The length of the leg of the 45-45-90 triangle is 6.
What is the hypotenuse?In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
In a 45-45-90 triangle, the length of each leg is equal to x, and the length of the hypotenuse is √2 times the length of a leg.
So if the hypotenuse is 6√2, then each leg has length:
x = (6√2)/√2 = 6
Hence, the length of the leg of the 45-45-90 triangle is 6.
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Upload the worksheet with your constructions below.
Answer:
hey! you can use it!!
Step-by-step explanation:
thanks
Mario & Luigi decide to invest in a Mushroom business, Mario invests $500,000 whilst Luigi invests $350,000. After their first year of business, they agree to split the profits within the same ratio of their initial investments. If the business made $3 million in profits, how much will Luigi receive?
a) a day
b) an hour
Amount Luigi received per day is $3,384.4 and Amount Luigi received per hour is about $141
What is Profit?Profit is the difference between the revenue that an economic entity has received from its outputs and the total cost of its inputs.
The amount Mario invests = $500,000
Amount Luigi invests = $350,000
The ratio in which the profit was split after their first year = Within the same ratio of their initial investments
The amount of profit made by the business = $3 million
The ratio of their initial investment = 500,000 : 350,000 = 10 : 7
Therefore, the ratio in which the profit is split = 10 : 7
The amount Luigi received in a year = (7/(10 + 7)) × 3 = 1235294 2/17
The time unit conversion from year to day is presented as follows;
Number of days in a year = 365 days
The amount Luigi received per day = (1235294 2/17)/365 = 3384 456/1241
= 3384.4
The amount Luigi received per day = $3,384.4
b) The number of hours in a day = 24 hours
Amount Luigi received per hour = (3384 456/1241)/24 = 141 19/1241
141 19/1241 = 141
The amount Luigi received per hour is about $141
Hence, amount Luigi received per day is $3,384.4
Amount Luigi received per hour is about $141
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How to convert 12in to mm?
The converted value of the 12inches to millimeters using scale factor is equal to ( 304.8 ) millimeters .
Units inch and millimeters both are the units used to measure length.Scale factor between inch and millimeter is equal to :One inch is equal to 25.4 millimeters
Now multiply both the side of the expression by 12 we get,
⇒ ( 12 × 1 ) inches = ( 12 × 25.4 ) millimeters
⇒ 12 inches = ( 304.8 ) millimeters
Therefore, using the scale factor of inches to millimeter the required 12 inches is equal to 304.8 millimeters.
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Ambers dinner bill is $36. 00 if amber leaves a 17% tip, how much tip will amber leave?
Answer:
$42.12
Step-by-step explanation:
if tip is 17% then she should pay 117% (this is 1.17)
$36 * 1.17 = $42.12
Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 9.
The volume of this solid is 18 cubic units.
This solid is a triangular prism with a triangular base and a height of 9 units. To calculate the volume of the solid, we can use the formula V=Bh, where B is the area of the base and h is the height. The base of the prism is a right triangle with sides of length 9, 9, and 6. We can use the Pythagorean Theorem to calculate the length of the hypotenuse of the triangle, which is equal to 12. We can then use the formula for the area of a triangle, A=1/2bh, to calculate the area of the base, which is equal to 27. We can then multiply this by the height, 9, to get the volume of the solid, which is 18 cubic units.
This solid is a triangular prism with a triangular base and a height of 9 units. To calculate the volume of the solid, we can use the formula V=Bh, where B is the area of the base and h is the height. The base of the prism is a right triangle with sides of length 9, 9, and 6.
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An average American consumes 75 liters of icecream in a year how many millimeters will 50 Americans consume in one week
I think I might have an answer to your question!
To convert liters to millimeters, we need to know the density of ice cream. The density of ice cream can vary depending on the type and composition of the ice cream.
According to a source, the density of ice cream is around 0.6 g/mL on average. Therefore, 1 liter of ice cream would weigh around 600 grams or 600,000 milligrams.
With this information, we can calculate the total amount of ice cream consumed by 50 Americans in one week as follows:First, we need to convert the annual consumption from liters to milliliters:
75 liters/year * 1000 milliliters/liter = 75,000 milliliters/year
Next, we need to calculate the amount consumed in one week by one American:
75,000 milliliters/year / 52 weeks/year / 1 American = 1,442 milliliters/week/American
Finally, we can calculate the amount consumed by 50 Americans in one week:
1,442 milliliters/week/American * 50 Americans = 72,100 milliliters/weekTherefore, 50 Americans will consume 72,100 milliliters of ice cream in one week.
Anita bought her phone one year ago for $400, and she wants to eventually sell it to help pay for an upgrade. She checked the manufacturer's website and found that her phone is currently valued at $308, and it will continue to depreciate each year.
Write an exponential equation in the form y - a(b)* that can model the value of Anita's phone, y, × years after purchase.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Answer:
y= 400(0.77)^x
Step-by-step explanation:
The value decreases by 23% from,400 to 308 in 1 year. so if this continues then the equation would be y=400(0.77)^x.
The 0.77 comes from decaying 23%, meaning 1-0.23 = 0.77
this is just a quick addition to the good reply above by "varnanaik"
so she bought it for 400 bucks, but hell a year later went down to 308? Let's find the rate of depreciation
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 308\\ P=\textit{initial amount}\dotfill &\$400\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases}[/tex]
[tex]308 = 400(1 - \frac{r}{100})^{1} \implies \cfrac{308}{400}=1-\cfrac{r}{100}\implies \cfrac{77}{100}=\cfrac{100-r}{100} \\\\\\ 77=100-r\implies r+77=100\implies r=\stackrel{ \% }{23} \\\\[-0.35em] ~\dotfill\\\\ A=400(1-\frac{23}{100})^x\implies A=400(1-0.23)^x\implies {\Large \begin{array}{llll} A=400(0.77)^x \end{array}}[/tex]
when can a correlation coefficient based on an observational study be used to support a claim of cause and effect?NeverWhen the correlation coefficient is close to -1 or +1.When the correlation coefficient is equal to -1 or +1.When the scatterplot of the data has little vertical variation.
A correlation between 0 and -1 or 0 and 1 indicates a weaker correlation, but still a statistically significant one.
A correlation coefficient based on an observational study can be used to support a claim of cause and effect when the correlation coefficient is statistically significant. This means that the correlation coefficient is so strong that it is unlikely to have happened by chance, and that there is likely a causal relationship between the two variables.
Mathematically, correlation coefficients are expressed as a number between -1 and 1.
A correlation coefficient of -1 indicates a perfectly negative correlation, where as one variable increases, the other decreases, and vice versa.
A correlation coefficient of 1 indicates a perfectly positive correlation where both variables move in the same direction.
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What is 68 weight in lbs?
The conversion of the weight 68 kg from Kilogram to lbs will be equal to 149.914 lbs.
The fundamental mass unit in the metric system is the kilogramme (kg). A kilogramme and 1,000 cubic centimetres of water have fairly similar masses.
One pound is approximately equal to 454 grams. One kilogram is the same as 2.20462 lbs.
One pound is equal to 0.45359237 kilograms.
To convert kilograms (kg) to pounds (lbs), you can use the following formula:
To convert kilograms to pounds, multiply your figure by 2.20462
To convert 68 kg to lbs, you can multiply 68 by 2.20462:
68 kg X 2.20462 lbs/kg
= 149.914 lbs
Therefore, 68 kg is equal to 149.914 lbs.
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The complete question may be:
What is 68 Kg weight in lbs?
Sergio had $500.00 saved for a family trip. Six weeks later he had saved $860.00. At what rate of change did Sergio savings grow
Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.
what is unitary method ?The component technique is a technique of troubles where you first calculate the worth of a single item, then multiply a certain value to get the answer. Simply defined, a single product value is extracted from either a specified multiple using the one method. For contrast, 40 pens will costs you 400 rs, or $1.01. The method used to execute this might be regulated. a solitary nation. anything seems to have a distinctive component. (Classic Algebra, Quantitative Analysis, Math and science of Matrix or Operators).
given
1% of $500 = $5
Total Saving from $500 to $ 860
860 / 5 = 172
Now percentage of growth :-
172/500 *100
17200/500 = 34.4
Hence, the rate of change Sergio savings = 34.4%
Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.
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The equation can be used to find q, the number of quarters equal to 60 dollars.
q over 4 equals 60
How many quarters are equal to 60 dollars?
Answer:
15
Step-by-step explanation:
q/4=60
Just divide 60 by 4. :)
The dimensions of a cone are shown in the diagram.
Which measurement is closest to the volume of the sugar cone in cubic inches?
the volume of the sugar cone is closest to 14.14 cubic inches.
How to determine?
The volume of a cone can be calculated using the formula V = (1/3)πr²2h, where r is the radius of the base, h is the height of the cone, and π is approximately 3.14.
In this case, the diameter of the cone is 3 inches, which means the radius, r, is half of that or 1.5 inches. The height of the cone is given as 6 inches.
Plugging these values into the formula, we get:
V = (1/3)π(1.5²2)(6)
V ≈ 14.14 cubic inches
Therefore, the volume of the sugar cone is closest to 14.14 cubic inches.
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A cylinder has a radius of 12 m and a height of 9 m. what is the exact volume of the cylinder? responses 108π m³ 108 pi, m³ 216π m³ 216 pi, m³ 972π m³ 972 pi, m³ 1296π m³
The volume of cylinder based on the dimensions of radius and height is 1296π m³.
The volume of cylinder can be calculated by the formula -
V = πr²h, where V refers to volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder.
Now, keeping the value of the dimensions in the formula to find the volume of cylinder.
V = π × 12² × 9
Taking square and performing multiplication on Right Hand Side of the equation
V = 1296π m³
Note that we have not kept the value of π in the formula to find the exact correct answer. Thus, the volume of 1296π m³.
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Big idea math (image)
Answer:
DB = approximately 16
Step-by-step explanation:
DEC is a right triangle => DC=10. Because all four sides are equal in a rhombus, then AD=AB=10. Then, because angle BAD is 53*2=106 degrees, we can use cosines. DB=sqrt(10^2+10^2-2*10*10cos(106deg))=15.9727102009.
what is definition of accuracy?
Answer: The fact of being correct and without any mistakes:
Step-by-step explanation: Hope this helps!
Identity the independent and dependent variables.
The equation y=12x+30 gives you the amount y (in dollars) in your savings account after x weeks. Please answer quickly!
The required in the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the equation y = 12x + 30, the independent variable is x, which represents the number of weeks. The dependent variable is y, which represents the amount of money in the savings account after x weeks.
The value of y depends on the value of x, so y is dependent on x. However, the value of x does not depend on the value of y, so x is independent.
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Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns $15 for each thirty-minute session and $25 for each sixty-minute session.
If she earned $230 this past weekend and had x thirty-minute sessions and x-2
sixty-minute sessions, what is the value of x?
daniel has read 80% of a book. He has more 8 pages to finish. How many pages are there in the book?
Using the percentage formula it is obtained that there are 40 number of pages in the book.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.
Let's use "x" to represent the total number of pages in the book.
According to the problem, Daniel has read 80 percentage of the book, which means he has read -
8/100 = 0.8x pages
He still has 8 pages left to finish, so we can set up an equation -
0.8x + 8 = x
Solving for x, we can subtract 0.8x from both sides -
0.8x + 8 - 0.8x = x - 0.8x
8 = 0.2x
Then, we can divide both sides by 0.2 to get -
x = 40
Therefore, there are 40 pages in the book.
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What do we mean by "LiFE"?
*
1 point
Taking choices that benefit the world on a microeconomic or macroecomomic level.
Taking choices that benefit the environment, whether on an individual, national or international level.
Striving towards establishing inclusive and resilient forums that are broad-minded.
Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.
Taking choices that benefit the world on a microeconomic or macroecomomic level.
Taking choices that benefit the environment, whether on an individual, national or international level.
Striving towards establishing inclusive and resilient forums that are broad-minded.
Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.
Which of the following is NOT a key feature of the function h(x)?
h of x equals the quantity x minus 5 end quantity squared when 0 is less than or equal to x is less than or equal to 4 and negative log base 4 of x plus 6 when x is greater than 4.
The domain of h(x) is [0, ∞).
The x-intercept of h(x) is (5, 0)
The y-intercept of h(x) is (0, 25).
The end behavior of h(x) is as x → ∞, h(x) → –∞.
The key feature that is NOT present in the function h(x) is "The x-intercept of h(x) is (5, 0)".
To find the x-intercept of a function, we need to set the y-value to 0 and solve for x. In the case of h(x), we have two different equations for different ranges of x:
h(x) = (x - 5)² when 0 ≤ x ≤ 4
h(x) = -log₄(x + 6) when x > 4
Setting the first equation to 0 and solving for x, we get:
0 = (x - 5)²
0 = x - 5
x = 5
However, this value of x does not fall within the range of 0 ≤ x ≤ 4, so it is not a valid x-intercept for this equation.
Setting the second equation to 0 and solving for x, we get:
0 = -log₄(x + 6)
log₄(x + 6) = 0
4⁰ = x + 6
1 = x + 6
x = -5
This value of x also does not fall within the range of x > 4, so it is not a valid x-intercept for this equation either.
Therefore, the function h(x) does not have an x-intercept of (5, 0), and this is the key feature that is NOT present in the function.
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Admission to Overjoy Amusement Park is $20 $ 20 per visit. However, with a season pass, which costs $40 $ 40 , each admission is $12 $ 12 . Complete the table and write a system of equations to represent the admission costs, where a is the number of admissions and c is the total cost. CLEAR CHECK Complete the table. Cost of Admission($ $ ) Number of Admissions Amount Spent on Season Pass($ $ ) Total Cost With season pass a c Without season pass a c Write a system of equations to represent this problem. With a season pass: Without a season pass:
Total cost with pass = $20a
Total cost without pass = $12a + 40
According to the information
We can write a system of equations for this problem,
Equation 1:
Cost with season pass = 12a + 40
Equation 2:
Cost without season pass = 20a
Therefore,
The system of equations that represents this problem is:
12a + 40 = c ...(i)
20a = c ...(ii)
Now making table for it:
Cost Number Amount Spent Total Cost With Total Cost Without
Ad. Ad. Pass ($) Season Pass Season Pass
20 a 0 20a + 0 20a
12 a 40 12a + 40 12a + 40
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Please solve this
the difference of twice a number and 6 is greater than -25. Write as an inequality
Answer:
x > -9.5
Step-by-step explanation:
2x - 6 > -25
2x > -19
x > -19/2
x > -9.5
$18 an hour is how much a year
The rate of $18 an hour will be approximately $157248 for a year .
In order to find how much $18 an hour is in a year,
We need to know how many hours are present in a year.
The number of weeks in 1 year is = 52 weeks ;
and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .
So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .
We get that 1 year consists of 8736 hours ,
Now , multiplying the number of hours by $18 ,
We get ,
⇒ 8736 × 18 = $157248 .
Therefore , $18 an hour will be $157248 for a year .
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pls help me
probability
2) The probability that in a cricket match, a batswoman did not hit a boundary, when she hits it 6 times out of 30 balls played, is 80%.
3) The probability of a family having:
i) 2 girls = 31.67%
ii) 1 girl = 54.27%
iii) No girl = 14.06%
iv) The sum of the probabilities = 1 or 100%
What is the probability?The probability refers to the likelihood that an expected event or outcome occurs when there are many possible outcomes.
We compute probability as the quotient of the the expected success and the total number of successes.
Probability lies between zero and one and is usually expressed as a decimal, fraction, or percentage.
2) Cricket Match:The number of boundary hits = 6
The total number of balls the batswoman played = 30
The probability that the batswoman did not hit a boundary = 1 - 6/30
= 0.8 or 80%.
The chance that the batswoman hit a boundary = 6/30 = 0.2 or 20%.
3) Girls in the Family:The total number of families with 2 children = 1,500
The number of families with 2 girls = 475
The number of families with 1 girl = 814
The number of families with 0 girl = 211
The probability of a family having:
i) 2 girls = 475/1,500 = 0.3167 or 31.67%
ii) 1 girl = 814/1,500 = 0.5427 or 54.27%
iii) No girl = 211/1,500 = 0.1406 = 14.06%
iv) The sum of the probabilities = 1 or 100%
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A fruit seller had 2520 apples and oranges. There were 2/3 as many apples as oranges. He threw some rotten apples away and the ratio of apples to oranges became 1 : 4. How many rotten apples did he throw away?
If the fruit seller threw some rotten apples away and the ratio of apples to oranges became 1 : 4. The fruit seller threw away 630 rotten apples.
To find the number of rotten apples that the fruit seller threw away, we will need to use the given information and set up equations to solve for the unknown variable.
Let's start by using the given information that there were 2/3 as many apples as oranges. We can set up an equation to represent this relationship:
2/3 O = A
Where O is the number of oranges and A is the number of apples.
We are also given that the fruit seller had 2520 apples and oranges in total. We can set up another equation to represent this relationship:
O + A = 2520
Now, we can use the first equation to solve for one of the variables in terms of the other. Let's solve for A in terms of O:
A = (2/3)O
Now we can substitute this expression for A into the second equation:
O + (2/3)O = 2520
Simplifying this equation gives us:
(5/3)O = 2520
Now we can solve for O:
O = (3/5)(2520) = 1512
Now that we know the number of oranges, we can use the first equation to solve for the number of apples:
A = (2/3)(1512) = 1008
So the fruit seller originally had 1008 apples and 1512 oranges.
We are also given that after throwing away some rotten apples, the ratio of apples to oranges became 1:4. We can set up an equation to represent this relationship:
(A - X)/O = 1/4
Where X is the number of rotten apples that were thrown away.
Substituting the values we found for A and O into this equation gives us:
(1008 - X)/1512 = 1/4
Cross-multiplying and simplifying gives us:
4(1008 - X) = 1512
4032 - 4X = 1512
4X = 2520
X = 630
Therefore, the answer to the question is 630.
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The graph linear function is shown on the coordinate grid what is the y-intercept of the graph of this function 4,8 -5 -7
The y-intercept of a linear function is the point at which the graph of the function crosses the y-axis. This point is represented by the coordinate (0, b), where b is the y-intercept.
In the given graph, we can see that the graph of the linear function crosses the y-axis at the point (0, -5). Therefore, the y-intercept of the graph of this function is -5.
To summarize, the y-intercept of the graph of this function is -5.
Answer: -5
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what teh awnser is plssssssssss
Interest earned on the cash balance in the bank is recorded by the bank as an increase in the depositor’s bank account.
What is the impact of interest earned?A savings account is a type of account that can be opened with a bank. Savings account earn interest based on the amount of money in their account at the end of the month.
here. we have.
The interest that is earned depends on the number of withdraws, interest rate paid on deposits and the amount deposited in the account. Deposits are recorded as a liability in the balance sheet of a bank. A liability is an obligation that has to be paid at sometime in the future.
This means that at the end of the month, the value of the money in the depositor's saving account increases by the value of interest paid.
For example, if the interest paid by a bank on deposits in a savings account is 10%. If an account has $1000 in the account, the value of the amount at the end of the month is 1,100 (1000 x 1.1).
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It is assumed that approximately 15% of adults in the US. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Why or why not? Choose the correct answer below ○ A. O B. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent. No, because the 30 adults represent more than 5% of the sample size, the trials are dependent No, because the 100 adults were selected without replacement, the selections are dependent. No, because the probability of being right-handed is greater, x must count the number of right-handed adults. C. O D.
D. No, because the probability of being left-handed is greater, x must count the number of left-handed adults.
The binomial probability formula can be used to calculate the probability of a certain number of successes (or left-handed individuals) in a given number of trials (100 adults). In order for the binomial probability formula to be used, the trials must be independent, meaning that the selection of one person does not affect the selection of the next one. Since the probability of being left-handed is greater, the binomial probability formula cannot be used in this case and x must count the number of left-handed adults.
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pls answer
The patch 2 is divided diognally into two triangles of equal areas.Tulips are planted in one triangular area.What is the area in which tulips are planted?
The area in which tulips are planted is 4247.625 square meters.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
To calculate the area of the triangle described as;
= 1/2 x length of the base segment x height of the triangle.
Given:
All the grass patches have equal areas.
From the diagram;
the shape of patch 2 is rectangular.
And the dimensions of the rectangle are 120.5 meters by 70.5 meters.
Two triangles of equal areas are formed by the division of patch 2 diagonally.
The area in which tulips are planted is,
= 1/2 x base x height
= 1/2 x 120.5 x 70.5
= 8495.25/2
= 4247.625 square meters.
Therefore, the area is 4247.625 square meters.
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How to convert 750 ml is how many ounces?
The value of volume 750 ml after converting to ounces is 25.36 ounces.
To convert 750 ml to ounces, we need to use a conversion factor. Knowing how to convert between ml and oz can help you accurately measure and mix ingredients for cooking, baking, or creating cocktails.
One fluid ounce is equal to 29.5735 milliliters. Therefore, we can multiply 750 ml by the conversion factor of 1/29.5735 to get the equivalent amount in ounces.
750 ml x (1/29.5735) = 25.36 oz
So, 750 ml is equal to 25.36 ounces.
This is a common conversion that you may encounter when dealing with liquids, especially in the United States, where ounces are the standard unit of measurement for volume.
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