Answer: the amount of money raised by the three for charity in all is 386.81
Step-by-step explanation:
Alexis raises 75.23 for charity.
Sue raises 3 times as much as Alexis. This means that the total amount of money raised by Sue is 3 × 75.23= 225.69
The amount of money that Manuel raises is 85.89.
The amount of money raised by all of them(Alexis, Sue and Manuel) would be sum of the amount of money raised by Alexis + the amount of money raised by Sue +
the amount of money raised by Manuel. This becomes
75.23 + 225.69 + 85.89 = 386.81
Answer: 386.81
Step-by-step explanation:
Alexia raises 75.23 = x
Sue raises 3 times Alexia = 3x
= 3 × 75.23
=225.69
Manuel raises 85.89
Total amount raised = Alexia + sue + Manuel
= 75.23 + 225.69 + 85.89
= 386.81
What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time) Substitute and multiply
Answer:
The interest after 3 years is $360
Explanation:
Given the principal amount (P) = $3000
Rate of interest (R) = 0.04
Time period (T) is given as 3 years
The Simple Interest is calculated by the formula;
[tex]SI = Principal \times Rate of Interest \times Time[/tex]
Substituting the values in the above formula,
[tex]SI = 3000 \times 0.04 \times 3[/tex]
SI = $360
Therefore, the interest after 3 years is $360
Answer:
$360
Step-by-step explanation:
A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be shown. If an examinee must answer 6 of the multiple-choice questions and 4 of the open-ended problems, in how many ways can the questions and problems be chosen?
A) 1260
B) 1296
C) 261,273,600
D) 21,772,800
Answer: A) 1260
Step-by-step explanation:
We know that the number of combinations of n things taking r at a time is given by :-
[tex]^nC_r=\dfrac{n!}{(n-r)!r!}[/tex]
Given : Total multiple-choice questions = 9
Total open-ended problems=6
If an examine must answer 6 of the multiple-choice questions and 4 of the open-ended problems ,
No. of ways to answer 6 multiple-choice questions
= [tex]^9C_6=\dfrac{9!}{6!(9-6)!}=\dfrac{9\times8\times7\times6!}{6!3!}=84[/tex]
No. of ways to answer 4 open-ended problems
= [tex]^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6\times5\times4!}{4!2!}=15[/tex]
Then by using the Fundamental principal of counting the number of ways can the questions and problems be chosen = No. of ways to answer 6 multiple-choice questions x No. of ways to answer 4 open-ended problems
= [tex]84\times15=1260[/tex]
Hence, the correct answer is option A) 1260
To solve the problem, use the combination formula to find the number of ways to choose 6 multiple-choice questions from 9 and 4 open-ended problems from 6, then multiply the results. The answer is Option(D) 1260.
Solution to the Question
To determine the number of ways to choose 6 multiple-choice questions out of 9, and 4 open-ended problems out of 6, we can use combinations.
The number of ways to choose 6 multiple-choice questions out of 9 is given by the combination formula:
C(9, 6) = 9! / (6! * (9-6)!) = 84.
Similarly, the number of ways to choose 4 open-ended problems out of 6 is given by:
C(6, 4) = 6! / (4! * (6-4)!) = 15.
Now, multiply these two results to get the total number of ways to choose the questions:
84 * 15 = 1260.
Therefore, the answer is A) 1260.
You measure 20 dogs' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 11.5 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight.
95% confidence interval would be (58.96, 69.04).
Step-by-step explanation:
Since we have given that
Number of dogs' weight = 20
Mean = 64 ounces
Standard deviation = 11.5 ounces
We need to find the 95% confidence interval.
So, z = 1.96
so, interval would be
[tex]\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=64\pm 1.96\times \dfrac{11.5}{\sqrt{20}}\\\\=64\pm 5.04\\\\=(64-5.04,64+5.04)\\\\=(58.96,69.04)[/tex]
Hence, 95% confidence interval would be (58.96, 69.04).
A statistical procedure used to determine whether observed frequencies at each level of one categorical variable are similar to or different from frequencies expected, is called the chi-square:
Answer:
This statement is true.In statistics, the chi-square test is used to prove a specific hypothesis, accepting or rejecting the null one. In order to find enough evidence to prove the hypothesis, we compare two group of frequencies, which belongs to two different groups (like a quasi-experimental design, with a control and experimental group). The researcher have set an expected frequency, based on the hypothesis, and then he/she will observe a frequency from the data recollected.
