Solving the equation: x - 1/x = 15/13
We will see that the value of x is 28/13
How to find the number?For a number x, we define the reciprocal number as 1/x.
We know that the difference between theses two is 15/13, then we can write:
x - 1/x = 15/13
(x² - x)/x = 15/13
(x² - x) = (15/13)*x
x² - x - (15/13)*x = 0
x² - (1 + 15/13)*x = 0
x² - (28/13)*x = 0
x*(x - 28/13) = 0
x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.
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What is the area of this figure?
The area of the figure is given as follows:
100.56 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 4 mm and 12 mm.Rectangle of dimensions 2 mm and 7 mm.Rectangle of dimensions 4 mm and 12 - 7 = 5 mm.Rectangle of dimensions 3 mm and 2 mm.Semicircle of radius 2 mm.The areas for each region are given as follows:
Rectangle of dimensions 4 mm and 12 mm -> 4 x 12 = 48 mm²Rectangle of dimensions 2 mm and 7 mm -> 2 x 7 = 14 mm².Rectangle of dimensions 4 mm and 12 - 7 = 5 mm -> 4 x 5 = 20 mm².Rectangle of dimensions 3 mm and 2 mm -> 3 x 2 = 6 mm².Semicircle of radius 2 mm -> 3.14 x 2² = 12.56 mm².Hence the total area is of:
48 + 14 + 20 + 6 + 12.56 = 100.56 mm².
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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)
The function [tex]f(x) = 4x^3 - 4[/tex] is a polynomial function. It takes an input value x and returns an output value f(x) based on the expression [tex]4x^3 - 4.[/tex]So the value of f(-1/2) is -4.5.
When we evaluate f(-1/2), we substitute -1/2 for x in the expression for f(x). This gives us:
[tex]f(-1/2) = 4(-1/2)^3 - 4[/tex]
The expression inside the parentheses, [tex](-1/2)^3,\\[/tex] is the cube of -1/2. To simplify this expression, we need to first raise -1/2 to the power of 3:
[tex](-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8[/tex]
Next, we substitute this value back into the expression for f(-1/2):
f(-1/2) = 4(-1/8) - 4
Now we can simplify the expression by multiplying 4 and -1/8:
f(-1/2) = -1/2 - 4
Finally, we subtract 4 from -1/2 to get the final answer:
f(-1/2) = -4.5
So the value of f(-1/2) is -4.5.
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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)?
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.
The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:
d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]
The vector equation of the line segment can be written as:
r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]
where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.
The parametric equations of the line segment are:
x(t) = t/2
y(t) = -4 + 5t/3
z(t) = 4 - 3t/4
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Find a vector equation and parametric equations for the line segment that joins P to Q?
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
Look at the expression and fill in the correct number in each blank.
The given expression has
term(s) with
1,500(1+1)*
factors.
The expression has 3 terms and 3 factors
What are the terms of the equationThe terms are the constant, the r term and the t term
The factors that are in the equation are 1500, 1 and 12
What is an exponential equation?An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.
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Find the length of the unknown side of the triangle.
10 ft
5 ft
The length of the unknown side of the triangle is?
The length of the unknown side is 11.2ft
How to determine the valueUsing the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.
From the image shown,we have the parameters as;
Hypotenuse = xOpposite side = 10ftAdjacent side = 5ftNow, substitute the values, we have;
x² = 10² + 5²
Find the squares
x² = 100 + 25
Add the values
x ² = 125
Find the square root
x = 11.2 ft
Hence, the value is 11.2ft
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20x - 30y = -50
-2y-x = -1
Please step by step
6x + 24/5x - 35 times 9x - 63/7x + 28 rational expression
Answer:
Step-by-step explanation:
6(x + 4)/5(x - 7) * 9(x - 7)/7(x + 4) =
Cancel the x + 4 and x - 7
54/35
which expressions will have a positive answer? assume all variables represent numbers larger than zero (select all that apply)
Answer:
bro do u have a pic i will give u your points back but i need a pic to help
Step-by-step explanation:
PQRS is a trapezium, and AB ∥ PS ∥QR. If PA = 3 cm, AQ = 1.4 cm, BR = 2.1 cm,
then SB =
Answer:
In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:
SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm
there are 30 people in a classroom. ignoring the potential of a leap-year birthday (so 365 days), what is the probability that at least one pair of people have the same birthday?
The probability that at least one pair of people have the same birthday, with 30 people in a classroom is approximately 0.7063.
To solve this problem, we can use the concept of the complement of an event. The complement of the event "at least one pair of people have the same birthday" is the event "no pair of people have the same birthday." So, we can find the probability of this complement event and subtract it from 1 to get the probability of the original event.
The probability that the first person has a unique birthday is 1, since there are no other people in the room yet. The probability that the second person also has a unique birthday is (364/365), since there are 364 remaining days in the year that they could be born on.
Similarly, the probability that the third person has a unique birthday is (363/365), and so on, down to the 30th person, whose probability of having a unique birthday is (336/365).
To find the probability that no pair of people have the same birthday, we can multiply these probabilities together:
P(no pair share a birthday) = 1 * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937
Therefore, the probability that at least one pair of people have the same birthday is:
P(at least one pair share a birthday) = 1 - P(no pair share a birthday) ≈ 1 - 0.2937 = 0.7063
So the probability that at least one pair of people have the same birthday is approximately 0.7063, which is quite high. This is known as the birthday problem or birthday paradox.
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Today a typical family of four spends $897. 20/ month for food. If inflation occurs at the rate of 4%/ year over the next 9 years, how much should the typical family of four expect to spend for food 9 years from now?
In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.
In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.
To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:
Future value = Present value * (1 + inflation rate)^n
where:
Present value = $897.20/month
Inflation rate = 4% per year
n = number of years
When we substitute the specified values, we get:
Future value = $897.20 * [tex](1 + 0.04)^9[/tex]
= $897.20 * 1.3981
= $1254.77 (to two decimal places in rounding)
Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.
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Someone quick help me with this please?
Answer:
Not equal and Congruent should be your answers
Answer these two questions, I am having difficulty understanding. Explanation would be nice but it is not required. Spam answers will be reported.
The amount of money that is take home pay would be = $3,491.91
The amount of money that is your fix expenses would be = $1,257.09
How to calculate the amount of money for fixed expenses?The amount of money that you make each month = $3,764.82.
The percentage of deduction made for FICA = 7.25%
That is;
= 7.25/100 × 3,764.82/1
= 27294.945/100
= $272.91
Therefore, the take home pay ;
= $3,764.82-$272.91
= $3,491.91
The percentage of the fixed expenses = 36% of the realised income.
That is, 36/100 × 3,491.91/1
= 125708.76/100
= $1,257.09.
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your three circles may not have intersected exactly at a single point. how could you improve your results
Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.
The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.
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What is the value of F?
In a recent school newspaper survey, 3,000 randomly selected teenagers were asked to cite their primary transportation method to school. Fifteen of 20 teenagers said they use their own car to get to school. A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093). Which of the following is a correct interpretation of the confidence level?
Ninety percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who drive their own car to school.
Ninety percent of all samples of this size would yield a confidence interval of (0.5907, 0.9093).
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
Ninety percent of all the samples of size 3,000 lie in the confidence interval (0.5907, 0.9093).
The correct interpretation of the 90% confidence interval is given as follows:
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
What is the interpretation of a x% confidence interval?It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.
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If the scale factor of figure A to figure B is 3:8 find the value of x
If the scale factor of figure A to figure B is 3:8, the value of x is 9.
We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -
3/8 = x/24
Applying the cross-multiplication rule, we get,
3 * 24 = 8 * x
Further solving for the value of x, we get,
x = (3 * 24) / 8
x = 9
Hence, the value of x is 9.
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The complete question is -
If the scale factor of figure A to figure B is 3:8 find the value of x.
Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6.25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent.
Answer: To determine the amount in Heidi's 401(k) account after 15 years, we need to calculate her total contribution each month and the interest earned on that contribution over the 15-year period.
First, let's calculate Heidi's contribution each month:
11% of $3,250 = $357.50
Next, let's calculate her employer's contribution each month:
6% of $3,250 = $195
Since Heidi's contribution is $357.50, and her employer matches her contribution up to 6% of her salary, her employer will contribute $195 each month.
So, Heidi's total contribution each month is $357.50 + $195 = $552.50
Next, we can use the formula for compound interest to calculate the balance in her 401(k) account after 15 years:
A = P * (1 + r/n)^(nt)
where:
A is the balance in the account after t years
P is the principal (initial deposit)
r is the interest rate
n is the number of times the interest is compounded in a year
t is the number of years
In this case, n = 12 (because interest is compounded monthly) and t = 15 (because the calculation is for 15 years). The principal P is $552.50 (Heidi's total contribution each month). The interest rate r is 6.25%.
Plugging in the values, we get:
A = $552.50 * (1 + 0.0625/12)^(12 * 15) = $552.50 * (1.00520833)^180
Using a calculator or spreadsheet software, we can calculate this value to be approximately $27,973.81.
So, the amount in Heidi's 401(k) account after 15 years, rounded to the nearest cent, is $27,973.81.
Step-by-step explanation:
What is the area of this compound figure? PLEASE HELP
The area of the composite figure is equal to 254 m² square metres.
How to calculate for the area of the figureThe composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:
area of the vertical rectangle = 19 m × 7 m
area of the vertical rectangle = 133 m²
area of the square = 5 m × 5 m
area of the square = 25 m²
area of the horizontal rectangle = 16 m × 6 m
area of the horizontal rectangle = 96 m²
total area of the composite figure = 133 m² + 25 m² + 96 m²
total area of the composite figure = 254 m²
Therefore, the area of the composite figure is equal to 254 m² square metres.
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Help please it´s urgent
Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
Answer: E
Step-by-step explanation:
The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.
Find the value of each variable show proofs
The sides of the right triangle are as follows:
x = 18 units
y = 15.6 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the sides of the right triangle using trigonometric ratios
tan 30° = opposite / adjacent
tan 30° = 9 / y
cross multiply
y = 9 / tan 30
y = 15.5884645362
y = 15.6 units
Let's find x
sin 30 = opposite / hypotenuse
sin 30° = 9 / x
x = 9 / 0.5
x = 18 units
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Write a polynomial for the area of the shaded region.
The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
19. The area is given as,
A = (x + 5)(3x)
A = 3x² + 15x
19. The area is given as,
A = (x + 4)(x + 2)
A = x² + 6x + 8
The polynomial for the shaded area will be 3x² + 15x and x² + 6x + 8.
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On the windowsill is a plant that is 3 inches tall. It is growing 4 inches per week. A second plant, which is 17 inches tall, is on the coffee table. It is growing 2 inches per week. Eventually the two plants will be the same height. How many weeks will that take? How tall will the plants be?
The two plants would have the same height in 7 weeks and the height would be 31 inches.
When would the plants have the same height?The form of the expression that represents the length of the plant on the window sill is:
initial length + (length of growth per week x number of weeks)
3 + (4 x w)
3 + 4w
The form of the expression that represents the length of the plant on the coffee table is:
initial length + (length of growth per week x number of weeks)
17 + (2 x w)
17 + 2w
When the two plants have the same height, the two expressions would be equal:
17 + 2w = 3 + 4w
17 - 3 = 4w - 2w
14 = 2w
w = 14/2
w = 7 weeks
Height of the plant = 3 + 4(7)
3 + 28 = 31 inches
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Which of the following statements about f(x)= -(x-4)² -1 are true? Select all that apply.
a) Vertex: (4, -1)
b) y-intercept: (0, -17)
c) x-intercept: (5, 0)
d) Axis of Symmetry: x = 4
e) x-intercept: (3, 0)
f) no x-intercepts
The following statements are true about the function f(x) = -( x-4) ² -1
1. The y intercept is (0,-17)
2. The axis of symmetry x = 4
3. The x intercept is (3,0)
What are quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.
