the constants separately,

a)3x × 4y

=(3×4))x×y)

=12xy

b)2p × 3q ×5r

=(2×3×5)(p×q×r)

=30pqr

Thus, the simplified form of the given expression a)3x×4y and 2p×3q×5r will be 12xy and 30pqr respectively.

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Answer:

C = pi d

C = 3 × 36

C = 108

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needed to be 20 characters long.....

the area of the mat is 27/25 square meters, or 1.08 square meters

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees. Area of rectangle is A = a*b

To find the area of the mat, we need to multiply its length by its width. The length of the mat is 1 and 4/5 meters, which can be written as 9/5 meters. The width of the mat is 3/5 meters. So the area of the mat is:

Area = length × width

Area = (9/5) meters × (3/5) meters

Area = (27/25) square meters

Therefore, the area of the mat is 27/25 square meters or 1.08 square meters.

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The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

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Answer:D

Step-by-step explanation:

Answer:

p(q-1)

Step-by-step explanation:

P is the common factor in both the terms, so remove that to go outside the brackets.

What goes inside the brackets depends on what the quotient is when you divide both terms by p.

Hers,

pq becomes q

p becomes 1

THe negative sign remains there because he divide the is positive. (One positive and one negative make a negative)

Hope this helps

Answer:

No

Step-by-step explanation:

It is a parallelogram as the sides do not form any 90° angle when you connect the points.

The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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Answer:

See below

Step-by-step explanation:

Answer choices:

1. The potato was launched from the ground.

2. The flight is symmetric about the line t = 2.

3. The potato reaches a maximum height of about 3 ft

4. The potato is in the air during the interval 0

5. The potato reaches its maximum height after about 3 seconds in flight.

6. h(2)=h(5)

Step-by-step explanation:

f(-2) = 3(-2) - 12

→ -6 - 12 = -18 ans.

hope this helps you !

Answer:

Step-by-step explanation:

circumference = diameter × π = 4π inches ≅ 12.56 inches

Quantity of Tanzanian blend used in my secret coffee blend = 40 pounds

Quantity of Queen city blend used in my secret coffee blend = 8 pounds

The ratio of Tanzanian blend to Queen city blend in my coffee blend = 40 : 8

Quantity of Tanzanian blend with me = 20 pounds

Quantity of Queen city bend needed to make my secret coffee blend =

Let the quantity of Queen city blend I will need be x .

\( \frac{40}{8} = \frac{20}{x} \)

\(8 \times 20 = 40 \times x\)

\(160 = 40x\)

\(x = \frac{160}{40} \)

\(x = 4\)

Therefore , I need to mix 4 pounds of queen city blend with my 20 pounds of Tanzanian blend to get my secret coffee blend .

4 pounds of  the Queen City coffee should you mix with it to get your secret blend.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

Yesterday If we mixed 40 pounds of the Tanzanian blend with 8 pounds of the Queen City blend.

In the same proportion, today there is 20 pounds of the Tanzanian coffee left in stock.

We need to calculate how many pounds of the Queen City coffee should you mix with it to get your secret blend.

Let x be the pounds of the Queen City coffee should you mix with it

Let us form a equation

40/8=20/x

Apply cross multiplication

40x=160

Divide both sides by 40

x=4

Hence 4 pounds of  the Queen City coffee should you mix with it to

get your secret blend.

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Answer:

used formula

Step-by-step explanation:

y-y1=m(x-x1)

Answer:

x = 35

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Then

1 exterior angle = 360° ÷ 8 = 45° , so

x + 10 = 45 ( subtract 10 from both sides )

x = 35

The value of x for the octagon considering the value of the exterior angle is; x = 35°

The sum of the exterior angles of a regular polygon is 360°

Now, we are told that the measure of an exterior angle of a regular polygon is (x + 10)°. Thus;

For an octagon, we have;

8(x + 10)° = 360°

8x + 80 = 360

8x = 360 - 80

8x = 280

x = 280/8

x = 35°

Thus, the value of x for the interior angle is 35°.

