The measures of central tendency include mean and mode, which include a third measure called median.
The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.
The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.
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Correct question is:
The measures of _________ include mean and mode. The third of those measures is ________.
Dividing the sum of all data values by the total frequency will give us the_____.
What is the measure of arc AC? PLS help
For 0 <3 days. the number of weeds in large garden is given by the function W that satisfies tbe differential equation dW/dt = 1/12(-318+ 24W). At time t = 2 days, there are 20 weeds in the garden Find d^2W/dt^2 when W = 14.
[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.
How to explain number?A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.
Is the number 111111 lucky?Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.
[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]
[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]
When [tex]W=14, \frac{dW}{dt}[/tex]
[tex]=\frac{1}{12}(-318+24*14)[/tex]
[tex]=\frac{18}{12}=1.5[/tex]
[tex]=2\frac{dW}{dt}=2*1.5[/tex]
[tex]=3[/tex]
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Part of your summer job is to count the number mosquitoes that get caught in traps around your city. At one trap, you count mosquitoes each week ("week 0" means the first day you counted) and record the following numbers:
Use a calculator or graphing technology to determine which of the following functions matches the numbers you counted in these first few weeks.
A) M (w) = 4(w) + 8
B) M (w) = 1.5 (8^w)
C) M (w) = 8 (1.5^w)
D) w = 8 (1.5^M)
Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).
by the question.
To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:
Week Mosquito Count
0 8
1 20
2 50
3 125
4 312
Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:
mosquito graph
Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.
To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.
Option B gives us the following mosquito counts for the first five weeks:
Week Mosquito Count
0 8
1 19.5
2 47.25
3 114.19
4 276.32
Option C gives us:
Week Mosquito Count
0 8
1 12
2 18
3 27
4 40.5
Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.
Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.
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1 Write a positive or negative number to represent each change in the high temperature. Tuesday's high temperature was 4 degrees less than Monday's high temperature.
Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.
Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.
The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.
As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.
using the formula no.
Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.
Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
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the complete question is
Write a positive or negative number to represent each change in the high temperature.
1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?
2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?
3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?
4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?
If Alyssa has 6 shirts, 4 skirts, and 10 pairs of shoes, how many possible outfits can she make?
Answer: 240
You multiply them. 6x4x10 :)
The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.
To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:
Number of shirts = 6
Number of skirts = 4
Number of pairs of shoes = 10
Substitute the values and multiply with each other
Total number of possible outfits
= 6 (shirts) × 4 (skirts) × 10 (shoes)
= 240 outfits.
Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.
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It measure the degree of accuracy of the sample mean as an estimate of the population mean
Answer:
The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.
Step-by-step explanation:
Further Mathematics Assignment 1) A bowl contains 7 cooked and 5 uncooked In how many ways can: a) 2 cooked or 3 uncooked eggs be selected. b) 2 cooked and 3 uncooked eggs be selected.
Please this is my school homework!
Please HELP!!!
15 MRKS
Therefore, the total number of ways to select 2 cooked and 3 uncooked eggs is 210 ways.
What is combination?In mathematics, a combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In other words, a combination is a selection of items from a larger set, without regard to the order in which they are chosen. The number of combinations of size r that can be chosen from a set of n elements is denoted by the symbol C(n, r), and is given by the formula:
C(n, r) = n! / (r! * (n-r)!)
where n! (pronounced "n factorial") is the product of all positive integers up to n, and r! is the product of all positive integers up to r.
Here,
a) To find the number of ways to select 2 cooked or 3 uncooked eggs, we need to use the combination formula, which is:
ⁿCₓ= n! / r!(n-r)!
where n is the total number of eggs, r is the number of eggs we want to select, and ! represents factorial.
For 2 cooked eggs, we can select them in:
⁷C₂ = 7! / 2!(7-2)! = 21 ways
For 3 uncooked eggs, we can select them in:
⁵C₃ = 5! / 3!(5-3)! = 10 ways
Therefore, the total number of ways to select 2 cooked or 3 uncooked eggs is:
21 + 10 = 31 ways
b) To find the number of ways to select 2 cooked and 3 uncooked eggs, we need to use the product rule of counting. That is, we need to multiply the number of ways to select 2 cooked eggs and 3 uncooked eggs.
The number of ways to select 2 cooked eggs is:
⁷C₂ = 21 ways
The number of ways to select 3 uncooked eggs is:⁵C₃ = 10 ways
Therefore, the total number of ways to select 2 cooked and 3 uncooked eggs is:
21 x 10 = 210 ways
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At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?
Answer: View answer in explanation below.
Step-by-step explanation: Let's use variables to represent the unknown quantities.
Let x be the number of $5 clearance mystery books purchased.
Let y be the number of $12 regular-priced science fiction books purchased.
We can set up a system of equations based on the given information:
5x + 12y = 126 (total amount spent)
x + y = total number of books purchased
We need to solve for x and y.
Let's use the second equation to solve for one variable in terms of the other:
y = total number of books purchased - x
Now we can substitute this expression for y into the first equation:
5x + 12(total number of books purchased - x) = 126
Simplifying and solving for x:
5x + 12total number of books purchased - 12x = 126
-7x + 12total number of books purchased = 126
-7x = -12total number of books purchased + 126
x = (12total number of books purchased - 126)/7
Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:
If total number of books purchased is 10:
x = (12(10) - 126)/7 = -6/7 (not a whole number)
If total number of books purchased is 11:
x = (12(11) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 12:
x = (12(12) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 13:
x = (12(13) - 126)/7 = 12/7 (not a whole number)
If total number of books purchased is 14:
x = (12(14) - 126)/7 = 18/7 (not a whole number)
If total number of books purchased is 15:
x = (12(15) - 126)/7 = 24/7 (not a whole number)
If total number of books purchased is 16:
x = (12(16) - 126)/7 = 30/7 (not a whole number)
If total number of books purchased is 17:
x = (12(17) - 126)/7 = 36/7 (not a whole number)
If total number of books purchased is 18:
x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)
So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.
A computer store sells Ultra Fast brand desktop and laptop computers. They tracked the sales of both kinds of computers over five days. The table shows the sales data. Make a double-line graph of the data.
The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.
What is double-line graph?A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.
To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:
Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.
Label the horizontal axis with the days from Day 1 to Day 5.
Label the vertical axis with the heading "Number of Computers Sold".
Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).
Connect the data points for desktop computer sales with a line.
Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).
Connect the data points for laptop computer sales with a line.
Use a different color or style for the line representing desktop sales and the line representing laptop sales.
Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.
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r=19m how to find the circumference
Answer: 119.38
Step-by-step explanation:
C = 2πr = 2·π·19 ≈ 119.38052
Jordy tried to prove that △ A B E ≅ △ B C D △ABE≅△BCDtriangle, A, B, E, \cong, triangle, B, C, D. A A B B C C D D E E Statement Reason 1 ∠ B C D ≅ ∠ A B E ∠BCD≅∠ABEangle, B, C, D, \cong, angle, A, B, E Given 2 ∠ C D B ≅ ∠ B E A ∠CDB≅∠BEAangle, C, D, B, \cong, angle, B, E, A Given 3 B D ↔ ∥ A E ↔ BD ∥ AE B, D, with, \overleftrightarrow, on top, \parallel, A, E, with, \overleftrightarrow, on top Given 4 ∠ C B D ≅ ∠ B A E ∠CBD≅∠BAEangle, C, B, D, \cong, angle, B, A, E Corresponding angles on parallel lines are congruent. 5 △ A B E ≅ △ B C D △ABE≅△BCDtriangle, A, B, E, \cong, triangle, B, C, D Angle-angle-angle congruence What is the first error Jordy made in his proof? Choose 1 answer: Choose 1 answer: (Choice A) A Jordy used an invalid reason to justify the congruence of a pair of sides or angles. (Choice B) B Jordy only established some of the necessary conditions for a congruence criterion. (Choice C) C Jordy established all necessary conditions, but then used an inappropriate congruence criterion. (Choice D) D Jordy used a criterion that does not guarantee congruence
Jordy's first error in his proof is option (c) Jordy established all necessary conditions, but then used an inappropriate congruence criterion
Jordy's first error in his proof is that he used an inappropriate congruence criterion to prove that the two triangles are congruent. He established all necessary conditions, but AAA congruence is only valid for proving congruence of triangles in certain special cases, such as when the triangles are similar.
