Answer:
4x - 1 > 15
4x > 16
x > 4
The solution set is all numbers greater than 4.
y + 6 < 10 or 2y - 3> 9
Answer:
2y - 3> 9 it is not y + 6< 10
Carolyn is carpeting her front room.
Work out how much carpet she needs by working out the area.
She will also need skirting boards around the sides of the room. To measure the boards needed, calculate the perimeter.
Area:
Perimeter:
Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.
To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:
Area = length x width = 5 x 3 = 15 square units
To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:
Perimeter = 2(length + width) = 2(5 + 3) = 16 units
To learn more about area click on,
https://brainly.com/question/526179
#SPJ1
What is 0.08% written as a decimal?
Pam is visiting a historic town with an old-fashioned water well in the town square. She drops
a pebble into the well from a height of 27 feet above the surface of the water.
To the nearest tenth of a second, how long does it take for the pebble to hit the water?
Hint: Use the formula h = -16t² + 5.
seconds
The time taken for the pebble to hit the water is 1.41 seconds.
What is the time taken for the pebble to hit the water?The time taken for the pebble to hit the water is calculated by using the equation of the motion as follows;
h = -16t² + 5
where;
h is the height of fall during the motiont is the time of motionwhen the height is 27 ft, the time of motion is calculated as;
-27 = -16t² + 5
16t² = 5 + 27
16t² = 32
t² = 32/16
t² = 2
t = √2
t = 1.41 seconds
Thus, the time of motion is determined by applying the equation of motion as shown above.
Learn more about time of motion here: https://brainly.com/question/24739297
#SPJ1
all I need to know is the answer to E!!! DUE TOMORROW!!!
Answer:
Step-by-step explanation:
To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.
It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.
Factor completely:
[tex] {5x}^{2} + 14x - 3[/tex]
Answer:
[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]
Step-by-step explanation:
To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)
And add up to give the coefficient of x (which is 14).
These two numbers are 5 and 3. We can then rewrite the expression as follows:
[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].
Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]
Mario is training for a mile-long swim race. In the first week of training, he swims 3/5 three times, 9/10 two times and 23/25 two times . How many total miles did he swim in the first week of training?
To find out how many total miles Mario swam in the first week of training, we need to add up the distances he swam each time:
3/5 + 3/5 + 3/5 + 9/10 + 9/10 + 23/25 + 23/25
To add these fractions, we need to find a common denominator. The smallest common multiple of 5, 10, and 25 is 50.
3/5 = 30/50
9/10 = 45/50
23/25 = 46/50
Now we can add the fractions:
30/50 + 30/50 + 30/50 + 45/50 + 45/50 + 46/50 + 46/50
= (30 + 30 + 30 + 45 + 45 + 46 + 46)/50
= 272/50
= 5.44
Therefore, Mario swam a total of 5.44 miles in the first week of training.
Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of angle U = 41.83 degree.
In the given right angle triangle
VW = 6
UV = 9
Since sinΘ = (opposite side)/(hypotenuse)
Therefore,
sin U = VW/UV
= 6/9
= 0.667
Take inverse of sin both sides
∠U = arcsin(0.667)
= 41.83
Hence ∠U = 41.83 degree
To learn more about triangle visit:
brainly.com/question/1058720
#SPJ1
What are the domain and range of the function f(x) x^2 +8x+7 over x+1
Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).
The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.
Step-by-step explanation:
combine like terms 6x^2 - 10x + 21x - 35 = 6x^2 + 11x - 35
Answer:
Step-by-step explanation:
6x² - 10x + 21x - 35 = 6x² + 11x - 35
6x² - 6x² + 11x - 11x - 35 + 35 = 0
0 = 0
The equation is an identity. Its solution set is {all real numbers}.
Apply the nearest neighbor algorithm to the graph above starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDA
Starting at vertex A and using the nearest neighbor algorithm, the path is: A-C-B-D-A, with a total distance of 95. This means visiting vertices in the order A, C, B, D, and back to A, and the total distance traveled is 95 units.
The nearest neighbor algorithm is used to find the shortest path between a set of points. Here are the steps to apply the algorithm in this case
Start at vertex A. Look for the closest neighboring vertex to A. In this case, the closest vertex is B, which is 7 units away from A. Move to vertex B and mark it as visited. Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is C, which is 11 units away from B.
