Given that a is an acute angle in a right triangle, cos a = [tex]\frac{15}{17}[/tex]. The trigonometric ratio sin a = [tex]\frac{8}{17}[/tex] and tan a = [tex]\frac{8}{15}[/tex].
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In any question,
cos a = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
[tex]hypotenuse^{2} = perpendicular ^2+base^2\\\\perpendicular = \sqrt{hypotenuse^2-base^2}[/tex]
perpendicular = [tex]\sqrt{17^2- 15^2} = 8[/tex]
sin a = [tex]\frac{perpendicular}{hypotenuse} = \frac{8}{17}[/tex]
tan a = [tex]\frac{perpendicular}{base} = \frac{8}{15}[/tex]
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Consider the graphed function.
What are the domain and the range of this function?
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step
What does this problem want to find:
⇒ domain and range
Let's find domain
⇒ distance covered by graph horizontally
⇒ [-5, 1)
Let's find range
⇒ distance covered by graph vertically
⇒ [-4, 7)
*note
use parentheses when endpoint is hollow⇒ those points are not included in domain and range
use brackets when the endpoint is filled⇒ those points are included in domain and range
Answer:
Domain: [-5, 1) Range: [-4, 7)Hope that helps!
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Domain of the function are the real values at which the function is defined, or has a unique value. generally domain is represented by the values that x - coordinate can take according to graph.
So, domain of given function is :
[ -5, 1 )here,
[ ] represents closed interval - that means it can have the extreme values too. ( ) represents open interval - that means it can have values between extremes but not extreme value.Similarly, range represents all the values that the function can have, and it is represented by the values that y - coordinate can have.
So, range of given function is :
[ -4, 7 )Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
A statement which does not describe a characteristic of the line of best fit for a scatter plot is that: A. the line of best fit should be the average of all the data points.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
The characteristics of a line of best fit.The statements which describe a characteristic of the line of best fit for a scatter plot include the following:
The line should be as close to the points as possible.The number of points above the line should be equal to the number of points below the line.The distance between the points above the line and the line should be relatively equal to the distance between the points below the line and the line.Read more on scatterplot here: brainly.com/question/6592115
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Find the net outward flux of f=a×r across any smooth closed surface in r3, where a is a constant nonzero vector and r=〈x,y,z〉
Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].
Flux is the presence of a pressure field in a detailed physical medium or the glide of electricity through a surface. In electronics, the term applies to any electrostatic field and any magnetic subject. Flux is depicted as "traces" in a plane that contains or intersects electric powered fee poles or magnetic poles.
The definition of flux is a flow of liquid from the body, or a regular movement or exchange. An instance of flux is diarrhea. An example of flux is an ever-converting list of the responsibilities of a particular process. regular or frequent alternate; fluctuation.
Flux is a go-platform computer program that adjusts a show's color temperature in keeping with vicinity and time of day, offering practical respite for the eyes. the program is designed to reduce eye stress at some stage in night-time use, supporting reducing the disruption of sleep patterns.
Our field is IR^3 be,
F= (bz-cy,cx-az,ay-bx)
Now divergence theorem says that Flux can be calculated by
[tex]\int\limits^ {} \, F.n = \int\limits^ {} \,( c.F) dv[/tex]
Now let's calculate the divergence of a vector field
F = (ia/ax + ja/ay + k*a/az)*((bz-cy)i+((x-dz))+(ay-bx)*k)
a/ax(bz-cy)+a/ay(cx-az)+a/az(ay-bx)
= 0+0+0
=0
Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].
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Describe the design and original dimensions of the photo you chose for Francesca to give as a gift.
Step-by-step explanation:
Transcribed image text: Choosing a Photo Francesca wants to give one of her photographs to a friend as a gift. Help her choose the photograph and determine the style and size of the mat she can afford 1. Describe the design and original dimensions of the photo you chose for Francesca to give as a gift. 2 points: 1 point for describing the photo and 1 point for including the dimensions) Photo description: The photo Shous Francasca and has Friend huagina. Dimensions (including units): The still Photo is a Xg meaning its width is indas and Langth is gind Finding the Total Area of the Photo and Mat 2. Francesca wants to glue her photo on top of a mat that will increase the length of each side. The mat border has a width of x, so the length of each side would increase by 2x inches. Represent the length and width of the mat with an expression. (2 points) Length: Width: 3. The area of the mat is the product of the length and width. Write an expression for area as the product of two binomials. Do not multiply.(1 point)
Solve each problem mentally. Type the answer in each box. 1. Bottle A contains 4 ounces of water, which is 25% of the amount of water in Bottle B. How much water is there in Bottle B? 2. Bottle C contains 150% of the water in Bottle B. How much water is there in Bottle C? 3. Bottle D contains 12 ounces of water. What percentage of the amount of water in Bottle B is this? %
Answer:
1. 16
2. 24
3. 75
Step-by-step explanation:
if the mean of the frequency distribution below is 5.2 find y
class mark : 2,4,6,8
frequency: 4,y,6,5
Find the product or type impossible[5 -2 4] [2 7 -3]
Answer:
Step-by-step explanation:
You can only multiply matrices if the number of columns in the matrix on the left is the same exact number as the number of rows in the matrix to the right of that other matrix.
The matrix on the left, |5 -2 4| has the dimensions
1 x 3 (1 row, 3 columns)
The matrix to its right, |2 7 -3| has the dimensions
1 x 3 (1 row, 3 columns).
Putting those dimensions next to each other in that order:
1 x 3 1 x 3
The bold print 3 and 1 have to be the same number (both 3's or both 1's) in order for the multiplication to work. This doesn't work; it's impossible.
Answer: -16
Step-by-step explanation:
i was on a unit exam typing in random numbers since i didn't know it and -16 is the right answer.
Geometry: complete this proof, ASAP!!!!!!!!!!!!!!!! It’s urgent
Answer:
1. AC is perpendicular to BD
1. Given
2. ACB is a right angle
2. Definition of perpendicular lines
3. Triangle ACB is a right triangle
3. Definition of right triangles
4. Angles 1 and 3 are complementary
4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.
Help please! I already know the answer isn't -2, -1 so I need help figuring out the rest!
A function is shown in the table.
x g(x)
−2 2
−1 0
0 2
1 8
Which of the following is a true statement for this function? (5 points)
Group of answer choices
The function is decreasing from x = 0 to x = 1.
The function is decreasing from x = −1 to x = 0.
The function is increasing from x = 0 to x = 1.
the function is increasing from x = 0 to x = 1
when x = 0, y = 2
when x = 1, y = 8
this shows an increase of +6, so we know this statement is true
we can see the rest are false simply because they state a decrease when there is an increase. this question is only confusing because we ask you about the increase and decrease in the function, when really its the same thing as asking about an increase or decrease in the y variable.
in other words, all youre looking for is the variation of the value of the y variable that is attached to the specific x variables.
hope this helps!!
Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the basketballs have enough air in them. Given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside six of Jake’s basketballs? Assume that the wall of each ball is infinitely thin.
Using the volume of a sphere, the total volume of air inside six of Jake's basketballs is of 2140.8 cubic inches.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
From the problem, since the properly inflated basketball measures 8.8 inches across, the diameter is of 8.8 inches, hence the radius is:
r = 8.8/2 = 4.4 inches.
Then the volume in cubic inches of a single ball is:
V = 4 x pi x (4.4)³/3 = 2140.8 cubic inches.
For the six balls:
6 x 356.8 = 2140.8 cubic inches.
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Compare and contrast expanding and simplifying algebraic expressions with simplifying numeric expressions. for example, compare simplifying 3(x – 2) (x – 1) with 3(5 – 2) (5 – 1).
The expression for 3(5 - 2) + (5 - 1) is 13.
What does it mean to simplify numerical expressions?Solving a math problem is the same thing as simplifying an expression. You strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing.For instance, if someone claims that x + 2 - 3 + 8 = 11 is a mathematical equation, you have to refute it.Given: 3(x-2) + (x-1)
3x-3(2)+x-1
3x - 6 + x - 1
Compared 3(x -2) + (x - 1) with 3(5 - 2) + (5 - 1), the value of x is 5.
Substitute x = 5 into the result
3x - 6 + x - 1
3(5) - 6 + 5 - 1
15 - 1 - 1
15 - 2 = 13
The expression for 3(5 - 2) + (5 - 1) is 13.
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Answer:
With algebraic expressions, you can’t add and subtract any terms like you can add and subtract numbers. Terms must be like terms in order to combine them. So, you can’t always simplify an algebraic expression by following the order of operations. You have to use the distributive property to rewrite the expression and then combine like terms to simplify. With numeric expressions, you can either simplify inside the parentheses first or use the distributive property first.
Step-by-step explanation:
had it correct in edg
Mario invests $1,500 in a savings account that earns 2% interest a year. He also plans to set aside $50 cash a month. x = number of years Savings account: f(x) = 1500(1.02)x Cash savings: g(x) = 50(12x) Which function represents the total amount Mario will save over x years?
Step-by-step explanation:
1500*.02*1=30
50*12*1=60
g(x)=50(12x) good
This table defines function f:
Answer:
Neither
Step-by-step explanation:
This function isn't even, because
[tex]f(x) = f( - x)[/tex]
Basically this mean for every x opposites the y value should be the same.
Here, 6 and -6 doesn't share the same y value, nor as -3,and 3.
This function isn't odd because
[tex]f( - x) = - f(x)[/tex]
Basically, this means our y values should be reflected about the orgin,
here, the y values does not switch signs for every x value and it's opposite itself , so this function isn't odd.
So The answer is neither
Write the equivalent expression to
Answer:
Step-by-step explanation:
Begin by changing the radical form to exponential form:
[tex]((1024w^{-2}x^{-3}y^6z^{-1)^2)^{\frac{1}{5} }[/tex] There are a couple of ways to do this, but let's distribute the power of 2 into the parenthesis first by using the power to power rule of multiplication:
[tex](1024^2w^{-4}x^{-6}y^{12}z^{-2})^{\frac{1}{5}[/tex] Now we can use the same rule of power to power and distribute the power of 1/5 in:
[tex]1024^{\frac{2}{5}}w^{-\frac{4}{5}}x^{-\frac{6}{5}}y^{\frac{12}{5}}z^{-\frac{2}{5}[/tex]
The first term simplifies down to 16, and then in order to make the negative exponents positive, we move them to the denominator of a fraction, leaving the positive one where it is:
[tex]\frac{16y^{\frac{12}{5}} }{w^{\frac{4}{5}}x^{\frac{6}{5} }z^{\frac{2}{5} } }[/tex] which is the third choice down
(2x² + 6x + 6) (3x - 2)
Answer:
6x³ + 14x² + 6x - 12
Step-by-step explanation:
(3x - 2)(2x² + 6x + 6)
6x³ - 4x² + 18x² - 12x + 18x - 12
6x³ + 14x² + 6x - 12
Answer: 6x³+14x²+6x-12
Step-by-step explanation:
Here, we can use the distributive property to multiply one of the factors by each term in the other. Below, I multiplied [tex]2x^2 + 6x + 6[/tex] by both 3x and -2.
[tex](2x^2+ 6x + 6) (3x - 2)\\3x(2x^2+ 6x + 6)-2(2x^2+ 6x + 6)\\6x^3+18x^2+18x-4x^2-12x-12[/tex]
Now, we can rearrange so that like terms are next to each other. Then, we can combine them to simplify.
[tex]6x^3+18x^2+18x-4x^2-12x-12\\6x^3+18x^2-4x^2+18x-12x-12\\6x^3+14x^2+6x-12[/tex]
100 points to whoever can answer this!
Answer:
10724.29
Step-by-step explanation:
mean means average
so to find an average you add everything together then divide it by the amount of variables
m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7
m = 75070/7
m = 10724.2857143
m = 10724.29
If Hiawatha held his bow 1.5 m off the ground and shot the arrow at a 45° angle with an initial velocity of 40 m/s, then the arrow’s height (in meters) off the ground can be modeled by the equation h(t)=−9.8t2+28t+1.5.
The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds
How to determine the time to reach 3 meters?The complete question is added as an attachment
The function is given as:
[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]
Set the height to 3
[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]
Subtract 3 from both sides
[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]
Apply the following quadratic formula
[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]
So, we have:
[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]
This gives
[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]
This gives
[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]
Expand
[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]
This gives
t = 0.054 and t = 2.80
0.054 is less than 2.80
This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds
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Select all the correct answers. a group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
Answer:
This study uses random sampling
This study uses a control group
This study uses a repeated measures design
Answer:
this study uses random sampling
this study uses a control group
this study uses a repeated measures design
Step-by-step explanation:
plato 2022
can someone help me really quick?
Answer:
Step-by-step explanation:
23 - (-2)
= 23 + 2
= 25
1) The mistake you made was to subtract 2 from 23 instead of subtracting -2 from 23.
2) Keep in mind the difference between the '-' used as a subtraction and the '-' used for indicating a negative number.
If you like, remember the mantra ' 2 negatives make a '+'.:-
2 - -4
= 2 + 4= 6.
Katie is planning to paint the gate of her house that has a glass panel. Painting the gate costs $4 per square foot. How much will she have to spend to paint the gate?
Answer:
$14.15
Step-by-step explanation:
6+4+.75+.4
The growth of a strain of bacteria can be modeled by the function graphed, where the x-values are the time in seconds and the y-values are the number of bacteria. how many bacteria are there initially? 0 2.7 2.8 4
There are (A) 2.7 bacterias initially.
What is a function?A function is an expression that establishes the relationship between the dependent and independent variables.A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To find the number of bacteria:
The graph shows that the function follows an exponential curve, and the starting point is at ( 0,2.7 ). The starting number of bacteria is then 2.7.Therefore, there are (A) 2.7 bacterias initially.
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The correct question is given below:
The growth of a strain of bacteria can be modeled by
the function graphed, where the x-values are the time
in seconds and the y-values are the number of
bacteria. How many bacteria are there initially?
(A) 2.7
(B) 2.8
(C) 4
Answer:
mine was b 2.7
Step-by-step explanation:
What is a fitted value for a multiple regression model and the data that is used to create it?
Fitted value is a prediction of the mean response value.
According to the statement
we have to explain the fitted value for the regression model and the data which uses to collect the value.
So, For this purpose, we know that the
A Fitted value is a statistical model's prediction of the mean response value when you input the values of the predictors, factor levels, or components into the model.
An the fitted value used in this model is called the predicted values of response variable in the case of multiple regression model.
And data which is used to create the fitted value is the simple data by which we create the fitted value by the predict the value of given data.
So, Fitted value is a prediction of the mean response value.
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Joy is training for a triathlon. she runs a distance of 2x miles, cycles a distance of (x2 7) miles, and swims a distance of (x − 2) miles. which simplified expression is equivalent to the total distance, in miles, joy covers? x2 3x 5 x2 3x 9 3x2 5 3x2 9
The simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.To find the simplified expression:
Given -
Distance cycled = x² + 7 milesDistance ran = 2x milesDistance swam = x - 2 milesThus,
Total distance she covers = x² + 7 + 2x + x - 2Total distance = x² + 3x + 5 milesTherefore, the simplified expression that is equivalent to the total distance, in miles, Joy covers is (A) x² + 3x + 5 miles.
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The complete question is given below:
Joy is training for a triathlon. She runs a distance of 2x miles, cycles a distance of (x2 + 7) miles, and swims a distance of (x - 2) miles. Which simplified expression is equivalent to the total distance, in miles, Joy covers?
(A) x2 + 3x + 5
(B) x2 + 3x + 9
(C) 3x2 + 5
(D) 3x2 + 9
Answer:
The person on top is right.
ITS A
Step-by-step explanation:
I need help with this math question.
Answer:
23 children and 9 adults
p <= 70/9
Step-by-step explanation:
Let x = # of adults and y = # of children. The number of children is 5 more than twice the number of adults, so x = 2y + 5. The total cost of entrance is $6525, so 225x + 150y = 6525.
x = 2y + 5
225x + 150y = 6525
x - 2y = 5
225x + 150y = 6525
75x - 150y = 375
225x + 150y = 6525
300x = 6900
x = 23
x = 2y + 5
23 = 2y + 5
18 = 2y
y = 9
225p + 3750 <= 5500
225p <= 1750
p <= 70/9
3.
Determine how much this home would cost to replace: 2,600 square feet at $86.00 per square foot
Answer: $
Answer: $223,600
Step-by-step explanation:
Since it is $86 per square foot and you're replacing the 2,600 square foot house you would just take 2,600 × 86 and get 223,600 dollars.
Match each quadratic function given in factored form with its equivalent standard form listed on the left. f(x) = (x 2)(x – 6) f(x) = (x – 4)(x 3) f(x) = (x – 12)(x 1) f(x) = (x – 3)(x 4)
standard form of the given equation are
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
What is quadratic function?A polynomial function with one or more variables in which the second-degree term is the highest degree is known as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic, in algebra.
What is standard form of a quadratic function?As long as an is not equal to zero, the quadratic function f(x) = a(x - h)2 + k is considered to be in standard form. The graph starts out in either an upward or a downward direction depending on the value of a. The point at the vertex of the symmetry is represented by the vertical line x = h. (h,k).
According to the given information:The standard form list.
1 . (x + 2)(x - 6)
= x² - 6x + 2x - 12
= x² - 4x -12
2. (x - 4)(x + 3)
= x² + 3x - 4x - 12
= x² - x - 12
3. (x - 12)(x + 1)
= x² + 1x - 12x - 12
= x² - 11x - 12
4. (x -3)(x + 4)
= x² + 4x - 3x - 12
= x² + x - 12
So the equivalent standard form of the give values are :
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
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I understand that the question you are looking for is:
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
f(x) = (x + 2)(x – 6)
f(x) = (x – 4)(x+3)
f(x) = (x – 12)(x+1)
f(x) = (x – 3)(x +4)
Find the average value of the function ()=3 on the interval [−3,3] and determine a number in this interval for which () is equal to the average value
The average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].
According to the given question.
We have a function.
F(x) = 3x^2
Since, we know that " the average value of a function is found by taking the integral of the function over the interval and dividing by the length of the interval".
Here, the given interval is [-3, 3]
Therefore, the length of the interval = 3 - (-3) = 3 + 3 = 6
Now, the average value of the given function f(x)
[tex]=\frac{1}{6} \int\limits^3_{-3} {3x^{2} } \, dx[/tex]
[tex]= \frac{1}{6} [\frac{x^{3} }{3} ]_{3} ^{-3}[/tex]
[tex]= \frac{1}{6} \frac{(3)^{3} -(-3)^{3} }{3}[/tex]
[tex]= \frac{1}{18} (27 + 27)[/tex]
= 2(27)/18
= 27/9
= 3
Hence, the average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].
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Time Remaining
59:15
A kite is inscribed within a square with a side lengths of 9 units.
A kite is inscribed in a square with a side length of 9 units.
What is the area of the kite?
27.5 square units
36.0 square units
40.5 square units
45.0 square units
Answer:
(c) 40.5 square units
Step-by-step explanation:
Assuming the kite is oriented so its diagonals are parallel to the sides of the square, each diagonal is 9 units long. The area of the kite is given by an appropriate formula.
What is a kite?A kite is a parallelogram with two pairs of adjacent congruent sides. Its diagonals meet at right angles. One diagonal bisects the other.
Kite areaThe formula for the area of a kite is ...
A = 1/2(d1)(d2) . . . . . where d1 and d2 are the lengths of the diagonals
In this problem, the inscribed kite has congruent diagonals, both of length 9 units.
The area of the kite is ...
A = 1/2(9)(9) = 81/2 = 40.5 . . . . square units
WILL GIVE BRAINLEST!!!
Kerry wants to know whether or not people will be voting in the upcoming presidential election. She posts signs giving the website for her survey. Which sampling method is described?
A. Unbiased Systematic Random Sample
B. Biased Convenience Sample
C. Unbiased Simple Random Sample
D. Biased Voluntary Response Sample
catherin worked 23 hours last week babysitting. She earned 126.50. What is her rate of pay?
Answer:5.50 a hour
Step-by-step explanation: