The probability that they have dinner at the health food restaurant is 0.643.
To calculate the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere, we need to use conditional probability.
Let A be the event that the first one to arrive has dinner at the health-food restaurant, and let B be the event that the first one to arrive waits only 20 minutes before leaving to eat elsewhere.
We want to find P(A|B), the probability that A occurs given that B occurs.
We know that P(A) = 0.3, the probability that the first one to arrive has dinner at the health-food restaurant. We also know that P(B|A) = 0.6, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they have dinner at the health-food restaurant.
To calculate P(B), the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere, we need to use the law of total probability:
P(B) = P(B|A) x P(A) + P(B|A') x P(A')
where A' is the complement of A, i.e., the event that the first one to arrive does not have dinner at the health-food restaurant. We know that P(A') = 1 - P(A) = 1 - 0.3 = 0.7, and we are given that P(B|A') = 0.1, the probability that the first one to arrive waits only 20 minutes before leaving to eat elsewhere given that they do not have dinner at the health-food restaurant.
Therefore, we can calculate P(B) as:
P(B) = P(B|A) x P(A) + P(B|A') x P(A')
= 0.6 x 0.3 + 0.1 x 0.7
= 0.21 + 0.07
= 0.28
Finally, we can calculate P(A|B) using Bayes' theorem:
P(A|B) = P(B|A) x P(A) / P(B)
= 0.6 x 0.3 / 0.28
= 0.643
Therefore, the probability that the first one to arrive has dinner at the health-food restaurant given that they will wait only 20 minutes before leaving to eat elsewhere is approximately 0.643 or 64.3%.
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SST Grocery Store has a display of 12-ounce cans of soft drink in cases of 24. Each case
measures 16.00 inches by 10.75 inches by 5.00 inches. How many cubic inches are needed if 360
cases are on display?
OA 619,200 cubic inches
OB 309,600 cubic inches
OC 61,920 cubic inches
OD 123,840 cubic inches
Cases are on display OA 619,200 cubic inches.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To calculate the number of cubic inches needed for 360 cases of 12-ounce cans of soft drink, we need to multiply the number of cases (360) by the volume of each case. The volume of each case can be calculated by multiplying its length (16 inches), width (10.75 inches) and height (5 inches):
Volume = 16.00 inches x 10.75 inches x 5.00 inches = 828 cubic inches
Therefore, 360 cases of 12-ounce cans of soft drink require (360 x 828) = 619,200 cubic inches.
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Which equation is true?
O 6 ÷ 10 60
O 6 ÷ 100 = 60
O 6 ÷ 100.6
100
O 6100 = 0.6
of the value than the 6 in 25 division
Answer:sry
Step-by-step explanation:i need points
The equation which is true is 6 ÷ 100 = 0.06
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 6
Let the second number be q = 100
Substituting the values in the equation , we get
A = p/q
A = 6/100
The value of A = 0.06
Hence , the equation is A = 0.06 and is true
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Bookwork code: A99
Calculator
not allowed
The table below shows the masses of some oranges in a crate.
If one of the oranges is chosen at random from the crate, what is the probability
that it has a mass of more than 80 g?
Give your answer as a fraction in its simplest form.
The probability that the orange has a mass of more than 80g is (y/x).
What is a probability? Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that one of the oranges is chosen at random from the crate of oranges.
Assume that the total number of oranges are {x} and the oranges with a mass of greater than 80 are {y}. So, we can write -
P{E} = y/x
Therefore, the probability that the orange has a mass of more than 80g is (y/x).
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What is the slope of a line that contains the points (14,-42) (-48,24)
Enter the correct answer as m=
PLEASE SHOW WORK
The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).
How is slope determined?The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.
The slope's formula is as follows:
m = (y₂-y₁)/x₂-x₁)
In the formula, replace the point values as follows:
m = (24-(-42))/(-48-14)
Make the fraction simpler:
m = (24-(-42))/(-48-14)
m = 66/-62
m = 1.06
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true or false: the rule of thirds is the process of dividing an image into thirds, using two horizontal lines and two vertical lines, and positioning the most important elements inside the squares the lines create.
True. The rule of thirds is a photography and visual arts guideline that involves dividing an image into thirds using two horizontal lines and two vertical lines, and then placing the image's most important elements at the intersection points or along the lines.
This aids in the creation of a balanced and visually appealing composition. This results in nine rectangular areas of equal size, with four intersection points where the lines cross.
The rule of thirds principle suggests that the points of intersection or the lines themselves are ideal places to position the composition's most important elements. The resulting image is more visually balanced and pleasing to the eye as important elements are placed in these areas.
It is important that, however, that the rule of thirds is not a hard and fast rule, and that there were times when breaking it can result in more dynamic and interesting compositions. The rule of thirds is merely a tool for artists and photographers to use in order to create more effective and engaging images.
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Bryanna's younger sister is stacking her toy blocks on top of each other to build a tall tower. If each block is 2.4 inches long, how many blocks will she have stacked if the tower reaches a height of 4 fe
name the ray that is opposite FH.
Answer: Ray HF is opposite of Ray FH
Step-by-step explanation:
Help please Hurry
What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails? (1 point)
O a
О b
• c
O d
The experimental probability is closer to the theoretical probability for group Y than group X.
The experimental probability and the theoretical probability for group X is the same.
The experimental probability and the theoretical probability for group Y is the same.
The experimental probability is closer to the theoretical probability for group X than group Y.
The conclusion that can be drawn about the number of trials and the probability is A. The experimental probability is closer to the theoretical probability for group Y than X.
How to find the probability ?The theoretical probability for picking a heads or tails is 50 % as there are only two outcomes of heads and tails.
The experimental probability for heads is 53 % in Group Y and 47 % for tails. This is close enough to the 50 % theoretical probability.
For group X, the experimental probability for heads for Group x is :
= 33 / 50
= 66 %
This is too far from the theoretical probability.
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Noreen can walk 1/3 mile in 12 minutes. What is her average speed in miles per hour?
Answer:4 mph
Step-by-step explanation:
Solve for x: xm=-3x+y
Answer:
x = y/(m + 3)
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ xm = -3x + y
Then the value of x will be,
→ xm = -3x + y
→ xm + 3x = y
→ x(m) + x(3) = y
→ x(m + 3) = y
→ x = y/(m + 3)
Hence, value of x is y/(m + 3).
a school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. how many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
There are 6,720 possible ways to arrange the committee in a row, with students grouped by grade.
2 seniors * 5 sophomores * 3 freshman * 2 juniors = 60
60 possible arrangements for the 4 grade levels
60 * 6 (the number of ways to arrange 6 people) = 360
360 * 6 (the number of ways to arrange 6 people) = 2160
2160 * 6 (the number of ways to arrange 6 people) = 12,960
12,960 / 2 (because the order of the two grade levels can be reversed) = 6,720
6,720 possible arrangements for the school dance committee.
The school dance committee is made up of 3 freshman, 5 sophomores, 2 juniors, and 2 seniors. To find out how many ways there are to sit the committee in a row at a meeting if the students must sit together by grade, we first need to calculate the number of possible arrangements for each grade level. Since there are 2 seniors, 5 sophomores, 3 freshman, and 2 juniors, there are 60 possible arrangements for the 4 grade levels. We then multiply this by 6, since there are 6 ways to arrange 6 people. This gives us 360 possible arrangements for the first two grade levels. We then multiply this number by 6 again, since there are 6 ways to arrange 6 people. This gives us 2160 possible arrangements for the first three grade levels. We multiply this number by 6 one more time, since there are 6 ways to arrange 6 people. This gives us 12,960 possible arrangements for all four grade levels. However, since the order of the two grade levels can be reversed, we must divide this number by 2. This gives us a total of 6,720 possible arrangements for the school dance committee.
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What is the value of x?
first to answer brainliest
Answer:
99
Step-by-step explanation:
We can set up and solve this equation:
X + X - 50 = X + 49
X = 99
Reeta has spent 2/7 of her salary on car repair work. She has 15. 000 rupees left with her. What is her salary?
As per unitary method, Reeta's salary is 21,000 rupees.
The unitary method is a technique of solving problems by assuming a unit value and then finding out the required value in terms of that unit.
In this problem, we can assume Reeta's salary to be the unit value and then find out how much she spent on car repair work and how much money she has left using this unit value.
Let's assume Reeta's salary to be x rupees. Now, according to the problem, she has spent 2/7 of her salary on car repair work. So, the amount of money she spent on car repair work can be calculated as:
2/7 * x
Using the unitary method, we can now find out how much money she has left with her. We know that she has 15,000 rupees left. So, we can set up the following proportion:
2/7 * x = x - 15,000
Simplifying this equation, we get:
2x = 7(x - 15,000)
2x = 7x - 105,000
5x = 105,000
x = 21,000
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Please help!
Solve for x
The value of x is 8 by using the concept of similar shapes and angles.
Ratios of similar shapes and angles.When one triangle can be generated from the other by equally scaling, the two triangles are said to be similar. The ratio of any two pairs of comparable sides of similar shapes is said to be equal to the ratio of the sides of any two similar shapes. The similarity of the two shapes indicates that all related angle pairs and sides are equal and proportionate.
From the given information, equating the similar sides in order to determine the unknown side is expressed as follows;
24/(3x+6) = 32/40
Cancel the common factor (3) from the left-hand side
8/(x + 2) = 32/40
Cancel the common factor (8) from the right-hand side.
8/(x+2) = 4/5
Cross multiply
4x + 8 = 40
4x = 40 - 8
4x = 32
x = 32/4
x = 8
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2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
x degrees + 65 degrees = 180 degrees
x degrees = z degrees
y degrees = 65 degrees
x degrees= 65 degrees
x degrees + y degrees + z degrees = 115 degrees
The equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z. The solution has been obtained by using angles and line.
What are angles and line?
Straight lines with little depth or width are present. There are many different types of lines, including perpendicular, intersecting, transversal, etc. A figure called an angle is one in which two rays originate from the same point.
We are given that 2 lines intersect to form 4 angles which are 65°, x°, y°, z°.
1. x° + 65° = 180°
We know that angles on a straight line form a linear pair i.e. their sum is 180°. So, this statement is true.
2. x° = z°
We know that vertically opposite angles are equal. So, x° will be equal to z°. Thus, this statement is true.
3. y° = 65°
We know that vertically opposite angles are equal. So, y will be equal to 65°. Thus, this statement is true.
4. x° = 65°
This statement is false because these are the angles on a straight line which must add up to 180°.
5. x° + y° + z° = 115°
We know that angles in a circle add upto 360°. We know one angle as 65°. So, the remaining angles should add upto 295°. Thus, the statement is false.
Hence, the equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z.
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Question: Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles as shown in the figure. Clockwise, from top, the angles are: 65 degrees, x, y, z.
x degrees + 65 degrees = 180 degrees
x degrees = z degrees
y degrees = 65 degrees
x degrees = 65 degrees
x degrees + y degrees + z degrees = 115 degrees
a class of 18 students is holding elections for class president, vice-president and secretary. how many different ways can the officers be elected?
There are 4,608 different ways that the class can elect a president, vice president, and secretary.
To find the number of different ways that a class of 18 students can elect a president, vice president, and secretary, we will use the formula for permutations, which is given by -
nPk = n! / (n - k)!
where n is the total number of items and k is the number of items to be selected in a specific order.
In this case, we are given n = 18 students and k = 3 positions.
Thus, the number of different ways to elect a president, vice president, and secretary will be -
18P3 = 18! / (18 - 3)! = 18! / 15! = 18 x 17 x 16 = 4,608
Therefore, there are 4,608 different ways that the class can elect a president, vice president, and secretary.
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Bob buys a big bag of beans for $2. 37. Find x, the number of dollars he gave the cashier if he received $17. 63 in change
Bob gave the cashier $15.26 for the bag of beans.
To find the value of x, we need to subtract the cost of the beans from the total amount given to the cashier. The cost of the beans is $2.37, and the change received is $17.63.
Therefore, the value of x can be calculated as:
x = Total amount given to the cashier - Cost of the beans
x = $17.63 - $2.37
x = $15.26
A cashier is an employee who works in a retail or service industry, responsible for handling cash, credit card payments, and providing customer service. They are often the first and last point of contact for customers in a business. Cashiers use a cash register or computer system to record transactions, and must be able to accurately count money, make change, and reconcile the cash drawer at the end of their shift.
They also need to be proficient in using technology, such as scanners and card readers, to process transactions. In addition, cashiers must have good communication skills to interact with customers, answer questions, and resolve any issues. Other responsibilities may include stocking shelves, maintaining a clean and organized workspace, and ensuring that customers receive accurate pricing and promotional discounts.
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Radical form (5x) -1/5
Simplify the algebraic expression by using the Distributive Property first and then combining like terms.
Explain your answer or show your work.
12x-18y/6 +4y
The value of the equation is A = ( 6x - 9y ) / ( 3 + 2y )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 12x - 18y ) / ( 6 + 4y )
On simplifying the equation , we get
Taking the common factor as 6 in the numerator , we get
A = 6 ( 2x - 3y ) / ( 6 + 4y )
Taking the common factor as 2 in the denominator , we get
A = ( 6/2 ) ( 2x - 3y ) / ( 3 + 2y )
On further simplification , we get
A = 3 ( 2x - 3y ) / ( 3 + 2y )
A = ( 6x - 9y ) / ( 3 + 2y )
Hence , the equation is A = ( 6x - 9y ) / ( 3 + 2y )
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the ogive shown is based on u.s. census data and shows the average annual personal income per capita for each of the 50 states. the data are rounded to the nearest thousand dollars. ogive showing cumulative percentage of data webassign plot what percentage of the states have average per capita income more than 32.5 thousand dollars?
The estimated percentage of states with an average per capita income greater than 32.5 k is:we need to use the ogive (cumulative frequency curve) to determine the percentage of states with an average per capita income greater than 32.5k.
Assuming that the ogive is a continuous curve, we can estimate the percentage by finding the value on the horizontal axis corresponding to the 50% mark on the vertical axis, and then subtracting it from 100%. From the graph, we can see that the 50% mark corresponds to a value of around 30 k, which is between the values for Oklahoma and Pennsylvania. To get a more accurate estimate, we can use linear interpolation between these two data points.
Let's assume that the values for Oklahoma and Pennsylvania are
(x₁,y₁) = (25k,40%) and (x₂,y₂) = (35k,60%)
respectively. Then the equation of the straight line connecting these two points is:
(y-y₁) =(y₂-y₁) / (x₂-x₁) * (x-x₁)
Substituting in the values gives:
y - 40 = (0.6 - 0.4)/(35 - 25) * (x - 25)
y - 40 = 0.02(x - 25)
y = 0.02x - 0.5
To find the value of x that corresponds to the 50% mark, we can set y = 50% and solve for x:
50 = 0.02x - 0.5
0.02x = 50.5
x = 2525
So the estimated value for x is 25.25k. Therefore, the estimated percentage of states with an average per capita income greater than 32.5k is:
scss
Copy code
100% - 40% - (10% * (32.5 - 25.25)/(30 - 25))
= 50.5%
Therefore, we estimate that about 50.5% of the states have an average per capita income greater than 32.5k.
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George ate a meal that included a steak, a loaded baked potato, and coleslaw. The coleslaw had 50 fewer calories than the baked potato. The steak had twice as many calories as the baked potato. The total number of calories in the meal was 1550 calories. Write an equation that could be used to find the number of calories in the loaded baked potato (where P presents the calories in the loaded baked potato). Then, SOLVE the equation.
Answer:
400 calories
Step-by-step explanation:
Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.
So the equation for the total number of calories in the meal is:
P + (P-50) + 2P = 1550
4P = 1600
P = 400
Therefore, the loaded baked potato had 400 calories.
Answer:
Below
Step-by-step explanation:
c oleslaw = p - 50
p = potato
s = 2 p Summed these = 1550
p-50 + p + 2p = 1550 Gather 'like' terms
4p - 50 = 1550 add 50 to both sides of the equation
4p = 1600 divide both sides by 4
p = 400 calories
Zera has a credit limit of $2,000 on her credit card. Each month, she charges about $200 and makes a payment of $125. Estimate the number of months that Zera can continue this pattern until she reaches her limit?
Answer: 80/3 months
Step-by-step explanation:
Let x be the number of months until Zera reaches her limit.
Then on month x, her charges are 200x, and her payments are 125x.
This leaves her with 200x - 125x = 75x dollars owed.
we need to see when this equals 2000, so she hits her limit:
2000 = 75x
.: x = 2000/75 = 80/3
She can continue her pattern for 80/3 months, (≈26.666667)
15 pts pls help me TvT
Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Let M be the midpoint of AB, so EM is perpendicular to AB.
Since OF is a diameter of the circle, angle EOF is a right angle.
Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.
The corresponding sides are proportional:
EF / EA = EO / EM.
EM is half the length of AB, which is the diameter of the semicircle,
EO must be equal to the radius of the semicircle.
Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,
EF = EA.
Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF
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What is the minimum value for the function shown in the graph?
Enter your answer in the box
-2x
4
05-
-05-
-15
-
-25
→
35
2
in
-65-
Find the equation of the line that passes through (3,1) and is parallel to y=3−2x
Answer:
87654321
Step-by-step explanation:
The frequency of people compared to the number of monthly text messages sent and received by a class are shown in the histogram.
A histogram titled Daily Text Messages. The x-axis is labeled Number of Sent Texts and has intervals of 1 to 15, 16 to 30, 31 to 45, 46 to 60, 61 to 75, 76 to 90, and 91 to 105. The y-axis is labeled Frequency and starts at 0, with tick marks every 2 units up to 12. There is a shaded bar for 1 to 15 that stops at 1, for 31 to 45 that stops at 3, for 46 to 60 that stops at 4, for 61 to 75 that stops at 4, for 76 to 90 that stops at 5, and for 91 to 105 that stops at 8. There is no shaded bar for the 16 to 30 interval.
Which of the following best describes the shape of the data, and why?
The data is symmetric because the majority of students sent fewer than 45 text messages.
The data is symmetric because some students have phones and some do not.
The data is skewed because most text messages are replied to and cause the number to be at least twice what it was originally.
The data is bimodal because the popular number of text messages to send is between 91 and 105.
The data is symmetric because some students have phones and some do not. The correct option is B.
What does histogram mean?A histogram is a simplified representation of the distribution of numerical data. The phrase was first used by Karl Pearson at the outset.
Rectangles are used in a histogram, a type of visual representation of statistical data, to show how frequently data points occur throughout a range of subsequent numerical intervals of equal width.
In the most common sort of histogram, the independent variable and dependent variable are shown along the horizontal axis and the vertical axis, respectively.
The histogram is a frequently used graphing tool. It is used to summarize data that is measured on an interval scale, whether it be continuous or discontinuous.
It is widely applied to give the primary properties of the data distribution a practical way to be illustrated.
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Answer: B. The data is symmetric because some students have phones and some do not.
Step-by-step explanation:
4x^-3 y^-2 for x = 2 and y = 1? Pls Show work
Answer:
To substitute x = 2 and y = 1 into the expression 4x^-3 y^-2, we simply replace x with 2 and y with 1:
4 * (2)^-3 * (1)^-2 = 4 * (1/8) * (1) = 4/8 = 0.5
So the expression 4x^-3 y^-2 evaluated at x = 2 and y = 1 is equal to 0.5.
Step-by-step explanation:
Sarah's cell phone company charges her $35 a month for phone service plus $0.25 for
every text message. How many text messages does Sarah send in one month if her bill
was $99?
Answer:
256 text
Step-by-step explanation:
Let's call the number of text messages Sarah sends in a month as "x".
So, the total cost of the text messages is $0.25 * x.
The total cost of the phone service and text messages is $35 + $0.25 * x = $99.
So, $35 + $0.25 * x = $99.
Subtracting $35 from both sides, we have:$0.25 * x = $99 - $35 = $64
Dividing both sides by $0.25, we have:x = 256
So, Sarah sent 256 text messages in one month.
60 children choose their favourite fruit out of apples bananas and watermelon 30% chose apples and 25% chose bananas How many children chose watermelon
Answer:
27 children.
Step-by-step explanation:
Let's call the number of children who chose apples x. Then, the number of children who chose bananas is 0.25x. The number of children who chose watermelon is 60 - x - 0.25x = 60 - 1.25x.
Since 30% of the children chose apples, we know that:
0.30 * 60 = x
So, x = 18, which means 18 children chose apples.
And since 25% of the children chose bananas, we know that:
0.25 * 60 = 0.25x = 15
So, 15 children chose bananas.
Finally, the number of children who chose watermelon is:
60 - 18 - 15 = 27 children.
help its a test and i really dont know the answer lol
Answer:
1. not a function
Since x=5 produces y=9 and y=0, it can't be a function
2. it is a function because there is one value of y for every value of x
3. A circle is not a function. because it doesn't pass the vertical line test
4. I think is d but not sure has been a while since I have done these questions so sorry if I am wrong :)
Step-by-step explanation:
have a nice day and good luck
