The solution to the system of equations -4x + 3y = -2 and y = x - 1 is x = -1 and y = -2.
What is the solution to the system of equations?Given the system of equations in the question:
-4x + 3y = -2
y = x - 1
Solve the system of equations by substituting the expression for y from the second equation into the first equation:
-4x + 3y = -2
Plug in y = x - 1:
-4x + 3( x - 1 ) = -2
Simplifying, we get:
-4x + 3x - 3 = -2
Solve for x:
-x = -2 + 3
-x = 1
x = -1
Now, plug x = -1 into equation 2 and solve for y:
y = x - 1
y = -1 - 1
y = -2
Therefore, the solution is x = -1 and y = -2.
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The volume of a cylinder is 1323pi cmcubed. The radius of the base of the cylinder is 7 cm. What is the height of the cylinder? The height of the cylinder is nothing cm. (Simplify your answer.)
The height of the cylinder with a given volume of 1323
cmcubed and a radius of 7 cm, divide the volume by the area of the base. The correct height is 27 cm.
The height of a cylinder given its volume and the radius of its base. To find the height, we'll use the formula for the volume of a cylinder, which is V = ()h, where V is the volume, is the radius and h is the height.
Step-by-step calculation:
The volume of the cylinder is given as 1323cmcubed.
The radius (r) of the base of the cylinder is given as 7 cm.
Plugging these values into the formula: 1323cm³= (7 cm)² imes h.
Simplify the equation: 1323cm³ = 49cm² imes h.
Divide both sides by 49cm² to find the height: h = 1323cm³ / 49cm².
The resulting height is therefore 27 cm, which is the solution to the problem.
The height of the cylinder is 27 cm.
AT a groyrey store salted peanuts in a shell cost 30 cents per ounce is 5$ enough money to buy 1 pound of peanuts if it is what amount of money will be leaft over
solve 4^x = 243 round to the nearest ten thousandth
Answer:
Value of x is 4.0
Step-by-step explanation:
Given:
[tex]4^x=243[/tex]
To find: Value of x.
We use the following rule,
[tex]log\,x^a=a.log\,x[/tex]
Consider,
[tex]4^x=243[/tex]
Take log on both sides.
[tex]log\,4^x=log\,243[/tex]
[tex]x\times log\,4=log\,243[/tex]
[tex]x=\frac{log\,243}{log\,4}[/tex]
[tex]x=\frac{2.386}{0.602}[/tex]
x = 3.962
x = 4.0 (nearest tenth)
Therefore, Value of x is 4.0
Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40
The box plot representing the data set 5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50 will have the values at 5 (minimum), 12.5 (Q1 - 25th percentile), 25 (median), 37.5 (Q3 - 75th percentile), and 50 (maximum). The data is arranged in ascending order, divided into quartiles, and the median of each quartile is found.
Explanation:To determine which box plot represents the data, we need to obtain the five-number summary of the data which includes the minimum, Q1 (25th percentile), median (Q2 - 50th percentile), Q3 (75th percentile), and the maximum.
Arrange the data in ascending order: 5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50Determine the minimum and maximum: Minimum is 5, Maximum is 50 Find the median (Q2): With 12 numbers, the median is the average of the 6th and 7th value, so (25+25)/2 = 25 Q1 is the median of the lower half of data (not including Q2): The median of 5, 5, 10, 15, 25, 25 is (10+15)/2 = 12.5 Q3 is the median of the upper half of data (not including Q2): The median of 30, 35, 40, 40, 45, 50 is (35+40)/2 = 37.5Therefore, the box plot that represents this data will have values at 5 (minimum), 12.5 (Q1), 25 (median), 37.5 (Q3), and 50 (maximum).
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Predict the vital capacity of a 20-year-old 5'5" female who weighs 120 pounds using the equation below: vc = (0.041) h - (0.018) a - 2.69
The predicted vital capacity of a 20-year-old, 5'5" female, using the provided equation, is approximately 3.97 liters.
Explanation:To predict the vital capacity of this 20-year-old 5'5" female who weighs 120 pounds using the given equation, we first need to convert the height from feet to centimeters since standard medical measurements are usually in metric units. The conversion is 1 foot = 30.48 cm. Therefore, 5'5" = 5*30.48 cm + 5*2.54 cm = 165.1 cm. Now we can substitute the height (h) and age (a) into the equation: vc = (0.041) h - (0.018) a - 2.69 = (0.041*165.1) - (0.018*20) - 2.69 ≈ 3.97 Liters. Therefore, the predicted vital capacity of this 20-year-old 5'5" female is approximately 3.97 liters.
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I really need help with this!!
Will constructed a figure on a graph using coordinates: M(2,3),N (8,3),AND
(5,2)
How long is the line segment M N in Will's graph?
If there is a very strong correlation between two variables, then the coefficient of correlation must be
Final answer:
If there is a very strong correlation between two variables, then the coefficient of correlation must be close to 1 or -1.
Explanation:
The correlation coefficient measures the strength and direction of the relationship between two variables. If there is a very strong correlation between two variables, then the coefficient of correlation must be close to 1 or -1. A correlation coefficient of 1 indicates a perfect positive correlation, meaning the variables increase and decrease together.
A correlation coefficient of -1 indicates a perfect negative correlation, where one variable increases while the other decreases.
Which property is used in the problem below?
2(x+4)=2x+8
the associative property
the commutative property
the distributive property
the additive identity property
the answer is The distributive property hoped I helped
A distribution reasonably well described by the normal curve has a mean of 60.00 with a standard deviation of 10.00 points. basing your prediction on the normal (z) curve, approximately what percent of the population would you predict will score within 10.00 points of the mean (between 50.00 and 70.00)?
Answer:
68%
Step-by-step explanation:
When the temperature is 68 F, the speed of the sound in air is approximately 343 meters per second. Approximately how many kilometers dose sound travel in five seconds?
Show all your work
Cancelling a dance class after several students hurt themselves is an example of which risk management strategy?
The scenario of cancelling a dance class due to student injuries is an example of the 'risk avoidance' strategy in risk management, which aims to avoid potential harm.
Explanation:Canceling a dance class due to multiple students getting injured is a risk management strategy known as risk avoidance. This strategy eliminates the risk by not participating in the activity that could lead to the risk. In this context, the dance class risks injury to the students. In such a scenario, the dance instructor or school chooses to avoid the risk (moral hazard) by cancelling the activity (i.e., the dance class), thereby protecting the students from further harm. This is a common approach employed in situations where the potential adverse outcomes of risk outweigh any potential benefits of the activity.
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The perimeter of a rectangle is 68cm the length is 4cm less than three time its width write a system of equation to find the dimension of the rectangle
BRAINLIEST please help?
A graph that displays bivariate data is called _________ ?
Positive Association
Strength of Association
Bivariate Data
Scatterplot
Two-Way Table
Two-Way Relative Frequency Table
No Association
Relative Frequency
Association
Negative Association
Answer:
Scatterplot
Step-by-step explanation:
Bivariate data means that the data is in two variables. For example, if the height of the students is plotted against their age, this data will be the bivariate data.
A bivariate data is represented using the graph known as Scatter Plot. One variable is plotted along x-axis and second variable is plotted against y-axis. After plotting the two variables we can observe the relation(association) between the two variable using the line of best-fit which models the relation between the two variables.
So, the answer to this question is Scatterplot.
A graph that displays bivariate data is called a Scatterplot. It represents two variables and can indicate Positive Association, Negative Association, or No Association, based on the scatter pattern.
Explanation:In the field of Statistics, a graph that displays bivariate data is referred to as a Scatterplot. Bivariate data represents two different variables, and a scatterplot is a graphical representation that uses dots to show the relationship, if any, between these two sets of data.
When looking at a scatterplot, the patterns of the dots can indicate associations. Positive Association is when as one variable increases, so does the other. Negative Association is when one variable decreases as the other increases. If the dots seem randomly scattered, it exhibits No Association.
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convert the following complex number into its polar representation 2+2i
Answer:
[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]
Step-by-step explanation:
The given complex number is:
[tex]2+2i[/tex]
Now, the polar from of the complex number [tex]z=a+ib[/tex] is [tex]z=r(cos{\theta}+isin{\theta})[/tex].
Finding the absolute value of r:
[tex]r=|z|={\sqrt{2^2+2^2}[/tex]
[tex]r=\sqrt8[/tex]
[tex]r=2\sqrt{2}[/tex]
Now, find the value of argument,
Using formula, [tex]{\theta}=tan^{-1}(\frac{b}{a})[/tex]
[tex]{\theta}=tan^{-1}({\frac{2}{2})[/tex]
[tex]{\theta}=tan^{-1}(1)[/tex]
[tex]{\theta}={\frac{\pi}{4}}[/tex]
Thus, the polar form is:
[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]
which is the required polar form.
Find the volume of the following solid figure. Use = 3.14. V = 4/3r3. A sphere has a radius of 5.7 inches. Volume (to the nearest tenth) = cubic inches.
Answer:
the answer is 775.3
Answer : The volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]
Step-by-step explanation :
To calculate the volume of sphere, we use the formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]
where,
r = radius of sphere
Given :
Radius of sphere = 5.7 inches
Now put all the given values in the above formula, we get:
[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{4}{3}\times 3.14\times (5.7inches)^3[/tex]
[tex]V=775.3\text{ inches}^3[/tex]
Thus, the volume of sphere will be, [tex]775.3\text{ inches}^3[/tex]
What is the volume of the pyramid?
https://static.k12.com/eli/bb/1458/3_84696/2_59509_5_84702/7a4a0ad2c3db47a5bb13d74edb27ae71bb21609c/media/8ee1c253d3ddab3cb61cec6450534e7b590f7487/mediaasset_1422977_1.jpg
3192 cm3 12,768 cm3 19,152 cm3 6384 cm3
The correct answer is 3192 cm3. I just did the test.
Patrick washes 21 cars per day. He is paid at a rate of $7.50 for every 3 cars he washes. How much is Patrick paid for each car he washes?
For each example below, determine whether a positive, negative, or no cause and effect relationship exists.
1) Smoking and cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day
3) The number of licks taken and the size of the Tootsie Pop
A positive relation between two things means that they are proportional to each other. One affects the other thing.
1) Smoking and cases of lung cancer. This is positive. As smoking affects lungs and can cause lung cancer. So, with increased smoking comes the increased risk of lung cancer thus increasing cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day - These two events are independent of each other. They are not based on each other. Hence, no relationship here.
A negative relation implies that if one thing increases, the other decreases.
3) The number of licks taken and the size of the Tootsie Pop. This is negative. As the number of licks increases, the size of the pop decreases.
If the probabilty of winning a lottery game is 7/100, does that mean that if you play the game 100 times, then you will win 7 times? explain.
Find the volume of a sphere with a great circle area of 201.06 square inches
Final answer:
To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.
Explanation:
To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.
First, let's solve the equation 4πr² = 201.06 for r:
4πr² = 201.06
r² = 201.06 / (4π)
r² ≈ 16.06
r ≈ √16.06 ≈ 4.01
Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:
V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches
Video games are on sale for 35% off if a particular game regularly sells for $99.50 what is the sales price
To find the sales price, multiply $99.50 by 35% to get the discount amount of $34.83, then subtract that from the original price, resulting in a sales price of $64.67.
Explanation:To calculate the sales price of a video game that has a discount of 35%, first determine the amount of the discount by multiplying the original price by the percentage of the discount. The original price of the video game is $99.50. Therefore, you calculate $99.50 × 0.35 to find the discount amount.
The discount amount is $34.825. Next, subtract the discount amount from the original price to find the sales price: $99.50 - $34.825 equals the sales price.
It's also important to round the discount to the nearest cent as currency, resulting in a discount of $34.83. Thus, the sale price of the video game will be $99.50 - $34.83, which equals $64.67.
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There are 7 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances?
Since one of the seven performers insists on being the first act, the remaining six performers can be arranged in '6!' (factorial of 6) ways. Therefore, there are 720 different ways to schedule the appearances of the variety show.
Explanation:This problem is a permutation problem. Since one performer insists on being the first act of the evening, this leaves 6 other acts that can be arranged in any order. In permutation, if you have 'n' different items, they can be arranged in 'n!' (n factorial) ways. The factorial of a number n, denoted as 'n!', is the product of all positive integers less than or equal to n.
In this case, 6 performers can be arranged in '6!' ways. The factorial of 6 (6!) is 6 * 5 * 4 * 3 * 2 * 1 = 720. Therefore, there are 720 different ways to schedule the appearances of the remaining 6 acts after the first performer has gone on.
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What does y=mx+b mean
Will give brainliest answer if right!! Thank you please help
Consumer reports stated that the sodium content, in milligrams, for a two tablespoon serving for 10 different brands is as follows: 120, 50, 120, 140, 150, 150, 110, 249, 171, 60 What is the mean of the data set? Type a numerical answer in the box. a0
Coach miller bought 5.15 pounds of ground beef to make burgers The cost of ground beef is $3.40 for each pound.What was the total cost for all of the ground beef?
The total cost of the ground beef bought by Coach Miller is calculated by multiplying the quantity (5.15 pounds) by the price per pound ($3.40). The total cost comes to $17.51.
Explanation:The subject of the question is a practical application of multiplication in Mathematics. Coach Miller bought 5.15 pounds of ground beef at a rate of $3.40 per pound. To calculate the total cost, you simply need to multiply the quantity (5.15 lbs) by the price per unit ($3.40/lb).
So the calculation will be: 5.15 (pounds) × $3.40 (cost per pound) = $17.51 So, the total cost for all of the ground beef would be $17.51.
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What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?
Solution:
A is the correct option.
Explanation:
We have been given that [tex](2r - 3s)^{12}[/tex]
The [tex]r^{th}[/tex] term of a binomial expansion [tex](a+b)^n[/tex] is given by
[tex]t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}[/tex]
For the given binomial expansion, we have
[tex]a=2r,b=-3s,r=2,n=12[/tex]
On plugging this value in the above formula, we have
[tex]t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s[/tex]
Therefore, the second term is -73728r^11 s
A is the correct option.
consider the enlargement of the pentagram
A man has 28 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 520 cents, how many dimes and how many quarters does he have?
To solve the problem, we can set up a system of equations. The solution is 12 dimes and 16 quarters.
Explanation:To solve this problem, we can set up a system of equations. Let's say the number of dimes is x and the number of quarters is y. We know that the total number of coins is 28, so we can write the equation:
x + y = 28
We also know that the value of the dimes is 10 cents and the value of the quarters is 25 cents. The total value of the change is 520 cents, so we can write the equation:
10x + 25y = 520
We can solve this system of equations using substitution or elimination. Let's use substitution:
From the first equation, we can express x in terms of y:
x = 28 - y
Substitute this value of x into the second equation:
10(28 - y) + 25y = 520
Simplify and solve for y:
280 - 10y + 25y = 520
15y = 240
y = 16
Now substitute this value of y back into the first equation to find x:
x + 16 = 28
x = 12
Therefore, the man has 12 dimes and 16 quarters.