ANSWER
[tex]\text{ P\lparen both students are junior\rparen = }\frac{1}{10}[/tex]EXPLANATION
Given information
The total number of junior students = 2
The total number of senior students = 3
The total number of students = 5
To determine the probability of picking two junior students, follow the steps below
Step 1: Define probability
[tex]\text{ Probability = }\frac{\text{ possible outcome}}{\text{ total outcome}}[/tex]Step 2: Find the probability of picking the first junior students
[tex]\begin{gathered} \text{ Probability = }\frac{possible\text{ outcome}}{total\text{ outcome}} \\ \text{ Probability of picking the first junior students is} \\ \text{ P\lparen Junior student\rparen = }\frac{2}{5} \end{gathered}[/tex]Assuming the first picking was successful, then, we will be left with 1 junior student and 3 senior students.
Therefore, the new total outcome can be calculated below
1 + 3 = 4 students
Step 3: Find the probability that the second picking will be a junior student
[tex]\begin{gathered} \text{ Probability = }\frac{\text{ possible outcome}}{\text{ total outcome}} \\ \text{ P\lparen picking the second junior student\rparen = }\frac{1}{4} \end{gathered}[/tex]Step 4: Find the probability that both students are junior students
[tex]\begin{gathered} \text{ P\lparen both students are junior students\rparen = }\frac{2}{5}\times\frac{1}{4} \\ \text{ P\lparen both students are junior students\rparen = }\frac{2}{20} \\ \text{ P \lparen both students are junior students \rparen = }\frac{1}{10} \end{gathered}[/tex]Hence, the probability that both students selected are juniors is 1/10
Which is the best estimate for 2 2/3 × 3 1/4
The best estimate of the real number expression; 2 ⅔ × 3 ¼ as given in the task content is; 8 ⅔.
What is the best estimate of the real number expression given?It follows from the task content that the best estimate of the real number expression given is to be determined.
On this note, the mixed numbers must be converted to fractions for ease of computation as follows;
Therefore; 2 ⅔ = 8 / 3.
And, 3 ¼ = 13 / 4.
Therefore, the required evaluation of the expression is;
2 ⅔ × 3 ¼ = 8 / 3 × 13 / 4
= 104/12
= 26 / 3
Hence, the best estimate for the given expression is; 26 / 3 Or 8 ⅔.
Read more on fractions multiplication;
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Find the equation of this line.(2,2) and (0,-4)
To find the equation;
x₁ = 2 y₁ = 2 x₂ = 0 y₂=-4
we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_{}-x_1)[/tex]substituting the values into the above;
[tex]y-2=\frac{-4-2}{0-2}(x-2)[/tex]Then, we will go ahead and evaluate;
[tex]y-2\text{ = }\frac{-6}{-2}(x-2)[/tex][tex]y-2\text{ =3(x-2)}[/tex]y - 2 = 3x - 6
add 2 to both-side of the equation
y = 3x -6+ 2
y = 3x -4
Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv
ANSWERS
• x = 5
,• m∠ZVW = 46°
,• m∠ZWV = 41°
EXPLANATION
The diagonals of a parallelogram bisect each other, so
[tex]11=5x+1[/tex]To find x subtract 1 from both sides of the equation,
[tex]\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}[/tex]Hence x = 5
By the SAS property, triangle VZW and XZY are congruent:
Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,
[tex]\angle ZVW\cong\angle\text{ZXY}[/tex][tex]m\angle ZVW=46[/tex]It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,
[tex]\angle\text{ZWV}\cong\angle\text{ZYX}[/tex][tex]m\angle ZWV=41[/tex]Solve the following equation.
(√x -7) (√x -2)= -18
Answer:NO SOLUTION
Step-by-step explanation:
Enter your answer, rounded to the nearest tenth, in the box.
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
its asking for the approximate depth of the river. but I don't know how to determine that
From figure, trngles VWX and VYZ are similar.
