Please help me with these two questions

Answer:

The mean of the combined group of 30 students is equal to 56.67

Step-by-step explanation:

Let

x ----> The sum of the notes of the 20 papers

y ----> The sum of the notes of the 10 papers

we know that

60=x/20 -----> x=60*20=1,200

50=y/10 -----> y=50*10=500

The mean of the combined group of 30 students is equal to

(x+y)/30

substitute

(1,200+500)/30=56.67

Answer:

1705/64

Step-by-step explanation:

A geometric series contains terms that are in the form [tex]a_1\cdot(r)^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is common ratio.

A common ratio is the number that is used to find the next term by multiplying previous term by [tex]r[/tex].

Now we can use a formula and we would be using [tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex] where n is the number of terms you are adding and [tex]a_1[/tex] is the first term and r is the common ratio.

Before we do that, I'm going to do this without that formula. Sum means we are just going to add these terms after finding them.

The first term is 20.

The second term is (1/4)(20)=5.

Third term is (1/4)(5)=5/4.

Fourth term is (1/4)(5/4)=5/16.

The fifth term is (1/4)(5/16)=5/64.

Now we add them (20)+(5)+(5/4)+(5/16)+(5/64)

Putting this into the calculator gives me: 1705/64.

Now let's do the formula way as well.

Again we have:

r=1/4

[tex]a_1=20[/tex]

n=5 since we adding the first 5 terms:

[tex]S_5=\frac{20(1-(\frac{1}{4})^5}{1-\frac{1}{4}}[/tex]

[tex]S_5=\frac{20(1-\frac{1}{1024}){\frac{3}{4}}[/tex]

[tex]S_5=\frac{20-\frac{20}{1024}}{\frac{3}{4}}[/tex]

Dividing by 3/4 is the same as multiply by 4/3.

[tex]S_5=(20-\frac{20}{1024})\frac{4}{3}[/tex]

[tex]S_5=20 \cdot \frac{4}{3}-\frac{20}{1024}\cdot\frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{256} \cdot \frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{20}{256 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{64 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{192}[/tex]

Multiplying first fraction by 64/64:

[tex]S_5=\frac{80(64)}{3(64)}-\frac{5}{192}[/tex]

[tex]S_5=\frac{5120}{192}-\frac{5}{192}[/tex]

{tex]S_5=\frac{5115}{192}[/tex]

Dividing to and bottom by 3:

[tex]S_5=\frac{1705}{64}[/tex].

Answer:

B

Step-by-step explanation:

Given

6x³ + 6 ← factor out 6 from each term

= 6(x³ + 1)

x³ + 1 is a sum of cubes and factors as

x³ + 1 = (x + 1)(x² - x + 1)

Hence

6x³ + 6 = 6(x + 1)(x² - x + 1)

With factor (x + 1) → B

Answer:

b) x + 1

Step-by-step explanation:

you can either

1) take (6x³ + 6) and divide by all the choices to see which one gives you a factor. You will realize that if you divide this by option b, you will be able to factorize the equation as follows:

(6x³ + 6) = 6(x+1)(x²−x+1)

Hence option b is a factor

or

2) (my preferred method), utilize the properties of functions and roots.

Let function f(x) = 6x³ + 6

any value of a which gives f(a) = 0 is a root , i.e (x-a) is a factor.

In this case, lets consider option b

let x + 1 = 0 -------> or x = -1

substitute this into the function f(x)

f(-1) = 6 (-1)³ + 6

f(-1) = -6 + 6 = 0

hence x = -1 is a root , or (x+1) is a factor.

as a sanity check, lets try choice a) x -1

let x - 1 = 0 -------> or x = +1

substitute this into the function f(x)

f(1) = 6 (1)³ + 6

f(1) = 6 + 6 = 12 ≠0

hence x = 1 is NOT a root , or (x-1) is NOT a factor.

You can do the same for c and d and find that they too are NOT factors.

Answer:

1/4

Step-by-step explanation:

Let the fraction be x/y

(x + 1)/y = 1/2

x/(y - 1) = 1/3          Cross multiply both equations.

====================

2*(x + 1) = y           Remove the brackets

2x + 2 = y

################

3x = y - 1               Add 1 to both sides.

3x + 1=y - 1+ 1

3x + 1 = y

#################

Equate both ys

3x + 1 = 2x + 2        Subtract 1 from both sides.

3x + 1-1 = 2x + 2 -1

3x = 2x + 1              Subtract 2x from both sides.

3x-2x = 2x-2x +1    Simplify

x = 1

==================

y = 3x + 1

y = 3(1) + 1

y = 3 + 1

y = 4

The original fraction was 1/4

Answer:

(f*g)(0)=-2

f(g(0))=5  I think you meant this one based on your answer. Please read lower half of explanation for this answer.  Please ask me any question on this that you have.

Step-by-step explanation:

(f*g)(0) means f(0)*g(0).

f(0) means to replace x with 0 in x^2+1 (since g(x)=x^2+1).

g(0) means to replace x with 0 in x-1 (since g(x)=x-2).

f(0)=0^2+1=0+1=1

g(0)=0-2=-2

So (f*g)(0)=f(0)g(0)=(1)(-2)=-2.

But I guess you didn't mean this because you said the answer is 5...

Oh maybe you mean

[tex](f \circ g)(0)[/tex]?

[tex](f \circ g)(0)[/tex] means [tex]f(g(0))[/tex].

So f(g(0))...we start with the inside first... that is g(0)?

g(0)=-2 (we found this above)

f(g(0))

f(-2)           ->I replaced g(0) with -2

Now f(-2) means to replace x with (-2) in x^2+1 (since f(x)=x^2+1)

So let's do that:

(-2)^2+1

4+1

5

:

starting value

-- :

the y-intercept is the starting value of the coin after no time has passed. :)

Answer:

The area is 5.5 cm squared.

Step-by-step explanation:

To find the area, you have to find the areas of the rectangle and the triangle separately and then add your two values together.

The formula for the area of a rectangle is as follows:

[tex]A=lw[/tex]

In this formula, "l" refers to length and "w" refers to width.

As shown in the diagram, your length is 1.5 cm and your width is 2 cm.

Simply plug these numbers into the formula and simplify.

[tex]A=1.5*2\\A=3[/tex]

The area of the rectangle is 3 cm squared.

Next, find the area of the triangle. The formula for the area of a triangle is as follows:

[tex]A=\frac{1}{2} bh[/tex]

In this formula, "b" refers to the measure of the base and "h" refers to the measure of the height.

Your base (b) is 2 cm.

To find your height, subtract the length of the rectangle (1.5 cm) from the total length of the shape (4 cm). This will give you a height of 2.5 cm.

Next, plug your values into the formula and simplify.

[tex]A=\frac{1}{2} *2*2.5\\A=1*2.5\\A=2.5[/tex]

The area of the triangle is 2.5 cm squared.

Add the area of the rectangle (3 cm squared) to the area of the triangle (2.5 cm squared), and you have the area of the entire figure (5.5 cm squared).

Note: Carlos' mistake in the problem is that he forgot to subtract the length of the rectangle from the length of the entire shape, and incorrectly used 4 cm as his height for the triangle rather than 2.5 cm.

Answer:

Option D is correct.

Step-by-step explanation:

Original Price of car = $38,000

Current Price of car = $28,500

The residual value of Sally's leased car = x = ?

Residual value * Original Price = Current Price

x * 38,000 = 28,500

x = 28,500/38,000

x = 0.75

Since we need to find percentage

Multiply the residual value with 100 i.e,

0.75 * 100 = 75%

Option D is correct.

Answer:

Unknown number, x=-4

Step-by-step explanation:

Forming the equation from the information provided above.  

9=2x+17

If we solve for the unknown number, we first collect like terms together.

2x=9-17

2x=-8

Divide both sides of the equal sign by 2 the coefficient of x

x=-4

Answer:

x = -4

Explanation:

We are given the following statement which we are to translate into a mathematical equation and then solve it:

'nine is seventeen more than two times a number'

Assuming [tex] x [/tex] to be the unknown number, this can be written as:

[tex] 9 = 2 x + 1 7 [/tex]

Solving for x:

[tex] 2 x = 9 - 1 7 [/tex]

[tex] 2 x = - 8 [/tex]

[tex]x=\frac{-8}{2}[/tex]

[tex]x=-4[/tex]

Therefore, the unknown number is -4.

Answer:

5/6 (if including 3)       4/6 (not including 3)

Step-by-step explanation:

1 and 2 are less than 3

4 and 6 are even

that leaves 5 and 3.

so 4 of the numbers are even or less than 3

Probability of rolling even number or number less than 3 is 2/3.

Probability is defined by the possibility of the event to happen which is ratio of no. of favorable outcomes and the total no. of outcomes.

Probability of event = P(E) = No. of favorable outcomes/Total No. of outcomes

Here given that the dice is fair and six-sided is rolled.

Total no. of outcomes by rolling the dice=6 i.e. {1,2,3,4,5,6}

No. of favorable outcomes of getting even no. =3 i.e. {2,4,6)

Probability of rolling an even no.=P(even)= No. of favorable outcomes/Total No. of outcomes = 3/6

No. of favorable outcomes of getting no. less than 3 =2 i.e. {1,2}

Probability of rolling no. less than 3=P(<3) =No. of favorable outcomes/Total No. of outcomes = 2/6

No. of favorable outcomes of getting even no and number less than 3 =1 i.e. {2}

Probability of rolling an even no. and no. less than 3 =P(even and <3) = P(even ∩ <3)= No. of favorable outcomes/Total No. of outcomes = 1/6

As we know P(A∪B)=P(A)+P(B)-P(A∩B)

Probability of rolling an even no.or no. less than 3 = P(even or <3) = P(even ∪ <3)= P(even)+P(<3)-P(even ∩ <3)

=(3/6)+(2/6)-(1/6)

=4/6

=2/3

Therefore probability of rolling even number or number less than 3 is 2/3.

Learn more about probability

here: https://brainly.com/question/14192140

#SPJ2

Answer:

10

Step-by-step explanation:

Each term is the sum of the two after it:

a_n = a_n+1 + a_n+2

The next term is:

a₄ = a₅ + a₆

31 = 21 + a₆

a₆ = 10

Answer:

80

Step-by-step explanation:

Let's say M is the number of men, W is the number of women, and C is the number of children.

M + W + C = 270

M/W = 4/5

W/C = 10/9

We have three equations and three variables, so we can solve this.  Let's use substitution.

W = 5/4 M

C = 9/10 W

Substitute into the first equation:

M + 5/4 M + 9/10 W = 270

Substitute again:

M + 5/4 M + 9/10 (5/4 M) = 270

Solve:

M + 5/4 M + 9/8 M = 270

8/8 M + 10/8 M + 9/8 M = 270

27/8 M = 270

M = 80

There are 80 men on the train.

Answer:

The measure of arc a is 86°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

so

86°=(1/2)[arc c+arc a]

see the attached figure with letters to better understand the problem

In this problem

Triangles ABO and CDO are congruent by SSS postulate theorem

∠AOB=∠COD

∠AOB=arc a -----> by central angle

∠COD=arc c -----> by central angle

therefore

The measure of arc a is congruent with the measure of arc c

arc a=arc c

so

86°=(1/2)[2arc a]

86°=[arc a]

arc a=86°

Answer:

4

Step-by-step explanation:

-36-9+14-31+66

=4

Since + - = - and - - = +

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]\bf A=5000\left(1+\frac{0.08}{12}\right)^{12\cdot 15}\implies A=5000(1.00\overline{66})^{180}\implies A\approx 16534.61[/tex]

Answer:

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Step-by-step explanation:

Recursive means you want to define a sequence in terms of other terms of your sequence.

The common ratio is what term divided by previous term equals.

The common ratio here is -6/2=18/-6=-54/18=-3.

Or in terms of the nth and previous term we could say:

[tex]\frac{a_n}{a_{n-1}}=r[/tex]

where r is -3

[tex]\frac{a_n}{a_{n-1}}=-3[/tex]

Multiply both sides by the a_(n-1).

[tex]a_n=-3a_{n-1}[/tex] where [tex]a_1=2[/tex]

Answer:

see explanation

Step-by-step explanation:

A recursive rule allows us to obtain any term in the sequence from the previous term.

These are the terms of a geometric sequence with common ratio r

r = - 6 ÷ 2 = 18 ÷ - 6 = - 54 ÷ 18 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

[tex]a_{n+1}[/tex] = - 3 [tex]a_{n}[/tex] with a₁ = 2

Answer:

Option C [tex]1,102\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral surface area of a cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=13.6\ in[/tex]

[tex]h=12.9\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]LA=2(3.14)(13.6)(12.9)[/tex]

[tex]LA=1,101.76\ in^{2}[/tex]

Round to the nearest square inch

[tex]LA=1,102\ in^{2}[/tex]

Answer:

D. In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!.

F. There are sixty-six ways to choose ten items from twelve.  

Step-by-step explanation:

The expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! as well option F.

From the information given, Lorelei evaluates the expression to determine how many different groups of ten she can make out of twelve items.

In this case, the expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! and that there are sixty-six ways to choose ten items from twelve.

Learn more about expressions on:

https://brainly.com/question/945593

Check the picture below.

Step-by-step explanation:

Given : The sales of a certain product after an initial release can be found by the equation [tex]s=12\sqrt{4t}+ 10[/tex], where s represents the total sales (in thousands) and t represents the time in weeks after release.

To find : Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release ?

Solution :

The equation [tex]s=12\sqrt{4t}+ 10[/tex]

where, s represents the total sales (in thousands) and t represents the time in weeks after release.

We put t=1,2,3,.....,12 and create a table

 t            [tex]s=12\sqrt{4t}+ 10[/tex]

 1                    34

 2                   43.94  

 3                   51.56

 4                   58

 5                   63.66

 6                   68.78

 7                   73.49  

 8                   77.88

 9                   82

 10                  85.89

 11                   89.59

 12                  93.13

Answer:

6

Step-by-step explanation:

m = 3

n = 1

Equation

m(m - n)     Substitute the givens

Solution

3(3 -1 )        Evaluate what is inside the brackets.

3(2)      multiply

6

Answer:

m=3 and n-1 ,find m2- mn

Step-by-step explanation:

Question 1:

In this question, it's asking you if the decreasing rate is linear or exponential.

The decreasing rate would be linear, due to the fact that it is decreasing at a constant rate of 11%. The decreasing rate doesn't change, which makes this linear.

Question 2:

In this question, it's asking you what would the component's cost be in 3 years if it started off at $120.

To find this, we're going to need multiply the price by -.11, and then subtract to get the price. We would repeat this until we reach 3 years.

Work:

[tex]120*-0.11=-13.2\\\\120-13.2=106.8\ \text{(Year 1)}\\\\106.8*-0.11= -11.748\\\\106.8-11.748=95.05\ \text{(Year 2)}\\\\95.05*-0.11=-10.4555\\\\95.05-10.4555=84.59\ \text{(Year 3)}\\\\\text{In year 3, the cost of the component would be \$84.59}[/tex]

Question 3:

In this question, it asks if the decline in price is linear or exponential.

The decline in price would be exponential, due to the fact that the decrease in price is not always the same, since it changes every year. The price doesn't decrease at the same price each year. As you see from question 2, the change in price is not the same each year.

The price decrease of the computer component is exponential. By using the exponential decay formula, the cost of the component that is $120 today will be approximately $84.96 in three years.

The decline in the price of a computer component that decreases at a rate of 11% per year is an exponential decline. This is because the price reduction each year is based on the current price of the component, not a fixed amount. To calculate the cost three years from now, we can use the formula for exponential decay:

New Value = Original Value × (1 - Rate of Decrease)^Number of Periods

If today's price is $120, the cost after three years would be:

New Price = $120 × (1 - 0.11)^3

New Price = $120 × (0.89)^3

New Price = $120 × 0.708

New Price = $84.96 (rounded to two decimal places)

Therefore, if the component costs $120 today, it will cost approximately $84.96 in three years.

B. 25 Km. The measure of BC is 25 km.

The easiest way to solve this problem is using the cosine theorem c = √a²+b²-2ab*cos A.

BC = √AC²+AB²-2(AC)(AB)*cos A

BC = √(21km)²+(14km)²-2(21km)(14km)*cos 89°

BC = √441km²+196km²-588km²*(0.017)

BC =√637km²-10.26km²

BC = √636.74km²

BC = 25.03km ≅ 25

Step-by-step explanation:

The elevator is descending, so its velocity is -5 m/min.  After 1 hour (or 60 minutes), the position is:

x = (-5 m/min) (60 min)

x = -300 m

It's position after one hour is -300 meters.

Check the picture below.

Answer:

Step-by-step explanation:

The cost function is

[tex]C=10n+150[/tex]

Where [tex]n[/tex] is the number of buckets of apples sold.

The revenue is defined as

[tex]r=15n[/tex]

The image attached shows both functions graphed in the same coordinate system. According with the graph, the break-even point is at (30,450), that is, 30 of buckets sold and $450 of revenue and cost.

In other words, we need to sell 30 buckets to have the cost and revenue equals.

Therefore, the answer is A.

Answer:

x =  -12.42    or  x = 2.42

Step-by-step explanation:

x^2 + 10x - 13 = 17

To solve this using the completing the square method, we will follow the  steps below;

First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation

x^2 + 10x - 13 + 13 = 17 + 13

x^2 + 10x  = 30

The next step is to add both-side of the equation  by square of half of the coefficient of x (that is ; half of 10 is 5, then we will add 5²  to both-side of the equation)

x^2 + 10x + 5²  = 30 + 5²

Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation

(x + 5)²   =   30 + 25

(x + 5)²   = 55

We will then take the square root of both-side of the equation

√(x + 5)²   = ±√55

x + 5  =  ±√55

To get the value of x, we will subtract 5 from both-side of the equation

 x + 5 - 5   =  ±√55 - 5

x =  ±√55  -  5

Either x = + √55 -5  = 7.42 -5 = 2.42

OR

x = -√55 - 5   = -7.42 - 5 = -12.42

Therefore either x =  -12.42    or  x = 2.42

 x =  -12.42    or   2.42

Answer:

I think it may be B, but double check

Answer:

B and D

Step-by-step explanation:

Considering the multiple choices and let us assume that x = 2,

Option A would be equal to [tex]\frac{3}{4}x[/tex],

so if x = 2, then;

        [tex]\frac{3}{4}x[/tex] = 1.5 (which is less than x)

Option B would give [tex]\frac{5}{4} x[/tex],

so if x = 2, then;

       [tex]\frac{5}{4} x[/tex] = 2.5 ( which is greater than x)

From option C,

      [tex]\frac{7}{8} x[/tex] = 1.75 (which is less than x)

From option D,

     [tex]\frac{9}{8} x[/tex] = 2.25 ( which is greater than x)

So, options B and D are expressions whose values are greater than x.

Answer:

Answer:

The solutions for the equation are:

x = 2  

x = − 4

Step-by-step explanation:

Answer:

x = - 4, x = 2

Step-by-step explanation:

Given

x² + 2x - 8 = 0

Consider the factors of the constant term ( - 8) which sum to give the coefficient of the x- term ( + 2)

The factors are + 4 and - 2, since

4 × - 2 = - 8 and 4 - 2 = + 2, hence

(x + 4)x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Answer:

[tex]\large\boxed{B.\ x=\pm1\ and\ x=\pm2\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^4-9x^2+8=0\\\\x^{2\cdot2}-9x^2+8=0\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(x^2)^2-9x^2+8=0\\\\\text{substitute}\ x^2=t\geq0\\\\t^2-9t+8=0\\\\t^2-t-8t+8=0\\\\t(t-1)-8(t-1)=0\\\\(t-1)(t-8)+0\iff t-1=0\ \vee\ t-8=0\\\\t-1=0\qquad\text{add 1 to both sides}\\t=1\geq0\\\\t-8=0\qquad\text{add 8 to both sides}\\t=8\geq0[/tex]

[tex]t=x^2\to x^2=1\ \vee\ x^2=8\\\\x^2=1\Rightarrow x=\pm\sqrt1\to x=\pm1\\\\x^2=8\Rightarrow x=\pm\sqrt8\to x=\pm\sqrt{4\cdot2}\to x=\pm\sqrt4\cdot\sqrt2\to x=\pm2\sqrt2[/tex]

Answer:

Step-by-step explanation:

Given is the equation of 4th degree in x,

[tex]x^4 - 9x^2 + 8 = 0[/tex]

Substitute [tex]x^2=u[/tex]

[tex]u^2-9u+8=0\\(u-1)(u-8)=0[/tex]

u=1 and u =8

i.e. [tex]x^2=1\\x^2 =8[/tex]

Solving we get

[tex]x=1,-1,2\sqrt{2}, -2\sqrt{2}[/tex]

Option B is right.