Unit 1: Functions
For the function f(x) = (x + 3)2 – 4 Fill in the missing values in the table and describe the key characteristics of
the function below.
X
-8
-5
-4
-3
-2
-1
0
f(x)
0
-3
-4
-3
0
x-intercept(s):
y-intercept(s):
5
4
Domain (possible x-values): Rang e (possible
y-values):
2
-10
4 5 8
8010
Family:
Growth:
Vertex? If
Function? If yes, why?
Symmetry? If yes, where?
yes, where?
sa

15th row of the Pascal's Triangle is used to expand [tex](2x+10y)^{15}[/tex]. There will be 16 terms in the expansion.

Pascal's Triangle is used to find the co-efficient for binomial expansions.

The nth row of the Pascal's Triangle gives the coefficients in the expansion of binomial expressions of degree n. For example, in the expansion of [tex](x+y)^2[/tex] , the binomial coefficients are 1,2,1 which is given in the 2nd row of Pascal's Triangle. Also the expansion has three terms, therefore. The Pascal triangle starts with 0th row consisting of only 1.

Here the given expression is [tex](2x+10y)^{15}[/tex] of degree 15. So its binomial coefficient is given in the 15th row of Pascal's triangle.

The number of terms in the binomial expansion of degree n will be n+1 because the coefficients in nth row will n+1 in number.

Hence there will be 16 terms in the expansion of [tex](2x+10y)^{15}[/tex].

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Answer:

The person above helped, and below I've attached a ss with all of the parts of this question answered - Hope it helps!

Step-by-step explanation:

Brainliest would be very much appreciated :) - hope you have a good day!

If all the widgets from the three machines are mixed together, then the probability that a good widget will be drawn at random is 0.78 or 78%.

Probability is defined as how likely an event is to occur, or how likely it is that a proposition is true.

If machine 1 makes 3000/hour and 80% are good, then the chances of it being good is 80% also or, 2400 out of 3000.

80% of 3000 is 2400

If machine 2 makes 4000/hour and 90% are good, then the chances of it being good is 90% also or, 3600 out of 4000.

90% of 4000 is 3600

If machine 3 makes 3000/hour and 60% are good, then the chances of it being good is 60% also or, 1800 out of 3000.

60% of 3000 is 1800

Mixing together the widgets from the three machines, use the formula to calculate the probability of an event which is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Probability(good) = (2400 + 3600 + 1800)/(3000 + 4000 + 3000)

Probability(good) = 7800/10000

Probability(good) = 0.78 or 78%

Hence, the probability that a good widget drawn at random is 0.78 or 78%.

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Answer:

Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.

Step-by-step explanation:

please make my answer as brainelist

The following equation  [tex]y=\frac{-2x}{3}+2[/tex]  represents the given line.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=3x+1. Where:

a= the slope. It can be calculated for [tex]a=\frac{\Delta y}{\Delta x}[/tex].

b= the constant term that represents the y-intercept.

For solving  linear equations, you should organize variables on one side of the equation and the numbers on the other side. When a number or variables change side, its signal also is changed.

For the given example: a=3 and b=1

The question gives:

Thus, you can write from the question information :

y=ax+b

0= -2/3*(3)+b

0= -2 + b

b=2

Now, you know the value of the slope and the constant term.

Therefore, the standard form for the linear equation is:

[tex]y=\frac{-2x}{3}+2[/tex]

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The required information is (B), (C), (D), and (I).

So,

A. Who paid for the survey? It is not required.

B. Who made up the population from which the sample was drawn? Needed.

We need to know if the sample is representative of the "college students" population, on which we are basing our conclusions.

C. What sampling strategy was used? Needed.

We want to know if the sample was chosen at random.

D. How large was the sample size? Needed.

This information is required to determine the accuracy of the results.

E. What are the colleges represented in the sample?

It's not necessary if we already know "B."

F. How many survey questions were there? It is not required.

G. How many people participated in the survey? It is not required.

H. What were the questions? It is not required.

I. Is the language in the questions clear, accurate, unbiased, and valid? Needed.

We want to know if the answer was unbiased and clear so that we can determine if the conclusions are also unbiased.

J. What day of the week was the survey held? It is not required.

Therefore, the required information is B, C, D, and I.

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The correct question is given below:

A survey indicates that the vast majority of college students own their own personal computers. What information would you want to know before you accepted the results of this​ survey? Select all that apply. A. Who funded the​ survey? B. What was the population from which the sample was​ selected? C. What sampling design was​ used? D. What was the sample​ size? E. What are the names of the colleges included in the​ sample? F. How many questions were asked in the​ survey? G. How many people conducted the​ survey? H. What questions were​ asked? I. Were the questions​ clear, accurate,​ unbiased, and​ valid? J. On what day of the week was the survey​ conducted? g

Answer:

janice wants to put a fire at the mid point between two of her trees in her backyard. the coordinates of tree A are (3, 5) and the coordinates of tree b are (-3,-3). step by step thinking we want tree A is coordinat at 35. three b coordinate is -3-3 .janice stand between centre that from A mark 6feet so At B is 3

Answer:-355/4

Step-by-step explanation:

Answer:

= -355/4

Step-by-step explanation:

= 5/4 + 4(3/4 - 12)(2)

= 5/4 + (-45)(2)

= 5/4 + -90

= -355/3

Answer:

18000

Step-by-step explanation:

18 000, тому що якщо ви заробляєте 6 000 і маєте 2% дефектних деталей, помножте на 3, щоб отримати 6% дефектних деталей, які дають вам 18 000

In one minute,  Charles can type in 3-minute 225 words.

In one minute,  Charles can type

 675/9 = 75 words.

Hence,  in  3 minutes  Charles can tape  [tex]75\times3[/tex] = 225 words  (if works with the same rate).

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The change in elevation will be 0.

It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.

Therefore, when it flew, the expression will be +168.

When it came down, the expression will be -168.

Therefore, the change in elevation will be:

= +168 - 168.

= 0

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Answer:

720cm³

Step-by-step explanation:

Volume of a cylinder is given by Base Area (A) x Height (h)

or V = Ah

Volume of cylinder A = 18 x 5 = 90 cm³

Base Area A = πr² where r is the radius of the base

For cylinder A, if radius = rₐ

Area = π x (rₐ)² = 18

We can see that cylinder B has twice the height of cylinder A. That means cylinder B radius is twice the radius of cylinder A

So radius of cylinder B = 2 x rₐ = 2rₐ

Base Area of Cylinder B = π x (2rₐ)² = 4π(rₐ)² = 4 x Base Area of cylinder A = 4 x 18 = 72

So while the heights are in the ration 1:2, the base areas are in the ratio 1:4 because the areas are directly proportional to the square of the radius

Hence Volume of Cylinder B = 72 x 10 = 720 cm³

Another way to look at this is that the volume of cylinder B = 8 (2 x 2 x2) times the volume of cylinder A = 8 x 90 = 720cm³

The answer is in the screenshot.

Answer:

negative 5 and 3/5

Step-by-step explanation:

-4-1&3/5

-5&3/5

negative 5 and 3/5(three fifths)

don't forget to mark as brainliest

Answer:

negative 5 and 3/5

Step-by-step explanation:

-4-1&3/5

-5&3/5

negative 5 and 3/5(three fifths)

don't forget to mark as brainliest

Step-by-step explanation:

It is found that the intercepts can be found from vertex form, if the graph is hovering above the x axis (k<0).

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x) At y-axis, we've got x = 0, so putting it will give us the y-intercept. Thus, y-intercept of y = f(x) is y = f(0)

If a quadratic equation is written in the form y=a(x-h)² + k

therefore it is called to be in vertex form. It is called so because when you plot this equation's graph, we will see vertex point(peak point) is on (h,k)

To convert the given equation to vertex form, We will take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

To find the intercepts, if the graph is hovering above the x axis (k<0) then there will be no real solutions for the x intercept.

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The magnification scale  used was 450:1

Saturn from Earth, it looks like it has a diameter of 20 μm.

d₁=20μm

Through a telescope, the diameter looks 9,000 μm long.

d₂= 9,000 μm

magnification scale = d₂/d₁

                                =  9,000 μm/20μm

                                =  450/1

magnification scale  used was 450:1

A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.

A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the dimensions of the original figure and the dimensions of the dilated (increased or lowered) figure are known, the scale factor can be determined. A rectangle, for example, has a length of 5 units and a width of 2 units. If we raise the size of this rectangle by a factor of two, the sides will become 10 and 4, respectively. As a result, we can use the scale factor to determine the dimensions of the altered figures.

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Maria's capital gain is 55.2%.

Here, we are given that Maria purchased 1,000 shares of stock for $35.50 per share in 2003.

Thus, the total cost price of these shares = 1000 × 35.5

= $35500

In 2007, she sold all of the stocks for $55.10 per share

Thus, the total selling price of these shares = 1000 × 55.1

= $55100

Now, absolute gain = selling price - cost price

Here, Maria's absolute gain will be-

= 55100 - 35500

= 19600

Now, her percentage gain will be given by-

Gain % = absolute gain/ initial value × 100

= 19600/35500 × 100

= 55.2

Thus, Maria's capital gain is 55.2%.

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Answer: 5

Step-by-step explanation:

[tex]\sqrt{20+5}[/tex]=

[tex]\sqrt{25}[/tex]=5

Answer:

√(20 + 5) = 5

Step-by-step explanation:

Let's solve the problem,

→ x = √(20 + 5)

→ x = √25

→ [ x = 5 ]

Hence, the answer is 5.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad T(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +x}{2}~~~ ,~~~ \cfrac{ 2 +y}{2} \right) ~~ = ~~ \stackrel{\textit{\LARGE A}}{(-1~~,~~0)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1+x}{2}=-1\implies 1+x=-2\implies \boxed{x=-3} \\\\\\ \cfrac{2+y}{2}=0\implies 2+y=0\implies \boxed{y=-2}[/tex]

Answer:

Step-by-step explanation:

7x - 3 = 2x - 18

5x = -15

x = -15 : 5

x = -3

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

check

7 * (-3) - 3 = 2 * (-3) - 18

-24 = -24

the answer is good

Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.