So, the ratio of corresponding sides of triangles will be equal. Hence,
[tex]\begin{gathered} \frac{VW}{VY}=\frac{WX}{YZ} \\ \frac{3}{62}=\frac{5}{d} \\ d=\frac{5\times62}{3} \\ =103.3\text{ m} \end{gathered}[/tex]Therefore, the approximate depth of the river is d=103.3 m.
solve for tangent x= -1 in radians without a calculator
Answer:
[tex]x\text{ = }\frac{3}{4}\pi\text{ or }\frac{7}{4}\pi[/tex]Explanation:
Here, we want to calculate the value of x without using a calculator
We have to look for the quadrants where the tan is negative
These are the second and the fourth quadrant
On the second quadrant, we have the reference angles as:
[tex]180-x[/tex]Mathematically in degrees:
[tex]\begin{gathered} \text{if tan x = 1} \\ x\text{ = 45 deg} \end{gathered}[/tex]Now, on the second quadrant, we have it that:
[tex]180-45\text{ = 135 deg}[/tex]On the fourth quadrant, we have the reference angle calculated as:
[tex]\begin{gathered} 360-\theta \\ \theta\text{ = 360-45} \\ \theta\text{ = 315 deg} \end{gathered}[/tex]Lastly, we have to convert these angles to radians
Mathematically, 1 pi is 180 degrees:
[tex]\begin{gathered} 1\text{ }\pi=\text{ 180 deg} \\ x\text{ = 135 deg} \\ x\text{ = }\frac{135\pi}{180}\text{ = }\frac{3}{4}\pi \\ \\ \text{Lastly:} \\ 1\pi\text{ = 180 deg} \\ x\text{ = 315 deg } \\ \\ x\text{ = }\frac{315}{180}\pi\text{ = }\frac{7}{4}\pi \end{gathered}[/tex]translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
Use the spinner shown in the figure below to find the probability indicated.Landing on green or a consonant
Based on the spinner, there are a total of 8 possible outcomes.
2 of which are green and 4 are consonants, however, 1 outcome is both consonant and a green (F green).
Therefore, the probability of landing on a green or consonant is:
[tex]\begin{gathered} P(A\text{ or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=\frac{2}{8}+\frac{4}{8}-\frac{1}{8} \\ P(A\text{ or B)}=\frac{5}{8} \end{gathered}[/tex]The probability of landing on a green or consonant is 5/8 or 62.5%.
1. How is the orientation of the triangie affected by the translation?
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
Solve the quadratic equations in questions 1 – 5 by factoring.1. x2 – 49 = 02. 3x3 – 12x = 03. 12x2 + 14x + 12 = 184. –x3 + 22x2 – 121x = 05. x2 – 4x = 5
Given:
There are given the equation:
[tex]-x^3+22x^2-121x=0[/tex]Explanation:
According to the question:
We need to find the value of x by using the factoring:
S0,
From the equation:
[tex]-x^{3}+22x^{2}-121x=0[/tex]Tthen,
[tex]\begin{gathered} -x^{3}+22x^{2}-121x=0 \\ -x(x^2-22x+121)=0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} -x(x^2-22x+121)=0 \\ x(x-11)^2=0 \\ x=0; \\ x-11=0 \\ x=11 \end{gathered}[/tex]Final answer:
Hence, the value of x by using factor method is shown below:
[tex]x=0,11[/tex]The scores at the end of a game are shown.List the scores in order from greatest to least.Scores:Vince:-0.5, Allison: 3/8, Mariah:-7/20
To arrange the numbers from greatest to least, let us begin by changing all the numbers to decimals.
Vince's Score: -0.5
Allison's Score: 0.375
By long division, we can convert the fraction to a decimal:
Mariah's Score: -0.35
By long division, we have:
Given that we have calculated the scores in decimal, we can clearly see the bigger and smaller numbers.
The order from biggest to smallest is:
Allison: 3/8, Mariah: -7/20, Vince: -0.5
How much money will he raise based on the two donations?
The neighbor will donate $0.25 for every 40ft run.
The aunt will donate $18 for every mile run.
To determine how much he will raise if he runs 5miles, you have to calculate the amount per donor and then add them:
Neighbor
1 mile is equal to 5280 feet
To determine how many feet correspond to 5 miles, multiply the distance by 5280
[tex]5\cdot5280=26400ft[/tex]Next, calculate how much we will make:
40ft → $0.25
26400ft → $x
[tex]\begin{gathered} \frac{0.25}{40}=\frac{x}{26400} \\ 26400\cdot\frac{0.25}{40}=26400\cdot\frac{x}{26400} \\ 165=x \end{gathered}[/tex]For running 5miles, Dustin will raise $165 from the neighbor.
Aunt
The aunt will donate $18 per mile run, to determine how much she will donate, multiply $18 by 5
[tex]18\cdot5=90[/tex]For running 5 miles, Dustin will raise $90 from the neighbor.
Next, add both amounts:
[tex]165+90=255[/tex]Dustin will raise $255 for running 5 miles.
2 points Bob flips a coin. He also spins the pointer on the spinner shown below. What is the probability that Bob flips the coin so that it lands tails up and spins the pointer so it stops on the letter R? * N E Your answer
Answer: 1/16 = 0.0625
Step by step solution:
The probability (P) of an event happening is
[tex]P=\frac{Numbe\text{r of ways it can happen}}{Total\text{ number of outcomes}}[/tex]When Bob flips the coin he has two options, head or tail. The probability that it lands tails up is:
[tex]P=\frac{1}{2}[/tex]The probability that the pointer stops on the letter R is:
[tex]P=\frac{1}{8}[/tex]Now, the probability of both events happening (tails up and pointer on R) is:
[tex]P=\frac{1}{2}\times\frac{1}{8}=\frac{1}{16}=0.0625[/tex]3. What is the domain of the relation described by the set of ordered pairs {(-2, 8), (-1, 1), (0, 0), (3, 5), (4, -2)}?{-2, -1, 0, 4,5){-2, 0, 1, 5, 8}{-2, -1,0,3,4}{-2, -1, 0, 1,5}
The domain is related to x axis coordinates. So, you have to take the x coordinate of each point
-2,-1,0,3,4
DONT IGNORE! PLEASE HELP ME! 50 POINTS!
Answer: The answer is C (or the third option)
Step-by-step explanation: The formula for finding the measure of interior hexagon angles is ( n − 2) × 180 °. This means that C is the correct answer
Find the perimeter of quadrilateral ABCD with vertices A(0,4), B(4,1), C(1, -3), and D(-3,0).25 units100 units5 units20 units
The perimeter is the sum of the length of each side of the quadrilateral. We would find the length of each side by applying the formula for finding the distance between two points which is expressed as
[tex]\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Thus, we have
[tex]\begin{gathered} ForAB,x1=0,y1=4,x2=4,\text{ y2 = 1} \\ \text{Distance = }\sqrt[]{(4-0)^2+(1-4)^2\text{ }}\text{ = }\sqrt[]{16\text{ + 9}} \\ AB\text{ = 5} \\ \text{For BC, x1 = 4, y1 = 1, x2 = 1, y2 = - 3} \\ \text{Distance = }\sqrt[]{(1-4)^2+(-3-1)^2}\text{ = }\sqrt[]{9\text{ + 16}} \\ BC\text{ = 5} \\ \text{For CD, x1 = 1, y1 = - 3, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-1)^2+(0--3)^2}\text{ = }\sqrt[]{16\text{ + 9}} \\ CD\text{ = 5} \\ \text{For AD, x1 = 0, y1 = 4, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-0)^2+(0-4)^2\text{ }}\text{ = }\sqrt[]{9\text{ + 16}} \\ AD\text{ = 5} \end{gathered}[/tex]Perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 5
Perimeter = 20 units
At a sale this week,a suit is being sold for $364. This is a 35% discount from the original price. What is the original price?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested original price, so we obtain the following:
So we have the following formula:
Discount Price=Original Price*(100%-Discount)
Clearing for "Original price":
Discount Price=Original Price*(100%-Discount)
Original Price=Discount Price/(100%-Discount)
Replacing with the given data:
Original Price=Discount Price/(100%-Discount)
Original Price=$364/(100%-35%)
Original Price=$364/(65%)
Original Price=$364/(0.65)
Original Price=$560
Finally we obtain that the original price is $560.
