(x - 12)(x + 5)/(x - 3)³≤0

Answer:

y = 3/5x + 7

Step-by-step explanation:

y = 3/5x + b

12 = 3/5(5) + b

12 = 5 + b

b = 7

y = 3/5x + 7

Answer: 37.33 % of items cost less than $7.5

Step-by-step explanation:

To find the percentage of items that cost less than $7.5, we would need to know the probability distribution function of the cost per item, as well as the specific parameters of the distribution (such as the shape parameter).

Since the information provided is that the cost per item follows an exponential distribution and the mean cost per item is $10.5,

We can use the cumulative distribution function (CDF) of the exponential distribution which is

F(x) = 1 - e^(-λx)

where x is the cost of the item, λ is the rate parameter and e is the base of the natural logarithm.

We know the mean is $10.5 , and in an exponential distribution the mean and the rate parameter are equal, so we can say λ = 1/10.5

To find the percentage of items that cost less than $7.5, we need to find the probability that X < 7.5, which is the same as finding F(7.5)

So, F(7.5) = 1 - e^(-λ*7.5) = 1 - e^(-0.714)

Then, we need to convert this probability to percentage, so we need to multiply it by 100

F(7.5) = (1 - e^(-0.714)) * 100 = 37.33 %

Therefore, 37.33 % of items cost less than $7.5

The quantity of ribbon that Ali started with was 16/21 feet, based on the mathematical operation of addition.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In the addition operation, two or more addends are added to obtain a result called the sum or total using the equation symbol (=) and the addition operand (+).

The quantity of ribbon attached to the rearview mirror = 2/7

The remaining quantity of ribbon after the attachment = 10/21

The quantity of ribbon Ali started with = 16/21 (2/7 + 10/21)

Thus, using the addition operation, we can conclude that Ali started with 16/21 feet of ribbon.

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The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) We must determine the score that corresponds to the 5th percentile of the normal distribution in order to determine the highest score that may fall inside the lowest 5% of scores.

We may use the standard normal table to determine that the 5th percentile corresponds to a standard normal score of -1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return to the original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

We must determine the 5th and 95th percentiles of the normal distribution in order to determine the range of scores that the middle 90% of scores fall inside.

The standard normal table may be used to determine that the 5th percentile corresponds to a normally distributed score of -1.28 and the 95th percentile corresponds to a standard normal rating of 1.28 using the mean and standard deviation supplied (3.6 and 0.75, respectively). We may use the following formula to return them to their original scale:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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The surface area of the triangular prism is 416  yd²

An equation is a expression that shows the relationship between numbers and variables.

The surface area of a solid object is the total area that the surface of the object occupies.

From the diagram:

Surface area = 2(10 yd * 10 yd) + 2(0.5 * 12 yd * 8 yd) + (10 yd * 12 yd) = 416  yd²

The surface area is 416  yd²

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Answer:

a) Common ratio r = [tex]\boxed{2}[/tex]

b) Formula for common ratio:
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

Formula for nth term:
[tex]a_n = a_1r^{n-1}[/tex]

(see explanation below for part b)

c) [tex]a_{10} = \boxed{1024}[/tex]

d) Recursive formula: [tex]\boxed{a_{n+1} = 2a_n}[/tex]

Step-by-step explanation:

a) The common ratio r for a geometric sequence is the ratio of any term(except the first) to the previous term. And this is a constant for that sequence

If we have a sequence [tex]a_1, a_2, a_3, a_4, a_5,....\\[/tex]

[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4}[/tex]

Here [tex]a_1[/tex] is the first term in the sequence

The sequence we have here is
2, 4, 8, 16

So
[tex]r = \dfrac{4}{2} = \dfrac{8}{4} = \dfrac{16}{8} = 2\\[/tex]
Answer to a)

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b) This part is confusing. Are they asking for a formula for the common ratio or a formula for the nth term? You can write both or check with your teacher

The explicit formula for the common ratio is

[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]

The explicit formula for the nth term, [tex]a_n[/tex] of a geometric sequence is
[tex]a_n = a_1r^{n-1}[/tex]

where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio
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c)
The formula for finding the nth term of a geometric sequence is
[tex]a_n = a_1r^{n-1}\\\\[/tex]

Therefore

[tex]a_{10} = a_1 r^{(10-1)} = a_1 \times r^9\\\\[/tex]

[tex]a_1 = 2, r = 2\\\\[/tex]

So
[tex]a_{10} = 2 \cdot 2^9 \\\\= 2 \cdot 512\\\\= 1024\\[/tex]ANSWER c)

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d)

A recursive formula is just an expression that denotes the relationship between one term and the next

We know that
[tex]r= \dfrac{a_{n+1}}{a_n} \\\\[/tex]

Multiplying both sides by [tex]a_n[/tex],

[tex]ra_n = a_{n+1}[/tex]

Or

[tex]a_{n+1} = ra_n\\\\[/tex]

For the specific case of r = 2 we get the recursive formula as

[tex]a_{n+1} = 2a_n[/tex]

ANSWER d)

The ordered pairs that satisfies the linear inequality x < - 3 are (-4, -3) and (-3, -3)

A linear inequality is a mathematical statement that describes a relationship between two or more variables that are not necessarily equal. It is similar to a linear equation, but instead of an equal sign, it uses one of the inequality signs: <, >, ≤, or ≥.

A linear inequality can also be represented graphically on a coordinate plane, by shading the region of the plane that satisfies the inequality. The solution set of a linear inequality is the set of all points that make the inequality true.

A linear inequality can also have infinitely many solutions, no solution or a unique solution. The solution set will be a region in a coordinate plane which is a half-plane, a line or a point depending on the inequality.

In the problem, the inequality x < -3 will have an ordered pair of solution of

(-∞, -3).

This implies that all values of x must lies from negative till infinity while y lies up to - 3.

In the options given, only (-4, -3) and (-3, -3) satisfies this criteria.

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Answer:

3.75 days

Step-by-step explanation:

To find out how long it takes to consume 13500 watt hours, you would divide 13500 by the number of watt hours consumed per day, which is 3600.

13500 / 3600 = 3.75

So it takes 3.75 days for the light bulb to consume 13500 watt hours.

Answer:

Answer and Explanation: As a fraction 3.83 (3 repeating) is 38399 3 83 99 . To convert 3.83 (3 repeating) to a fraction, we ignore the units as they will remain units. We then set up one equation of our unknown x being equal to 0.83333... and another that is 100 times greater, 100x=83.3333...

Answer:

  y = 3x -1

Step-by-step explanation:

You want the equation of the line through the points (0, -1) and (1, 2), among others.

The y-value when x=0 is the y-intercept. The table shows you it is -1.

The slope is the difference in y-values when x-values increase by 1. For the first two points in the table, the y-value shows an increase of ...

  2 -(-1) = 3

This means the slope is 3.

The slope-intercept equation of a line is ...

  y = mx +b . . . . . . . where m is the slope, and b is the y-intercept

For your line, we have determined m=3, b=-1, so the equation is ...

  y = 3x -1

Answer:

x < 40

Step-by-step explanation:

x/5-3<5

=5×x/5 -3×5 < 5×5

=x - 15 < 25

NOTE 5 will cancel 5 living x.

=x < 25 + 15

x < 40.

Therefore x is 40.

Answer:

102 in.²

Step-by-step explanation:

the given figure is made up of a triangle and a rectangle. we can find out the areas of two of them separately and then add it up for the area of the whole figure as

area of rectangle:-

= length* breadth

= 15 * 5 in.²

= 75 in.²

area of triangle :-

= 1/2 *base*height

= 1/2*9*6in.²

= 27in.²

Total area

= 75 + 27 = 102in.² { required answer }

Answer:

D)  102 in²

Step-by-step explanation:

The given composite figure is made up of a triangle and a rectangle.

