Set up an equation and show all work to solve. Round final answers to the nearest hundredth.
Answers
The value of x in the right triangle is 10.43 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 the triangle is 180 degrees. Therefore, let's find the value of x in the right triangle.
tan 41 = opposite / adjacent
opposite side = x
adjacent side = 12
Therefore,
tan 41° = x / 12
cross multiply
x = 12 tan 41°
x = 12 × 0.86928673781
x = 10.4314408538
Therefore,
x = 10.43 units
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Related Questions
A savings account starts with $312.50. After 9 years of continuous compounding at an interest rate, r, the account has $1250.
What is the interest rate percentage?
Round the answer to the nearest hundredth.
Answers
The interest rate is approximately 15.14%.
What is compound interest?The interest yοu earn οn interest is knοwn as cοmpοund interest. Simple maths can be used tο demοnstrate this: if yοu have $100 and it earns 5% interest annually, yοu will have $105 at the end οf the first year.
We can use the fοrmula fοr cοmpοund interest:
[tex]A = P (1 + r/n)^{(nt)[/tex]
where:
A = final amount
P = initial principal (starting balance)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = time (in years)
Using the information given in the problem, we have:
P = $312.50
A = $1250
t = 9 years
Substituting these values into the formula, we get:
[tex]1250 = 312.50 (1 + r/n)^{(n*9)[/tex]
Dividing both sides by 312.50, we get:
[tex]4 = (1 + r/n)^{(n*9)[/tex]
Taking the ninth root of both sides, we get:
[tex](1 + r/n)^n = 1.167[/tex]
As n approaches infinity (continuous compounding), the left side of the equation approaches [tex]e^r[/tex], where e is the mathematical constant approximately equal to 2.71828. Therefore, we can rewrite the equation as:
[tex]e^r = 1.167[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(e^r) = ln(1.167)[/tex]
Using the property that [tex]ln(e^x) = x[/tex], we simplify the left side to:
r = ln(1.167)
Using a calculator, we find:
r ≈ 0.1514
Therefore, the interest rate is approximately 15.14%.
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Kings Park Water Works uses water meters that measure water usage in ccf. They charge $0.18 per ccf of water. If Jack's previous meter reading was 34,765 ccf and his present water reading is 36,900 ccf, what was his water bill
for the service period?
Answers
The water bill for the given service period is: $384.30
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Usually, the variable we will use represents an unknown quantity especially in a real-life scenario.
We are given the parameters as:
Jack's previous meter reading = 34,765 ccf
Jack's present water reading = 36,900 ccf
Cost per ccf of water
Difference in water reading = 36900 - 34765
Difference = 2135 ccf
Thus:
Water bill for service period = 0.18 * 2135
= $384.30
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The Triple L investment club is considering purchasing a certain stock. After considerable research, the club members determine that there is a 50% chance of making $9,000, a 10% chance of breaking even, and a 40% chance of losing $7,200. Find the expectation of this purchase.
Answers
Answer:
$1,620
Step-by-step explanation:
If you are looking for a way to make some money, you might be tempted by the offer of a purchase that has a positive expectation. But before you jump into it, you should know what expectation really means and how to calculate it. Expectation is not the same as the actual outcome of a purchase. It is just an average of what you can expect to get in the long run, based on the probabilities of different outcomes. Sometimes you might get more than the expectation, sometimes less, and sometimes nothing at all. For example, suppose you have a chance to buy a lottery ticket that costs $7,200 and has a 50% chance of winning $9,000, a 10% chance of winning nothing, and a 40% chance of losing your money. How do you know if this is a good deal or not? You can use the formula for expectation to find out:
Expectation = (50% x $9,000) + (10% x $0) + (40% x -$7,200)
Expectation = (0.5 x 9,000) + (0.1 x 0) + (0.4 x -7,200)
Expectation = 4,500 + 0 - 2,880
Expectation = 1,620
The expectation of this purchase is $1,620. This means that on average, you can expect to make $1,620 from this purchase in the long run. But this does not mean that you will always make $1,620 every time you buy the ticket. Sometimes you might win $9,000 and be very happy. Sometimes you might lose $7,200 and be very sad. And sometimes you might win nothing and be very bored. The expectation is just an average of all these possible outcomes.
So what does this mean for your decision? Well, it depends on how much you value risk and reward. If you are a risk-taker who likes to gamble and doesn't mind losing money sometimes, then you might go for the purchase with a positive expectation. After all, you have a chance to make more money than you spend in the long run. But if you are a risk-averse person who prefers to play it safe and avoid losses, then you might stay away from the purchase with a positive expectation. After all, you have a chance to lose money or break even in the short term.
The choice is yours. But remember: expectation is not reality. It is just a mathematical tool to help you evaluate your options. Don't let it fool you into thinking that you know what will happen in the future. The only thing that is certain is uncertainty, and luckily this is just Mathematics!
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧
1) The volume of a container varies jointly with the square of its radius, r, and its height, h. The container,
has a height of 12 centimeters, a radius of 7 centimeters, and a volume of 616 cubic centimeters. What is
the volume of a container to the nearest cubic centimeter with a radius of 5 centimeters and a height of 5
centimeters?
Answers
The required volume of the container to the nearest cubic centimeter with a radius of 5 centimeters and a height of 5 centimeters is approximately 131 cubic centimeters.
We are given that the volume of the container varies jointly with the square of its radius, r, and its height, h. This can be expressed mathematically as:
[tex]V = k * r^2 * h[/tex]
where V is the volume of the container, r is the radius, h is the height, and k is a constant of proportionality.
To find the value of k, we can use the given values for the height, radius, and volume of the container:
[tex]V = k * r^2 * h\\616 = k * 7^2 * 12\\k = 616 / (7^2 * 12)\\k = 1.047[/tex]
Now we can use this value of k to find the volume of a container with a radius of 5 cm and a height of 5 cm:
[tex]V = k * r^2 * hV = 0.708 * 5^2 * 5V = 130.875[/tex]
Therefore, the volume of the container to the nearest cubic centimeter with a radius of 5 centimeters and a height of 5 centimeters is approximately 131 cubic centimeters.
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Resolve 1-2x²/(x²+1)(x²+3x-2) to partial fraction
Answers
Let's first factorise the denominator of the given expression:
x²+1 can't be factorised any further, so let's work on the second factor:
x²+3x-2 = (x-1)(x+2)
Therefore, the denominator of the given expression becomes: (x²+1)(x-1)(x+2)
Now, let's assume that the expression is equal to a sum of two fractions:
1-2x²/(x²+1)(x-1)(x+2) = A/(x²+1) + B/(x-1) + C/(x+2)
Multiplying both sides by the denominator, we get:
1-2x² = A(x-1)(x+2) + B(x²+1)(x+2) + C(x²+1)(x-1)
Let's first put x=1 and solve for B:
1-2(1)² = B(1²+1)(1+2) + C(1²+1)(1-1)
1-2 = 4B
B = -1/2
Next, let's put x=-2 and solve for C:
1-2(-2)² = A(-2-1)(-2+2) + B((-2)²+1)((-2)+2) + C((-2)²+1)(-2-1)
1-8 = 15C
C = 7/-15
Finally, we can solve for A by putting x=0:
1-2(0)² = A(0-1)(0+2) + B((0)²+1)((0)+2) + C((0)²+1)(0-1)
1-0 = -2A + 2B - C
1 = -2A + 2(-1/2) - (7/15)
6/15 = -2A
A = -3/10
Therefore, the given expression can be resolved into partial fractions as:
1-2x²/(x²+1)(x-1)(x+2) = (-3/10)/(x²+1) + (-1/2)/(x-1) + (7/15)/(x+2)
I hope that helps!
A college savings fund is opened with a $12,000 deposit. The account earns 6.55% annual interest compounded continuously. What will the value of the account be in 18 years?
$26,704.29
$38,704.29
$27,013.46
$39,013.46
Answers
Answer:
Step-by-step explanation:
38,704.29
i hope its right
Given: F(x) = 3x 2+ 1, G(x) = 2x - 3, H(x) = x F(-2) =
Answers
Answer:
baljeet by 5x2
Step-by-step explanation:
A city currently has 139 streetlights. As part of a urban renewal program, the city council has decided to install 6 additional streetlights at the end of each week for the next 104 weeks. How many streetlights will the city have at the end of 48 weeks?
Answers
Answer:
Step-by-step explanation:
200.00 division ➗️ 66
Choose the TWO systems of equations that have no solution.
Responses
A 3x = 2 − 4y and 4y = 7 − 3x3x = 2 − 4y and 4y = 7 − 3x
B x + 2y = 10 and 2y = 6 + 5xx + 2y = 10 and 2y = 6 + 5x
C x = 8 − y and y = 6 + 5xx = 8 − y and y = 6 + 5x
D 3x + 2y = 5 and 2y = 6 − 3x3x
Answers
Answer:
Step-by-step explanation:
A because its graph
Graph the line passing through (-5,1) whose slope is m=-5/6
Answers
Answer:
Step-by-step explanation:
Let's find the equation of the line:
y - y1 = m(x - x1)
y - 1 = (-5/6)(x + 5)
y = -5/6x -25/6 + 1
y = -5/6 x - 19/6
So when x = 0, y = -19/6.
Now plot the 2 points (-5, 1) and (0, -19/6) and draw a line through them to graph the line.
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 50%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answers
Answer:
Equally Likely & Unlikely
Explanation:
If terriers make up 50% of the dog shelter that means the 50% that's left is split between the labradors and golden retrievers and the way they're split can be in any way so there's a way anyone can pick any kind of dog no matter the probabilities.
(Also go easy on me if I'm wrong, I'm only in 7th grade)
Lori buys a video game that costs $32 kate buys one that costs 20% more than loris how much does kates video game cost
Answers
Answer: Kate's video game costs $38.40.
Step-by-step explanation: Kate's video game costs 20% more than Lori's game, which means Kate's game costs $32 + (20% of $32) = $32 + $6.40 = $38.40. Therefore Kate's video game costs $38.40.
Kate's video game costs $38.40.
To find out, we can first calculate 20% of $32 to get the amount of the increase:
20% of $32 = 0.20 x $32 = $6.40
Then we can add that amount to the original cost of $32 to get Kate's total cost:
$32 + $6.40 = $38.40
May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
A 90° clockwise rotation around the origin is represented by the rule (x, y) → (y, -x). Which statement about perpendicular lines is not
true?
Answers
The statement that is not true about perpendicular lines is:
"Perpendicular lines are rotated 90° clockwise around the origin into lines that are parallel."
What are perpendicular lines?
Perpendicular lines are lines that intersect at a right angle (90 degrees).
A 90° clockwise rotation around the origin interchanges the x and y-coordinates and changes the sign of the new x-coordinate. So, if a point (x,y) is rotated 90° clockwise around the origin, it becomes the point (y,-x).
Now, let's consider the statement about perpendicular lines:
"Perpendicular lines are rotated 90° clockwise around the origin into lines that are still perpendicular."
This statement is actually true. A 90° clockwise rotation around the origin preserves the angle between two lines, so if two lines are perpendicular before the rotation, they will still be perpendicular after the rotation.
Therefore, the statement that is not true about perpendicular lines is:
"Perpendicular lines are rotated 90° clockwise around the origin into lines that are parallel."
This statement is false because a 90° clockwise rotation around the origin does not turn perpendicular lines into parallel lines. Instead, perpendicular lines are still perpendicular after the rotation, as mentioned above.
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The smaller circles are congruent. Find the area of the shaded region. Round your answer to the nearest hundredth.
Answers
Answer:
56.552 m²
Step-by-step explanation:
Recall the equation for the area of a circle;
A = πr²
r of smaller circles = 3m
r of larger circle = 3m x 2 = 6m
Area of each smaller circle: 28.274 m²
Area of the larger circle: 113.1 m²
To find the area of the shaded region, take the area of the larger circle - the area of the smaller circle(s).
113.1 m² - 2(28.274 m²) = 56.552 m²
Answer:
The area of the shaded region is 56.55 m² rounded to the nearest hundredth.
Step-by-step explanation:
From inspection of the given diagram, the radius of the two congruent unshaded circles is 3 m.
As the two congruent unshaded circles touch each other and touch the circumference of the larger circle, the radius of the larger circle is the diameter of one of the unshaded circles, i.e. 6 m.
To calculate the area of the shaded region, subtract the areas of the congruent unshaded circles from the area of the larger circle.
The formula for the area of a circle is πr², where r is the radius.
Therefore:
[tex]\begin{aligned}\textsf{Area of shaded region}&=\textsf{Area of larger circle}-2(\textsf{Area of unshaded circle})\\&=\pi \cdot 6^2-2(\pi \cdot 3^2)\\&=36\pi-2(9\pi)\\&=36\pi-18\pi\\&=18\pi\\&=56.5486677...\\&=56.55\;\sf m^2\;(nearest\;hundredth)\end{aligned}[/tex]
Therefore, the area of the shaded region is 56.55 m² rounded to the nearest hundredth.
(72x - 48y) - (61x + 27y)
Answers
Answer: 11x-75y
Step-by-step explanation: Hope this is what you're looking for.
Answer:
11x -75y
Step-by-step explanation:
To solve this problem you first have to distribute and simpify.
In this problem you have a -(61x+27y), the parentnesses and the - sign in front tells us you need to distribute the parentnessess. Doing this gives us an answer of -61x -27y.
The next step is to combine like terms and simiplfy.
[tex](72x-61x)+(-48y-27y)\\\\11x -75y[/tex]
So know we have our answer.
If an arc with a measure of 34 degrees has a length of 38pi inches, what is the circumference of the circle?
Answers
Answer:
None of these answers are correct
Step-by-step explanation:
arc length =0/360×2pir
38pi=34/360×2×pi×r
38=1496r/2520
cross multiply
1496r=38×2520
1496r=95760
divide both sides by 1496
1496r/1496=95760/1496
r=64.01
C=2pir
C=2×22/7×64.01
C=402.35in
Suppose that it costs $12 to place a classified advertisement in the newspaper, plus $4 for each line. Then the cost to place an ad x lines long is given by y dollars, where y equals 4 x plus 12. Express as an ordered pair the fact that a 5 line ad costs $32.
Answers
a 5 line ad costs $32. Expressing this as an ordered pair, we have (5, 32).
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
We are given that the cost of placing an ad x lines long is given by y = 4x + 12.
To find the cost of a 5 line ad, we can substitute x = 5 into the equation:
y = 4x + 12
y = 4(5) + 12
y = 20 + 12
y = 32
Therefore, a 5 line ad costs $32. Expressing this as an ordered pair, we have (5, 32).
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Find the measure of 4
Answers
Answer:
The measure of the angle is 22 degrees.
For the line y
4x + 2, create a table to
show the values of x and y where x is
between 1 and 3.
=
-
Answers
The table of values of the equation y = 4x + 2 is added below
Creating the table of valuesFrom the question, we have the following parameters that can be used in our computation:
y = 4x + 2
To create a table for the line y = 4x + 2 where x is between 1 and 3, we simply substitute values for x within the given range and solve for y.
x y
1 6
2 10
3 14
Therefore, when x is between 1 and 3, the corresponding values of y for the line y = 4x + 2 are 6, 10, and 14.
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ind the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.
μ=47 and σ=9; n=4
Answers
The standard deviation of the sampling distribution of sample means is 4.5.
What is standard deviation?
Standard deviation is a statistical measure that is used to quantify the amount of variability or dispersion of a set of data values around their mean or average. It is calculated as the square root of the variance, which is the average of the squared differences from the mean.
The standard deviation of the sampling distribution of sample means (also known as standard error) is given by:
σ/√n
where σ is the population standard deviation and n is the sample size.
Substituting the given values, we get:
9/√4 = 4.5
Therefore, the standard deviation of the sampling distribution of sample means is 4.5.
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Each of 350 guests will be served two chocolate-dipped strawberries. How many pounds of straw- berries should you purchase?
Answers
To serve two chocolate-dipped strawberries to each of the 350 guests, you should buy about 21.875 pounds of strawberries.
How many pounds of strawberries will I need to serve 700 people?There are some straightforward adjustments you need to make if your recipe calls for a pint of fresh strawberries. A pint weighs around 3/4 pounds . So, you would require about 525 pounds of strawberries to feed 700 visitors.
Assume that two strawberries covered in chocolate weigh 1 ounce each. One strawberry therefore weighs 1/2 ounce.
By dividing the weight of one strawberry by the total quantity of strawberries required, we can calculate the total weight of strawberries required:
Strawberries' total weight = (one strawberry's weight) x. (total number of strawberries needed)
Total strawberries required = (number of guests) x (number of strawberries per guest)
The total quantity of strawberries required is: Assuming that there will be 350 guests and that everyone will receive two chocolate-dipped strawberries:
350 multiplied by two equals 700 strawberries in total.
The total amount of strawberries required is thus:
350 ounces of strawberries total weight is (half an ounce each strawberry) multiplied by 700 strawberries.
Since there are 16 ounces in a pound, the total weight of strawberries must be divided by 16 to convert to pounds:
strawberries weigh 21.875 pounds total (350 ounces divided by 16 ounces per pound).
For each of the 350 guests to receive two chocolate-covered strawberries, you should buy about 21.875 pounds of strawberries.
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1. An acrobat is on a platform that is 25 feet in the air. She jumps down at an initial vertical velocity of 4 ft/s. Write a quadratic function to
represent the height h of the acrobat t seconds after the jump. If a safety net is placed 5 feet above the ground, how long will it take for her to land safely on the net?
Answers
Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:
t = 1 second.
To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:
[tex]h(t) = -16t^2 + vt + h0[/tex]
Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:
[tex]h(t) = -16t^2 + 4t + 25[/tex]
To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:
[tex]-16t^2 + 4t + 25 = 5[/tex]
Simplifying this equation, we get:
[tex]-16t^2 + 4t + 20 = 0[/tex]
Dividing both sides by -4, we get:
[tex]4t^2 - t - 5 = 0[/tex]
Now we can use the quadratic formula to solve for t:
[tex]t = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]
Where a = 4, b = -1, and c = -5. Plugging in these values, we get:
[tex]t = (1 ± \sqrt(1 + 4(4)(5))) / 8[/tex]
Simplifying this equation, we get:
[tex]t = (1 ± 9) / 8[/tex]
So, the two solutions are:
[tex]t = 1 and t = -5/4[/tex]
Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:
t = 1 second.
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Find the parametrization of C
Answers
The parametrization of C, given the line segment would be r(t) = (3t, 4t).
Using the parametrization to evaluate the expression gives 41.67.
How to find the parametrization ?To find the parametrization of the line segment from (0, 0) to (3, 4). We can use the following formula:
r(t) = (1 - t)A + tB, where A and B are the endpoints of the line segment, and t is the parameter ranging from 0 to 1.
A = (0, 0)
B = (3, 4)
r(t) = (1 - t)(0, 0) + t(3, 4)
r(t) = (3t, 4t)
Now, we have the parametrization of the line segment C: r(t) = (3t, 4t).
To evaluate the integral ∫_{C} (x² + y²) ds. We will need to calculate the derivative of r(t) with respect to t:
dr(t)/dt = (3, 4)
Now, find the magnitude of the derivative:
||dr(t)/dt|| = √(3² + 4²) = √(9 + 16) = √25 = 5
x² + y² = (3t)² + (4t)² = 9t² + 16t² = 25t²
Set up the integral:
∫_{C} (x² + y²) ds = ∫_{0}^{1} 25t²(5) dt = 125 ∫_{0}^{1} t² dt
Integrate with respect to t:
125 [t^3/3] |_{0}^{1} = 125(1/3 - 0) = 125/3
The value of the integral ∫_{C} (x² + y²) ds is 125/3.
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Write as a product
2xy^2-y-2x+y^3
Answers
With our solver, you can easily simplify complex algebraic expressions like 2xy^2-y-2x+y^3. Our state-of-the-art algorithm quickly identifies like-terms, combines them, and arrives at the simplified solution.
Whether you're a student struggling with your math homework or a professional looking to solve complex equations quickly and accurately, our solver is the perfect solution for you.
Say goodbye to long hours spent working through complex equations on paper, and hello to the future of mathematical expression solving. Try our ultimate expression solver today and see the difference it can make in your work!
A bookstore had 90 copies of a magazine. Yesterday , it sold 1/3 of them. Today, it sold 1/6 of what remained. How many copies does the bookstore have left?
Answers
A bookstore had 90 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/6 of what remained. The bookstore now has 50 copies left.
The problem involves figuring out how many copies of a magazine a bookshop still has after selling a certain percentage of its initial stock over two days. We can deal with the issue by taking the following actions:
Take into account the problem's estimate of the bookshop's initial stock of 90 copies.
Multiply the starting amount by 1/3 to get the number of copies sold yesterday by the bookshop, which is 30.
To determine the number of copies still available at the bookshop, which is 60, subtract the total number of copies sold from the number of copies sold yesterday.
Increase the excess number of duplicates by 1/6 to get the quantity of duplicates sold today at the bookshop.
The final number of copies available at the bookshop, 50, can be determined by subtracting the number of copies sold today from the number of copies that are still available.
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Solve for x show all work
log₂ (3x) + 4 log₁₂ (3)=0
Answers
log₂ (3x) + 4 log₁₂ (3) = 0
We can use the properties of logarithms to simplify and solve for x.
Property 1: logₐ (xy) = logₐ (x) + logₐ (y)
Property 2: logₐ (xⁿ) = n logₐ (x)
Applying Property 1 to the first term, we get:
log₂ (3x) + 4 log₁₂ (3) = log₂ (3) + log₂ (x) + 4 log₁₂ (3)
Now, we can apply Property 2 to the second term:
log₁₂ (3) = log₂ (3) / log₂ (12)
Substituting this back into the equation:
log₂ (3) + log₂ (x) + 4 (log₂ (3) / log₂ (12)) = 0
Now, we can combine the logarithms using Property 1:
log₂ (3x) + (1 + 4 (log₂ (3) / log₂ (12))) log₂ (3) = 0
Next, we can simplify the expression inside the parentheses:
1 + 4 (log₂ (3) / log₂ (12)) = 1 + (4 / log₂ (12)) log₂ (3)
Now, we can bring all the logarithms to one side of the equation and simplify further:
log₂ (3x) + (1 + (4 / log₂ (12)) log₂ (3)) = 0
log₂ (3x) + (1 + 0.3923 log₂ (3)) = 0 (approximating log₂ (12) to 3.5849)
Subtracting (1 + 0.3923 log₂ (3)) from both sides of the equation:
log₂ (3x) = -1 - 0.3923 log₂ (3)
Finally, we can eliminate the logarithm by exponentiating both sides with base 2:
2^(log₂ (3x)) = 2^(-1 - 0.3923 log₂ (3))
3x = 2^(-1) / 2^(-0.3923 log₂ (3))
3x = 1 / (2^(-0.3923 log₂ (3))) / 2
3x = 1 / (2^(-0.3923 log₂ (3) + 1))
Now, we can simplify the expression inside the parentheses:
3x = 1 / 2^(0.6077 log₂ (3) + 1)
Finally, we can rearrange the equation to solve for x:
x = 1 / (3 * 2^(0.6077 log₂ (3) + 1))
And that's the solution for x in the given equation.
Answer/Solution
x is x = 1/432.
Step-by-step explanation:
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solve 1/5y =10.62536263
Answers
Answer:
y = 53.12681315
Step-by-step explanation:
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A local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. The school board plans to construct a 90% confidence interval for the difference in proportions of households who would support starting the school year a week earlier. Are the conditions for inference met?
Yes, the conditions for inference are met.
No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met.
Answers
By answering the presented question, we may conclude that As a result, equation the area above the x-axis and below the curve t2 + 4t + 2, y = e-t with 0 t 2 is roughly 18.49 square units.
What is equation?A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.
[tex]t = (-4 ± √(4^2 - 412))/2*1\st = (-4 + √12)/2\st = (-4 + 2√3)/2\\t = (-4 + 2√3)/2 = -2 + √3\\[/tex]
We can now integrate the difference between the curve and the x-axis as t increases from 0 to 2:
[tex]Area = ∫[0,2] (e^-t - (t^2 + 4t + 2)) dt[/tex]
For the first term, we may use integration by parts to get:
[tex]Area equals [-e-t - 1/2(t2 + 4t + 2)2 + 2(t2 + 4t + 2)]\\Area = (-e^-2 - 1/2(18 + 16√3)^2 + 2(18 + 16√3)) - (-1 - 2) (-1 - 2)\\Area = -e^-2 + 17 + 16√3 ≈ 18.49[/tex]
As a result, the area above the x-axis and below the curve t2 + 4t + 2, y = e-t with 0 t 2 is roughly 18.49 square units.
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All the conditions for inference are met, and we can proceed with constructing a confidence interval for the difference in proportions.
What is statistical inference?The technique of assessing the outcome and drawing conclusions from data with random variation is known as statistical inference. Additionally known as inferential statistics. Applications of statistical inference include hypothesis testing and confidence intervals.
To check the conditions for inference, we need to verify the following:
1. Randomness condition: The problem states that both samples were selected randomly, so this condition is met.
2. Independence condition: Since each household is sampled independently from each other, this condition is met.
3. Large Counts Condition: We need to check if the sample sizes are large enough to use normal approximation. The expected counts for each category should be at least 10.
For households with school-aged children:
Sample size: n1 = 40Proportion of households in the sample who responded "yes": p1 = 38/40 = 0.95Expected count of households who responded "yes": n1p1 = 40*0.95 = 38For households without school-aged children:
Sample size: n2 = 45Proportion of households in the sample who responded "yes": p2 = 25/45 = 0.56Expected count of households who responded "yes": n2p2 = 45*0.56 = 25.2Since both expected counts are greater than 10, the Large Counts Condition is met.
Therefore, all the conditions for inference are met, and we can proceed with constructing a confidence interval for the difference in proportions.
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Out of 63 cars in a used car lot, 60 cars are either silver or have air
conditioning. There are 18 silver cars and 57 cars that have air
conditioning. What is the probability that a randomly selected car is
silver and has air conditioning?
Answers
The probability that a randomly selected car is silver and has air conditioning is 23.81%.
How to find the probability ?The probability that a car is silver and has air conditioning will take the form :
P( Silver ∩ Air conditioning ) = P(Silver ) + P(Air conditioning) - P(Silver ∪ Air conditioning)
The individual probabilities would be:
P (Silver ) = 18/63
P ( Air conditioning ) = 57/63
P (Silver ∪ Air conditioning) = 60/63
So then the probability is:
P( Silver ∩ Air conditioning ) = (18/63) + (57/63) - (60/63)
= (18 + 57 - 60)/63
= 15/63
= 5/21
= 23.81%
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-5u+6=-12u+62???????
Answers
Answer:
Step-by-step explanation:
[tex]-5u+6=-12u+62\\\textrm{Add }12u \textrm{ to both sides. }\\-5u+12u+6=-12u+12u+62\\7u+6=62\\\textrm{Subtract 6 from both sides.}\\7u+6-6=62-6\\7u=56\\\textrm{Divide both sides by}7.\\\frac{7u}{7}=\frac{56}{7}\\ u=8[/tex]
