The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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Calculator Q15. y is directly proportional to x.
When x = 500, y = 50
b) Calcualte the value of y when x = 60.
If y is directly proportional to x, when x = 60, y = 6.
What is proportional?Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.
What is directly proportional?Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.
In the given question,
If y is directly proportional to x, we can use the formula:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the given values:
y = kx
50 = k(500)
Solving for k:
k = 50/500
k = 0.1
Now that we know the value of k, we can use the formula to find the value of y when x = 60:
y = kxy = 0.1(60)
y = 6
Therefore, when x = 60, y = 6.
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The lowest temperature ever recorded on earth was -89.2°C recorded in Antarctica in 1983.How many degrees Fahrenheit was that,to the nearest degree
The lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit.
To convert the temperature of -89.2°C to Fahrenheit, we can use the formula:
[tex]F = (C * 1.8) + 32[/tex]
Substituting:
°F = (-89.2 × 1.8) + 32
°F = -128.56 + 32
°F = -97
Therefore, the lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit. It's important to note that this is just an approximation as we rounded the result to the nearest degree. However, it gives us a good idea of how extremely cold the temperature was. It's worth mentioning that at such low temperatures, it's important to take appropriate precautions to avoid any adverse health effects.
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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.
An amount of $5000 is invested at 6% per year until it triples in value. When will that be?
Answer:
50 years
Step-by-step explanation:
Assuming it doesn't compound, 5,000*3 = 15,000.
5,000 * 6% = 5,000 * 0.06 = 300.
15,000 / 300 = 50 years.
The sets M and N intersect such that n(M) = 31, n(N) = 18
and n(MUN) = 35. How many elements are in both M and N?
There are 14 elements in both M and N.
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines.
An element (or member) of a set is any one of the distinct objects that belong to that set. Writing means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example , are subsets of A.
The principle of inclusion and exclusion (PIE) is a counting technique that computes the number of elements that satisfy at least one of several properties while guaranteeing that elements satisfying more than one property are not counted twice.
We can use the inclusion-exclusion principle to find the number of elements in both M and N.
n(MUN) = n(M) + n(N) - n(M∩N)
Substituting the given values, we have:
35 = 31 + 18 - n(M∩N)
Simplifying this equation, we get:
n(M∩N) = 14
Therefore, there are 14 elements in both M and N.
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 choose all the shapes with at least one pair of perpendicular sides
According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.
What is the definition of perpendicular sides?Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:
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the weyland corporation, owns five offices that it leases to other businesses. the lease per square foot differs by building due to its location and amenities. currently, all buildings are fully leased, and detailed data is given below. calculate the weighted average price per square foot of the five offices owned by weyland corp. round your answer to 2 decimal places (include zero if necessary). price per sq. ft. ($) number of sq. ft. building 1 75 125,000 building 2 85 37,000 building 3 90 77,500 building 4 45 35,000 building 5 50 40,000
The weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.
Building Price per square ft ($) Number of sq. ft Building 1 75 and 125,000, Building 2 85 and 37,000, Building 3 90 and 77,500, Building 4 45 and 35,000, Building 5 50 and 40,000. Now, the formula to calculate weighted average price per square foot is,
Weighted Average Price per square foot = [ (Price per sq. ft of Building 1 * Number of sq. ft of Building 1) + (Price per sq. ft of Building 2 * Number of sq. ft of Building 2) + (Price per sq. ft of Building 3 * Number of sq. ft of Building 3) + (Price per sq. ft of Building 4 * Number of sq. ft of Building 4) + (Price per sq. ft of Building 5 * Number of sq. ft of Building 5) ] / Total sq. ft of all buildings.
Applying the values in the formula,
Weighted Average Price per square foot = [(75 * 125000) + (85 * 37000) + (90 * 77500) + (45 * 35000) + (50 * 40000)] / (125000 + 37000 + 77500 + 35000 + 40000)= [9375000 + 3145000 + 6975000 + 1575000 + 2000000] / 297500= 23092500 / 297500= 77.72
Therefore, the weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.
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In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16. 50 kg?
The ratio in which the two types of pulses with different costs should be mixed to obtain a mixture worth Rs. 16.50 per kg is 1:2 or 0.5:1.
Let's start by assigning some variables to the problem. Let x be the ratio of the first type of pulses (costing Rs. 15 per kg) and y be the ratio of the second type of pulses (costing Rs. 20 per kg). We can then write:
x + y = 1 (since the two types of pulses make up 100% of the mixture)
We also know that the cost of the final mixture is Rs. 16.50 per kg. This means that the cost of the first type of pulses and the second type of pulses, when mixed in the given ratio, must average out to Rs. 16.50 per kg. We can express this as:
15x + 20y = 16.50(x + y)
Simplifying this equation, we get:
15x + 20y = 16.50x + 16.50y
3y = 1.5x
y/x = 0.5
This tells us that the ratio of the second type of pulses to the first type of pulses should be 0.5. We can also express this as a ratio of x:y, which would be 1:2. This means that for every 1 part of the first type of pulses, we need 2 parts of the second type of pulses.
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identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. if sample data consist of weights measured in grams, what units are used for these statistics and parameters?
(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.
(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.
The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.
A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.
(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.
(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.
Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.
Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.
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< Find the unique polynomial with real coefficients that meets these conditions. Degree 4; zeros at x = 3, x = -4, and x = 2-i; f(0) = -180
the unique polynomial we're looking for is: f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).
How find the polynomial with factors?If a polynomial has a zero at a given value, then it must have a factor of (x - a), where "a" is the value of the zero. Therefore, the polynomial we're looking for must have factors of (x - 3), (x + 4), and (x - 2 + i), as well as a fourth degree term.
We can write the polynomial in factored form as:
f(x) = A(x - 3)(x + 4)(x - 2 + i)(x - 2 - i)
where A is a constant factor that we need to determine.
Expanding this expression, we get:
f(x) = A(x⁴ - 7x³ - 8x² + 106x - 240)
To find A, we can use the fact that f(0) = -180:
f(0) = A(0⁴ - 7(0)³ - 8(0)² + 106(0) - 240) = A(-240) = -180
Solving for A, we get:
A = [tex]\frac{-180}{-240}[/tex] = 3/4
Therefore, the unique polynomial we're looking for is:
f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).
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A baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes, if any, would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point? Pick two answers.
The velocity increases.
The velocity decreases.
The velocity remains a constant value.
The acceleration increases.
The acceleration decreases.
The acceleration remains a constant value
The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.
A type of motion known as upward motion involves an item moving up against the pull of gravity.
The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.
The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.
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Una pelota es lanzada horizontalmente desde la azotea de un edificio de 54 m de altura y Llega al suelo a 32 m de la base. Cuál fue la rapidez inicial de la pelota?
The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.
A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.
Height of building = 54 m
Height of ground from base = 32 m Calculates the initial speed of the ball.
Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,
d = 1/2×g×t²
where g --> acceleration due to gravity
t --> time
d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².
So, 54 m = (1/2) × 9,81 m/s² × t²
=> t² = 54/4.90
=> t² = 540/49
=> t² = 11.02 sec²
=> t = 3.31963 ~ 3.32 sec
So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,
=> 32 m = 0 + v₀ₓ × 3.32 sec
=> v₀ₓ = 32/3.32
=> v₀ₓ = 9.6385 ≈ 9.64 m/sec
Hence, required value is 9.64 m/sec.
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Complete question:
A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?
HELP ASAP!!!
The graph shows two accounts with the same principle and annual interest rate. Use the graph to estimate the anwser to each question.
A) About how much more compound interest than simple interest is earned after 35 years?
B) About how much more compound interest than simple interest is earned after 45 years?
The answers are:
(A) More compound interest than simple interest after 35 years: $260
(B) More compound interest than simple interest after 45 years: $445
What is Compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
The interest you earn on interest is known as compound interest.
Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.
You will wind up with $110.25 at the conclusion of the second year.
Now, calculate according to the given graph as follows:
(A) More compound interest than simple interest after 35 years:
870 - 610 = $260
(B) More compound interest than simple interest after 45 years:
1150 - 705 = $445
Therefore, the answers are:
(A) More compound interest than simple interest after 35 years: $260
(B) More compound interest than simple interest after 45 years: $445
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The probability density function of X, the lifetime of a certain type of device (measured in months) is given by f(x) = 0 if x < 2121/x^2 if x > 21 f(x) Find the following: P(X > 48) = The cumulative distribution function of X: f(x)= if x < 21if x > 21 The probability that at least one out of 7 devices of this type will function for at least 44 months:
The probability that at least one out of 7 devices of this type will function for at least 44 months is 1 - 0.9779167, or 0.0220833.
The probability density function of X, the lifetime of a certain type of device, is given by [tex]f(x) = 0 if x < 21; 1/x^2 if x > 21.[/tex]To find the probability that X > 48
we can use the cumulative distribution function of[tex]X: f(x) = 0 if x < 21; 1 - 1/x^2 if x > 21[/tex]. Therefore, the probability that[tex]X > 48[/tex] is 1 - 1/48^2, or 0.9609375.To find the probability that at least one out of 7 devices of this type will function for at least 44 months
we can use the binomial distribution formula.
The probability is given by [tex]P(X ≥ 1) = 1 - P(X = 0)[/tex]. Using the cumulative distribution function.
The probability that X = 0 is given by [tex]1 - 1/44^2, or 0.9779167.[/tex]
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Can someone help me out?
The probability of a. rolling an even or 3 is 2/3. b. Rolling an even or a number greater than 2 is 5/6. c. Rolling an odd or a number less than 6 is 5/6. d. Rolling a 2 and a 4 is 0.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. A sample space is made up of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail. An experiment is a trial or procedure carried out to generate a result.
Given that, you roll a single fair 6 sided die.
a. Rolling an even or 3:
P(even or 3) = P(even) + P(3) - P(even and 3)
P(even or 3) = 1/2 + 1/6 - 0
P(even or 3) = 2/3
b. Rolling an even or a number greater than 2:
P(even or >2) = P(even) + P(>2) - P(even and >2)
P(even or >2) = 1/2 + 4/6 - 1/3
P(even or >2) = 5/6
c. Rolling an odd or a number less than 6:
P(odd or <6) = P(odd) + P(<6) - P(odd and <6)
P(odd or <6) = 3/6 + 5/6 - 1/3
P(odd or <6) = 5/6
d. Rolling a 2 and a 4:
P(Rolling a 2 and a 4) = 0.
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I need some help with this
Answer:
27+2.25π
Step-by-step explanation:
Cube's volume is 3x3x3 = 27
The radius of the hemisphere is 3/2 = 1.5
Volume of a sphere is 4/3 π r^3
Plug in: 4/3 π 1.5^3 = 4.5π
Divide by 2: 2.25π
Total volume: 27+2.25π
Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy
We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".
What is the correct expression?Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".
Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".
Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.
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Difference between 6z and z to the power of 6
Answer:
[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]
The mathematical statement in the form of expression can be written as 15625z⁶.
What is algebraic expression?An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is to find the mathematical statement -
"Difference between 6z and z to the power of 6"
We can write the given mathematical statement in the form of expression as -
(6z - z)⁶
(5z)⁶
5⁶ x z⁶
125 x 125 x z⁶
15625z⁶
Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.
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Help me pls!! #percents
Pls us the formula on the page!!
Answer needs to be $3.64
I just need to know how to get it bc it says the answer in the page…
Step-by-step explanation:
Total price of the 4 toys = 4 x $1.50 = $6.00
tax is 6% of 6.00
= .06 * $ 6.00 = $ .36 which is added to the purchase price
$ 6.00 + .36 = $ 6.36 change from a $10 will be
$ 10.00 - 6.36 = $ 3.64
Answer: $3.64
Step-by-step explanation:
If we're using the formula, tax = % of whole, we will need to fill some values.
The whole is $6, as it's the total money you need to pay before tax
% can be written as 6/100, as we are being charged 6% in tax, and percent is written as 1/100
"of" is just a way to say * in english
So our equation is tax = 6/100 * 6
Which means tax = 36/100
Then, you add the tax to the original value, to get $6 + $0.36 = $6.36
Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.
PLS HELP ME ASAP I WILL MARK THE BRAINLIEST
Answer:
The formula for the nth term of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.
In this case, a1 = -8 and r = -2. Therefore, we have:
a2 = a1 * r = (-8) * (-2) = 16
a3 = a2 * r = 16 * (-2) = -32
a4 = a3 * r = (-32) * (-2) = 64
So, the next three terms of the sequence are 16, -32, and 64.
Answer:
a₂ = 16
a₃ = -32
a₄ = 64
Step-by-step explanation:
The general formula for a geometric sequence is:
[tex]a_n=a_1 \cdot r^{n-1}[/tex]
where:
a₁ is the initial term.r is the common ratio.Substitute the given values of a₁ and r into the formula to create an equation for the nth term:
[tex]\implies a_n=(-8) \cdot (-2)^{n-1}[/tex]
To find the values of a₂, a₃ and a₄, substitute n = 2, n = 3 and n = 4 into the equation.
[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{2-1}\\&=(-8) \cdot (-2)^{1}\\&=(-8) \cdot (-2)\\&=16\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_3&=(-8) \cdot (-2)^{3-1}\\&=(-8) \cdot (-2)^{2}\\&=(-8) \cdot (4)\\&=-32\end{aligned}[/tex]
[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{4-1}\\&=(-8) \cdot (-2)^{3}\\&=(-8) \cdot (-8)\\&=64\end{aligned}[/tex]
andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
Transversals of Parallel lines: corresponding angles
The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
What are corresponding angles?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.
Either both are acute or both are obtuse.
By creating an F shape, we can typically identify comparable angles.
So, now after reading the description we know exactly what are corresponding angles.
Now, we can easily tell that the pair of corresponding is:
∠HIK and ∠EFI
Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
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3/4 divided by 1/3 as a fraction
Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{3}[/tex]
[tex]\frac{3}{4}[/tex] × [tex]\frac{3}{1}[/tex] = [tex]\frac{9}{4}[/tex] ( to divide we make the other fraction reciprocal)
[tex]\frac{9}{4}[/tex] as mixed fraction= [tex]\frac{1}{4}{2}[/tex]
James has 27 metres of red wire and 12 metres
of black wire. He needs to cut both wires into
smaller pieces so that all of the smaller pieces are
the same length and there is no wire left over. The
length of each piece must be a whole number of
metres.
What is the longest he can make each smaller
piece of wire? Give your answer in metres (m).
Answer:
3m
Step-by-step explanation:
red wire = 27
black wire= 12
so, we take HCF (highest common factor)
which would be 3 so all the wires would be cut into 3m long.
I hope it helps.
Answer:2m
Step-by-step explanation:
as the factors of 12 are:1, 2, 3, 4, 6 and 12
and the factors of 26 are:1, 2, 13 and 26
so if you are talking meters 2 would be the longest
i hope you get this right x
GEOMETRY
determine whether each pair of triangles is similar. give details about each set of sides or angles. give the theory used. write a similarity statement.
The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
What is the Angle Side Angle Congruence Theorem?The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:
m < W = m < Z.m < V = m < Y.The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.
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4. Alice is creating a pyramid with toy rectangular-prism-shaped blocks
that measure 1 inch by 2 inches by 2 inches. She places 8 blocks in
the first row. Then she places 6 blocks on top of the first row and 4
blocks on top of the second row. If she continues the pattern until
the top row has 2 blocks, what is the volume of the final pyramid?
The final pyramid has a volume of 16 cubic inches. To find this, first multiply the number of blocks in each row together. 8 blocks in row 1 = 8 x 2 x 2 = 32; 6 blocks in row 2 = 6 x 2 x 2 = 24; 4 blocks in row 3 = 4 x 2 x 2 = 16; and 2 blocks in row 4 = 2 x 2 x 2 = 8. Then add all these numbers together to get 32 + 24 + 16 + 8 = 80. Finally, divide this number by 3 to get the volume, 80/3 = 16.
4. A parking lot in the shape of a trapezoid has an area of 2,930.4 square meters. The length of one base is 73.4 meters, and the length of the other base is 3760 centimeters. What is the width of the parking lot? Show your work.
The parking lot has a width of around [tex]0.937[/tex] meters.
Are meters used in English?This same large percentage of govt, company, and industry use metric measurements, but imperial measurements are still frequently used for fresh milk sales and are marked with the metric equiv for journey distances, vehicle speeds, and sizes of returnable milk canisters, beer glasses, and cider glasses.
How much in math are meters?100 centimeters make up one meter. Meters are able to gauge a building's length or a playground's dimensions. 1000 meters make up one kilometer.
[tex]3760 cm = 37.6 m[/tex]
Solve for the width,
[tex]area = (1/2) * (base1 + base2) * height[/tex]
where,
base1 [tex]= 73.4 m[/tex]
base2 [tex]= 37.6 m[/tex]
area [tex]= 2,930.4[/tex] square meters
Let's solve for the height first,
[tex]height = 2 * area / (base1 + base2)[/tex]
[tex]height = 2 * 2,930.4 / (73.4 + 37.6)[/tex]
[tex]height = 2 * 2,930.4 / 111[/tex]
[tex]height = 56.16 m[/tex]
We nowadays can apply the algorithm to determine the width.
[tex]width = (area * 2) / (base1 + base2) * height[/tex]
[tex]width = (2 * 2,930.4) / (73.4 + 37.6) * 56.16[/tex]
[tex]width = 5856.8 / 111 * 56.16[/tex]
[tex]width = 5856.8 / 6239.76[/tex]
[tex]width = 0.937[/tex]
Therefore, the width of the parking lot is approximately [tex]0.937[/tex] meters.
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find the inverse of the function
F(x) = x² + 2x₁ [-1, 00]
use the y-and -x intercept to write the equation of the line y intercept (0,6), x intercept (-2,0)
Answer:
3x -y = -6
Step-by-step explanation:
You want the equation of the line with intercepts (0, 6) and (-2, 0).
Intercept formThe equation of the line with x-intercept 'a' and y-intercept 'b' is ...
x/a +y/b = 1
For the given intercepts, the equation is ...
x/(-2) +y/6 = 1
Standard formIn standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:
3x -y = -6
__
Additional comment
You can get slope-intercept form by solving for y, or you can recognize that ...
slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3
Since you already know the y-intercept, you can write the slope-intercept equation as ...
y = 3x +6
There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.
Gerard wrote down the sum of squares of two (23?)2 + (1?2)² = 7133029 numbers, as shown. Unfortunately some of the digits cannot be seen because they are covered in ink. What is the last digit of the first number? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Answer:
We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.
Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.
So, the last digit of the first number is 3. And the answer is (A) 3