Answer:
So when the two vehicles meet, the van has travelled 87.5 km and the car has travelled 150 km.
Step-by-step explanation:
(a) Let's call the time it takes for the two vehicles to meet "t". We know that the distance between the two towns is 237.5 km, and the combined speed of the two vehicles is 35 km/h + 60 km/h = 95 km/h. Using the formula distance = speed × time:
237.5 = 95t
Solving for t:
t = 237.5/95
t ≈ 2.5 hours
So the two vehicles will meet on the way 2.5 hours after 11.30 a.m., which is at 2.00 p.m.
(b) To find how far each vehicle has traveled when they meet, we can use the formula distance = speed × time again. The van travels at 35 km/h for 2.5 hours, so it travels:
distance = speed × time = 35 km/h × 2.5 hours = 87.5 km
The car travels at 60 km/h for 2.5 hours, so it travels:
distance = speed × time = 60 km/h × 2.5 hours = 150 km
So when the two vehicles meet, the van has traveled 87.5 km and the car has traveled 150 km.
Please help me with this please
The subtraction of the two matrix is [31 6 12 -14 57 ]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
What is the matrix subtraction?The subtraction of the two matrix is calculated as follows;
The result to 4 multiplied by D is calculated as;
4[D] = [28 -24 12 -32 -36]
[8 -36 -24 24 36]
[32 8 20 -40 -12]
[40 -12 -16 12 - 28]
[4 -8 16 -20 -8 ]
The result to 3 multiplied by B is calculated as;
3[B] = [-3 -30 -24 -18 21]
[27 -9 -6 6 9]
[-15 -6 21 0 -21]
[30 -24 3 27 30]
[18 15 6 -24 -27]
The subtraction of the two matrix is calculated as follows;
4[D] - 3[B] = [31 6 12 -14 57]
[-19 -27 -18 18 27 ]
[ 47 14 -1 -40 9 ]
[10 12 -19 -15 -58]
[-14 -23 10 4 19]
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Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, what was the reserve rate? And what are the steps to solve?
Tthe reserve rate was approximately 0.9434, or 94.34%.
How to solve for the reserve rateThis is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:
sum = a(1 - r^n) / (1 - r)
where a = 3000r is the first term.
As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:
3000r/(1-r) = 50,000
Solving for r, we get:
r = (50,000)/(3000 + 50,000) = 0.9434
Therefore, the reserve rate was approximately 0.9434, or 94.34%.
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Parametric Functions
Answer:
Step-by-step explanation:
it think it 23 becasue u add
1 divide it by 2
Carlos draws a square on a coordinate plane. One vertex is located at (5, 3). The length of each side is 3 units. Which of the following ordered pairs could be another vertex?
As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .
what is coordinates ?The placement of a point in a particular space or on a certain graph is represented by coordinates, which are numbers. Coordinates are normally two figures written in parenthesis and separated by a comma in two-dimensional space, where x denotes the point's horizontal position and y denotes its vertical position. Three integers enclosed in parentheses and separated by commas are used to indicate coordinates in three-dimensional space. The three numbers are generally represented as (x, y, z), where x, y, and z stand for the positions all along x-, y-, and z-axes, respectively. The location of objects, points, and other entities in space is described using coordinates frequently in the domains of mathematics, physics, engineering, and many others.
given
Any other vertex must be three units away from the specified vertex because the square has three units on each side.
The distance between the supplied vertex (5, 3) and each of the possible answers can be calculated using the distance formula:
Option A: Distance between (1 and 3) = sqrt((1 - 5)2 + (3 - 3)2) = sqrt(16) = 4 (not three units away)
Option B: Distance between (8 and 6) = sqrt((8 - 5)2 + (6 - 3)2) = sqrt(27) (not three units away)
Option C: (4, 0)
Distance is equal to sqrt((4 - 5)2 + (0 - 3)2 = sqrt(10) (not three units away)
Option D: Distance = sqrt((2 - 5)2 + (1 - 3)2) = sqrt(10) for the pair (2, 1). (not three units away)
As A is the only option that is three units distant from (5, 3), the response is: A) (1, 3) (1, 3) .
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Which of these are statistical questions? Select ALL that Apply Question 1: How many minutes does it usually take each teacher to get from home to work? Question 2: During the past year did you work for more than 50 weeks? Question 3: During the past year how many hours did each teacher usually work each week? Question 4: How many extra hours did each doctor work each week?
The statistical questions are:
Question 1: How many minutes does it usually take each teacher to get from home to work?Question 3: During the past year how many hours did each teacher usually work each week?Question 4: How many extra hours did each doctor work each week?What is a statistical question?
A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.
In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.
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Study the system of equations below.
x + y =-4
x - y = 10 What is the solution to the system of
equations?
A (-4, 10)
B (10, 4)
C(3,-7)
D(7,-3)
Answer:
Option C
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:
2x = 6
Simplifying, we get:
x = 3
Substituting x = 3 into either of the original equations, we get:
3 + y = -4
Solving for y, we get:
y = -7
Therefore, the solution to the system of equations is (3, -7), which is option C.
I deposited #300.00 in a bank for
four years. If it earned simple
interest at the rate of 6% per annum,
how much interest did I get for the
four years?
Answer:
Simple interest= PRT/100
parameters
price =300
Rate=6%
Time=4years
300*6*4/100
7200/100
=72
Find the graphed inequality below
The inequality represent the given graph is y≤1.4x+2.5.
From the graph, the line passes through (0, 2.5) and (3.5, 0).
Here, slope (m) = (3.5-0)/(2.5-0)
= 3.5/2.5
= 1.4
Substitute m=1.4 and (x, y)=(0, 2.5) in y=mx+c, we get
2.5=1.4(0)+c
c=2.5
So, the equation of a line is y=1.4x+2.5
So, the inequality is y≤1.4x+2.5
Therefore, the inequality represent the given graph is y≤1.4x+2.5.
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ACTIVITY 3: Given the following functions, find the following:
The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
Calculating the composite functionsGiven that we have the function definitions
The composite functions are calculated below
(g o f)(x) = g(f(x))
(g o f)(x) = (f(x))² - 5f(x)
So, we have
(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)
Evaluate
(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]
Next, we have
(j o g)(x) = j(g(x))
(j o g)(x) = 3g(x) + 1
So, we have
(j o g)(x) = 3(x² - 5x) + 1
(j o g)(x) = 3x² - 15x + 1
Next, we have
(g o h)(x) = g(h(x))
(g o h)(x) = (h(x))² - 5h(x)
So, we have
(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)
Evaluate
(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]
Lastly, we have
(g o g)(-2) = g(g(-2))
(g o g)(-2) = (g(-2))² - 5g(-2)
So, we have
(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))
(g o g)(-2) = 126
Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
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College Level Trigonometry!!!
An equation that models the position of the object at time t is:
s(t) = -2cos(2πt/5).
How to interpret the trigonometric graph?The general form for the equation that will model a wave is:
±a (sin/cos) (2π(x - p)/T)
where:
a is the amplitude
p is the phase shift
T is the period.
The ± will become +ve provided that the graph starts in the positive direction, and the will become -ve provided it starts in the negative direction.
The (sin/cos) will become sine provided the graph starts at 0 before it is being shifted. Then, it becomes cosine provided that the graph starts at the amplitude.
In this case, our graph begins at negative, and the at the amplitude that has no phase shift, the ±ve will become -ve, (sin/cos) will now become cos, and p will become zero. Plugging in the values that were given in the problem, we see that a = 2 and T = 5.
Thus, this equation is: s(t) = -2cos(2πt/5).
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Answer:
The IQR (interquartile range) of 13 is the most accurate measure of variability to use in this case, since the data is skewed and contains some outliers.
The IQR is a measure of variability that is less sensitive to extreme values than the range, and is calculated as the difference between the upper and lower quartiles (the 75th and 25th percentiles). It provides a measure of the spread of the middle 50% of the data, which is useful for understanding the typical range of donations received.
In this case, the IQR is calculated as follows:
- The median of the data is 51 (the value in the middle).
- The lower quartile (Q1) is the median of the lower half of the data, which is 42.
- The upper quartile (Q3) is the median of the upper half of the data, which is 54.
- The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 54 - 42 = 12.
So the IQR of 13 is a useful measure of variability to use for this data set, since it captures the spread of the middle 50% of the data while being less sensitive to the outliers at the higher end of the distribution.
A, B and C form the vertices of a triangle.
BC = 6.9cm and
∠
CBA = 137°.
Given that the area of the triangle is 12.6cm2, calculate the perimeter of the triangle rounded to 1 DP
Triangle ABC is dilated to create triangle A'B'C'. If AB=12 and A'B'=9, what is the scale factor of the dilation?
If the side AB=12 and side A'B'=9, then the scale factor of the dilation is 3/4.
The "Scale-Factor" of a dilation is the ratio of the corresponding side lengths of the two similar figures.
In this case, we can find the scale factor by dividing the length of side A'B' by the length of the corresponding side AB:
So, scale factor = A'B'/AB,
Substituting the values,
We get,
Scale factor = 9/12,
Scale Factor = 3/4,
Therefore, the scale factor of the dilation is 3/4. This means that all corresponding side lengths of the dilated triangle A'B'C' are 3/4 of the length of the corresponding side lengths of the original triangle ABC.
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What type of distribution is pictured in this histogram?
Responses
Bimodal
Normal
Skewed
The type of distribution pictured in this histogram is skewed.
What is a skewed distribution?
A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.
In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.
There are two types of skewed distributions: positively skewed and negatively skewed.
The distribution in the image is positively skewed as its is pulled towards the left.
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8.6×10 ^7 bacteria are measured to be in a dirt sample that weighs 1 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 19 grams.
scientific notation to express the number of bacteria that would be in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex].
what is scientific notationWith scientific notation, one can express extremely big or extremely small values.
When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be represented as 6.5 108 in scientific notation.
The given number of bacteria in the dirt sample is 8.6 × [tex]10^7[/tex], and the weight of the sample is 1 gram. To find the number of bacteria in a sample weighing 19 grams, we can use the following proportion:
number of bacteria / weight of sample = constant
We can solve for the constant by using the given information:
8.6 ×[tex]10^7[/tex] / 1 gram = constant
constant = 8.6 × [tex]10^7[/tex]
Now we can use this constant to find the number of bacteria in a 19-gram sample:
number of bacteria / 19 grams = 8.6 × [tex]10^7[/tex]
number of bacteria = 8.6 ×[tex]10^7[/tex] × 19 grams
To express the answer in scientific notation, we can multiply the two numbers and adjust the exponent accordingly:
number of bacteria = 1.634 × [tex]10^9[/tex]
Therefore, the number of bacteria in a sample weighing 19 grams would be 1.634 ×[tex]10^9[/tex]
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A car salesperson sells a used car for $8,800 and earns 9% of the sale price as commission. How many dollars does the salesperson earn in commission?
Answer:
Step-by-step explanation:
8,800x0.09=792. The salesperson earns $792 in commission.
Answer:
$792
Step-by-step explanation:
8800×0.09= 792
9÷100=0.09
commission =$792
Who can help mee??
well, let's find out how much she made on each week
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]
m<1 =
m<3 =
m<5=
m<7=
m<2 =
m<4=
m<6=
Explain how you found m<3.
Explain how you found m<1.
By using the corresponding angles, vertically opposite angles, alternate interior angles, and linear pair theorems, the measure of the angles are:
m ∠1 = 39°
m ∠2 = 141°
m ∠3 = 141°
m ∠4 = 39°
m ∠5 = 39°
m ∠6 = 141°
m ∠7 = 39°
Calculating the measure of anglesFrom the question, we are to calculate the measure of the unknown angles in the given diagram
By the Linear pair theorem,
We can write that
m ∠5 + 141° = 180°
Thus,
m ∠5 = 180° - 141°
m ∠5 = 39°
Likewise
m ∠7 + 141° = 180°
m ∠7 = 180° - 141°
m ∠7 = 39°
By the vertical angles theorem,
We can write that
m ∠6 = 141° (Vertically opposite angles)
By the corresponding angles theorem,
We can write that
m ∠2 = 141° (Corresponding angles)
m ∠2 = m ∠3 (Vertically opposite angles)
Therefore,
m ∠3 = 141°
m ∠4 = m ∠5 (Alternate interior angles)
m ∠4 = 39°
m ∠1 = m ∠4 (Vertically opposite angles)
Therefore,
m ∠1 = 39°
Hence,
The measure of angle 1 is 39°
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Please I need some help as soon as possible
Answer:
[tex] {m}^{2} + 7m - 30 = [/tex]
[tex](m - 3)(m + 10)[/tex]
The sum of two numbers is 49. One number is 23 more than the other. Find the numbers.
The larger number is:
The smaller number is:
Answer:
Larger number: 36
Smaller number: 13
Find the circumference of a circle that has a diameter of
2.75 yards. Round your answer to the nearest yard.
Answer:
3 yards
Step-by-step explanation:
When Sarah opens a map of her neighborhood on her cell phone, she notices that the park near her house is 0.5 cm wide. She zooms in until it is 3 times as large. If the park is 15 m wide, what is the scale of her zoomed-in map?
A 10cm=1 m
B 1cm= 10 m
C 1cm= 30 m
D 3cm= 10m
The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.
To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.
Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.
15 m = 1500 cm
Next, we can set up a proportion:
0.5 cm / x = 1500 cm / (3x)
where x is the scale of the zoomed-in map.
Simplifying the proportion, we get:
0.5(3x) = 1500
1.5x = 1500
x = 1000
Therefore, the answer is (B) 1cm = 10 m.
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I would love some help please 11-13
(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) 2x/3 + 4 = 10 equation does x = 9.
Hence the correct option is (b).
(11) The given expression is,
3/y + 2y/4 = 3/y + y/2
Substituting the value of y = 4 we get,
3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].
Hence the correct option is (b).
(12) The given expression is,
12/y + 3y/4
Substituting y = 8 in the given equation we get,
12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].
Hence the correct option is (c).
(13) Given the solution is x =9.
For first option: (2/3)*9 - 6 = 6 - 6 = 0
2x/3 - 6 = 12 does not satisfied by x = 9.
