The probability that kids will be able to write something about both the French and Spanish classes after he is finished with the interviews is 91/100.
Given 25 kids has enrolled in atleast one foreign language class. 18 kids are in French class and 21 kids are in Spanish class.
We have to find the probability that kids will be able to write something about both the French and Spanish classes after Michael is finished with the interviews.
Let F is a set showing students knowing French,
S be a set showing students knowing Spanish ,
FS= Showing students both enrolled in one languages.
FS=F+S-(F∪S)
=18+21-25
=14
F-18-14=4
S=21-14
=7
4 outcomes lead to Michael being able to write both the languages are (F,S),(FS,S)(FS,F)(FS,FS)
Required probability is the sum of all the probabilities of (F,)(FS,S)(FS,F)(FS,FS)
P(F,S)=[tex]4C_{1}*7C_{1}/25C_{2}[/tex]
=(4*7)/300
=28/300
P(FS,S)=[tex](14C_{1}*7C_{1} )/25C_{2}[/tex]
=14*7/300
=98/300
P(FS,F)=[tex](14C_{1}*4C_{1} )/25C_{2}[/tex]
=14*4/300
=56/300
P(FS,FS)=[tex]14C_{2}/25C_{2}[/tex]
=91/300
Required probability=28/300+98/300+56/300+91/300
=(28+98+56+91)/300
=273/300
=91/100
Hence the probability that kids will be able to write both the languages is 0.91.
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please help its due soon! :(
Which statement describes the end behavior of this function?
f(x) = log(x − 2)
A.
As the value of x decreases, the value of f(x) moves toward positive infinity.
B.
As the value of x increases, the value of f(x) moves toward positive infinity.
C.
As the value of x increases, the value of f(x) moves toward negative infinity.
D.
As the value of x decreases, the value of f(x) moves toward a constant.
Answer:
So, the correct answer is that as x gets bigger, f(x) moves towards positive infinity.
Landon is lying in the grass looking at the top of a tree that is 200 m away. The angle of elevation between Landon's head and the top of
the tree is 36 degrees.
What is the height of the tree?
O 145 m
O 275 m
O 118 m
162 m
200 m
The height of the tree which is the opposite side of the right triangle is 145 meters.
How to find height when given angle of elevation?The angle of elevation is 36 degrees.
The situation forms a right angle triangle.
Therefore,
base of the triangle = 200 m
Hence, using trigonometric ratios,
tan 36 = opposite / adjacent
tan 36 = x / 200
x = 200 tan 36
x = 200 × 0.726542528
x = 145.308505601
x = 145.31 m
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look at image please answer both
6. The system of equations has no solution.
7. B. Tables - 15 lbs, chairs - 3.5 lbs.
How to Find the Solution to the System of Equations?The values of x and y that makes two equations equal is the solution of a system of equations.
6. 3x + 4y = 12 --> eqn. 1
y = 3 - 3/4x --> eqn. 2
Substitute y = (3 - 3/4x) into eqn. 1 to find x:
3x + 4(3 - 3/4x) = 12
3x + 12 - 3x = 12
12 = 12 [unable to solve further for x]
This means that the system of equations has no solution.
7. t = tables
c = chairs
3t + 5c = 62.5 --> eqn. 1
3t + 2c = 52 --> eqn. 2
Subtract
3c = 10.5
c = 3.5 [chairs]
Substitute c = 3.5 into eqn. 2
3t + 2(3.5) = 52
3t + 7 = 52
3t = 52 - 7
3t = 45
t = 15 [table]
Therefore, the answer is: B. Tables - 15 lbs, chairs - 3.5 lbs.
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john and Tyrone each go for a morning jog before work. John's jogging pace is represented by' the equation y=5x where y is the the number of miles he jogs, and x is the number is the number of hours he jogs. Tyrones pace is given by the graph. Choose the statement that correctly compares their unit rates.
Answer:
The answer is B. Tyrone's unit rate is 1 more mile per hour then John’s unit rate.
Step-by-step explanation:
First of all at the bottom is what the graph and the answer options are.
Hope this helped! :D
simplify square root one minus cos squared theta, need explanation please
WHAT IS THE AVERAGE NUMBER OF POINTS THAT CHANGED HANDS
The average number of points will be 15 points.
How to calculate the average?It should be noted that average or mean simply means the total added values fall the data in a set which is then divided by the number of data.
Let the assumed points be 10, 12, 24, 15, 23, and 6.
