Check the picture below.
so the pebble will hit the ground when h(t) = 0.
It's noteworthy that the pebble is falliing off a cliff, so it was at rest, so its initial velocity is 0, so in essence is falling as fast as gravity can drop it.
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&0\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&256\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+256\implies 0=-16t^2+256\implies 16t^2=256 \\\\\\ t^2=\cfrac{256}{16}\implies t^2=16\implies t=\sqrt{16}\implies t=4 ~~ seconds[/tex]
your friend is binging half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket
Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.
Explain about the fraction:An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.
Given data:
fraction of crate brought by friend = 1/2
Total number of ice buckets = 6
Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets
Fraction of crate in each bucket = (1/2) / 6
Fraction of crate in each bucket = 1 / (2*6)
Fraction of crate in each bucket = 1/12
Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.
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find the measurement of angle A and round the answer to the nearest tenth.
(Show work if you can plsss).
Answer:
40.8°
Step-by-step explanation:
SohCahToa
use tan
tan^-1(19/22)
=40.81508387
=40.8
Answer:
Step-by-step explanation:
Here,
Opposite side is 19
Adjacent side is 22
To find : The value of Angle A, that is X°.
Formula
Tan X° = Opposite side/Adjacent side
Tan X° = 19/22 = 0.863 ( approximately )
X° = Tan inverse (0.863)
X° = 40.79° ~ 40.8°
Rounding off this to nearest tenth is 41°.
Hence,
X° = 41°
That is,
Angle A is 45°.
I will be given brainliest!!!!
Answer:2/3
Step-by-step explanation:
its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD
Answer: 2/3
Step-by-step explanation:
The corresponding side of AD is A'D'.
AD = 30
A'D' = 20
Scale factor = 2/3 because AD * 2/3 = A'D'
If I'm wrong, please tell me.
plsss answer i'll give 50
Step-by-step explanation:
I know it not all but this is what I have
Graph the equation y=x2+4x-5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answer:
Roots = (1, 0) and (-5, 0)
Vertex = (-2, -9)
Two additional points = (-4, -5) and (0, -5)
Step-by-step explanation:
The given equation y = x² + 4x - 5 is a quadratic equation with a positive leading coefficient. Therefore, the shape of the curve is a parabola that opens upwards.
The roots of a quadratic equation are the x-values that satisfy the equation y = 0. They are the points at which the curve crosses the x-axis.
To calculate the roots of the given equation, set it to zero and solve for x.
[tex]\begin{aligned}x^2+4x-5&=0\\x^2+5x-x-5&=0\\x(x+5)-1(x+5)&=0\\(x-1)(x+5)&=0\\\\\implies x-1&=0 \implies x=1\\\implies x+5&=0 \implies x=-5\end{aligned}[/tex]
Therefore, the roots of the equation are (1, 0) and (-5, 0).
The x-value of the vertex of a quadratic function in the form ax² + bx + c is -b/2a.
For the given equation y = x² + 4x - 5, a = 1 and b = 4.
To find the x-value of the vertex, substitute these values into the formula:
[tex]x_{\sf vertex}=\dfrac{-b}{2a}=\dfrac{-4}{2(1)}=-2[/tex]
To find the y-value of the vertex, substitute the x-value of the vertex into the given equation:
[tex]y_{\sf vertex}=(-2)^2+4(-2)-5=-9[/tex]
Therefore, the vertex is (-2, -9).
To find two other points on the curve, substitute two values of x into the equation.
[tex]\begin{aligned}x=-4 \implies y&=(-4)^2+4(-4)-5\\&=16-16-5\\&=0-5\\&=-5\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies y&=(0)^2+4(0)-5\\&=0+0-5\\&=0-5\\&=-5\end{aligned}[/tex]
The axis of symmetry of a quadratic equation is the vertical line that divides the parabola into two mirror images. The x-value of the vertex is the axis of symmetry. Therefore, the axis of symmetry is x = -2.
To graph the given equation:
Plot the roots (1, 0) and (-5, 0).Plot the vertex (-2, -9).Plot two additional points (-4, -5) and (0, -5).Draw the axis of symmetry x = -2.Draw a parabola that is symmetrical about the axis of symmetry and passes through the plotted points.electric utility poles in the form of right cylinders are made out of wood that costs $23.89 per cubic foot. calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 30 ft. round your answer to the nearest cent.
The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.
To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.
Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.
Using the formula, we get:
V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3
Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.
Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99
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we wish to estimate the proportion of all college students who are working while going to school to within 4% at the 90% confidence level. we believe the true proportion is around 40%. how large a sample should we take to get the desired accuracy?
To estimate the sample size required for estimating the proportion of college students who are working while going to school with a desired accuracy of 4% at a 90% confidence level, we can use the following formula:
n = (Z^2 * p * (1-p)) / (E^2)
where:
n is the sample size
Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645)
p is the estimated proportion (or expected proportion) of the population
E is the desired margin of error
Given:
Desired accuracy (E): 4% or 0.04
Confidence level (Z-score): 1.645 (corresponding to 90% confidence level)
Estimated proportion (p): 0.40 (or 40%)
Plugging the values into the formula, we get:
n = (1.645^2 * 0.40 * (1-0.40)) / (0.04^2)
n = 0.1239 / 0.0016
n ≈ 77.4375
Rounding up to the nearest whole number, the estimated sample size required to achieve the desired accuracy is 78.
So, a sample size of at least 78 college students would be needed to estimate the proportion of college students who are working while going to school with a margin of error of 4% at a 90% confidence level, assuming an estimated proportion of 40%.
Keiko paid $15. 84 for a 7. 48 - kg bag of dog food. A few weeks later, she paid $16. 58 for a 7. 94 - kg bag at a different store. Find the unit price for each bag
The unit price for the first bag is $2.12 per kilogram and the unit price for the second bag is $2.09 per kilogram.
To find the unit price, we need to divide the total cost by the weight of the bag.
For the first bag
Unit price = Total cost / Weight
Unit price = $15.84 / 7.48 kg
Unit price = $2.12/kg
Therefore, the unit price for the first bag is $2.12 per kilogram.
For the second bag
Unit price = Total cost / Weight
Substitute the values in the equation
Unit price = $16.58 / 7.94 kg
Unit price = $2.09/kg
Therefore, the unit price for the second bag is $2.09 per kilogram.
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In the graph below, line k with equation y = -k makes a 45° angle with the x- and y- axes.
Rx: (2, 5)
1. (-2, 5)
2. (-2, -5)
3. (2, -5)
In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).
What is a graph?The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.
The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)
Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).
Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).
The point (2,5) will change to if it is reflected across the line y=x (5,2).
Therefore, the correct option is 1. (-2, 5).
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which expressions are equivalent to 8 13 ?
The next four equivalent fractions of 8/13 are:
16/2624/3932/5240/65What are some equivalent fractions of 8/13?Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.
In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.
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52 no one can win more than one prize? multiple choice 16,129,423 16,497,400 15,281,283 16,300,400
The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,
To solve this problem, we can use the formula for permutations, which is:
nPr = n! / (n - r)!
where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).
Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:
52P52 = 52! / (52 - 52)! = 52!
Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.
Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.
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A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 2/5 of the remaining copies. How many copies does the bookstore still have
Therefore , the solution of the given problem of unitary method comes out to be 45 copies of the magazine are still available at the bookstore.
Definition of a unitary method.Use the tried-and-true core approach, the real variables, nor any useful information you learn from the general and detailed questions to finish the project expression. Customers may be given another chance to taste the products in response. If these improvements don't happen, we'll miss out on significant advancements in programming comprehension.
Here,
Let's figure out how many issues of the magazine are still available in the store.
Given: There were 90 copies in all when the bookstore opened.
1/6 of the total copies were sold at the bookstore yesterday.
=> 15 copies were sold yesterday = (1/6) * 90.
=> Total copies - Copies sold yesterday = 90 - 15 = 75 Remaining copies after yesterday's sale
=> 2/5 of the remaining copies were sold in the bookstore today.
30 copies were sold today, which
=> (2/5) * 75.
The quantity of copies left after today's sale equals the quantity left after yesterday's sale. - Today's sales of copies:
=> 75 - 30 = 45
45 copies of the magazine are still available at the bookstore.
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what is the circumference of a circle witya diameter of 25cm and 2.5cm
Answer:
To find the circumference of a circle with diameter 25cm, we can use the formula:
Circumference = π × Diameter
where π (pi) is a mathematical constant approximately equal to 3.14159.
Substituting the diameter of 25cm, we get:
Circumference = π × 25cm
= 3.14159 × 25cm
= 78.53975cm
Therefore, the circumference of the circle with diameter 25cm is approximately 78.54cm.
To find the circumference of a circle with diameter 2.5cm, we can again use the same formula:
Circumference = π × Diameter
Substituting the diameter of 2.5cm, we get:
Circumference = π × 2.5cm
= 3.14159 × 2.5cm
= 7.85398cm
Therefore, the circumference of the circle with diameter 2.5cm is approximately 7.85cm.
a doctor can complete 3 examinations in 2 hours. how many examinations can the doctor complete in 4 hours? hint: use the proportion 3 exams : 2 hours :: x exams : 4 hours. 5 exams 5 exams 6 exams 6 exams 7 exams 7 exams 8 exams
Answer:
6 examinations
Step-by-step explanation:
We Know
A doctor can complete 3 examinations in 2 hours.
How many examinations can the doctor complete in 4 hours?
We see
4 hours is 2 hours times 2
We take
3 x 2 = 6 examinations
So, the doctor can complete 6 exams in 4 hours.
Jessica wants to add a border around the edge of the solar panels to help protect them from weather events. Write the standard form expression that represents the amount of border material Jessica will need. Enter the correct answer in the box.
answer : 8c^2 + 24c - 6
The standard form expression that represents the amount of border material Jessica will need is 2L + 2W - 2x - 2y = -2B
To create this expression, we need to consider a few things. Firstly, we need to know the length and width of the solar panels. Let's say the length of the solar panel is L and the width is W. We also need to know the width of the border that Jessica wants to add. Let's call this value B.
The total amount of material needed for the border will be the sum of the material needed for the four sides of the solar panel. Each side will need a length of B, so the total length of the material needed will be 2B + 2L + 2W.
However, we can simplify this expression by putting it into standard form. Standard form expressions are written in a specific way that makes them easier to read and work with. In standard form, the expression is written as Ax + By = C, where A, B, and C are constants and x and y are variables.
To put the expression 2B + 2L + 2W into standard form, we need to group the variables together and move the constants to the other side of the equation. This gives us the expression 2L + 2W - Ax - By = -2B, where A and B are both equal to -2, and C is equal to -2B.
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Answer:
8c^2 + 24c - 6
Step-by-step explanation:
I got it right on edmentum
HELP ASAP PLEASE!! DUE IN 10 MINS
1. A hamburger combo meal in Poland costs approximately $1.13.
2. A hamburger combo meal in Mozambique costs approximately $5.12.
A hamburger combo meal in Poland will equals to;To find the dollar price of a hamburger combo meal in Poland, we need to divide the price in Polish Zlotys by the exchange rate for January:
= 5.08 Polish Zlotys / 4.5
= $1.13
A hamburger combo meal in Mozambique will equals to:To find the dollar price of a hamburger combo meal in Mozambique, we need to divide the price in Mozambique Meticals by the exchange rate for February:
= 338 Mozambique Meticals / 66.00
= $5.12
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Given f(x)= raiz 6x and g(x)= 1/x-6 Which value is in the domain of f g
The domain of the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to (-∞, 6) U (6, ∞).
Function f(x) = √6x
And g(x)= 1/ (x-6
Composition function fog is ,
fog(x) = f(g(x))
Domain of fog(x),
First, find the domain of g(x),
Here,
g(x) = 1/(x-6)
The denominator of g(x) cannot be equal to zero,
So we must exclude x = 6 from the domain of g(x).
The domain of g(x) is equal to ,
domain of g(x) = {x | x ≠ 6}
The range of g(x) is,
As x approaches 6 from the left, g(x) approaches negative infinity,
And as x approaches 6 from the right, g(x) approaches positive infinity.
Range of g(x) = (-∞, 0) U (0, ∞)
Now, the domain of fog(x),
fog(x)
= f(g(x))
= √6g(x)
=√ 6 (1 /(x - 6 ) )
Square root sign must be non-negative.
Since the range of g(x) does not include zero,
Exclude the part of the range that is less than zero.
The domain of fog(x) is,
domain of fog(x)
= {x | g(x) > 0}
= {x | x < 6} U {x | x > 6}
The domain of fog(x) consists of all real numbers except x = 6.
Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).
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The above question is incomplete, the complete question is :
Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.
josse is collecting signatures for a petition.
He currently has 520signatures.
He has 6 more weeks to collect the signatures he needs.
He needs at least 1000 signatures before he can submit his petition
explain pliss
The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.
What is number line?A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.
Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.
He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.
We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:
6x ≥ 480
Dividing both sides by 6, we get:
x ≥ 80
This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.
The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.
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Which statement about subnetting is correct?
A. Subnetting applies only to IPv4 networks, unless you are using classless interdomain routing.
B. Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage.
C. Subnetting in IPv4 involves the CIDR protocol, which runs at Layer 3; in IPv6, this protocol, and hence subnetting, is not used.
D. Because the subnet mask field is so much larger in IPv6, it is easier to subnet in this newer protocol stack than in IPv4.
The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.
Hence, the correct option is B.
In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.
IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.
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for which data frequency is seasonality not a problem? group of answer choices monthly. weekly. annual. daily. quarterly.
Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
What is annual data frequency?Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.
What is GDP?GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.
According to the given informationSeasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.
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One computer can process a payroll in 6 hours a new computer can do it in 4 hour how long would it take both computers together
Both computers working together can process the payroll in 2.4 hours.
Let's denote the time it takes for both computers working together to process the payroll as "t".
We can use the formula:
work done = rate x time
where "work done" is the same in both cases, as they are processing the same payroll. Therefore, we can set up an equation using the rates :
1/6 + 1/4 = 1/t
We can simplify the left-hand side of the equation:
2/12 + 3/12 = 1/t
5/12 = 1/t
Multiplying both sides by 12t:
5t = 12
t = 12/5
t = 2.4
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please help it’s a review question but i don’t get it
Possible translations such that the graph passes through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up.Translate the graph three units right and two units down.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Two possible translations for the function to pass through the point (1,2) are given as follows:
Translate the graph one unit right and one unit up, considering that the function passes through the point (0, 1), hence x + 1, y + 1.Translate the graph three units right and two units down, considering that the function passes through the point (-2, 4).More can be learned about translations at brainly.com/question/28174785
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find the volume of a cylinder with a diameter of 16 mi and a height of 5 mi
Answer: 320π or approximately 1005.31 mi
Step-by-step explanation:
The formula for the volume of a cylinder is
π r² h
we need to find the radius which is 16/2 = 8
plug in and solve
π 8² *5
π 64 *5
320π or approximately 1005.31 mi
what is the ratio of the area of triangle to the area of triangle ? express your answer as a common fraction.
Thus, the ratio of the area of larger triangle to the area of smaller triangle
is found as 5:1.
Explain about the ratios:An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.
Given data:
Dimension of larger triangle: base B = 10 cm, Height H = 5 cm.Dimension of smaller triangle : base b = 5 cm, Height H = 2 cm.Area of triangle = 1/2* base * height
Ratios:
area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)
area of larger triangle / area of smaller triangle = B*H / b*h
area of larger triangle / area of smaller triangle = 10*5 / 5*2
area of larger triangle / area of smaller triangle = 50 / 10
area of larger triangle / area of smaller triangle = 5/ 1 = 5:1
Thus, the ratio of the area of larger triangle to the area of smaller triangle
is found as 5:1.
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Complete question:
what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.
Dimension of larger triangle: base B = 10 cm, Height H = 5 cm.
Dimension of smaller triangle : base b = 5 cm, Height H = 2 cm.
There are 549 coins in a bottle.
ſ of the coins are £1 coins.
164 of the coins are 50p coins.
The rest of the coins are 20p coins.
Work out the total value of the 549 coins in pounds (£).
+
Total marks: 4
The total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.
Let's start by finding the number of £1 coins in the bottle. We know that ſ (one-half) of the coins are £1 coins, so:
ſ × 549 = 1/2 × 549 = 274.50
Since we can't have half a coin, we know that there are either 274 or 275 £1 coins in the bottle.
Next, we know that there are 164 50p coins in the bottle.
To find the number of 20p coins, we can subtract the number of £1 and 50p coins from the total number of coins:
549 - 274 (or 275) - 164 = 111 (or 110)
So, there are either 110 or 111 20p coins in the bottle.
To calculate the total value of the coins, we can multiply the number of each type of coin by its value and then add them up:
Value of £1 coins = £1 × 274 (or 275) = £274 (or £275)
Value of 50p coins = £0.50 × 164 = £82
Value of 20p coins = £0.20 × 111 (or 110) = £22.20 (or £22)
Total value = £274 (or £275) + £82 + £22.20 (or £22) = £378.20 (or £379)
Therefore, the total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.
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Please help Thank you
The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:
a)sinθ=0.5
b)cosθ=0.866
c)tanθ=0.577
What is trigonometric-ratios ?
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.
Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]
hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]
=[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]
=[tex]\sqrt{16+48}[/tex]
=8
a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]
Sin θ=[tex]\frac{4 }{8}[/tex]
Sin θ=[tex]\frac{1}{2}[/tex]
Sin θ=0.5
b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]
=[tex]\frac{4\sqrt{3} }{8}[/tex]
=[tex]\frac{\sqrt{3} }{2}[/tex]
=[tex]\frac{1.732}{2}[/tex]
Cos θ=0.866
c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]
=[tex]\frac{4}{4\sqrt{3} }[/tex]
=[tex]\frac{1}{\sqrt{3} }[/tex]
tan θ=0.577
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the teacher has a small class with only 7 students. the teacher grades their homework and reports scores of: 10, 7, 8, 12, 9, 11, and 13. what is the median?
Answer:
10
Step-by-step explanation:
To find the median in a set of data, organize the data from least to greatest.
Here, our data is the homework scores, those being:
10, 7, 8, 12, 9, 11, 13
Let's organize them in ascending order, like so:
7, 8, 9, 10, 11, 12, 13
The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.
We can find that the number in the middle is 10.
Thus, the median of the scores is 10.
The use of heuristics rather than algorithms is most likely to _____.
A. yield more accurate solutions to problems
B. save time in arriving at solutions to problems
C. minimize the overconfidence phenomenon
D. involve greater reliance on language skills
B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.
The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.
They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.
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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.
B. save time in arriving at solutions to problems . The correct answer is:
Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.
One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.
However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.
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2. There are 80 girls in the sophomore class of 200 students. Find the ratio of girls to non-girls.
Answer: 2 girls to 3 non-girls
Step-by-step explanation:
80 are girls
120 are boys (200-80)
80:120
simplify
2:3
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x for extra services. Sorry my mind is numb I have had a butt ton of work cut out for me.
Yes, the situation is a linear function as y = 30 + 5x is representing the standard form of a linear equation y = mx + b where m is the slope and b is the y-intercept.
Function is equal to ,
y = 30 + 5x
General form of the linear function is written as
y = mx + b
Here, the slope of the equation is 5,
This implies that for every additional service bought the cost increases by $5.
The y-intercept of the equation is 30.
This represents the initial cost of getting the dog groomed without any additional services.
The graph of this function will be a straight line.
And the relationship between the cost and the number of extra services bought will be linear.
When the number of extra services bought increases the cost of grooming the dog will increase by a constant amount .
Here the constant amount is equals to $5 per service.
Therefore, the function y = 30 + 5x is representing a linear function with slope 5 and y-intercept 30.
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The above question is incomplete, the complete question is:
The function y =30+5x represents the cost y (in dollars) of having your dog groomed and buying x extra services. Does this situation represent a linear function? Explain