Answer:
24% of those surveyed liked neither
Step-by-step explanation:
Set concepts:
We use set concepts to solve this question.
I am going to say that:
P(A) is the percentage of people that liked to swim.
P(B) is the the percentage of people that liked to run.
The percentage of people that liked at least one of these activities is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.
The percentage of people that liked neither is:
[tex]P = 1 - P(A \cup B)[/tex]
Of those surveyed, 58% said they liked to swim and 36% said they liked to run.
This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]
18% said they liked both swimming and running
This means that [tex]P(A \cap B) = 0.18[/tex]
What percent of those surveyed liked neither?
At least one:
[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]
Neither:
[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]
24% of those surveyed liked neither
George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct first step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.
Answer:
Circle O is similar to Circle X because they have the same radius
Does anyone know the answer?
Answer:
5.44
Step-by-step explanation:
From Trigonometry Identity,
Sin65= CB/AB
CB = AB Sin65
= 6 × Sin65
= 5.4378
= 5.44{ to the nearest hundredth}
a researcher is testing reaction times between the dominant and non-dominant hand. they randomly start with each hand for 20 subjects and their reaction times in milliseconds are recorded. test to see if the reaction time is faster for the dominant hand using a 5% level of significance. the hypotheses are:
Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.
Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.
The null and alternative hypotheses for testing if the reaction time is faster for the dominant hand can be formulated as follows:
Null hypothesis (H0): The reaction time for the dominant hand is not faster than the non-dominant hand.
Alternative hypothesis (Ha): The reaction time for the dominant hand is faster than the non-dominant hand.
To test these hypotheses, we can perform a paired t-test because the same subjects are tested with both hands. The paired t-test compares the means of the paired observations and determines if there is a statistically significant difference between them.
Using a 5% level of significance (α = 0.05), we can calculate the test statistic and compare it to the critical value from the t-distribution with (n-1) degrees of freedom, where n is the number of subjects.
If the calculated test statistic falls in the critical region (i.e., the p-value is less than 0.05), we reject the null hypothesis and conclude that there is evidence to suggest that the reaction time for the dominant hand is indeed faster.
If the calculated test statistic does not fall in the critical region (i.e., the p-value is greater than or equal to 0.05), we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a difference in reaction times between the dominant and non-dominant hand.
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The null and alternate hypothesis tests are:
H₀: μd = μnd
H₁: μd < μnd
Given data:
The hypotheses for testing if the reaction time is faster for the dominant hand can be stated as follows:
Null Hypothesis (H₀): The reaction time is the same for the dominant and non-dominant hand.
Alternative Hypothesis (H₁): The reaction time is faster for the dominant hand.
Mathematically, these can be represented as:
H₀: μd = μnd
H₁: μd < μnd
Where:
μd is the population mean reaction time for the dominant hand.
μnd is the population mean reaction time for the non-dominant hand.
To test these hypotheses, a statistical test such as a paired t-test can be used. The test will compare the means of the paired observations (reaction times for the dominant and non-dominant hand) and determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
The significance level of 5% (0.05) indicates that if the p-value obtained from the test is less than 0.05, we would reject the null hypothesis and conclude that there is evidence to support the claim that the reaction time is faster for the dominant hand.
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Suppose we want to choose a value of x at least 5 units away from 14.A) Think about some values of x that meet this constraint.B) Write an inequality that represents all values of x that meet this constraint. Hint. no answer givenC) On the number line below, represent all values of x that meet this constraint. Clear All Draw: Line segments and raysClosed dotOpen dot
Answer:
(a) [9, 19]
(b) [tex]9 \leq x \leq 19[/tex]
(c)See attachment
Step-by-step explanation:
We want to choose a value of x at least 5 units away from 14.
(a)Now, 14-5=9 and 14+5=19
The possible values of x ranges is in the closed interval [9,19]
(b) Since x is at least 5 units away from 14, we have:
[tex]|14-x|\leq5[/tex]
Solving the absolute inequality
[tex]-5 \leq 14-x \leq 5\\$In $ -5 \leq 14-x\\ x \leq 14+5\\x \leq 19\\\\$In $ 14-x \leq 5\\ 14-5 \leq x\\9 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\9 \leq x \leq 19[/tex]
(c)To draw the number line, we use a closed dot since we have a less than or equal to sign.
Inequalities are used to represent unequal expressions.
The inequality that represents the scenario is [tex]\mathbf{|x-14| \ge 5}[/tex]Some possible values of x are: 5 and 20Represent the value with x.
A value that is at least 5 from 14 can take any of the following forms:
[tex]\mathbf{14 -x \ge 5}[/tex]
[tex]\mathbf{x-14 \ge 5}[/tex]
The inequalities can be combined as:
[tex]\mathbf{|x-14| \ge 5}[/tex]
The values of x are solved as follows:
[tex]\mathbf{14 -x \ge 5}[/tex]
[tex]\mathbf{14 - 5 \ge x}[/tex]
[tex]\mathbf{9\ge x}[/tex]
Rewrite as:
[tex]\mathbf{x \le 9}[/tex]
Similarly, we have:
[tex]\mathbf{x-14 \ge 5}[/tex]
[tex]\mathbf{x \ge 14 + 5}[/tex]
[tex]\mathbf{x \ge 19}[/tex]
So, we have:
[tex]\mathbf{x \le 9}[/tex] or [tex]\mathbf{x \ge 19}[/tex]
This can be combined as:
[tex]\mathbf{9 \ge x \ u\ x \ge 19}[/tex]
Some possible values of x are: 5 and 20
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prove the identity of sin(x+y)-sin(x-y)=2 cos(x) sin(y)
Answer: I dont have one for sure but I can explain why this is true.
Step by Step:
sin(x+y)−sin(x−y)=sinxcosy+sinycosx−(sinxcosy−sinycosx)
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinxcosy+sinycosx−sinxcosy+sinycosx
=sinycosx+sinycosx
=2sinycosx
henceforth proved.
If the following inequality is divided by −2, what is the resulting inequality? −2x≤−20
Step-by-step explanation:
When dividing by a negative number, you "flip" the inequalities sign so you would divide -20 by -2 which would leave you with 10. X is left where it is and you flip the inequalities sign to a ≥ sign.
final answer =
x ≥ 10
341 is 55% of what number? Round your answer to the nearest hundredth
Your answer will be 620!
Answer:
the number is 620.
Step-by-step explanation:
in other words the question is 55% of what number is 341?
let the number be Y.
[tex]\frac{55}{100}*Y=341[/tex]
[tex]\frac{55Y}{100}=341[/tex]
[tex]55Y=341*100[/tex]
[tex]55Y=34100[/tex]
[tex]Y=\frac{34100}{55}[/tex]
Y=620
How many cups of pineapple juice are needed to make 6 gallons of punch
Answer:
17
Step-by-step explanation:
A new car is purchased for 25000 dollars.The value of the car depreciates at 8.25% per year.What will the value of the car be,to the nearest cent,after 15 years?
Answer:
da,
Step-by-step explanation:
Please answer this correctly
Answer:
n = 4
Step-by-step explanation:
These triangles are similar, so you can set up a proportion like this:
[tex]\frac{20}{n} =\frac{10}{2}[/tex]
→Cross multiply:
[tex]\frac{40}{10n}[/tex]
→Divide 40 by 10:
n = 4
Kelly has $800, which she divides between two savings accounts. One account earns 2% simple interest and the other earns 5%. If she earns $31 in interest between the two accounts, how much is in each?
Answer:
On the first account, she invests $300, earning 0.02*300 = $6.
On the second acount, she invests 800 - 300 = $500, earning $25.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
In this question:
Two acounts, one with 2% interest(I = 0.02) and the other with 5% interest(I = 0.05).
Each account has two earnings, that i will call [tex]E_{1}[/tex] and [tex]E_{2}[/tex]
Two investments adding up to 800. I will call the first investment P and the second is 800 - P.
Time is not given, but for simplicity, i will use 1 year.
First investment:
I at 2%. The earnings are [tex]E_{1}[/tex].
[tex]E_{1} = 0.02P[/tex]
Second Investment:
Earnings [tex]E_{2}[/tex], at 5%. So
[tex]E_{2} = 0.05(800 - P)[/tex]
The earnings add to 31, so [tex]E_{1} + E_{2} = 31[/tex], then
[tex]E_{2} = 31 - E_{1}[/tex]
So
[tex]31 - E_{1} = 0.05(800 - P)[/tex]
[tex]31 - 0.02P = 0.05(800 - P)[/tex]
[tex]31 - 0.02P = 40 - 0.05P[/tex]
[tex]0.03P = 9[/tex]
[tex]P = \frac{9}{0.03}[/tex]
[tex]P = 300[/tex]
So:
On the first account, she invests $300, earning 0.02*300 = $6.
On the second acount, she invests 800 - 300 = $500, earning $25.
