Vector g is from the red jet ski to the green boat. The magnitude is √26 and the direction angle is 248.7°, the component form of vector g is approximately (-3.8, -1.4).
To write the component form of vector g, we need to determine the horizontal and vertical components of the vector.
Given:
Magnitude of g = √26
Direction angle = 248.7°
To find the horizontal component (g_x) and vertical component (g_y) of vector g, we can use the following trigonometric formulas:
g_x = magnitude * cos(angle)
g_y = magnitude * sin(angle)
Substituting the given values:
g_x = √26 * cos(248.7°)
g_y = √26 * sin(248.7°)
Now, let's calculate the values:
g_x = √26 * cos(248.7°) ≈ -3.8
g_y = √26 * sin(248.7°) ≈ -1.4
Therefore, the component form of vector g is approximately (-3.8, -1.4).
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The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth of coffee makers, which of the following is a valid possible price for them?
A. $15
B. $30
C. $40
D. $55
The possible price for the items if the store sells $600 is (c) $40
How to determine the possible price for the items?From the question, we have the following parameters that can be used in our computation:
The supply-demand graph
If the store sells $600, then there is a supply worth of $600
The equation of the supply line is calculated as
y = mx + c
Where
c = y = 0
i.e. c = 100
So, we have
y = mx + 100
Using another point on the graph, we have
30m + 10 = 400
So, we have
m = 13
This means that
y = 13x + 100
For a supply of 600, we have
13x + 100 = 600
So, we have
13x = 500
Divide by 13
x = 38.4
Approximate
x = 40
Hence, the possible price for the items is (c) $40
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Slope of Linear Equations
Which description best compares the graph given by the following equations:
5x-3y = -5
2x-y = 8
parallel
perpendicular
intersecting but not perpendicular
Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995.
Year Retail Sales
0 85.851
3 108.426
6 141.781
9 169.256
12 202.297
15 222.266
Let
be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t)= 9.44 t +84.182.
Use the above scatter plot to decide whether the linear model fits the data well.
The function is not a good model for the data
The function is a good model for the data.
Estimate the retails sales in the U. S. in 2016.
billions of dollars.
Use the model to predict the year that corresponds to retails sales of $241 billion.
The function is a good model for the data.
The retail sales in the U.S. in 2016 is estimated to be 282.24 billion dollars.
The year that corresponds to retail sales of $241 billion is 2020.
How to calculate the valueThe function F(t)= 9.44 t +84.182 is a linear model for the data. This means that the graph of the function is a straight line.
The scatter plot shows that the data points are close to a straight line. This means that the function is a good model for the data.
To estimate the retail sales in the U.S. in 2016, we need to find the value of F(11). F(11) = 9.44 * 11 + 84.182
= 282.24.
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What are the approximate polar coordinates for the point with rectangular coordinates (–2, 4)? Give θ in degrees rounded to the nearest thousandth.
|x – 4| > –3 will have what type of solution set
Answer:
The inequality |x – 4| > –3 represents an absolute value inequality.
The absolute value of any real number is always non-negative, meaning it is greater than or equal to zero. Therefore, the left side of the inequality, |x – 4|, will always be greater than or equal to zero.
Since the right side of the inequality, -3, is also greater than or equal to zero, this means that the inequality |x – 4| > –3 holds true for all real numbers x. In other words, there are no restrictions on the value of x.
The solution set for this inequality is the set of all real numbers, often represented as (-∞, +∞).
Answer:
(−∞,∞)
Step-by-step explanation:
|x – 4| > – 3
Since |x – 4| is always positive and - 3 is negative, |x – 4| is always greater than - 3, so the inequality is always true for any value of x.
All real numbers
The result can be shown in multiple forms.
All real numbers
So, the answer is (−∞,∞)
Determine the length of the missing side of the triangle. Round your answer to the
hundredths place.
Answer:
670
We can use the pythagorus theorum which says
The square of hypotenuse is equal to the square of perpendicular added to sq of base
Step-by-step explanation:
Use h2=p2+b2
H=6.708
Rounding to the hundredth place the answer is 670.8
Using Pythagoras Theorem (since the triangle is a right angled triangle)
[tex]( {hyp}^{2}) = ( {base}^{2} ) + ( {per}^{2} )[/tex]
[tex]( {hyp}^{2} ) = ( {3}^{2} ) + ( {6}^{2}) [/tex]
[tex]( {hyp}^{2} ) = 9 + 36[/tex]
[tex] {hyp}^{2} = 45[/tex]
Taking under root on both sides
[tex]hyp = 6.7[/tex]
Hence the missing side is 671
What is the mode of this data set?
{4, 15, 6, 11, 7, 4, 3, 14}
Answer:
4
Step-by-step explanation:
A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)
There are 2 companies in town that seem to have a reasonable deal on fencing.
Company 1 will charge $200 for the first 150 ft of fencing and $18 for each additional
foot. Company 2 will charge you $450 for the first 75 ft of fencing and $15 for each
additional foot. Determine which company has the better deal. Provide evidence to
support your answer..
To determine which company offers the better deal, we compare the total costs for different amounts of fencing. Company 1 has a better deal for less than 608 ft of fencing, while Company 2 is more cost-effective for 608 ft or more.
To determine which company offers the better deal for fencing, we need to compare the total cost for a specific amount of fencing between the two companies.
Let's consider the amount of fencing required as "x" feet.
Company 1 charges $200 for the first 150 ft of fencing and $18 for each additional foot. So, the total cost for x feet of fencing with Company 1 can be calculated as:
Cost1 = $200 + $18 × (x - 150)
Company 2 charges $450 for the first 75 ft of fencing and $15 for each additional foot. Thus, the total cost for x feet of fencing with Company 2 is:
Cost2 = $450 + $15 × (x - 75)
To determine which company offers the better deal, we need to find the range of x values for which Cost1 is less than Cost2. Let's set up the inequality:
Cost1 < Cost2
$200 + $18 × (x - 150) < $450 + $15 × (x - 75)
Now, we can solve this inequality to find the range of x values where Company 1's cost is less than Company 2's cost.
$200 + $18x - $2700 < $450 + $15x - $1125
Combining like terms:
$18x - $2499 < $15x - $675
Subtracting $15x from both sides:
$3x - $2499 < - $675
Adding $2499 to both sides:
$3x < $1824
Dividing both sides by $3 (since x represents feet, we can ignore the currency):
x < $1824 / $3
x < 608
Therefore, for any value of x less than 608 feet, Company 1 has a better deal. However, when x is equal to or greater than 608 feet, Company 2 offers a better deal.
To provide evidence supporting this answer, let's consider an example:
Suppose we need 200 feet of fencing.
Using Company 1:
Cost1 = $200 + $18 × (200 - 150)
Cost1 = $200 + $18 × 50
Cost1 = $200 + $900
Cost1 = $1100
Using Company 2:
Cost2 = $450 + $15 × (200 - 75)
Cost2 = $450 + $15 × 125
Cost2 = $450 + $1875
Cost2 = $2325
In this example, Company 1's cost is $1100, while Company 2's cost is $2325. Hence, for 200 feet of fencing, Company 1 provides the better deal.
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sett up 12-5*9√49-5²
Answer:
-328
Step-by-step explanation:
Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order
Brackets: there are no brackets, move on to indices/order
Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25
Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25
Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.
I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1
through 43) and matching the number on the gold ball (1 through 34). If one ticket is purchased, what is the probability
of winning the jackpot?
The probability of winning the jackpot with one ticket is P ( A ) = 1/34
Given data ,
To calculate the probability of winning the jackpot in the lottery, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (winning outcomes).
Total number of possible outcomes:
For the white balls, there are 43 numbers to choose from, and we need to select 5 distinct numbers in any order. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of options and r is the number of selections. In this case, we have 43 white balls and need to choose 5, so the number of possible outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43! / (5! * 38!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there are 34 numbers to choose from, and we need to select 1 number. So the number of possible outcomes for the gold ball is simply 34.
Therefore, the total number of possible outcomes is:
Total outcomes = (43 * 42 * 41 * 40 * 39) * 34
Number of favorable outcomes (winning outcomes):
To win the jackpot, we need to match all 5 distinct numbers from the white balls and the number on the gold ball. Since order doesn't matter for the white balls, we can use the combination formula again:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have 43 white balls and need to choose 5, so the number of favorable outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there is only 1 winning number.
Therefore, the number of favorable outcomes is:
Favorable outcomes = (43 * 42 * 41 * 40 * 39) * 1
Probability of winning the jackpot:
The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Plugging in the values, we get:
Probability = [(43 * 42 * 41 * 40 * 39) * 1] / [(43 * 42 * 41 * 40 * 39) * 34]
Simplifying, we find:
Probability = 1 / 34
Hence , the probability of winning the jackpot with one ticket in this lottery is 1 in 34.
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Solve the following equation for B over the interval [0,2pi]
, giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list.
The solution of the equation for B over the interval [0,2π] is undefined
How to solve the equation for B over the interval [0,2π]From the question, we have the following parameters that can be used in our computation:
-√3tan(β) = tan(β)sin(β)
Divide both sides of the equation by tan(β)
so, we have the following representation
-√3 = sin(β)
Rewrite as
sin(β) = -√3
Take the arc sin of both sides
β = undefined
Hence, the solution of the equation for B over the interval [0,2π] is undefined
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D. Determining the best job to take based on the pay. when considering a new job. a. Job A is 40 hours per week and pays $15 per hour (gross pay) with no tips. b. Job B is 30 hours per week and pays $5 per hour (gross pay) plus tips (which average $350 per week).
The job A is the best job based on pay scale
Given data ,
a) Job A:
Hours per week: 40
Hourly rate: $15
On simplifying the equation , we get
Gross pay per week: 40 hours * $15/hour = $600
b) Job B:
Hours per week: 30
Hourly rate: $5
On simplifying the equation , we get
Gross pay per week: 30 hours * $5/hour = $150
In addition to the base pay, Job B also offers tips averaging $350 per week.
Considering the total compensation for each job:
Total compensation for Job A: $600 per week (base pay)
Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week
Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.
Hence , if the decision is solely based on pay, Job A would be the better choice.
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Warm-Up
What is the approximate area of the shaded region?
Select the correct answer.
O 15.45 cm²
O69.53 cm²
128.54 cm²
18 cm
182.47 cm²
4
Answer:
The answer is 69.63cm²
Step-by-step explanation:
d=18
r=d/2=18/2=9cm
Area of shaded portion =Area of square -Area of circle
A=18²-pi×9²
A=69.53cm²
Answer:
69.53 centimeters squared.
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:
Area = [tex]side^{2}[/tex]Inserting 18 as our side length:
Area = [tex]18^{2}[/tex] = 324Therefore, the area of the square without the circular gap is 324 [tex]cm^{2}[/tex].
To solve for the area of a circle, we can use the formula:
Area = π[tex]r^{2}[/tex]But wait, we are given the diameter, not the radius!
No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.
18 ÷ 2 = 9Inserting 9 into the formula for the radius:
Area = π × [tex]9^{2}[/tex] = 81π = 254.47 (Rounded to 2 decimal points)Now we can subtract this from the squares area.
324 - 254.47 = 69.53The closest to match this approximation is [tex]69.53cm^{2}[/tex].
NO LINKS!! URGENT HELP PLEASE!!!
4. Use the theorems for interior and exterior angles of a polygon to find:
a. The sum of the interior of a 73-gon.
b. The number of sides of a regular polygon if the sum of the interior angles is 2700°
c. The number of sides of a reguluar polygon if the exterior angle is 7.2°
Answer:
see explanation
Step-by-step explanation:
a
the sum of the interior angles of a polygon is calculated as
sum = 180° (n - 2) ← n is the number of sides
here n = 73 , then
sum = 180° × (73 - 2) = 180° × 71 = 12,780°
b
here sum of interior angles = 2700° , then
180° (n - 2) = 2700° ( divide both sides by 180° )
n - 2 = 15 ( add 2 to both sides )
n = 17
number of sides is 17
c
the sum of the exterior angles of a polygon = 360°
given the polygon is regular then each exterior angle is congruent , so
number of sides = 360° ÷ 7.2° = 50
Answer:
a) 12870°
b) 17
c) 50
Step-by-step explanation:
Part aThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:
[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]
Therefore, the sum of the interior angles of a 73-gon is 12870°.
[tex]\hrulefill[/tex]
Part bThe Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.
Given the sum of the interior angles of a regular polygon is 2700°, then:
[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 17.
[tex]\hrulefill[/tex]
Part cAccording the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.
Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.
[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 50.
The following is a parallelogram. What does A=, B=, X=, QR= and Angle QRS=
Answer:
a = 4
b=2
x=18
QR =16+1=17
Angle QRS =59
Step-by-step explanation:
4a+1 = 2a + 9
2a = 8
a = 4
6b = 11b-10
-5b=-10
-b= -2
b=2
6x+13 = 7x - 5 (opposite angles are equal)
-x=-18
x=18
QR =16+1=17
Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)
HELP PLEASE 30 POINTS
Four transformations of the function f(x)=4x
are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
The expression that shows the result of that transformation are:
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
The given function is f(x) =4ˣ.
We have to find the transformations applied to the function f(x).
Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.
f(x) =4ˣ
We have to find 3f(x), f(3x), f(x+3) and f(x)+3.
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
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What are the vertex and range of y = |3x + 6| − 4?
A (−2, −4); −∞ < y < ∞
B (−2, −4); −4 ≤ y < ∞
C (0, −4); −∞ < y < ∞
D (0, −4); −4 ≤ y < ∞
For the given function:
Vertex is at (-2, -4) and range is −4 ≤ y < ∞
Hence, Option b is correct.
The given function is
y = |3x + 6| − 4
We can see that it is consist of absolute value function or mod function.
Since we know that,
An absolute value function is an algebraic function in which the variable is contained inside the absolute value bars.
The absolute value function is also known as the modulus function, and its most frequent form is f(x) = |x|,
where x is a real integer. In general, the absolute value function may be represented as f(x) = a |x - h| + k,
where a denotes how far the graph extends vertically, h represents the horizontal shift, and k represents the vertical displacement from the graph of f(x) = |x|.
If the value of 'a' is negative, the graph opens downwards; otherwise, it opens upwards.
The appropriate method of finding range and vertex both is to plot its graph:
Therefore after plotting graph we get,
Vertex is at (-2, -4)
And range is (-4 , ∞) ⇒ −4 ≤ y < ∞
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¿De cuántas maneras es posible formar los grupos del torneo de liga de futbol de primera división? Recordemos que en la primera división del futbol en México participan 18 equipos, y para el torneo de la liga se forman dos grupos de cinco equipos y dos grupos de 4 equipos. Se sugiere que al resolverlo se vaya restando la cantidad de equipos que se han considerado para el primer grupo, después para el segundo grupo y así para cada grupo. Finalmente aplicar la regla del producto para encontrar las diferentes formas.
Note that his is solved using the principle of Combination, and there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
How is this so ?Let 's compute the number of ways to form the groups using combinations.
First group - 5 teams
C(18, 5) = 18! / (5! * (18-5)!) = 8568
Second group - 5 teams
C(13, 5) = 13! / (5! * (13-5)!) = 1,287
Third group - 4 teams
C(8, 4) = 8! / (4! * (8-4)!) = 70
Fourth group - 4 teams
C(4, 4) = 4! / (4! * (4-4)!) = 1
Now, applying the product rule
Total ways = 8568 x 1,287 x 70 x 1 = 771891120
Therefore, there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.
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Translation
In how many ways is it possible to form the groups of the first division soccer league tournament? Let's remember that 18 teams participate in the first division of soccer in Mexico, and for the league tournament, two groups of five teams and two groups of 4 teams are formed. It is suggested that when solving it, the number of teams that have been considered for the first group be subtracted, then for the second group and so on for each group. Finally apply the product rule to find the different shapes.
find the area of the triangle whoose side are 12,16 and 21 units
Answer:
[tex]A =[/tex] 95.45
Step-by-step explanation:
[tex]A=s(s﹣a)(s﹣b)(s﹣c)[/tex]
[tex]s=a+b+c[/tex]
Solving for A
A=1
4﹣[tex]a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1[/tex]
4-[tex]124+2·(12·16)2+2·(12·21)2﹣164+2·(16·21)2﹣214≈95.45123[/tex]
≈ 95.45123
Derivative for 2/x is ?
Answer:
[tex]-2x^{-2} \ \text{or} \ -\frac{2}{x^2}[/tex]
Step-by-step explanation:
Find [tex]\frac{d}{dx}[\frac{2}{x} ][/tex].
(1) - Pull out the constant
[tex]\frac{d}{dx}[\frac{2}{x} ]\\\\\Longrightarrow 2\frac{d}{dx}[\frac{1}{x} ][/tex]
(2) - Flip the fraction
[tex]2\frac{d}{dx}[\frac{1}{x}]\\\\\Longrightarrow 2\frac{d}{dx}[x^{-1}][/tex]
(3) - Apply the power rule]
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right}\\\\\\2\frac{d}{dx}[x^{-1}]\\\\\Longrightarrow 2[(-1)x^{-1-1}]\\\\\Longrightarrow 2[-x^{-2}]\\\\\therefore \boxed{\boxed{\frac{d}{dx}[\frac{2}{x} ] =-2x^{-2} \ \text{or} \ -\frac{2}{x^2}}}[/tex]
Thus, the problem is solved.
Use Juliana's text message data to answer the questions.
What was the mean number of text messages that Julianna sent per day
The mean number of text messages that Julianna sent per day is 7.
To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.
Total number of text messages sent:
13 + 0 + 4 + 4 + 5 + 6 + 17 = 49
Total number of days: 7
Mean = Sum of all observations/number of observations
Mean =Total number of text messages sent/Total number of days
Mean number of text messages per day: 49 / 7
= 7
Therefore, 7 is the mean number of text messages that Julianna sent per day.
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Use julianna’s text message data to answer the questions.
Text messages sent:
Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17
1. What was the mean number of text messages that julianna sent per day ?
A. 4
B.6
C.8
D.7
11. The height of a plant over 4 weeks is shown in the graph below.
Height of Plant (cm)
16
23
Week
What is the rate of growth of the plant, in centimeters per week?
A 2
B. 3
C. 8
D. 12
The rate of growth of the plant is 2 centimeters per week.
Calculate the change in height divided by the change in time (weeks) to find the plant's growth rate.
To calculate the rate of growth of the plant, we need to determine the change in height per week.
Given:
Initial height = 4 cm
Final height = 12 cm
Weeks = 4
To find the rate of growth, we can use the formula:
Rate of growth = (Final height - Initial height) / Weeks
Substituting the given values into the formula:
Rate of growth = (12 cm - 4 cm) / 4 weeks
Rate of growth = 8 cm / 4 weeks
Rate of growth = 2 cm/week
Therefore, the rate of growth of the plant is 2 centimeters per week.
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What is the answer please
The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.
How to find the volume of the cylinder of heightTo calculate the volume of a cylinder, you can use the formula:
Volume = π * (radius²) * height
Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:
radius (r) = 8 cm / 2 = 4 cm
The height (h) of the cylinder is 12 cm.
substitute these values into the formula:
Volume = π * (4 cm)² * 12 cm
Volume = π * 16 cm² * 12 cm
Volume ≈ 602.19 cm³ (rounded to two decimal places)
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If I have $25. How many cheeseburgers can I get if they are 2.50 each?
Answer: 10 cheeseburgers
Step-by-step explanation: 25/2.5=10
Answer:
10
Step-by-step explanation:
To determine the number of cheeseburgers you can get with $25, you can divide the total amount of money by the cost of each cheeseburger.
$25 ÷ $2.50 = 10
Therefore, with $25, you can get 10 cheeseburgers if each cheeseburger costs $2.50.
In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
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Answer:
[tex]\{0.559,0.641\}[/tex]
Step-by-step explanation:
[tex]\displaystyle CI_{95\%}=\frac{336}{560}\pm1.96\sqrt{\frac{\frac{336}{560}(1-\frac{336}{560})}{560}}\approx\{0.559,0.641\}[/tex]
From the observation deck of a skyscraper, Brandon measures a 45
angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship is 1140 m
What is the angle of depression?
Under the horizontal line, the angle of depression is measured, typically in degrees. It aids in figuring out how steep or incline the line of sight is in relation to the horizontal plane. The line of sight is steeply directed downward and increases with the angle of depression.
In many different disciplines, such as surveying, navigation, engineering, and physics, the angle of depression is frequently utilized.
We know that;
Tan 45 = x/1140
x = 1140 Tan 45
= 1140 m
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Pure acid is to be added to a 10% acid solution to obtain 90L of 84% solution. How many liter of 10% solution should be in the mixture?
Answer:
16 liters of the 10% acid solution should be in the mixture.
Step-by-step explanation:
Let x represent the volume of the 10% acid solution to be added.
The volume of pure acid added would be (90 - x).
The equation to solve is: 0.1x + (90 - x) = 0.84(90)
Simplifying, we get: 0.1x + 90 - x = 75.6
Combining like terms, we have: -0.9x + 90 = 75.6
Subtracting 90 from both sides: -0.9x = -14.4
Dividing by -0.9: x = 16
Therefore, 16 liters of the 10% acid solution should be in the mixture.
How many ways can you arange 2 Letters picked
from A, B, C, D? order matters
When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).
Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 x 3 x 2 x 1) / (2 x 1)
= 24 / 2
= 12
Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.
~~~Harsha~~~
Answer:
Step-by-step explanation:
When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.
The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:
P(n, r) = n! / (n - r)!
where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.
In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).
Using the formula, we can calculate:
P(4, 2) = 4! / (4 - 2)!
= 4! / 2!
= (4 × 3 × 2 × 1) / (2 × 1)
= 24 / 2
= 12
Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.
its ixl please help