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The correct answer to this question is C. The sample mean,  being greater than 30 is not a requirement for testing a claim about a population mean with a known standard deviation, sigma.

The other three options are important requirements for testing such a claim. A simple random sample is necessary to ensure that the sample is representative of the population. Knowledge of the population standard deviation is also crucial because it is used in calculating the test statistic, z-score.

Therefore, option C is the odd one out as it is not a requirement for testing a claim about a population mean with a known standard deviation.

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Answer:

3/4

Step-by-step explanation:

Step 1: find the least common denominator: 14/20+1/20

Step 2: add the two fractions together: 15/20

Step 3: simplify the fraction: 3/4

Hope that helps

Answer:

A and D

Step-by-step explanation:

Fallacies are erroneous beliefs or failures in reasoning that render arguments and claims unsound.

In this regard, this answer will provide you with the twelve fallacies found in Module 5 Key Points and an example of each of them.

1. Ad hominem - Attacking the character or personality of someone to discredit their argument. Example: Sarah's argument is incorrect because she is not a native speaker.

2. Appeal to authority - Accepting a claim because it is made by someone who is perceived to be an authority on the subject. Example: The celebrity claims that the weight-loss pills are effective, so they must be.

3. Appeal to emotion - Using emotions to persuade someone instead of using logical reasoning. Example: If you don't support animal rights, you are heartless.

4. Bandwagon - Suggesting that an idea or belief is true simply because many people support it. Example: Everyone loves a particular television show, so it must be great.

5. Begging the question - Using a premise to prove a conclusion that is already implicit in that premise. Example: The Bible is the word of God because it says so in the Bible.

6. False dilemma - Presenting only two options when there are more options available. Example: You are either with us or against us.

7. Hasty generalization - Making a broad conclusion based on limited evidence. Example: All math teachers are strict because my math teacher is strict.

8. Non sequitur - Making a conclusion that does not follow logically from the evidence presented. Example: All cats have tails, so they are better pets than dogs.

9. Post hoc - Assuming that one event is the result of another event without any evidence to support the claim. Example: I ate an apple before I got sick, so the apple must have caused my illness.

10. Red herring - Introducing an irrelevant topic to distract from the main issue. Example: We should not spend money on space exploration because there are homeless people on the streets.

11. Slippery slope - Suggesting that one event will lead to a series of events with catastrophic results without any evidence to support the claim. Example: If we legalize marijuana, people will start using harder drugs, and society will collapse.

12. Strawman - Misrepresenting or distorting an argument to make it easier to attack. Example: You believe in evolution, so you must be an atheist. These are the twelve fallacies found in Module 5 Key Points with examples for each of them.

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Using the binomial distribution, it is found that the number of students that would be expected to select a gold-wrapped candy  from the bag is given by:

The candies are chosen with replacement, which means that for each student, the probability of choosing a gold wrapped candy is independent of any other student, hence the binomial distribution is used.

The expected value of the binomial distribution is:

\(E(X) = np\)

In this problem:

Then, the expected value is:

\(E(X) = np = 15\times \frac{1}{3} = 5\)

Hence, option B is correct.

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Answer: $240

Step-by-step explanation:

To find 200% of the full price of the annual pass, which is $120, we can simply multiply $120 by 200%.

$120 * 200% = $120 * 2 = $240

So, 200% of the full price of the annual park pass, which is $120, is $240.

Answer:

Any value you choose for x will make the equation a TRUE statement.

Answer: The flower grew  0.88 inches during the week

Step-by-step explanation:

Height of flower in the previous week = 3.25 inches

Height of flower the next week = 4.125inches

height the flower added during the week = 4.125 inches - 3.25inches

=0.875 inches

Rounding to the nearest hundredths becomes 0.88 inches