A city has 4 voting districts. Records from previous years show what proportion of residents live in each district. A political analyst wondered if those proportions still held true, so they took a random sample of 120 residents. Here are their results along with a chi-square goodness-of-fit test:District A B C DHypothesized 0.39 0.27 0.15 0.19 Observed 58 22 12 28 Expected 46.80 32.40 18.00 22.80 Components 2.68 3.34 2.001.19 x² = 9.20, DF = 3 P-value = 0.027 Which voting district contributed the most to the test statistic?

The function that has the least minimum value is the following function.

Function k(x).

From the graph given, looking at it's vertex, the minimum value of function f(x) is given as follows:

-7.

From the table given, the minimum value of function g(x) is given as follows:

-5, due to the symmetry from x = 0 to x = 2.

Function h(x) is defined as follows:

h(x) = 2(x - 1)².

Which has a minimum value of zero, as the y-coordinate of the vertex is not changed with the transformation.

Using a graphing calculator, as shown by the image at the end of the answer, the minimum value of function k(x) is given as follows:

-9.

Which is the least minimum value of all these functions.

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The magnitude of the current induced in the wire is 1.2×10^{-8} and direction of the current induced in the wire is counter clockwise.

In the given question,

A rectangle (W = 20 cm, H = 30 cm) and has a resistance of(R) = 5.0 mΩ.

B(s) = 4.0 μT and B(b) = -2.5

t(s) = 2.0 s

From the question

dB(1)/dt = B(s)/t(s)

dB(1)/dt = 4 μT/2

As μ = 10^{-6}

dB(1)/dt = 2×10^{-6} T/s

dB(2)/dt = 1/2dB(1)/dt

dB(2)/dt = 2×10^{-6} /2

dB(2)/dt = 1×10^{-6} T/s

dB(3)/dt = B(b)dB(1)/dt

dB(3)/dt = -2.5×2×10^{-6} T/s

dB(3)/dt = -5×10^{-6} T/s

Now the change in magnetic field is,

dB/dt = dB(1)/dt + dB(2)/dt + dB(3)/dt

dB/dt = 2×10^{-6} + 1×10^{-6}/2 - 5×10^{-6}

dB/dt = - 2×10^{-6}

Now finding the area

Area = 1/2 wh

Firstly converting the w and h in m

So w = 0.20 m, h = 0.30 m

Area = 1/2 *0.20*0.30

Area = 0.03 square m

The induced EMF is

EMF = -AdB/dt

EMF = -(0.03)*(- 2×10^{-6})

EMF = 0.06×10^{-6}

The magnitude of the current induced in the wire is

I = EMF/R

I = 0.06×10^{-6}/5

I = 0.012×10^{-6}

I = 1.2×10^{-8}

Now, the direction of the current induced in the wire is counter clockwise.

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The right question is:

Figure (a) shows a wire that forms a rectangle (W = 20 cm, H = 30 cm) and has a resistance of 5.0 mΩ. Its interior is split into three equal areas, with magnetic fields B(1), B(2), and B(3). The fields are uniform within each region and directly out of or into the page as indicated. Figure (b) gives the change in the z components B(z) of the three fields with time t; the vertical axis scale is set by B(s) = 4.0 μT and B(b) = -2.5 B(s) and the horizontal axis scale is set by t(s) = 2.0 s. What are the magnitude and direction of the current induced in the wire?

For this problem, it is best to consider E to be the case in which she has all of the green ones, and then apply the formula for calculating the probability of a complement. 

. To determine the likelihood that she will receive all of the green  ones, we must first determine two values: the total number of possible outcomes, n(S), and the total number of favorable outcomes for the given event. Because she selects 8 marbles from a total of 11, n(S) = C(11, 8) = 165. To get all the green  ones, she must first select three red marbles from a set of three, and then select the remaining five marbles.

from the 8 non-red ones. There are (3,3)(8, 5) = 56 ways to do this. Thus,

() =56/165

. The probability of not occurring is then (′) = 1 −56/165=109/165

, so this is the probability that she does  get all the green one.

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Answer:

164

Step-by-step explanation:

Assuming that you are allowed to use graphing tools:

f(x) is below g(x) for interval [1,3]

g(x) is below f(x) for interval [3,5]

Rules of finding area between two graphs:

[tex]\int\limits^a_b {|upper - lower|} \, dx[/tex]

For interval [1,3]:

[tex]\int\limits^3_1 {g(x) - f(x)} \, dx[/tex]

[tex]\int\limits^3_1 {|(2x^{3} - 10x^{2} +29x+8)-(3x^{3}-3x^{2} -x+8) } \, dx[/tex]

[tex]\int\limits^3_1 {-x^{3} -7x^{2} +30x} \, dx[/tex]

[tex]= [-\frac{1}{4}x^{4} - \frac{7}{3}x^{3} + 15x^{2}]^3_1[/tex]

[tex]= [-\frac{1}{4}3^{4} - \frac{7}{3}3^{3} + 15*3^{2}] - [-\frac{1}{4}1^{4} - \frac{7}{3}1^{3} + 15*1^{2}][/tex]

[tex]= -\frac{81}{4} - \frac{189}{3} + 135+\frac{1}{4} + \frac{7}{3}- 15\\[/tex]

[tex]= \frac{118}{3}[/tex]

For interval [3,5]

[tex]\int\limits^5_3 {f(x)-g(x)} \, dx[/tex]

[tex]\int\limits^5_3 {|(3x^{3}-3x^{2} -x+8)-(2x^{3} - 10x^{2} +29x+8)|} \, dx[/tex]

[tex]\int\limits^5_3 {|x^{3}+7x^{2} -30x|} \, dx[/tex]

[tex]= [\frac{1}{4}x^{4} +\frac{7}{3}x^{3} - 15x^{2}]^5_3[/tex]

[tex]= [\frac{1}{4}5^{4} +\frac{7}{3}5^{3} - 15*5^{2}] -[\frac{1}{4}3^{4} +\frac{7}{3}3^{3} - 15*3^{2}][/tex]

[tex]= \frac{625}{4} +\frac{875}{3} - 375 -\frac{81}{4}} -\frac{189}{3} + 135[/tex]

[tex]=\frac{374}{3}[/tex]

Total area

[tex]= \frac{118}{3} + \frac{374}{3}\\[/tex]

[tex]= 164[/tex]

The temperature of the pizza that Suraj took from the freezer, after 2 minutes, given the graph, is 10 degrees Celsius.

The temperature of the pizza that Suraj took from the freezer and put in the oven, is shown on the graph. To find the temperature of this pizza after 2 minutes, given the line in the graph, look at the point where the 2 minutes on the x - axis, intercepts with the line.

This point on the y - axis is 10 degrees Celsius.

This simply means that at 2 minutes, Suraj's pizza slice had a temperature of 10 degrees Celsius.

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Therefore for computing the annual return we simply fund with coupon rate in percentage is 90 dollar

What is a percent simple definition?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

The additional sum of money over the principal sum of deposit or loan is called compound interest.

The yearly return on $ 3 ,000 investment will be $90.

This can be estimated as:

Investment = $3,000

Coupon rate in percentage = 3%

The computation of yearly return can be estimated as:

= $3,000 × 3%

= $90

Therefore for computing the annual return we simply fund with coupon rate in percentage.

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Answer:

A reflection of a point over the line y=−x is shown. The rule for a reflection in the origin is (x,y)→(−y,−x) .

The perimeter of the right triangle is 26 units.

From the given graph, the measure of side AB= 8 units and the measure of side BC= 7 units.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

By Pythagoras theorem,

AC²=AB²+BC²

⇒ AC²=8²+7²

⇒ AC²=113

⇒ AC=10.63

≈ 11 units

Perimeter =AB+BC+AC

= 8+7+11

= 26 units

Therefore, the perimeter of the right triangle is 26 units.

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The rate of change in sales volume when the price is $22 is -0.107 and When the price increases $1, the sales volume will decrease by -48

The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity

According to the question,

y denotes the weekly sales volume and p denotes the price per unit

Equation is [tex]y = \frac{32}{3p + 1^{\frac{-2}{5}}}[/tex]

(a) We have to find the rate of change in sales volume when price is $22

Differentiating the equation w.r.t p,

[tex]\frac{dy}{dp} = \frac{-32(3)}{(3p + 1^\frac{-2}{5})^2}[/tex]

Putting value of p = 22

=> [tex]\frac{dy}{dp} = \frac{-32(3)}{(3(22) + 1^\frac{-2}{5})^2}[/tex]

=> -96 / (66 + 1 - 2(22)(1))²

=> -96 / 897

=> -0.107

(b) To find If the price increases $1, the sales volume will decrease by

Replacing p = 1

=> dy/dp = -96/2

=> -48

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Answer:

the degree is 6

Step-by-step explanation:

To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.

Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:

x0 = a

x1 = a + (b - a)/n

x2 = a + 2(b - a)/n

...

xn = b

The width of each subinterval is (b - a)/n.

We can then use these points to define the upper sum and lower sum as follows:

Upper sum = ∑ (b - a)/n * max(f(x))

Lower sum = ∑ (b - a)/n * min(f(x))

where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.

To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.

Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.

For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.

In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.

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The arithmetic mean for this value is M=3.1.we can calculate this data from frequency distribution.

It is sum of collection of number divided by the count of numbers.Its value   can be positive or negative both.The collection is often a set of results from an experiments and observational study.

It is often used as a parameter in statistical distribution or as a result to summarize the observations of an experiment survey.It is simplest way to used to measure the average.Its also measure frequency distribution by considering all of the observations.

Now we are using formula  for arithmetic mean

 A.M= Sum of (fx)/sum of (f)

by putting values in this formula we have

A.M= 31/10

A.M= 3.1

Hence 3.1 is the arithmetic mean for given frequency data.

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In the new graph, the price appears that is increase from 2002 to 2003 is 25% and 100%. Hence, option A is correct.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from.

Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the data mentioned in the question,

Average cost to rent studio in 2002 = 400 and,

Average cost to rent studio in 2003 = 500

Then percent increase from year 2002 to 2003 will be,

% increase = (500 - 400)/400 × 100

% increase = 25%

Then, % increase from 2002 to 2003 is 25%,

(200 - 100)/100 × 100 = 100%.

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The cost of the boots is (b) $100

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

Markup rate = 50%

Markup price of the boot = $150

The cost of the boots can be calculated using the following equation

Markup price of the boot = cost of the boots * (1 + Markup rate)

Substitute the known values in the above equation, so, we have the following representation

150 = cost of the boots  * (1 + 50%)

This gives

150 = cost of the boots  * (1.5)

Divide by 1.5

cost of the boots = $100

Hence, the cost of the boots is $100

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As per the estimated percentage, the test statistic is 0.6167 or 61.67%

What is the percentage?

The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have given that in Arkansas than Virginia. the sample results show that rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.

And we need to find the test statistics.

While we looking into the given situation we have identified the following values,

=> H0 : p = 0.577

=> Ha : p ≠ 0.577

Now, we have estimated the proportion of stay-at-home residents in Arkansas is calculated as,

Here the Proportion of stay-at-home residents in Arkansas is written as,

=> p = 74/120 = 0.6167

Therefore, the test statistic is 0.6167.

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Answer:

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

Given

To factor it completely, factor out the common factor x + 3:

The sum of squares of error, treatment, within and between four painters are: 330, 692, 110 and 43.25.

The data provided is for the dying time of four different types of paint.

One-way ANOVA can be used to determine whether all the four paints have the same drying time.

Use Excel to perform the one-way ANOVA.

Go to Data → Data Analysis → Anova: Single Factor

A dialog box will open. Select the data. Select "Grouping" as Columns.

Press OK.

The output is attached below.

The required values are as follows:

(1) Sum of Squares of Treatment (Between Subjects):

SST = 330

(2) Sum of Squares of Error (Within Subjects):

SSE = 692

(3) Mean Squares Treatment (Between Subjects):

MST = 110

(4) Mean Squares Error (Within Subjects):

MSE = 43.25

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The upper control limit is 16.4 if our  desired confidence interval is 99.73%.

Given 131 population

standard deviation  = 5

sample size = 11.

mean   = 131/11 = 11.9.

determine the upper control limit if desired

confidence interval is 99.73%

What is Confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time.

Confidence interval = sample mean ± margin of error

Upper limit  = sample mean + margin of error.

margin of error = z* * population of standard deviation/[tex]\sqrt{n}[/tex].

margin of error = 3.00 * 5/[tex]\sqrt{11}[/tex].

value of z* for 99.73% confidence interval  is 3.00.

so margin of error = 4.5.

Upper limit  = 11.9 + 4.5

Upper limit  = 16.4

The upper control limit is 16.4 if our  desired confidence interval is 99.73%.

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The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.

What is multiple regression?

A probit model is a type of regression in statistics where the dependant variable can only take two values.

We have:

Regress smoker on cubic polynomials of age

If we use linear probability model.

Here the data are missing, but we can say about the estimate that:

Only the estimate intercept is statistically significant at the 5% level is wrong,

Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.

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The total hours worked is 40 hours, the total wage for the week is $238, the Total tax is 12.15%, and the paycheck after taxes is $209.44

Taxes are compulsory payments made by a government organization, whether local, regional, or federal, to people or businesses.

Given:

Pay Rate: $5.95 per hour,

Hours Worked: M-8, T-7, W-8, T-9, F-8,

FICA Tax (7.65 %),

State Income Tax (at 3%),

City Income Tax (1.5%),

Calculate the total working hours as shown below,

Total working hours = 8 + 7 + 8 + 9 + 8 = 40 hours

Calculate the total tax,

Total tax = 7.65 + 3 + 1.5 = 12.15%

Calculate total wage,

Total wage =  no of hours × 5.95

Total wage = 40 × 5.95 = $238

Paycheck after-tax deduction = Total wage - 12.15 % of $238

Paycheck after-tax deduction = 238 - 28.56

Paycheck after-tax deduction = $209.44

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Answer:Each player would get 9 cards each with a reaminder of 4 cards left

Step-by-step explanation:6 times 9 is 54 + 4 is 58

Answer: 9

Step-by-step explanation:

To figure out the given problem below:

P = 6

C = 58

You have to divide the problem.

So [tex]58[/tex] ÷ [tex]6 = 9[/tex].

the flux of curI(F) through the surface area in the figure as with integral:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

First, we calculate the curl of F: curI(F) = (2z, -2x, 2y).

Next, we apply Stokes' Theorem to calculate the flux of curI(F) through the surface in the figure. We start by computing the line integral of F around the boundary of the surface. This is given by:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

We can now evaluate this line integral by splitting it into a sum of integrals:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

= 2∫x dx + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32∫dz + 4∫yz dz

= 2x^2/2 + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32z + 4yz^2/2

= x^2 + 4yz∫dx + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

Finally, we can evaluate the flux of curI(F) through the surface in the figure as:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

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Answer: you need to have at least $312,500 in your account at the beginning.

Step-by-step explanation:

The total amount of money you will need to withdraw over the 25-year period is $30,000 * 25 years = $750,000. To find the total amount of interest you will earn, we need to use a compound interest formula. The formula for compound interest is:

A = P(1 + r/n)^nt

where A is the total amount of money you will have in your account after 25 years, P is the initial amount of money in your account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In our case, we have A = $750,000, P = ?, r = 8%, n = 1 (since the interest is compounded annually), and t = 25. Plugging these values into the formula, we get:

$750,000 = P * (1 + 0.08/1)^1 * 25

We can simplify this equation to:

$750,000 = P * 1.08^25

To find the value of P, we can divide both sides of the equation by 1.08^25:

$750,000 / 1.08^25 = P

We can use a calculator to compute the value of 1.08^25, which is approximately 2.4. This means that the initial amount of money you need in your account is $750,000 / 2.4 = $312,500.

Therefore, to be able to withdraw $30,000 each year for 25 years and earn 8% interest on your account, you need to have at least $312,500 in your account at the beginning.

A commuter passes through two traffic lights on their way to and from work. Let X1 represent the number of lights the commuter must stop at while traveling to work, and X2 represent the number of lights he must stop at. stop when returning from work. It is connected to the population mean.

a) P(To=0) = 0.2*0.2 = 0.04

P(To=1) = 0.2*0.4 + 0.4*0.2 = 0.24

P(To=2) = 0.4*0.4 + 0.2*0.2 + 0.4*0.2 = 0.36

P(To=3) = 0.2*0.4 + 0.4*0.4 = 0.24

P(To=4) = 0.2*0.2 = 0.04

b) µTo = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 = 2

It is equal to the population mean µ.

c) sTo2 = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 = 0.56

It is equal to the population variance s2.

d) E(To) = 0*0.04 + 1*0.24 + 2*0.36 + 3*0.24 + 4*0.04 + 5*0 + 6*0 + 7*0 + 8*0 = 2

V(To) = (0-2)2*0.04 + (1-2)2*0.24 + (2-2)2*0.36 + (3-2)2*0.24 + (4-2)2*0.04 + (5-2)2*0 + (6-2)2*0 + (7-2)2*0 + (8-2)2*0 = 0.56

e) P(To = 8) = 0

P(To = 7) = 0.2*0.2*0.2*0.2 = 0.0016

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The population standard deviation of {5, 8, 8, 5} is 3

The given population is

{5, 8, 8, 5}

The mean of the population = Sum of the terms /  Number of Terms

Find the values and substitute the values in the equation

Sum of terms = 5 + 8 + 8 +5

= 26

Number of terms = 4

The mean of the population= 26 / 4

= 6.5

The variance of the population = (5 - 6.5)^2 + (8 - 6.5)^2 + (8 - 6.5)^2 + (5 - 6.5)^2

= (-1.5)^2 + (1.5)^2 + 1.5^2 + (-1.5)^2

= 2.25 + 2.25 + 2.25 + 2.25

= 9

The standard deviation of the population  = [tex]\sqrt{9}[/tex]

= 3

Therefore, the standard deviation is 3

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Step-by-step explanation:

{(3, 7), (3, 6), (5, 4), (4, 7)} Is not a function

{(1, 5), (3, 5), (4, 6), (6, 4)} is a function

{(2, 3), (4, 2), (4, 6), (5, 8)} is not a function

{(0, 4), (3, 2), (4, 2), (6, 5)} is a function

Answer:

This is a math equation about GCD { GREATEST COMMON DIVISOR }
7 groups
Each group [ 4 red marbles / 5 blue marbles ]

Step-by-step explanation: { I will use the . as mutiply }

So first let's take a little of analysis
We take a as the groups that should be made, a ∈ N*
In the question, we can see: 28 can be divisible to a / 35 can be divisible to a

Because of that, we know that a is the smallest so a is: GCD ( 28, 30 )
Now, let's factorize numbers into prime factors:
28 = [tex]2^{2} . 7[/tex]
35 = 5.7
Choose common prime factors: 2,3,5,7
[ Because we are doing GCD, we will need to choose the common prime factors as index number the smallest. ]
GCD ( 28, 30 ) =  7
So a = 420 groups
The red marbles in each group: 28 ÷ 7 = 4 marbles
The blue marbles in each group: 35 ÷ 7 = 5 marbles

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Answer:

x=8

Step-by-step explanation:

Simplify 2(x+1)−x.

Simplify each term.2x+2−x=10

Subtract x from 2x.x+2=10

Move all terms not containing x to the right side of the equation.

Subtract 2

from both sides of the equation.x1−2

Subtract 2 from x = 10-2

subtract 2 from 10

hope that helps!

Answer:  8

Step-by-step explanation:

First, let's write out the equation:

2(x+1) - x = 10

So, we need to find the value of x.

Let's take an estimate of what x could be.

So, we know it has to be 5-10, because that is over when we add x to one, then multiply by 2.

So, numbers 5-7 couldn't be it, because the value of x is lower than 10. So, we have to guess if it's 8 or 9

Let's use both numbers to solve if it's correct:

2(8+1) - 8 =10

18 - 8 = 10

or

2(9+1) - 8 =10

20 - 8 = 12

So, we have 8 as our answer.

So, x = 8