Therefore, by comparing this two frequencies (the expected with the observed), the researcher is able to demonstrate the hypothesis.
Which fraction is equivalent to 0.65?
A) 5/13
B) 13/20
C) 19/25
D) 27/35
In a canoe race, A team paddles downstream 480 m in 60 seconds. The same team makes the trip upstream and 80 seconds. Find the teammates rate in Stillwater and the rate of the current period
Answer: The rate in still water is 8m/s
The rate in current period is is 6 m/s
Step-by-step explanation:
In a canoe race, A team paddles downstream 480 m in 60 seconds. The same team makes the trip upstream and 80 seconds.
We observe that it took the team more time paddling upstream than paddling downstream even though it was the same distance.
Let us assume that on paddling downstream, they paddled in the same direction with the current. This means that they paddled on still water. On paddling upstream, they paddled in the opposite direction of the current.
Let the speed of the boat or teammates be
x m/s
Let the speed of the current be
y m/s
Distance = speed × time
Distance travelled on still water or downstream
= (x+y) × 60 = 60(x+y)
Distance travelled on upstream
= (x-y) × 80 = 80(x-y)
Since the distance is 480 miles for both upstream and downstream,
60(x+y) = 480
x + y = 480/60 = 8 - - - - - -1
80(x-y) = 480
x - y = 480/80 = 6 - - - - - -2
Adding equation 1 and 2,it becomes
2x = 14
x = 14/2 = 7 m/s
y = 8 - x = 8-7
y = 1 m/s
Rate in still water = x +y = 7+1 = 8m/s
Rate in current period = x - y = 7 - 1 = 6m/s
help me with out this one thanks!
Answer:
9.5
Step-by-step explanation:
It keeps repeating the line goes all the way up then it keeps going to 9 then to 9.5 in the middle of 9 so it means its in between 10 so its 9.5 to 9 then 9.5 it repeats so mostly the answer is 9.5
hope i helped
please mark me as brainliest please
The length of the escalator is 30 feet and the distance between the floors is 12 feet. Find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator.
Answer:
Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet
Step-by-step explanation:
Given:
Length of escalator = 30 feet
Distance between the floors = 12 feet
To find the distance from base of escalator to the point on the first floor directly below the top of the escalator we will create the figure for the situation.
From the figure we see that a triangle ABC is formed.
We see that the Δ ABC is a right triangle.
Applying Pythagorean theorem for right triangle ABC to find the missing side.
[tex]AB^2=BC^2+AC^2[/tex]
AB = 30 feet
BC = 12 feet
Plugging in values in the theorem.
[tex]30^2=12^2+AC^2[/tex]
Solving for AC.
[tex]900=144+AC^2[/tex]
Subtracting both sides by 144.
[tex]900-144=144+AC^2-144[/tex]
[tex]756=AC^2[/tex]
Taking square root both sides.
[tex]\sqrt{756}=\sqrt{AC^2}[/tex]
[tex]27.5=AC[/tex]
∴ [tex]AC=27.5[/tex] feet.
∴ Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet
To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The distance is approximately 27 feet.
Explanation:To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The length of the escalator represents the hypotenuse of a right triangle, and the distance between the floors represents one of the legs.
We can use the formula a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. Substituting the given values, we have 12^2 + b^2 = 30^2. Simplifying the equation, we get b^2 = 30^2 - 12^2. Calculating the value, we find that b^2 = 756, which means b is equal to the square root of 756. Rounding to the nearest foot, the distance from the base of the escalator to the point on the first floor directly below the top of the escalator is approximately 27 feet.
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Which of the following is a radical equation? x + StartRoot 5 EndRoot = 12 x squared = 16 3 + x StartRoot 7 EndRoot = 13 7 StartRoot x EndRoot = 14
Answer:
The equation [tex]7\,\sqrt{x} =14[/tex] is a radical equation.
Step-by-step explanation:
If the equations given are (as I can read them from your typing):
a) [tex]x+\sqrt{5} =12[/tex]
b) [tex]x^2=16[/tex]
c) [tex]3+x\,\sqrt{7} =13[/tex]
d) [tex]7\,\sqrt{x} =14[/tex]
The only radical equation is the last one : [tex]7\,\sqrt{x} =14[/tex], because it is the only one where the unknown appears inside the root. The name "radical equations" is associated with the fact that the unknown is contained inside the root and therefore the process involved in solving for the unknown will need to include the elimination of the root via algebraic methods to free the unknown.
Notice that the options a) and c) have roots, but what appears inside them are numbers (5 and 7 respectively), and not an unknown like "x". Equation b) doesn't contain a root, and wouldn't classify as a radical equation.
A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Thus, by above definition, we will have the fourth option: [tex]7\sqrt{x} = 14[/tex] as a radical equation.
Given the equations: [tex]x + \sqrt{5} = 12\\[/tex] [tex]x^2 = 16[/tex] [tex]3 + x\sqrt{7} = 13\\[/tex] [tex]7\sqrt{x} = 14[/tex]Explanation:A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Since only in the fourth option we see there's root over x which is a variable here, thus the fourth option: [tex]7\sqrt{x} = 14[/tex] is a radical equation.
Rest of the options, although containing roots, aren't having variables inside the root, thus they aren't classified as radical equations.
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Find the probability of each outcome when a biased die is rolled, if rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers on the die and it is equally likely to roll a 2 or a 4.
Answer:
Let's x be the probability for 1, 3, 5 and 6.
The probability for 2 and 4 is going to be 3x.
The sum of the probabilities of all possible outcomes is always 1.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
x + 3x + x + 3x + x + x = 1
10x = 1
x = 1/10
The probability of obtaining 1, 3, 5 or 6 is 1/10
The probability for 2 and 4 is 3/10
The probability of rolling a 2 or a 4 is [tex]$\frac{3}{14}$[/tex], and the probability of rolling any of the other numbers (1, 3, 5, or 6) is [tex]$\frac{1}{14}$.[/tex]
To solve this problem, we need to distribute the total probability of 1 (since the sum of all probabilities must equal 1) among the six outcomes of the die according to the given conditions.
Let's denote the probability of rolling a 2 or a 4 as $p$. According to the problem, rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers. Therefore, the probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3}$.[/tex]
Since there are two outcomes with probability $p$ (rolling a 2 and rolling a 4) and four outcomes with probability $\frac{p}{3}$ (rolling a 1, 3, 5, or 6), we can set up the following equation to represent the total probability:
[tex]\[ 2p + 4\left(\frac{p}{3}\right) = 1 \][/tex]
Now, let's solve for $p$:
[tex]\[ 2p + \frac{4p}{3} = 1 \][/tex]
[tex]\[ \frac{6p + 4p}{3} = 1 \][/tex]
[tex]\[ \frac{10p}{3} = 1 \][/tex]
[tex]\[ 10p = 3 \][/tex]
[tex]\[ p = \frac{3}{10} \][/tex]
So, the probability of rolling a 2 or a 4 is[tex]$p = \frac{3}{10}$.[/tex]
The probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3} = \frac{3}{10} \times[/tex] [tex]\frac{1}{3} = \frac{1}{10}$.[/tex]
However, we must remember that the total probability must be distributed equally between rolling a 2 and rolling a 4. Since they are equally likely, each has a probability of half of $p$:
[tex]\[ p_{2} = p_{4} = \frac{p}{2} = \frac{3}{10} \times \frac{1}{2} = \frac{3}{20} \][/tex]
Now, we can state the final probabilities for each outcome:
- The probability of rolling a 1 is [tex]$\frac{1}{10}$.[/tex]
- The probability of rolling a 2 is [tex]$\frac{3}{20}$.[/tex]
- The probability of rolling a 3 is [tex]$\frac{1}{10}$.[/tex] - The probability of rolling a 4 is [tex]$\frac{3}{20}$.[/tex]
The probability of rolling a 5 is [tex]$\frac{1}{10}$.[/tex]
Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs?A. 7B. 9C. 14D. 16E. 23
There are 9 students in only one of the two clubs.
Step-by-step explanation:
Since we have given that
Number of students = 36
Number of students are in chess club = 10
Number of students are in bridge club = 13
Number of students are not in either club = 20
So, Number of students in both the club is given by
[tex]Total=n(chess)+n(bridge)-n(both)+n(neither)\\\\36=10+13-n(both)+20\\\\36=43-n(both)\\\\36-43=n(both)\\\\-7=-n(both)\\\\n(both)=7[/tex]
Number of students only in chess = 10-7 =3
Number of students only in bridge = 13-7=6
Hence, there are 3+6=9 students in only one of the two clubs.
Determine the temperature of 2.6 moles of gas contained in a 5.00-L vessel at a pressure of 1.2atm.
Answer:
28.108 K.
Step-by-step explanation:
Given: Pressure (P)= 1.2atm
Number of moles (n)= 2.6 moles
Volume (V)= 5.00-L
Now finding the temperature (T).
Formula; T= [tex]\frac{P\times V}{n\times R}[/tex]
R is a constant factor which makes other factors work together.
There is a numerical value for R which we use is [tex]0.0821 \times \frac{L.atm}{mole.K}[/tex]
∴ Temperature (T)= [tex]\frac{1.2\times 5}{2.6\times 0.0821 \frac{L.atm}{mol.K} }[/tex]
⇒ Temperature (T)= [tex]\frac{6}{0.21346} = 28.1083\ K[/tex]
∴ Temperature is 28.108 K
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?
Answer:
6 minutes
Step-by-step explanation:
Machine A produces x boxes in 10 minutes
In one minute, the machine produces x/10 boxes
Machine B produces 2x boxes in 5 minutes
In one minute, the machine produces 2x/5 boxes
Therefore in one minutes, both boxes working together will produce
= 2x/5 + x/10
=5x/10
=x/2 boxes
To produce 3x boxes, the time required
= 3x/(x/2)
= 3 × 2
= 6
It take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes in 6 minutes
explain with words how you find the area of the figure. then find the area.
image attached
Answer:
13x² -3x
Step-by-step explanation:
A horizontal line from the corner of the "notch" will divide the figure into two rectangles whose dimensions are given. The total area is the sum of the areas of those rectangles. Each area is the product of length and width.
A = A1 + A2
= x(3x-7) + 2x(5x+2)
= 3x² -7x +10x² +4x
= (3+10)x² +(-7+4)x
= 13x² -3x
The area is 13x² -3x.
pls help asap
Given the number of people that are going on the trip, what is the total amount you will you spend on food and lodging each day?
$525 each day
Given the number of people that are going on the trip, what is the total amount you will spend on luggage for everybody?
$230 for everyone
Now use the amount you spend on Daily expenses to make an equation in y=mx+b form that will give you the expenses (y) for any amount of days (x).
Total Expense equation:
Answer:
y=525x+230
Step-by-step explanation:
525 is spent everyday. x is the number of days, so with each day $525 is spent.
$230 is a one time cost, regardless of how many days they stay on the trip.
Use the graph below to fill in the blank with the correct number: f(0) = _______ X, Y graph. Plotted points negative 3, 0; negative 2, 2; 0, 1; and 1, negative 2.
Answer:
f(0) = 1
Step-by-step explanation:
The ordered pair with first number 0 has second number 1. Each pair corresponds to (x, f(x)), so that pair has x=0 and f(0) = 1.
Answer:
[tex]f(0)=1[/tex]
Step-by-step explanation:
The given points are
[tex](-3,0), (-2,2),(0,1),(1,-2)[/tex]
Remember that each point has the form [tex](x,y)[/tex], where [tex]y=f(x)[/tex].
That means if we need to find [tex]f(0)[/tex], then we just need to look for the pair that belong to [tex]x=0[/tex].
If you observe, the pair we are looking for is [tex](0,1)[/tex], which relation is
[tex]f(0)=1[/tex].
Therefore, the answer is 1, that is, [tex]f(0)=1[/tex].
A furniture company is introducing a new line of lounge chairs next quarter. These are the cost and revenue functions, where x represents the number of chairs to be manufactured and sold: R(x) = 1,248x – 8.32x2 C(x) = 36,400 – 83.2x For the company to make a profit on the chairs, the selling price can go no lower than $ and no higher than $.
Answer:
lower limit: $208upper limit: $956.80Step-by-step explanation:
For cost and revenue functions C(x) = 36400-83.2x and R(x) = 1248-8.32x², you want to know the selling price limits that will let the company make a profit.
ProfitProfit is the difference between revenue and cost.
P(x) = R(x) -C(x)
P(x) = 1248-8.32x² -(36400-83.2x) . . . . . . use the given functions
P(x) = -8.32(x² -160x +4375) . . . . . . . . remove common factor
P(x) = -8.32(x -35)(x -125) . . . . . . factor
The profit will be zero when the factors are zero, for x = 35 and x = 125.
PriceWe have to assume the demand function is found by dividing the revenue by the number of chairs sold.
R(x) = x(price) = x(1248 -8.32x)
Then the price is ...
price = 1248 -8.32x . . . . . . . . . . . where x is the number of chairs sold
When selling 125 chairs, the price is ...
1248 -8.32(125) = 208 . . . . . dollars
When selling 35 chairs, the price is ...
1248 -8.32(35) = 956.80 . . . . dollars
For the company to make a profit, the selling price can go no lower than $208 and no higher than $956.80.
__
Additional comment
These prices will result in 0 profit, as the number of chairs sold makes the revenue equal to the cost. If we require sales of 36 to 124 chairs, so profit is positive, then the price limits are $216.32 and $948.48. Profit will be maximized when 80 chairs are sold for $582.40 each.
The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of____________.
a) the test statistic
b) a confidence interval.
c) a p-value
d) the alternative hypothesis
The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of p value
hence option (c) is correct
Test statistic is a way to check the authenticity of null hypothesis that is considered. Test statistic is extremely important to accept and reject the null hypothesis.
The data from the experiment is fed into the equation and compares your result with the expected results of null hypothesis.
Test statistic is a number calculated from statistical test of a hypothesis.
It shows how closely our data matches with the distribution expected under null hypothesis of the distribution.
Confidence interval
Confidence interval is the range of plausible values of a random variable with a certain percentage of confidence level. Confidence level shows that how much certainty or uncertainty in test statistic considering the null hypothesis to be true. It is expressed in percentage. 98% , 95% and 90% Confidence intervals are a few examples.
p- value is the probability of a happening of a particular event is a random chance or some other event with similar probability or any rarer event considering null hypothesis to be true.
Alternate hypothesis
Alternate hypothesis is the opposite of Null hypothesis. Null hypothesis is the generally or by default accepted hypothesis which is tested by various statistical tests.
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The perimeter of kite LMNO is 36 feet. Side MN = 8x – 3 and side NO = 2x + 1. Find the value of x.
Answer: 85.333 or 256 over 3.
Answer: x = 2
Step-by-step explanation:
The diagram of the kite is shown in the attached photo.
The perimeter of the kite is the distance around the kite.
The kite has 2 pairs of equal sides.
This means that
Side ML = side MN and side NO =
side LO
If Side MN = 8x – 3 and side NO = 2x + 1, then The perimeter of the kite is ML + MN + NO + LO
The perimeter of kite LMNO is given as 36 feet.
Therefore
ML + MN + NO + LO = 36
8x – 3 + 2x + 1 +8x – 3 + 2x + 1 = 36
8x + 8x + 2x+ 2x -3 +1 - 3 + 1
20x -4 = 36
20x = 40
x = 40/20 = 2
Gabe went ot lunch with his best friend the bill costs 16.40 dollers before trax and tip he paid a 9 persent tax and left a 20 persent tip howm much did gabe spend
Answer:
Step-by-step explanation:
Gabe went out for lunch with his best friend the bill costs $16.40
This amount was before tax and the tip that he wanted to give.
He paid a 9 percent tax on the bill. The amount of the 9 percent tax is 9/100 × 16.40 = 0.09 × 16.40 = $1.476
He left a 20 percent tip. This means that amount left as tip is 20/100 × 16.40 = 0.2×16.40 = $3.28
The amount that Gabe paid would be the sum of the bill, the tip and the amount paid on tax. It becomes
16.40 + 1.476 + 3.28 = $21.156
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?
A) $94.03
B) $96.75
C) $98.78
D) $102.07
E) $105.3
Answer:
B)$96.75
Step-by-step explanation:
5pound bag cost = $13.85
10pound bag cost= $20.43
25pound bag cost = $32.25
The least quantity of bag the customer can by is 65 pounds = (2*25 pound)+ 10 pound + 5pound = $98.78
But careful examination will show actually that since the most the customer can buy is 80 pound, then buying 25pound in three places give him even a lot cheaper than buying the least amount
75 pound = 3*25 pound = 32.25*3 = $96.75.
Therefore the least amount in cost the customer can buy is $96.75
There are two cookie jars: jar 1 contains two chocolate chip cookies and three plain cookies, and jar 2 contains one chocolate chip cookie and one plain cookie. Blind- folded Fred chooses a jar at random and then a cookie at random from that jar. What is the probability of him getting a chocolate chip cookie?
Answer:
P = 0.55 or 55 %
Step-by-step explanation:
First step: Fred has probability of 0,5 when chossing jar 1 or jar 2
Second step : The probability of chossing one chocolate chp cookie in jar 1 is 3/5 and from the jar 2 is 1/2
Then the probability of Fred to get a chocolate chip cookie is
P ( get a chocolate chip cookie ) =( 0.5 * 3/5) +( 0.5* 1/2)
P = 0.3 + 0.25
P = 0.55 or 55 %
A truck driver drives from Chicago to Cincinnati in 14 hours. The distance traveled is 840 miles. Write the average speed as a unit rate in fraction form
Answer:
60 miles/hour
Step-by-step explanation:
840 miles divided by 14 hours
840/14=60 miles per hour
There are statistical analyses beyond simple descriptive measures, statistical inference, and differences tests including ________, which determine whether a stable relationship exists between two variables.
A) associative analyses
B) analysis of variance analyses
C) regression analyses
D) predictive analyses
Answer:
Associative analysis
Step-by-step explanation:
Associative analysis is an approach that is used to analyses the peoples mental representation , focusing on meaning and similarities and differences across the culture.It determined that relationship that is hidden in the large data set.It determine the relationship in between two variable as well.
Based on data from Bloodjournal.org, 10% of women 65 years of age and older have anemia, which is a deficiency of red blood cells. In tests for anemia, blood samples from 8 women 65 and older are combined. What is the probability that the combined sample tests positive for anemia? Is it likely for such a combined sample to test positive?
Answer:
the probability that the combined sample tests positive for anemia is ≈ 0,38.
Thus it is 38% likely that such a combined sample to test is positive.
Step-by-step explanation:
The combined sample tests positive if at least one of the 8 women has anemia.
Let p be the probability that a women 65 years of age and older have anemia
Then p=0.1
The probability that one of the 8 women has anemia and others does not is:
p×[tex]p^{7}[/tex] .
Since there are 8 combinations of this probability is possible, the probability that at least one of the 8 woman has anemia is:
8×p×[tex]p^{7}[/tex] =8×0.1×[tex]0.9^{7}[/tex] ≈ 0,3826
The probability that a combined sample of blood from 8 women aged 65 and older tests positive for anemia is approximately 56.95%, making it likely for the sample to test positive. This probability is calculated using the complement rule in probability.
To determine the probability that a combined sample of blood from 8 women aged 65 and older tests positive for anemia, we need to use the complement rule and properties of probability.
Given:
- Probability that one woman has anemia (success): 10% or 0.10
- Probability that one woman does not have anemia (failure): 90% or 0.90
- Number of women sampled: 8
The probability that all 8 women do not have anemia can be calculated as:
[tex](0.90)^8[/tex]
Now let's compute this:
[tex](0.90)^8[/tex] ≈ 0.4305
This means there is an approximately 43.05% probability that none of the 8 women have anemia. Therefore, the probability that at least one woman in the sample has anemia is:
1 - 0.4305 ≈ 0.5695 or 56.95%
Since the probability is greater than 50%, it's quite likely that such a combined sample will test positive for anemia.
A woman drives 169/4 miles to work each day . She stops for coffee at a shop that is 2/5 of the way to her job . How far does the woman drive before she stops for coffee?
Answer: the woman drives 16.9 miles before she stops for coffee
Step-by-step explanation:
A woman drives 169/4 miles to work each day. She stops for coffee at a shop that is 2/5 of the way to her job.
To determine how far the woman drives before she stops for coffee, we will multiply the total miles to her job each day by the fraction of the total miles that she drives before stopping at the coffee shop. It becomes
2/5 × 169/4 = 16.9 miles
If [tex]x-12\sqrt{x} +36=0[/tex], what is the value of x?
A. [tex]6[/tex]
B. [tex]6^{2}[/tex]
C. [tex]6^{3}[/tex]
D. [tex]6^{4}[/tex]
Answer:
x = 36
Step-by-step explanation:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
Subtract x and 36 from both sides.
[tex] -12\sqrt{x} = -x - 36 [/tex]
Divide both sides by -1.
[tex] 12\sqrt{x} = x + 36 [/tex]
Square both sides.
[tex] 144x = x^2 + 72x + 1296 [/tex]
Subtract 144x from both sides.
[tex] 0 = x^2 - 72x + 1296 [/tex]
Factor the right side.
[tex] 0 = (x - 36)^2 [/tex]
[tex] x - 36 = 0 [/tex]
[tex] x = 36 [/tex]
Since the solution of the equation involved squaring both sides, we musty check the answer for possible extraneous solutions.
Check x = 36:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
[tex] 36 - 12\sqrt{36} + 36 = 0 [/tex]
[tex] 36 - 12\times 6 + 36 = 0 [/tex]
[tex] 36 - 72 + 36 = 0 [/tex]
[tex] 0 = 0 [/tex]
Since 0 = 0 is a true statement, the solution x = 36 is a valid solution.
Complete the square to determine the minimum or maximum value of the function defined by the expression.
−x² + 10x + 5
A. maximum value at 30
B. minimum value at 30
C. maximum value at −30
D. minimum value at −30
Please provide a full explanation, thank you!
Answer:
A. maximum value at 30
Step-by-step explanation:
−x² + 10x + 5
First, factor out the leading coefficient from the first two terms:
-1 (x² − 10x) + 5
Take half of the next coefficient, square it, then add and subtract the result.
(-10/2)² = 25
-1 (x² − 10x + 25 − 25) + 5
-1 (x² − 10x + 25) + 25 + 5
-1 (x² − 10x + 25) + 30
Factor the perfect square.
-1 (x − 5)² + 30
The equation is now in vertex form. This is a downwards parabola with a vertex at (5, 30). Since the parabola points down, the vertex is a maximum.
Mr. Ruiz was a principal at Wilson high for 6 years. He became principal after teaching at the school for 13 years. He first began teaching two years after graduating from college in 1973. During what years was Mr. Ruiz principal of Wilson high
Answer:
From years 1988 to 1994
Step-by-step explanation:
The trick in this question is to start from last conditions.
Mr. Ruiz graduated in 1973. Started to teach 2 years after, which means, 1975.
He taught for 13 years, which means from 1975 to (1975 + 13)1988.
He became principle only after teaching for 13 years, which means he started to be principle for 1988. And he continued to be for 6 years which means, (1988 + 6) 1994.
Thus, years for which Mr. Ruiz was principle were From 1988 to 1994.
The recipe makes 20 portions of potato soup. Richard follows the recipe but wants to make 4 portions. Complete the amounts of each ingredient that he needs. 120 ml oil 280 g onion 1.8kg potatoes 2.2 l milk
Answer:
Oil: 24 ml; Onion: 56 g; Potatoes: 0.36 kg; Milk: 0.44 l
Step-by-step explanation:
First, we see how much of the soup recipe he wants make.
4 portions out of 20 portions = 4/20 = 1/5 = 0.2
He wants to make 0.2 of the amount of the recipe.
Now we multiply every amount by 0.2
Oil: 0.2 * 120 ml = 24 ml
Onion: 0.2 * 280 g = 56 g
Potatoes: 0.2 * 1.8 kg = 0.36 kg
Milk: 0.2 * 2.2 l = 0.44 l
Richard needs to use a scaling factor to reduce the amounts of each ingredient to make 4 portions of potato soup, resulting in 24 ml oil, 56 g onion, 360 g potatoes, and 0.44 liters of milk. Devon will require 37.5 liters of soup for a party of 100 guests.
To scale down the recipe from 20 portions to 4 portions of potato soup, Richard needs to multiply each ingredient by the scaling factor, which is 4/20 or 1/5. Here's how to calculate the amounts needed:
Oil: 120 mlTherefore, for 4 portions, Richard needs 24 ml of oil, 56 g of onion, 360 g of potatoes, and 0.44 liters of milk.