What is a possible value for the missing term of the geometric sequence 1250.

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

Answer:x= 14/3 or 4 1/2

Step-by-step explanation:

Answer: x = \(\frac{14}{3}\)

2x + 5 / 3 = 11

=> 2x + \(\frac{5}{3}\) = 11

          2x = 11 - \(\frac{5}{3}\)

          2x = \(\frac{33}{3}\) - \(\frac{5}{3}\)

          2x = \(\frac{28}{3}\)

=>         x = \(\frac{28}{3}\) / 2

            x = \(\frac{28}{3}\) x \(\frac{1}{2}\)

            x = \(\frac{28}{6}\)

            x = \(\frac{14}{3}\)

SO x = \(\frac{14}{3}\)

HOPE IT HELPS ^^

The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term

To find the seventh term of a geometric sequence, we can use the formula:

\(an = a1 * r^(n-1),\)

where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

In this case, we are given a2 = -7 and r = 1/2.

Using the formula, we can find a1 by substituting n = 2:

a2 = a1 * (1/2)^(2-1).

We know that a2 = -7, so we can rewrite the equation:

-7 = a1 * (1/2)^1,

-7 = a1 * (1/2).

Now, let's solve for a1:

a1 = -7 * (2/1),

a1 = -14.

We have found that the first term, a1, is equal to -14.

Now, we can find the seventh term, a7, by substituting n = 7 into the formula:

a7 = (-14) * (1/2)^(7-1),

a7 = (-14) * (1/2)^6,

a7 = (-14) * (1/64),

a7 = -14/64,

a7 = -7/32.

Therefore, the seventh term of the geometric sequence is -7/32.

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The number of plants 3 : 8 have if 3:7 has 10 plants is 11 plants.

Ratio refers to a number representing a comparison between two named things. It is also the relative magnitudes of two quantities usually expressed as a quotient.

So,

3 : 7

= 3 + 7

= 10 plants

Then,

3 : 8

= 3 + 8

= 11 plants

In conclusion, 3 ratio 8 has 11 plants.

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Therefore, all possible values of aa that satisfy the conditions are aa such that a<34a<43​.

To find all possible values of aa such that the quadratic equation ax2+(2a+2)x+a+3=0ax2+(2a+2)x+a+3=0 has two roots with a distance greater than 1 on the number line, we can use the discriminant.

The discriminant of a quadratic equation ax2+bx+c=0ax2+bx+c=0 is given by Δ=b2−4acΔ=b2−4ac. For the equation to have two distinct real roots, the discriminant must be greater than 0.

In our case, the discriminant is Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4.

For the equation to have two distinct roots with a distance greater than 1, we want Δ>12Δ>12, which simplifies to −4a+4>1−4a+4>1.

Solving this inequality, we have −4a>−3−4a>−3, which leads to a<34a<43​.

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Answer:

20

Step-by-step explanation:

\(4 \times 5 = 20\)

Answer:

Shift 1 units towards left and then stretch vertically 3 

Answer:  The graph of y=x^2 would look like the one shown below.

Step-by-step explanation:

Answer: conjugate

Step-by-step explanation: A P E X

The other root of that same function is the radical conjugate.

A polynomial is an expression consisting of variables, exponents, and coefficients of the variables joined by a plus or minus sign.

The expression is

7-√5

If this expression is a root of a polynomial, and 7+√5 is the root of the same polynomial then the radical is called radical conjugate.

A radical conjugate is an expression in which is there is at least one radical term, which is the same to the other expression with the same two terms and different signs.

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approximately 41.17% to 60.162% of the stocks in the population exceed the 20th price of the confidence interval

a. The practical interpretation of the confidence interval is that we are 90% confident that the proportion of all stocks in the population that exceed the 20th price lies between 0.41171 and 0.60162.

This means that, based on the sample data, we can estimate that approximately 41.17% to 60.162% of the stocks in the population exceed the 20th price.

b. The sample size of 75 can be considered relatively large for this problem. In statistical inference, larger sample sizes tend to provide more accurate and reliable estimates.

With a sample size of 75, we have a reasonable amount of data to make inferences about the population proportion. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample proportion approaches a Normal distribution.

In this case, the sample size of 75 is large enough to assume the approximate Normality of the sample proportion's distribution, allowing us to use the Simple Asymptotic method to construct the confidence interval.

Therefore, we can have confidence in the reliability of the estimate provided by the confidence interval.

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The formula to find the volume of a sphere is:

V = (4/3)πr^3

Substituting r = 3, we get:

V = (4/3)π(3^3) V = 113.1 cubic inches

To find the time it takes Sarah to inflate the balloon, we can use the formula:

time = volume / rate of inflation

Substituting the values we know, we get:

time = 113.1 / 200 time = 0.5655 minutes

Rounding to the nearest tenth, the time it takes Sarah to inflate the balloon is approximately 0.6 minutes.

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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Considering the area of the hole, it is found that there is a 4.9% probability of hitting a ball into the circular hole.