In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flower (e). An F2 generation was created by crossing two F1 individuals (each BbEe). The data below are the counted number of flowers from each phenotype in the F2 generation.
White short= 206
Red, short= 83
White, tall= 85
Red, tall= 30
Required:
a. What is your null hypothesis?
b. What is your expected phenotypic ratio based on Mendelian inheritance?
Question Completion
(a)What is your null hypothesis?
(b)What is your expected phenotypic ratio based on Mendelian inheritance?
(c)Calculate the expected number of flowers you should have gotten based on the Mendelian inheritance. Then calculate a chi-square value, degrees of freedom, and a p-value.
Chi-square statistic: _____Degrees of freedom (# phenotypes -1): P-value:(d)Interpret your results. Do you reject it or fail to reject your null hypothesis (please restate the null)?
Answer:
(a)[tex]H_0:$The given data fit the predicted phenotype[/tex]
(b)9:3:3:1
(c)
Chi-square statistic: 3.8914Degrees of freedom (# phenotypes -1) =3P-value: 0.2734(d)We fail to reject the null hypothesis.
Step-by-step explanation:
In the flowering plant, white flowers (B) are dominant over red flowers (b), and short plants (E) are dominant over tall flowers (e). An F2 generation was created by crossing two F1 individuals (each BbEe).
(a)The null hypothesis is:
[tex]H_0:$The given data fit the predicted phenotype[/tex]
(b)The gametes are BE, Be, bE and be.
The offsprings are presented in the table below:
[tex]\left|\begin{array}{c|cccc}&BE&Be&bE&be\\--&--&--&--&--\\BE&BE&BE&BE&BE\\Be&BE&Be&BE&Be\\bE&BE&BE&bE&bE\\be&BE&Be&bE&be\end{array}\right|[/tex]
The expected phenotypic ratio based on Mendelian inheritance
BE:Be:bE:be=9:3:3:1
(c)
[tex]\left|\begin{array}{c|c|c|c|c|c}$Phenotype&Observed&$Expected&O-E&(O-E)^2&\dfrac{(O-E)^2}{E} \\-----&--&--&--&--&--\\$White short(BE)&206&\frac{9}{16}*404 \approx 227 &-21&441&1.9427\\$Red, short(bE)&83&\frac{3}{16}*404 \approx 78 &5&25&0.3205\\$White, tall(Be)&85&\frac{3}{16}*404 \approx 78 &7&49&0.6282\\$Red, tall(be)&30&\frac{1}{16}*404 \approx 25 &5&25&1\\-----&--&--&--&--&--\\$Total&404&--&--&--&3.8914\end{array}\right|[/tex]
Therefore:
Chi-square statistic: 3.8914Degrees of freedom (# phenotypes -1): 4-1 =3P-value: 0.2734(d) Our null hypothesis is:
[tex]H_0:$The given data fit the predicted phenotype[/tex]
Since p>0.05, the given data fit the predicted phenotypic ratio.
We, therefore, fail to reject the null hypothesis.
The difference in the observed and expected are sosmall that they can be attributed to random chance.
line a passes through (0,3) & (-4,8) line b passes through (0,5) & (5,9) lines a & b are?
Answer:
line a )y=-5/4x+3
line b) y=4/5+5
The perimeter of the triangle shown to the right is 321 meters. Fin the length of each side.
first side: x meters
second side: 3x meters
third side: (4x-3) meters
Answer: First side is 40.5 meters. Second side is 121.5 meters. The third side is 159.
Step-by-step explanation:
x + 3x + 4x -3 = 321
8x - 3 =321
+3 +3
8x = 324
x = 40.5
Second Side: 3(40.5) = 121.5
Third side: 4(40.5) - 3 = 159
Check: 159 + 121.5 + 40.5 = 321
In a basket of fruit, 5/6 of the pieces of fruit are apples. There are 20 apples in the display. The equation 5/6f= 20 can be used to find how many pieces of fruit f are the basket. Use words and numbers to explain how to solve the equation to find how many pieces of fruit are in the basket.
Answer:
There are 24 pieces of fruit in the basket.
Step-by-step explanation:
There are 24 pieces of fruit in the basket because to find how many there are you would do [tex]\\ \frac{6}{5\\}\\ \\[/tex] · [tex]\frac{5}{6}[/tex]f = 20 · 6/5 times 5/6 cancels out, and 20 time 6/5 is 24. 20/24 can also simplify to 5/6.
Hope this helps!
(Make sure to stream ON, Black Swan. Boy With Luv, Mic Drop, and etc.!)
a television set was sold during a clearance sale for dollar 299.00the television was sold at a discount of 70 percent, what was the list price?
Answer:
$996.67
Step-by-step explanation:
The discounted price is ...
(list price)(100% -70%) = $299.00
list price = $299.00/0.30 . . . . . divide by 0.30
list price = $996.67
Kyle's car gets about 30 miles per gallon. About how many miles can KyleKyle drive on 11.1 gallons of gas? At $2.90 a gallon, about how much would that amount of gas cost?
A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday's mail. In actuality, each one may arrive on Wednesday, Thursday, Friday, or Saturday. Suppose the two arrive independently of one another, and for each one P(Wed.) = 0.3, P(Thurs.) = 0.4, P(Fri.) = 0.2, and P(Sat.) = 0.1. Let Y = the number of days beyond Wednesday that it takes for both magazines to arrive (so possible Y values are 0, 1, 2, or 3).
Required:
Compute the pmf of Y.
Answer:
Step-by-step explanation:
Let the events be
W = Wednesday
T = Thursday
F = Friday
S = Saturday
The corresponding probability are
P (W) = 0.3
P (T) = 0.4
P (F) = 0.2
P (S) = 0.1
Let Y = number of days beyond wednesday that takes for both magazines to arrive
(so possible Y values are 0, 1 , 2 ,3)
The possible outcome are 4² = 16
(W,W) (W,T) (W,F) (W,S)
(T,W) (T,T) (T,F) (T,S)
(F,W) (F,T) (F,F) (F, S)
(S,W) (S,T) (S,F) (S,S)
The values associated for each of the following as follows
Y(W,W) =0, Y(W,T) =1, Y(W,F)=2, Y (W,S)=3
Y(T,W)=1, Y (T,T)=1, Y (T,F)=2, Y (T,S)=3
Y(F,W)=2, Y (F,T)=2, Y (F,F)=2, Y (F, S)=3
Y(S,W)=3, Y (S,T)=3, Y (S,F)=3, Y (S,S)=3
The probability mass function of Y is
P(Y=0)=0.3(0.3)=0.9
P(Y=1) = P[(W,T) or (T,W) or (T,T)]
= [0.3(0.4) + 0.3(0.4) + 0.4(0.4)]
=0.4
P(Y = 2) = P[(W,F) or (T,F) or (F,W) or (F,T) or (F,F)]
=0.3(0.2) + 0.4(0.2) + 0.2(0.3) + 0.2(0.4) + 0.2(0.2)]
=0.32
P(Y =3) = P[(W,S) or (T,S) or (F,S) or (S,W) or (S,T) or (S,F) or (S,S)]
= [0.3(0.1) + 0.4(0.1) + 0.2(0.1) + 0.1(0.3) + 0.1(0.4) + 0.1(0.2) + 0.1(0.1)]
= 0.19
Let C(q) represent the cost and R(q) represent the revenue, in dollars, of producing q items.
a. If C(50) = 4900 and C'(50) = 27, estimate C(52)
C(52)= $___________________
b. If C'(50) = 27 and R'(50) =37, approximately how much profit is earned by the 51st item?
The profit on the 51st itme is ____________________ dollars.
c. if C' (100) =41 and R'(100)= 37, should the company produce the 101st item?
The company _______________________ produce the 101st item
Answer:
(a)$4954
(b)$10
(c)The company should not produce the 101st item.
Step-by-step explanation:
(a)
[tex]C'(50)=\dfrac{C(52)-C(50)}{52-50} \\\\C(50) = 4900,C'(50) = 27\\\\$Therefore:\\27=\dfrac{C(52)-4900}{52-50}\\C(52)-4900=27*2\\C(52)=4900+54\\C(52)=\$4954[/tex]
(b)If C'(50) = 27 and R'(50) =37
Cost will increase by $27Revenue will increase by $37Therefore, the profit earned on the 51st item
[tex]=R'(50)-C'(50)[/tex]
=37-27
=$10
(c)If C'(100) = 41 and R'(100) =37
Cost will increase by $41Revenue will increase by $37Therefore, the profit earned on the 101st item
Profit [tex]=R'(100)-C'(100)[/tex]
=37-41
=-$4
The company should not produce the 101st item. It would lose $4 if it does.
2 Points
What is the value of y? 2y 50 y+10
Answer:
y= -5/24
Step-by-step explanation:
2y=50y+10
1: Subtract 50y from both sides.
2y−50y=50y+10−50y
−48y=10
2: Divide both sides by -48.
−48y /48y=10/-48
y= -5/24
Adam works for an agency
Please help. What would be the proper proof for this problem? Prove: line BE congruent line BD.
Answer:
line AB is congruent to line CB . proof: given
line AE is congruent to line CD . proof: definition of a rectangle
angle EAB is congruent to angle BCD . proof: definition of a rectangle
triangle ABE is congruent to CBD . proof: SAS
line BE is congruent to line BD . proof: CPCTC
Step-by-step explanation:
Sorry if I'm wrong on this, but I hope you understand the general idea!
A family uses 12,986.64 Swiss francs per year to pay a mortgage that requires US dollars. Approximately how much, in US dollars, does the family spend per month on the mortgage?
1 US dollar = 0.9019 Swiss francs
1 Swiss franc = 1.11 US dollar
A.)$975
B.)$1,080
C.)$1,200
D.)$1,440
Answer:
C
Step-by-step explanation:
Per year: 12,986.64 * 1.11 = 14,415.1704 US dollars
Per month: 14,415.1704/12 = 1,201.2642 US dollars
Answer: c 1,200
explanation: 1,200 ÷ 12,986.64 = 0.09240265please help!! simplify. Your answer should only contain positive exponents. 2m squared times 2m to the power 3. m to the power 4 times 2m to the power 3
Answer:
A).4m^(+5)
B).2m^ (+7)
Step-by-step explanation:
First let me convert the expression to words for easy simplification and evaluation.
2m squared times 2m to the power 3.
= 2m² * 2m³
m to the power 4 times 2m to the power 3
= m⁴ * 2m³
So to evaluate.
We just multiply and get our answer.
For 2m² * 2m³
= (2*2)(m²*m³)
= 4(m(²+³))
= 4m^(+5)
For m⁴ * 2m³
= 2(m⁴*m³)
= 2m(⁴+³)
= 2m^ (+7)
Please answer this question !!! 20 points and brainliest !!
Answer:
see below
Step-by-step explanation:
The first answer choice is the only one that has the first sale correctly represented. Each term is the product of the number of pens of the type and the cost of pens of that type.
12 dozen roller-ball pens will have a cost of 12x
5 dozen ballpoint pens will have a cost of 5y
The total cost of these will be 116 (dollars).
The equation is written ...
12x +5y = 116 . . . . . . . this equation is only found in choice A
1/2 of 30 = 1/4 of ??
Answer:60
Step-by-step explanation:
⅟₂ of 30=15
¼ of 60=15
Half of thirty is 15 so u need to know what ¼ of something makes 15 so all u have to do is times 15 by 4 and there got ur answer this will not go for every question thoThe required value is 60.
What is proportion?The size, number, or amount of one thing or group as compared to the size, number, or amount of another is considered as proportion.
Given that, 1/2 of 30 = 1/4 of ??
So, 1/2 of 30 = 15
a/b = c/d
ad = bc
Let the unknown value be x,
Therefore,
30 / 2 = x / 4
2x = 120
x = 60
Hence, the value of unknown element is 60.
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Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.3, and 0.5, respectively. What is the expected number of books a customer will purchase?
Answer:
Expectation number of books a customer will purchase = 1.3
Step-by-step explanation:
x : 0 1 2
p(x) :0.2, 0.3, and 0.5
Expectation
E(X) = ∑x P(x)
= 0 X 0.2 +1 X 0.3+ 2 X 0.5
= 1.3
Expectation E(X) = 1.3
Expectation number of books a customer will purchase = 1.3
cual de las siguientes rectas son perpendiculares a la recta de la ecuación 4x+6y-6=0
Answer:
Ok, i will answer in English.
The first step is to know that when we have a linear equation like:
y = a*x + b
any line with a slope equal to -1/a will be perpendicular to our line.
So first let's write our equation in the standard form:
4x + 6y - 6 = 0
6y = -4x + 6
y = (-2/3)*x + 1
then the slope is (-2/3)
then the slope of the perpendicular line will be:
-(1/(-2/3)) = 3/2
So the only thing any line with the equation:
y = (3/2)*x + c
where c can be any real number, is perpendicular to 4x+6y-6=0
Why do I need to pay to see answers....
I just need like 5 answers and I'm never coming on here again.
Answer:
same problem with me.That's what happened
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(x)).
Answer:
2x+1
Step-by-step explanation:
that's a hard question
we know that g(x)= x-3
so f(g(x))= f(x-3)
we put it in the equation :
f(x-3)= 2(x-3) +7 = 2x-6+7 = 2x +1
