We can solve the system of equations x + y = 44 and y = 10x by substitution. When we substitute y = 10x into the first equation, we find that x = 4. Substituting x = 4 into the equation y = 10x gives y = 40.
Explanation:To solve the system of equations by substitution, we first identify the two equations given: x + y = 44 and y = 10x. We can use the second equation as our substitution into the first equation. This gives us x + 10x = 44, which simplifies to 11x = 44. Solving for x, we divide both sides by 11 to get x = 4.
Next, we substitute x = 4 into the second initial equation, y = 10x, which gives us y = 10*4 = 40.
So, the solution to this system of equations is x = 4 and y = 40.
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A recent poll taken by the movie theatre industry shows that 28% of the population attends a movie in a theater at least once a month. A sample of 300 people shows that only 12% of people attends a movie in a theater at least once a month. To determine whether this sample supports the population proportion of 0.28, a simulation of 100 trials is run, each with a sample size of 200 and a point estimate of 0.12. The minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28. What is the margin of error of the population proportion using half the range?
Answer:
The margin of error for this population proportion using half the range = ±0.09
Step-by-step explanation:
Confidence Interval is basically an interval of range of values where the true proportion can be found with a certain level of confidence.
Margin of Error is the width of the confidence interval about the central proportion.
For this question, the minimum sample proportion from the simulation is 0.10, and the maximum sample proportion from the simulation is 0.28, hence, the confidence interval for the question is (0.10, 0.28).
The width of this confidence interval = (Upper limit of the interval) - (Lower limit of the interval) = 0.28 - 0.10 = 0.18.
Hence, the margin of error for this population proportion using half the range, is 0.18/2 = 0.09.
Written appropriately as ±0.09.
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I don’t know I need help fast
What can be concluded about a cylinder and a cone with the same height and radius measures? Check all that apply.
A. The cone has the greater volume.
B. The cone and cylinder have the same base area.
C. The volume of the cone is 1/3 the volume of the cylinder.
D. The cylinder can fit inside the cone.
E. The cone and cylinder have the same diameter.
The cone has a greater volume than the cylinder, and their base areas are equal, but the cone's volume is 1/3 of the cylinder's volume.
A. The cone has the greater volume.
B. The cone and cylinder have the same base area.
C. The volume of the cone is 1/3 the volume of the cylinder.
Adam is making a rectangular frame. The frame is 24.2 feet long and 16.25 feet wide.
The formula for the area of a rectangle is A=bh.
What is the area of the frame?
Enter your answer as a decimal in the box.
(__ ft2
–3x + 1 + 10x = x + 4
Y = 4x + 2 y = x + 5 on a graph
Twenty-five percent of 66 is ______
Which word is an antonym for the word thrive?
Jasper knew we was going to thrive in his new school
A) fail
B) learn
C) worry
D) be busy
The antonym for the word thrive would be A. Fail Hope this helps :)
The required antonym for the word thrive is fall. Option A is correct.
The word "thrive" means to prosper, succeed, or flourish. Therefore, the antonym for "thrive" would be a word that represents the opposite, such as "fail." When someone fails, they do not achieve success or prosper in their endeavors. In the given sentence, Jasper is confident that he will thrive in his new school, indicating that he expects to do well and succeed. Choosing the word "fail" as the antonym creates a clear contrast, as it represents the opposite outcome of not being able to thrive or achieve success.
Thus, the requried antonym for the word thrive is fall. Option A is correct.
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Which one is bigger 11 g or 10,800 mg
what is the equation of a circle with a center located at (4,-1) and a radius of 9
The equation for a circle with the given information would be (x - 4)^2 + (y + 1)^2 = 81.
This is because the base form of a circle is:
(x - x1)^2 + (y - y1)^2 = r^2
In which, x1 is the x coordinate of the center and y1 is the y coordinate of the center. r is the radius of the circle. So we plug in to those and simplify.
(x - 4)^2 + (y - -1)^2 = 9^2
(x - 4)^2 + (y + 1)^2 = 81
PLEASE HELP! EASY 10 POINTS
If the height of your he sailboat is 3 centimeters, what is the height in meters, of the actual boat
Factor by grouping Ab+4+a+4b
Answer:
Factor by grouping Ab+4+a+4b
[tex](b+1)(a+4)[/tex]
Step-by-step explanation:
Factor by grouping:
[tex]ab+4+a+4b[/tex] (1)
We have some common terms, the term a and the number 4: [tex]ab+a+4+4b\\a(b+1)+4(b+1)[/tex]:
Now, we have other common term, (b+1)
[tex]a(b+1)+4(b+1)\\(b+1)(a+4)[/tex]
What is the range of the function graphed below?
Option: C is the correct answer.
The range of the function which is graphed is:
C. All real numbers.
Step-by-step explanation:Domain of a function--
The domain of a function are the set of all the possible x values for which the function is defined.
Range of a function--
The range of a function are the set of all the possible values which are attained by a function in it's defined domain.
By looking at the graph of the given function we observe that the function is strictly increasing and it takes all the real values i.e. it takes all the values from (-∞,∞).
Hence, the answer is: Option: C
Describe the effect on the SURFACE AREA of multiplying the dimensions by 1/5.
A small submarine starts at –1,260 feet in relation to sea level. Then it descends 5 feet per minute for 12 minutes. What is the new position of the submarine in relation to sea level? –1,260 + (–5)(12) = –1,260 + 60 = –1,200
The new position of the submarine in relation to sea level is -1,200 feet.
Your calculation is correct. To find the new position of the submarine in relation to sea level after descending at a rate of 5 feet per minute for 12 minutes, you can use the formula:
New position = Initial position - (Rate of descent * Time)
In this case:
New position = -1,260 feet - (5 feet/minute * 12 minutes)
= -1,260 feet - 60 feet
= -1,200 feet
So, the new position of the submarine in relation to sea level is -1,200 feet.
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Which is the equation in slope intercept form for the line that passes through (-2,4) and is parallel to 2x + y = 4
what is the square root of 50 to the nearest tenth
shari has 1 1/2 gallons of orange juice. She wants to serve the orange juice equally among her 12 friends. How many ounces of juice will each friend receive
Part a) What do you know that will help you set up the equation to solve this problem?
Part b) Write the equation that allows you to solve for the height.
Part c) What is the height of the trapezoid (including units)
At a local used car lot, one out of every three cars is red. If the car lot had 54 cars on it, how many cars are red SHOW WORK PLZ
To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3. The calculation is: Number of red cars = 54 * (1/3) = 18 cars.
Explanation:To determine how many cars in the lot are red, we need to find one-third of the total number of cars. In this case, we are told that one out of every three cars is red, so the probability of a randomly chosen car being red is 1/3.
To calculate how many cars out of 54 are red, we can multiply the total number of cars by the probability of a car being red:
Number of red cars = 54 * (1/3) = 18 cars
Therefore, there are 18 cars that are red in the lot.
What is the smallest 9 digit number ni the form, aaa,aaa,aaa such that is divisible by 9??
Plz help!!
The smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9 is 111,111,111 because the sum of its digits is 9, which follows the divisibility rule for 9.
To find the smallest 9-digit number in the form aaa,aaa,aaa that is divisible by 9, we need to use the divisibility rule for 9. A number is divisible by 9 if the sum of its digits is also divisible by 9. Since we are looking for the smallest such number, we start with the smallest non-zero digit, which is 1.
The smallest 9-digit number where all digits are the same would be 111,111,111. Adding all the digits together, 1+1+1+1+1+1+1+1+1 equals 9, which is divisible by 9. Therefore, 111,111,111 is the smallest 9-digit number of the form aaa,aaa,aaa that is divisible by 9.
John's dog weighted 7 pounds when we got him. The dog's weight tripled each year for two years. How many ounces does John's dog now weigh?
Find the coordinate that divides the directed line segment from A(-2,-4) to B(8,1) in the ratio of 2 to 3
8182÷k=1363.6666667
A- 9
B-2
C-6
Find the radius of a circle that has an area of 100π ft2
you are about take an 8 question multiple choice test .each of these questions has 4 answers (A,B,C,D). how many ways can you answer the test if you leave an answer for each question
[tex] 4^8=65536 [/tex]
4^8 = 65536 answer is correct
Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches. π , √5 ,√8 ,2√5
(a)Without using your calculator, approximate the decimal equivalent of each number to the nearest tenth.
(b)Order the ribbon sizes from least to greatest. Use the original numbers given.
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find: Surface area of the pyramid
Answer:
The surface area of the pyramid is [tex]228\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the Pyramid is equal to
[tex]SA=B+LA[/tex]
where
B is the area of the base of the pyramid
LA is the lateral area of the pyramid
In this problem we have
[tex]B=36\ cm^{2}[/tex]
Find the lateral area LA
Remember that the lateral area is the area of its four lateral faces
so
Multiply the area of a lateral face by 4 (because is a regular quadrilateral)
[tex]LA=(4)(48)=192\ cm^{2}[/tex]
Find the surface area SA
substitute the values
[tex]SA=36+192=228\ cm^{2}[/tex]
The surface area of the pyramid is 228 square cm.
What is the regular quadrilateral pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2.
The surface area of the pyramid is;
[tex]\rm Surface \ area=B + LA[/tex]
Where; B is the area of the base of the pyramid, LA is the lateral area of the pyramid.
The area of a lateral face by 4 (because is a regular quadrilateral) is;
[tex]\rm LA=4(48)=192[/tex]
Substitute all the values in the formula;
[tex]\rm Surface \ area=B + LA\\\\\rm Surface \ area=36+192\\\\\rm Surface \ area=228[/tex]
Hence, the surface area of the pyramid is 228 square cm.
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can anyone help me please