In general, AAA congruence is not a valid congruence criterion. This highlights the importance of choosing the correct congruence criterion when proving that two triangles are congruent, as using an invalid or inappropriate criterion can lead to an incorrect conclusion.
Therefore, the correct option is (c) Jordy established all necessary conditions, but then used an inappropriate congruence criterion
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write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is
The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.
Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b
F is the opposing force of friction. Together, these two forces determine the net force acting on the object.
Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.
Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.
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What is the domain of the square root function graphed below?
The inequality that represents x is x ≥ 0/
A square root function is defined ?The basic square rοοt οperatiοn. (οften knοwn as the "square rοοt functiοn") is a mapping that applies tο the set οf nοnnegative real numbers. The square rοοt functiοn, in geοmetric terms, cοnverts a square's area tο its side length.
The οrder οf pοsitive numbers is preserved by the square functiοn: greater numbers have larger squares. The square, then, is a mοnοtοnic functiοn οn the range [0, +]. With negative numbers, absοlute values are mοre significant than squares, making it a mοnοtοnically decreasing functiοn οn [(, 0]].
Here, The domain of the graph is domain : [0, +∞)
With this, we can clearly state that 0 < x < +∞
Thus, The inequality that represents x is x ≥ 0
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5 ft
8 ft
6:ft
Find the area.
10 ft
5 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.
The area of the composite figure with the given subshapes is 99.13 square feet
How to determine the area of the composite figureGiven the following parameters:
The composite figure with the following shapes
Semi-circle with diameter 8 ft
Triangle with base of 8 ft and height of 6 feet
Rectangle of 10 by 5 feet
The area of the composite figure is the sum of the individual areas
So, we have
Area = 1/2 * π(8/2)² + 1/2 * 8 * 6 + 10 * 5
Evaluate
Area = 99.13
Hence, the area is 99.13 square feet
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Look at photo and let me know the answers to the three blanks ASAP! Thank you!
a) Heating cost for a month with 25°F is $67.10
b) Heating cost for a month with 0°F is $98.60
c) Decrease in the monthly heating cost is $1.26
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(25) + 98.60
y = 67.10
Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.
(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(0) + 98.60
y = 98.60
Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.
(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.
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Which expression below gives the average rate of change of the function h(x) = 4x+2 +7 on the interval -3 ≤ x ≤ 5?
A. (43+2+7)-(45+2+7)
-3+5
B. (45*2 + 7)-(4+2+7)
5-3
C. (45+2+7)-(43+2+7)
5+3
D. (45+²+7)+(42+7)
5+3
Answer:
C. (45+2+7)-(43+2+7) / 5+3
Step-by-step explanation:
To find the average rate of change of h(x) on the interval -3 ≤ x ≤ 5, we need to evaluate the following expression:
[h(5) - h(-3)] / (5 - (-3))
We have:
h(5) = 4(5) + 2 + 7 = 29
h(-3) = 4(-3) + 2 + 7 = -5
Substituting into the formula, we get:
[29 - (-5)] / (5 - (-3)) = 34 / 8 = 17 / 4
Therefore, the expression that gives the average rate of change of the function h(x) on the interval -3 ≤ x ≤ 5 is:
C. (45+2+7)-(43+2+7) / 5+3
find the equation of the line with the given properties. express the equation in general form or slope intercept form. perpendicular to the line -4x+y=43 ; contains the point (-8,10)
The equation of the required line in slope-intercept form is y = -1/4x + 8.
