There are 4,377 different ways to distribute the 96 children into groups, with each group having a minimum of 5 children and a maximum of 20 children. (By division)
To determine the number of ways to distribute the 96 children into groups, we need to find the number of divisors of 96 that are between 5 and 20.
First, let's find the divisors of 96. The divisors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
Next, we need to consider the divisors that fall within the range of 5 to 20. In this case, the divisors are 6, 8, 12, and 16.
Now, we can calculate the number of ways to distribute the children into groups using the divisors:
For each divisor, we divide the total number of children (96) by the divisor to determine the number of groups.
Number of ways = Number of groups = Total number of children / Divisor
For the divisor 6: Number of groups = 96 / 6 = 16 groups
For the divisor 8: Number of groups = 96 / 8 = 12 groups
For the divisor 12: Number of groups = 96 / 12 = 8 groups
For the divisor 16: Number of groups = 96 / 16 = 6 groups
Finally, we sum up the number of ways for each divisor:
Number of ways = Number of ways for divisor 6 + Number of ways for divisor 8 + Number of ways for divisor 12 + Number of ways for divisor 16
= 16 + 12 + 8 + 6
= 42
Therefore, there are 42 different ways to distribute the 96 children into groups, with each group having a minimum of 5 children and a maximum of 20 children.
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Find the volume of the
rectangular prism below
Answer:
480Step-by-step explanation:
multiply all three values
The box plots compare the weekly earnings of two groups of salespeople from different clothing stores. Find and compare the IQRs of the box plots. Group A IQR = $ . Group B IQR = $ . Group A's IQR is Group B's IQR, so the salaries in the middle 50% for Group A are spread out as those for Group B.
Answer:
Group A, IQR = 700
GROUP B, IQR =.450
Group A's IQR is greater
The values in the middle 50%.of Group A are more spread out Than those of Group B.
Step-by-step explanation:
Data for.each group :
The IQR = Q3 - Q1
From the boxplot :
Group A:
Q1 = 1100 ; Q3 = 1800
IQR = 1800 - 1100 = 700
Group B:
Q1 = 1400; Q3 = 1850
IQR = 1850 - 1400 = 450
Greater IQR = Group A
The values in the middle 50%.of Group A are more spread out Than those of Group B.
Does the figure below have rotational symmetry? Explain.
A.)Yes; it can be rotated 360° or less and match the original figure.
B.)Yes; it can be rotated 180° or less and match the original figure.
C.)No; it does not match the original figure after any rotation of 180° or less.
D.)No; it does not match the original figure after any rotation of 360° or less.
Answer:
B.) Yes; it can be rotated 180° or less and match the original figure.
Step-by-step explanation:
You have to trust me its b I did the quiz on Pearson Conexus. I would show a picture but I'm on pc and don't know how to .
My answer will help.
Anyways, have a great day/night !! <3
Step-by-step explanation:
Does the figure below have rotational symmetry? Explain.
A.)Yes; it can be rotated 360° or less and match the original figure.
B.)Yes; it can be rotated 180° or less and match the original figure.
C.)No; it does not match the original figure after any rotation of 180° or less.
D.)No; it does not match the original figure after any rotation of 360° or less.
I need help with surface area
Answer:
Surface Area varies by object/shape.
Ask your teacher/learning helper for those formulas of surface area
Step-by-step explanation:
Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
simply this number 15min :3hours
Answer:
1 min : 12 min
Step-by-step explanation:
To simplify the given ratio, convert both to the same unit of time.
1 hour = 60 minutes
3 hours = 3 x 60 minutes
= 180 minutes
So that,
15 min : 3 hours = 15 min : 180 min
divide through by 15 to have;
15 min : 180 min = 1 min : 12 min
Thus the simplified form of the number give is 1 min : 12 min.
What does this mean in discrete Math?
L(C) = L(R) ∩ L(S) and there is an underline in the top of L(S)__L(S)
can you please translate this to english?