The area of a circle of radius r is given by:

\(A = \pi r^2\)

In this problem, the hole has a diameter of 1 ft, hence it is radius is of r = 1 ft/2 = 0.5 ft, and it's area is given by:

\(A = \pi \times (0.5)^2 = 0.7854 \text{ft}^2\)

Hence the probability is given by:

p = 0.7854/16 = 0.049 = 4.9%

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If the test statistic value falls within the critical region, we reject the null hypothesis (H0) at the given significance level (α).

If the test statistic value falls outside the critical region, we do not reject the null hypothesis.

To determine the decision regarding the null hypothesis based on a test statistic value and a critical region, we need to compare the test statistic value to the critical value(s) of the test.

Since the question does not provide information about the significance level or the directionality of the test, we cannot determine the critical region or make a decision about the null hypothesis based on the test statistic value alone.

More information is needed to interpret the result of the test.

At the specified significance level (), we reject the null hypothesis (H0) if the test statistic value is inside the crucial zone.

If the test statistic result is outside of the acceptable range, the null hypothesis is not rejected.

The test statistic value to the test's critical value(s) in order to decide whether to reject the null hypothesis based on a test statistic value and a crucial area.

We cannot establish the crucial area or choose the null hypothesis based only on the test statistic value since the question does not specify the significance level or directionality of the test.

To understand the test's outcome, more details are required.

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Answer:

2(18k+21)-9

6(7+6k)-9

Step-by-step explanation:

Answer:

\(6(6k + 7) - 9 \\ = 6(7 + 6k) - 9 \\ 6k + 7 = 7 + 6k(both \: have \: same \: meaning) \\ thank \: you\)

The measure of angle A is 112 degrees. Hence, option d is correct.

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Similarly, since the angle of the cut is 36 degrees, the angle opposite it (angle BCD) is also 36 degrees. Since angles BCD and BDC add up to 90 degrees (because triangle BCD is a right triangle), angle BDC measures 54 degrees (90 - 36 = 54).

Now, we can find angle BDA by subtracting angle ADB and angle BDC from 180 degrees:

angle BDA = 180 - angle ADB - angle BDC

= 180 - 58 - 54

= 68

Finally, we can find angle A by subtracting angle BDA from 180 degrees:

angle A = 180 - angle BDA

= 180 - 68

= 112

Therefore, the measure of angle A is 112 degrees. Hence, option d is correct.

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Complete question:

Answer:

Evaluate

18p

3

−6p

2

+3p−1

Rewrite the expression

18p

3

+3p−6p

2

−1

Factor out 3p from the expression

3p(6p

2

+1)−6p

2

−1

Factor out −1 from the expression

3p(6p

2

+1)−(6p

2

+1)

Solution

(3p−1)(6p

2

+1)

Answer:

rate of change: -3000 feet per minute

the rate of change is showing how many feet the plane descents each minute

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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\(\huge\boxed{45^\circ}\)

See the attached diagram.

Together, angles BDC and ADB form a right angle, which is 90 degrees.

The angles are split straight down the middle, meaning they're equal to each other. This means each one is equal to half of 90 degrees, which is 45 degrees.

w = 231 - 46

hope it helps...!!

Answer:

185

Step-by-step explanation:

\(x + 46 = 231 \\ x = 231 - 46 \\ x = 185\)

Using this regular expression can help you easily match phone numbers with hyphens, with or without an area code.

To match a phone number with hyphens, we can use the following regular expression:
^\d{3}-\d{3}-\d{4}$|^\d{3}-\d{4}$
This regular expression consists of two parts separated by the pipe symbol (|). The first part ^\d{3}-\d{3}-\d{4}$ matches phone numbers with area code, hyphens after the first three and second three digits, and seven digits after the second hyphen. The second part ^\d{3}-\d{4}$ matches phone numbers without an area code, hyphen after the first three digits, and four digits after the hyphen.
Let's break down the regular expression:
- ^: Matches the beginning of the string
- \d{3}: Matches any digit three times
- -: Matches the hyphen character
- \d{4}: Matches any digit four times
- $: Matches the end of the string
- |: Separates the two parts of the expression
For example, this regular expression would match the following phone numbers:
- 555-555-5555
- 555-5555
But it would not match phone numbers without hyphens or with different separators, such as (555) 555-5555 or 555.555.5555.
In summary, using this regular expression can help you easily match phone numbers with hyphens, with or without an area code.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: slope \:\: of \:\: line = \cfrac{3}{2}\)

____________________________________

\( \large \tt Solution \: : \)

The equation of line is written in slope - intercept form

\(\qquad \tt \rightarrow \: f(x) = \dfrac{3}{2} x - 4\)

if we compare it with general slope - intercept equation of line :

\(\qquad \tt \rightarrow \: f(x) = mx + c\)

[ m represents slope of line ]

\(\qquad \tt \rightarrow \: m = \dfrac{3}{2} \)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

\(\frac32\)

Step-by-step explanation:

Hello!

An equation of a line is usually written in slope-intercept form.

Slope Intercept Form: \(y = mx + b\)

If we compare our given equation with the format:

This means that \(\frac32\) would be our slope for the line.