In this case, the average number of points will be:
= (10 + 12 + 24 + 15 + 23 + 6)/6
= 90/6
= 15 points
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Please help me it’s trig!!!!!!!
The measure of angle of ∠BAM (θ) will be 9°. Then the correct option is D.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
ABCD is a rectangle with AB = 3BC.
And M is the mid-point of BC.
2BM = BC
Then the tangent of angle of ∠BAM (θ) will be
tan θ = (BM) / (AB)
tan θ = (BM) / (3BC)
tan θ = (BM) / (3 × 2BC)
tan θ = 1/6
θ = tan⁻¹ (1/6)
θ = 9.46°
θ ≅ 9°
Then the correct option is D.
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The rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds. What is the probability that the total weight of the samples will exceed 530 pounds? Group of answer choices
Binomial distribution will be used to know the probability that the total weight of the samples will exceed 530 pounds.
It is given that the rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds.
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
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What is the slope of the line?
Answer:
3/1
Step-by-step explanation:
left one and three up
For the following exercises, determine whether each of the following relations is a function.
1. y = 2x + 8
Answer:
The relation y=2x+8 is a function because the two different output values of the function have the one unique input value.
Step-by-step explanation:
The given relation is y=2x+8.
It is required to determine the relation is a function.
This solution can be obtained by using the concept of function. First write the given relation y=2x+8 and determine whether the given relation is a function.
Step 1 of 1
The given relation is y=2x+8.
This relation shows that the two different output values of the function have one unique input value and this relation is a linear function.
Hence, the relation is a function.
please assist me on this question
Answer:
x = 175 units
Step-by-step explanation:
x is to (49 + 576) as 49 is to x
x/ 625 = 49/x cross multiply
x^2 = 30625
x=175
Answer:
x = 175 units
Step-by-step explanation:
x is to (49 + 576) as 49 is to x
x/ 625 = 49/x cross multiply
x^2 = 30625
x=175
HOPE THIS HELPS LOVE -3-
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Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
URGENT NEED ANSWER NOWWWWW!!!!!!WORTH 27 POINTS!!!
Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
a.10x+25=5x+50
b.10x-25=5x-50
c.10x+50=5x+25
d.10x-50=5x-25
Answer:
A
Step-by-step explanation:
because for black diamond its 10x+25
and for bunny hill its 5x+50
Many electronic devices use disposable batteries, which eventually have to be replaced. Assume that for one particular brand and type of battery, the distribution of the hours of useful power can be approximated well by a Normal model. The mean is 140 hours, and the stand deviation is 4 hours. The marketing department wants to write a guarantee for battery life. What lifespan should they quote so that they can expect 98% of the batteries to meet the guarantee
They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.
Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.
We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.
We have to use z test for this .
μ=140 hours and σ=4 hours
Z=X-μ/σ
When p value is 0.98 then from z table z value will be 2.58.
Z=X-140/4
2.58=X-140/4
2.58*4=X-140
10.32=X-140
X=150.32
after rounding off we will get 150 hours.
Hence they should quote 150 hours of lifetime on batteries.
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Answer:
132
Step-by-step explanation:
Noise levels at 5 volcanoes were measured in decibels yielding the following data: 108,133,140,129,136 1. Construct the 98% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
2. Calculate the sample standard deviation for the given sample data. 3. Find the critical value that should be used in constructing the confidence interval.
The confidence interval or the mean noise level is (108.17,150.23) and sample standard deviation is 12.52.
Given noise levels:108,133,140,129,136. and confidence level 98%.
We have to find the confidence level and the sample standard deviation of the given data.
Confidence level=98%.
n=5
Sample standard deviation=[tex]\sqrt{(x-x bar)^{2} /n-1}[/tex]
=[tex]\sqrt{626.8/4}[/tex]
=[tex]\sqrt{156.7}[/tex]
=12.52
critical t value at 98% confidence level with degree of freedom(5-1) is 3.747
Standard error= critical t*s/[tex]\sqrt{n}[/tex]
Standard error is the difference between the real values and calculated values.
=3.747*12.52/[tex]\sqrt{5}[/tex]
=46.91/2.23
=21.03
Upper confidence interval=Mean +standard error
=129.2+21.03
=150.23
Lower confidence interval=Mean - standard error
=129.2-21.03
=108.17
Hence the confidence interval is (108.17,150.23) ,sample standard deviation is 12.52 and critical t value is 3.747.
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The proper sequence of steps in implementing the model in Excel presented in the textbook is: a. Represent the decision variables, organize the data, represent the objective function, represent the constraints, and represent the bounds on the decision variables. b. Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables. c. Organize the data, represent the objective function, represent the decision variables, represent the constraints, and represent the bounds on the decision variables. d. Organize the data, represent the bounds on the decision variables, represent the objective function, represent the constraints, and represent the decision variables.
The proper sequence of steps in implementing the model in Excel presented in the textbook is option b which is organize the data, represent the decision variables, represent the objective function, represent the constraints and represent the bounds on the decision variables.
Given process of implementing the model in Excel and we have to choose the correct process.
The process of implementing the model in Excel is as under:
1) Organize the data: In excel, to organize the data we have to put similar items in the same column. We have to design the data so that all rows have similar items in the same column. We have to keep a range of data separate and leave at least one blank column and one blank row between a related data range.
2) Represent the decision variables: Now we have to represent the decision variables according to which logical function performs tasks.
3)Represent the objective function: It is important because on the basis of this all the logical function perform tasks.
4) Represent the constraints: In excel when we are using solver we have to now represent the constraints of the objective function.
5) Represents the bounds on the decision variables.
Hence the proper sequence of steps in implementing the model in excel is Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.
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Find the area of all the letters!!!!
The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the given letters
J = 0.5 × 8 ft × 6 ft = 24 ft²
K = 8ft × 9ft = 72 ft²
L = 6ft × 9ft = 54 ft²
M = 10ft × 9ft = 90ft²
N = 0.5 × 8 ft × 6 ft = 24 ft²
U = 0.5 × 16 yd × 15 yd = 120 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
W = 16 yd × 16 yd = 256 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
X = 0.5 × 16 yd × 15 yd = 120 yds²
A = 5 in × 10 in = 50 in²
B = 10 in × 12 in = 120 in²
C = 5 in × 12 in = 60 in²
D = 5 in × 10 in = 50 in²
E = 5 in × 12 in = 60 in²
F = 10 in × 12 in = 120 in²
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Writing Exercises
84. Using your own words, explain the difference between a monomial, a binomial, and a trinomial.
Answer: a monomial has one term, binomial has 2 terms, and trinomial has 3.
Step-by-step explanation:
using a bit of greek and latin roots, we can observe that all 3 terms have the same suffix of nomial in them. From this, we know that mono means one, bino means two, and tri means 3. Fun fact, there's also polynomial (if you did or didn't know), which is multiple terms more than 3.
Which of the expressions below are equal to 8x² + 30x + 18?
Select all that apply.
A) (4x + 3) (2x + 6)
B) 6x² + 20x + 2x² + 10x + 18
C) 2(4x² + 15x + 9)
D) 4(2x² + 7x + 4)
Answer:
A, C, and D
Step-by-step explanation:
A) (4x + 3) (2x + 6) is equal to 8x² + 30x + 18 because when you multiply two binomials, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, (4x + 3) (2x + 6) can be rewritten as (4x)(2x) + (4x)(6) + (3)(2x) + (3)(6). This can further be simplified to 8x² + 24x + 18.
C) 2(4x² + 15x + 9) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 2(4x² + 15x + 9) can be rewritten as 2(4x²) + 2(15x) + 2(9). This can further be simplified to 8x² + 30x + 18.
D) 4(2x² + 7x + 4) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 4(2x² + 7x + 4) can be rewritten as 4(2x²) + 4(7x) + 4(4). This can further be simplified to 8x² + 28x + 16.
2. Please answer the question on exponential growth or decay. Round to
the nearest whole number or penny if the question is concerning money if
necessary.
A company promises to release a new
smartphone model every month. Each
model's battery life will be 3% longer than
the previous model's. If the current
model's battery life is 748.0 minutes, what
will the latest model's battery life be 10
months from now?
Your answer
is 7 1/5•49 7/5 equivalent to 49 2/10 • 7 1/5
We can calculated each one out :
7 1/5 x 49 7/5 = 36/5 x 252 / 5 = 9072 / 25
49 2/10 x 7 1/5 = 980 / 10 x 36/5 = 35280 / 50 = 3528 / 5
or a much simpler way is that because both multiplication has 7 1/5 so we only have to compare the other terms, and since 49 7/5 is not equal to 49 2/10 these are not equal. and i didnt notice that till now.
If a linear function contains the pairs (5,7) and (9,11), which pairs should have the reciprocal function to this one?
Please choose an answer.
a.
(7.5) and (11.9)
b.
