Use The Diagrams To Answer The Following Questions Number 6 (2024)

Answer:

n+3

Explanation:

Given the expression:

[tex]\frac{1}{3}(3n+9)[/tex]

To simplify, we first open the bracket.

[tex]=\frac{1}{3}(3n)+\frac{1}{3}(9)[/tex]

We can then divide common factors:

[tex]\begin{gathered} =\frac{3n}{3}+\frac{9}{3} \\ =n+3 \end{gathered}[/tex]

The simplified form is: n+3

A fiar coin is tossed 3 times in succession.

The results for each experiment is displayed as follows;

[tex]\begin{gathered} \text{HHH} \\ \text{HHT} \\ \text{HTH} \\ \text{THH} \\ \text{HTT} \\ \text{THT} \\ \text{TTH} \\ \text{TTT} \end{gathered}[/tex]

On each toss from the above results, the probability of getting a tail would include all results that has a tail come up. That would be;

[tex]P\lbrack\text{Event\rbrack}=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}}[/tex][tex]P\lbrack\text{tail\rbrack}=\frac{4}{8}[/tex]

Note that to get a tail on the "second toss" would mean to get a result with a tail as the second out of three. We have 7 outcomes with tails. However 4 of these has a tail as a second outcome, hence we have the required outcome as 4 out of a total of 8.

ANSWER:

Probability of getting a tail on the second toss is

[tex]P\mleft\lbrace\text{tail}\mright\rbrace=\frac{1}{2}[/tex]

The two polynomials are multiplied as follows:

[tex](6-5g)(-3g+9)[/tex]

Open the first bracket as follows:

[tex](6-5g)(-3g+9)=6(-3g+9)-5g(-3g+9)[/tex]

Open the two brackets as follows:

[tex]\begin{gathered} 6(-3g+9)-5g(-3g+9)=-18g+54+15g^2-45g \\ =15g^2-63g+54 \end{gathered}[/tex]

Hence the multiplication of the polynomials results in:

[tex](6-5g)(-3g+9)=15g^2-63g+54[/tex]

2) The symbol used to repesent sum is '+'. Thus, the algebraic expression for the the sum of 8 and p is

8 + p

Given the word problem, we can deduce the following information:

1. Fernando picks a marble at random.

2. Without putting the first marble back, he picks a second marble at random.

To determine if the events are dependent or independent, we first note that dependent events influence the probability of other events, while independent events do not affect one another.

Since Fernando picks a marble without putting the first marble back, the probability of the second pick is affected.

Therefore, the answer is dependent.

The ordered pair is (- 5, - 2)

This means that when x = - 5, y = - 2

To determine if the ordered pair is a solution of the linear equation, We would substitute the values into the equation. If we substitute x = - 5 into the equation and y gives us - 2, then it is a solution.

Therefore,

y = - 5 - 1/2 = - 5 - 0.5

y = - 5.5

Since it is not - 2, then the answer is B

B- no it is not a solution

ed pai

Cost = Revenue

Then

300x + 180 = 390x

x= (390-300)/180= 180/90 = 2

Now graph both functions

ANSWER:

1st option: y = -3/2x + 5

STEP-BY-STEP EXPLANATION:

We have that the equation in its slope-intercept form is the following:

[tex]\begin{gathered} y=mx+b \\ \\ \text{ where m is the slope and y-intercept is b} \end{gathered}[/tex]

Two lines are parallel when the slope is the same, therefore, the line parallel to this line must have a slope equal to -3/2.

We can see that option 2 is the same line, therefore, they cannot be parallel, so the correct answer is 1st option: y = -3/2x + 5

Hello there. To solve this question, we'll have to remember some properties about mixed fractions.

5 book weight a total of 6 2/5 pounds. If each book weighs the same amount, how much does each book weigh?

We start by converting the fraction from the mixed fraction notation to the normal notation:

Therefore we have:

Now, suppose each book weigh x pounds. 5 books weight will be equal to 5x.

If 5 books weigh 32/5, then we have the following equation:

Divide both sides of the equation by a factor of 5

To find the value of this fraction, the trick is to multiply it by 4/4 (when the denominator is 25):

Each book weighs 1.28 pounds.

Given:

The batting averages are given in stemplot way.

The objective is to determine what batting average does 0.35│6 denotes.

Explanation:

In stemplot method, the stem represents all common digits other than one place value in the given set of data. The leaf represents the variation of once place for the respective stem data.

Then the given expression 0.35│6 represents the stem value as 0.35 and 6 as the leaf value.

Thus. one occurence of batting average is 0.356.

Hence, option (B) is the correct answer.

Explanation: To solve a derivate we can use a simple technique presented below

- First, we take the exponent and multiply it by the function. Second, we subtract a unit of the exponent. Let's visualize it better on the drawing below

Step 1: Now we can use the same concept to calculate all the derivates we need as follows

Final answer: So the final answers are

[tex]\begin{gathered} letter_{\text{ }}a=5x^4 \\ letter_{\text{ }}b=20x^3 \\ letter_{\text{ }}c=60x^2 \\ letter_{\text{ }}d=120x \end{gathered}[/tex]

.

Given

Distance = 30 km

Time = 1 1/2 hours = 3/2 hours

Find

rate in km per hour

Explanation

we need to find the rate in km per hour.

as we now the rate is also called a speed

so , speed = distance/time

[tex]\begin{gathered} rate=\frac{distance}{time} \\ \\ rate=\frac{30}{\frac{3}{2}} \\ \\ rate=\frac{30\times2}{3} \\ \\ rate=\frac{20km}{h} \end{gathered}[/tex]

Final Answer

Therefore, the rate of ship is 20km/hr

so , the correct option is 1.

To transform

[tex]x^2+8x+15=0[/tex]

Make it a perfect square

since 8x/2 = 4x, then

We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1

[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]

Now we will make the bracket to the power of 2

[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]

Add 1 to both sides

[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]

The answer is C

Okay, here we have this:

Let's take the endpoints of UCONN as x and those of SCSU as y. So:

x=y+2

And:

So the UCONN points of the first half are: x/3. And since they were tied SCSU had the same points at the first half.

And those UCONN points of the second half are 2x/3, and the SCSU points at the end were then x/3+48.

So, we obtain that:

y=x/3+48

x=(x/3+48)+2

x=x/3+50

x-x/3=50

2x/3=50

2x=150

x=75

And, replacing in y:

y=75/3+48=25+48=73

Finally we obtain that the final score was: UCONN 75: SCSU 73

[tex]11\ge x\leq49[/tex]

The question is asking for a number less or equal than 11 and less or equal to 49, then by the options we have, the number would be:

[tex]11\ge8\leq49[/tex]

We know that:

[tex]\tan\theta=1.19[/tex]

where theta is the angle we are trying to find; to get the angle we take the inverse tangent at both sides of the equation. Then:

[tex]\begin{gathered} \tan^{-1}(\tan\theta)=\tan^{-1}1.19 \\ \theta=50 \end{gathered}[/tex]

Therefore, the angle we are looking for is 50°

Given the point:

(x, y) ==. (9, 6)

Let's write the equation of the horizontal line that goes through the given point.

On a horizonal line, every point on the line has the same value of y.

The slope of a horizontal line is 0.

Since every point on a horizontal line has the same value of y, to find the equation of a horizontal line, we are to use the y-coordinate of the point to find the equation of the horizontal line.

We have:

y-coordinate of the point = 6

Hence, the equation of the horizontal line that goes through the point is:

y = 6

ANSWER:

y = 6

[tex](x+3)^{2}+(y-2)^{2}=4[/tex]

1) The first step is to divide the coefficient b by 2

[tex]\begin{gathered} b=6\therefore\frac{6}{2}=3 \\ b=-\frac{4}{2}\therefore=-\frac{4}{2}=-2 \end{gathered}[/tex]

2) So now, let's add to both sides those squared numbers to both sides of the equation and then write them as binomials:

[tex]\begin{gathered} x^2+6x+3^2+y^2-4x+(-2)^2=-9+9+4 \\ (x+3)^2+(y-2)^2=4 \end{gathered}[/tex]

Note that this is the Equation of the Circle in its standard form, whose radius is 4

Solution:

Given:

Collinear points are the points that lie on the same straight line or in a single line.

Hence, from the image given, the points that lie on the same straight line are; F, E, G

Therefore, option D is the correct answer.

The area of a parallelogram can be determined by multiplying its height by its base following the formula:

[tex]A=h\cdot b[/tex]

If you know the area and the height of the parallelogram you can determine the length of the base. To do so, you have to divide the area by the height:

[tex]b=\frac{A}{h}[/tex]

We know that the area of the window is A=31ft² and the height is h=33ft, you can calculate the length of the base as follows:

[tex]undefined[/tex]

Given

[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]

To write the expressions of

[tex]\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}[/tex]

And to evaluate,

[tex](h-g)(-3)[/tex]

Explanation:

It is given that,

[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]

Then,

[tex]\begin{gathered} (h\cdot g)(x)=h(x)\cdot g(x) \\ =\left(x-3\right)\cdot\left(2x^2\right) \\ =2x^3-6x^2 \end{gathered}[/tex]

Also,

[tex]\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}[/tex]

And,

[tex]\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2\times9) \\ =-6-18 \\ =-24 \end{gathered}[/tex]

Hence, the answer is,

[tex]\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}[/tex]

[tex]S(t)=3.71(1.112)\placeholder{⬚}^t[/tex]

a) Use the model to estimate the sales in 2015 in billions of dollars

Evaluate the function for t=15

[tex]\begin{gathered} S(15)=3.71(1.112)\placeholder{⬚}^{15} \\ \\ S(15)\approx18.24 \end{gathered}[/tex]The sales in 2015 will be $18.24 billion

b) Use the model to estimate the sales in 2024 in billions of dollars

Evaluate the function for t=24

[tex]\begin{gathered} S(24)=3.71(1.112)\placeholder{⬚}^{24} \\ \\ S(24)=47.41 \end{gathered}[/tex]The sales in 2024 will be $47.41 billion

The points we have are:

(2,13) and (4,6)

I will label this points as follows:

[tex]\begin{gathered} x_1=2 \\ y_1=13 \\ x_2=4 \\ y_2=6 \end{gathered}[/tex]

To find the equation for this line, first we need to find the slope between the points with following slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope.

Substituting our known values:

[tex]\begin{gathered} m=\frac{6-13}{4-2} \\ m=\frac{-7}{2} \end{gathered}[/tex]

Next, we need to use the point-slope equation:

[tex]y=m(x-x_1)+y_1[/tex]

And substitute our values, including the slope:

[tex]y=-\frac{7}{2}(x-2)+13[/tex]

Using the distributive property to multiply -7/2 by x and by -2:

[tex]\begin{gathered} y=-\frac{7}{2}x+7+13 \\ y=-\frac{7}{2}x+20 \end{gathered}[/tex]

Answer:

[tex]y=-\frac{7}{2}x+20[/tex]

We will have the following:

*Earn: By definition represents a positive value, since you cannot "earn" a negative quantity.

*Deposit: Deposits are "neutral" since they represent the movement of money but not neccesarily an increase, and sometimes it can be also a payment, so it can also be net negative.

*Increase: By definition is a positive value.

*Raise: By definition is a positive value.

So, it is false. Reason:

A deposit represents a net neutral, since it is refering to the movement of money but not it's increase neccesarily, and sometimes is also a negative, since it can be used as payment, thus representing a net negative value.

Answer:

1/4

Step-by-step explanation:

In total, there are 4 suits of cards: spades, clubs, hearts, and diamonds.

This way, the probability of drawing a heart from a standard deck of cards is:

[tex]\frac{1}{4}[/tex]

1.- Area

[tex]\begin{gathered} \text{Area of the circle = 3.14 x (4)}^2 \\ \text{Area of the circle = 50.24 ft}^2 \end{gathered}[/tex]

2.- Area of the extended table

Area = 50.24 + (8 x 4)

Area = 50.24 + 32

Area = 82.24 ft^2

Second question

Area = 3.14 x (5)^2

Area = 25 x 3.14

Area = 78.5 ft^2

The area of the larger circle is smaller than the area of the table with the extension.

Take into account that for a polynomial function, the possible roots are given by the following quotient:

roots = p/q

where p is the constant of the function (and its factors) and q is the coefficient of the term with the greates degree (variable with greatest exponent) or its factors.

Then, based on the previous explanation, you have:

p = -9

q = 5

factors -9: -1, 1, -3, 3, -9, 9

factors 5: -1, 1, -5, 5

Hence, the possible factors are:

±1, ±3, ±9, ±1/5, ±3/5, ±9/5

and the roots:

roots = {i(√15)/5 , -i(√15)/5, √3, -√3}

The roots can be also obtained by using quadratic formula for x^2, and then, by applying square root to the result to obtain x.

To find the absolute value of -1 1/2 +5​ you make the addition:

You can write the mixed number also as -3/2 (because -1 is equal to -2/2 and -2/2 and 1/2 is -3/2).

You add fractions as follow:

[tex]\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}[/tex]

You can write the 5 as 5/1:

[tex]-\frac{3}{2}+\frac{5}{1}=\frac{-3\cdot1+5\cdot2}{2\cdot1}=\frac{-3+10}{2}=\frac{7}{2}[/tex]

As the addition of the given numbers is 7/2, the absolute value or the distance is:

[tex]\lvert\pm a\rvert=a[/tex]

[tex]\lvert-1\frac{1}{2}+5\rvert=\lvert\frac{7}{2}\rvert=\frac{7}{2}[/tex]Then, the distance is 7/2

Surface Area of a Sphere

For a sphere of radius r, the surface area can be calculated as:

[tex]A=4\pi r^2[/tex]

A frog's egg has a diameter of d = 1.2 mm. The radius is half the diameter, thus:

r = 1.2 mm/2 = 0.6 mm

Calculating the surface area:

[tex]A=4\pi(0.6mm)^2[/tex][tex]A\approx4.5mm^2[/tex]

Choice D