Select all sets of triangles that can be provencongruent using Side-Angle-Side(SAS).
SOLUTION
We want to select all triangles from the image that can be proven by the side angle side theorem which states that
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Now looking at the triangles
We can see that triangles in number 1, 2, 3 follows this theorem.
4 does not because the equal angles are not present
5, the triangles are congruent, but do not follow the SAS theorem
6 follows as we can see the equal sides and angle
7 shows two equal angles only, but we need one equal angles and two equal sides.
Hence the answer is 1, 2, 3 and 6 only
The ages (in years) of the 6 employees at a particular computer store are the following.31, 41, 35, 22, 38, 31Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)
The standard deviation of the population = 6.08
Explanations:The given ages of the employers are:
31, 41, 35, 22, 38, 31
Find the mean of the dataset:
[tex]\begin{gathered} \mu\text{ = }\frac{\sum ^{}_{}x_i}{N} \\ \mu\text{ = }\frac{31+41+35+22+38+31}{6} \\ \mu\text{ = }\frac{198}{6} \\ \mu\text{ = }33 \end{gathered}[/tex]Find the summation of the square of each deviation from the mean
[tex]\begin{gathered} \sum ^6_{i\mathop=0}(x_i-\mu)^2=(31-33)^2+(41-33)^2+(35-33)^2+(22-33)^2+(38-33)^2+(31-33)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=(-2)^2+(8)^2+(2)^2+(-11)^2+(5)^2+(-2)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=4+64+4+121+25+4 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=222 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{222}{6}} \\ \sigma\text{ = }\sqrt[]{37} \\ \sigma\text{ = }6.08 \end{gathered}[/tex]The standard deviation of the population = 6.08 (rounded to 2 decimal places)
The local weather report states that there is 3/5 a chance of rain today, but it is more likely to rain tommorrow than today. What is a possible probability of rain for tommorrow? A.0.4 B. 0.5 I C. 0.6 D. 0.7
D. 0.7
Explanations:Probability is the chance (likelihood) that an event will take place
The probabilty that it will rain today = 3/5 = 0.6
There is more likelihood that it will rain tomorrow that today.
This means that the probabilty that it will rain tomorro is greater than the probability that it will rain today.
Therefore, the probability of rain tomorrow is more than 0.6
Only option D (0.7) is greater than 0.6, and it is the only correct choice
Answer each part. If necessary, round your answers to the nearest hundredth.(a) Abdul runs 3 miles in 17 minutes.How many miles does he run per minute?I miles per minute(b) It takes 37 pounds of seed to completely plant a 4-acre field.How many pounds of seed are needed per acre?pounds per acre
To determine the speed of Abdul, we can divide 3 miles by 17 minutes.
[tex]\frac{3mi}{17\min}=\frac{0.17647mi}{\min}\approx\frac{0.18mi}{\min }[/tex]Therefore, Abdul runs approximately 0.18 miles per minute.
Hello, I need help completing and showing appropriate steps for this problem. Thank you so much!
