4.
F=1.80 + 32
so
(a) Work out the value of F when C=2

(b) Work out the value of C when F= 50

Answer:

(0, - 1). thats the answer

The value of the 3rd term in the expansion of (x+6) ^6 will be as follows:

540x^4

What is expansion?

Expanding brackets, also known as multiplying out, seeks to eliminate the set of brackets by multiplying each phrase inside a bracket by the term on the outside and subsequently accumulating similar phrases. When solving equations, extending brackets, which is the opposite of factorization, is frequently an essential step.

Here in the question,

We have,

(x+6) ^6

Expanding it we get:

= x^6 + 36x^5 + 540x^4 +4320x³ + 19440x² + 46656x + 46656

So, the 3rd term of the expansion is 540x^4.

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The value of the 3rd term in the expansion of \((x+6) ^6\) will be as follows: \(540x^4\). The correct answer is option (c).  \((6\ \ 4)36x^4\)

By multiplying each phrase inside a bracket by the word on the outside and then accumulating similar phrases, expanding brackets, also known as multiplying out, aims to eliminate the set of brackets. Extending brackets, which is the opposite of factorization, is frequently a crucial stage in the solution of equations.

An affine transformation termed expansion, in which the scale is expanded, is also referred to as an enlargement or dilation. It is also sometimes referred to as an enlargement and is the polar opposite of a geometric constriction.

Here in the question,

We have,

\((x+6) ^6\)

Expanding it we get:

\(= x^6 + 36x^5 + 540x^4 +4320x^3 + 19440x^2 + 46656x + 46656\)

So, the 3rd term of the expansion is \(540x^4\).

The correct answer is option (c). \((6\ \ 4)36x^4\)

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The length of the ramp is solved to be 15.33 feet

The length of the ramp is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a right triangle of

adjacent = 15 feet

hypotenuse = length of the ramp = ?

The length of the ramp is calculated using cos, CAH

let the angle be x

cos x = adjacent / hypotenuse

cos 12 =  15 / hypotenuse

hypotenuse = 15 / cos 12

hypotenuse = 15.334

length of ramp = 15.33 feet

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Answer

The answer is 12 for sure

Step-by-step explanation:

i just solved it like any other equation

1 i added 3/4 on both sides

2 then i added 5 on both sides

3 after you equation should look like 1 1/4x = 15

4 then i divided and it should be x = 12

pls mark brainliest

The value of x is "12".

\(\to \frac{1}{2}x-5=10-\frac{3}{4}x \\\\\to \frac{1}{2}x+ \frac{3}{4}x=10+5 \\\\\to \frac{2+3}{4}x=15 \\\\\to \frac{5}{4}x=15 \\\\\to x=15 \times \frac{4}{5}\\\\\to x=3 \times 4\\\\\to x=12\)

Therefore, the final value of x is "12".

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The missing numbers are 17,66,13, 9 3 and 15 respectively .

The rules given to us are-

first row consist of a number which is the sum of two numbers of middle row

Third row consist of a number which is the product of two numbers of middle row

The first part

The sum of 6 and 11 is 17 and the product of 6 and 11 is 66

       17

6                11

       66

The second part

To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13

       13

4               9

       36

The third part

To find the numbers of middle row we need to find the factors of 45 that sum up to 18

The factors of 45 are 3*3*5

The factor 15 and 3 satisfy both the requirements

       18

3                15

       45

Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively

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27 2/10

   or

27 1/5

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

The recursive definition of the arithmetic sequence -34, -21, -8 is:

It is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

\(a_n = a_1 + (n - 1)d\)

In which \(a_1\) is the first term of the sequence.

An arithmetic sequence can also be defined recursively, as follows:

In this problem, the sequence is given as follows:

-34, -21, -8.

Hence the first term and the common ratio are given as follows:

Hence the recursive definition of the sequence is:

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the idea being, that we first off move the recurring part to the left-hand-side by simply multiplying it by some power of 10 and then we use the decimal part as variable, let's proceed.

\(0.3838\overline{38}~\hspace{10em}x=0.\overline{38} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|lll|l}\cline{1-3} &&&\\ 100x&=&38.\overline{38}\\ &&38+0.\overline{38}\\ &&38+x\\[1em]\cline{1-3} \end{array}\qquad \implies \begin{array}{llll} 100x=38+x\implies 99x=38\\\\ x=\cfrac{38}{99} \end{array}\)

The longest side of the other triangle is 37.8 cm

From the question, the sides of the triangle are given as

This means that

Ratio = Corresponding sides of the triangles

So, we have

Ratio = Longest sides : Shorters sides

Substitute the known values in the above equation

So, we have the following equation

18 : 7 = Longest side : 14.7

Multiply 18 : 7 by 2.1

So, we have

37.8 : 14.7 = Longest side : 14.7

So, we have

Longest side = 37.8

Hence, the longest side  is 37.8 cm

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The expanded form for given expression y(3.05x−3.75​)−2.25y will be in form of a linear equation = 3.05yx - 6y.

What is linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now

By Solving y(3.05x−3.75​)−2.25y

=3.05yx -3.75y - 2.25y

=3.05yx - 6y

Hence,

            expanded form will be in form of a linear equation = 3.05yx - 6y.

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Answer:

Step-by-step explanation:

I=prt/100

5000×2×2=20000÷10

I=2000

Answer:

skp

Step-by-step explanation:

Answer:

r=60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

3-r/8=-9/2

r/8=3-(-9/2)

r/8=3+9/2

r/8=6/2+9/2

r/8=15/2

r=(15/2)*(8/1)

r=120/2

r=60

Answer:

Goku died you I just started watching

\(\longrightarrow \sf \$ \: 307.2\)

Since painting is done on outer surface of cubical block we will have to find its surface area which is given by-

\(\green{ \underline { \boxed{ \sf{Surface \: area \:of \:Cube = 6a^2}}}}\)

\(\begin{gathered}\\\quad \sf Surface \: area \:of \:Cube = 6\times(3.2)^2 \\\end{gathered} \)

\(\begin{gathered}\\\implies \quad \sf 6\times 3.2\times3.2 \\\end{gathered} \)

\(\begin{gathered}\\\implies \quad \sf 61.44 cm^2 \\\end{gathered} \)

Now,

\(\maltese \sf Cost \:of \:painting \: 1 \: cm² = \$ 5\)

\( \sf Cost \: of \: painting \: 61.44 \:cm²=61.44×5\)

\(\sf\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad=\$ 307.2\)

\(\leadsto\)Thus it would cost $ 307.2 to paint the entire cubical block.

Hello!

For A//B, the alternate-internal angles must be equal.

So:

5x = 115

x = 115/5

x = 23

If x = 23, A//B.

The answer is x = 23.

The equation used to determine the population is y = 1500(1.11)ˣ.

What is the exponential function?

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Here, we have

Given: the population of Exponentville is 1500 in 2010, and the population increases each year by 11%.

We have to find the equation used to determine the population, y, of exponentially x years after 2010.

Initial population = 1500

Population increases each year by 11%.

x = years

The equation is :

y = 1500(1+11/100)ˣ

y = 1500(1.11)ˣ

Hence, the equation used to determine the population is y = 1500(1.11)ˣ.

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Answer:

the standared deviation =2.87 so it is small

Step-by-step explanation:

to calculate the standard deviation of those numbers:

1- Work out the Mean (the simple average of the numbers)

(7+6+5+8+9+1+0+4+3+2)/10=4.5

Then for each number: subtract the Mean and square the result.

[(7 - 4.5)^2 + ... + (2 - 4.5)^2]/10=8.25

√8.25=2.87≅3

Answer:

A. Small

Step-by-step explanation:

Yes, you can be certain that there are at least two guests who had the same number of handshakes. This is due to the Pigeonhole Principle.

As the party organizer, you shake hands with all 80 guests, which means you have 80 handshakes. The guests can have a minimum of 0 handshakes (if they don't shake hands with anyone except you) and a maximum of 79 handshakes (if they shake hands with everyone except themselves). There are 80 guests (excluding yourself), so there are 80 "pigeonholes" for the number of handshakes. The range of possible handshakes among the guests is from 0 to 79, which creates 80 possible outcomes or "pigeons."

According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons. In this case, there are 80 pigeonholes (guests) and 80 pigeons (possible handshakes). Therefore, at least two guests must have had the same number of handshakes.

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Step-by-step explanation:

refer to the picture.. hope this helps :)

Answer:

58 gallons of gas

Step-by-step explanation:

1,284/372= 3.5 Rounded

16.6 * 3.5= 58.1 gallons of gas

In order to determine the critical values for an independent-samples T-test, the following information needs to be known:

The critical values for an independent-samples t test are used to determine if the differences between two samples are statistically significant. In order to calculate the critical values, the size of the sample (n), the significance level (alpha), the degrees of freedom (df), and the type of t-test (one-tailed or two-tailed) must be known. The degrees of freedom are equal to the number of observations in the sample minus

The size of the sample is the total number of observations in the two samples. The significance level is the probability of making a type-I error (rejecting the null hypothesis when it is true). Finally, the type of t-test is used to determine if the test is one-tailed (testing for a difference in one direction) or two-tailed (testing for a difference in both directions). Once all of this information is known, the critical values can be calculated to determine if the differences between the two samples are statistically significant.

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Answer:

55

Step-by-step explanation:

(a) Here is a graph with six nodes (labeled as A, B, C, D, E, F) and eight edges connecting them:

     A --- B

    / \   / \

   /   \ /   \

  F --- C --- D

   \   / \   /

    \ /   \ /

     E --- F

(b) To determine the number of faces in the graph, we can use Euler's formula, which states that for a planar graph (a graph that can be drawn on a plane without any edges crossing), the number of faces (including the infinite face) is given by: F = E - V + 2, where F is the number of faces, E is the number of edges, and V is the number of vertices (nodes).

In our graph, we have: V = 6 (A, B, C, D, E, F),E = 8. Using the formula, we can calculate the number of faces: F = 8 - 6 + 2, F = 4. Therefore, the graph has four faces.

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A rhombus with MK = 24 m, JL = 20, ∠MJL = 50°. So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

We need the information about the measurements or a description of the missing measures in the rhombus. We can make it MK = 24 m, JL = 20, ∠MJL = 50° for example. Since it's a rhombus, all sides are equal in length. Therefore, NK = MK = 24 m, JM = JL = 20 m, and ML = NL.

To find ML (or NL), we can use the Law of Cosines on the triangle MJL. In this case,

ML² = JM² + JL² - 2(JM)(JL)cos(∠MJL):

ML² = 20² + 20² - 2(20)(20)cos(50°)

ML² = 400 + 400 - 800cos(50°)

ML² ≈ 617.4

Taking the square root of both sides, we get ML ≈ √617.4 ≈ 24.8 m.

So, NK = 24 m, NL = 24.8 m, ML = 24.8 m, and JM = 20 m.

The complete question is The quadrilateral below is a rhombus. Given MK = 24 m, JL = 20, ∠MJL = 50°. Find NK, NL, ML, and JM. Any decimal answers should be rounded to the nearest tenth.

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The expressions that represent the total number of berries in the Berry Blast smoothies that Luther made today is 3 + b = 20

Let the number of strawberries be x

Let the number of b berries be y

If at work today, he made 20 Berry Blast smoothies, then;

x + y = 20

SInce x = 3 and y = b, then;

3 + b = 20

The expressions that represent the total number of berries in the Berry Blast smoothies that Luther made today is 3 + b = 20

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Answer:

50 degrees

Step-by-step explanation:

Vertical angles in geometry. If you don't know what that is, here is a brief summary:

each of the pairs of opposite angles made by two intersecting lines.

Answer:

Ok, so to find the volume of a sphere, the volume is 4/3 (3.14 which is pie) times the radius cubed so r^3

so the radius of this sphere is 2 because 4-2=2

Step-by-step explanation:

so now we do 4/3 times 3.14 times 2^3 power=

now first we multiply 4/3 times 2 to the 3rd power bc we dont need to multiply pie (3.14) your answer would be 10.66667 so its 10.66667 pie (3.14) so round 10.66667 it would just be 10.7 because the 7 round up the 6 to a 7. Hope this helps!

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

The if statement evaluates the test expression inside the parenthesis ().

If the test expression is evaluated to true, statements inside the body of if are executed.

If the test expression is evaluated to false, statements inside the body of if are not executed.

The part of the statement following "if" is called the antecedent, and the part of the statement following "then" is called the consequent in conditional statements.

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In conditional statements, the part of the statement following 'if' is called the antecedent.

The antecedent is the condition that needs to be true for the consequent to occur.

The consequent is the part of the statement that follows 'then.'

An antecedent is a noun or pronoun that denotes a specific being, place, object, or clause.

It's also referred to as a referent. Without an antecedent, a sentence may be insufficient or nonsensical since it is

required to establish what or to whom a pronoun in a sentence is referring.

In summary, a conditional statement is structured as "if (antecedent) then (consequent)."

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Of the given options, "Oligarchic rule must be abolished in South Africa" most closely represents Nelson Mandela's belief as spoken in his inaugural address.

Nelson Mandela's inaugural address marked a pivotal moment in South Africa's history, as he became the country's first democratically elected president after decades of apartheid rule. In his speech, Mandela emphasized the need for equality, justice, and the dismantling of oppressive systems. While the specific phrase "oligarchic rule must be abolished in South Africa" may not be directly mentioned, the sentiment aligns with Mandela's vision for a democratic and inclusive South Africa.

Mandela strongly believed in the principles of democracy, freedom, and equal rights for all South Africans. His fight against apartheid was rooted in the belief that the system of racial segregation and discrimination was unjust and had to be dismantled. Mandela spoke out against the continued apartheid system and laws, advocating for their complete elimination. He recognized that apartheid, although it may have been deemed understandable by some in the past, was fundamentally wrong and had to be eradicated for the sake of a unified and prosperous nation. In his inaugural address, Mandela emphasized reconciliation and the importance of building a united South Africa. While the exact phrase "apartheid was once an understandable policy in South Africa, but not anymore" may not be present, Mandela's words conveyed the idea that the old system of apartheid was no longer acceptable or justifiable. He sought to move the country forward by embracing a new era of equality, where all citizens, regardless of race or background, could participate fully in the democratic process and enjoy equal rights and opportunities.

In conclusion, while the provided options do not directly mirror Nelson Mandela's exact words, the statement that "oligarchic rule must be abolished in South Africa" best reflects his belief in dismantling oppressive systems and establishing a democratic society based on equality and justice.

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