Move to vertex C and mark it as visited. Look for the closest neighboring vertex to C that has not been visited. In this case, the closest vertex is D, which is 18 units away from C. Move to vertex D and mark it as visited.
Look for the closest neighboring vertex to D that has not been visited. In this case, the closest vertex is B, which is 15 units away from D. Move to vertex B and mark it as visited.
Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is E, which is 20 units away from B. Move to vertex E and mark it as visited.
Look for the closest neighboring vertex to E that has not been visited. In this case, the closest vertex is A, which is 24 units away from E. Move to vertex A and mark it as visited. All vertices have been visited, so the algorithm is complete.
The list of vertices visited, starting and ending at A, is A, B, C, D, B, E, A and the distance is 95.
To know more about vertices:
https://brainly.com/question/14815086
#SPJ1
Which of the following sets of numbers could not represent the three sides of a right
triangle?
11, 60, 61}
{14, 48, 50
{46, 60, 75}
(39,80,89}
Answer: D
Step-by-step explanation: it equals 181
On October 12, 2020, the number of new cases of Covid 19 in Milwaukee was 235. On Oct. 22, 2020, the number of new cases in Milwaukee was 395.
a. Create an exponential model for new cases in terms of days.
b. Based on your model, what would be the number of new cases on Oct. 31, 2020?
c. The actual number of new cases on Oct. 31, 2020, was 1043. How well does this fit your model?
a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:
235 = a * b ^ 0
395 = a * b ^ 10
Solving for a and b, we get:
a = 235
b = (395/235)^(1/10) = 1.067
Therefore, the exponential model for new cases in Milwaukee is:
y = 235 * 1.067 ^ x
b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:
y = 235 * 1.067 ^ 19 = 1018.5
Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.
c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.
What number of hours corresponds to making $41
what are the answers to these questions?
The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
The total surface area of the can is therefore:
A = 2πr² + 2πrh
We know that the volume of the can is 810 cm³, which is given by:
V = πr²h
We can solve this equation for h to get:
h = V/(πr²)
Substituting this expression for height h into the equation for the surface area, we get:
A = 2πr² + 2πr(V/(πr²))
Simplifying, we get:
A = 2πr² + 2V/r
Now we have an equation for the surface area of the can in terms of the radius, r.
To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.
dA/dr = 4πr - 2V/r² = 0
Solving for radius r, we get:
[tex]r = (810/\pi)^1^/^3[/tex]
r=∛810/3.14
r=6.35 cm
Now find h:
h = 810/πr²
h=810/3.14×6.35²
h=810/126.6
h=6.39 cm
Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
100 POINTS!
Question:
Answer: the answer is f
Step-by-step explanation:
Answer:
answer is f
Step-by-step explanation:
Samantha gets paid $18.50 for each soccer game she referees. If she is a referee for 12 games and spends $59.99 for a new pair of cleats, how much money
does she have?
Answer:
$162.01
Step-by-step explanation:
amount of money she earns: 12($18.50) = $222
spends $59.99
amount of money after her purchase: $222-$59.99=$162.01
limit x->oo (sqrt(x^2-9x+1)-x)=?
I solved it up until -9x+1/((√x^2-9x+1)+x) but I don't know what to do after this.
Note that the limit of the expression as x approaches infinity is 1/2.
How did we arrive at this conclusion ?start by multiplying both the numerator and denominator by the conjugate expression
√ (x ² - 9x + 1) + x,
this will eliminates the root in the numerator
lim x->∞ [(√(x ² - 9x + 1) - x) * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)
Expanding the numerator
lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)
Simplifying further:
lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)
we can see that the 1/x ² term approaches zero, and the expression simplifies to
lim x->∞ [(1 - 0)] / (√(1 - 0) + 1)
= 1/2
So it is correct to state that the limit of the expression as x approaches infinity is 1/2.
Learn more about limit:
https://brainly.com/question/29795597
#SPJ1
Cami cut 17 1\2
inches off a rope that was 50 inches long. How is the length of the remaining rope in inches written in decimal form?
After Cami cut 17¹/₂ inches of a rope that was 50 inches long, the length of the remaining rope in inches, written in decimal form, is 32.5 inches.
How is the remaining length of the rope determined?To determine the remaining length of the rope, we apply subtraction operation.
However, since the cut rope was expressed in fractions, we can convert it to decimals before the subtraction.
The total length of the rope = 50 inches
The cut portion of the rope = 17¹/₂ inches
The remaining portion = 32¹/₂ inches or 32.5 inches (50 - 17¹/₂)
Thus, the remaining portion of the rope after Cami cut 17¹/₂ inches is 32.5 inches.
Learn more about fractions and decimals at https://brainly.com/question/29404890 and https://brainly.com/question/4721701.
#SPJ1
pls help me on algebra here is screenshot
Answer:
The answer to the question provided is option 2.
what principal will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021?
A principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
To calculate the interest earned by a principal at a given interest rate over a certain period of time, we use the following formula:
Interest = Principal x Rate x Time
In this case, we need to find the principal, so we can rearrange the formula as follows:
Principal = Interest / (Rate x Time)
First, we need to calculate the time period in years between February 4, 2021, and July 6, 2021.
February 4, 2021 to July 6, 2021 is 152 days or approximately 0.416 years (calculated as (July 6, 2021 - February 4, 2021) / 365).
Principal = 55.99 / (0.0975 x 0.416) = $1,380.89 (rounded to the nearest cent)
Therefore, a principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.
Learn more about Interest here
https://brainly.com/question/25845758
#SPJ1
real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged," meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.
Real-estate agent tested the effect of staging on home sale prices. Out of 10 comparable homes, 5 were staged. Staged homes sold for $15k more on average, with no skewness or outliers.
Based on the information given, the real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home.
The hypothesis is that empty homes sell for lower prices than staged homes. The agent randomly assigned 5 empty homes to be staged and obtained a list of 10 comparable homes.
The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. There was no strong skewness or outliers in the dot plots of the two samples.
To know more about standard deviation:
https://brainly.com/question/23907081
#SPJ1
Which choice is the correct graph of |x|< 3
The graph that shows the solution set for the given inequality is the one in option B.
Which one is the graph of the given inequality?Here we want to identify the graph of the inequality:
|x| ≤ 3
So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.
(We use closed circles because these values are also solutions for the inequality).
With that in mind, we can see that the correct option in this case will be graph B.
Learn more about inequalties at:
https://brainly.com/question/24372553
#SPJ1
Can someone help me solve this? I don’t quite understand
According to the graph, the function that best describes the graph is
[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).
As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.
While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.
And then the next line is moves downwards from the range of x whose value is greater than 6.
Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).
To know more about graph here
https://brainly.com/question/17267403
#SPJ1
PLEASE HELP WITH THE IMAGE!! DUE TOMORROW!!!
The calculations of the down payments, monthly income or payments are as follows:
Part 1:
Annual income = $226,000
Federal Tax = $62,582
State Tax = $16,385
Local Tax = $5,537
Healthcare = $4,520
Yearly income = $136,976
Monthly income = $11,414.67.
Part 2:
Down payment = $150,000
The amount to borrow (Mortgage loan) = $600,000
Estimated interest = $810,000
Total installment payments = $1,410,000
Monthly payment = $3,916.67.
Part 3:
Down payment = $2,902.50
Mortgage loan = $16,447.50
Estimated interest = $3,700.69
Interest + Mortgage loan = $20,148.19
Monthly payment = $335.80.
Part 1:
Annual income = $226,000
Federal Tax:
25% of $89,350 = $22,337.50
28% of $97,000 = $27,160.00
33% of $39,650 = $13,084.50
Total federal tax = $62,582
State Tax = 7.25% of $226,000 = $16,385
Local Tax = 2.45% of $226,000 = $5,537
Healthcare = 2% of $226,000 = $4,520
f) Total of Federal, State, Local, and Healthcare = $89,024
Yearly income = $136,976 ($226,000 - $89,024)
Monthly income = $11,414.67 ($136,976 ÷ 12)
Part 2:
a) House price = $750,000
b) Down payment = 20%
= $150,000 ($750,000 x 20%)
c) Mortgage loan = $600,000 ($750,000 - $150,000)
d) Interest rate = 4.5%
Number of mortgage years = 30 years
Mortgage period in months = 360 months (30 x 12)
Estimated interest = $810,000 ($600,000 x 4.5% x 30)
Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)
Monthly payment = $3,916.67 ($1,410,000 ÷ 360)
Part 3:
Price of car = $19,350
Down payment = 15%
= $2,902.50 ($19,350 x 15%)
Mortgage loan = $16,447.50 ($19,350 - $2,902.50)
Number of years = 5 years
Mortgage period in months = 60 months (5 x 12)
Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)
Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)
Monthly payment = $335.80 ($20,148.19 ÷ 60)
Learn more about down payments and monthly payments at https://brainly.com/question/29064552.
#SPJ1
I will give brainlyest
Determine if the relationship between x and y is linear or not linear. Explain.
Answer: To determine if the relationship between x and y is linear, we need to graph the data and look for a straight-line pattern.
If the graph shows a straight-line pattern, then the relationship is linear. If the graph shows a curve or a non-linear pattern, then the relationship is not linear. So it is linear
Step-by-step explanation: can i get brainliest :D
Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the table, find the probability that the person is or .
Note that the following probability as a simplified fraction and as a decimal is: 0.88617886178 and 109/123
How is this so?Note that the key phrase here is “given that this person is a man.”
This means that all we are interested in is the row labeled Male.
Married Never Div Widowed Total
Male 69 40 11 3 123
We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.
⇒ (69 + 40) / 123.
⇒ 109/123
or 0.886179
Learn more about probability at:
https://brainly.com/question/30034780
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
Express the following probability as a simplified fraction and a decimal.
if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.
Married Never Married Divorced Widowed Total
Male 69 40 11 3 123
Female 67 33 20 5 125
Total 136 73 31 8 248
Question 1.Express the probability as a simplified fraction
Romero Company has a target capital structure that consists of $3.3 million of debt capital, $3.5 million of preferred stock financing, and $4.3 million of common equity. The corresponding weights of its debt, preferred stock, and common equity financing that should be used to compute its weighted cost of capital (rounded to the nearest wo decimal places) are:
The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.
To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.
In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.
The weights for each component are calculated as follows:
Weight of debt = Market value of debt / Total market value of capital structure
= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.286 or 28.6%
Weight of preferred stock = Market value of preferred stock / Total market value of capital structure
= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.304 or 30.4%
Weight of common equity = Market value of common equity / Total market value of capital structure
= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)
= 0.410 or 41.0%
These weights can be used to calculate the weighted cost of capital for Romero Company.
To learn more about WACC click on,
https://brainly.com/question/12956302
#SPJ1
I have no idea how to solve this problem.
(a) The domain of f of g is {1, 8}.
(b) The range of f of g is {0, 1}.
What is the domain and range of f of g?The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.
(a) Domain of f of g:
The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.
To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.
(b) Range of f of g:
The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.
We have:
f(g(1)) = f(8) = 0
f(g(4)) = f(2) = 1
f(g(8)) = f(0) = 1
Therefore, the range of f of g is {0, 1}.
Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.
Learn more about domain here: https://brainly.com/question/26098895
#SPJ1
What’s the correct answer to problem 14?
The distance between the two lines is about 6/√17 units, which is approximately 1.46 units
To find the distance between two parallel lines, we need to find the length of the perpendicular segment that connects them.
Both lines have the same slope (4), so they are parallel and never intersect.
The shortest distance between them will be the perpendicular distance between any point on one line and the other line.
Let's choose a point on the first line, say (0, -1), and find the perpendicular distance from this point to the second line.
We can use the formula for the distance between a point (x₁, y₁) and a line in slope-intercept form y = mx + b:
Distance = |m(x₁) - y₁+ b| /√m² + 1
Plugging in the values for the second line, we get:
Distance = |4(0) - (-1) + 5| / √4² + 1
Distance = 6 / sqrt(17)
Therefore, the distance between the two lines is about 6/√17 units, which is approximately 1.46 units
To learn more on Distance click:
https://brainly.com/question/15172156
#SPJ1