The first step is to factorise the quadratic expression on the right side of the equation. The expression is
x^2 + 9x + 20
We would find two terms such that their sum or difference is 9x and their product is 20x^2. The terms are 5x and 4x. Replacing 9x with 5x and 4x, it becomes
x^2 + 5x + 4x + 20
By factorising, it becomes
x(x + 5) + 4(x + 5)
Since x + 5 is common, it becomes
(x + 4)(x + 5)
Thus, the original expression becomes
x/(x + 4) + 3/(x + 5) = (x + 2)/(x + 4)(x + 5)
The lowest common multiple of the denominators on both sides of the equations is (x + 4)(x + 5). We would multiply each term in the equation by
(x + 4)(x + 5). It becomes
(x + 4)(x + 5)x/(x + 4) + 3(x + 4)(x + 5)/(x + 5) = (x + 2)(x + 4)(x + 5)/(x + 4)(x + 5)
By cancelling out common terms in the numerator and denominator, we have
x(x + 5) + 3(x + 4) = x + 2
We would expand the parentheses on both sides by multiplying the terms inside with the term outside. It becomes
x^2 + 5x + 3x + 12 = x + 2
By collecting like terms, we have
x^2 + 5x + 3x - x + 12 - 2 = 0
x^2 + 7x + 12 = 0
Again, We would find two terms such that their sum or difference is 7x and their product is 12x^2. The terms are 4x and 3x. Replacing 7x with 4x and 3x, it becomes
x^2 + 4x + 3x + 12 = 0
By factorising, it becomes
x(x + 4) + 3(x + 4) = 0
Since x + 4 is common, it becomes
(x + 3)(x + 4) = 0
x + 3 = 0 or x + 4 = 0
x = - 3 or x = - 4
The solutions are x = - 3 or x = - 4
change this standard form equation into slope intercept form 6x - 2y=-8
we have the equation
6x-2y=-8
Convert to slope-intercept form
y=mx+b
so
Isolate the variable y
step 1
Adds 2y both sides
6x-2y+2y=-8+2y
6x=-8+2y
step 2
Adds 8 both sides
6x+8=-8+2y+8
6x+8=2y
step 3
Divide by 2 both sides
3x+4=y
rewrite
y=3x+4the perimeter of a square box is 12x + 32 drag number to complete an equivalent expression that shows the premier has four times the side length of the box
The perimeter of the box is given as
12x + 32
To write an equivalent expression that shows the premier has four times the side length of the box , we would factorise the expression. It becomes
4(12x/4 + 32/4)
= 4(3x + 8
During a lab Jill made a solution that was 3% water. Rewrite this percent as a fraction in simplest form.
use the diagram at the right name the following three points ray
From the geometric diagram below
(1) Three diagram
[tex]\text{ Points JQE is a 3 points}[/tex](2) A ray
[tex]RP\text{ is a ray}[/tex](3) Two intersecting lines but not perpendicular
[tex]\text{ line RF and line NI are the two intersecting lines but not perpendicular}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q17
Solution:
Given the image;
Thus, there is a local maximum at;
[tex]x=-2[/tex]CORRECT OPTION: Yes
The local maximum is;
[tex]y=4[/tex]the triangles are similar. find the similarity ratio of the first to the second
To get the similarity ratio between both triangles, write down a ratio between two similiar sides. Let's take the base, for example
[tex]4\colon6[/tex]Simplifying,
[tex]2\colon3[/tex]Thereby, the similarity ratio between both triangles is:
[tex]2\colon3[/tex]Ans: Option B
it says use the table to rewrite the expression you wrote for problem 2. rewrite that expression so that both terms are written with the same exponent number 4. says use the distributive property simplify the expression you wrote for problem 3.number 5. says write your expression as the product of a decimal times a power of 10.number 6 says write your solution in scientific notation and number 7. says Evaluate (7.4 x 10^15 -- (9.9 x 10^13number 8 says Evaluate (8.9 x 10^5) + (6.5) x 10^6
7)
Given data:
The given expresson is a=7.7x10^15-(9.9x10^13)
The given expression can be written as,
a=770x10^13-9.9x10^13
=(770-9.9)x10^13
=760.1x10^13.
8)
Given data:
The given expresson is b=8.9x10^5-(6.5)x10^6
The given expression can be written as,
b=8.9x10^5-65x10^5
=(8.9-65)x10^5
=-56.1x10^5