Here are the steps to find the equation of the line:
Step 1: Find the slope of the given line in slope-intercept form
y = mx + c
-4x + y = 43 ⇒ y = 4x + 43... (1)
Here, the slope (m1) of the given line is 4.
Step 2: Find the slope of the required line as the two lines are perpendicular to each other.
m1 × m2 = -1
[As the given line and the required line are perpendicular to each other]
4 × m2 = -1 ⇒ m2 = -1/4
So, the slope (m2) of the required line is -1/4.
Step 3: Write the equation of the required line in point-slope form.
y - y1 = m(x - x1)
[Using the point-slope formula]
Let (x1, y1) = (-8, 10)m = -1/4
Putting the values in the above formula, we get
y - 10 = -1/4(x - (-8)) ⇒ y - 10 = -1/4(x + 8)... (2)
Step 4: Simplify the above equation to get the required equation of the line in slope-intercept form.
y - 10 = -1/4x - 2 ⇒ y = -1/4x + 8... (3)
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The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent
If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%
To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.
Let the cost price of each article be "C" and the selling price of each article be "S".
Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:
20C = 16S
We can simplify this equation to:
S = (20/16)C = (5/4)C
Now, let's calculate the profit earned on the sale of 16 articles:
Profit = Total Selling Price - Total Cost Price
Profit = 16S - 20C
Profit = 16(5/4)C - 20C
Profit = 5C/2
The profit earned is 5C/2. The profit percent can be calculated as:
Profit Percent = (Profit / Cost Price) x 100
Profit Percent = (5C/2) / (20C) x 100
Profit Percent = 25%
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80% off of the sale price $90 what is the original price
Answer: So that means the answer is $112.5
Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.
YES THIS IS RIGHT!!!!
A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass-spring system is disturbed from its rest state by the force F(t) = 100cos(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.
Determine the spring constant k.
k = ? Newtons / meter
Formulate the initial value problem for y(t), where y(t) is the displacement of the object from its equilibrium rest state, measured positive in the downward direction. (Give your answer in terms of y,y′,y′′,t.)
Differential equation: ?
Initial conditions: y(0) = ? and y′(0) = ?
Solve the initial value problem for y(t).
y(t) = ?
Plot the solution and determine the maximum excursion from equilibrium made by the object on the time interval 0 ≤ t < [infinity]. If there is no such maximum, enter NONE.
maximum excursion = ? meters
Using Hooke's law the maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.
To find the spring constant k, we use Hooke's law:
F = -ky
where F is the weight of the object, and y is the distance it is stretched from its rest position. At equilibrium, F = mg = 10 × 9.81 = 98.1 N. Thus,
98.1 = -k × 0.098
k = -1000 N/m
The equation of motion for the system is given by:
my'' + ky = F(t)
Substituting the given values, we get:
10y'' + (-1000)y = 100cos(8t)
y'' - 100y = 10cos(8t)
with initial conditions y(0) = 0 and y'(0) = 0.
The characteristic equation is r² - 100 = 0, with roots r = ±10i. The complementary solution is therefore y_c(t) = c1cos(10t) + c2sin(10t).
For the particular solution, we assume a form of yp(t) = Acos(8t) + Bsin(8t), and substitute it in the differential equation to get:
-64Acos(8t) - 64Bsin(8t) - 100(Acos(8t) + Bsin(8t)) = 10cos(8t)
Solving for A and B, we get A = -1/6 and B = 0. Thus, the particular solution is yp(t) = (-1/6) × cos(8t).
The general solution is therefore y(t) = c1cos(10t) + c2sin(10t) - (1/6)*cos(8t). Applying the initial conditions, we get c1 = 0 and c2 = 0, so the particular solution is simply y(t) = (-1/6) × cos(8t).
The maximum excursion from equilibrium can be found by taking the absolute value of y(t) and finding its maximum value. We have:
|y(t)| = (1/6) × |cos(8t)|
The maximum value of |cos(8t)| is 1, so the maximum excursion is 1/6 meters.
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Please simplify the following expression while performing the given operation.
(-3+i)+(-4-i)
Hence, the abbreviated formula is -7 + 0i, or just -7.
What is the simplifying rule?The terms in the parentheses can be immediately simplified. So, we can carry out the operations indicated by the brackets in the following order: multiplication, addition, subtraction, division. Note: The brackets should be shortened in the following order: (),, []. Simplify: 14 + (8 - 2 3) for Example 2.
We must combine like terms in order to make the phrase simpler.
First, we can individually merge the real and made-up parts:
The genuine parts add out to -3 - 4 = -7.
i - i = 0 is the imaginary part's total.
Hence, the abbreviated formula is -7 + 0i, or just -7.
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Complete question:
Please simplify the following expression while performing the given operation. (-3+i)+(-4-i)
Which of these subsets are subspaces ofM2×2? For each one that is a subspace, write it as a span. For each one that is not a subspace, state the condition that fails. (a). A = {((a, 0), (0, b)): a+b = 5}
Let X and Y be two matrices in A. We can write X = ((x,0),(0,y)) and Y = ((z,0),(0,w)). If we add X and Y, we get((x+z,0),(0,y+w)). The sum is in A if and only if x+z+y+w=5.
Subset of M2x2:A subset of M2x2 is a set that contains some elements of M2x2.
A subset of M2x2 can be considered as a subspace if it meets the following conditions:
it contains the zero vector, it is closed under addition, and it is closed under scalar multiplication.M2x2 is a set of 2x2 matrices with real entries. M2x2 has 4 elements, which are (1,0), (0,1), (0,0), and (1,1).Let A = [tex]{((a,0),(0,b)):a+b=5}.[/tex]To determine if A is a subspace of M2x2, we need to verify that A meets the following conditions:
it contains the zero vector, it is closed under addition, and it is closed under scalar multiplication.Zero vector:To find the zero vector, we need to find a matrix in A such that [tex]a+b=0.[/tex] We can easily see that this is not possible because (a,0) and (0,b) are non-negative, and their sum cannot be zero. Therefore, A does not contain the zero vector.Addition:A is closed under addition if the sum of any two matrices in A is also in A. Let X be a matrix in A and c be a scalar. We can write X = ((x,0),(0,y)). If we multiply X by c, we get((cx,0),(0,cy)). The product is in A if and only if cx+cy=5c. Therefore, A is not closed under scalar multiplication.for such more questions on subset matrices
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Round your answer to the nearest hundredth
Answer:
AB ≈ 4.73
Step-by-step explanation:
using the sine ratio in the right triangle
sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{AB}[/tex] ( multiply both sides by AB )
AB × sin25° = 2 ( divide both sides by sin25° )
AB = [tex]\frac{2}{sin25}[/tex] ≈ 4.73 ( to the nearest hundredth )
Please help me with my math!!
Answer:
The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.
Since a = -3 < 0, the parabola opens downwards and has a maximum point.
To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:
x = -3
y = -3(-3+3)^2 + 4 = 4
Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.
Hence, the answer is option C
Answer:
C) Maximum point; 4
Step-by-step explanation:
Given parabola:
[tex]y=-3(x+3)^2+4[/tex]
The given parabola is in vertex form:
[tex]\boxed{y = a(x - h)^2 + k}[/tex]
where:
(h, k) is the vertex of the parabola.a is the leading coefficient.By comparing the given equation with the vertex form, we can see that:
a = -3h = -3k = 4As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.
The vertex of the parabola is (h, k) = (-3, 4).
Therefore, the maximum value of y is 4, which occurs at x = -3.
Sally has 3:4 as many beads as Kelly. Kelly has 18 more beads than Sally. Find the average number of beads the girl have
The average number of beads that the girls have is 63
Let's start by using algebra to represent the given information:
Let b be the number of beads that Sally has.
Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.
Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).
Putting these together, we can write the equation:
(3/4)b = b + 18
Solving for b, we get:
b = 72
So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.
The average number of beads that the girls have is (72 + 54)/2 = 63 beads
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ABC is an isosceles triangle, where AB=AC, BC=24cm and perimeter of triangle ABC=60cm. Then, Prove That: Angle BAC > Angle ABC
Let's assume that the measure of angle BAC is less than or equal to the measure of angle ABC.
Since AB = AC, then angles BAC and BCA are also equal. Let's denote the measure of angle BAC as x, then the measure of angle ABC and angle BCA is also x.
According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side. In our case, we have:
AB + BC > AC
AB + 24 > AC
2AB + BC > 2AC
2AB + 24 > 2AC
2AB > 2AC - 24
AB > AC - 12
Since AB = AC, then AC - 12 < AB = AC, which means AC < AC + 12. This is a contradiction, and therefore our assumption that the measure of angle BAC is less than or equal to the measure of angle ABC is false.
Therefore, we can conclude that Angle BAC > Angle ABC.
The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.
The figure shows an angle with a measure of 52 degrees.
A. Find the complement of the angle shown.
B. Find the supplement of the angle shown.
Show all your work.
The complement of the angle is 38 degrees and the supplement of the angle is 128 degrees.
Find the complement of the angle shown.The given angle is
Angle = 52 degrees
To find the complement of an angle, we need to subtract its measure from 90 degrees.
Therefore, the complement of an angle with a measure of 52 degrees is:
90 degrees - 52 degrees = 38 degrees
So, the complement of the angle shown is 38 degrees.
Find the supplement of the angle shown.To find the supplement of an angle, we need to subtract its measure from 180 degrees.
Therefore, the supplement of an angle with a measure of 52 degrees is:
180 degrees - 52 degrees = 128 degrees
So, the supplement of the angle shown is 128 degrees.
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1. meredith has 10 reports to file. if each report takes an average of 75 minutes to file, how long will it take her to file 70% of them? a. 5 hours b. 6 hours, 30 minutes c. 8 hours, 45 minutes d. 10 hours
Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?
Here, the total number of reports = 10
Average time to file one report = 75 minutes
To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:
75 × 7 = 525 minutes
We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:
525 ÷ 60 = 8 hours 45 minutes
Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
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If Joe has 40 apples and bob steals 5, how many apples does Joe have
Joe aura 35 pommes.
40-5=35
Can you help me with this?
16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.
What is equatiοn οf line?The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.
16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.
Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:
x + 2y = 14
2y = -x + 14
y = (-1/2)x + 7
The slοpe οf the line is -1/2.
Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.
Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:
y - y1 = m(x - x1)
where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.
y - 5 = (-1/2)(x - (-6))
y - 5 = (-1/2)x - 3
y = (-1/2)x + 2
17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)
perpendicular equations slope would be negative reciprocal to the current line.
The slope in y = -(2/3)x + 4, is m = -(2/3),
The negative reciprocal of -(2/3) is 3/2
Now, applying the x and y values in pοint-slοpe fοrm
y - 6 = 3/2(x - (-4))
y = 3/2(x+4) + 6
y = (3/2)x + 6 + 6
y = (3/2)x + 12
18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.
Lets find the slope using slope formula
[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]
[tex]\rm m = \dfrac{1}{3}[/tex]
Now, using the point slope form
y - 1 = 1/3(x - 3)
y = 1/3(x - 3) + 1
y = (1/3)x - 1 + 1
y = (1/3)x
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