In discrete mathematics, the expression "L(C) = L(R) ∩ L(S)" means that the language generated by the grammar or automaton represented by C is equal to the intersection of the languages generated by the grammars or automata represented by R and S.
The term "L(C)" refers to the language generated by C, which represents the set of all valid strings or sequences that can be produced by the grammar or automaton C. Similarly, "L(R)" and "L(S)" represent the languages generated by R and S, respectively.
The intersection (∩) symbol signifies the common elements or strings that are present in both L(R) and L(S). In other words, it represents the set of strings that can be generated by both R and S.
As for the underline symbol in the expression "L(S)__L(S)", it is commonly used to denote the closure or complement of a language. However, without additional context or information, it is difficult to determine the exact meaning in this case. It could indicate a specific operation or property related to the language L(S), which would require further clarification.
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a building brick weighs 2.7 kilograms. work out the weight of 840 bricks. give the answer in tonnes
Answer:
2.268 tons
Step-by-step explanation:
Multiply 840 to 2.7 to figure out the weight of 840 bricks.
840 x 2.7 = 2268 kilograms
Convert 2268 kilograms into tons which will be 2.268 tons.
How did I convert? Divide 2268 by 1000 because 1 ton = 1000 kilograms.
answer these please
Answer:
why shoulds i answer them?
Step-by-step explanation:
Okay okay fine i will answer them just add me first!
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.1 million cells per microliter and a standard deviation of 0.4 million cells per microliter. (a) What is the minimum red blood cell count that can be in the top 26% of counts? (b) What is the maximum red blood cell count that can be in the bottom 16% of counts? (a) The minimum red blood cell count is million cells per microliter. (Round to two decimal places as needed.)
The minimum red blood cell count that can be in the top 26% of counts is approximately 5.37 million cells per microliter. The maximum red blood cell count that can be in the bottom 16% of counts is approximately 4.602 million cells per microliter.
(a) The minimum red blood cell count that can be in the top 26% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.26.
Using the standard normal distribution table or a calculator, we find that the z-score is approximately 0.675.
We can then use the z-score formula to find the corresponding value in the original distribution: minimum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (0.675 * 0.4) = 5.37 million cells per microliter.
(b) The maximum red blood cell count that can be in the bottom 16% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.16.
Using the standard normal distribution table or a calculator, we find that the z-score is approximately -0.994.
Using the z-score formula, we can find the corresponding value in the original distribution: maximum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (-0.994 * 0.4) = 4.602 million cells per microliter.
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The life expectancy of Lagrangian Toads is normally distributed with a mean of 15 years and a standard deviation of 2 years. If we have a population of 1500 Lagrangian Toads, then how many do we expect to live between 9 years and 19 years?
we expect around 1464 Lagrangian Toads to live between 9 years and 19 years.
To solve this problem, we need to calculate the probability that a Lagrangian Toad's life expectancy falls between 9 years and 19 years, given a normal distribution with a mean of 15 years and a standard deviation of 2 years.
First, we calculate the z-scores for the lower and upper bounds of the desired range:
Lower z-score = (9 - 15) / 2 = -3
Upper z-score = (19 - 15) / 2 = 2
Next, we use the z-scores to find the cumulative probability using a standard normal distribution table or calculator.
P(Z < -3) ≈ 0.0013
P(Z < 2) ≈ 0.9772
To find the probability between these two z-scores, we subtract the lower probability from the upper probability:
P(-3 < Z < 2) ≈ 0.9772 - 0.0013 = 0.9759
This means that approximately 97.59% of the Lagrangian Toads in the population are expected to live between 9 years and 19 years.
To find the number of Lagrangian Toads in this range, we multiply the probability by the total population size:
Number of Lagrangian Toads = 0.9759 * 1500 ≈ 1463.85
Rounding to the nearest whole number, we expect around 1464 Lagrangian Toads to live between 9 years and 19 years.
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Slope -1/3, y-intercept = 5
Answer:
y=-1/3x+5
Step-by-step explanation:
I know the equation would be y=-1/3x+5 because of slope intercept form.
y=mx+b
y= the y coordinate of a point on the graph
m= slope of the graph
x= the x coordinate of a point on the graph
b= y intercept
We know the slope of the graph is -1/3, and we know the y- intercept of the graph is 5.
So, the equation is y=-1/3x+5.
Can someone help me with this. Will Mark brainliest.
Answer:
√53
Step-by-step explanation:
Use the distance formula to find the distance between the two coordinates
Solve the equations for points!!
(Only 3)
Answer:
-2 , -10 & -99
Step-by-step explanation:
1)
⇒ x + 6 = 4
⇒ x = 4-6
⇒ x = (-2)
2)
⇒x - (-4) = -6
⇒ x + 4 = -6
⇒ x = -6-4
⇒ x = -10
3)
⇒2(x-1) = -200
⇒ x - 1 = -200/2
⇒ x - 1 = -100
⇒ x = 1 - 100
⇒ x = (-99)
Answer:
1. x= -2 2. ×= -10 3. x= -99
Step-by-step explanation:
1. x+6 = 4
x = 4-6
x = -2
2. x-(-4) = -6
x+4 = -6
x = -6 - 4
x = -10
3. 2(x-1) = -200
2x - 2 = -200
2x = -200 +2
2x = -198
x = -99
PLZ HELP!!!!!!
What is the quotient ? 1 O 73 O 78
sorry im on my school computer so the picture is blocked :(
Answer:
A.) 1/7^8
Step-by-step explanation:
guy in the comments said it and i got it write, so this is for the people that cant see the comments.
Find the real potential, Φ(x,y), and the complex potential, (F(z), between the parallel plates at y = x and y = x+k, which have potentials of 0 V and 300 V, respectively.
The real potential, between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation in two dimensions. The first paragraph provides a summary of the answer, followed by an explanation in the second paragraph.
The real potential, Φ(x, y), is given by the equation Φ(x, y) = C1x + C2y, where C1 and C2 are constants determined by the boundary conditions. In this case, the boundary conditions are Φ(x, x) = 0 V and Φ(x, x + k) = 300 V. By substituting these conditions into the equation, we can solve for the constants C1 and C2 and obtain the real potential Φ(x, y) between the plates.
The complex potential, F(z), is related to the real potential by the equation F(z) = Φ(x, y) + iψ(x, y), where ψ(x, y) is the stream function. The stream function can be determined by solving the equation ∇²ψ = 0, subject to the same boundary conditions as the real potential. Once the stream function is obtained, the complex potential F(z) can be calculated.
In conclusion, the real potential, Φ(x, y), and the complex potential, F(z), between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation and using the appropriate boundary conditions. The real potential is given by Φ(x, y) = C1x + C2y, where the constants C1 and C2 are determined by the given potential values on the plates. The complex potential is obtained by combining the real potential with the stream function, which is determined by solving the Laplace equation for the stream function with the same boundary conditions.
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(x – 6)2 = y + 7, find the vertex.
Celiac disease is a digestive disease that damages the small intestine and affects the absorption of food. People who have this disease cannot tolerate gluten, which is a protein found in many grain products such as wheat, barley, and rye. In recent years, the incidence of diagnosed cases of this disease has risen dramatically. The following data has been collected on the incidence of celiac disease since 1950. Years Since 1950 0 8 16 24 32 40 48 52 56 60 Diagnosed Cases of 10 11 14 13 11 9 12 18 31 Celiac x 1000 a. Create a scatter plot of this data. Answer: b. What regression model would best fit this model? Answer: c. Find an appropriate equation for the curve of best fit. Answer: d. Using your model, how many cases of celiac disease may be diagnosed in 2020?
a. The scatter plot of the data shows the incidence of diagnosed cases of celiac disease since 1950.
b. A linear regression model would best fit this data.
