Answer:
Step-by-step explanation:
Anne bought a piece of ribbon that is 7 over 9 m long. She used 3 over 18 m of it to tie a birthday present. She then used the remaining ribbon to form squares of sides 1 over 16 m. What was the maximum number of squares she could form?
Answer:
9 squares
Step-by-step explanation:
Anne bought a piece of ribbon = 7 over 9 m long = 63 m²
she used = 3 over 18 m = 54 m²
left = 9 m²
maximum number of squares she could form of 1 m = 9
Ali, Basti and Cian stand at three points A, B and C respectively. Suppose that the measure of angle ABC is 50 degrees , the measure of angle BAC is 60 degrees and Ali is exactly 150 ft away from Basti. Find the distance between Basti and Cian.
To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.
Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.
Using the law of sines, we can set up the following equation:
sin(50°) / 150 = sin(60°) / x
To solve for "x", we can rearrange the equation:
x = (150 * sin(60°)) / sin(50°)
Using a calculator, we can evaluate the expression:
x ≈ (150 * 0.866) / 0.766
x ≈ 168.4 ft
Therefore, the distance between Basti and Cian is approximately 168.4 ft.
Find the length of the line joining A (3,5) and B (1,3)
Answer:
2√2 units.
Step-by-step explanation:
To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points A and B into the formula, we have:
d = sqrt((1 - 3)^2 + (3 - 5)^2)
= sqrt((-2)^2 + (-2)^2)
= sqrt(4 + 4)
= sqrt(8)
= 2sqrt(2)
Therefore, the length of the line joining points A and B is 2√2 units.
Integral of 1/(x+cosx)
The integral is ln|x + cos(x)| + C, where C represents the constant of integration.
To find the integral of the function 1/(x + cos(x)), we can employ a combination of algebraic manipulation and the use of standard integration techniques. Here's the solution:
First, let's rewrite the integral in a slightly different form to simplify the process:
∫(1/(x + cos(x))) dx
We notice that the denominator, x + cos(x), is not amenable to direct integration. To overcome this, we employ a substitution. Let's set u = x + cos(x). Now, differentiate u with respect to x: du/dx = 1 - sin(x).
Rearranging this equation, we get dx = du/(1 - sin(x)).
Substituting these values, the integral becomes:
∫(1/(u(1 - sin(x)))) du
Next, we simplify further by factoring out 1/(1 - sin(x)) from the integral:
∫(1/(u(1 - sin(x)))) du = ∫(1/u) du = ln|u| + C
Replacing u with its original expression, we have:
ln|x + cos(x)| + C
Therefore, the answer to the integral is ln|x + cos(x)| + C, where C represents the constant of integration.
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A population has 75 observations. One class interval has a frequency of 15 observations. The relative frequency in this category is:
Answer:
The relative frequency in this category is 0.2
Step-by-step explanation:
The relative fraquency of a category is given by the number of observations in this category divided by the total number of observations.
In this question:
The category of interest has 15 observations.
In total, the population has 75 observations.
So the relative frequency is:
\(\frac{15}{75} = \frac{1}{5} = 0.2\)
A sandwich shop offers 4 types of bread, 5 meats, 7 cheeses, 4 condiment options, and you can pick veggies or no veggies. How many sandwiches are possible?
Answer:
Step-by-step explanation: OK so I don't know if I'm exactly right on this but what I would do is I would first read it more than 1 time and I would see that the sandwich shop offers 4 types of bread, that's 4 different types of bread. Then it says 5 meats, 7 cheeses, 4 condiment options, and you can pick veggies or no veggies. So what I did was I multiplied 4 by 5 and got 20, then I multiplied 7 by 4 and got 28, then I added 20 and 28 and got 48 sandwiches are possible. Then to make sure I was correct I did 4 times 5 times 7 times 4 by accident and I got 560. So I don't know which one is correct but I just thought that I could at least try to help you because even I have problems with problems like this one too. So I hope I helped you even a little bit.
Ruby, Joey and sully are baking cookies together. they need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. Ruby brought 2 cups of flour and 1/4 cup of butter, Joey brought 1 cup of flour and 1/2 cup of butter, sully brought 1 1/4 cups of flour and 3/4 cup of butter. if the students have plenty of other ingredients that they need. how many whole batches of a dozen cookies can they make.
Answer:
4
Step-by-step explanation:
Amounts needed for 1 batch of 1 dozen cookies:
3/4 cup flour
1/3 cup butter
It's easier to create a table with all amounts to find the total amount of flour and total amount of butter available.
Ruby Joey Sully Total
Flour 2 1 1 1/4 4 1/4
Butter 1/4 1/2 3/4 1 1/2
The table above shows the total amount of flour is 4 1/4 cups, and the total amount of butter is 1 1/2 cups.
Flour:
Amount available: 4 1/4 cups
Amount needed for 1 batch: 3/4 cup
(4 1/4 cups)/(3/4 cup) = 17/4 * 4/3 = 17/3 = 5 2/3
The amount of flour is enough for 5 2/3 batches.
This makes 5 full batches.
Butter:
Amount available: 1 1/2 cups
Amount needed for 1 batch: 1/3 cup
(1 1/2 cups)/(1/3 cup) = 3/2 * 3/1 = 9/2 = 4 1/2
The amount of flour is enough for 4 1/2 batches.
This makes 4 full batches.
The amount of flour is enough for 5 batches, but the amount of butter is enough for only 4 batches, so the greatest number of whole batches they can make is 4.
I need the answers for the table below.
The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively
Given the function :
tan(πx)/7xSubstitute the given value of x to obtain the corresponding f(x) values :
x = -0.6
f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358
x = -0.51
f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350
x = -0.501
f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967
x = -0.5
f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959
x = -0.4999
f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958
x = 0.499
f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951
x = -0.49
f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188
x = -0.4
f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125
Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
6⅓ ft²
Step-by-step explanation:
Area of the figure = area of a trapezoid
= ½(a + b)h
Where,
a = 11⅓ft = 34/3 ft
b = 34/3 + 15/2 = (68 + 45)/6 = 113/6 ft
h = 6 ft
Plug in the values
Area = ½(34/3 + 113/6)*6
= (34/3 + 113/6)*3
= (68 + 113)/3
= 181/3
= 6⅓ ft²
6) 1,1,3,8,19, 41
a) 60
b) 81
c) 90
d) 101
Analogias
The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.
To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:
1 1 3 8 19 41
0 2 5 11 22
Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.
Let's check if the differences between consecutive terms are square numbers:
2 = 1²
5 = 2² + 1²
11 = 3² + 2²
22 = 4² + 3²
Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:
41 + 57 = 98
Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.
Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.
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PLEASE HELP ME ON QUESTION ASAP!!
IF YOU HAVE A TOPIC LIST IN YOUR EXAMS AND IT SAYS AVERAGES AND THE RANGE ARE YOU GOING TO BE HAVING MEAN AND RANGE IN YOUR TEST OR MEAN, RANGE MODE, MIDPOINT BASICALLY ALL OF IT ? IF ANSWERS CORRECT ILL RATE YOU FIVE STARS, GIVE YOU A THANKS AND MAYBE EVEN BRAINLIEST (sorry for caps)
Answer:
Step-by-step explanation:
Typically yes you need to know
Mean
Median
Mode
and Range
Mean = average, add all numbers then divide by how many
Median = midpoint, middle number. Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers
Mode = numbers that occurs the most in the list of numbers
Range = This is the largest number minus the smallest number.
Question 6 of 10
What is the solution to the system of equations graphed below?
y = -2x + 4
y=x-5
Answer:
the solution to the system of equations is (x, y) = (3, -2).
Step-by-step explanation:
y = -2x + 4 (Equation 1)
y = x - 5 (Equation 2)
To solve for x, we can equate the right sides of the equations:
-2x + 4 = x - 5
Now, we can solve for x:
-2x - x = -5 - 4
-3x = -9
x = (-9) / (-3)
x = 3
Substituting the value of x back into Equation 2, we can solve for y:
y = 3 - 5
y = -2
A rectangular pyramid has a base that is 14 yards long and 14 yards wide. The pyramid's slant height is 12 yards. What is its surface area?
The surface area of the rectangular pyramid is approximately 387.6 square yards.
To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base is:
Area of base = length x width
Area of base = 14 yards x 14 yards
Area of base = 196 square yards
To find the area of the four triangular faces, we need to first find the height of each triangle using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the legs (the two shorter sides) is equal to the square of the hypotenuse (the longest side).
In this case, the hypotenuse is the slant height of the pyramid, which is 12 yards. The legs are half the length and width of the base, which are both 7 yards.
So we have:
h² + 7² = 12²
h² + 49 = 144
h² = 95
h = √95
Now we can find the area of each triangular face using the formula:
Area of triangle = 1/2 x base x height
The base of each triangle is 14 yards, and the height is √95 yards. So we have:
Area of triangle = 1/2 x 14 yards x √95 yards
Area of triangle = 7√95 square yards
There are four triangular faces, so the total area of the four triangular faces is:
Total area of triangular faces = 4 x 7√95 square yards
Total area of triangular faces = 28√95 square yards
Finally, we can find the total surface area by adding the area of the base and the area of the four triangular faces:
Total surface area = Area of base + Total area of triangular faces
Total surface area = 196 square yards + 28√95 square yards
Total surface area ≈ 387.6 square yards (rounded to one decimal place)
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32-39 Fill in >,< or = for each prob
3
15
4
-6
-8
-15
Fill in the inequality for each problem as follows 32 > -39, 3 < 15, 4 > -6 and -8 > -15
How to fill in the correct sign for each problem?Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
We have different inequality signs as follows:
Greater than (>)
Less than(<)
Less than or equal to (≤)
Greater than or equal to (≥)
Given:
32__-39
3__15
4__-6
-8__-15
For 32__-39:
Since 32 is greater than -39. we can write:
32 > -39
For 3__15:
Since 3 is less than 15. we can write:
3 < 15
For 4__-6:
Since 4 is greater than -6. we can write:
4 > -6
For -8__-15:
Since -8 is greater than -15. we can write:
-8 > -15
Thus, fill in for each problem accordingly
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Complete Question
Fill in >,< or = for each prob
32__-39
3__15
4__-6
-8__-15
Manny can paint the office by himself in 5 hours. Dave can do the same job in 8 hours. How long will it take them to do it working together?
Answer:
3 hrs 4.6 mins
Step-by-step explanation:
1/5 + 1/8 = 1/x
x = 40/13
If f(x) = (4784), what is 13)?
Answer:
f(x)=4784
f(13)= 0 because there is x value on the right hand side
4
(Graphing Proportional Relationships LC)
The table shows a proportional relationship.
x 12 8 24
y 3 26
Describe what the graph of the proportional relationship would look like.
O Aline passes through the point (0, 0) and continues through the point (3, 12).
O Aline passes through the point (0, 0) and continues through the point (2,8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Question 2(Multiple Choice Worth 2 points)
(Graphing Proportional Relationships MG)
The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)
For the first question:
The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.
The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.
Now, let's analyze the answer options:
A. A line passes through the point (0, 0) and continues through the point (3, 12).
This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.
B. A line passes through the point (0, 0) and continues through the point (2, 8).
This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).
C. A line passes through the point (0, 0) and continues through the point (6, 24).
This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.
D. A line passes through the point (0, 0) and continues through the point (12, 3).
This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).
Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.
For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?
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Quit smoking: In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine patch
Answer:
The p-value of the test is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.
Step-by-step explanation:
Test if less than half of HIV-positive smokers have used a nicotine patch:
At the null hypothesis, we test if the proportion is of at least half, that is:
\(H_0: p \geq 0.5\)
At the alternative hypothesis, we test if the proportion is below 0.5, that is:
\(H_1: p < 0.5\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
0.5 is tested at the null hypothesis:
This means that \(\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5\)
In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking.
This means that \(n = 444, X = \frac{202}{444} = 0.455\)
Value of the test statistic:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{0.455 - 0.5}{\frac{0.5}{\sqrt{444}}}\)
\(z = -1.9\)
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.455, which is the p-value of z = -1.9.
Looking at the z-table, z = -1.9 has a p-value of 0.0287.
The p-value is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.
if two rectangles have the same area what do u know abt the measures of their sides
Find a cubic polynomial that goes through points (4, – 22) and (3, - 26) and has tangents with slopes
respectively 11 and — 2 there. Check your work with a graphing utility.
f() =
Let f(x) = ax ³ + bx ² + cx + d.
The graph of f(x) passes through (4, -22) and (3, -26), which means f (4) = -22 and f (3) = -26, so that
64a + 16b + 4c + d = -22
27a + 9b + 3c + d = -26
When the question says it has tangents at some point, I take that to mean the slope of the tangent line at that point is the given number. So f ' (4) = 11 and f ' (3) = -2. We have
f '(x) = 3ax ²+ 2bx + c
so that
48a + 8b + c = 11
27a + 6b + c = -2
Solve the system:
• Eliminate d :
(64a + 16b + 4c + d) - (27a + 9b + 3c + d) = -22 - (-26)
→ 37a + 7b + c = 4
• Eliminate c :
(48a + 8b + c) - (27a + 6b + c) = 11 - (-2)
→ 21a + 2b = 13
(48a + 8b + c) - (37a + 7b + c) = 11 - 4
→ 11a + b = 7
• Eliminate b, then solve for a and the other variables:
(21a + 2b) - 2 (11a + b) = 13 - 2 (7)
-a = -1
a = 1 → b = -4 → c = -5 → d = -2
Then
f(x) = x ³ - 4x ² - 5x - 2
A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
The mass percentage of Cesium in the sample is 25.0 %. (Correct choice: C)
How to find the mass percentage of an element in a mixture
Herein we find the case of a mixture of two elements: Cesium, Iodine, whose Cesium mass percentage can be determined by the following formula:
%m = [mCs / (mCs + mI)] × 100 %
Where:
mCs - Mass of Cesium, in grams.mI - Mass of Iodine, in grams.If we know that mCs = 100 g and mI = 300 g, then the Cesium mass percentage is:
%m = [100 g / 400 g] × 100 %
%m = 25 %
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Evaluate the following expression.
2⁵ + (10 - 7)⁴ + 6
Answer:
the answer is 119 hope this helps
Step-by-step explanation:
Answer:
119
Step-by-step explanation:
2 to the power of 5 is 32 and 10 - 7 = 3 and 3 to the power of 4 is 81 and 81 + 32 is 113 and 113 + 6 = 119
Find the missing length in the image below
Let it be x
Using basic proportionality theorem
\(\\ \sf\longmapsto \dfrac{x}{10}=\dfrac{14}{7}\)
\(\\ \sf\longmapsto \dfrac{x}{10}=2\)
\(\\ \sf\longmapsto x=10(2)\)
\(\\ \sf\longmapsto x=20\)
What value equivalents to 5 7/8
Which function models the relationship shown by the line?
A
y = -3.3 + 2
B
y
= 12 + 2
с
y= -3x + 6
D
y=-3x + 6
10x+3-4x is equivalent to 6x+3
Answer:
True
X is equal to all real numbers
Step-by-step explanation:
10x -4x = 6x
6x + 3 = 6x + 3
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
0.7cm^2
Step-by-step explanation:
1/2(2+5)*1/5
1/2(7)*1/5
3.5*1/5
0.7
You are given the equation 12 = 3x + 4 with no solution set. Part A: Determine two values that make the equation false. Part B: Explain why your integer solutions are false. Show all work.
\(12=3x+4 \\ \\ 8=3x \\ \\ x=8/3\)
So, two integer values are 1 and 2 since they are not the solution to the equation.
A line is reflected. Which of these could be the result?
b bcause i knew it and i mean i have a 5.0 gpa
Which of the following is the most significant greenhouse gas due to its long lifespan in the environment?
A. Carbon dioxide
B. Argon dioxide
C. Oxygen
D. Nitrogen Oxide
Answer:
Carbon dioxide
Step-by-step explanation:
I think it’s carbon dioxide because, it is the most significant greenhouse gas. I also think it’s the carbon dioxide because the question is asking which one it is and I chose carbon dioxide.