Power is the result of multiplying same number for n number of times. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.

The correct solution,

3² ∙ 9⁴

= 3² ∙ (3²)⁴

= 3²  ∙ 3⁸

= 3¹⁰

Hence, Juan multiplied the bases together, and added the power together, therefore, his solution is wrong.

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12% of  students are enrolled in less than three courses and taking a math course

For given question,

50% of students are enrolled in less than three courses and 33% of students are taking a math class.

The probability that the students are enrolled in less than three courses is 0.5

P(A) = 0.5

The probability that the students are taking a math class is 0.33

P(B) = 0.33

if 71% of students are either enrolled in less than three courses or taking a math course.

P(A ∪ B) = 0.71

We need to find the percentage of students that are enrolled in less than three courses and taking a math course.

i.e., we need to find P(A ∩ B)

We know that, P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∩ B) = 0.5 + 0.33 - 0.71

P(A ∩ B) = 0.12

So, 12% of  students are enrolled in less than three courses and taking a math course.

Therefore, 12% of students are enrolled in less than three courses and taking a math course.

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Answer:

the length of one side of square is 3

Answer:

The area will decrease by 9%.

Step-by-step explanation:

The area of a rectange is given by the formula below.

[tex]\boxed{\text{Area of rectangle}= \text{length}×\text{width}}[/tex]

Let the original length and width of the rectangle be L and W respectively.

Start by finding the original area:

Original dimensions

Length= L= 100%L

Width= W= 100%W

Original area= LW

Let's find the dimensions of the new rectangle in terms of L and W.

New dimensions

Length= (100% +30%)L= 130%L

Width= (100%-30%)W= 70%W

New area

[tex] = \frac{130}{100} L \times \frac{70}{100} W[/tex]

[tex] = \frac{91}{100} LW[/tex]

= 91% LW

Comparing the new area with the original area:

100% LW- 91% LW= 9% LW

∴ The area will decrease by 9%.

*Note that percentage is equivalent to dividing a number by 100.

The amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.

What is average ?

The average is the ratio of the sum of the number of a given set of values to the total number of values present in the set.

It is given that restaurant earns $1073 on Friday and $1108 on Saturday.

The amount which restaurant needs to earn on Sunday to average $1000 per day over the three-day period can be calculated by finding the average.

The average is given by ratio of sum of amount on each day from Friday to Sunday and divide it by number of days.

Let's assume amount earn on Sunday is $x.

So ,

[tex]\frac{1073 + 1108 + x}{3}[/tex] = 1000

1073 + 1108 + x = (1000 × 3)

2181 + x = 3000

Let's solve this equation to get the value of x.

x = 3000 - 2181

x = $819

So , amount earn by restaurant is $819.

Therefore , the amount the restaurant needs to earn on Sunday to average $1000 per day over the three-day period is $819.

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Answer:

False

Step-by-step explanation:

The scale is for length only, when converting to area scale, you have to square both sides of the scale.

1 in² = 144 ft²

Answer:

Mass is the property of a body that measure its inertia. It is taken as the measure of the amount of material it contains and have weight in gravitational field

Mass is also refers as the weight of an object. It is measured in grams (g) and kilograms (kg)

Radius of an object is defined as a straight line from the centre of a circular object to the circumference of the circular object

According to the data given of five planets  

(a) The planet which has greatest mass is Mars that is 6.42 x 1023 kg

Radius of a given object can be calculated by dividing the diameter of the given object by 2.

(b) Radius of the mercury = Diameter given in kilometers / 2

                                          = 4.88 × 10³ / 2

                                          = 2.44 x 103 km

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Answer:

[tex]\bold{\dfrac{9}{11}}[/tex]

Step-by-step explanation:

I will use the dot notation for multiplication

We have
[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4[/tex]

Convert 4 to a fraction:
[tex]4=\dfrac{4}{1}[/tex]

Therefore

[tex]\dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \:4 \\\\= \dfrac{3}{11}\cdot \dfrac{3}{4}\cdot \dfrac{\cancel {4}}{1}\\\\[/tex]

Cross-cancel common factor 4
[tex]=\dfrac{3}{11}\cdot \dfrac{3}{1}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{b}\cdot \dfrac{c}{d}=\dfrac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\dfrac{3\cdot \:3}{11\cdot \:1}[/tex]

[tex]=\bold{\dfrac{9}{11}}[/tex]

A real valued function f(x) is said to be decreasing on the interval [a,b] for all x1,x2 if x1 < x2, And f(x1) > f(x2)

A function is said to be increasing if we increase the value of the independent variable the function also increases and a function is said to be decreasing if we increase the value of the independent variable the function decreases.

According to the given question real-valued function f (x) is said to be increasing on the closed interval [a, b] if for all x1, x2 ∈ [a, b], if x1 < x2, then f (x1) < f (x2).

A real valued function f(x) is said to be increasing on the interval [a,b] if a < b, And f(a) < f(b).

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