To cover a 2000 sq ft wall, we will need 5 gallons of paint.
what is area?
Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.
To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:
Conversion factor = 1 gallon / (400 sq ft/gallon)
So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:
Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons
Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.
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On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 2 kg weighs 4 N. Calculate the mass of another object that weights 18 N.
Answer:
Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:
w = k * m
where k is the constant of proportionality.
To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:
4 N = k * 2 kg
Solving for k, we get:
k = 4 N / 2 kg = 2 N/kg
Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:
m = w / k
Substituting w = 18 N and k = 2 N/kg, we get:
m = 18 N / 2 N/kg = 9 kg
Therefore, the mass of the object that weighs 18 N is 9 kg.
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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Use the slip and y-intercept to identify the equation of this line
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
Jeff surveyed all the students at his school and reported the fraction of students who liked each flavor of sherbet.
Six-sevenths liked cherry.
One-ninth liked grape.
Three-fifths liked orange.
Four-elevenths liked strawberry.
Which list has the flavors in order from least liked to most liked?
A. grape, strawberry, orange, cherry
B. grape, orange, strawberry, cherry
C. orange, cherry, grape, strawberry
D. cherry, grape, orange. strawberry
HELLO PLEASE HELP!
i only need help with the second problem which is:
5. For 0≤x≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
please and thanks!
From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: The formula is (Number/Variable, Math Operator, Number/Variable).
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.
For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing. However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.
For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.
Therefore, g is increasing on the interval [-3, 6).
To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
g(x) = ∫_{-2}^{x} f(t) dt
On the interval [-3, 0), f(t) = 3, so we have
g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt
Simplifying the integrals, we get:
g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)²
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The expression of g in terms of x is increases on the interval [-3, 6) and for 0 ≤ x ≤ 6 is g(x) = [tex]6 - \frac{1}{2(x-2)^2}[/tex].
What is a mathematical expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.
For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing.
However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.
For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.
Therefore, g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
[tex]g(x) = \int{-2}^{x} f(t) dt[/tex]
On the interval [-3, 0), f(t) = 3, so we have
[tex]g(x) = \int_{-2}^{0} 3 dt + \int_{0}^{x} (-t + 3) dt[/tex]
Simplifying the integrals, we get:
[tex]g(x) = 6 - \frac{1}{2(x-2)^2}[/tex], for 0 ≤ x ≤ 6
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)².
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The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?
According to the question the magnitude of the resulting force is 5.83.
What is magnitude?Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.
The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.
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7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.
Check the picture below.
[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]
Make sure your calculator is in Degree mode.
Answer:
4.31 in5.52 inStep-by-step explanation:
You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.
Trig functionsThe mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:
Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse×Sin
Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse×Cos
ApplicationThe given triangle will have opposite and adjacent sides of ...
opposite = (7 in)sin(38°) ≈ 4.31 in
adjacent = (7 in)cos(38°) = 5.52 in
The leg lengths of the triangle are 4.31 inches and 5.52 inches.
The sum of a number and three is no more than eight
Answer:5
Step-by-step explanation: hope this helps
Use the following number line to choose the correct statement. R x P > S S > Q × R Q × R > S
Answer:
Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.
So, the first statement "R x P > S" is not true, because S is to the right of both R and P.
The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.
The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:
Q x R > S
Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?
Answer:
The amount of persons who have heard in 30mins would be:
45 persons
At a train station in the morning rush hour, the Westbound train arrives every 9 minutes, and the Eastbound train arrives every 15 minutes. If both trains were just in the station, after how many minutes will both trains again be in the station at the same time?
Step-by-step explanation:
Find the LCM of 9 and 15
West 9 18 27 36 45
East 15 30 45 In 45 minutes
Write a fraction that has a value greater than 3/8 using 3 as the numerator
Answer: 3/4
Step-by-step explanation:
Any number as the denominator of the fraction that is less than 8 (the denominator) will give you a fraction greater than 3/8.
Another different answer could be 3/5 or 3/6.
A fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
The given fraction is 3/8.
Here, 3/8 = 0.375
We need write the fraction which is greater than 3/8 using 3 as the numerator is 3/6 = 0.5
Therefore, a fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.
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Help pleasee
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
What is exponential decay:Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.
Exponential decay is modeled by the following formula:
[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]
where A is the amount after time t, A₀ is the initial amount,
T is the half-life, and t is the time elapsed
Here we have
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:
[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]
Simplifying, we get:
2 = A₀ × (1/2)⁴
2 = A₀ × (1/16)
A₀ = 2 × 16
A₀ = 32 mg
So the initial mass of the sample was 32 mg.
For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:
[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]
A ≈ 0.198 mg
Therefore,
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
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An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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A principal of $1500 is invested at 8.5% interest, compounded annually.
How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
The investment will be worth approximately $4468 after 14 years.
What is annual interest rate?Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.
According to question:The following equation can be used to determine the future value of an investment using compound interest:
FV = P * (r/n + 1)(n*t)
Where:
FV is the investment's future value.
The principal is P. (initial investment)
The annual interest rate is represented by r,
The number of times the interest is compounded annually by n (expressed as a decimal).
t is the time (in years)
In this case:
P = $1500
r = 8.5% = 0.085
n = 1 (compounded annually)
t = 14
With these values entered into the formula, we obtain:
FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]
= $4467.56
Therefore, the investment will be worth approximately $4468 after 14 years.
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How do I solve this problem?
The measure of angle CFE is determined as 29⁰.
What is the measure of angle CFE?The measure of angle CFE is calculated by applying the following formula.
The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠CFE = ¹/₂( arc angle CE )
arc CE = 360 - 302 (sum of angles in a circle)
arc CE = 58⁰
m∠CFE = ¹/₂ x 58
m∠CFE = 29⁰
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How to find the circumference of a circle
Answer: To find the circumference of a circle, there are 2 formulas.
Step-by-step explanation:
The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!
The owner of a sports complex wants to carpet a hallway connecting to buildings. The carpet costs $1.50 per square foot. How much does it cost to carpet the hallway?
Answer:
$526.75 i believe
Step-by-step explanation:
Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.
Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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Which is the closest to the area of the shaded region in the given square containing a circle? (Use ≈ 3.14.)
10 m
21.5 square meters
50 square meters
O 78.5 square meters
O 100 square meters
5m
The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option
21.5 square metersWhat is a square?A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.
The figure is a composite figure comprising of a square and a circle
The radius of the circle, r = 5 meters
The side length of the square = 10 meters
The value of π = 3.14
The area of the square = 10 m × 10 m = 100 m²
The area of the circle = π × (5 m)² = 25·π m²
The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;
The area of the shaded region = (100 - 25·π) m²
The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²
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The table contains some points on the graph
of an exponential function. Based on the
table, which function represents the same
relationship?
Answer: 1st one
Step-by-step explanation:
Alberto gets a fish tank
Jackson is on point. Of all fish, catfish make up one-third of the total.
How much gravel does Alberto add to the tank in pounds?The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.
Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.
Zebra danios make up half of all the fish.
More fancy guppies than catfish, by a factor of two.
x = guppies
2x = catfish
x + 2x = 1/2 of the fish population
3x = 1/2 of the fish population
3x * 2 = 6x
x = 1/6 number of fancy guppies
catfish:
2x = 2(1/6) = 2/6 = 1/3 catfish.
Jackson is on point. Of all fish, catfish make up one-third of the total.
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The complete question is,
Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?
A machine in a factory makes chairs at rate of two chairs every 10 minutes how much time does the machine take to make five chairs how many minutes would it take for the factory to fulfill an order for 32 chairs show your work or explain how you determine your answers
4. Tamara claims that Sweet Grove apple juice tastes better than Bushels apple juice. Isaac claims that there is no difference between the 2 types of apple juice. Tamara and Isaac would like to find the answer to the following question: Do more 6th graders prefer Sweet Grove apple juice or Bushels apple juice? a. Is this a statistical question? Explain your reasoning. 5. Explain how this question can be answered with an experiment
Answer: a. Yes, this is a statistical question since it includes collecting information from a test of 6th graders and utilizing factual strategies to analyze the comes about and draw a conclusion approximately the inclinations for Sweet Grove and Bushels apple juice.
b. Draw a conclusion based on the results of the experiment, and report any limitations or assumptions made during the experiment.
Step-by-step explanation:
if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
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The width of the set of the shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves If there are 80 feet of wood to use to build the set of shelves what should the dimensions the set of shelves be?
The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
What is a linear equation?When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.
Given:
Width of the set of shelves = 5 times the height of the set of shelves
Number of shelves = 3
Total amount of wood available = 80 feet
Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".
Using the first given information, we can write the equation:
Width (w) = 5 times the height (h) ==> w = 5h
Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.
Finally, we are given that we have 80 feet of wood available to build the shelves.
Using these equations, we can substitute w = 5h into the equation for the total amount of wood:
3w + 4h = 80
Substituting w = 5h, we get:
3(5h) + 4h = 80
15h + 4h = 80
19h = 80
h = 80/19
So, the height of the set of shelves is approximately 4.21 feet.
Now, substituting this value of h back into w = 5h, we get:
w = 5(4.21)
w = 21.05
So, the width of the set of shelves is approximately 21.05 feet.
Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
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Elliot read a report from a previous year saying that 6 % 6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240 240240 adults in his city to test H 0 : p = 0.06 H 0 :p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H a : p ≠ 0.06 H a :p =0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where p pp is the proportion of adults in Elliot's city that bike to work. The sample results showed 21 2121 adults who biked to work, and the corresponding test statistic was z ≈ 1.79 z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?
Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:
H0: p = 0.06
Ha: p ≠ 0.06
α = 0.05/2 = 0.025
The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:
P-value = P(Z ≤ -1.79 or Z ≥ 1.79)
= P(Z ≤ -1.79) + P(Z ≥ 1.79)
= 0.0364 + 0.0364
= 0.0728
Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.
Step-by-step explanation:
What is the range of the relation whose graph is shown?
The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-4, 4} or -4 ≤ x ≤ 4.
Range = {-1, 1} or -1 ≤ y ≤ 1.
Read more on domain here: brainly.com/question/17440903
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Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm
Answer:
16.77 cm²
Step-by-step explanation:
Area of rectangle = L x W
L = 4.3 cm
Width = 3.9 cm
Let' solve
4.3 x 3.9 = 16.77 cm²
So, the area of the rectangle is 16.77 cm²