For the following right triangle, find the side length x. Round your answer to the nearest hundredth
Answers
The side length x of the given right angle triangle is: 14.97
How to use Pythagoras Theorem?When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.
According to the Pythagoras Theorem, the following equation can be written as:
x² = 18² - 10²
x = √224
x = 14.97
Thus, that is the missing length of the given right triangle
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Related Questions
need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
Answers
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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Write the equation of the line in slope-intercept form.
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/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}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]
Sally is putting her dominions back into their storage tin. She wants to know how many dominoes can fit in the tin. While placing the dominoes in the tin, she counts how many dominos can be stacked on top of each other and she finds that to be 3 dominoes. She counts how many can be set side-by-side and she finds that to be 9 dominoes. Finally she counts how many can be placed end-to-end in the tin and she finds that to be 4 dominoes. Sally knows she can use addition to figure out how many total dominoes fit in the tin. She also knows that 27 dominoes fit in one row in the tin when she stacks up as many as she can in that row. Write an expression using only addition to show how Sally can determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked
Answers
The expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is (Number of rows stacked ÷ 0.75) x (9 x 4)
Sally can use the fact that she can fit 3 dominoes stacked on top of each other, 9 dominoes side-by-side, and 4 dominoes end-to-end in the tin to figure out how many dominoes can fit in the tin. Since she knows that 27 dominoes fit in one row stacked, she can use addition to determine the total number of dominoes that can fit in the tin.
First, she can find the number of dominoes that can fit in one layer of the tin by multiplying the number of dominoes that fit side-by-side and the number that fit end-to-end: 9 x 4 = 36.
Then, she can divide the total number of dominoes that fit in one row (27) by the number of dominoes that can fit in one layer (36): 27 ÷ 36 = 0.75.
This means that each layer of the tin can hold 0.75 rows of dominoes.
To find the total number of dominoes that can fit in the tin, Sally can multiply the number of layers by the number of dominoes in each layer: Number of layers x Number of dominoes in each layer = Total number of dominoes that can fit in the tin.
Therefore, the expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is:
Total number of dominoes = Number of layers x Number of dominoes in each layer
Total number of dominoes = (Number of rows stacked ÷ 0.75) x (9 x 4)
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I been trying to figure this out but im bad with squares even though it sounds easy.
Answers
Answer:
13in :)
Step-by-step explanation:
KJASJDAJK its oki! The formula for the area of a square is Side x Side= Area, meaning you can just square root the area (since its a square all sides should be the same length) sqrt of 169 would give you 13!
Select the correct answer from each drop-down menu. A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11 The first equation of this system is y = x + 3. The second equation of this system is y = 3x − . The solution of the system is ( , ).
Answers
The first equation of this system is y = 2x + 3, the second equation is y = 3x - 1, and the solution of the system is (4, 11).
a) The first equation of this system can be found by using the points given in the first table. We can use the two points (-1, 1) and (0, 3) to find the equation of the line passing through them using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
The slope of the line passing through (-1, 1) and (0, 3) is (3-1)/(0-(-1)) = 2/1 = 2.
Substituting one of the points in the slope-intercept form, we get 1 = 2(-1) + b, which gives us b = 3. Therefore, the equation of the line is y = 2x + 3.
b) Similarly, we can use the points given in the second table to find the equation of the second line. Using the points (0, -1) and (2, 5), we get the slope as
(5-(-1))/(2-0)
= 6/2
= 3.
Substituting one of the points in the slope-intercept form, we get
-1 = 3(0) + b, which gives us b = -1.
Therefore, the equation of the second line is y = 3x - 1.
c) To find the solution of the system, we need to find the point of intersection of the two lines. We can do this by solving the two equations simultaneously.
Substituting the second equation in the first, we get:
2x + 3 = 3x - 1
Simplifying, we get x = 4.
Substituting x = 4 in either of the equations, we get y = 11. Therefore, the solution of the system is (4, 11).
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What type of transformation is modeled?
Answers
The type of transformation modeled in the graph is Reflection across y-axis.
How many different coordinate transformations are there?The three different kinds of coordinate transformation are listed below. The motor's three-phase current and voltage are transformed by the Clark transformation from their original natural coordinates to two-phase static coordinates determined with reference to the stator.
What is the transformational rule?Because the domain or range values of the function f(x) have changed, rules of transformations assist in changing f(x) to a new function f'(x). With the use of these transformational rules, the function can be stretched or compressed as well as transformed vertically or horizontally.
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Write a word problem to match -2.75>x
Answers
A word problem that matches the inequality -2.75 > x is:
John has a balance of $25 in his bank account and wants to withdraw some money and he needs to withdraw at least x dollars, but not more than $2.75.
How to write a word problem to match -2.75>x?A word problem that matches the inequality -2.75 > x is:
John has a balance of $25 in his bank account and wants to withdraw some money. He needs to withdraw at least x dollars, but not more than $2.75.
What is the largest possible value of x that John can withdraw and still have a positive balance in his account?
In this scenario, the variable x represents the amount that John can withdraw from his account, and the inequality -2.75 > x means that x must be less than -2.75 (i.e., negative and greater in magnitude than 2.75)
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A pair of standard dice are rolled. Find the
probability of rolling a sum of 3 with these dice.
Answers
To find the probability of rolling a sum of 3, we need to count the number of ways we can roll a sum of 3 and divide by the total number of possible outcomes.
The only ways to get a sum of 3 are by rolling a 1 on the first die and a 2 on the second die, or vice versa. There is only one way to roll each of these outcomes. Therefore, there are 2 ways to roll a sum of 3.
So the probability of rolling a sum of 3 is:
Probability of rolling a sum of 3 = Number of ways to roll a sum of 3 / Total number of possible outcomes
Probability of rolling a sum of 3 = 2 / 36
Probability of rolling a sum of 3 = 1 / 18
Therefore, the probability of rolling a sum of 3 with a pair of standard dice is 1/18 or approximately 0.056.
An annual depreciation rate is the percent that the value of an item decreases each year. A company purchases technology for $5,000. The company uses the function $r=1-\sqrt[3]{\frac{S}{5000}}$
to relate the annual depreciation rate $r$ (in decimal form) and the value $S$ (in dollars) of the technology after 3 years. Find $S$ when $r=0.15$ .
Answers
First, we can solve the equation $r=1-\sqrt[3]{\frac{S}{5000}}$ for $S$, to get:
$\sqrt[3]{\frac{S}{5000}} = 1-r$
Cubing both sides, we get:
$\frac{S}{5000} = (1-r)^3$
Multiplying both sides by 5000, we get:
$S = 5000(1-r)^3$
Now, we can substitute $r=0.15$ into this equation, to get:
$S = 5000(1-0.15)^3$
Simplifying:
$S = 5000(0.85)^3$
$S = 5000(0.614125)$
$S = 3070.63$
Therefore, the value of the technology after 3 years is $S = \$3070.63$.
Find the endpoints of the latus rectum of the parabola below.
(y - 1)? = 16(x + 1)
Answers
Answer:
(3, 9) and (3, -7)
Step-by-step explanation:
You want the end points of the latus rectum for the parabola defined by ...
(y -1)² = 16(x +1)
Vertex and scale factorCompare the given equation to the form ...
(y -k)² = 4p(x -h)
we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.
Latus rectumSince the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...
(h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)
__
Additional comment
If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).
On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).
I Need help pleaseeeeeee
Answers
Answer:
A
Step-by-step explanation:
according triangle inequality,
the sum of any two sides of a triangle is larger than the remaining side.
so a + b > c is correct
Marc conducted a gravity experiment for a school science project. He found the experimental value of gravity to be 10.14 m/s2. The accepted value of gravity is 9.81 m/s2. What is Marc’s approximate percent error?
Answers
Answer:
3.36%
Step-by-step explanation:
(10.14-9.81)/(9.81)(100)=3.36% error
What is the answer to (x^2)+(2x)-(5)=0
Answers
The solution to the given quadratic equation is [tex]=-1\pm \sqrt{6}[/tex]
What is a quadratic equation?A quadratic equation is an equation whose highest power is raised to the power of 2. Mathematically it is written in the form ax² + bx + c. There are many ways in which we can solve a quadratic equation such as:
FactoringQuadratic formulaCompleting the square methodFrom the given information, we have:
x² + 2x - 5 = 0
Using the quadratic formula method;
[tex]=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
here;
a = 1b = 2c = -5[tex]=\dfrac{-2\pm \sqrt{2^2-4(1)(-5)}}{2(1)}[/tex]
[tex]=\dfrac{-2\pm \sqrt{4+20}}{2}[/tex]
[tex]=\dfrac{-2\pm \sqrt{24}}{2}[/tex]
[tex]=\dfrac{-2\pm 2\sqrt{6}}{2}[/tex]
[tex]=-1\pm \sqrt{6}[/tex]
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Can you help me answer this question?
Answers
Step-by-step explanation:
The constant of proportionality is just the slope of the line
using 0,0 and 3,2 points
slope = (y1-y2 ) / ( x1-x2) = (0-3) / ( 0-2) = 3/2 = constant of proportionality
In 2010, the sea turtle population was twice the amount of turtles as in 2005. How many sea turtles were there in 2010?
Answers
Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.
Let x be the number of sea turtles in 2005.
According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.
We can set up an equation:
2x = number of sea turtles in 2010
We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.
Alejandro is learning how to play guitar. One day out of the week, he attends a 45-minute lesson. The remaining days of the week, he practices guitar for 25 minutes per day. What total number of minutes does Alejandro spend at his lesson and practicing in 3 weeks?
Answers
Answer:
3 x 195 = 585 minutes
Step-by-step explanation:
In one week, Alejandro attends a 45-minute lesson and practices for (6 x 25) = 150 minutes (assuming a 7-day week). So, the total number of minutes that Alejandro spends on his guitar in one week is:
45 + 150 = 195 minutes
In 3 weeks, the total number of minutes that Alejandro spends on his guitar is:
3 x 195 = 585 minutes
Therefore, Alejandro spends 585 minutes on his guitar in 3 weeks, including attending a 45-minute lesson once a week and practicing for 25 minutes on the remaining days of the week.
Answer: The mean absolute deviation is approximately is 11.43.
What is the measure (in radians) of central angle θ in the circle below?
Enter an exact expression. (in radians)
HELP NEEDED ASAP
Answers
The measure (in radians) of central angle θ in the circle below is π/3.
We have,
radius = 3 cm
Arc length = π
We can use the formula relating the arc length (s) to the central angle (θ) and radius (r) of a circle:
s = r Ф
Now,
π = 3 x Ф
Ф = π/3
Thus,
The measure (in radians) of central angle θ in the circle below is π/3.
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Add 2 1/3 + 4 5/8 writ your answer as a mixed number
Answers
Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.
The volume of the following square pyramid is
48^3. What is the length of 'l'? Round your answer to the nearest hundredth.
Answers
The length of 'l' is approximately equal to 331.13 units
Volume refers to the amount of space occupied by a three-dimensional object. In other words, it is the measure of how much space an object takes up.
The formula to calculate the volume of a square pyramid is:
Volume = (1/3) x Base Area x Height
where the base area is the area of the square base, and the height is the perpendicular distance from the apex to the base.
Let's substitute the given values in the formula and solve for the height:
48³ = (1/3) x l² x h
Multiplying both sides by 3, we get:
3 x 48³ = l² x h
Dividing both sides by l², we get:
h = (3 x 48³) / l²
Now, we can substitute the value of h in the original formula to get:
48³ = (1/3) x l² x [(3 x 48³) / l²]
Simplifying this equation, we get:
48³ = 48³
This equation is true, which means our solution is correct. Therefore, the length of 'l' is equal to the square root of (3 x 48³), which is approximately equal to 331.13 units (rounded to the nearest hundredth).
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 24x2 − 6xy − 2. The friends have already collected the following number of cans:
Jessa: 9x2
Tyree: 6x2 − 4
Ben: 4xy + 3
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
Answers
Therefore , the solution of the given problem of expressions comes out to be the buddies need to gather to reach their objective is
9x² - 10xy - 1.
What does an expression exactly mean?It is preferred to employ shifting numbers, which may also prove to be increasing, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.
Here,
Part A:
=> Jasmine: 9x²
=> 6x² - 4 for Tyree
=> Ben: 4xy + 3
These three phrases added together represent the total amount of canned food collected:
=> 9x² + (6x² - 4) + (4xy + 3)
=> 15x² + 4xy - 1
As a result, the expression for how many cans of food the three buddies have so far amassed is 15x² + 4xy - 1.
Part B's collection objective is 24x² - 6xy - 2.
Collection total: 15x² + 4xy - 1
The distinction between these two phrases shows the quantity of cans the buddies still need to gather:
=> (24x² - 6xy - 2) - (15x² + 4xy - 1)
=> 9x² - 10xy - 1
As a result, the phrase for how many more cans the buddies need to gather to reach their objective is 9x² - 10xy - 1.
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Do you use integration by parts to solve this problem? If so, how? I can't seem to figure out the right answer
Answers
The integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] is (2/3)[tex]e^{3/2}[/tex] - (4/9).
To find the integral of [tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] , we can use integration by parts. Let u = ln x and dv = [tex]x^{1/2}[/tex] dx. Then du/dx = 1/x and v = (2/3) [tex]x^{3/2}[/tex] .
Using the formula for integration by parts, we have:
∫[tex]x^{1/2}[/tex]lnx dx = uv - ∫v du/dx dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - ∫(2/3) [tex]x^{3/2}[/tex] * (1/x) dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (2/3) ∫ [tex]x^{1/2}[/tex] dx
= ln x * (2/3) [tex]x^{3/2}[/tex] - (4/9) [tex]x^{3/2}[/tex] + C
where C is the constant of integration.
To evaluate the definite integral from 1 to e, we substitute e for x in the expression above and subtract the result when x = 1:
[tex]\int\limits^e_1 {x^{1/2}lnx } \, dx[/tex] = [(2/3) [tex]e^{3/2}[/tex] ln e - (4/9) [tex]e^{3/2}[/tex] ] - [(2/3)[tex]1^{3/2}[/tex]ln 1 - (4/9)[tex]1^{3/2}[/tex]]
= (2/3) [tex]e^{3/2}[/tex] - (4/9)
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write 15 dollars and 95 cents as a mixed number (and then reduce)
Answers
Answer:
15 19/20
Step-by-step explanation:
95 cents means 95/100 then reduce that and you get 19/20 and then on the end you still have the $15
System of equations
2x + 3y = 4
3x + 5y = 7
10x + 15y = 20
-9x - 15y = -21
Find the solution of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
Enter the correct answer.
DONE
Answers
Answer:-₍1,3₎
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:
$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$
$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$
Adding the equations, we get:
$10x + 15y - 9x - 15y = 20 - 21$
Simplifying, we get:
$x = -1$
Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:
$2(-1) + 3y = 4$
Solving for $y$, we get:
$y = 2$
Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:
$3(-1) + 5(2) = 7$
$10(-1) + 15(2) = 20$
Both equations are true, so our solution is correct.
Game dice for a particular child’s game are numbered 1-10 what is the likehood of rolling a single one and ending up with an even number
Answers
Dice game for a particular child’s game are numbered 1-10. Then, the likelihood of rolling a single one and ending up with an even number is 1/20.
The probability of rolling a single one is 1/10, since there is only one die face with the number one out of ten possible outcomes.
The probability of rolling an even number is 5/10, since half of the die faces are even numbers (2, 4, 6, 8, 10) out of ten possible outcomes.
To find the likelihood of both events happening together, we need to multiply their individual probabilities;
P(rolling a single one and ending up with an even number) = P(rolling a single one) x P(ending up with an even number)
= (1/10) x (5/10)
= 1/20
Therefore, the likelihood of rolling a single one and ending up with an even number is 1/20.
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1. Bill scored the following number of points in a basketball games: 22, 18, 19, 16, 32, 24, 19, 20, 22 and 22
a. Box and Whisker plot:
b. What is the range:
c. Are there any outliers?
IQR:
Answers
b. The range is 32 - 16 = 16. and IQR 4
c. 32
how to find range?a. Here is a box and whisker plot to represent the given data:
The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.
b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.
c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.
The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:
IQR = Q3 - Q1
= 22 - 18
= 4
where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).
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i really don’t understand this so i would really appreciate help
Answers
Answer:
[tex]6\sqrt{2}+3\sqrt{10}[/tex]
Step-by-step explanation:
Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.
[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]
Simplify each square root part:
[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]
Since the square root parts are different, you cannot simplify any further.
What is the answer to this question pls
51°
4
109°
Answers
The length of unknown side is,
⇒ 4.92
We have to given that;
A triangle is shown in image.
Let the length of unknown side = x
Now, From trigonometry formula we get;
⇒ tan 51° = x / 4
⇒ 1.23 = x / 4
⇒ x = 1.23 × 4
⇒ x = 4.92
Thus, the length of unknown side is,
⇒ x = 4.92
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Mr. and Mrs. Tran hope to send their son to college in twelve years. How much money should they invest now at an interest rate of 8.5% per year, compounded continuously, in order to be able to contribute $9000 to his education?
Answers
$3988.71 should be invested by them to be able to contribute $9000 to his education.
We can use the continuous compound interest formula:
[tex]A = Pe^{(rt)[/tex]
where A is the future value, P is the present value, r is the interest rate, and t is the time in years.
We know that A = $9000, r = 0.085 (8.5% expressed as a decimal), and t = 12.
Solving for P, we get:
[tex]P = A / e^{(rt)}\\\\P = 9000 / e^{(0.085*12)}\\\\P = \$ \ 3988.71[/tex]
Therefore, Mr. and Mrs. Tran should invest approximately $3988.71 now in order to have $9000 in twelve years, assuming continuous compound interest at a rate of 8.5% per year.
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A research study indicated a negative linear relationship between two variables: the number of hours per week spent exercising (exercise time) and the number of seconds it takes to run one lap around a track (running time). Computer output from the study is shown below.
A figure of a computer output is shown. At the top is a table with two rows. The first row reads variable, N, mean, S E mean, and standard deviation. The second row reads running time, 11, 74.81, 2.21, and 7.33. Below this is a second table with three columns labeled predictor, coefficient, and S E coefficient. The first row reads constant, 88.01, and 0.49. The second row reads exercise time, negative 2.20, and 0.07. At the bottom it reads S equals 0.76 and R squared equals 99 percent.
Assuming that all conditions for inference are met, which of the following is an appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 ?
Answers
Answer:
The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.
The t-statistic for testing the slope coefficient is calculated as follows:
t = (b1 - 0) / SE(b1)
where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.
From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.
Therefore, the t-statistic is:
t = (-2.20 - 0) / 0.07 = -31.43
This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.
The 20 members of the photography club are trying to raise at least $1,400 for
new photography equipment. They have already raised $540.
Let m represent the amount of money each member must raise, on average, to meet
their goal. Write an expression for the total amount of money going to be raised.
b Write an equation that represents the club raising all the money.
с
Solve the equation. What does the solution mean in context of the scenario?
d Write an inequality representing the amount of money each member must raise,
on average, to meet or exceed their goal.
Write an inequality showing the possible average amount of money each club member
needs to raise.
Answers
Answer:
i dont know if this helps, im not sure if you are telling me to do all of these things or B, c, d are answer
Step-by-step explanation:
To find the total amount of money that the photography club will raise to meet their goal, we can multiply the average amount of money each member must raise by the number of members in the club:
Average amount of money each member must raise = m
Number of members in the club = 20
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = m x 20
We know that the club is trying to raise at least $1,400, and they have already raised $540. Therefore, the amount of money they still need to raise is:
Amount of money still needed to reach goal = $1,400 - $540
Amount of money still needed to reach goal = $860
We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money still needed to reach goal
m x 20 = $860
We can solve for "m" by dividing both sides of the equation by 20:
m = $860 / 20
m = $43
Therefore, the total amount of money the club will raise to meet their goal is:
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = $43 x 20
Total amount of money to be raised = $860
B))) We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money already raised + Amount of money still needed to reach goal
We know that the club has already raised $540 and they need to raise $860 more to reach their goal of $1,400. Therefore, we can substitute these values in the equation:
Total amount of money to be raised = $540 + $860
Total amount of money to be raised = $1,400
So the equation that represents the club raising all the money is:
$1,400 = $540 + $860
C)))) To solve the equation:
$1,400 = $540 + $860
We can simplify the right-hand side of the equation by adding $540 and $860:
$1,400 = $1,400
This equation is true, which means that it is a consistent equation. The solution to this equation is that the club will be able to raise all the money they need to buy the new photography equipment.
In the context of the scenario, the solution means that the club will be able to meet their goal of raising at least $1,400 for new photography equipment. They have already raised $540, and they need to raise $860 more to reach their goal. The equation shows that the total amount of money they will raise is exactly $1,400, which is the amount they need to meet their goal.
D))))) To represent the amount of money each member must raise, on average, to meet or exceed their goal, we can use the following inequality:
Average amount of money each member must raise ≥ Total amount of money still needed to reach goal / Number of members in the club
We know that the total amount of money still needed to reach the goal is $860, and there are 20 members in the club. Therefore, we can substitute these values in the inequality:
Average amount of money each member must raise ≥ $860 / 20
To simplify the right-hand side of the inequality, we can divide $860 by 20:
Average amount of money each member must raise ≥ $43
This inequality shows that each member must raise at least $43, on average, to meet or exceed their goal of raising $1,400.
To show the possible average amount of money each club member needs to raise, we can use the following inequality:
0 < Average amount of money each member must raise ≤ Total amount of money still needed to reach goal / Number of members in the club
This inequality shows that the average amount of money each member must raise is greater than 0 (since each member must contribute something), but it is less than or equal to $43 (which is the minimum amount each member must raise to meet or exceed their goal).
