Using translation concepts, it is found that the correct option regarding the function is:
The function h(x) is decreasing on the interval (3, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
[tex]f(x) = \sqrt{x}[/tex]
Which increases on (0, ∞).
The translated function is given by:
[tex]g(x) = -2\sqrt{x - 3}[/tex]
With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:
The function h(x) is decreasing on the interval (3, ∞).
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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A bottle contains 1 2/5 litres of orange squash. To make one drink, 1/200 of a litre of squah is needed. How many drinks can be made from the bottle of squash?
Answer:
280 drinks
Step-by-step explanation:
Capacity of bottle [tex]=1\frac{2}{5}=\frac{7}{5}\: l[/tex]Squash needed to make one drink [tex]=\frac{1}{200}\:l[/tex]Total number of drinks [tex]=\frac{7}{5}\div\frac{1}{200}[/tex][tex]=\frac{7}{5}*200[/tex][tex]=7*40[/tex][tex]=280[/tex]Answer:
280 drinks. We need to divide 1 2/5 by 1/200 in order to get this answer.
Help pls!
Which rational function has zeros at x = -1 and x = 6 ?
Answer:
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Step-by-step explanation:
Let's factorize the 1st option :
⇒ [tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
⇒ [tex]f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}[/tex]
⇒ [tex]f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}[/tex]
===============================================================
Finding the zeros :
⇒ Factors of numerator should be equated to 0
x + 1 = 0 ⇒ x = -1x - 6 = 0 ⇒ x = 6=============================================================
Solution :
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Answer:
first option
Step-by-step explanation:
the zeros are determined by the numerator of the rational function.
given that the zeros are x = - 1 and x = 6 , then the corresponding factors are
(x + 1) and (x - 6) , that is
(x + 1)(x - 6) ← expand using FOIL
= x² - 5x - 6
the rational function is then
f(x) = [tex]\frac{x^2-5x-6}{x^2-4}[/tex]
If a male student is selected at random, what is the probability the student is a freshman?
The probability that the student selected at random is a freshman is; 29%
How to find the Probability?
From the given table;
Total number of male students = 4 + 6 + 2 + 2 = 14
Number of freshmen students = 4 students
Thus;
Probability that the student selected at random is a freshman is;
P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%
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I need help, please. I don’t understand
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
One year, the population of a city was 358,000. Several years later it was 286,400. Find the percent decrease.
A percentage is a way to describe a part of a whole. The percentage decrease is 20%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
One year, the population of a city was 358,000. Several years later it was 286,400. Therefore, the percentage decrease is,
Percentage decrease = (358,000-286,400)/(358,000) × 100% = 20%
Hence, the percentage decrease is 20%.
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Which of the following tables represents a function?
Reason:
Choices A, C and D have repeated x values. It allows us to rule them out.
Table A has x = 6 repeating. Table C has x = 3 and x = -3 repeated. Table D has x = 4 and x = 5 show up twice each.
Whenever we have repeated x values, it indicates we do not have a function. A function is only possible when each x value goes to exactly one y value only.
Table A has the input x = 6 lead to y = 2 and y = -2 at the same time. Table C and table D are a similar story. So this is another way to rule out choices A, C and D.
Luckily table B has no repeated x values. Each x input leads to exactly one and only one y output. Therefore, table B is a function.
Side Note: the y values can repeat, but the function won't be one-to-one.
Evaluate the expression.
1/4 × 2/5 ÷ 1/3
Write your answer as a fraction or as a whole or mixed number.
it would help if you answered it as a fraction pls
Answer:
The answer is [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
what is the simple interest of $16000 interested for 5 years at 4% p.a?
Answer:
3200
Step-by-step explanation:
Simple interest = PRT/100
= (16000 × 5 × 4%\)/100
= 320000/100
= 3200
Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).
The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a length of an arc of a circle of radius 7 is approximately 10.99 cm.
The radius r = 7 cm
The arc length l = 10.99 cm
We know,
l = rθ
θ is the central angle.
θ = l/r = 10.99/7 = 1.57 radians
To convert 1.57 radians into the degree multiply it by 180/π
θ = 89.95 degree
Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
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If cos θ= 12 /13 and θ is located in the Quadrant I, find sin (2 θ ), cos(2 θ ), tan(2 θ )
Answers: sin(2∅) = 120/169, cos(2∅) = 119/169, tan(2∅) = 120/119
What are trigonometric functions?Trigonometric functions are used to establish the relationship between the sides and the angles of a right angle triangle.
Analysis:
If cos∅ = adjacent/hypotenuse = 12/13,
Then, opposite of the right angled triangle = [tex]\sqrt{13^{2} - 12^{2} }[/tex] = 5
sin∅ = 5/13, cos∅ = 12/13, tan∅ = 5/12
sin(2∅) = 2sin∅cos∅ = 2(5/13)(12/13) = 120/169
cos(2∅) = [tex]cos^{2}[/tex]∅ - [tex]sin^{2}[/tex]∅ = [tex](\frac{12}{13}) ^{2}[/tex] - [tex](\frac{5}{13} )^{2}[/tex] = 144/169 - 25/169 = 119/169
tan(2∅) = sin(2∅) / cos(2∅) = 120/169 ÷ 119/169 = 120/119
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9(w – 4) – 7w = 5(3w – 2)
Answer:
-2 =w
Step-by-step explanation:
9(w – 4) – 7w = 5(3w – 2)
The first step is to distribute
9w -36 - 7w = 15w -10
Combine like terms
2w -36 = 15w -10
Subtract 2w from each side
2w -36 -2w = 15w-10-2w
-36 = 13w -10
Add 10 to each side
-36+10 =13w-10+1-
-26 = 13w
Divide by 13
-26/13 =13w/13
-2 =w
When surveyed, the ratio of students who preferred Science class to English class was 5:4. If 90 students were surveyed, how many students chose Science?
50 students preferred science...
Explanation:
we can consider the numbers 5 and 4 in the ratio as units
now we need to know how much each unit represent
units = 5 + 4 = 9
my sample = 90 students
each unit = 90/9 = 10 students
so each unit represents 10 students
back to the ratio
who preferred science = 5
who preferred English = 4
Number of students choose Science = 5 * 10 = 50
Which expression is equal to p + (q + r)?
(p + q) ⋅ r
(p + q) + r
p + qr
q + pr
Answer:
(p + q) + r
is the correct answer
Find the exact length of side a.
The exact length of a which is equivalent to BC is 7units
Cosine ruleA triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule
c² = a² + b² - 2abcosC
Given the following parameters
b = 2
c = 5√3
theta = 30 degrees
Substitute
c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2
c² = 79 - 30
c² = 49
c = 7 units
Hence the exact length of a which is equivalent to BC is 7units
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Hypothesis Test for the Population Mean (II)
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
You are to write this code block yourself.
Use Step 3 to help you write this code block. Here is some information that will help you write this code block. Reach out to your instructor if you need help.
The dataframe for your team is called your_team_df.
The variable 'pts' represents the points scored by your team.
Calculate and print the mean points scored by your team during the years you picked.
Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it. (Hint: this is given in the problem statement)
Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
Calculate and print the test statistic rounded to two decimal places.
Calculate and print the P-value rounded to four decimal places.
The test statistic is -0.46 and the p-value is gotten as 0.3340
How to Calculate the P-value?The question is not complete because the data from the sample is 105, 107, 117, 106, 110.
Mean of sample is;
Mean = (105 + 107 + 117 + 106 + 110)/5
Mean; x' = 109
From online standard deviation calculator, the standard deviation of the sample is; S = 4.848
Now, the claim is that your team scored an average significantly less than 110 points. Thus, let's define the hypothesis as;
Null Hypothesis; μ = 110
Alternative Hypothesis; μ < 110
standard error of the mean; S_m = S/√n
S_m = 4.848/5
S_m = 2.17
Thus, the t-statistic is;
t = (x' - μ)/S_m
t = (109 - 110)/2.17
t = -0.46
Degree of freedom for this sample size is;
D.F = N - 1 =5 - 1 = 4
From online p-value from t-score calculator, we have;
p-value = 0.3340
The p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
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If the length of a rectangle is 6 more than twice the width and the total perimeter is 84cm, what is the rectangle's length?
Step-by-step explanation:
length = 2×width + 6
84 = 2×length + 2×width
now using the first in the second equation :
84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width
84 = 6×width + 12
72 = 6×width
width = 12 cm
length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm
If investments double every 9 years and you start with a $600 investment, how much money would you have after 27 years? First, complete the equation: Future Amount = 600 (1 + [?]) ↑ ↑ initial amount growth rate Hint: Doubling means a 100% growth rate. time periods Enter
Answer:
600(1+1)^3 with future amount being 4800
Step-by-step explanation:
The amount of the money after 27 years will be $4800.
What is the amount?The quantity of money anyone has is termed as the amount. The solution to the question is given as follows:-
Given that investments double every 9 years and you start with a $600 investment. how much money would you have after 27 years?
We know that the amount is getting double in every 9 years so the number of times the amount will get doubled will be = 27 / 9 = 3
Future amount = 600(1+1)³
Future amount = 600 ( 2 )³
Future amount = 600 ( 8 ) = $4800
Therefore the amount of the money after 27 years will be $4800.
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2. A used PlayStation 4 is on sale for 10% off the regular price of $160.00. If the sales tax rate is 9%, how much would I pay for the DVD player?
Answer:
$156.96
Step-by-step explanation:
10% off of $160.00 would be $16.00 so minus that by $160.00. Which then equals $144.00. Sales tax should be reduced to the sale price. So that would make it 144 times 0.09 for the 9% which equals $12.96 then add the $144.00 which then makes it $156.96. Hope it helps and I'm not wrong about sales tax:)
Find the range of the following equation for the domain {-4, 0, 3} f (x) = -2x^2 -3
The range of the function is {-34, -2, -20}
How to determine the range?The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
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Quadrilateral abcd has vertices a(1,0) b(5,0) c (7,2) d(3,2). use slope to prove that abcd is a parallelogram.
[tex]m_{\overline{AB}}=\frac{0-0}{1-5}=0\\m_{\overline{CD}}=\frac{2-2}{3-7}=0\\\\\therefore \overline{AB} \parallel \overline{CD} \text{ because } m_{\overline{AB}}=m_{\overline{CD}}[/tex]
[tex]m_{\overline{BC}}=\frac{2-0}{7-5}=1\\m_{\overline{AD}}=\frac{2-0}{3-1}=1\\\\\therefore \overline{BC} \parallel \overline{AD} \text{ because } m_{\overline{BC}}=m_{\overline{AD}}[/tex]
As ABCD has two pairs of opposite parallel sides, ABCD is a parallelogram.
solve w^2 + 7w - 18 = 0
with the steps pls
Answer:
w=2 w = -9
Step-by-step explanation:
w^2 + 7w - 18 = 0
We can factor this equation
What 2 numbers multiply to -18 and add to 7
9*-2 = -18
9+-2 = 7
(w-2) (w+9) = 0
Using the zero product property
w-2 = 0 w+9 =0
w=2 w = -9
Answer:
[tex]w_1=2\\w_2=-9[/tex]
Step-by-step explanation:
This is going to be solved using the quadratic formula.
1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].
Use the standard form, [tex]ax^2+bx+c=0[/tex] , to find the coefficients of our equation,
[tex]w^2+7w-18=0[/tex]:
a = 1
b = 7
c = -18
2. Plug these coefficients into the quadratic formula
The quadratic formula gives us the roots for [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:
[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
7 additional steps:
a = 1
b = 7
c = -18
[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]
Simplify exponents and square roots
[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]
Perform any multiplication or division, from left to right:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]
to get the result:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]
3. Simplify square root [tex]\sqrt{121}[/tex]
Simplify 121 by finding its prime factors:
121 ( 11 * 11)
The prime factorization of 121 is 11^2
Write the prime factors:
[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]
Group the prime factors into pairs and rewrite them in exponent form:
'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]
Use the rule [tex]\sqrt{x^2=x}[/tex] to simplify further:
[tex]\sqrt{11^2}=11[/tex]
4. Solve the equation for w
[tex]w=\frac{-7\pm11}{2}[/tex]
The ± means two answers are possible.
Separate the equations:
[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_1=\frac{-7+11}{2}[/tex]
[tex]w_1=\frac{4}{2}[/tex]
[tex]w_1=2[/tex]
[tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_2=\frac{-18}{2}[/tex]
[tex]w_2=-9[/tex]
---------------------
Why learn this
In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can in turn be used to predict the curve of an object in motion, such as a ball kicked by football player or shot out of a cannon. When it comes to an object’s movement through space, what better place to start than space itself—with the revolution of planets around the sun in our solar system. The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.---------------
Terms and topics
Solving quadratic equations using the quadratic formulaSimplifying radicalsFind prime factors-----------
Learn more:
https://brainly.com/question/1214333https://brainly.com/question/13603021Marc is trying to determine how many blue marbles are in a bag of `100` marbles. he can only fit `10` marbles in his hand at a time. he takes `11` samples of `10` marbles, returning the marbles to the bag each time. based on these results, how many of the `100` marbles do you expect are blue
Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.
What is a boxplot?A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:
MinimumFirst quartileMedianThird quartileMaximumFor this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:
Median = 4 × 10
Median = 40.
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What is the exact value of x
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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Is y=2x-3 a funtion?
Answer:
yes
Step-by-step explanation:
Yes.
The graph of y = 2x - 2 is a straight line sloping up to the right.
It passes the vertical line test, so it is a function.
14 friends go out for dinner and the bill for food and drink comes to £130. The friends decided to add a 5% tip on the top of this total. If they divide this expense equally between them, How much does each friend pay?
The amount each friend does pay is £9.75
How to calculate the pay of each friend using fractions and arithmetic operations?We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.
From the given information:
The 5% of 130 = £6.5Total amount paid = £130 + £6.5 = £136.5Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]
The cost of each friend = £9.75
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What is 1 2/3 multiple 2/3
Answer:
[tex]1\frac{1}{9}[/tex]
Step-by-step explanation:
Given the following question:
[tex]1\frac{2}{3} \times\frac{2}{3}[/tex]
In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.
[tex]1\frac{2}{3} =3\times1=3+2=\frac{5}{3}[/tex]
[tex]\frac{5}{3} \times\frac{2}{3}[/tex]
[tex]5\times2=10[/tex]
[tex]3\times3=9[/tex]
[tex]=\frac{10}{9}[/tex]
Convert the improper fraction into a mixed number:
[tex]\frac{10}{9}[/tex]
[tex]\frac{10}{9} =10\div9=1\frac{1}{9}[/tex]
[tex]=1\frac{1}{9}[/tex]
Your answer is "1 1/9."
Hope this helps.
Write the following as algebraic expressions. r decreased by 3
Answer:
r - 3
Step-by-step explanation:
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to write the verbal phrase "r decreased by 3" as an algebraic expression.
[tex]\triangle~\fbox{\bf{KEY:}}\star[/tex]
Think about it. "decreased by". If we decrease a number by another number, what happens to the first number?Here we decrease the variable "r" by 3.
Remember, variables always represent some number.
Let's think about it this way...
///\\\////\\\\////\\\///\\\///\\\///\\\///\\\///\\///\\///\\///\\///\//\\///\\\///\\\///\\\///\\///\\\///\
So we have a number r, and we decrease it by 3.
Now its value is less than the original value.
We subtracted 3 from the original value of r, and now its value is less than the original one.
Thus, "decreased by" is the same as "subtracted" in mathematics.
r decreased by 3 ⇒ [tex]\star\large\pmb{r-3}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
A group of friends are playing a trivia game. players spin a spinner 2 times to find the 2 categories of trivia questions they will be asked. the spinner has 5 sections. the "music" and "sports" sections are each 1-half the size of the 3 larger sections.
to the nearest percentage, what is the probability that a player will be asked a math question ,begin emphasis,and then,end emphasis, a music question? enter the answer in the box.
The probability that a player will be asked a math question and then a music question is 0.03125
How to determine the probability?The size of the sections are given as:
Music = 0.5
Sport = 0.5
Others = 1
So, the total size is:
Total = 0.5 + 0.5 + 1 + 1 + 1
Evaluate
Total = 4
The probability of asking a math question is:
P(Math) = 1/4 = 0.25
The probability of asking a music question is:
P(Music) = 0.5/4 = 0.125
The required probability is:
P(Math and Music) = P(Math) * P(Music)
This gives
P(Math and Music) = 0.25 * 0.125
Evaluate
P(Math and Music) = 0.03125
Hence, the probability that a player will be asked a math question and then a music question is 0.03125
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