Question 1: The length of the line segment from the point where the ball is kicked to the point where it crosses the goal line is approximately 55.9462 meters.

Question 2: The ball crosses the goal line at approximately t* = 2.1753 seconds.

Question 3: The arc length of the curve from the point where the ball is kicked to the point where it crosses the goal line requires evaluating an integral, which can be done using symbolic manipulation software like Maple or an online integration tool.

Question 4: The tangential component (at) and normal component (an) of the acceleration vector for the ball's motion when it crosses the goal line are both approximately 9.8 m/s^2.

Question 1: To find the length of the line segment from the point where the ball is kicked to the point where it crosses the goal line, we can use the distance formula in three-dimensional space.

Given points:

Point A: (-4, 0, 0)

Point B: (2, 55, 2)

Using the distance formula:

Distance AB = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Substituting the coordinates of points A and B:

Distance AB = sqrt((2 - (-4))^2 + (55 - 0)^2 + (2 - 0)^2)

Distance AB = sqrt(6^2 + 55^2 + 2^2)

Distance AB ≈ 55.9462 meters (rounded to 4 significant figures)

Therefore, the length of the line segment from the point where the ball is kicked to the point where it crosses the goal line is approximately 55.9462 meters.

Question 2: The ball is kicked at time t = 0. To find the time t* at which the ball crosses the goal line, we need to solve for t in the equation when z-coordinate equals 0.

Given equation:

10.642t - 4.9t^2 = 0

Factoring out t:

t(10.642 - 4.9t) = 0

Setting each factor to zero:

t = 0 (at the initial kick)

10.642 - 4.9t = 0

Solving the equation:

10.642 - 4.9t = 0

4.9t = 10.642

t = 10.642 / 4.9

t ≈ 2.1753 seconds (rounded to 4 significant figures)

Therefore, the time t* at which the ball crosses the goal line is approximately 2.1753 seconds.

Question 3: To find the arc length of the curve from the point where the ball is kicked to the point where it crosses the goal line, we need to integrate the speed along the curve C from t = 0 to t = t*.

Given curve:

C(t) = 3.055ti + 28.000tj + (10.642t - 4.9t^2)k

The speed along the curve C is given by the magnitude of the velocity vector:

|v(t)| = sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)

Calculating the derivatives:

dx/dt = 3.055i

dy/dt = 28.000j

dz/dt = 10.642 - 9.8t

Plugging these values into the speed equation:

|v(t)| = sqrt((3.055)^2 + (28.000)^2 + (10.642 - 9.8t)^2)

The arc length of the curve from t = 0 to t = t* is given by the integral:

Arc Length = ∫[0,t*] |v(t)| dt

To evaluate this integral, it is recommended to use a symbolic manipulation package such as Maple or an online integration tool. The expression for the integrand can be obtained as:

integrand = sqrt((3.055)^2 + (28.000)^2 + (10.642 - 9.8t)^2)

Using an integration tool or software, the integral can be evaluated with the limits of integration [0, t*].

Question 4: To find the tangential component (at) and normal component (an) of the acceleration vector when the ball crosses the goal line, we need to differentiate the velocity vector.

Given velocity vector:

v(t) = 3.055i + 28.000j + (10.642 - 9.8t)k

Differentiating each component:

dv/dt = -9.8k

The tangential component of the acceleration vector is given by the derivative of the speed:

at = |dv/dt| = |-9.8| = 9.8 m/s^2

The normal component of the acceleration vector is given by the magnitude of the acceleration vector:

an = |a(t)| = sqrt(at^2 + an^2) = sqrt((9.8)^2 + 0^2) = 9.8 m/s^2

Therefore, the tangential component (at) of the acceleration vector is 9.8 m/s^2, and the normal component (an) is also 9.8 m/s^2 (both rounded to four significant figures).

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In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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The best approximation of the area of the circle is 113.04 square inches.

A circle is a shape with all points equidistant from a central point, known as the center. The distance from the center to any point on the edge of the circle is called the radius.

It can be calculated using the formula π \(r^2\), where r is the radius.

Since the diameter of the circle is 12 inches, the radius would be half of that which is 6 inches.

So, the area would be approximately 3.14 * \(6^2\) = 113.04 square inches.

Therefore, The best approximation of the area of the circle is 113.04 square inches.

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Answer:

3

Step-by-step explanation:

3x-3=2x

3x-2x=3

x=3

Answer:

x=3

Step-by-step explanation:

3x - 3 = 2x

-3x -3x

-3 = -x

The x cannot be a negative so you divide both sides by -1 and then the answer becomes x=3

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The correct answer will be option B which is the ends of the graph will extend in the opposite direction.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given equation is as follows:-

y = 2x⁶ + 9x⁵ -7x³ -1

When the term -3x⁶ is added the equation will be reduced in the following form.

y = -3x⁶+2x⁶ + 9x⁵ -7x³ -1

y =-x⁶+9x⁵ -7x³ -1

When we plot the graph of the above equation we will see that the graph will be reduced to the form in which both the ends of the graph lie opposite to each other.

The graph of the equation is attached with the answer below.

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Answer:

B is the correct answer

Step-by-step explanation: