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Part 1
At a​ factory, two machines pack bottles into boxes for shipping. Machine A can pack 8 boxes per​ minute, and Machine B can pack 11 boxes per minute. Both machines have been packing boxes for some​ time, and the difference between the number of boxes that Machine B has packed and the number of boxes that Machine A has packed is less than 200. Write and solve an inequality to find the possible lengths of time to the nearest second that the machines have been working. Describe the possible solutions.

Mr. Phillips can fill 10 bottles of paint with the 64 ounces of blue paint and five bottles of paint with the 12 ounces of yellow paint, for a total of fifteen 6-ounce bottles.

He has 64 ounces of blue paint and 12 ounces of yellow paint. In order to figure out how many 6-ounce bottles of paint he can fill with the quantities of pain, he must divide the amount of paint by the size of the bottles. For the blue paint, he needs to divide 64 ounces by 6 ounces, which will equal 10.6 (rounded down to 10). For the yellow paint, he needs to divide 12 ounces by 6 ounces, which will equal 2 (rounded up to 3). This means that he can fill 10 bottles of paint with the 64 ounces of blue paint and three bottles of paint with the 12 ounces of yellow paint, for a total of thirteen 6-ounce bottles. The process of figuring out how many bottles of paint can be filled with the given amounts of paint is a simple one. It requires the painter to divide the amount of paint by the size of the bottles. Once the painter knows the answer, they can use it to accurately fill the appropriate number of bottles for their project. This is an important skill for a painter to have as it helps them plan for the necessary supplies and create a successful project.

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Answer:

6.25

Step-by-step explanation:

The values of f and g that has been worked out is given as 6 and 8

This is a question that would examine the combination of two shapes into one.

We have area of a triangle = base * height / 2

this would give

f * 4 / 2 = 60 - 48

2f = 12

divide through by 2

f = 12 / 2

f = 6

we have f * g = 48

given that the value of f = 6

g * 6 = 48

6g = 48

Divide through by 6 to get the value of f

6 g / 6 = 48 / 6

g = 8

Hence the value of f is given as 6 and the value of g is given as 8

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The correlation coefficient between X and Y is approximately -0.483.

We must first determine the mean and standard deviation for both X and Y in order to calculate the correlation coefficient between X and Y.

X has a mean of:

(-5 + 1 + 2 + 11)/4 = 2.25 is the mean of X.

Y has a mean of:

average of Y = (5 + 3 - 3 + 0)/4 = 1.

The value of X's standard deviation is

s_X = sqrt([(-5 - 2.25)^2 + (1 - 2.25)^2 + (2 - 2.25)^2 + (11 - 2.25)^2]/3) = 5.1478

The value of Y's standard deviation is

s_Y = sqrt([(5 - 1)^2 + (3 - 1)^2 + (-3 - 1)^2 + (0 - 1)^2]/3) = 3.7712

After that, we can figure out the correlation between X and Y:

cov(X, Y) = [(-5 - 2.25) × (5 - 1) + (1 - 2.25) × (3 - 1) + (2 - 2.25) × (-3 - 1) + (11 - 2.25) × (0 - 1)]/3 = -7.25

We can finally determine the correlation coefficient:

r = cov(X, Y)/(s X, s Y)=-7.25/(5.1478 3.7712)=-0.483

Thus, roughly -0.483 is the correlation coefficient between X and Y.

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Answer:

-4721613632.87 or -4721613632.9 or -4721613633

Step-by-step explanation:

10x9.2^-13 = 10x-472161363.287 = -4721613632.87 or you can round -4721613632.9 or -4721613633

The probability that there will be at least 81 cartoons on a coming Saturday is given as follows:

0.011 = 1.1%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 65, \sigma = 7[/tex]

The probability that there will be at least 81 cartoons is one subtracted by the p-value of Z when X = 81, hence:

Z = (81 - 65)/7

Z = 2.29

Z = 2.29 has a p-value of 0.989.

Hence:

1 - 0.989 = 0.011 = 1.1%.

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Answer:

So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.

Step-by-step explanation:

Let's use algebra to solve the problem:

Let's say the number of boys in the classroom is "b", and the number of girls is "g".

From the problem statement, we know that:

g > b (the number of girls is greater than the number of boys)

g/b = 7/5 (the ratio of girls to boys is 7:5)

We can use the second equation to write g in terms of b:

g/b = 7/5

g = (7/5) * b

Now we can substitute this expression for g into the first equation:

g > b

(7/5) * b > b

Simplifying this inequality:

7b/5 > b

7b > 5b

2b > 0

b > 0

So we know that b is positive.

To find the exact value of b, we can use the fact that the ratio of g to b is 7:5:

g/b = 7/5

(7/5) * b/b = 7/5

7b/5b = 7/5

7/5 = 7/5

This equation is true for any value of b (as long as b is positive), so we don't actually get a unique solution for b. However, we can still make a statement about the relationship between b and g:

g/b = 7/5

g = (7/5) * b

g = (7/5) * 5x

g = 7x

So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.

Answer:

B = (5/7)G where B and G are the numbers of Boys and Girls,

Step-by-step explanation:

The ration of girls to boys is 7/5. If we let G and B represent the numbers of Girls and Boys, we can write:

   G/B = 7/5

The problem dioes not tell us the number of either boys or girls, so we cannot calculate the number of boys, as the question seems to ask.  If the actual number of girls is provided, then we can calculate the number of boys:

  G/B = 7/5

   5G = 7B  [Multiply both sides by 5B]

    7B = 5G and so

              B = (5/7)G

If, for example, there were 14 girls, there would be B = (5/7)*(14) or 5 Boys.

The exponential function that passes through (0,3) and (1,6) is [tex]f(x) = 3(2^{x})[/tex]

An exponential function is a mathematical function in which an independent variable appears in the exponent. In other words, the function has the form f(x) = [tex]a^{x}[/tex], where 'a' is a constant greater than 0 and not equal to 1, and 'x' is the independent variable.

To find the exponential function that passes through (0,3) and (1,6), we need to determine the values of 'a' and 'b' in the function [tex]f(x)=a(b^{x})[/tex].

First, we can use the point (0,3) to find the value of 'a'. Plugging in x=0 and y=3, we get:

3 = [tex]ab^0[/tex]

3 = a

Next, we can use the point (1,6) to find the value of 'b'. Plugging in x=1 and y=6, we get:

6 = [tex]ab^1[/tex]

6 = 3b

b = 2

Now that we have the values of 'a' and 'b', we can write the exponential function in the form [tex]f(x)=a(b^{x})[/tex]. Substituting 'a' and 'b' into the equation, we get: [tex]f(x) = 3(2^{x})[/tex]

Therefore, the exponential function that passes through (0,3) and (1,6) is [tex]f(x) = 3(2^{x})[/tex]

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Answer:

2 kph

Step-by-step explanation:

10 kilometers in 5 hours.

1 hour = ?

10/5 = 2 Kilometers

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Answer:

The answer will be B. y= -3x +6

If the volume of the frustum is 2855 cm³ and the value of r  = 28.4

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point called the apex or vertex.

Volume of the = (1/3*п*R²*H) + 1/3*п*r²*h

2855 = 1/3*22/7*10*30 + 1/3*22/7*r²*3

2855 = 314.3 + 66r²/21

2540.7 *21= 66r²

53354.7 = 66r²

r² = 808.4

r √808.4

Therefore the value of r = 28.4

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The sοlutiοn οf the given prοblem οf cubοid cοmes οut tο be the cubοid has a density οf abοut 6.0 g/cm³.

In geοmetry, a hypercube is a cοncrete οr muti shape. A hypercube is a cοnvex pοlygοns with 12 sides, 6 rectangular faces, and 8 edges. A cubοid is anοther term fοr the creature. An οbject with six square sides is called a cube. Bricks and literature are amοng the items fοund in bοxes. The main differences between cubic but alsο cubic are as fοllοws.

Here,

This equatiοn can be changed tο read density = mass/vοlume. Since we already knοw the mass (534 g), we can use the rearranged methοd tο determine the vοlume.

=> Vοlume = L, W, and H, and mass = 534 g.

=>  density equals mass/vοlume

=>  weight = 534/ (L x W x H)

The CRC Encyclοpedia οf Chemistry and Physics states that nickel has a density οf 8.908 g/cm³.

Thus, we can enter this number as a substitute in οur fοrmula tο οbtain:

=>  density =  534/(L, W, H)

=> 8.908 g/cm³.

Tο sοlve fοr density, we can rewrite this equatiοn as fοllοws:

=>  density =  534/(L, W, H)

=>  6.0 g/cm³ (tο 1 decimal place)

Cοnsequently, the cubοid has a density οf abοut 6.0 g/cm³.

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Answer:

5 is the answer

Step-by-step explanation:

[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 11 &\implies x -11=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -11 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{now, assuming that}}{a=1}\hspace{3em}1( x +2 )( x -11 ) =y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-9x-22=f(x) \end{array}} ~\hfill[/tex]

Answer:

Below

Step-by-step explanation:

Year 0  = 800

Year 1 =  400

Year 2  = 200

Year 3 = 100

Year 4 = 50

Year 5 = 25

From year 2 to year 4 = 150 dollars decrease in 2 years = 75 dollars per year

this is just a quick addition to "jsimpson11000" good reply above

so we know the decrease is exponential, that means we have an equation about V = abᵗ, now, hmmm who knows what "ab" is, now, once we know that, then we can get the "slope" from t=2 to t=4, so let's  use the table to get it.

[tex]{\Large \begin{array}{llll} V=ab^t \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t=3\\ V=100 \end{cases}\implies 100=ab^3 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t=5\\ V=25 \end{cases}\implies 25=ab^5\implies 25=ab^3b^2\implies \stackrel{\textit{substituting from above}}{25=(100)b^2} \\\\\\ \cfrac{25}{100}=b^2\implies \cfrac{1}{4}=b^2\implies \sqrt{\cfrac{1}{4}}=b\implies \boxed{\cfrac{1}{2}=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]100=ab^3\implies 100=a\left( \cfrac{1}{2} \right)^3\implies 100=\cfrac{a}{8}\implies \boxed{800=a} \\\\\\ ~\hfill {\Large \begin{array}{llll} V=800\left( \frac{1}{2} \right)^t \end{array}}~\hfill[/tex]

now let's find the slope

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ V(t)= 800\left( \frac{1}{2} \right)^t\qquad \begin{cases} t_1=2\\ t_2=4 \end{cases}\implies \cfrac{V(4)-V(2)}{4 - 2} \\\\\\ \cfrac{(50)~~ - ~~(200)}{2}\implies \text{\LARGE -75}[/tex]

so is a negative slope, because is Decay or decrement, however you're expected to enter it as positive, so in essence just the absolute value change.

well, let's pick any two random x-values on the quadratic, hmmm say let's use x = 4  and x = 7, so hmm f(4) = 5 and f(7) = 32, that'd give us the points of (4, 5) and (7 , 32).

To get the equation of any straight line, we simply need two points off of it, let's use those two above.

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{32}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{32}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{4}}} \implies \cfrac{ 27 }{ 3 } \implies 9[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 9}(x-\stackrel{x_1}{4}) \\\\\\ y-5=9x-36\implies {\Large \begin{array}{llll} y=9x-31 \end{array}}[/tex]

Check the picture below.

Refer to the attached images.

From the graph and the given information, the value of the given function, fg(-3), is 9

From the question, we are to determine the value of the function, fg(-3).

First , we will determine the value of g(-3)

From the given information,

g(x) = 1/(2 + x)

Substitute x = -3 in the function to determine the value of g(-3)

g(-3) = 1/(2 + (-3))

g(-3) = 1/(2 - 3)

g(-3) = 1/-1

g(-3) = -1

Now,

fg(-3) = f(g(-3))

Thus,

fg(-3) = f(-1)

Now, we will determine the value of f(-1) from the given graph.

From the graph, we can read that the value of f(-1) is 9

Hence,

The value of fg(-3) is 9

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The equation for the line with a slope of 5/6 and passing through the point (22,12) is y=5/6x - 16.

The equation for the line with a slope of 5/6 and passing through the point (22,12) can be expressed as y=5/6x + b. To calculate the value of b, we can plug in the given point's coordinates, (22,12), into the equation. This will result in the equation 12=5/6(22)+b. Solving for b, we get b=-16. Therefore, the equation for the line is y=5/6x-16.

In summary, we can express the equation for the line with a slope of 5/6 and passing through the point (22,12) as y=5/6x - 16. To calculate the value of b, we plugged the point's coordinates, (22,12), into the equation, resulting in the equation 12=5/6(22)+b. Solving for b, we got b=-16. Thus, the equation for the line is y=5/6x - 16.

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Answer:

Step-by-step explanation:

variable means we can put any value to it.

the variable is 2x

the constant is +1

Answer: The total number of possible outcomes in the lottery can be calculated by finding the number of ways to choose 5 distinct numbers out of 70, and then multiply that by the number of possible choices for the gold ball (1 out of 25). So:

Total number of outcomes = (70 choose 5) * 25 = 25,989,600

To win the jackpot, the player must match all 5 white ball numbers and the gold ball number. The number of ways to do this is simply 1, since there is only one winning combination.

Therefore, the probability of winning the jackpot with a single ticket is:

Probability of winning = (number of winning outcomes) / (total number of outcomes) = 1 / 25,989,600

So the probability of winning the jackpot with a single ticket is approximately 0.00000003846, or 1 in 25,989,600.

Step-by-step explanation:

As X is a discrete uniformly distributed random variable with a mean of 5, a variance of 4, and a range of values from 1, 2, 3, 5, 6, 7, 8, and 10, we know that X can have any one of these values with an equal probability of 1/10.

Calculating the likelihood that X will have a number equal to or greater to 6 is necessary to get [tex]P(X > =6)[/tex]. Due to the fact that X is a continuous uniformly distributed random variable.

We may calculate this probability simply counting all number of potential values for X that are greater or equal to to 6, dividing by the entirety of the potential values for X, and then adding the results together.

The probability of X is more than or equivalent to 6 is given by the fact there are a total of 5 variables of X that are at least equal to 6, namely: 6, 7, 8, 9, and 10.

[tex]P(X > =6) = 5/10 = 1/2[/tex]

Thus, (b) 1/2 is the right response.

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To decrease the probability of type I error in order to avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

The researchers should decrease the significance level to decrease the probability of type I error. This is because a type I error occurs when the null hypothesis is rejected when it is actually true. In this case, the null hypothesis is that the diagnostic tool is not effective in detecting the condition.

If the researchers decrease the significance level, they are decreasing the probability of making a type I error, which means they are less likely to conclude that the diagnostic tool is effective when it is actually not. This will help the researchers avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

In general, the significance level (also known as the alpha level) is the probability of making a type I error. By decreasing the significance level, the researchers are making the criteria for rejecting the null hypothesis more stringent, which reduces the likelihood of making a type I error.

It is important to note that decreasing the significance level will also decrease the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false.

However, in this case, the researchers are more concerned with avoiding the more consequential error of falsely concluding that the diagnostic tool is effective, so decreasing the significance level is the appropriate action to take.

In conclusion, the researchers should decrease the significance level to decrease the probability of type I error in order to avoid the more consequential error of falsely concluding that the diagnostic tool is effective.

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44. cos(x+1x​)

46. sec(x+1x​)

47. tan−1(2x+1​x​)

16.cscxcosx+cotx

17.1+sinx

18.1+cosx

19. cotx−1

29. True

30 True

31. True

32. True

33. True

40. False. The equivalent expression is sin2θ−1+tan2θcos2θ​

41.  False. The equivalent expression is 3sin2θ+4cos2θ−3

42.  False. The equivalent expression is cotθ+cosθsecθ+tanθ​−sec2θ

For the following exercises, find the function if sint=x+1x​:

For the following exercises, simplify the first trigonometric expression by writing the simplified form in terms of the second expression:

For the following exercises, verify the identity:

For the following exercises, determine whether the identity is true or false. If false, find an appropriate equivalent expression:

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The rate of increase is 1% and the variable x represents when the population will double

The rate of increase is determined by the value of the exponent x. In this case, x represents the number of years that have passed since the population was at its initial value.

The exponent x increases by 1 for each year that passes, indicating that the population is increasing by a factor of 1.01 each year.

Therefore, the rate of increase is 1%, or 0.01 as a decimal.

The variable x represents when the population will double

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When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.

Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.

When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.

Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.

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In conclusion, we find evidence of significant differences in hardness measurements between the four types of tips, based on the one-way ANOVA. The LSD method can be used to investigate specific differences between pairs of means.

The residuals appear to be randomly distributed and normally distributed, indicating that the assumptions of the ANOVA are reasonable.

To determine if there is a difference in hardness measurements between the tips, we can conduct a one-way ANOVA with the null hypothesis that the mean hardness measurements are equal for all four tips and the alternative hypothesis that at least one mean is different.

We can use Fisher's LSD method to investigate specific differences between the tips. The LSD method tests for significant differences between any pair of means using the formula:

LSD = tα(ν) × SE

where tα(ν) is the critical value of the t-distribution with α level of significance and (n-1) degrees of freedom, and SE is the standard error of the means, which is calculated as:

SE = √(MSE/n)

where MSE is the mean square error from the ANOVA and n is the sample size for each group.

First, we can perform the one-way ANOVA using software or a calculator. The results show that the F-statistic is significant at the 0.05 level with p-value < 0.05, which indicates that we reject the null hypothesis and conclude that there is at least one significant difference between the means.

Next, we can calculate the LSD for α = 0.05 and degrees of freedom (n-1) = 12 using the formula above. We obtain:

LSD = 2.179 × √(2.695/4) = 1.31

The LSD value indicates that if the difference between any two means is greater than 1.31, we can conclude with 95% confidence that the two means are significantly different.

To analyze the residuals, we can plot the residuals versus the fitted values and check for patterns or non-constant variance. We can also perform a normal probability plot of the residuals to check for normality.

The residual plot shows no clear patterns or trends, and the points appear to be randomly scattered around zero. The normal probability plot shows that the residuals follow a roughly straight line, indicating that they are approximately normally distributed.

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Answer:

Let x be the number of watermelons the farmer needs to sell to earn at least $200.

The amount of money earned from selling x watermelons is 8x dollars.

After paying $50 to rent the booth, the farmer's profit is 8x - 50 dollars.

The problem states that the farmer wants to earn at least $200, so we can set up the following inequality:

8x - 50 ≥ 200

Adding 50 to both sides, we get:

8x ≥ 250

Dividing both sides by 8, we get:

x ≥ 31.25

Since the number of watermelons must be a whole number, the farmer needs to sell at least 32 watermelons to earn at least $200 after paying for the booth.

Answer:

The length of x is (10√3)/3.

Step-by-step explanation:

Using the trigonometric ratios of a 30-60-90 triangle, we know that the side opposite the 30-degree angle is half the length of the hypotenuse. Therefore, we have:

x/2 = (5/√3)

Multiplying both sides by 2, we get:

x = 10/√3, which can be simplified to:

x = (10√3)/3

So the length of x is (10√3)/3.

Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]

The length of JG is 5 units if ∠EDH ≅ ∠EDG. Thus option b is the correct answer as per the given relation.

The Given data is as follows:

∠EDH ≅ ∠EDG

Here in the question it is given that, ∠EDH is similar to ∠EDG

The corresponding sides of two triangles are congruent are similar to each other.

EH=9, EJ=4.

EH = EG

EG = 9 -------equation(1)

EG = EJ+JG

EG = 4+JG -------equation(2)

From equations 1 and 2, we get

9 = 4 + JG

9 - 4 = JG

JG = 5 units

Therefore, we can conclude that the length of JG is 5 units.

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The complete question is-

In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?

a. 4 units

b. 5 units

c. 6 units

d. 9 units

Answer: 5

Step-by-step explanation:

∠EDH ≅ ∠EDG, EH=9, EJ=4.Corresponding sides of two triangles are congruent.                         (CPCTC)              .... (1)From the given figure it is clear that        ... (2)Using (1) and (2), we getSubtract 4 from both the sides.

Answer:

x ≈ 17

Step-by-step explanation:

using the cosine ratio in the right triangle

cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] ( multiply both sides by x )

x × cos62° = 8 ( divide both sides by cos62° )

x = [tex]\frac{8}{cos62}[/tex] ≈ 17 ( to the nearest whole number )