The equation f(x) = -(x-4)² -1 can be expanded as
f(x) = -x²+8x-16-1 = -x²+8x-17
therefore when x = 0
the y-intercept = -17
therefore the y intercept = (0,-17)
The x intercept of the function,
when y = f(x) and y = 0
-(x-4)² = 1
-(x-4) = 1
-x+4 = 1
-x = -3
x = 3
the x intercept of the function is (3,0)
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I NEED HELP ON THIS ASAP!!!!
Answer: Look below :)
Step-by-step explanation:
Hello again Sarah!
a. the dashed line indicated our answer will use > or <
furthermore, we can see two points, (0,2) and (1,6) on the graph.
So the slope is: 4/1 = 4
and the y intercept can be visually seen as 2
Since the shaded part is to the right, we will use <
The final equation is: y < 4x + 2
I wont show working for the others, but its pretty similar:
b. [tex]y \geq 0.5x - 3[/tex]
c. y < 0.75x - 2
Shade ______ line
for greater than (>).
[tex]above \: the \: line[/tex]
Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~
Now, put the value of x in each of the choices provided to check if its equal to 8.
[tex]\qquad \sf \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) = 8.1632[/tex]
[tex]\qquad \sf \dashrightarrow \: p( - 2) \approx 8[/tex]
Since the value satisfy the first equation, the correct choice will be (A)
What is the measurement of this angle? 60 degrees 120 degrees
The measure of angle DBC is 60 degrees
Any triangle's three angles always sum to 180 degrees. Therefore, if you only have two angles available, add them up, and then take 180 away from the result.
The computation of the measure of angle ABC is shown below:
Given that
Angle ABC is 120 degrees
And, the measure of angle BAC is 60 degrees
So based on the above information
The measure of angle is
= Angle ABC - Angle ABD
= 120 degrees - 60 degrees
= 60 degrees
hence, the measure of angle DBC is 60 degrees
Q - Angle ABC is equal to 120 degrees. The measure of angle ABD is 60 degrees. What is the measure of angle DBC?
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in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the ___________ come from a normal distribution.
The answer to the given fill in the blanks is "Residual". in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the Residual come from a normal distribution.
In linear regression, we make several assumptions about the relationship between the predictor variable and the response variable. One of these assumptions is that the residuals (the differences between the predicted values and the actual values) follow a normal distribution with a mean of zero and constant variance. To check this assumption, we can create a normal quantile plot of the residuals. A normal quantile plot is a graphical method that compares the distribution of the residuals to a normal distribution. If the residuals are normally distributed, the plot should follow a straight line. If the plot deviates from a straight line, it suggests that the residuals are not normally distributed. A non-normal distribution of residuals can have several implications, such as indicating the presence of outliers or influencing the accuracy of the model’s prediction. Therefore, checking for normality of residuals is a crucial step in evaluating the model's assumptions and determining whether the model is appropriate for the data.
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The blood platelet count of a group of women have bell-shaped distribution with a mean of 245.5 and a standard deviation of 68.2 (all units are 1000 cells/ L) Using the empirical rule, fill in the blanks below (Round to the nearest hundredth):
a. Approximately 95% of healthy women in this group
b. Approximately 99.7% of healthy women in this have blood platelet counts between
group have blood platelet counts between
and(1000 cells/ ML). and (1000 cells/ ML).
The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8
The given parameters are:
μ = 248.5
[tex]\sigma = 61.1\\[/tex]
(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7
Start by calculating the z-score, when x = 126.3 and x = 370.7
[tex]Z = \frac{(x-u)}{\sigma}[/tex]
So, we have:
x = -2
Also,
x = 2
The empirical rule states that:
Approximately 95% of the data lies within 2 standard deviations of the mean.
Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.
(b) The percentage with platelet count between 65.2 and 431.8
Start by calculating the z-score, when x = 65.2 and x = 431.8
So, we have:
Z =-3
Also:
Z = 3
The empirical rule states that:
Approximately 99.7% of the data lies within 3 standard deviations of the mean.
Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8
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