Answer with Step-by-step explanation:
We have to determine the value of x on solving the system of linear equations:
2x-y = 11
x+3y = -5
2x-y=11
Adding y on both sides and subtracting by 11 on both sides, we get
y=2x-11
Putting value of y in x+3y = -5
x+3(2x-11) = -5
x+6x-33 = -5
7x -33 = -5
adding 33 on both sides, we get
7x= 28
Dividing by 7 on both sides, we get
x=4
Hence, Correct option is:
d. 4
Numbers 1-30 are written on cards and placed in a bag. One card is drawn. Find each probability.
a. drawing an even number or a 1.
b. drawing an even number or a multiple of 7.
Answer:
A. [tex]\frac{8}{15}[/tex] There are 15 even number and then there is 1 so 16 possibilities in total.
B. [tex]\frac{19}{30}[/tex] There are 15 even numbers and there are 4 multiples of 7 so 19 in total.
The question requires calculating the probability of drawing an even number or a 1, and an even number or a multiple of 7 from cards numbered 1 to 30. For the first case, the probability is 16/30 and for the second case, it's 17/30, considering mutually exclusive events and counting each outcome only once.
The question involves calculating the probability of drawing specific cards from a set of numbered cards. To find the probability of a particular outcome, we divide the number of ways that outcome can occur by the total number of possible outcomes.
Probability of drawing an even number or a 1
In the set of numbers 1-30, there are 15 even numbers (2, 4, 6, ..., 30) and one number 1. Since the events 'drawing an even number' and 'drawing a 1' are mutually exclusive, we add the probabilities. There are 16 favorable outcomes (15 even numbers + 1), out of a total of 30 possible outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
= 16/30
Probability of drawing an even number or a multiple of 7
Again, from numbers 1-30, we have 15 even numbers. The multiples of 7 up to 30 are 7, 14, 21, and 28. Of these, 14 and 28 are also even numbers and have already been counted. Therefore, we have 2 additional unique multiples of 7 (7 and 21) to consider. Thus, there are 17 favorable outcomes (15 even numbers + 2 unique multiples of 7).
Probability = 17/30
A Brainliest for the correct answer
if 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes, what fraction of the girls in class have neither blue or brown eyes? need help
The fraction of the girls in class have neither blue or brown eye is 1 /12.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We have been given that if 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes.
We are asked the fraction of the girls in class have neither blue or brown eyes.
Thus, we get;
1 - ( 2/3 + 1 /4 )
= 1 - ( 8 / 12 + 3 / 12 )
= 1 - 11 / 12
= 12 / 12 - 11 /12
= 1 /12
Therefore,
the fraction of the girls in class have neither blue or brown eye is 1 /12.
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The sum of two numbers is 154. if four timesfour times the smaller number is subtracted from the larger number, the result is 14. find the two numbers.
a parking lot can hold cars and small trucks. the scatter plot shows how many cars and trucks parked at the parking lot each day for a week. What is the daily average number of trucks at the lot that week? round to the bearest tenth if neccessary.
the answer to your question that is above is 3.3
Answer:
Daily average number of trucks at the lot that week are 3.3
Step-by-step explanation:
Given a parking lot which can hold cars and small trucks. The scatter plot show parking lot each day for a week in the given graph. We have to find the daily average number of trucks at the lot that week.
In order to find the daily average we have to add the no. of trucks park daily in a week the take the average dividing by 7.
No. of trucks park in a parking lot day-by-day in week are
2, 3, 3, 4, 6, 2, 3
We take the average as
[tex]\frac{2+3+3+4+6+2+3}{7}=\frac{23}{7}=3.28\sim3.3[/tex]
Hence, daily average number of trucks at the lot that week are 3.3
There are entrees available at a restaurant. from these, archie is to choose for his party. how many groups of entrees can he choose, assuming that the order of the entrees chosen does not matter?
Jeff Simmons sold 27 cars last month.This 36 fewer cars than he sold during the same time period one year ago
In 2.5 hours, Mr. Castelli drives a distance of 125 miles. He wants to know his average driving speed in meters per minute. Complete the table to find Mr. Castelli's average driving speed in meters per minute by using the units as a guide. [Note: 1 mile is approximately equal to 1.62 kilometers] miles per hourkilometers per hourmeters per hourmeters per minute
Which property is illustrated by the following equation?
- 10 + 8 = 8 + ( - 10 )
Marianna buys a snack combo for $2.50 if the sales tax rate is 8% what is the total price of the combo including tax
To find the total price of an item including sales tax, convert the tax rate to a decimal and multiply by the item's cost. The total cost for a $2.50 snack combo with an 8% tax is $2.70.
The question involves calculating the total price of an item including sales tax. To find the total cost including tax, we need to first figure out the amount of sales tax by converting the tax rate from a percent to a decimal. Then, we will multiply this decimal by the initial cost of the item to get the tax amount.
Here's a step-by-step explanation using the provided example:
Convert the sales tax rate from a percent to a decimal: 8% as a decimal is 0.08.Multiply the decimal tax rate by the cost of the item: 0.08 \\times $2.50 = $0.20.Add the tax to the initial cost to get the total price: $2.50 + $0.20 = $2.70.Therefore, the total price of the snack combo including an 8% sales tax is $2.70.
A high-speed catamaran operates between city and city
b. the catamaran can make the 157-mile trip in about 2 1/2 hours. find the catamaran speed for this trip.
mVUT =175, mVUJ=17x-3, and mJUT=17x+8. Find x
Final answer:
To find the value of x, the student needs to set up an equation based on the sum of angles in a triangle, which is given as 175 degrees. The algebraic expressions for the other angles are used to establish the equation, which is solved for x, resulting in x = 5.
Explanation:
The student is asking for help with a geometric problem where the sum of the measures of angles in a triangle is given along with two algebraic expressions for the other angles. The fact that the angles add up to 175 degrees helps us establish an equation: mVUT = mVUJ + mJUT. Substituting the given values, we get 175 = (17x-3) + (17x+8). Simplifying this, we get 175 = 34x + 5. Subtracting 5 from both sides, we get 170 = 34x. Dividing both sides by 34, we find that x = 170 / 34, which simplifies to x = 5. Therefore, the value of x is 5.
Which of the following statements best describes the relationship between a line and a point in a plane?
A doctor see each of her patients of 25 minutes durning a typical appointment how many patients can she see in a typical 7 1/2 hour day
The doctor can see 18 patients in 7 1/2 hour.
What is Unitary Method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
We have,
A doctor see each of her patients of 25 minutes.
Time = 7 1/2 hour = 15/2 hour = 15 x 30 = 450 minutes
So, In 7 1/2 hour the doctor can see
= (15/2) / 25
= 450/25
= 18 Patients.
Thus, the doctor can see 18 patients.
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Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by $2 from that of each adjacent book. The price of the book at the extreme right is equal to the price of the middle book plus a book adjacent to the middle one. Give an expression for the cost of the $n$th book in terms of $n$
The weekly demand and supply functions for Sportsman 5 × 7 tents are given by
p = −0.1x^2 − x + 33
p = 0.1x^2 + 2x + 13
respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity. Find the equilibrium price.
To find the equilibrium quantity and price for tents, we equated the demand -0.1x² - x + 33 with the supply 0.1x² + 2x + 13, solved the equation, and found the equilibrium quantity to be 500 units and the equilibrium price to be $25.50.
To find the equilibrium quantity and price for the Sportsman 5 x 7 tents, we need to set the demand function equal to the supply function.
Demand function: p = -0.1x² - x + 33
Supply function: p = 0.1x² + 2x + 13
Setting them equal to each other:
-0.1x² - x + 33 = 0.1x² + 2x + 13
Now, combine like terms to solve for x:
-0.1x² - 0.1x² - x - 2x + 33 - 13 = 0
-0.2x² - 3x + 20 = 0
To find the equilibrium quantity x, we solve this quadratic equation.
By dividing the entire equation by -0.2 to simplify:
x² + 15x - 100 = 0
The factored form of the equation is (x + 20)(x - 5) = 0, this yields two solutions for x: x = -20 (which we dismiss as a negative quantity that does not make sense in this context) and x = 5. Therefore, the equilibrium quantity is 5 (in hundreds of units).
To find the equilibrium price, substitute x = 5 into either the demand or supply function:
p = -0.1(5)² - (5) + 33
p = -2.5 - 5 + 33
p = 25.5
So the equilibrium price is $25.50.
What is the answer for 7-2n=n-14
Graph the image of the given triangle, reflected across the y-axis for 2.
Graph the image of the given triangle after the transformation that has the rule (x, y)→(x, −y) for 3.
1: up two, down four
For question 2 graph:
-7, -4
-9, -7
2, -9
For question 3 graph:
-5, 2
2, -7
4, 3
Question 5 just divide 360 / 13
You will get 27.69.. just round 27.7
When the blue trapezoid is translated to the green one, the new coordinates of the point (0, 0) will be
A) (-6, -2).
B) (-2, -8).
C) (-8, -6).
D) (-6, -8).
Answer: The correct option is (D) (-6, -8).
Step-by-step explanation: we are given to find the new co-ordinates of the point (0, 0) when blue trapezoid is translated to the green one in the figure.
As shown in the given figure, to translate blue trapezoid to green one,
the x-coordinate of each vertex of blue trapezoid is decreased by 6 units,
and
the y-coordinate of each vertex of blue trapezoid is decreased by 8 units.
So, the new co-ordinates of the point (0 0) becomes
(0, 0) ⇒ (0-6, 0-8) = (-6, -8).
Therefore, the new co-ordinates of the point (0 0) are (-6, -8).
Thus, (D) is the correct option.
In a lottery, a 4 digit number from 0000 to 9999 is randomly selected. Find the probability that the number selected begins with a 3 and ends in a 2 or 0.
Since the choices is from 0000 to 9999, therefore there are a total of 10,000 possibilities.
The possibilities that the number begins with a 3 and ends in a 2 or 0 is:
possibilities = 1 * 10 * 10 * 1 + 1 * 10 * 10 * 1 = 200
Therefore the probability is:
P = 200 / 10,000 = 0.02 = 2%
So there is a 2% probability.
Final answer:
The probability that a randomly selected 4-digit number begins with a 3 and ends with a 2 or 0 is 0.0200 or 2%.
Explanation:
To find the probability that a randomly selected 4-digit number begins with a 3 and ends in a 2 or 0, we can use the rule of product for independent events. Since the first digit must be 3, there is one choice for the first digit. For the second and third digits, they can be any number from 0 to 9, so we have 10 choices for each. The last digit can be either 2 or 0, which provides 2 possibilities.
Thus, the total number of favorable outcomes is 1 (for the first digit) × 10 (for the second digit) × 10 (for the third digit) × 2 (for the last digit) = 200 favorable outcomes. The total number of possible 4-digit numbers is 10000 (ranging from 0000 to 9999).
So the probability is calculated as the number of favorable outcomes divided by the number of total possible outcomes: Probability = 200 / 10000 = 0.02. After rounding to four decimal places, as instructed, the probability is 0.0200 or 2%.
Please help with all 3 questions and show all work thank you.
1) Find the area and perimeter of a rectangle with base 8 in. and height 15 in.
2) Find the distance between the points B(-2, 14) and C(3, 8) to the nearest tenth.
3) The midpoint of segment XY is (6, -3). The coordinates of one endpoint are X(-1,
Find the coordinates of endpoint Y.
If a polygon has eight sides then it is an octagon. True or False
Students received these scores: 70, 75, 80, 90, 95, 95, and 100. the score of 95 is what?
Add 5/12 + 69/10 enter you answer below as a fraction in lowest terms using the slash ( / ) as the fraction bar
Write a function rule for that table.
Defined by two lines or rays diverging from a common point.
A) arc
B) angle
C) parallel lines
D) perpendicular lines
Defined as bounded by two distinct end points that contain every point on the line between its end points.
A) circle
B) line segment
C) parallel lines
D) perpendicular lines
Answer:
1. Angle
2. Line Segment
Step-by-step explanation:
Two lines or rays diverging from a common point defines an 'angle', which is a figure forming from two rays starting from the same end-point.
Now, a figure bounded by two distinct end points which contain every point on the line between its end points defines a 'line segment'.
Hence, the answer are: Angle and Line Segment respectively.
The formula for the area of a triangle is a = 1 2 bh, in which b represents the length of the base and h represents the height. if a triangle has an area of 192 mm2 and the height is 16 mm, what is the measure of the base?
What percent of 52 is 12? Round your answer to the nearest tenth.
The percent of 52 which result in 12 would be 23%.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.
We need to find the percent of 52 which result in 12.
Let the unknown number is represneted by b.
It can be written as;
52% x b = 12
52/100 x b = 12
0.52 x b = 12
b = 12/0.52
b = 23%
Therefore, the percent of 52 which result in 12 would be 23%.
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The quotient Of triple a number and 9 is decreased by the sum of the number and 5? Expression please
2 times as many as 8 is 16
Answer:
or 16 is the result of doubling 8
Step-by-step explanation: