100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!

The point y = -x² - 3x + 2 cuts the x-axis are x = -3.6 and 0.6

From the question, we have the following parameters that can be used in our computation:

y = -x² - 3x + 2

The point it cut the x-axis is when y = 0

Using the above as a guide, we have the following:

-x² - 3x + 2 = 0

So, we have

x² + 3x - 2 = 0

When solved using a graphing tool, we have

x = -3.6 and 0.6

Hence, the point it cuts the x-axis are x = -3.6 and 0.6

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Answer:

Yes

Step-by-step explanation:

In terms of grade level because he can conduct through the age of the students in variation the interest of each student is different so we might say that lower students like from grade 1 might not be interested in the news that was forecast in the television but with higher leverage considering its maturity and experience will define much more appropriate in receiving news school.

Answer:

B - f(x)=3x^2-3x+2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Degree of the quadratic function is 2.The leading co-efficient is the co-efficient of the term with highest degree (that is 2).

f(x) = 2x² + 3x - 3

This function satisfies the given condition.

The leading term is 2x² and its co-efficient is 2 and the constant term is (-3)

Answer:

same side interior

Step-by-step explanation:

they are on the SAME SIDE as the transversal (diagonal line) which means that they can't be alternate. also, they are inside (interior) of the two horizantal parallel lines. this means that they must be same side interior

Answer:

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

There are 12 months in a year.

Multiply 25 by the number of months to get the number of e-mails per year:

Answer:

300

Step-by-step explanation:

To calculate the number of emails sent in a year based on an average of 25 emails per month, you simply multiply the average monthly emails by the number of months in a year.

Average emails per month: 25

Number of months in a year: 12

Therefore,

Emails per month × Months per year

25 × 12 = 300 emails per year

So, on average, a person would send about 300 emails in a year.

Answer: 10

Step-by-step explanation:

Answer:

4.1 = 4.10

Step-by-step explanation:

Extra 0 at the end of 4.10 doesn't change the quantity of the number, so 4.1 is equal to 4.10

The events A and B are dependent events.

The probability of event B will be different from the initial probability of selecting a black sock (event A).

Two events are considered independent if the outcome of one event does not affect the probability of the other event.

The outcome of event A (choosing a black sock) directly affects the probability of event B (choosing a black sock again).

To explain further, let's consider the initial scenario:

You have 10 white socks and 14 black socks in your drawer.

The total number of socks is 24.

The first sock, there are two possibilities:

Either it is a black sock or a white sock.

If event A occurs and you select a black sock, the total number of black socks in the drawer decreases to 13, while the total number of socks decreases to 23.

If event B to occur (selecting a black sock again), the probability is now influenced by the fact that you have one less black sock and one less sock in the drawer.

The probability of event B will be different from the initial probability of selecting a black sock (event A).

The outcome of event A affects the probability of event B, the two events are dependent.

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The total number of teams that are in the NFC from the given two way frequency table is: 16 teams

A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.

Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data

From the attached two way table, we see that:

Total number of animals = 15

Total number of non-animals = 17

Total Number of NFC = 16

Total number of AFC = 16

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If triangles ΔXYZ is congruent to ΔJKL, then the segment which corresponds to KJ is YX.

Given that, two triangles ΔXYZ and ΔJKL are congruent to each other.

So the corresponding vertices are,

Vertex X of ΔXYZ corresponds to vertex J of ΔJKL

Vertex Y of ΔXYZ corresponds to vertex K of ΔJKL

Vertex Z of ΔXYZ corresponds to vertex L of ΔJKL

Now, the segment which corresponds to KJ in ΔXYZ will be the segment formed by joining the vertices that corresponds to K and J.

We already have,

K corresponds to Y and J corresponds to X.

So the equivalent segment is YX.

Hence the segment required is YX.

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The required expression is (x / 5) + 9

Given that we have to build an equation for the statement "9 more than the quotient of x and 5,

So,

This expression represents the quotient of x divided by 5, and then adding 9 to the result.

Therefore,

"9 more than the quotient of x and 5" can be written mathematically as:

(x / 5) + 9

Hence the required expression is (x / 5) + 9

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5. The probability that exactly four adults out of 19 say cashews are their favorite nut is approximately 0.252.

6. The probability that 12 or more stolen bikes will be returned out of 335 is approximately 0.181.

a. Probability of exactly four adults saying cashews are their favorite nut:

n = 19 (number of trials)

k = 4 (number of successes)

p = 0.49 (probability of success)

Using the formula, we have:

P(X = 4) = (¹⁹C₄) * 0.49⁴ * (1 - 0.49)¹⁵

Calculating the binomial coefficient:

((¹⁹C₄) = 19! / (4! * (19 - 4)!) = 3876

Calculating the probability:

P(X = 4) = 3876 * 0.49⁴ * (1 - 0.49)¹⁵ ≈ 0.252

b. Probability that 12 or more stolen bikes will be returned:

n = 335 (number of trials)

k = 12, 13, ..., 335 (number of successes, from 12 to 335)

p = 0.03 (probability of success)

We want to find the sum of probabilities for k = 12 to 335.

P(X ≥ 12) = P(X = 12) + P(X = 13) + ... + P(X = 335)

Calculating each probability:

P(X = k) = (³³⁵C k) * [tex]0.03^{k}[/tex] * (1 - 0.03) [tex]^{335 - k}[/tex]

Calculating the binomial coefficients for each k:

(³³⁵ C ₁₂) = 335! / (12! * (335 - 12)!) ≈ 7.27587e+22

(³³⁵ C ₁₃) = 335! / (13! * (335 - 13)!) ≈ 2.21733e+23

...

(³³⁵ C ₃₃₅) = 335! / (335! * (335 - 335)!) = 1

Calculating the probabilities and summing them up:

P(X ≥ 12) ≈ P(X = 12) + P(X = 13) + ... + P(X = 335) ≈ 0.181

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The maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

To maximize the objective function z = 4x + 4y subject to the given constraints, we can solve this linear programming problem using the graphical method.

First, let's graph the feasible region determined by the constraints:

1. Graph the line 2x + 4y = 28:

  Rewrite the equation in slope-intercept form: y = -0.5x + 7

  Plot two points on the line: (0, 7) and (14, 0), and draw a line through them.

2. Graph the line 5x + 6y = 50:

  Rewrite the equation in slope-intercept form: y = (-5/6)x + (25/3)

  Plot two points on the line: (0, 25/3) and (10, 5/3), and draw a line through them.

3. Shade the region that satisfies the constraints:

  Shade the region below the line 2x + 4y ≤ 28.

  Shade the region below the line 5x + 6y ≤ 50.

  The feasible region is the intersection of the shaded regions.

Next, we evaluate the objective function at the corner points of the feasible region to determine the maximum value.

The corner points of the feasible region are:

A: (0, 7)

B: (0, 25/6)

C: (14/3, 4)

D: (10, 5/3)

Evaluate the objective function at each corner point:

z(A) = 4(0) + 4(7) = 28

z(B) = 4(0) + 4(25/6) = 50/3

z(C) = 4(14/3) + 4(4) = 92/3

z(D) = 4(10) + 4(5/3) = 140/3

The maximum value of z is obtained at z(C) = 92/3.

Therefore, the maximum value of z = 4x + 4y, subject to the given constraints, is 92/3, which occurs when x = 14/3 and y = 4.

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Hello !

100% - 60% = 40%

=> 40% of police officers have ride-alongs

                                                                      total

number of policier            258          ?           ??

frequency in %                  60%        40%      100%

3.1 Calculate the number of of the police officers have ride-alongs with teenagers who want to join the police force

? = 258 x 40 ÷ 60 = 172

3.2 Calculate the total

?? = 258 + 172 = 430

In total there are 430 police officers.

Have a good day !

Answer: y = 550x

Step-by-step explanation:

The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².

To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,

We can use the standard equation for a parabola in vertex form:

y = a(x - h)² + k

In this equation, (h, k) represents the coordinates of the vertex.

Since we want the vertex to be at the origin (0, 0), the equation becomes:

y = ax²

To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.

Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.

In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).

Plugging in the value of f (8) into the formula, we can solve for 'a':

8 = 1/(4a)

32a = 1

a = 1/32

Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²

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The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.

Given that,

A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.

Radius of each lipstick = 0.6 inch

Height of the lipstick = 2.4 inches

Now,

Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.

Area = 2π (0.6) (2.4) + 2π (0.6)²

        = 2.88π + 0.72π

        = 3.6π

Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.

Hence the area is 10.8π square inches.

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The third root of 11 lies between the whole numbers 2 and 3.

The estimate of a non-exact root of x is done finding two numbers, as follows:

The number for this problem is given as follows:

Cubic root of 11.

For the parameters, we have that:

Hence the third root of 11 lies between 2 and 3, as 2³ < 11 < 3³.

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The caluclated values are:

N = 500:

SEM = 9 * √[(500 - 48) / (500 - 1)] / √(48)

= 1.24 (rounded to 2 decimals)

N = 5000:

SEM = 9 * √t[(5000 - 48) / (5000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

N = 50000:

SEM = 9 * √[(50000 - 48) / (50000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

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The traveler will need (y / x) dollars to purchase y yen.

To determine the number of dollars the traveler will need to purchase a certain amount of yen, we need to divide the desired amount of yen by the exchange rate.

Let's assume the traveler wants to purchase y yen.

and, the exchange rate is 1 dollar = x yen.

To find the number of dollars, we can set up the following equation:

y yen × (1 dollar / x yen) = (y / x) dollars

Therefore, the traveler will need (y / x) dollars to purchase y yen.

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To calculate the number of dollars needed to purchase a specific amount of Japanese yen, we'll need the exchange rate between the two currencies. However, the exchange rate provided in your question is missing. Please provide the exchange rate between the US dollar (USD) and the Japanese yen (JPY) so that I can help you calculate accurately.

The required sign that makes the statement true is "||".

The given options are 7, 22, 64, and V.

To express a percentage in mathematical notation, we divide the number by 100. In this case, 67.18% can be written as 0.6718.

Using the "||" symbol, we can write the equation as: 0.6718 || 7 = 22.

