The amount the family spend on items other than food and housing is PhP25000 over the time.
How to determine the amount spend?You should understand that budget involves the summary of income and expenditure of a person or individual over a period of time
If total expense is $50,000 and the spend 20% on food 30% on housing
Which make is 50% on both hosing and food leaving 50% on other expenses
Which makes half of the total budget
You have to work out 50% of 50000 to get
50/100* $50000 =PhP25000
This therefore means that the family spends PhP25,000 on items other than food and housing
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Complete question
The circle graph represents a family's monthly budget. If the total monthly budget is $50,000,
how much does the family spend on items other than food and housing?
Find the sum of the geometric sequence if the first term is -8, the common ratio is -3 and there are 10 terms
Answer:
Step-by-step explanation:
The sum of a geometric sequence can be found using the formula
Sn = a₁ (1 - rⁿ⁻¹)/ (1 - r)
where a₁ is the first term, r is the common ratio, and n is the number of terms.
In this case, a₁ = -8, r = -3, and n = 10.
Plugging these values into the formula, we get
Sn = -8 (1 - (-3)⁹⁻¹) / (1 - (-3))
Sn = -8 (1 + 3⁹) / 4
Sn = -8 (1 + 19683) / 4
Sn = -8 × 19684 / 4
Sn = -4920
predict how many sit ups each person can do in 12 seconds 1. janet does 3 sit ups in 2 seconds 2. paulo does 5 sit ups in 6 seconds 3. shah does 3 sit ups in 4 seconds
The predicted number of sit ups each person can do in 12 seconds, using a proportional relationship model are;
Janet 18 sit ups
Paulo 10 sit ups
Shah 9 sit ups
What is a proportional relationship?A proportional relationship is one in which the values of the output variable are a constant multiple of the values of the variables in the set of the input values.
The data for the number of sit ups each person can do with time are as follows;
1. Janet does 3 sit ups in 2 seconds
2. Paulo does 5 sit ups in 6 seconds
3. Shah does 3 sit ups in 4 seconds
The rates at which each person does sit ups, using a proportional relationship between the number of sit ups and time and the the constant of proportionality in the proportional relationship is the rate of sit ups per person which are;
Rate = (Number of sit ups)/(Time)
The rate at which Janet does sit ups = (3 sit ups)/(2 seconds), m = 1.5 sit ups/second
Rate at which Paulo does sit ups = (5 sit ups)/(6 seconds), m = (5/6) sit ups/second
Rate at which Shah does sit ups = (3 sit ups)/(4 seconds), m = (3/4) sit ups/second
The number of sit ups each person can do, n, in a specified time, t, can be found using the formula;
n = m × t
Where;
n = The number of sit ups
m = The rate at which the person does sit ups
t = The time duration
Therefore, the number of sit ups each person can do in 12 seconds are therefore;
The number of sit ups Janet can do in 12 seconds is; n = 1.5 × 12 = 18
Janet can do 18 sit ups in 12 seconds
Number of sit ups Paulo can do in 12 seconds is; n = (5/6) × 12 = 10
Paulo can do 10 sit ups in 12 seconds
Number of sit ups Shah can do in 12 seconds is; n = (3/4)×12 = 9
Shah can do 9 sit ups in 12 seconds
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a correlation is best expressed by . group of answer choices are built from research reviews describes the statistical relationship between two variables a collection of assertions predictions about the relationship between variables
A correlation is a statistical measure of the relationship between two variables and is expressed as a numerical value between -1 and 1.
A correlation is a measure of the relationship between two variables that is expressed as a numerical value between -1 and 1. To calculate a correlation, start by collecting data on the two variables. Then, calculate the covariance, which is the sum of the product of the differences between the two variables, divided by the number of data points. Finally, calculate the correlation by dividing the covariance by the product of the standard deviations of the two variables. The correlation can range from -1, which signifies a perfect negative correlation, to 1, which signifies a perfect positive correlation. A correlation of 0 indicates that there is no correlation between the two variables.
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the perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm. the length of side p is 4 cm and the lengths of q and r are equal
The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.
What is a triangle ?
triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
Given ,
The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.
the length of side p is 4 cm
Let the lengths of q and r are x and y respectively.
The perimeter of an isosceles triangle = (p+2q)
So,
p+2q = 9
4+2q = 9
2q = 9-4
2q = 5
q = 5/2
q = 2.5 cm
Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .
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a rectangular room is 14 feet by 20 feet. the ceiling is 8 feet high. a. find the length and width of the smaller wall. by (express your answer in feet) b. find the area of the smaller wall. (express your answer in square feet) c. find the area of the larger wall. (express your answer in square feet) d. find the total area of the four walls in the room. (express your answer in square feet) e. if a gallon of paint costs $36.50 and it covers 350 square feet on average, what is the cost of painting the room walls with two coats of paint?
Answer:
a. The length and width of the smaller wall are 14 feet and 8 feet, respectively.
b. The area of the smaller wall is 14 feet x 8 feet = 112 square feet.
c. The area of the larger wall is 20 feet x 8 feet = 160 square feet.
d. The total area of the four walls in the room is 112 square feet + 112 square feet + 160 square feet + 160 square feet = 544 square feet.
e. To find the cost of painting the room walls with two coats of paint, we need to know the total area of the walls, and the cost of one gallon of paint. We can use the information provided: a gallon of paint covers 350 square feet on average and the cost of one gallon of paint is $36.50.
We can divide the total area of the walls by the coverage of one gallon of paint, then multiply that by the cost of one gallon of paint.
544 square feet / 350 square feet/gallon * $36.50/gallon = $38.34
So the cost of painting the room walls with two coats of paint is $38.34.
Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work. Parallelogram with base of 20 feet, height of 15 feet, and triangular base of 4 feet.
According to the given information the area of the parallelogram is 300ft².
How do parallelograms function?A geometric shape having parallel sides in two dimensions is called a parallelogram. It is a type of four-sided polygon where each parallel set of sides is the same length (commonly referred to as a quadrilateral). The adjacent angles of such a parallelogram add up approximately 180 degrees.
Width of parallelogram = 20 feet.
Base of triangle = 4 feet.
Height of triangle = 15 feet.
To figure out the parallelogram's surface area:
To begin with, we would calculate the triangles' surface areas.
Note: The parallelogram supplied can be divided into two (2) triangles.
the triangle's surface area formula.
The formula: yields the triangle's area mathematically.
[tex]\begin{matrix}\mathrm{\ Area\ }=\frac{1}{2}\times\mathrm{\ base\ } \times\mathrm{\ height\ } \\\mathrm{\ Area\ }=\frac{1}{2}\times4\times15\\\mathrm{\ Area\ }=2\times15\\\mathrm{\ Area\ }=\mathbf{30}f^2\\\end{matrix}[/tex]
For the two (2) triangles:
[tex]Area =2\times30\\Area =\mathbf{60}ft^2[/tex]
For the rectangle left:
[tex]Length =15ft.\\Width =20-4=16ft.\\Area = length \times width\\Area =15\times16\\Area =\mathbf{240}ft^2[/tex]
Now, the area of the parallelogram:
Area of parallelogram =60+240
Area of parallelogram [tex]=\mathbf{300}{\rm ft}^2[/tex]
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Hello, I need the answers kind of fast can someone please help me<3
Question: Find the value of x.
Answer:
Step-by-step explanation:
Cross multiply
(2x + 6 + 2x)/(x² + 3x) = 1
(4x + 6) = x² + 3x
x² - x - 6 = 0
x² - 3x + 2x - 6 = 0
x(x - 3) + 2(x - 3) = 0
(x + 2)(x - 3) = 0
x = -2,3
10. what is the probability of selecting either a red or blue tile from one of the bags? show a mathematical equation to support your answer
The probability of selecting a red or a blue tile from one of the bags is 1. This can be calculated by adding the probability of selecting a red tile (6/10) and the probability of selecting a blue tile (4/10) together. The equation for this is P(Red or Blue) = P(Red) + P(Blue), which simplifies to 10/10, or 1.
The probability of selecting either a red or blue tile from one of the bags can be calculated using the following equation:
P(Red or Blue) = P(Red) + P(Blue)
where P(Red) is the probability of selecting a red tile and P(Blue) is the probability of selecting a blue tile.
In this case, P(Red) = 4/10 and P(Blue) = 6/10. Therefore, the probability of selecting either a red or blue tile from one of the bags is:
probability of selecting
P(Red or Blue) = 4/10 + 6/10
P(Red or Blue) = 10/10
P(Red or Blue) = 1
This means that there is a 100% chance of selecting either a red or blue tile from one of the bags.
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23g of silver is used to make a dice.
The dice is in the shape of a cube of side 1.3 cm.
Work out the density of silver.
Answer:
10.469g/cm^3
Step-by-step explanation:
The formula for density is density = mass/volume
The volume is 1.3x1.3x1.3 which is 2.197
The mass is 23g
23/2.197 is about 10.469
nikki has to travel a total of 351 miles. she travels the first 216 miles in 4 hours. it takes her 2.5 hours to travel the rest of the way. is she going faster, slower, or the same speed for the second part of her trip? (hint: how far did she travel on the second part of her trip?)
Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.
Nikki has to travel a total of 351 miles, and she travels the first 216 miles in 4 hours. The second part of her trip is the remainder of the distance she needs to travel, so we can calculate it by subtracting the distance she traveled in the first part from the total distance:
Second part of the trip = 351 miles - 216 miles = 135 miles
It takes Nikki 2.5 hours to travel the second part of her trip. To calculate her speed, we can divide the distance she traveled by the time it took her:
Speed = Distance / Time
Speed for the second part of the trip = 135 miles / 2.5 hours = 54 miles/hour
To compare her speed during the first and second parts of the trip, we can calculate the speed of Nikki during the first part of the trip:
Speed for the first part of the trip = 216 miles / 4 hours = 54 miles/hour
Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.
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Find the quadratic equation whoose root are as given (3+✓5) and (3 - ✓5)
Answer:
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.
The roots of a quadratic equation are the values of x that make the equation equal to zero.
Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:
ax^2 + bx + c = 0
(x - (3+√5))(x - (3-√5)) = 0
(x - 3 - √5)(x - 3 + √5) = 0
(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0
x^2 - 6x + 9 - 5 = 0
x^2 - 6x + 4 = 0
So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0
Step-by-step explanation:
Segment MN has endpoints on a sphere. If segment MN does not pass through the center of the sphere, the most specific name for segment MN is BLANK ( options : chord, diameter, radius)
If segment MN passes through the center, the most specific name for segment MN is BLANK ( options : chord, diameter, radius)
Segment MN lies on a plane that intersects the center of a sphere. The intersection between the sphere and the plane is the BLANK ( options : diameter, great circle, radius, tangent)
Please help me out! Math 3 Q4
The intersection between the sphere and the plane is the is diameter.
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius.
Given that, segment MN has endpoints on a sphere. If segment MN does not pass through the center of the sphere.
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
So, the most specific name for segment MN is chord.
Here, segment MN lies on a plane that intersects the center of a sphere.
A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
Therefore, the intersection between the sphere and the plane is the is diameter.
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Ris is a botanist who works for a garden that many tourists visit. the function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is the number of seeds she planted. the function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks. part a: write a composite function that represents how many flowers iris can expect to bloom over a certain number of weeks. (4 points) part b: what are the units of measurement for the composite function in part a? (2 points) part c: evaluate the composite function in part a for 30 weeks. (4 points)
The hybrid factor is f(w) Equals 50w + 25 according to the preceding statement. The hybrid value is measured in units of f (flowers) and w (weeks), etc. 30 weeks of Part A's synthesis function equal 1525.
What exactly are function and example?A task is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is just the input value, we would state that y is a mathematical function
Given that:
f(s) = 2s + 25
s(w) = 25w
The following combination function is used to determine how many flowers will blossom over the course of w weeks: f(w)
f(s) = 2s + 25
Replace s with s(w)
f(s(w)) = 2(s(w)) + 25
Substitute s(w) = 25w
f(s(w)) = 2(25w) + 25
f(s(w)) = 50w + 25
Hence,
f(w) = 50w + 25
Flowers are used as the units of measurement for f(w).
30 weeks of flowers translates to:
w = 30
So, we have:
f(30) = 50*30+25
f(30) = 1525
Thus, there will be 1525 blossoms throughout the course of 30 weeks.
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a local school board wants to estimate the difference in the proportion of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. they survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 38 households respond yes. they survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. the school board plans to construct a 90% confidence interval for the difference in proportions of households who would support starting the school year a week earlier. are the conditions for inference met?
The local school board should reject the null hypothesis since 0.000034 < 0.05.
There is sufficient evidence that the true proportion of households with school-aged children that would support starting the school year a week early is significantly different from the true proportion of households without school-aged children.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Thus, The local school board should reject the null hypothesis since 0.000034 < 0.05.
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What are the zeros of the function?
Answer: -1 and 3
Step-by-step explanation:
The zeros of a function are where the graph of the function intersects the [tex]x[/tex]-axis.
Answer: -1 and 3
Step-by-step explanation:
Finding the zeros of the function is the same as solving for the function, or what values of x make y equal 0. In this case, it is the x-intercepts, as shown by the graph. These values are -1 and 3, see attached.
algebra equation…. help help help help help help
The solution to the system of equations is (0, -5) or (4, 3).
What is the system of equations?
A system of equations is a set of two or more equations with the same variables. A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously.
To solve the system of equations, we'll substitute the second equation into the first:
x^2 + (2x - 5)^2 = 25
Expanding the square in the second equation:
x^2 + 4x^2 - 20x + 25 = 25
5x^2 - 20x = 0
5x(x - 4) = 0
So x = 0 or x = 4.
For x = 0:
y = 2x - 5 = -5
For x = 4:
y = 2x - 5 = 3
Hence, the solution to the system of equations is (0, -5) or (4, 3).
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If p varies directly as r square p =3.2 when r=4 find the value of p when r=6.5
Answer:
I hope this is right :)..
find the area of the parallelogram with vertices a(−3, 0), b(−1, 5), c(7, 4), and d(5, −1).
The parallelogram's surface area is 24 square units as a result.
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A quadrilateral is referred to as a parallelogram in geometry.
The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.
Here points are a(−3, 0), b(−1, 5), c(7, 4), and d(5, −1).
= 1/2 [-3 (4 + 1) - 1 (- 7 - 20)]
= 1/2 [-3 (5) - 1 (-27)]
= 1/2 [-15 + 27]
= 1/2 [12]
= 6 sq units
Area of parallelogram abcd = Area of triangle abc + Area of triangle acd
= 18 + 6
= 24 sq units.
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Find the equation of the line passing through the given point and parallel to the given line.
Answer in standard form: 2x+y = 3
Answer in slope intercept form: y = -2x+3
Both equations describe the same line. Select one of those formats to write to your teacher.
=======================================================
Reason:
The equation 2x+y = 9 solves to y = -2x+9; it is of the form y = mx+b
m = -2 = slopeb = 9 = y interceptThe parallel line will also have a slope of -2. Parallel lines have equal slopes, but different y intercepts.
The slope-intercept answer is of the form y = -2x+b
Plug in (x,y) = (-1,5) and solve for b.
y = -2x+b
5 = -2*(-1)+b
5 = 2+b
3 = b
b = 3
We go from y = -2x+b to y = -2x+3 which is in slope intercept form.
Adding 2x to both sides gets us 2x+y = 3 which is in standard form.
I need to find X AND Y HELPPP
The values of variables in the kite is - x = 35°, y = 12.5°. The angles measures of the kite are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.
What is a kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry. Another name for kites is deltoids.
The given angles of the kite are -
∠a = (3x+5)°
∠b = y°
∠c = (2y-20)°
∠d = (4x-30)°
According to the properties of kite -
The two angles are equal where the unequal sides meet.
So, ∠a = ∠d
(3x+5)° = (4x-30)°
3x - 4x = -30 - 5
-x = -35
x = 35°
Substituting to find the value of ∠a -
∠a = (3x+5)°
∠a = [3(35)+5]°
∠a = (105+5)°
∠a = 110°
Substituting to find the value of ∠d -
∠d = (4x-30)°
∠d = [4(35)-30]°
∠d = (140-30)°
∠d = 110°
According to the properties of the kite ∠ADC = 90°.
So, ∠c = 90°/2 as line BD is a bisector.
(2y-20)° = 90°/2
2(2y-20)° = 90°
(4y - 40)° = 90°
4y = 90° - 40°
4y = 50°
y = 12.5°
Substituting to find the value of ∠b -
∠b = y°
∠b = 12.5°
Substituting to find the value of ∠c -
∠c = (2y-20)°
∠c = [2(12.5)-20]°
∠c = (25-20)°
∠c = 5°
Therefore, the value of angles are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.
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Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them. x g(x) 0 2 5 4 10 6 The slope of f(x) is greater than the slope of g(x). The slope of f(x) is less than the slope of g(x). The slope of f(x) is equal to the slope of g(x). The slope of g(x) is undefined.
The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.
What is the slope of a line's equation?A line's slope or gradient is a number that defines both its direction and its steepness. The slope may be calculated using the following formula: slope = (y2-y1)/ (x2-x1). The coordinate points on the equation of line g(x) are (0, 2), (5, 4) and (10, 6) while the coordinate points on the equation of line f(x) are (3, 1) and (0, -1).
The slope of the line g(x) is now (4-2)/(5-0) =2/5.
The slope of a line f(x) is (-1)/. (0-3)
=2/3
The slope of a line f(x) exceeds the slope of a line g. (x). As a result, option A is the right response.
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a set of $16$ positive integers has mean, median, and unique mode all equal to $16.$ what is the largest possible value of one of the numbers in the set?
For a set of 16 positive integers to have a mean, median, and mode all equal to 16, the numbers in the set must all be equal to 16. Therefore, the largest possible value of one of the numbers in the set is 16.
The mean, median and mode of a set of numbers are all measures of the "typical" or "central" value of the set.
The mean is the sum of all the numbers divided by the number of elements in the set, the median is the middle value when a set of numbers is arranged in order of magnitude, and the mode is the number that appears most frequently in the set.
In this case, if all the 16 integers in the set are equal to 16, then the mean, median, and mode will all be 16 as well. Since the question states that the median, mode, and mean are all equal to 16, the only way for this to be true is if all the 16 integers in the set are equal to 16. So the largest possible value of one of the numbers in the set would be 16.
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Please help with this one
The vertex of the quadratic equation:
f(x) = 2x^2 - 8
is (0, -8)
How to find the vertex of the quadratic equation?For a general quadratic equation:
a*x^2 + b*x + c
The vertex is located at the x-value:
x = -b/2a
Here we have the quadratic equation:
f(x) = 2x^2 - 8
Then the values are:
a = 2
b = 0
c = -8
Then the vertex is at:
x = 0/2*2 = 0
To get the y-value of the vertex, we need to evaluate on x = 0.
f(0) = 2*0^2 - 8 = -8
So the vertex is (0, -8).
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several different types of cheese are produced in the shape of a wheel. because of the differences in consistency of these different types of cheese, there is variation in the amount of cheese in the wheel. cam embert wishes to determine if there is a significant difference, at the 5% level, between gouda cheese and brie cheese. she randomly samples 18 wheels of gouda and finds the mean is 1.3 pounds with a standard deviation of 0.31 pound and 13 wheels of brie and finds a mean of 0.95 pounds and a standard deviation of 0.26 pound. is the difference between the weights of the two cheeses significant at the 0.05 level of significa
There is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
What is standard deviations?Standard deviation is a measure of how spread out a set of numbers is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. In other words, it is a measure of how much the values in a dataset differ from the mean, or average, value. Standard deviation is a useful tool for understanding the distribution of data and can be used to identify outliers and compare data sets.
To answer this question, we must use a two-tailed hypothesis test, where the null hypothesis is that there is no difference between the two cheeses. The alternative hypothesis is that there is a significant difference between the two cheeses.
Using the sample data provided, we are able to calculate the test statistic, which in this case is 2.02. This can be compared to the critical value from the t-distribution table, which is 1.711 for a 5% level of significance and 31 degrees of freedom.
Since the test statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
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125 five pences in pounds?
Answer:
125 pounds = 2500 five pence
Answer:
Step-by-step explanation
£1.00=100p
125p=£1.25refer to exercise 75. how surprising would it be for more than 4 elk in the sample to survive to adulthood? calculate an appropriate probability to support your answer.
According to the given possibility the event of more than 4 elk surviving to adulthood is not surprising and the appropriate probability is 0.1402.
Here we have given that it be for more than 4 elk in the sample to survive to adulthood.
Then the probability is calculated by using the binomial probability,
And here we have to use the addition rule for mutually exclusive event, then we get,
=> P(AUB) = P(A or B) = P(A) + P(B)
At the possibility of k = 5 we have the binomial probability to be evaluated as follows:
=> P(X = 5) = 21 (0.44)⁵ (0.56)² ≈ 0.1086
At the possibility k = 6 then the binomial probability to be calculated as,
=> P(X = 6) = 7(0.44)⁶ (0.56)¹ ≈ 0.0284
Finally at the value of k = 7 then the binomial probability to be evaluated as,
=> P(X = 7) = 1 (0.44)⁷(0.56)° ≈ 0.0032
Therefore the two different numbers of successes are impossible on same simulation is by applying the addition rule for mutually exclusive events is calculated as,
=> P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
=> 0.1086 +0.0284 + 0.0032
=> 0.1402
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if y is divided by x, the quotient is p and the remainnder is r, what is the relations between x, y, p, r
If the number y is divided by x, the quotient is p and the remainder is r , then the relation between x,y,p,r is given by the expression [tex]y=xq+r[/tex] .
What is Euclid's Division Lemma ?
The Euclid's Division Lemma states that for two positive integers , a and b , then there exist unique integers q and r such that : [tex]a=bq+r,\; \; where \; 0\leq r < b[/tex] ;
here , the number y is divided by x , that means , the divisor is "x" , the dividend is "y" ,
the quotient is denoted by "q" ;
and the remainder is denoted by "r" ;
So , According to Division Lemma :
we can write ; the relation between x,y,p,r as ⇒ [tex]y=xq+r[/tex] , where [tex]where \; 0\leq r < x[/tex] .
Therefore , the relation between x,y,p,r is [tex]y=xq+r[/tex] .
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Consider the point (-4, -2). What will be the coordinates of the new point if we
-Reflect it across the line y=x
-Translate it 2 units to the right and 3 units up?
The coordinates of the new point after applying the given set of transformation is given by the ordered pair (0, -1).
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is given by this transformation rule:
(x, y) → (y, x)
Ordered pair A = (-4, -2) → Ordered pair A' = (-2, -4).
Next, we would apply a translation of 2 units to the right and 3 units up:
(x, y) → (x + 2, x + 3)
Ordered pair A' = (-2, -4) → (-2 + 2, -4 + 3) → Ordered pair A' = (0, -1).
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a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
Probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
a standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. two of the suits (heart suit and diamond suit, called `hearts' and `diamonds') are red, the other two (spade suit and club suit, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
A standard deck of 52 cards has 26 red cards ( of Hearts and Diamonds) and 26 black cards ( of Spades and Clubs).
Probability of drawing the first red card = 26/52
Probability of drawing the second red card = 25/51
So, probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
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what is the probability that their total completion time in the maze for all rats is between 6 and 8 minutes
The probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.
The probability that their total completion time in the maze for all rats is between 6 and 8 minutes can be calculated using the Binomial Distribution formula. The formula is P = (nCr) * (p^r) * (1-p)^(n-r), where n is the number of trials, r is the number of successes, and p is the probability of success.
In this case, n = 4 (4 rats), r = 2 (completion time between 6 and 8 minutes), and p = 0.5 (50% chance of success). Therefore, P = (4C2) * (0.5^2) * (1-0.5)^(4-2) = 0.375.
This means that the probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.
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