This means that the majority of adults, as represented by the 42% in the survey, would erase all of their personal information online if given the opportunity.
The null hypothesis (H0) states that there is no significant difference or relationship between the variables being tested. In this case, the null hypothesis would be: A minority of adults would not erase all of their personal information online if they could.
The alternative hypothesis (H1) states that there is a significant difference or relationship between the variables being tested. In this case, the alternative hypothesis would be: A minority of adults would erase all of their personal information online if they could.
To summarize:
Null Hypothesis (H0): A minority of adults would not erase all of their personal information online if they could.
Alternative Hypothesis (H1): A minority of adults would erase all of their personal information online if they could.
In this survey, 42% of the randomly selected adults indicated that they would erase all of their personal information online if they could. If the null hypothesis were true, we would expect the percentage to be significantly lower than 42%. Therefore, based on the survey results, we reject the null hypothesis and accept the alternative hypothesis
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OB.
6
5
O C. square
O D. parallelogram
4
0 1 2 3 4 5
-1
-2
The vertices of a quadrilateral on the coordinate plane are (2, 4). (-4, -2). (-2, 4), and (4, -2). What type of quadrilateral has these vertices?
O A. rectangle
trapezoid
X
The opposite sides of the quadrilateral are parallel and equal in length, we can conclude that it is a parallelogram. Otion D. parallelogram
The quadrilateral with the vertices (2, 4), (-4, -2), (-2, 4), and (4, -2) is a parallelogram.
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.
Therefore, if we can show that the opposite sides of this quadrilateral are parallel and equal in length, then we can conclude that it is a parallelogram.
In order to show that the opposite sides of the quadrilateral are parallel and equal in length, we need to find the slope of each side. Recall that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
[tex]$$m = \frac{y_2 - y_1}{x_2 - x_1}$$[/tex]
Let's begin by finding the slope of the line passing through (2, 4) and (-4, -2):
[tex]$$m = \frac{-2 - 4}{-4 - 2} = \frac{-6}{-6} = 1$$Next,[/tex]
Let's find the slope of the line passing through (-2, 4) and (4, -2):
[tex]$$m = \frac{-2 - 4}{4 - (-2)} = \frac{-6}{6} = -1$$[/tex]
Since the slopes of these two lines are equal in magnitude but opposite in sign, we know that they are parallel. Therefore, opposite sides of the quadrilateral are parallel. To show that opposite sides are equal in length, we can use the distance formula:
[tex]$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$[/tex]
The distance between (2, 4) and (-4, -2) is:
[tex]$$d = \sqrt{(-4 - 2)^2 + (-2 - 4)^2}
= \sqrt{36 + 36}
= \sqrt{72}$$[/tex]
The distance between (-2, 4) and (4, -2) is:
[tex]$$d = \sqrt{(4 - (-2))^2 + (-2 - 4)^2}
= \sqrt{36 + 36}
= \sqrt{72}$$[/tex]
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The dot plot shows the time trials of an experiment. Each number on the dot plot represents the amount of time, in seconds, it took to complete a trial. How many time trials were recorded during the experiment? Enter the answer in the box. time trials A number line ranging from 15 to 25 with two dots over 15, three dots over 17, two dots over 19, two dots over 20, one dot over 21, four dots over 23, one dot over 24, and three dots over 25.
There were 18 time trials recorded during the experiment.
To determine the number of time trials recorded during the experiment, we count the total number of dots on the dot plot.
According to the given information, we have:
- Two dots over 15
- Three dots over 17
- Two dots over 19
- Two dots over 20
- One dot over 21
- Four dots over 23
- One dot over 24
- Three dots over 25
By adding up these counts, we get:
2 + 3 + 2 + 2 + 1 + 4 + 1 + 3 = 18
Therefore, there were 18 time trials recorded during the experiment.
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Drag each tile to the correct box.
Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.
f(x) = x² + 3x
interval: [-2, 3]
f(x) = 3x - 8
interval: [4, 5]
>
f(x)=x²-2x
interval: [-3, 4]
Reset
V
f(x)=x²-5
interval: [-1, 1]
The given functions from Greatest to least value based on the average rate of change in the specified interval is as follows:f(x) = x² + 3x > f(x) = 3x - 8 > f(x) = x² - 2x > f(x) = x² - 5.
Given: Four functions and the interval for each function. We are supposed to arrange the given functions from greatest to least value based on the average rate of change in the specified interval. We need to evaluate the slope of each function for the given interval and then arrange the functions accordingly.
The slope of a line gives us the rate of change of the function. Slope of a line between two points is given by the following formula: Slope of the line, m = (y₂ - y₁)/(x₂ - x₁)We have been given 4 functions:
Function 1: f(x) = x² + 3xInterval: [-2, 3]Now let's evaluate the slope of the above function for the given interval:Let's take the two points: (-2, f(-2)) and (3, f(3))Substituting x = -2 in the function f(x), we get:f(-2) = (-2)² + 3(-2) = -4Substituting x = 3 in the function f(x), we get:f(3) = 3² + 3(3) = 12
Now we have two points: (-2, -4) and (3, 12)Slope of the line, m = (y₂ - y₁)/(x₂ - x₁) = (12 - (-4))/(3 - (-2)) = 16/5Therefore, the slope of the function 1 in the given interval is 16/5.Function 2: f(x) = 3x - 8Interval: [4, 5]Now let's evaluate the slope of the above function for the given interval:
Let's take the two points: (4, f(4)) and (5, f(5)
)Substituting x = 4 in the function f(x), we get:f(4) = 3(4) - 8 = 4Substituting x = 5 in the function f(x), we get:f(5) = 3(5) - 8 = 7Now we have two points: (4, 4) and (5, 7)
Slope of the line, m = (y₂ - y₁)/(x₂ - x₁) = (7 - 4)/(5 - 4) = 3
Therefore, the slope of the function 2 in the given interval is 3.
Function 3: f(x) = x² - 2xInterval: [-3, 4]Now let's evaluate the slope of the above function for the given interval:
Let's take the two points: (-3, f(-3)) and (4, f(4))Substituting x = -3 in the function f(x), we get:f(-3) = (-3)² - 2(-3) = 15Substituting x = 4 in the function f(x), we get:f(4) = 4² - 2(4) = 8
Now we have two points: (-3, 15) and (4, 8)Slope of the line, m = (y₂ - y₁)/(x₂ - x₁) = (8 - 15)/(4 - (-3)) = -7/7 = -1Therefore, the slope of the function 3 in the given interval is -1.Function 4: f(x) = x² - 5Interval: [-1, 1]Now let's evaluate the slope of the above function for the given interval:
Let's take the two points: (-1, f(-1)) and (1, f(1))
Substituting x = -1 in the function f(x), we get:f(-1) = (-1)² - 5 = -4Substituting x = 1 in the function f(x), we get:f(1) = 1² - 5 = -4Now we have two points: (-1, -4) and (1, -4)Slope of the line, m = (y₂ - y₁)/(x₂ - x₁) = (-4 - (-4))/(1 - (-1)) = 0Therefore, the slope of the function 4 in the given interval is 0.
Arranging the functions from greatest to least value based on the slope of each function:
Function 1: f(x) = x² + 3x
Interval: [-2, 3]
Slope = 16/5
Function 2: f(x) = 3x - 8
Interval: [4, 5]
Slope = 3
Function 3:
f(x) = x² - 2x
Interval: [-3, 4]
Slope = -1
Function 4: f(x) = x² - 5
Interval: [-1, 1]
Slope = 0
Therefore, the given functions from greatest to least value based on the average rate of change in the specified interval is as follows:f(x) = x² + 3x > f(x) = 3x - 8 > f(x) = x² - 2x > f(x) = x² - 5.
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Use the IDEAL model of problem-solving to solve the task below showing clearly all necessary actions taken in each of the stages: A teenager's age is increased by 2 gives a perfect square. His age decreased by 10 gives the square root of that perfect square. He is 5 years older than the sister. How old is his sister?
Answer:
I - Identify the problem:
The problem is to find the age of the teenager's sister.
D - Define the problem:
Let's define the age of the teenager as "x" and the age of his sister as "y". The problem states that:
- x + 2 = a perfect square
- √(x + 2 - 10) = a perfect square
- x = y + 5
We need to find the value of "y".
E - Explore possible solutions:
First, let's solve the equation x + 2 = a perfect square. We can try different values of perfect squares until we find one that is 2 more than a multiple of 10:
- 4 + 2 = 6 (not a multiple of 10)
- 9 + 2 = 11 (not a multiple of 10)
- 16 + 2 = 18 (not a multiple of 10)
- 25 + 2 = 27 (not a multiple of 10)
- 36 + 2 = 38 (not a multiple of 10)
- 49 + 2 = 51 (not a multiple of 10)
- 64 + 2 = 66 (not a multiple of 10)
- 81 + 2 = 83 (not a multiple of 10)
- 100 + 2 = 102 (a multiple of 10)
So, x = 100.
Now, we can solve the equation √(x + 2 - 10) = a perfect square by substituting x = 100:
√(100 + 2 - 10) = √92 = 2√23
So, the perfect square is 2√23.
Now, we can use the third equation to find y:
x = y + 5
100 = y + 5
y = 95
A - Act on the chosen solution:
The age of the teenager's sister is 95.
L - Look back and evaluate:
We can check if the solution is correct by verifying that:
- x + 2 = 102 (a perfect square)
- √(x + 2 - 10) = 2√23 (a perfect square)
- x = y + 5 = 100 (the teenager's age)
- y = 95 (the sister's age)
Therefore, the solution is correct.
In the year 2013, John's boat had a value of $16,000. When he bought the boat in 2007 he paid $29,000. If the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
Answer: 7.47%.
Step-by-step explanation: To find the annual rate of change in the boat's value, we need to calculate the depreciation rate. The difference between the boat's value in 2007 ($29,000) and 2013 ($16,000) is $13,000. This represents the total depreciation over 6 years, giving an average depreciation of $2,166.67 per year. To find the percentage rate of change, we need to divide this by the original value and multiply by 100: $2,166.67/$29,000 x 100 = 7.47%. Therefore, the annual rate of change in the boat's value was approximately 7.47%.
I NEED HELP WITH THIS QUESTION!
The equation of the quadratic function is x² - 8x + 55/4
What is quadratic function?A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
A quadratic function is represented by;
f(x) = ax² + bx + c.
The quadratic function of a graph can be obtained from the zeros of the graph.
The zeros or root of the graph here are 5/2 and 11/2
if a and b are the roots
a+b = 2.5 +5.5 = 8
ab = 55/4
The equation is derived by
x² -(a+b)x + (ab)
= x² - 8x + 55/4
f(x) = 4x² - 8x + 55
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To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.
The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.
Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:
1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.
2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.
3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.
4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.
5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.
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PLEASE HELP ME ASAP ILL GIVE BRAINLIEST
The absolute value function that matches the graph is given as follows:
y = -|x + 1| + 1.
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
In which a is the leading coefficient.
The coordinates of the vertex in this problem are given as follows:
(-1, 1).
Hence:
y = a|x + 1| + 1.
The function is reflected over the x-axis with a slope of -1, hence the leading coefficient a is given as follows:
a = -1.
Thus the function is:
y = -|x + 1| + 1.
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I keep getting this wrong. Please help!
==================================================
Explanation:
I'll use the template
y = Asin(kx)+C
where,
|A| = amplitudek = used to find the periodC = midlineThe highest and lowest we can go on the curve is y = 7 and y = -5 respectively. This is a distance of 7 - (-5) = 7 + 5 = 12 units. Half of this vertical distance is the amplitude, so we get 12/2 = 6 as the amplitude. This leads to either A = 6 or A = -6. I'll go with A = 6 for now.
One maximum point is at (-7.5, 7) and its adjacent neighbor max point is (2.5, 7)
This is a horizontal gap of 2.5 - (-7.5) = 2.5+7.5 = 10 units. This is the period of the sine curve because the graph repeats itself every 10 horizontal units along the x axis.
T = period = 10
k = 2pi/T
k = 2pi/10
k = pi/5
The last thing to determine is the value of C. To find this value, find the midpoint of the min and max.
C = (ymin + ymax)/2
C = (-5+7)/2
C = 2/2
C = 1
----------
To recap, we found these values
A = 6k = pi/5C = 1So we have
y = Asin(kx)+C
update to
y = 6sin( (pi/5)x ) + 1
which is the same as writing [tex]\text{y} = 6\sin\left(\frac{\pi}{5}\text{x}\right)+1[/tex]
You can use a graphing tool such as Desmos or GeoGebra to confirm the answer is correct. Refer to the diagram below.
if Y is 2/5 of X, work out the ratio X:Y
Answer:
Step-by-step explanation:
y = 2/5 of x
y = 2x/5
5y = 2x
5:2
If f(x)=1/x, which equation describes the graphed function
y = f(x+2) +1 is the equation which describes the graphed function.
What is translation?Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape.
When F crosses the x-axis when it is poitive. +1 indicates a 1 unit down translation.
So, the equation will be y = f(x+2) + 1. y = f(x+2) -1 is the equation which describes the graphed function.
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What is the slope of the line represented by the equation y = –y equals negative StartFraction 2 Over 3 EndFraction minus 5 x. – 5x?
–5
–negative StartFraction 2 Over 3 EndFraction.
StartFraction 2 Over 3 EndFraction.
5
The slope of the line represented by the equation y = –2/3(x) - 5 is -2/3.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, a linear equation that models it is given by;
y = mx + b
y = –2/3(x) - 5
By comparison with the slope-intercept form, we have the following:
Slope, m = -2/3.
y-intercept or vertical intercept = (0, -5).
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Complete Question:
What is the slope of the line represented by the equation y = –2/3(x) - 5.
The graph of the function f(x) = (x-4)(x + 1) is shown
below.
Which statement about the function is true?
The correct statement about the function in this problem is given as follows:
The function is decreasing for all real values of x where x < 1.5.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph of the function, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.Hence the intervals of this problem are given as follows:
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answer ASAP I will brainlist
The system has exactly one solution. The solution is (13, 8)
All three countries had the same population of 8,000 in 2023
How to calculate the solution to the system of equations
From the question, we have the following parameters that can be used in our computation:
Country A: -x + 20y = 147
Country B: -x + 10y = 67
Country C: y = 8
So, we have
-x + 20y = 147
-x + 10y = 67
y = 8
Substitute 8 for y in the first and second equations
So, we have
-x + 20 * 8 = 147
-x + 10 * 8 = 67
Evaluate the products
-x + 160 = 147
-x + 80 = 67
So, we have
x = 160 - 147
x = 80 - 67
Evaluate
x = 13
x = 13
Hence, the solution to the system of equations is (13, 8)
The interpretation is that all three countries have the same population in a particular year
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help please. the question(s) are below in pictures.
The graph of the function and the quadratic functions indicates that we get;
First part;
(A) f(x) = -x² + 8 has a maximum value greater than the graph's function
Second part;
(A) The minimum value for both functions is 2
What is a quadratic function?A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where, a ≠ 0, and a, b, and c are numbers.
First Part;
The x-value at the maximum point of a quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)
The maximum point on the graph is; (0, 3)
The maximum value of the function, f(x) = -x² + 8, can be found from the equation for the x-value of the maximum point of a quadratic function as follows;
x = -0/(2×(-1) = 0
Therefore, the y-coordinate of the maximum point is; x = f(0) = -0² + 8 = 8
The maximum point of f(x) = -x² + 8 is therefore; (0, 8)
The correct option is therefore; (A) f(x) = -x² + 8 has a maximum value greater than the graph's function
Second part;
The minimum value of the function f(x) = x² + 2·x + 3, can be found using the relation for finding the x-value of the minimum or maximum values, which are critical values of a quadratic equation as follows;
The x-value at the minimum point is; x = -2/(2×1) = -1
The y-value at the minimum point is therefore; f(-1) = (-1)² + 2×(-1) + 3 = 2
The coordinates of the minimum point of the function, f(x) = x² + 2·x + 3, therefore is; (-1, 2).
The correct option is therefore, option A
A. The minimum value of both function is 2
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Takeru is planning to paint the walls of his bedroom, which is shaped like a rectangular prism. The bedroom has 1 window and 2 doors. The dimensions of the window and doors are shown in the table. If 1 gallon of paint covers about 150 square feet, how many gallons of paint are needed to cover the walls of a room that is 20ft long, 15ft wide, and 8ft high?
The number of gallons is 4.1
How to determine the areaFrom the information given, we have that;
1 gallon of paint is equivalent to 150 square feet
Since we have 2 doors, the area of a rectangular prism is
Area = lw
Area =20(15)
Area = 300 (2) = 600 ft²
For the window, we have;
Area = 3(5) = 15
The total area of the wall is;
Total area = 615 ft²
Then, if;
1 gallon = 150 square feet
x = 615 square feet
cross multiply
x = 4. 1 gallons
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A training field is formed by joining a rectangle and two semicircles as shown below. The rectangle is 89 m long and 67 m wide. What is the length of a training track running around the field?
Answer: 155
Step-by-step explanation:
(a) Copy and complete the table of values for y= 2x²-x-4 for-3 ≤x≤3.
X
y
-3
17
-2 -1
0
(c) Use the graph to find the:
-4
1
2 3
(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis,
draw the graph of y=2x²-x-4 for -3 ≤x≤3.
(i) roots of the equation 2x2-x-4 = 0;
(ii) values of x for which y increases as x increases,
(iii) minimum point of y.
The minimum point of y is (0, -4).
X | y
-3 | 17
-2 | -4
-1 | -7
0 | -4
1 | -1
2 | 4
3 | 11
Using these values, we can proceed with the requested tasks:
(b) To draw the graph of y = 2x² - x - 4, we will use a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis. Here's how the graph looks:
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
----+---+---+---+---+---+---+--
-3 -2 -1 0 1 2 3
The graph will have a parabolic shape, opening upward.
(i) To find the roots of the equation 2x² - x - 4 = 0, we need to find the x-values where the graph intersects the x-axis. From the graph, we can see that the roots are approximately x = -2 and x = 1. These are the values where the graph crosses the x-axis.
(ii) To find the values of x for which y increases as x increases, we need to identify the intervals on the x-axis where the graph is moving upwards. From the graph, we can see that as x increases from -3 to -2, and from 1 to 3, y is increasing. Therefore, the values of x for which y increases as x increases are x ∈ (-3, -2) and x ∈ (1, 3).
(iii) To find the minimum point of y, we need to locate the vertex of the parabolic graph. From the graph, we can see that the vertex is approximately at x = 0, y = -4. Therefore, the minimum point of y is (0, -4).
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please help!!! if i don’t get this test right then i fail and i really can’t ! i’ll mark brainlyist ! pleasee
anyone
Answer:
208 cubic units
Step-by-step explanation:
The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:
The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.
Now, let’s calculate the volume of the rectangular prism:
The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160
Now, add up the volumes of the rectangular and triangular prisms:
160 + 48 = 208 cubic units
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.
To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.
The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.
Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.
To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:
£72 / 5 = £14.40
Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.
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2 pt =____mL
a) 240
b) 480
c) 1,340
d) 960
Answer:
946ml
Step-by-step explanation:
multiply the value in pt by 473.176473
So, 2 pt × 473.176473 = 946 ml
Hope this helps
Mark me as Brainliest
2 Pints is equal to 946.35295 Milliliters and a pint is a unit of volume equal to two cups of liquid, or one-eighth of a gallon.
Some facts about pint i.e., pt :
It is a unit of measurement for volume or volume in both the Imperial and US systems of measurement.A pint is a unit of measurement used to measure the volume or capacity of liquids. It is also used in the US system of measurement and the British Imperial system of measurement. Use the "pt" symbol to represent a pint. Half pint refers to half pint capacity. This equals 8 fluid ounces or 1 cup. In other words, measuring half a pint tells you how many pints are in your cup.To learn more about pint, refer to:
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The question is -
Convert 2 Pints to Milliliters. How big is 2 pints? What is 2 pints in milliliters?
solution to the inequality
Answer:
x ≥ - 9
Step-by-step explanation:
[tex]\frac{x}{-3}[/tex] ≤ 3
multiply both sides by - 3 to clear the fraction, reversing the symbol as a result of multiplying by a negative quantity.
x ≥ - 9
Answer:
Step-by-step explanation:
x/-3 < 3
x < -1
Write your answer using decimals, if necessary.
square centimeters
The area of the figure in this problem is given as follows:
131 cm².
How to obtain the area of the figure?The figure is a composite figure, hence the total area of the figure is given by the sum of the areas of each part that compose the figure.
The figure is composed as follows:
Right triangle of sides 16 cm and 7 cm.Rectangle of dimensions 4 cm and 11 cm.Rectangle of dimensions 4 cm and 1 cm.Rectangle of dimensions 3 cm and 9 cm.Hence the area of the figure is given as follows:
A = 0.5 x 16 x 7 + 4 x 11 + 4 x 1 + 3 x 9
A = 131 cm².
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McDonald’s has two specials for chicken nuggets going on for the month of February. They are selling 5 chicken nuggets for $2.25 or 20 chicken nuggets for $10.00. Which special is the better buy? Justify your answer.
The first special of 5 chicken Nuggets for $2.25 is the better buy in terms of cost per nugget. Customers would pay less per nugget with this option compared to the second special of 20 chicken nuggets for $10.00.
To determine which chicken nugget special is the better buy, we need to compare the cost per nugget for each option.
For the first special, we can calculate the cost per nugget by dividing the total cost ($2.25) by the number of nuggets (5):
Cost per nugget = $2.25 / 5 = $0.45
For the second special, we can calculate the cost per nugget by dividing the total cost ($10.00) by the number of nuggets (20):
Cost per nugget = $10.00 / 20 = $0.50
Based on the calculations, the first special (5 chicken nuggets for $2.25) has a lower cost per nugget ($0.45) compared to the second special (20 chicken nuggets for $10.00) which has a cost per nugget of $0.50.
Therefore, the first special of 5 chicken nuggets for $2.25 is the better buy in terms of cost per nugget. Customers would pay less per nugget with this option compared to the second special of 20 chicken nuggets for $10.00.
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A line segment is part of a line and is bounded by two endpoints.
In geometry, a line segment is defined as a part of a line that is bounded by two distinct endpoints. It is usually represented by a straight line with a defined length. A line segment is an essential element of geometry, and it is used to measure distance, solve problems, and create shapes.
A line segment is different from a line in that it has a defined length and endpoints, while a line has no endpoints and extends infinitely in both directions. In other words, a line is a set of points that extends infinitely in both directions, while a line segment has a finite length. A line segment can be named using its endpoints, which are the two points that define its boundaries. For instance, if AB is a line segment, A and B are its endpoints.A line segment can be measured using a ruler or other measuring devices. It is measured by finding the distance between its endpoints in a straight line. The length of a line segment is always positive, and it can be represented in different units, such as inches, centimeters, or meters.In geometry, line segments are used to create different shapes, such as triangles, rectangles, and polygons. They are also used to measure angles and distances in geometric figures. For example, if you want to find the area of a rectangle, you can use line segments to measure its length and width.Overall, line segments are essential elements of geometry that are used to measure distance, create shapes, and solve problems.For such more question on segment
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8) Given:U is the midpoint of SR and QT
Prove: QS=TR
Answer:
U is the midpoint of SR and QT (given).
QU is congruent to UT (definition of midpoint).
SU is congruent to UR (definition of midpoint).
Angle QUS is congruent to angle TUR (vertical angles are congruent).
∆QUS is congruent to ∆TUR (SAS).
QS is congruent to TR (CPCTC).
The diameters of apples from a certain farm follow normal distribution with mean 4 inches and standard deviation 0.4 inch.
Apples can be size-sorted by being made to roll over mesh screens. First the apples are rolled over a screen with mesh size
3.5 inches. This separates out all the apples with diameters less than 3.5 inches. Second, the remaining apples are rolled
over a screen with mesh size 4.3 inches. Find the proportion of apples with diameters greater than 4.3 inches.
• Round your answer to four decimal places.
The proportion of apples with diameters greater than 4.3 inches is given as follows:
0.2266.
How to obtain the proportion?The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 4, \sigma = 0.4[/tex]
The z-score of a measure X is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The proportion is one subtracted by the p-value of Z when X = 4.3, hence it is given as follows:
Z = (4.3 - 4)/0.4
Z = 0.75
Z = 0.75 has a p-value of 0.7734.
1 - 0.7734 = 0.2266.
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A spinner with 10 equal sized slices has 4 yellow slices, 3 red, and 3 blue slices. Kala spun the dial 1000 times and got the following results.
Kala spun the spinner 1000 times and got the following results:
- Yellow: 400 times
- Red: 300 times
- Blue: 300 times
1. Calculate the amount of sales tax:
- The item costs $350 before tax.
- The sales tax rate is 14%.
- To find the sales tax amount, multiply the cost of the item by the tax rate:
Sales tax = $350 * 0.14 = $49.
2. Determine the total cost of the item including tax:
- Add the sales tax amount to the original cost of the item:
Total cost = $350 + $49 = $399.
3. Analyze the spinner results:
- The spinner has 10 equal-sized slices.
- There are 4 yellow slices, 3 red slices, and 3 blue slices.
- Kala spun the dial 1000 times.
4. Calculate the frequency of each color:
- Yellow: Kala got 400 yellow results out of 1000 spins.
- Red: Kala got 300 red results out of 1000 spins.
- Blue: Kala got 300 blue results out of 1000 spins.
5. Calculate the probability of landing on each color:
- Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.
- Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.
- Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.
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Insert Parentheses to make the equality true. 1+2x3+4x5=29
Answer:
(1+2)x3+4x5
Step-by-step explanation:
Answer:
((1+2)x3) + (4x5) = 29
Step-by-step explanation:
Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,
we get,
((1+2)x3) + (4x5) = 29
This is true because,
(3x3) + (4x5) = 29
(9) + (20) = 29
29 = 29
use true diagram below and the given information to choose the conclusion that is true.
the last 2 options are: m m m
Using the diagram attached in the problem, the conclusion that can be true is
angle B > angle E
How to arrive at the conclusionInformation given in the problem, let us know that
side AC is greater than side CDside AB is equal to side EDSide BC is equal to side CEWith this information and knowing that a longer side will make a larger angle we can say that
angle B > angle E, since side AC is greater than side CD
side AC is the opposite to angle B (which is greater) and side CD is the opposite to angle E
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