(5.7) and (11.9)
c.
(5.7) and (9.11)
d.
(7.5) and (9.11)
The new coordinates will be ( 7,5) and (11,9) , Option A is the correct answer.
What is a Reciprocal Function ?The reciprocal function is the inverse of the function, such that 1/ f(x) is the reciprocal of f(x).
The given linear function has pairs of points
(5,7) and (9,11)
The reciprocal of this will be
interchanging of the coordinates
Therefore the new coordinates will be
( 7,5) and (11,9)
Option A is the correct answer.
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someone help me with this pleaseeeeeeeeeeeeee
Answer:
[a] 11 feet
[b] 7 feet
[c] 10 feet
Step-by-step explanation:
See attached. We will pull different details from the graph and information given to solve the different problems,
Answer:
See below
Step-by-step explanation:
Using the equation (instead of the graph....my answer got deleted for using the graph instead of the equation)
When the ball leaves fingers x = 0 :
a) -1/25 ( 0-10)^2 + 11 = 7 ft
b) max height will be at - b/2a
-1/25 ( x^2 -20x +100 ) + 11 <====expand
-1/25 x^2 + 4/5x +7 a = -1/25 b= 4/5
then - b/2a = - 4/5 / (2* -1/25) = 10=x
sub in this value of x into the equation to find max height = 11ft
c) when x = 15
-1/25 ( 15-10)^2 + 11 = 10 ft
Given: ABCD is a quadrilateral, Segment AB is congruent to Segment CD, <1 is congruent to <2 Prove: ABCD is a parallelogram
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.
We need to prove that ABCD is a parallelogram.
How to prove a given quadrilateral is a parallelogram?If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.
From the given quadrilateral ABCD:
AB=CD (Given)
∠1=∠2 (Given)
AC=AC (Diagonal)
From ASA congruency ΔABC and ΔADC are congruent.
By CPCT, AD=BC and ∠ABC=∠ADC.
Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.
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please answer this question with steps
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1
= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms
= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators
= ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify
= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]
Answer:
Step-by-step explanation:
[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]
[tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]
[tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]
[tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]
If the cost for both models continues in this pattern will the cost of model be ever be lower than the cost of model a explain
Answer:
NO
Step-by-step explanation:
Use the information provided to answer Part A and Part B for question 22.
Point P is plotted on the number line.
Point Q is the opposite of point P. Determine the location of point Q on the
number line. Explain how you determined the location of point Q on the
number line.
Enter your answer and your explanation in the space provided.
Point S is located at
number
on the number line. A student claims that the location
of point S is to the right of the location of point P on the number line.
Explain whether the student's claim is correct or incorrect.
• Write an inequality that describes the relationship between the value of
point P and the value of point S.
Enter your explanation and your inequality in the space provided.
The inequality is explained below.
How to illustrate the inequality?Inequality is a statement of an order relationship between two numbers or algebraic expressions
In this vase, with a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.
Therefore, both points are the same distance away from 0 just in opposite directions.
That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.
This method only works when it is specifically stated that the two points are opposite from each other.
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A game of chance has a spinner with five equal-sized sections, The results of 625 spins are shown below. For which color is the difference between the theoretical probability and experimental probability greatest? Explain.
The color that has the greatest difference between the theoretical and experimental probability is yellow.
Which color has the greatest difference?Theoretical probability of each color = number of color in each section / total number of sections
1/5 = 0.2
Experimental probability is based on the result of an experiment that has been carried out multiples times
Experimental probability
Experimental probability of choosing orange = 118 / 625 = 0.19
Difference = 0.2 - 0.19 = 0.01
Experimental probability of choosing purple = 137 / 625 = 0.22
Difference 0.22 - 0.2 = 0.02
Experimental probability of choosing brown = 122 / 625 = 0.20
0.2 - 0.2 = 0
Experimental probability of choosing yellow = 106 / 625 = 0.17
0.20 - 0.1696 = 0.0304
Experimental probability of choosing green = 142 / 625 = 0.23
0.2272 - 0.20 = 0.0272
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conplete the sentences below for the numbers 16,-9, and -15
Step-by-step explanation:
1. The number to the right of 0 is 16.
2. The number that is the least is -15.
3. -15 is smaller than 0 than -9 is.
Which of the following functions cannot be odd?
Polynomials
Rationals
Trigonometric
Exponential
Step-by-step explanation:
Exponential can't be odd, because any exponential function has a range that isn't defined for all reals