This equation represents the statement "0.6718 is to 7 as 22 is to 100." The vertical bar "||" signifies the ratio or proportion between the numbers. The double vertical bars "||" typically represent the symbol for "is equivalent to" or "is parallel to" in various contexts.

Therefore, the sign "||" makes the statement true.

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Answer:

The original number was 4.

Step-by-step explanation:

We can construct an equation to model the given situation, using a variable x to represent the original number:

"the quantity of 6 minus a number"

[tex](6 - x)[/tex]

"four times the quantity"

[tex]4(6 - x)[/tex]

"is 8"

[tex]4(6 - x) = 8[/tex]

We can solve for x in this equation.

[tex]4(6 - x) = 8[/tex]

↓ applying the distributive property ... [tex]A(B+C) = AB + AC[/tex]

[tex]24 - 4x = 8[/tex]

↓ adding 4x to both sides

[tex]24 = 8 + 4x[/tex]

↓ subtracting 8 from both sides

[tex]16 = 4x[/tex]

↓ dividing both sides by 4

[tex]4 = x[/tex]

[tex]\boxed{x = 4}[/tex]

So, the original number was 4.

Zero:

x = 0,

Multiplicity:

1,

Effect:

Intersects x-axis at x = 0

Zero:

x = 1,

Multiplicity:

1,

Effect:

Intersects x-axis at x = 1

Zero:

x = -2/5,

Multiplicity:

3,

Effect:

Intersects x-axis at x = -2/5 =0 with a steep curve

The zeros, multiplicity, and effect of the function f(x) = 3x(x - 1)˚ (5x + 2)³, we need to factor the expression.

First, let's identify the zeros by setting the expression equal to zero and solving for x:

3x(x - 1)˚ (5x + 2)³ = 0

Setting each factor equal to zero:

3x = 0 --> Zero: x = 0

x - 1 = 0 --> Zero: x = 1

(5x + 2)³ = 0 --> Zero: x = -2/5

Now, let's determine the multiplicity and effect of each zero:

Zero:

x = 0

To determine the multiplicity, we look at the exponent of the factor (x) in the expression.

The factor x has a multiplicity of 1 since it appears once.

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = 0.

Zero:

x = 1

Similar to the previous case, the factor (x - 1) has a multiplicity of 1 since it appears once.

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = 1.

Zero:

x = -2/5

The factor (5x + 2) has a multiplicity of 3 because it appears cubed (exponent of 3).

The effect of this zero is that it is a root of the function and causes the graph to intersect the x-axis at x = -2/5 with a steep curve, as it is raised to the power of 3.

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Answer:

  see below

Step-by-step explanation:

You want to show that csc²(θ) -cot²(θ) -sin²(θ) = cos²(θ).

It often works well to express the trig functions in terms of sine and cosine. The identity sin²(θ) +cos²(θ) = 1 is also useful.

  [tex]\csc^2\theta-\cot^2\theta-\sin^2\theta=\cos^2\theta\\\\\dfrac{1}{\sin^2\theta}-\dfrac{\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{1-\cos^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\\dfrac{\sin^2\theta}{\sin^2\theta}-\sin^2\theta=\cos^2\theta\\\\\\1-\sin^2\theta=\cos^2\theta\\\\\cos^2\theta=\cos^2\theta\qquad\text{Q.E.D.}[/tex]

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Answer:

three more couches are needed to increase the truckload to one ton.

Step-by-step explanation:

First, let's calculate the weight of the five couches:

5 couches * 250 pounds/couch = 1250 poundsSince one ton is equal to 2000 pounds, we can subtract the weight of the couches from one ton to find out how much additional weight is needed:

2000 pounds - 1250 pounds = 750 poundsEach couch weighs 250 pounds, so we can divide the additional weight needed by the weight of each couch to determine how many more couches are needed:

750 pounds / 250 pounds/couch = 3 couches Therefore, three more couches are needed to increase the truckload to one ton.

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.

Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.

Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.

Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.

To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.

1.2 The set model:

To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.

1.3 The length model:

To show 25/7 on a length model, draw a line of 25 units and divide it into seven equal parts. Each part represents 1/7 or 25/7.

Step 5/5

Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:

Now we know that the perimeter of the rectangle is given by the formula:

So, for this rectangle:

54 = 2(5x + x)

Simplifying and solving for x, we get:

54 = 2(6x)

27 = 6x

x = 4.5 cm

Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm.

The difference between 1/5 and 2/10 is that they are different representations of the same value.

The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.

"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.

The diagram can be used to illustrate fraction concepts.

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Answer:B,C

hope it helps

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (3, - 2 )

m = [tex]\frac{-2-(-5)}{3-4}[/tex] = [tex]\frac{-2+5}{-1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, - 2 )

- 2 = - 3(3) + c = - 9 + c ( add 9 to both sides )

7 = c

y = - 3x + 7 ← equation of line

Using a t-distribution with 21 degrees of freedom (since n-1 = 22-1 = 21), and a 95% confidence level, we can find the critical value from a t-table or calculator.

The critical value is ±2.080.

Rounded to three decimal places, the critical value is 2.080.