c. The equation for the curve of best fit is y = 0.603x + 8.821, where y represents the number of diagnosed cases of celiac disease (per 1000) and x represents the years since 1950.
d. Using the regression model, approximately 10.835 cases of celiac disease may be diagnosed in 2020.
a. To create a scatter plot of the data, we plot the number of diagnosed cases of celiac disease (y-axis) against the years since 1950 (x-axis). Each data point represents a pair of (x, y) values. For example, the first data point would be (0, 10), the second (8, 11), and so on.
b. In this case, a linear regression model would best fit the data because the scatter plot suggests a roughly linear relationship between the years since 1950 and the number of diagnosed cases of celiac disease.
c. To find the equation for the curve of best fit, we can use linear regression. We calculate the slope and intercept of the line that minimizes the sum of squared distances between the data points and the line. The equation of a line is y = mx + b, where m is the slope and b is the intercept. By performing linear regression on the given data points, we obtain the equation y = 0.603x + 8.821.
d. To estimate the number of diagnosed cases of celiac disease in 2020, we substitute x = 70 (since 2020 is 70 years since 1950) into the equation y = 0.603x + 8.821. Solving the equation, we find that y is approximately equal to 10.835. Therefore, using the regression model, around 10.835 cases of celiac disease may be diagnosed in 2020.
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2000 x 0.045 x 7 =
5000 x 0.07 x 20 =
28000 x 0.09 x 1 =
7500 x 0.035 x 2 =
4000 x 0.045 x 2.5 =
Answer:
639.8
7000
2520
525
450
..........
the sign test is a 1-sample median test. which of the choices below is the null hypothesis of a sign test? question 8 options: the sample median equals 0. the population median is greater than 0. the sample median does not equal 0. the population median equals 0.
The null hypothesis of a sign test is "the population median equals 0." This hypothesis assumes that the median of the population, from which the sample is drawn, is equal to zero.
The sign test is a non-parametric statistical test used when the data is measured on an ordinal scale or when the assumptions for parametric tests are not met.
In a sign test, we compare the observed data to a specified value, typically denoted as "M0" or "m0." This value represents the hypothesized population median.
The null hypothesis assumes that the population median is equal to the specified value. In this case, the specified value is zero.
The alternative hypothesis, in contrast, would state that the population median is not equal to the specified value.
During the sign test, we focus on the signs of the differences between the observed values and the specified value. We count the number of positive and negative differences.
The test statistic is the smaller of the two counts, and its probability distribution is approximated by the binomial distribution.
By comparing the test statistic to the critical values from the binomial distribution, we determine whether there is enough evidence to reject the null hypothesis.
In summary, the null hypothesis for a sign test is that the population median is equal to the specified value, which in this case is zero.
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How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 59 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ≈21°C.
ompute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)
lower limit
°C
upper limit
°C
The 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
The 95% confidence interval (CI) for the mean temperature in the crown of the balloon is calculated as follows. We first assume that the population distribution is normal with a standard deviation (SD) of σ = 6°C as per the given data. We will then use the z-distribution to calculate the required confidence interval.
The formula for calculating the 95% confidence interval is given by
CI (mean) = x ± z × (σ/√n)
Where 'x' is the mean, 'z' is the z-score associated with the 95% CI, 'σ' is the standard deviation, and 'n' is the number of samples taken.
For the given data the confidence interval is calculated as:
CI (Mean) = 97 ± 1.96 × (6/√59)
CI (Mean) = 97 ± 1.22
Therefore, the 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
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A dolphin jumps from the water at an initial velocity of 16 feet per second. The equation h + -16t^2 + 80t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?
Answer:
100feet
Step-by-step explanation:
Given the height reached by a dolphin expressed by the equation is h = -16t^2 + 80t. At maximum height, the velocity is zero, hence;
v(t) = dh/dt = -32t + 80
0 = -32t + 80
32t = 80
t = 80/32
t = 2.5secs
Substitute t = 2.5 into the height formula h = -16t^2 + 80t
h = -16(2.5)^2 + 80(2.5)
h = -100+200
h = 100feet
Hence the maximum height the dolphin jumps is 100feet
How do I do this one?
Step-by-step explanation:
[tex]16 {x}^{2} - 25 = 0 \\ 16 {x}^{2} = 0 + 25 \\ 16 {x}^{2} = 25 \\ {x}^{2} = \frac{25}{16} \\ x = \sqrt{ \frac{25}{16} } \\ = 1.25 \: or \frac{5}{4} \: or1 \frac{1}{4} [/tex]
Do note that this question might have two answers as Square roots will actually give you a positive and negative solution. Clarify with your teacher about this.
Answer:
x=0.09765625 or rounded up as 0.1
Step-by-step explanation:
first you have to add 25 to the 0 and subtract it from the sid it is on. making it look like this
16x²=25
256x=25
now divide both sides by 256 and you get
x=0.09765625 or rounded up as 0.1
Question 1 of 10
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(0,0) (10,-2)
The equation of the following line is y= -1/5x.
Option F is correct.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
From the graph we have the coordinates as (0, 0) and (10, -2)
So, the slope of the line is
= (-2 - 0) / (10- 0)
= -2/ 10
= 1-5
and, using the slope intercept is
y= mx+ b
y= -1/5x + b
Now, put x= 0 and y= 0 in above equation
0 = 1/5(0) + b
b= 0
So, the Equation of line is
y= -1/5x
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Quadrilateral PQRS is a rectangle. Describe the error in finding the value of x
Answer:
∠PSR=90°
m∠QSR= 90-m∠QSP
x= 90-58=32°
Step-by-step explanation:
The actual value of the x is 32°.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Given quadrilateral is a rectangle.
All the four interior angles of a rectangle is perpendicular angle or is 90 degrees.
So measure of ∠PSR = 90°
m ∠QSR + m ∠QSP = 90°
Given that m ∠QSP = 58°
Substituting,
m ∠QSR + 58° = 90°
m ∠QSR = 90° - 58°
= 32°
So x° = 32°
Hence the error is that both the angles are made to be equal instead of making the sum of the angles equal to 90°.
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please help!!!! it’s due asapppp !!!!!
Mary is using a one-sample t-test on the following group: Subject #15: 7.5 hours Subject #27: 6 hours Subject #48: 7 hours Subject #80:6.5 hours Subject #91: 7.5 hours Subject #82: 8 hours Subject #23:5.5 hours Select the two TRUE statements. a.) The t-distribution that Mary uses has skinnier tails than a standard distribution. b.) The value for the degrees of freedom for Mary's sample population is six. c.) The t-distribution that Mary uses is taller than a standard distribution. d.) Mary would use the population standard deviation to calculate a t- distribution. e.) Mary would use the sample standard deviation to calculate a t-statistic. Teems need to be seleted
The two true statements are: b.) The value for the degrees of freedom for Mary's sample population is six, and e.) Mary would use the sample standard deviation to calculate a t-statistic.
a.) The t-distribution that Mary uses does not have skinnier tails than a standard distribution. In fact, the t-distribution has fatter tails, which accounts for the increased variability when working with small sample sizes.
b.) The degrees of freedom for Mary's sample population can be calculated as the number of subjects minus one, which in this case is 7 - 1 = 6. So statement b is true.
c.) The t-distribution that Mary uses is not taller than a standard distribution. The shape of the t-distribution is similar to the standard normal distribution, but it is slightly flatter.
d.) Mary would not use the population standard deviation to calculate a t-distribution. Instead, she would use the sample standard deviation, which provides an estimate of the population standard deviation.
e.) Mary would use the sample standard deviation to calculate a t-statistic. The t-statistic measures the difference between the sample mean and the hypothesized population mean, relative to the variability in the sample.
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The table gives the number of yeast cells in a new laboratory culture.
Time(hours) Yeast cells Time(hours) Yeast cells
0 18 10 509
2 39 12 597
4 80 14 640
6 171 16 664
8 336 18 672
(a) Plot the data and use the plot to estimate the carrying capacity for the yeast population. (Round the answer to the nearest ten.)
K = ___680_________ (from multiple choice)
(b) Use the data to estimate the initial relative growth rate. (Use the first two points of the data.)
___________________
(c) Find an exponential model for these data.
P(t) =___________________________
(d) Find a logistic model for these data.
P(t) =__________________
(e) Use your logistic model to estimate the number of yeast cells after 5 hours. (Round the answer to the nearest whole number.)
________________________ yeast cells
The carrying capacity for the yeast population, estimated from the plot, is 680 cells. The initial relative growth rate can be determined using the first two points of the data.
(a) From the plot of the data, we observe that the yeast population levels off or stabilizes around the value of 680 cells. This value represents the carrying capacity of the yeast population in the laboratory culture. (b) To estimate the initial relative growth rate, we use the first two points of the data: (0, 18) and (2, 39). The relative growth rate can be calculated by dividing the change in the number of yeast cells by the change in time. In this case, the change in cells is 39 - 18 = 21, and the change in time is 2 - 0 = 2. Therefore, the initial relative growth rate is 21 / 2 = 10.5 cells per hour.
(c) An exponential model for the data can be determined by fitting an exponential function to the data points. Using the initial point (0, 18) as the initial condition, we can write the exponential model as P(t) = P₀e^(kt), where P(t) represents the number of yeast cells at time t, P₀ is the initial number of cells, k is the growth rate constant, and e is the base of the natural logarithm. Substituting the given data, we can solve for the values of P₀ and k. The exponential model for these data is P(t) = 17.08e^(0.189t).
(d) A logistic model accounts for the carrying capacity of the yeast population. It is given by the formula P(t) = K / (1 + ae^(-kt)), where K represents the carrying capacity, a is a constant related to the initial condition, and k is the growth rate constant. Using the given data, we can solve for the values of K, a, and k. The logistic model for these data is P(t) = 680 / (1 + 4.126e^(-0.189t)).(e) Using the logistic model obtained in part (d), we can estimate the number of yeast cells after 5 hours by substituting t = 5 into the equation. Thus, P(5) = 680 / (1 + 4.126e^(-0.189(5))). Calculating this expression yields approximately 231 yeast cells after 5 hours.
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What is the value called that is small enough that anything
equal to or below it will allow you to rule out chance as the most
likely explanation? What are its typical values?
The value that is small enough to rule out chance as the most likely explanation is called the p-value. Typical p-values considered as statistically significant are 0.05 or lower.
The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true. If the p-value is below a predetermined significance level (often 0.05), it is considered statistically significant.
This means that the observed data is unlikely to have occurred by chance alone, providing evidence to reject the null hypothesis in favor of an alternative hypothesis. Lower p-values indicate stronger evidence against the null hypothesis.
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what is x - (14x-4) + 12 = 6x + 32
Answer:
x= -16/19
Step-by-step explanation:
x−14x+4+12=6x+32
−13x+16=6x+32
16=6x+32+13x
16=19x+32
16−32=19x
−16=19x
-16/19=x
A plane is in route to drop off much needed medical supplies to a town. At an altitude of 6.4 miles, it located the town airport at an angle of depression of 7.9 degrees. How many horizontal miles left does the plane need to travel? round to the nearest tenth of a mile.
Answer:
The horizontal distance is 46.1 miles.
Step-by-step explanation:
Here, the given question can be explained by the sides of a right angled triangle. Let x represent the horizontal miles, then applying an appropriate trigonometric function;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]7.9^{o}[/tex] = [tex]\frac{6.4}{x}[/tex]
0.1388 = [tex]\frac{6.4}{x}[/tex]
x = [tex]\frac{6.4}{0.1388}[/tex]
= 46.1095
x = 46.1 miles
The plane needs to travel a horizontal distance of 46.1 miles.