Rectangle

[tex]\begin{aligned}\textsf{Area of a rectangle}&=\sf length \times width\\&=15 \times 5\\&=75\; \sf in^2\end{aligned}[/tex]

Triangle

[tex]\begin{aligned}\textsf{Area of a triangle}&=\sf \dfrac{1}{2} \times base \times height\\\\&=\dfrac{1}{2} \times (15-3-3) \times (11-5)\\\\&=\dfrac{1}{2} \times 9 \times 6\\\\&=\dfrac{9}{2} \times 6\\\\&=\dfrac{54}{2} \\\\&=27\; \sf in^2\end{aligned}[/tex]

Therefore, the area of the given composite figure is:

[tex]\begin{aligned}\textsf{Area of composite figure}&=\textsf{Area of rectangle}+\textsf{Area of triangle}\\&=75+27\\&=102\; \sf in^2\end{aligned}[/tex]

Answer:

below

Step-by-step explanation:

The derivative of the given equation gives the RATE (slope) in the given year

Derivative = -.0102 t^2 +.232 t  -.341

 for  t =  16 this equals .7598      <=====this one is greater

   for t = 19 this equals  .3848  

Answer:

i xibfvlmow 10 seconds

Step-by-step explanation:

k

[tex]\overline{A}[/tex]  = {0, 1, 4, 5, 6, 7, 8}, [tex]\overline{B}[/tex] =  {2, 4, 7, 9}, A ∪ B =  {0, 1, 2, 3, 4, 5, 6, 8, 9} and

A ∩ B = {3}.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Given,

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is a universal set.

A = {2, 3, 9} and B = {0, 1, 3, 5, 6, 8}.

[tex]\overline{A}[/tex] = (U - A) = {0, 1, 4, 5, 6, 7, 8}.

[tex]\overline{B}[/tex]= (U - B) = {2, 4, 7, 9}.

A ∪ B = U - {7}.

A ∪ B =  {0, 1, 2, 3, 4, 5, 6, 8, 9}.

A ∩ B = {3}

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Answer:

he never made a mistake, so the answer is A

Step-by-step explanation:

these are in line with integers and their rules.

The rule that's being applied there's if numbers of the same base are being divided, maintain the base and subtract the powers.

The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)

Reflect in the x-axis

Since,

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

thus new coordinates will be,

J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)

Rotate 180 degrees about the origin

Since,

When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

Thus new coordinates will be

J(4, 4), K(3, 4), L(1, 1), M(4,1)

Therefore, After applying the given operation the new coordinates of the quadrilateral will be  J(4, 4), K(3, 4), L(1, 1), and M(4,1).

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2 × 10³ is an exponential expression, which has a standard form as 2000.

Exponential expressions are just a way to write powers in short form. The exponent

indicates the number of times the base is used as a factor. So in the case of 32 it can

be written as 2 × 2 × 2 × 2 × 2 = 25, where 2 is the “base” and 5 is the “exponent”.

The expanded form comes in a variety of forms. Exponents are employed. The expanded form of that expression is what is stated above.

One more makes use of multipliers like 1, 10, 100, 1000, and so forth. The expression broadens in that form as...

10^2 = 1×100

Another expanded form uses the expanded form's individual digits, setting the others to zero.

10^2 = 100

The standard format is...

10^2 = 100.

Thus, 2 × 10³ is an exponential expression, which has a standard form as 2000.

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The measure of the arcs in relationship to the central angles measures are:

4. 40°

5. 50°

6. 90°

7. 180°

8. 140°

9. 130°

10. 220°

11. 230°

12. 320°

13. 180°

14. 310°

15. 270°

The relationship is that the measure of the central angle is the same as the measure of the arc it subtends in a circle.

4. Measure of arc AB = measure of central angle AOB

Substitute

Measure of arc AB = 40°

5. Measure of arc DC = measure of central angle DOC

Substitute

Measure of arc DC = 50°

6. Measure of arc BC = 180 - 40 - 50 = 90°

7. Measure of arc AED = 180°

8. Measure of arc BD = 90 + 50 = 140°

9. Measure of arc AC = 40 + 90 = 130°

10. Measure of arc BAD = 180 + 40 = 220°

11. Measure of arc ADC = 180 + 50 = 230°

12. Measure of arc ACB = 360 - 40 = 320°

13. Measure of arc ABD = 180°

14. Measure of arc CED = 360 - 50 = 310°

15. Measure of arc BAC = 40 + 180 + 50 = 270°

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Answer:

3.8729

Step-by-step explanation:

Answer:

1,000 was the interest charge which leaves you with 24000 as the regular vaule

Step-by-step explanation:

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

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Suppose Fawn plans to take a sample to determine a 90 percent confidence interval for the population mean weight of chocolate in every package. Fawn should take a sample size of at least 43, to have a 90% confidence interval of plus or minus 3 grams in the weight of chocolate in every package.

Generally, Fawn can use the formula for the sample size needed to estimate a population mean with a certain level of confidence:

n = (z*σ / E)^2

Where:

So the sample size needed is:

n = (1.645 * 12 / 3)^2

n= (5.48)^2

n = 43.296

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The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x + y + z) / (4xy²)

The expression if x = -3, y = 5, and z = 2. Then the value of the expression is given as,

⇒ (-3 + 5 + 2) / (4 × (-2) × (2)²)

⇒ - 4 / 32

⇒ - 1 / 8

The value of the expression (x + y + z) / (4xy²) at x = -3, y = 5, and z = 2 will be - 1/8.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$200\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (200)(0.10)(1) \implies I = 20~\hfill \underset{total~amount~in~savings}{\stackrel{200~~ + ~~20}{\text{\LARGE 220}}}[/tex]

Answer:

$ 220

Step-by-step explanation:

i = prt = 200 * .1 * 1  = 20  dollars interest

  add in her original deposit of 200 for a total of 220 dollars

An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.

Let d represent the amount of cash in dollars and p represent the amount of prizes.

Since the  grand prize winner is guaranteed to win at least $500,

So, p + d ≥ 500

Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

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Answer:The function is linear because we are dealing with a straight line.

Step-by-step explanation:

Answer: The answer is C

Step-by-step explanation: This is because the equation has a greater than or equal to sign (≥). This mean that there will be a closed dot. Also, when it comes to inequalities, the sign points to where the line will be drawn, (greater than is to the right and less than is to the left), which indicates that the answer is C

A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.

The circle, the ellipse, the parabola, and the hyperbola are examples of conic sections.

Using a third variable (t or ), parametric equations are utilized to express the x and y variables in terms of a less complex way.

The parametric equation for a circle is given by: x=r cos(t) +h, y=r sin(t) +k, where r is the radius of the circle and (h, k) is the center of the circle. The equation for a circle is (x- h)2+(y- k)2 = r2.

A circle with a radius of three and a center at (-1, 4) is a conic section with the parametric equations X=3cos(t)-1 and Y=3sin(t)+4.

The circle's equation is (x + 1)2 + (y - 4)2 = 32.

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6.28 cubic centimeters is the volume of the gap in the jar.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylindrical jar contains three glass balls each has a diameter of 2cm

Let us find the volume of each sphere.

Volume of sphere=4/3×πr³

As diameter is 2 then radius is 1.

Volume of each sphere=4.186

Volume of three spheres=3×4.186=12.56

Now let us find the volume of cylinder.

The diameter of cylinder will be 2 and height is 6 cmas there are 3 spheres of diameter 2cm.

Volume of cylinder=πr²h

=3.14×1×6

=18.84 cubic centimeters.

So the volume of the gap in the jar = 18.84-12.56

=6.28 cubic centimeters.

Hence, 6.28 cubic centimeters is the volume of the gap in the jar.

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