The height of the tree to the nearest foot is 27 feet.
How to find the height of a tree?The height of the tree can be found as follows:
The height of the tree can be found using trigonometric ratios. Therefore,
let
tan ∅ = opposite / adjacent
Therefore,
opposite side = adjacent tan ∅
Hence,
height of the tree = 20 + x tan 45° = x tan 75°
20 + x tan 45° = x tan 75°
20 tan 45 + x tan 45° = x tan 75°
20 tan 45 = x tan 75° - x tan 45°
20 tan 45 = x(tan 75 - tan 45)
20 tan 45 = x(3.73205080757 - 1)
2.73205x = 20
x = 20 / 2.73
x = 7.32600732601
x = 7.34
Therefore,
height of the tree = x tan 75°
height of the tree = 7.34 × tan 75°
height of the tree = 27.3186119114
height of the tree = 27 ft
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Use the associative property to simplify the expression.
43 +30+70
OA. 43+30+70 = 73 +70 = 143
OB. 43+ (30+70) = 43+ 100 = 143
OC. 43+ 10(3 + 7) = 43 + 10(10) = 143
OD. 43 +70+ 30 = 113 +30 = 143
SUBMIT
Answer:jjj
Step-by-step explanation:because
You need to score at least 1500 points on your new video game to abstain the high score. You get 300 points after completing each level. Write a solve an inequality to find the number of levels you must bet to obtain the high score.
Answer:
the answer is 4
Step-by-step explanation:
hope this helps
Kirk prepared 24 kilograms of dough after working 4 hours. How much dough did Kirk prepare if he worked for 7 hours? Solve using unit rates.
If Kirk had worked for 7 hours he would have made 42 kg of dough.
What is unit rate?A unit rate means a rate for one of something.
Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.
Calculating the unit rates,
Since, he worked for 4 and made 24 kg,
So, in 1 hour = 24/4 = 6 kg
Therefore, in 1 hour he will make 6 kg
Therefore, in 7 hours he will make = 7x6 = 42 kg
Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.
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1.an alternative to ols is least absolute deviation (lad) regression, in which the regression line is selected to minimize the sum of the absolute vertical differences (rather than squared differences) between the line and the data. explain how this might reduce sensitivity to outliers.
The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.
LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.
Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.
The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.
In mathematical terms, the OLS method can be represented as follows:
minimize the sum of squared vertical differences,
min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²
However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.
In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.
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12. The energy E stored in an elastic band varies as the square of the
energy stored
extension x. When the elastic is extended by 3 cm, the
is 243 joules. What is the energy stored when the extension is 5 cm?
What is the extension when the stored energy is 36 joules?
carthworm is thought
a)The energy stored when the extension is 5 cm is given by A = 675 Joules
b) The extension when the energy is 36 Joules is x = ( 2/√3 ) cm
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The energy E stored in an elastic band varies as the square of the energy stored extension x
So , the equation is E = kx²
And , when x = 3 cm , E = 243 Joules
Substituting the values in the equation , we get
243 = k ( 3 )²
9k = 243
k = 27
a)
Now , when the extension x = 5 cm
The energy stored when the extension is E = kx²
On simplifying , we get
E = 27 ( 5 )²
E = 27 x 25
E = 675 Joules
b)
When the energy is E = 36 Joules
E = kx²
36 = 27 ( x )²
On simplifying , we get
x² = ( 36 / 27 )
Taking square roots on both sides , we get
x = ( 6/3√3 ) cm
x = ( 2/√3 ) cm
Hence , the equation is E = kx²
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A wellness director at a company in New York City wants t0 investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on typical workday: Is it appropriate to use the confidence interval found in part (a) to conduct the investigation? Explain your answer: In the STATE, DO, PLAN, CONCLUDE
The population mean, 9,009, 10,585 employees, and 9,009, 10,585 steps are the solution.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency.