For second option: (2/3)*9 + 4 = 6 + 4 = 10
So, x = 9 satisfies 2x/3 + 4 = 10.
For third option: 3*9 - 12 = 27 - 12 = 15
So x = 9 does not satisfy 3x - 12 = 21.
For fourth option: 3*9 + 12 = 27 + 12 = 39
So x = 9 does not satisfy 3x + 12 = 19.
Hence the correct option is (b).
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For positive acute angles A and B, it is known that tanA= 4/3 and sinB= 53/28 . Find the value of sin(A−B) in simplest form.
The value of sin(A-B) is 2334/6625
What is trigonometric identity?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Example of trigonometric identity include;
cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.
1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ
1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ
Sin(A-B) = = sin A cos B- cos Asin B
if tan A = 4/3, then 4 is the opp and 3 is the adj,
hyp² = 4²+3²
= 16+9
hyp² = 25
hyp = √25
= 5
cos A = 3/5 and sinA = 4/5
if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp
adj = √ 53²-28²
adj = √ 2809 - 784
adj = √2025
adj = 45
cos B = 45/58
sin(A-B) = 4/5 × 45/58 - 3/5× 28/53
= 18/29 - 84/265
= (4770-2436)/6625
= 2334/6625
therefore the value of sin(A-B) = 2334/6625
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PLEASE SOMEONE !! 15 POINTS!!!
Answer:
The answer is -5
Step-by-step explanation:
Each number moves down 5 as it moves to the right 1. Right is positive, and down is negative. -5 divided by 1 is -5.
The percent of US citizens that use the internet on a daily basis is shown on the graph, where the year 2000 corresponds to x=0. Use the concepts of y-intercept and slope of the line to find the equation that best models the given data. Answer in slope intercept form.
An equation of the linear function represented by the graph in slope-intercept form is y = 3x + 60.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (75 - 60)/(5 - 0)
Slope (m) = 15/5
Slope (m) = 3
At data point (0, 60) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 60 = 3(x - 0)
y = 3x + 60
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which of these shapes have rectangular cross sections options. Orectangular prism O triangular prism cylinder D cone ✔cy Osquare pyramid triangular pyramid
The correct options are rectangular prism, square pyramid.
What are the shapes have rectangular cross sections?When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.
The shapes that have rectangular cross sections when they are cut perpendicular to the base are:
Rectangular prism
Square pyramid
Therefore, the correct options are rectangular prism, square pyramid.
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Complete question:
Question 6(Multiple Choice Worth 5 points)
(Reflections MC)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.
N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)
Please Fast only have 10 minutes.
The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).
What is the image coordinates?To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2 from the y-coordinates of each vertex:
N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)
M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)
O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)
Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)
So the reflected vertices are:
The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have a y-coordinate of -6.
The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so one need to move down 3 units to have a y-coordinate of -5.
The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so one need to move down 5 units to have a y-coordinate of -7.
So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)
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Answer:
D) N′(−5, −6), M′(−2, −5), O′(−3, −7)---------------------
Given triangle MNO with vertices:
N = (-5, 2), M = (-2, 1) and O = (-3, 3)It is reflected in line y = - 2.
This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.
Since y = - 2 is the line of symmetry, it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.
Using midpoint equation, find the y-coordinates.
Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7So the coordinates of the image are:
N′(−5, −6), M′(−2, −5), O′(−3, −7)This is matching the option D.
See attached for visual representation of the problem.
Erica spins a spinner with equal sections numbered 1 through 4 and selects a colored tile from a bag. Based on the tree diagram given, what is the probability of spinning a 2 or 3 on the spinner and drawing a blue tile?
Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.
Here,
Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).
The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.
To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:
P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)
= (1/2) x (1/3)
= 1/6
To know more about probability,
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Average Weekly Earnings in Canada
Occupation 2010 2008
Forestry, logging and support $971 $812
Manufacturing $977 $943
Transportation and warehousing $900 $873
Construction $1071 $1023
Retail trade $501 $486
1. Calculate the mean (average) weekly earnings of workers in the occupations
listed for 2010.
Answer: To calculate the mean weekly earnings for each occupation in 2010, we need to add up the weekly earnings for each occupation and divide by the number of occupations.
For Forestry, logging and support:
Mean weekly earnings = (971) / (1) = $971
For Manufacturing:
Mean weekly earnings = (977) / (1) = $977
For Transportation and warehousing:
Mean weekly earnings = (900) / (1) = $900
For Construction:
Mean weekly earnings = (1071) / (1) = $1071
For Retail trade:
Mean weekly earnings = (501) / (1) = $501
Therefore, the mean weekly earnings for workers in the listed occupations in 2010 are:
Forestry, logging and support: $971
Manufacturing: $977
Transportation and warehousing: $900
Construction: $1071
Retail trade: $501
Step-by-step explanation: