Add a bicycle shop all bicycles are on sale for $25 off the regular price if P represents the regular price in dollars of a bicycle which expression gives the sale price in dollars
Answers
Answer:
p-25
Step-by-step explanation:
Related Questions
URGENT!!! due in 20 minutes GRAPH TRANSLATIONS 2 questions. Will mark brainliest!!!!
Answers
Answer:
Function f is translated to the right 2 units, and then up 1 unit to obtain function g.
To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:
Function f is translated to the right 2 units.
Function f is translated up 1 unit.
Function f is translated to the right 2 units, and then up 1 unit to obtain function g.
To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:
Function f is translated to the right 2 units.
Function f is translated up 1 unit.
Step-by-step explanation:
Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x^2 + 49y^2 + 1134x − 882y + 3969 = 0
Answers
Answer:
882y,com hi
Step-by-step explanation:
hi hi hi hi hi hi hi hi hi
Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
What is the answer to this P(A)=.49 P(A’)=?
Answers
Answer:
\(P(A')=0.51\)
Step-by-step explanation:
A rule of complementary events states that:
\(P(A)+P(A')=1\)
We know that P(A) is 0.49. Substitute:
\(0.49+P(A')=1\)
Subtract 0.49 from both sides:
\(P(A')=0.51\)
So, the complement probability to P(A) is P(A'), or 0.51.
And we're done!
Which sides can make a triangle the question is in the photo
Answers
Answer: I believe it is 10cm 9cm 9cm
Step-by-step explanation:
Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side
Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?Shawn rounded a number to the nearest tenth and got 6.5 6 . 5 . When he rounded it to the nearest whole number, he got 6 6 . Which number could be the number he rounded?
Answers
The numbers could be:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
Shawn rounded a number to the nearest tenth and got 6.5.
When he rounded it to the nearest whole number, he got 6.
Now,
The number = 6.45
Rounded to the nearest tenth = 6.5
Rounded to the nearest whole number = 6
The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
Thus,
The possible numbers are:
6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.
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Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
Answers
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : \(\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}\)
GGRRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}\)
GGGRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}\)
GGGGR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
GGGGG : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
The sum is \(\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}\)
Probability that you do not eat green candy after you eat a red candy =\(\frac{1}{5}\)
so m = 1 and n = 5
m + n =6
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Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
Answers
1. A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
In this case, the spinner's outcome of landing on region three is independent of landing on region six. Each spin is unrelated to the previous spin, and the outcome of one region does not affect the outcome of the other region. Therefore, the events are independent. The probability of landing on both region three and region six is the product of their individual probabilities: 1/8 * 1/8 = 1/64.
2. A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?
In this scenario, the events are overlapping. A jersey can be both purple and have a number greater than 5 at the same time. Therefore, the probability of it being purple or having a number greater than 5 is the sum of their individual probabilities, minus the probability of the overlapping event (purple jerseys with a number greater than 5). There are 4 purple jerseys out of 10 total jerseys, and there is 1 jersey with a number greater than 5 out of 10. However, there is one jersey that satisfies both conditions (purple and number greater than 5), so we need to subtract it from the sum. So the probability is (4/10 + 1/10) - (1/10) = 4/10 = 2/5.
3. A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?
In this scenario, the events are mutually exclusive. A chocolate cannot be both a milk chocolate and have no peanuts inside at the same time. Therefore, the probability of it being a milk chocolate or having no peanuts inside is the sum of their individual probabilities. There are 6 milk chocolates out of 10 total chocolates, and there are 7 chocolates without peanuts out of 10. So the probability is 6/10 + 7/10 = 13/10, which is greater than 1. However, probabilities cannot exceed 1, so we need to take the maximum value of 1. Therefore, the probability is 1.
4. You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?
In this case, the events are independent. The outcome of the coin flip does not affect the outcome of the die roll. The probability of the coin landing heads up is 1/2, and the probability of the die showing an even number is 1/2. To find the probability of both events occurring, we multiply their individual probabilities: 1/2 * 1/2 = 1/4.
I hope this clarifies the nature of each event. Let me know if you have any further questions!
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
I need help on this question
Answers
Answer:
46√3
Sorry, it's a lot of steps to elaborate on.
Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
Answers
x + 5
(43) + 5 = 48
What is the converse of the conditional statement?
"If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid."
Responses
A. If a quadrilateral is not a trapezoid, then it does not have exactly one pair of parallel sides.
B. If a quadrilateral does not have exactly one pair of parallel sides, then it is not a trapezoid.
C. If a quadrilateral does not have exactly one pair of parallel sides, then it is a trapezoid.
D. If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.
Answers
Answer:
D. If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides.
Step-by-step explanation:
The converse of a statement is formed by switching the hypothesis and the conclusion.
Hypothesis: The part after the "if".Conclusion: The part after the "then".Given statement:
"If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid."Therefore:
Hypothesis: "a quadrilateral has exactly one pair of parallel sides"Conclusion: "it is a trapezoid."Converse statement:
"If a quadrilateral is a trapezoid, then it has exactly one pair of parallel sides."What is the justification for step 2 in the solution process?12 - x = 7x +32Step 1: -X = 7x + 20Step 2: -8x = 20
Answers
The subtraction property of equality
Option A is correct
Explanation:The given equation is:
12 - x = 7x + 32
Subtract 12 from both sides
12 - 12 - x = 7x + 32 - 12
-x = 7x + 20 (Step 1)
From step 1 above, subtract 7x from both sides
-x - 7x = 7x - 7x + 20
-8x = 20 (Step 2)
Since we subtracted 7x from both sides to get step 2, the justification for step 2 is the subtraction property of equality
In 25 years, a bond that paid 4.75% simple interest earned $4,750 interest. What was the principal of the bond in dollars?
Answers
Answer:
$ 4000Step-by-step explanation:
Given,
Rate ( R ) = 4.75 %
Time ( T ) = 25 years
Simple Interest ( I ) = $ 4,750
Principal ( P ) = ?
Finding the principal
We know that,
\( \boxed{ \sf{principal = \frac{interest \: \times 100}{ \: time \: \times \: rate} }}\)
plug the values
⇒\( \sf{ \frac{4750 \times 100}{4.75 \times 25} }\)
Calculate
⇒\( \sf{\frac{475000}{118.75} }\)
⇒$ \( \sf{4000}\)
Hope I helped!
Best regards!!
Answer:
2000
Step-by-step explanation:
if 3 bannanas cost of 50 cents, how many bananas can be bought for 20 dollars?
Answers
Answer:
120 bananas
Step-by-step explanation:
$20 = 2000 centsCreate a proportion: \(\frac{3}{50} = \frac{x}{2000}\) Cross multiply, then divide: 3 × 2000 = 6000, 6000 ÷ 50 = 120So, you can buy 120 bananas for $20I hope this helps!
There are total 120 bananas that can be bought for 20 dollars.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Cost of 3 bananas = 50 cents,
Since 1 dollar = 100 cents
Cost of 3 banana = 0.5 dollars
In 20 dollars, number of bananas that can be bought
= 3 x 2 x 20
= 120
Total 120 bananas can be bought for 20 dollars.
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8.032×10^-4 in standard form
Answers
Answer:
0.0008032
Step-by-step explanation:
Hope this helps!
Answer:
80,320
Step-by-step explanation:
Examine the worked problem and solve the equation
Answers
Answer:
The solution is 9
write all the numbers less than 100 which are common multiples of 3 and 4
Answers
Answer:
12, 24, 36, 48, 60, 72, 84, 96
Step-by-step explanation:
The smallest natural number that is a common multiple of 3 and 4 is 12. The answer is all multiples of 12 less than 100.
Answer: 12, 24, 36, 48, 60, 72, 84, 96
Round to the nearest whole number 30.76
Answers
Answer:
31
Step-by-step explanation:
The correct answer is 31.
Since 7 is greater than 5, you add a 1 in replace of the 0 to get 31.
Answer:
31
Step-by-step explanation:
30.76 is more then 30.50 therefore you round forward and get 31.
how to round 831,756 nears hundred thousand
Answers
Answer:
800,000
Step-by-step explanation:
If the number was above 850,000 it would round up. If the number was 849,999 or below it would round down. In other words, you look at the number to the right of the hundred thousands place, or the number in the tens of thousands place, and if it is 5 or above you round up. 4 and below you round down.
The equation x + c = k has a solution of x = 2. Both cand k are rational numbers.
Select all the statements that must be true in all cases.
cis 2 greater than k.
cand k must be whole numbers.
The solution x = 2 is the only solution.
If c is a whole number, k is also a whole number.
I need help ASAP PLEASE
Answers
Answer:
The solution x = 2 is the only solution
If c is a whole number, k is also a whole number.
What is the completely factored form of f(x) = x^3-7x^2 2x +4?
Answers
a system of equations is shown. y=3x+2 y=x-2 , Graph the system of equations to show its solution
Answers
To graph the two lines, we can plot two points on each line and connect them with a straight line. For y = 3x + 2, we can choose x = 0 and x = 1 to get the points (0, 2) and (1, 5), respectively. For y = x - 2, we can choose x = 0 and x = 1 to get the points (0, -2) and (1, -1), respectively.
In the graph: The red line represents y=3x+2 and the blue line represents y=x-2
Explain the term straight line
A straight line is a geometric figure that extends infinitely in both directions and has no curvature or bends. It is the shortest distance between two points and can be described using various mathematical equations, such as y = mx + b, where m is the slope and b is the y-intercept. Straight lines are used in various fields, including geometry, physics, and engineering, to represent and analyze the relationships between objects or points.
According to the given information
To graph the system of equations y = 3x + 2 and y = x - 2, we can plot the two lines on the same coordinate plane and find the point where they intersect.
First, we can find the point of intersection by setting the two equations equal to each other:
3x + 2 = x - 2
Simplifying, we get:
2x = -4
x = -2
Substituting this value of x back into one of the equations, we get:
y = (-2) - 2 = -4
So the solution to the system of equations is the point (-2, -4).
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7. Convert the following:
A. 623.5 °F to K
B. 0.0083 miles to cm
C 3027.2 ml to ounces
D. 0.885 kg to pounds
Answers
So, K = (623.5 + 459.67) x 5/9 = 873.28 K (rounded to two decimal places)
B. To convert miles to centimeters, we use the conversion factor: 1 mile = 160934.4 cm
So, 0.0083 miles = 0.0083 x 160934.4 = 1334.74 cm (rounded to two decimal places)
C. To convert milliliters to ounces, we use the conversion factor: 1 ml = 0.033814 oz
So, 3027.2 ml = 3027.2 x 0.033814 = 102.37 oz (rounded to two decimal places)
D. To convert kilograms to pounds, we use the conversion factor: 1 kg = 2.20462 lbs
So, 0.885 kg = 0.885 x 2.20462 = 1.95 lbs (rounded to two decimal places)
Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.
Answers
The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)
The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.
Here we have given the inequality (x² - 5)/ (x - 36) < 0
And we need to find the solution in inequality notation and in interval notation.
In order to find the inequality notation, we have to solve the given inequality, then we get.
(x² - 5)/ (x - 36) < 0
(x² - 5) < 0
x² < 5
x < √5
While we looking into the inequality we must know that the denominator must not be 0.
So, the interval notation can be written as,
=> (-∞ . -√5]∪[√5,36)
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What is the vertex of the graph of g(x)=|x-8|+6
Answers
The vertex of the function g(x) = |x - 8| + 6 is (8, 6)
How to determine the vertex of the function?From the question, we have the following parameters that can be used in our computation:
g(x) = |x - 8| + 6
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
This means that the vertex is
Vertex = (8, 6)
Remove the x value
y = 6
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 6
So, the range is y ≥ 6
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HELP!!
Calculate the residuals for your scatterplot in step 2d.
Answers
In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:
Step 1: Plot the data on a scatterplot.
Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.
Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.
Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.
Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.
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Are the ratios 2:1 and 19:10 equivalent?
Answers
Answer:
No.
Step-by-step explanation:
2:1 and 19:10 are not equivalent.
Simply, because if you divide 9 by any number with the 10, it is not going to stay as a whole number. For example, 19 divided by 2 equals 9.5. 19 divided by 5 equals 3.8. So, no they are not equivalent.
Answer: No
Explanation: You can't divide 2 into 19 but you can with 1 and 10. If 19 were a 20, it'd be equivalent.
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 1 of 2: Suppose a sample of 1453 suspected criminals is drawn. Of these people, 377 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answers
Answer:
The proportion of people who were caught after being on the 10 Most Wanted list is 0.259.
Step-by-step explanation:
Proportion of people who were caught after being on the 10 Most Wanted list.
Number of people caught divided by the size of the sample.
In this question:
377 people caught.
1453 suspected criminals.
Then
\(p = \frac{377}{1453} = 0.259\)
The proportion of people who were caught after being on the 10 Most Wanted list is 0.259.
f(x)= a(x+p)² +q and g(x)= 0 3 3.1 x + p 1. The turning point of f is (1;4) and the asymptotes of g intersect at the turning point of f. Both graphs cut the y-axic at 3. 3.2 3.3 3.4 a 10 g +94 (1:4) Determine the equation of f Determine the equation of g Determine the coordinates of the x-intercept of g For which values of x will f(x) ≥ g(x)? [9]
Answers
Step-by-step explanation:
Let's solve the given questions step by step:
1. Determine the equation of f:
From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:
f(x) = a(x + p)^2 + q
Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:
4 = a(1 + p)^2 + q
This gives us one equation involving a, p, and q.
2. Determine the equation of g:
The equation of g is given as g(x) = 0.3x + p1.
3. Determine the coordinates of the x-intercept of g:
The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.
Setting g(x) = 0, we can solve for x:
0 = 0.3x + p1
-0.3x = p1
x = -p1/0.3
Therefore, the x-intercept of g is (-p1/0.3, 0).
4. For which values of x will f(x) ≥ g(x)?
To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.
f(x) = a(x + p)^2 + q
g(x) = 0.3x + p1
We need to find the values of x for which f(x) ≥ g(x):
a(x + p)^2 + q ≥ 0.3x + p1
Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.
To summarize:
We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).