The term "activity tracker" refers to gadgets, including watches and bands, that record your physical activity, such as walking, jogging, and skipping. They only count your steps and inform you of your daily objectives. They are quite useful for tracking blood pressure and other things.
The 95% confidence interval between 9,009 and 10,585 steps was used to estimate the mean number of steps taken by City employees.
The likelihood of the various values may be estimated using the confidence interval. It may be utilised to derive conclusions about the population mean.
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En los mitos y leyendas latinoamericanas, los personajes femeninos suelen representar males que infligen daño a los hombres.¿por que sucede esto?
A possible explanation for why female characters in Latin American myths and legends often represent evils that inflict harm on men is the patriarchal nature of those societies.
Why are women seen as inflicting evil on men in Latin American myths ?In such societies, women were often seen as weaker and more vulnerable than men, and their perceived subservience reinforced the idea that they were not to be trusted. In addition, women were often seen as a threat to male power and authority, and as a result, they were often depicted as malevolent figures who used their cunning and sexuality to manipulate men.
Another explanation is that the portrayal of female characters as evils in these myths and legends was a way of maintaining social order and control. By demonizing women, men were able to justify their own actions and maintain their position of power and control over women.
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In a class & 60 students the most number of students who passed Ga is 6 more than the number that passed fante. Every student passed at least one of the two subjects and 8 students passed both subjects (1) How many students passed Ga?
Answer: 37
Step-by-step explanation:
let x be the number of students who pass "fante". Then the number of students who passed "Ga" will be x + 6.
with the added information that 8 students passed both we can say:
(x + x + 6) - 8 = 60
2x + 6 = 68
2x = 62
x = 31
.: x + 6 = "only Ga pass" = 37
The question does not make it clear if it is asking for students who *only* passed Ga, or students who passed Ga + those who passed both. I'll assume the former though. Otherwise the answer would be 37 + 8 = 45 students
Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn. Each station runs for an equal amount of time. If it takes 49 minutes for the first 7 stations to water, how long does it take to water all parts of her lawn?
The amount of time it require to water all the parts of her lawn is, 63 minutes
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
Ms. Reynold's sprinkler system has 9 stations that water all parts of her front and back lawn.
Each station runs for an equal amount of time
it takes 49 minutes for the first 7 stations to water
The amount of time it require to water stations = ?
First, we need to calculate time required to water 1 station,
t = Total time taken / Total station watered
= 49 / 7
= 7 minutes/station
So
Time for water all parts = 7 x 9
= 63 minutes
Hence, the required time is 63 minutes
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Help, please. 50 points
The trapezoid is made up of a rectangle and a triangle. The total area of the trapezoid is 75 square centimeters. what is the length of the base of the triangle?
Step-by-step explanation:
use the pythagors theorm b square = h2 -p2
then the 10 cm is parallel so use area of right angled triange =1/2 b×p
Tara has been planting young trees in her garden. The maple tree that is 10 inches taill is
growing 4 inches per month, whereas the oak tree that is 25 inches taill is growing 1 inch per
month. In a few months, the two trees will be the same height. What will that height be?
Write a system of equations, graph them, and type the solution.
The system of the equations are:
y = 10 + 4x
y = 25 + x
The height of tree is 30 inches tall.
The graph is given below.
The solution is (5, 30).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation
We have,
Maple tree:
The maple tree that is 10 inches tall is
growing 4 inches per month,
This can be written as,
y = 10 + 4x _____(1)
Where y is the height of the tree.
Oak tree:
The oak tree is 25 inches tall and is growing 1 inch per
month.
This can be written as,
y = 25 + x ______(2)
Where y is the height of the tree.
Now,
From (1) and (2),
In a few months, the two trees will be the same height.
So,
10 + 4x = 25 + x
4x - x = 25 - 10
3x = 15
x = 5
Now,
y = 10 + 4x = 10 + 4 x 5 = 10 + 20 = 30
y = 25 + x = 25 + 5 = 30
Thus,
The height of tree is 30 inches tall.
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A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 4 hours?
The equation represents how many grams of the compound will remain after 4 hours m(4) = 0.285m₀
Radiation and decay are important concepts in nuclear physics. The rate at which radioactive compounds decay is measured in terms of half-life and the decay constant.
To solve this problem, we can use the exponential decay equation, which describes the rate of decay of a radioactive substance.
In this scenario, we are interested in finding the remaining mass of the radioactive compound, which can be obtained by multiplying the number of remaining atoms by the atomic mass of the substance. The equation for the remaining mass is:
m(t) = N(t) x m
where:
m(t) represents the mass of the radioactive substance remaining at time t.
N(t) is the number of radioactive atoms remaining at time t.
m is the atomic mass of the substance.
To determine the values of N0 and λ for our radioactive compound, we can use the decay rate given in the problem. If the compound decays at a rate of 27% per hour, it means that the remaining fraction of the substance after each hour is 0.73 (i.e., 100% - 27% = 73%). Therefore, the decay constant can be calculated as follows:
ln(0.73) = -λ
λ = 0.312
Next, we can use the initial mass of the compound (320 grams) and the exponential decay equation to find the remaining number of atoms at 4 hours:
[tex]N(4) = N_0 \times e^{-0.312 x 4}[/tex]
N(4) = N₀ x 0.285
Since we don't know N₀, we can express it in terms of the initial mass and the atomic mass:
N₀ = m₀ / m
where:
m₀ is the initial mass of the radioactive compound.
m is the atomic mass of the substance.
Substituting this into the previous equation, we get:
N(4) = (m₀ / m) x 0.285
Finally, we can use the equation for the remaining mass to find the answer:
m(4) = N(4) x m
m(4) = (m₀ / m) x 0.285 x m
m(4) = 0.285m₀
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Mrs. Martinez and Ms. Jones' classes are competing for best average homework completion over the course of the semester.
According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.
How do average and mean differ?The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.
Comparing the median and average.By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.
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help me please i actually cant do this
Answer:
a: Angle 1 and Angle 3
b: Angle 8 and Angle 5
c: Angle 2 and Angle 9
d: Angle 5 and Angle 3
e: none of the above
NEED THIS DONE ASAP Please
The expression which represents the perimeter of the rectangle is 2x + 14
Area of the rectangle = 4x + 12Area of the rectangle if x = 7 is 40 square unitsThe following expressions represent the descriptions respectively;
6x
(x - 5)
(x + 2.99)
The total cost of membership of each gym is represented by;
Gym A total cost = 80 + 25m
Gym B total cost = 40m
What is the expression to represent the perimeter of a rectangle?Length= x + 3
Width = 4
Perimeter of a rectangle= 2(length + width)
= 2{(x + 3) + 4}
= 2(x + 3 + 4)
= 2(x + 7)
Perimeter of the rectangle = 2x + 14
Area of the rectangle= length × width
= (x + 3) × 4
Area of the rectangle = 4x + 12
If x = 7
Area of the rectangle = 4x + 12
= 4(7) + 12
= 28 + 12
= 40 square units
If x is the cost of each apple, the total cost of 6 apples = 6x
Adam is x years old. John is 5 years younger.
So, John's age = (x - 5) years
Ben spent x dollars on a book and $2.99 on a pack of pencil.
Ben spent a total of x + 2.99
Gym A total cost:
80 + 25m
Gym B total cost:
40m
Where,
number of months= m
If m = 6 months
Gym A total cost:
80 + 25m
= 80 + 25(6)
= 80 + 150
= $230
Gym B total cost:
40m
= 40(6)
= $240
Therefore, the gym which is the best deal for 6 months is gym A
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Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {1, 3, 7}
A ∪ B?
The value for A∪B in probability form is 3/4. The value for A∪B in data set form is {5, 6, 8}.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event U has data - U = {1, 2, 3, 4, 5, 6, 7, 8}
The event A has data - A = {6, 8, 10}
The event B has data - B = {5, 6, 9, 12}
The event C has data - C = {1, 3, 7}
The probability formula is -
Probability = No. of outcomes that is favorable / Total number of outcomes
The value for A∪B is -
A∪B = 3/4
The value of A∪B in data set is the values that are present in U data set and in A and B data set.
So, the value is - {5, 6, 8}
Therefore, the value is 3/4 or {5, 6, 8}.
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36-7p=-7(p-5) solve for P
Step-by-step explanation:
36 - 7p = -7(p-5)
= 36 - 7p = -7p + 35
= 36 - 35 = - 7p + 7p
= 1 = 0
am confused at the last part
I don't know if p= 1 or it 0 = 1
A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. The bottom 1. 5% of students must go to summer school. What is the minimum score you would need to stay out of this group?
A minimum score of 182 is required to stay out of the bottom 1.5% of students and avoid going to summer school.
To find the minimum score required to avoid going to summer school, we need to determine the score that separates the bottom 1.5% of students from the rest of the distribution. This score is also known as the cutoff or the critical value.
We know that the test scores have a normal distribution with a mean of 400 and a standard deviation of 100. To find the critical value, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can standardize the test scores using the z-score formula:
z = (x - mu) / sigma
where x is the test score, mu is the mean, and sigma is the standard deviation.
Substituting the given values, we get:
z = (x - 400) / 100
To find the z-score corresponding to the bottom 1.5% of the distribution, we can use a standard normal table or a calculator. The area to the left of this z-score is 0.015, which corresponds to a z-score of approximately -2.17.
Now we can solve for x, the minimum score required to stay out of the bottom 1.5%:
-2.17 = (x - 400) / 100
x = -2.17 * 100 + 400
x ≈ 182
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10.a) Which numbers less than 100 have exactly 3 factors (including 1 and the number itself)?
b) Which two numbers less than 100 have exactly 5 factors?
c) Which number less than 100 has exactly 7 factors?
Step-by-step explanation:
a)
any prime number has only 2 (1 and the number itself).
almost every even number has 1, 2, a factor of 2 and the number itself. so that did not work either.
following that line of thought, the only possible solutions are square numbers of prime numbers :
4, 9, 25, 49
they have only 1, its square root and the number itself as factors.
b)
in the same line of thinking it must be powers of 4 of prime numbers :
2⁴ = 16
with the factors 1, 2, 4, 8, 16
3⁴ = 81
with the factors 1, 3, 9, 27, 81
c)
and so, it must be a power of 6 of a prime number.
the only one possible is
2⁶ = 64
with the factors 1, 2, 4, 8, 16, 32, 64
if the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 9 in. beyond its natural length?
The answer is 1.25 ft-lb. This can be calculated by multiplying 15 ft-lb by (9 in. / 12 in. per ft), which equals 1.25 ft-lb. The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb.
1. Convert 9 in. to feet by dividing 9 in. by 12 in. per ft.
2. Multiply the result (0.75 ft) by 15 ft-lb, which equals 1.25 ft-lb.
The amount of work needed to stretch a spring 9 inches beyond its natural length is 1.25 ft-lb. This can be found by taking the given work required to stretch the spring 1 foot (15 ft-lb) and multiplying it by the ratio of the desired distance (9 in.) to 1 foot (12 in. per ft). First, the desired distance of 9 inches must be converted to feet by dividing it by the conversion factor of 12 inches per foot. This results in 0.75 feet. This number is then multiplied by the given work of 15 ft-lb to yield 1.25 ft-lb of work. This is the amount of work needed to stretch the spring 9 inches beyond its natural length.
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the cosine and secant functions are ---select--- functions, and the sine, cosecant, tangent, and cotangent functions are ---select--- functions
The sine, cosine, cosecant, and secant functions have a period 2π;
the tangent and cotangent functions have period π.
The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.
If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. The period is the interval between two occurrences of the wave.
The complete question is-
The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.
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The triangles are similar.
What s the value of x?
See the attachment for the problem to be answered.
Answer: x=4
Step-by-step explanation: as you saw everything is multiplied by 5 this means the 4 became a 20.
3x+8=20
-8 on both sides
3x=12
divide both sides by 3
x=4
show all your work. indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. a certain type of bird lives in two regions of a state. the distribution of weight for birds of this type in the northern region is approximately normal with mean 10 ounces and standard deviation 3 ounces. the distribution of weight for birds of this type in the southern region is approximately normal with mean 16 ounces and standard deviation 2.5 ounces. (a) calculate the z -scores for a weight of 13 ounces for a bird living in the northern region and for a weight of 13 ounces for a bird living in the southern region.
The z-score for a weight of 13 ounces for a bird living in the northern region is 1 and in the southern region is -1.2.
A z-score, also known as a standard score, is a statistical measure that indicates how many standard deviations an observation or data point is above or below the mean of the distribution.
z = (x - μ) / σ
where
x = value of the variable
μ = mean of the distribution
σ = standard deviation of the distribution.
In northern region, x = 13 ounces, μ = 10 ounces, σ = 3 ounces
z - score = (13 - 10) / 3
= 1
In southern region, x = 13 ounces, μ = 16 ounces, σ = 2.5 ounces
z - score = (13 - 16) / 2.5
= -1.2
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A system of equations is shown.
y=x+1
x-2y=-4
Which represents the solution of this system?
O(-2, -3)
O(-2, 3)
(2, -3)
(2, 3)
customers arrive according to a poisson process, stay for a time g and then leave. what is the joint distribution of customers remaining and having left
The joint distribution of X(t) and Y(t) is P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
The joint distribution of customers remaining and having left can be expressed using the Poisson process as follows:
Let N(t) be the number of customers that arrive in the time interval [0, t], and let S₁, S₂, S₃, ... be the sequence of service times for each customer, where S_i is the time the i-th customer spends in the system (i.e., waiting and being served). Let Y(t) be the number of customers who have left the system by time t, and let X(t) be the number of customers who are still in the system at time t.
The joint distribution of X(t) and Y(t) can be written as:
P(X(t) = k, Y(t) = n) = P(N(t) = k + n) * P(sum of S_i for i = 1 to k + n > t) * P(sum of S_i for i = 1 to k + n - 1 <= t)
where the first term on the right-hand side represents the probability that k + n customers arrive in the time interval [0, t], the second term represents the probability that the sum of service times for the first k + n customers exceeds t (i.e., there are still k + n customers in the system at time t), and the third term represents the probability that the sum of service times for the first k + n - 1 customers is less than or equal to t (i.e., the first k + n - 1 customers have left the system by time t).
The distribution of X(t) and Y(t) can be quite complex, depending on the distribution of service times and the arrival rate of customers. However, in some special cases, closed-form expressions for the joint distribution can be derived. For example, if the service times have an exponential distribution and the arrival rate of customers is constant, then the joint distribution of X(t) and Y(t) is given by the following formula:
P(X(t) = k, Y(t) = n) = ((μt)^k / k!) * (μt)^(n+1) * e^(-μt)
where μ is the rate parameter for the exponential distribution of service times.
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Cameron has a bag of 24 letter tiles. Some are vowles and some are consonants. He randomly chooses a letter tile and places it back in the bag. He chose 4 vowels and 2 consonants. How many vowels are likely in the bag?
In all, Cameron removed 6 tiles (3 consonant vowels and 4 vowel consonants). Take that amount, 6, then divide it by the 24 vowels in total. 24/6=4. It provides you four. Then you multiply that number, 4, by the number of consonant vowels he removed, which is 3, for a total of 6, or 4*2. your response is six vowels.
The five distinct vowel letters are A, E, I, O, and U. The English language has vowels in practically every word and phrase, making them incredibly prevalent. Any letter of the alphabet that isn't a vowel is referred to as a consonant (a, e, i, o, u).All of the non-vowel sounds in the English alphabet are consonants. Vowels, the loud sounds that make up each syllable's core and are separated by consonants. Letters A and O stand in for vowels, whereas B, C, D, F, J, K, M, N, P, Q, S, T, V, X, and Z stand in for consonants.
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Lillian makes 480 sandwiches 25% of them are tuna sandwiches 45% of them are ham sandwiches and the rest are egg sandwiches how many egg sandwiches does Lillian make?
Answer:
144 egg sandwiches
Step-by-step explanation:
[tex]25\% + 45\% = 70\%[/tex], and [tex]100\% - 70\% = 30\%.[/tex] Thus, [tex]30\%[/tex] of the [tex]480[/tex] sandwiches are egg sandwiches. Since "of" means multiply, we have [tex]30\% \cdot 480.[/tex] We know [tex]30\% = \frac{30}{100} = \frac{3}{10},[/tex] so we can rewrite it as [tex]\frac{3}{10} \cdot 480.[/tex] We cancel [tex]480[/tex] with [tex]10[/tex] which is [tex]480 \div 10 = 48.[/tex] We multiply [tex]48[/tex] by the numerator, [tex]3,[/tex] to get [tex]48 \cdot 3 = 144.[/tex] Thus, Lillian makes [tex]\boxed{144 \text{ egg sandwiches.}}[/tex]
Find y.
Round to the nearest tenth:
y
x
27°
350 ft
y = [? ]ft
The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of the variable 'y' is given by the tangent of the angle 27°. Then we have
tan 27° = y / 350
y = 350 tan 27°
y = 178.3
The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.
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The missing diagram is given below.
A pole that is 3.5 tall casts a shadow that is 1.77 long. At the same time, a nearby building casts a shadow that is 43.5 long. How tall is the building? Round your answer to the nearest meter.
The height of the building is approximately 79.22 meters, rounded to the nearest meter.
To calculate the angle of elevation, we use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.
We know that the pole is 3.5 meters tall, and its shadow is 1.77 meters long. We can use this information to calculate the angle of elevation of the sun's rays, which is the angle formed between the horizontal line and the line of sight from the top of the pole to the sun.
In this case, the opposite side is the height of the pole (3.5 meters), and the adjacent side is the length of the shadow (1.77 meters). Therefore, we have:
tan(angle of elevation) = opposite/adjacent = 3.5/1.77
Using a calculator, we can find that the angle of elevation is approximately 63.24 degrees.
Now, we can use this angle to find out the height of the building. We know that the shadow of the building is 43.5 meters long, and we want to find its height, which is the opposite side of the right triangle formed by the angle of elevation and the length of the shadow. Therefore, we have:
tan(63.24 degrees) = opposite/43.5
Solving for the opposite, we get:
opposite = 43.5 * tan(63.24 degrees) = 79.22 meters
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(2x^-2y^3/3xy^-4) write answer only using positive exponents
By using only the positive exponents , the answer of the expression (2x⁻²y³/3xy⁻⁴) is (2y⁷)/(3x³) .
The Exponents, are defined as a shorthand way of representing the repeated multiplication of a base number by itself. The exponent is the small raised number that indicates how many times the base number is multiplied by itself.
For example, in the expression 2⁴, the base number is 2 and the exponent is 4,
We use the law of exponents to simplify the expression :
the expression is : (2x⁻²y³/3xy⁻⁴) ;
by using the rule that : a⁻ⁿ = 1/aⁿ ;
we get ;
⇒ (2y³y⁴)/(3xx²) ;
On adding the exponents having the same base ,
we get ;
⇒ (2y⁷)/(3x³) ;
Therefore , the simplified value of (2x⁻²y³/3xy⁻⁴) is (2y⁷)/(3x³) .
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The given question is incomplete , the complete question is
Write answer only using positive exponents , (2x⁻²y³/3xy⁻⁴) .