Victor bought 10 packages of the largest-grain sandpaper.
What does "spent 50 balance 51" mean?Total money spent (20+15+9+6) = 50; total money left over (30+15+6+0) = 51. Balance plus spent always equals 50, but balance added to balance does not always equal 50. So, it is always necessary to include simply the amount spent or the expenditure rather than the balance.
Thus, we know how much he spent:
2S + (61 - 2S) = 61 - S
$1 on sandpaper with the biggest grit. We can condense this phrase as follows:
61 - S = 61 - 2S
Adding S to both sides, we get:
S = 0
Then we know that he spent:
2L + Ly = 61
Spending money on sandpaper. Additionally, since he purchased two packages of the finest sandpaper, the price of those two packages is:2S = 2L
We can substitute 2L for 2S in the first equation:
2L + Ly = 61
Simplifying, we get:
2L + L(2/3)L = 61
Multiplying both sides by 3/2, we get:
3L² = 91.5
Taking the square root of both sides, we get:
L ≈ 5.27
determine how many packages of the coarsest sandpaper Victor purchased:
2L + Ly = 61
2(5.27) + 5.27y = 61
10.54 + 5.27y = 61
5.27y = 50.46
y ≈ 9.56
Rounding to the nearest whole number, we get:
y = 10
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I NEED HELP ON THIS ASAP!!!
The system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
What is system of inequalities?A group of two or more linear inequalities are grouped together and graphed on a coordinate plane to discover the solution that concurrently solves all of the inequalities. Each inequality forms a half-plane on the coordinate plane, and the location where all the half-planes overlap is where the system is solved. Each point inside the feasible area meets all of the system's inequalities. This region is known as the feasible region. To identify the optimum solution given a set of constraints, systems of linear inequalities are frequently utilised in optimization issues.
Let us suppose the number of boards of Mahagony sold = x.
Let us suppose the number of black walnut boards sold = y.
According to the given problem the equation can be set as follows:
x ≤ 260 (the company has 260 boards of mahogany available)
y ≤ 320 (the company has 320 boards of black walnut available)
x + y ≤ 360 (the company expects to sell at most 360 boards of wood)
Hence, the system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
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Mrs. Perez's class donated 99 different products for the food drive. One-ninth of it was vegetables,2/3 pasta,
and 2/9 was soup. How much of each product did they donate?
Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.
What does the term "simplify expression" mean?The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible
vegetables = (1/9) x 99
Simplifying this expression, we get:
vegetables = 11
So the class donated 11 units of vegetables.
Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:
pasta = (2/3) x 99
Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.
Which expression should I simplify?
A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.
veggies = 1/9 times 99
When we condense this statement, we get:
eleven vegetables
Hence, the class gave away 11 units of produce.We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:
spaghetti equals (2/3) x 99
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● Thornton
1 centimeter =
50 kilometers
Peter's mother is a pilot. She often makes deliveries
near their community. Peter and his mother flew from
Charlton to Thornton to make a mail delivery. Then they
continued on to Avon and Ashton and returned to Charltc
How many kilometers did Peter and his mother
travel in all?
The answer is 250 kilometers. Peter and his mother traveled a total distance of 250 kilometers on their mail delivery.
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.
1 centimeter is equal to 0.01 kilometers, so 50 kilometers would be equal to 5,000 centimeters. The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.
Charltc to Thornton is 1,000 centimeters, Thornton to Avon is 1,500 centimeters, Avon to Ashton is 1,000 centimeters, and Ashton to Charltc is 1,500 centimeters. This gives us a total of 5,000 centimeters, or 50 kilometers.
This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times, since they flew from Charltc to Thornton, then to Avon, then to Ashton, and then back to Charltc). This gives us 250 kilometers, which is the answer to the question.
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Peter and his mother traveled a total distance of 250 kilometers on their mail delivery. The answer is 250 kilometers.
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.
1 centimeter = 0.01 kilometers,
so 50 kilometers = 5,000 centimeters.
Charlton to Thornton= 1,000 centimeters,
Thornton to Avon= 1,500 centimeters,
Avon to Ashton= 1,000 centimeters,
and Ashton to Charlton= 1,500 centimeters.
Total distance= 1,000+1,500+1,000+1,500
= 5,000 centimeters, or 50 kilometers.
The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.
This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times.
=50*5
=250
Since they flew from Charlton to Thornton, then to Avon, then to Ashton, and then back to Charlton.
250 kilometers is the answer to the question.
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Question:
Peter's mother is a pilot. She often makes deliveries near their community. Peter and his mother flew from Charlton to Thornton to make a mail delivery. Then they continued on to Avon and Ashton and returned to Charlton. How many kilometers did Peter and his mother travel in all?
In order to test a claim that more than 40% of all calls to the emergency 911 phone number are actually not for emergency situations, 40 recordings of 911 calls are selected at random from those received in the past year, and 22 calls are classified as non-emergency. What are the p-value and conclusions for this test?A. P-value = 0.0264. There is strong evidence to show that no more than 40% of 911 calls are actually not emergency, at significance level a-0.05.B. P-value = 0.0264. There is strong evidence to show that more than 40% of 911 calls are actually not emergency, at significance level a 0.05.C. P-value = 0.0528. There is no strong evidence to show that more than 40% of 911 calls are actually not emergency, at significance level a 0.05.D. P-value = 0.0528. There is strong evidence to show that more than 40% of 911 calls are actually not emergency, at significance level a=0.05.
Answer:
0.005
Step-by-step explanation:
Given the function y = 4x + 3 do the following. Find its average rate of change: from x = 2 to x = 5
Answer: 4 is the average rate of change
Step-by-step explanation:
The equation to find the average rate of change is:
[tex]\frac{f(x_{2})-f(x_{1} ) }{x_{2}-x_{1} }[/tex]So f(2)= 11 and f(5)=23 then you plug these numbers in:
[tex]\frac{23-11}{5-2}[/tex] = [tex]\frac{12}{3}[/tex] = 4
in a school of hundred students, 40 are in the hockey team and 70 are in the football team.
Each student is in at least one team. Find the number of students who are in both teams.
Answer: There are 10 students who are in both the hockey and football teams.
Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.
The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):
Total = Hockey + Football - Both
Substituting the given values, we get:
100 = 40 + 70 - Both
Simplifying, we get:
Both = 40 + 70 - 100
Both = 10
Therefore, there are 10 students who are in both the hockey and football teams.
What is the y-intercept of y = 2/3 x + 2? Responses A (3, 2)(3, 2) B (2, 3)(2, 3) C (-3, 0)(-3, 0) D (0, 2)
Answer:
Y intercept is (0,2) Answer D.
Step-by-step explanation:
I included a graph for equation y=2/3 x + 2.
Fractions MUST SHOW WORKING!!
Total seats in plane: 186
108+64+14
5/7 of 14 is: 10
14÷7= 2
2x5= 10
5/16 of 64 is: 20
64÷16=4
5×4= 20
5/9 of 108 is: 60
108÷9= 12
12x5= 60
60+20+10=90
90/186 of seats are being used
simplified: 15/31
No
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 2 , 5 , 8 ,Find the 41st term.
The 41st term of the sequence is 121.
What is a sequence?In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.
Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.
The given sequence is 2 , 5 , 8 , ...
The common difference is:
d = 5 - 2 = 3
The nth term of a sequence is given as:
an = a1 + (n-1)d
Substituting the value we have:
an = 2 + (n-1)3
an = 3n - 1
a41 = 3(41) - 1 = 122 - 1 = 121
Hence, the 41st term of the sequence is 121.
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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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compute the determinants in exercises 9-14 by cofactor expansions. at each step, choose a row or column that involves the least amount of computation. [\begin{array}{ccc}6&3&2&4&0\\9&0&-4&1&0\\8&-5&6&7&1\\3&0&0&0&0\\4&2&3&2&0\end{array}\right]
Answer:
Step-by-step explanation:
Tiago sells sunflower oil in large tins and extra-large tins.
The large tin and the extra-large tin are mathematically similar.
The volume of the extra-large tin is 75% more than the volume of the large tin. Both tins are cylinders.
The radius of the large tin is 20 cm.
Calculate the radius of the extra-large tin.
Answer:
24 cm (to nearest cm)
Step-by-step explanation:
XLV = extra large tin volume (cm³)
LV = large tin volume (cm³)
XLR = extre large tin radius (cm)
LR = large tin radius (cm) = 20
XLV = 1.75 × LV
Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;
We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;
This means the volumetric scale factor or multiplier is ×1.75;
Subsequently, we know:
XLV = 1.75 × LV
Similarly, there is a relationship between the radii of the tins;
The relationship is, however, slightly different;
[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]
We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;
Easy way to figure this is radius is in cm, volume is in cm³;
So:
XLR = 1.205... × LR
XLR = 1.205... × 20
XLR = 24.101... --> 24 cm (to nearest cm)
Question 8 (4 points)
For a meat raffle, 100 tickets were sold.
The following were prizes:
number of winners
1
4
15
prize
grand prize - $1000 cash
$250 meat package
$50 meat package
What is the probability of winning the grand prize? 1/20
What is the expected value for someone buying a single ticket for $10.00 ? $
Solve and then answer the question below.
*MUST SHOW WORK*
Half a number plus eight is fourteen minus a number. How many solutions does this equation have?
To answer the question, this equation has only one solution, which is x = 4.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.
by the question.
Let's start by setting up the equation:
[tex]1/2x + 8 = 14 - x[/tex]
where x is the number, we're trying to find.
Now let's simplify the equation by combining like terms:
[tex]3/2x + 8 = 14[/tex]
Subtracting 8 from both sides:
[tex]3/2x = 6[/tex]
Multiplying both sides by 2/3:
[tex]x = 4[/tex]
So, the solution to the equation is x = 4.
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A love expert carried out a study to quantify the effect of love songs on emotion. To do so, he used 30 volunteers. He random
Publishers
assigned the 30 volunteers to listen to either a love song or classical music. Then he asked them to draw a heart on a piece of paper. He measured the size of the heart drawn from bottom to top, in inches, for each person. The results are displayed in the stem and leaf plots.
The analysis of the data to obtain the confidence interval of the difference in the means indicates;
99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct options are;
Name of Procedure
Two sample interval for [tex]\bar{x}[/tex]₁ - [tex]\bar{x}[/tex]₂Random
The volunteers are randomly selectedWe have a random sample of 15 subjects who listen to love songsWe have a random sample of 15 subjects who listen to classical music10%
The 10% condition is metNormal/Large Sample
The stemplot of the classical music sample data shows no strong skewness or outliersThe stemplot of the love song music sample data shows no strong skewness or outliers99% CI = (-0.302, 2.301)
Conclude;
We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
What is a confidence interval?A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.
The two-sample t-test can be used to construct the 99% confidence interval as follows;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
Where;
[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups
s₁, and s₂ = The sample standard deviations
n₁ and n₂ = The sample sizes
df = The degrees of freedom
t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2
The data indicates;
n₁ = n₂ = 15
[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63
[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13
Therefore, we get;
([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)
= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)
= 1 ± 2.763 × 0.469
= 1 ± 1.301
The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).
The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
The correct statements, placed in the box are;
Name of Procedure;
Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂
Random
The volunteers are randomly selected
The random condition is met
We have a random sample of 15 subjects who listen to a love song
We have a random sample of 15 subjects who listen to classical music
10%
The 10% condition is met
15 < 10% of all subjects like these who listen to love songs
15 < 10% of all subjects like these who listen to classical music
Normal/Large Sample
The Normal/Large condition is met
The stemplot of the classical music sample data shows no strong skewness or outliers
The stemplot of the love song music sample data shows no strong skewness or outliers
Therefore;
99% CI = (-0.301, 2.301)
Conclude;
We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.
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The temperature recorded at Bloemfontein increased from -2 degrees C to 13 degrees C.what is the difference in temperature
Answer: 15
Step-by-step explanation:
13--2 = 13 + 2 = 15
Given a square with area a, you can use the formula P = 4a² to find the
perimeter P of the square. Find the perimeter of a square that has an area of 64 m².
The perimeter of the square is 256 m.
What ia area?Area is a measure of the amount of two-dimensional space enclosed by a closed figure or shape. It is usually measured in square units, such as square meters, square feet, or square centimeters.
What is a Square?A square is a regular quadrilateral with four equal sides and four right angles. It is a special case of a rectangle and a rhombus, and its properties are a combination of both.
In the given question,
We can start by using the formula for the area of a square, which is:
a = s²
where a is the area and s is the length of one side of the square.
If the area of the square is 64 m², then we have:
64 = s²
Solving for s, we get:
s = √64 = 8 m
Now, we can use the formula for the perimeter of a square in terms of its area:
P = 4a²
Substituting a = 64, we get:
P = 4(64) = 256 m
Therefore, the perimeter of the square is 256 m.
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Hi pls help me! Correct my answers if they’re wrong and I need help with 5-9! Thank you :D
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
an amusement park charges a $ entrance fee. it then charges an additional $ per ride. which of the following equations could bum so use to properly calculate the dollar cost, , of entering the park and enjoying rides?
The equation you would use to properly calculate the dollar cost of entering the park and enjoying rides is Total Cost = Entrance Fee + (Number of Rides x Ride Fee).
In this case, Total Cost is the cost of entering the park and enjoying rides, Entrance Fee is the fee for entering the park, Number of Rides is the number of rides you will be taking, and Ride Fee is the fee charged for each ride.
Thus, plugging in the given values, the equation becomes Total Cost = Entrance Fee + (Number of Rides x Ride Fee).
Therefore, if the Entrance Fee is $ and each ride costs an additional $ , the Total Cost of entering the park and enjoying rides is $ .
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Consider the following exponential probability density function. f(x) = 1/3 4 e^-x/3 for x > 0 a. Write the formula for P(x < x_0). b. Find P(x < 2). c. Find P(x > 3). d. Find P(x < 5). e. Find P(2 <.x <5).
The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.
The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:
F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx
a. Write the formula for P(x < x_0):
Using integration, we can solve this formula as follows:
F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]
= [-4e^(-x_0/3) + 4]/3
b. Find P(x < 2):
To find P(x < 2), we simply substitute x_0 = 2 in the above formula:
F(2) = [-4e^(-2/3) + 4]/3
≈ 0.4866
Therefore, the probability that x is less than 2 is approximately 0.4866.
c. Find P(x > 3):
To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:
P(x > 3) = 1 - P(x < 3) = 1 - F(3)
= 1 - [-4e^(-1) + 4]/3
≈ 0.3528
Therefore, the probability that x is greater than 3 is approximately 0.3528.
d. Find P(x < 5):
To find P(x < 5), we simply substitute x_0 = 5 in the above formula:
F(5) = [-4e^(-5/3) + 4]/3
≈ 0.6321
Therefore, the probability that x is less than 5 is approximately 0.6321.
e. Find P(2 < x < 5):
To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:
P(2 < x < 5) = P(x < 5) - P(x < 2)
= F(5) - F(2)
= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3
≈ 0.1455
Therefore, the probability that x is between 2 and 5 is approximately 0.1455.
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1. Describe the historical data on Nando’s sales, including a discussion of thegeneral direction of sales and any seasonal tendencies that might beoccurring. 2. Discuss, giving your justifications, which time series forecasting techniquesare appropriate for producing forecasts with this data set. 3. Apply the appropriate forecasting techniques and compare the models basedon ex post forecasts. Choose the best model. 4. Use your chosen forecasting model to generate forecasts for each of themonths in year 2021. 5. Discuss how these forecasts might be integrated into the planning operationsand policy makings in NIH
In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.
The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.
In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.
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I need help pls help me find the area:
Answer:
Step-by-step explanation:
348.55
Which expressions are equivalent to (x−2)2
?
Select the correct choice
The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)
Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:
(x-2)² = (x-2) * (x-2)
= x * x - 2 * x - 2 * x + 2 * 2
= x² - 4x + 4
So, the expression (x-2)² is equivalent to x² - 4x + 4.
However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:
(x-2)² = (x-2) * (x-2)
= (x-2)²
So, (x-2)² is equivalent to itself.
Hence the correct option is (B).
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Complete Question:
Which expressions are equivalent to (x−2)²?
Select the correct choice.
A. (x + 2) (x - 2)
B. x² - 4x + 4
C. x² - 2x + 5
D. x² + x - 2x
PLS HELP MEEEEEEE ASAP
Answer:
[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]
Step-by-step explanation:
[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]
Each side has length of a?
[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]
In which condition vector a.b has the minimum value? Write it.
Answer:
if it is perpendicular to eacha other I e 0
solve( 3x^ 2)+2y +4=0
Answer:
Step-by-step explanation:
You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.
Find the unknown lengths in these similar triangles. (Round off to two decimal places.)
The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.
What is triangle?A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.
Here,
1. Let x be the length of FH. We have:
AB/EF = BD/FH
12/8 = 10/x
Cross-multiplying, we get:
12x = 80
x = 80/12
x ≈ 6.67
Therefore, FH ≈ 6.67.
2. Let y be the length of EG. We have:
AC/BD = FH/EG
15/9 = 5/y
Cross-multiplying, we get:
5y = 135
y = 135/5
y ≈ 27
Therefore, EG ≈ 27.
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what is the surface area of a cube if all sides are equal to 2
लगाउनुहोस् । The capacity of a closed cylindrical tank of height 2 m. is 3080 liters. Find the base area of the tank.
11.87 m² metal sheet would be needed to make the base area of tank.
Volume of the cylinderVolume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters
Let us assume that Radius of cylinder = r
Then Volume of cylinder = π ×r² ×h
= 2π ×r²× m³
1 m³ = 1000 liters
= 2000 π r² liters
Volume of tank = Capacity
2000 π r² = 3080
=> 2000 × (22/7) × r² = 3080
=> r² = 49/100
=> r = 7/10 m
=> r = 0.7 m
Base Area of tank = TSA = 2πrh + 2πr²
= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²
= 3.0772 +8.792
= 111.87 m²
Hence, 11.87 m² metal sheet would be needed to make it.
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the heights of adult men can be approximated as normal with a mean of 70 and standard eviation of 3 what is the probality man is shorter than
Question: The heights of adult men can be approximated as normal, with a mean of 70 and a standard deviation of 3, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.
Let X be the height of an adult man, which follows a normal distribution with mean μ = 70 and standard deviation σ = 3. Then, we need to find the probability that a man is shorter than some height, say x₀. We can write this probability as P(X < x₀).To find P(X < x₀), we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation. This yields a new random variable Z with a standard normal distribution. Mathematically, we can write this transformation as:Z = (X - μ) / σwhere Z is the standard normal variable.
Now, we can find P(X < x₀) as:P(X < x₀) = P((X - μ) / σ < (x₀ - μ) / σ) = P(Z < (x₀ - μ) / σ)Here, we use the fact that the probability of a standard normal variable being less than some value z is denoted as P(Z < z), which is available in standard normal tables.
Therefore, to find the probability that a man is shorter than some height x₀, we need to standardize the height x₀ using the mean μ = 70 and the standard deviation σ = 3, and then look up the corresponding probability from the standard normal table.In other words, the probability that a man is shorter than x₀ can be expressed as:P(X < x₀) = P(Z < (x₀ - 70) / 3)We can now use standard normal tables or software to find the probability P(Z < z) for any value z.
For example, if x₀ = 65 (i.e., we want to find the probability that a man is shorter than 65 inches), then we have:z = (65 - 70) / 3 = -1.67Using a standard normal table, we can find that P(Z < -1.67) = 0.0475. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%. Thus, P(X < 65) = 0.0475 or 4.75%. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.
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