On solving the provided question we can say that by null hypothesis There is insufficient proof to conclude that student attendance has changed.
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
This is a z-test for a proportion.
[tex]H0:p=.34 H1:p not=.34\\\alpha=0.01 ... this is a\\2-tailed test\\critical values are +2.58, -2.58\\p=.34 (given) q=1-p=.66\\p^=.33\\z=(p^-p)/sqrt(pq/n)\\z=(.33-.34)/sqrt(.34*.66/8302)\\z=-.01/.0051961\\z=-1.92[/tex]
1.96 does not fall in the reject region
There is insufficient proof to conclude that student attendance has changed.
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7y+10x=−11 4y−3x=−15
X=
Y=
Answer:
x= 108/61; y=-163/61
Step-by-step explanation:
Which data outcome of the number of customers in line would best support opening another cash register? Homework Help 1DF. Range/variance/standard deviation (population and sample) and shape of distribution, examples 2 (DOCX) High mean with high standard deviation Low mean with high standard deviation High mean with small standard deviation Low mean with small standard deviation
High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.
What is standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
We have to find from the given options which data outcome of the number of customers in line would best support opening another cash register.
The number of customer in the line having high mean with small standard deviation means deviation in data small and data cluster around mean. High mean I'm play high number of customer in line. This help to opening another cash register.
Hence, High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.
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A homeowner needs two loads of gravel for a driveway to their new house. One load of gravel weighs 7 tons and the second load weighs 8,000 pounds . What is the total weight of the gravel, in tons, used for the driveway?l1 toas87 tons7,8 tons
12 tons of gravel has been used for the driveway.
Weight of first load = 7 tons
Weight of second load = 8000 pounds
There are 2000 pounds (lb) in one US customary ton (t). Both tons and pounds are measurements of mass/weight in the US customary and imperial systems of measurement. However, the definitions of the ton vary in both systems. For example, there are 2240 pounds in an imperial ton, and 2204.6226 pounds in a metric ton.
The US ton is mostly used in the United States and Canada. The imperial ton was mostly used in the UK, and still is to a degree, but since the UK began the process of metrication, the metric ton is also used in the UK.
Convert pounds to tons:
1 pound = 0.0005 ton
8000 pounds = 4 ton
Then,
Weight of second load = 4 ton
Total weight of the gravel, in tons = Weight of first load + Weight of second load
= 8 tons + 4 tons
= 12 tons
Thus, 12 tons of gravel has been used for the driveway.
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What are types of solutions?
There are three main types of solutions found in mathematics for a given problem or equation: No solution, Unique solution, and Infinitely many solutions.
Solutions in mathematics are a set of values that can be assigned to the variables of an equation or a system of equations so that it holds true. In other words, it is a set of values that satisfies the equation or system of equations.
Types of solutions:
No solution: In this situation, there is no set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Unique solution: In this situation, there is only one set of values that can be assigned to the variables of an equation or system of equations so that it holds true.
Infinitely many solutions: In this situation, there are infinitely many sets of values that can be assigned to the variables of an equation or system of equations so that it holds true. This situation arises when the given equation is not independent.
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(3 points) To the appropriate number of significant figures, if the density of the metal cube is 2.3 x 10-3 kilograms/microliters, what is the length of one side of a cube if the mass is 88 milligrams
if the density of the metal cube is 2.3 x 10⁻³ kilograms/micro liters, 2968 cm. is the length of one side of a cube if the mass is 88 milligrams
What is significant figure?The amount of digits that contribute to the correctness of a value—often a measurement—are known as significant figures. The first digit that is non-zero is where we begin counting significant figures.
The number of significant single digits (0 through 9 inclusive) in an expression's coefficient is referred to as the significant figures in scientific notation. The amount of accuracy or assurance an expert or scientist uses to state a quantity is indicated by the number of significant figures in a statement.
The given mass of the metal cube is 2.3 × 10⁻³kg/micro-liters or 2300000 gm/liter
The density of the metal cube is 88 mg or 0.088 gm.
Now, we know that density, d = mass/volume.
So, volume of the metal cube,
V = mass/density
V = (2300000/0.088)
V = 26136363.7 L
Now, we know that volume of a cube is a³ where a is the length of a side of the cube. So, a³ = 26136363.7 L or 26136363.7 dm³.
So, a = 296.8 dm or 2968 cm.
So, the length of one side of the cube is 2968 cm.
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Which is true about the legs of a 45 − 45 − 90 triangle?
A. The legs of a 45-45-90 triangle are congruent.
B. Now, a 45-45-90 triangle will be a right triangle because one of the angles is 90°.
C. Further, it will also be an isosceles triangle since the two angles are equal and the sides opposite to equal angles in a triangle are always equal.
D. Since it becomes an isosceles triangle, the two of its legs will definitely be equal, or congruent to each other.
A 45-45-90 triangle is a right and isosceles triangle, whose legs are congruent or equal, and have one right angle of 90°. Thus all the statements are correct.
A 45-45-90 triangle is a special kind of triangle, which has the following characteristics:
It’s isosceles with two congruent or equal sides and two congruent anglesIt has one right angle of 90° and two acute angles of 45°The length of the hypotenuse is √2 times the length of a leg. Thus the ratio of the length of sides is 1 : 1 : √2The attached picture gives a better understanding of these characteristics.
If we take a look at the given problem, we can conclude that all the given statements are correct.
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I need help What would the answer be
restaurants often slip takeout menus under zach's apartment door. so far, zach has collected 18 menus, including 4 for japanese food. what is the probability that one of zach's takeout menus, selected at random, will be from a japanese restaurant? write your answer as a fraction or whole number. p(japanese) =
So, the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.
The probability of selecting a Japanese restaurant menu from Zach's collection of 18 menus is found by taking the number of Japanese restaurant menus (4) and dividing it by the total number of menus in the collection (18). This can be written mathematically as:
p(japanese) = 4/18
So the probability of selecting a menu from a Japanese restaurant is 4/18, which can also be simplified as 2/9.
In other words, if Zach selects a menu at random from his collection, there is a 2/9 chance that it will be from a Japanese restaurant.
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the washington family and the bennett family each used their sprinklers last summer. the water output rate for the washington family's sprinkler was per hour. the water output rate for the bennett family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?
30 hours of use by the Washington family sprinkler and 35 hours of use by the Bennett family sprinkler.
We can find how long was each sprinkler used by substitution method.
Let W = hours of use by the Washington family
65 - W = hours of use by the Bennett family
According to the question we get
15W + 40(65 -W) = 1850
15W + 2600 - 40W = 1850
-25W = -750
W = 30
Now, put the value of W in 65 - W to calculate the hours used by the Bennett family
65 - W = 65 - 30 = 35
Thus, the amount of time used for sprinklers by the Washington family and the Bennett family is 30 hours and 35 hours, respectively.
--The given question is incomplete, the complete question is
"The Washington family and the Bennett family each used their sprinklers last summer. The water output rate for the Washington family's sprinkler was 15L per hour. The water output rate for the Bennett family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1850L. How long was each sprinkler used?"--
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please do this it's due tommrow
Answer: 10. equal 0.27
11. 5.12
12. 3.35
Step-by-step explanation:
10. 0.9 * 0.3 = 0.27
11. 1.6 * 3.2 = 5.12
12. 0.5 * 6.7 = 3.35
13. 0.81*7.3 = 5.873
14. 5.6*3.9 = 21.84
15. 1.2 * 0.05 = 0.06
please answer this i dont understand
The possible solution would be 10 bags of popcorn and 3 pretzels.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, 'x' represents the number of bags of popcorn purchased and 'y' represents the number of bags of pretzels purchased.
Therefore,
x + y ≥ 13 and 7x + 5y ≤ 85.
The possible solution to these inequalities is where the graph of two intersects which is at (10, 3).
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the region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ)
The region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]
Now, According to the question:
We will first draw both of them on the same plane and then find their point of intersection. Then using the given information, we will shade the region whose area we have to find.
The point of intersection of r = 1 + cos(θ) and r = 3 cos(θ)
1 + cos(θ) = 3 cos(θ)
1 = 2 cos(θ)
=> cos(θ) = 1/2
=> θ = [tex]cos^-^1[/tex][tex]\frac{1}{2}[/tex]
=> θ = ±[tex]\frac{\pi }{3}[/tex]
So, two curves intersect at θ = ± [tex]\frac{\pi }{3}[/tex]
Area of the cardioid,
[tex]A_1 = \int\limits^\pi _\frac{\pi }{3} {\frac{1}{2}(1+cos\theta)^2 } \, d\theta= \frac{1}{2} \int\limits^\pi _\frac{\pi }{3} (1+cos^2\theta+2cos\theta) } \, d\theta=\frac{1}{2}[/tex]
[tex]\int\limits^\pi _\frac{\pi }{3} {(1 + \frac{cos2\theta+1}{2} +2cos\theta)} \, d\theta[/tex]
=> [tex]A_1 = \frac{1}{2}[\theta+\frac{1}{2}(\frac{sin2\theta}{2} +\theta)+2sin\theta ]^\pi _\frac{\pi }{3}[/tex]
=> [tex]A_1= \frac{1}{2}[\frac{3\pi }{2}+0+0-\frac{\pi }{2}-\frac{\sqrt{3} }{8} -\sqrt{3} ][/tex]
=> [tex]A_1= \frac{1}{2} [\pi +\frac{-9\sqrt{3} }{8} ]\\\\A_1 = \frac{\pi }{2} - \frac{9\sqrt{3} }{16}[/tex]
Area of the circle,
[tex]A_2 = \int\limits^\frac{\pi }{2} _\frac{\pi }{3} {\frac{1}{2}(3cos\theta)^2 } \, d\theta \\\\A_2 = \frac{9}{2} \int\limits^\frac{\pi }{2} _\frac{\pi }{3} \frac{cos2\theta+1}{2}d\theta\\ \\A_2 = \frac{9}{4}[\frac{sin2\theta}{2}+\theta ]^\frac{\pi }{2}_\frac{\pi }{3}[/tex]
[tex]A_2 = \frac{9}{4}[0+\frac{\pi }{2} -\frac{\sqrt{3} }{4} -\frac{\pi }{3} ][/tex]
[tex]A_2=\frac{9}{4}[\frac{\pi}{6}-\frac{\sqrt{3} }{4} ][/tex]
[tex]A_2= \frac{3\pi }{8}-\frac{9\sqrt{3} }{16}[/tex]
Area of the shaded region,
[tex]A = A_1-A_2[/tex]
[tex]A = \frac{\pi }{2} - \frac{9\sqrt{3} }{16} - \frac{3\pi }{8}+\frac{9\sqrt{3} }{16}[/tex]
[tex]A = \frac{\pi }{8}[/tex]
This is the area of the shaded region in the first and the second quadrant. We see that by symmetry, the area of the shaded region in the first and the second quadrant is equal to the area of the shaded region in the third and the fourth quadrant.
So, the total area is 2 ×[tex]\frac{\pi}{8}[/tex] = [tex]\frac{\pi}{4}[/tex]
Hence, the region inside cardioid r = 1 + cos(θ) and outside the circle r = 3 cos(θ) is equal to [tex]\frac{\pi}{4}[/tex]
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Solve for X, Leave in simplest radical form
The value of y is 2. The study of triangular relationships between angles and side lengths is known as trigonometry.
What are trigonometric relations?When the number under the root sign has no square factors, a radical is said to be in its simplest form. For instance, 72 can be divided by 4 to get 218. Radicals - The symbol nx used to denote a root is referred to as a radical and is thus interpreted as "x radical n" or "the nth root of x." The horizontal line, the quantity underneath it, and the quantity n printed to the left are referred to as the vinculum, radicand, and index, respectively, in the radical symbol. The square root symbol, which has the value of 1.414, is used to symbolise the square root of 2, also known as root 2. Mathematicians frequently utilise this number.The study of triangular relationships between angles and side lengths is known as trigonometry.
The six trigonometric functions are cosec, sec, cot, sin, and tan.
Allow the angle to be, so that
The opposite or hypotenuse of sin
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be ΔABC
The triangle ABC is a right angled triangle and the angles inside the triangles are 45° , 45° and 90°
Now , from the given figure
From the trigonometric relations
tan θ = x / √2
Now , θ = 45°
So , tan 45° = x / √2
And , tan 45° = 1
So , the value of x = √2
And from trigonometric relations ,
hypotenuse² = base² + length²
y = √ ( √2 )² + ( √2 )²
y = √4
y = 2
Hence , The value of x = √2
The value of y = 2
The complete question is,
Solve for X. Leave your answer in simplest radical form if necessary.
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12 13 14 15 16 17 18 19 20 at the fisher farm, the weights of zucchini squash are normally distributed, with a mean of 5 ounces and a standard deviation of 0.7 ounces. which weight represents the 8th percentile? find the z-table here. 3.56 ounces 4.01 ounces 5.59 ounces 5.98 ounces
12 13 14 15 16 17 18 19 20 at the fisher farm, the weights of zucchini squash are normally distributed, then Weight represents the top 10% of the zucchinis is 5.9
The formula for calculating a z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
We're looking for:
Weight is 10% of zucchinis at the top.
Top 10% = 90% of the population
90th percentile Z score is 1.282.
Hence
1.282 = x - 5 / 0.7
1.282 × 0.7 = x - 5
0.8974 = x - 5
x = 5 + 0.8974
x = 5.8974
5.9 ounces, roughly.
The top 10% of the zucchinis have a weight of 5.9 ounces.
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Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.
Answer:
29$
Step-by-step explanation:
1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$
Chloe is trying to find three consecutive, positive integers such that six times the largest is equal to the twice sum of the two smaller integers.
set up an equation that models the numbers chloe is trying to find
An equation that models the numbers is x, x+1, x + 2
The term equation is known as a condition on a variable such that two expressions in the variable have equal value
Here we know that Chloe is trying to find three consecutive, positive integers such that six times the largest is equal to the twice sum of the two smaller integers.
Then the given parameters are written as the three consecutive positive numbers Chloe is trying to find are x, x+1, x + 2
Here we have the conditions of the three positive numbers are written as,
=> 6 × (x + 2) = 2 × (x + x + 1)
Now, we have to check if the three consecutive numbers can be 4, 5, and 6 by substituting the values as written as,
=> x + 2 = 6
=> x + 1 = 5
Then the value of x is 4
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Determine the principal stresses and the absolute maximum shear stress.
The principal stresses are the maximum normal stresses in the x, y, and z directions.
These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.
The principal stresses are determined using Mohr's circle and the absolute maximum shear stress is equal to one-half the difference between the two principal stresses.
The principal stresses are the maximum normal stresses in the x, y, and z directions.
These are typically determined using Mohr's circle. The absolute maximum shear stress is the maximum shear stress that can act on a given material, which is equal to one-half the difference between the two principal stresses.
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Which formula describes the range?
On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.
A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).
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A baby weigh 3. 35 kilogram at birth. Suppoe the baby' weight contantly increae every two month by 1. 2 kilogram, what i hi weight in the ame unit in the 6th month?
After 6 months of birth the weight will become 6.95 kg.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
from given condition, a baby weigh 3. 35 kilogram at birth and the baby weight constantly increase every two month by 1. 2 kilogram.
so, the weight after 2 months of birth is 3.35 kg + 1.2 kg = 4.55 kg
and the weight after 4 months of birth is 4.55 kg + 1.2 kg = 5.75 kg
and the weight after 6 months of birth is 5.75 kg + 1.2 kg = 6.95 kg
Therefore, after 6 months of birth the weight will become 6.95 kg.
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Some please help me with this: 2y - z + z^2
2y - z + z^2 is an algebraic expression. It represents a mathematical operation that includes three different terms: 2y, -z and z^2. It can be simplified depending on the context and the values of y and z.
In the given expression, 2y is the coefficient of y, which is multiplied by y. -z is subtracted from 2y and z^2 is added to the result.
In order to simplify this equation, you could combine like terms, which means combining the same variable or powers of the same variable with each other.
This expression does not have any like terms, so it can't be simplified anymore.
It can be evaluated by replacing y and z with specific values and then performing the mathematical operations in the given order.
Which of the following would be the standard deviation for this sample data set: 5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5?1.801.722.685.36
The standard deviation for this sample data set is 1.93.
What is deviation ?
Deviation refers to the difference between an individual value or observation and the average or mean value of a set of data. It can also refer to the extent to which a variable or set of data deviates from a standard or expected value.
To calculate the standard deviation for a sample data set, we first need to find the mean (average) of the data. In this case, the mean of the data set {5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5} is 5.45.
Once we have the mean, we can calculate the variance by taking the average of the squared differences between each data point and the mean. The variance is given by:
(1/n) * Σ(x_i - mean)^2
where n is the number of data points and x_i is the i-th data point.
The variance for this data set is 3.70.
Finally, we take the square root of the variance to get the standard deviation.
So, the standard deviation for this sample data set is 1.93.
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laura is drawing a rectangle. the width will be 3 centimeters, and the area will be at least 18 square centimeters. let x represent the length of the rectangle. which inequality describes the problem?
The inequality that describes the problem is 3x ≥ 18.
This means that the length of the rectangle (x) must be greater than or equal to 6 centimeters in order to ensure that the area of the rectangle is at least 18 square centimeters.
To calculate this, we need to rearrange the equation to x ≥ 6. This is done by dividing both sides of the equation by 3, which gives us the result of x ≥ 6.
To demonstrate this, we can assume that the length of the rectangle is 7 centimeters (x = 7). Plugging this value into the equation 3x ≥ 18 gives us 3(7) ≥ 18, which simplifies to 21 ≥ 18. Since this is true, we know that the length of the rectangle (7 centimeters) satisfies the inequality 3x ≥ 18.
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State the center point and radius of the circle. Write the equation of the circle in standard and general form.
The equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
What is equation of the circle?
A closed curve that is drawn from a set point known as the center and has all of its points at exactly the same distances from it is termed a circle. The formula for a circle with the coordinates (h, k) in its center and radius is [tex](x-h)^2+(y-k)^2=r^2[/tex]
This represents the equation's conventional form. As a result, the equation for the circle is simple to find if we also know the coordinates for the radius of the circle.
Here according to the graph the center of the circle is (2,-1) and radius of the circle = 2+2=4 unit.
Now using circle equation then
=> [tex](x-p)^2+(y-q)^2=r^2[/tex]
Where p=2 , q=-1 and r=4 then
=> [tex](x-2)^2+(y-(-1))^2=4^2[/tex]
=> [tex](x-2)^2+(y+1)^2=16[/tex]
Hence the equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
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In what ratio is the line segment joining the points (- 3 2 and 6'1 is divided by Y axis?
Y-axis divides the line segment formed by the points ( -3 ,2) and ( 6,1) in the ratio equals to 1 :2.
As given in the question,
Coordinates of the line segment is given by :
( x₁ , y₁ ) = (-3, 2)
(x₂ , y₂ ) = ( 6,1)
Let the ratio of the given line segment divided by the y -axis that is ( x, y) = ( 0, y ) be m : n given by the formula:
( x, y ) = [ ( mx₂ + nx₁) /(m +n) , (my₂ + ny₁ ) / ( m + n ) ]
Substitute the values we get,
( 0 ,y ) = [ ( 6m -3n) /(m +n) , (1m + 2n ) / ( m + n ) ]
⇒ ( 6m -3n) /(m +n) = 0
⇒ 6m -3n = 0
⇒ 6m = 3n
⇒m : n = 1 : 2
Therefore, y-axis divides the given line segment into the ratio 1 : 2.
The above question is incomplete, the complete question is :
In what ratio is the line segment joining the points (- 3 2) and (6,1) is divided by Y-axis?
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Becky has 14 pints of pudding. How many cups of pudding does she have?
Answer:
28 cups
Step-by-step explanation:
[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{14}[/tex]
1 x 14 = 14, so 2 x 14 = 28
consider an urn with 3 red balls, 2 blue balls, and 7 black balls. three balls are selected at random with replacement, i.e. each time a ball is selected it is returned to the urn. (a) what is the probability of selecting one red and two black balls? (b) what is the probability of selecting exactly two black balls? (c) what is the probability of selecting exactly two balls of the same color?
(a) 21/144 probability of selecting 1 red and 2 black. (b) 35/144 probability of selecting 2 black. (c) 61/144 probability of selecting 2 same color.
What is probability ?
Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will occur with certainty. The probability of an event can also be expressed as a percentage or a fraction. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
(a) The probability of selecting one red and two black balls is (3/12) * (7/12) * (7/12) = 21/144.
(b) The probability of selecting exactly two black balls is (7/12) * (7/12) * (5/12) = 35/144.
(c) The probability of selecting exactly two balls of the same color is (3/12) * (3/12) + (2/12) * (2/12) + (7/12) * (7/12) = 61/144.
(a) 21/144 probability of selecting 1 red and 2 black. (b) 35/144 probability of selecting 2 black. (c) 61/144 probability of selecting 2 same color.
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A car has a 16-gallon fuel tank. when driven on a highway, it has a gas mileage of 30 miles. how many gallons are left in the tank when the car has traveled the following distances on the highway? 90 miles 246 miles per gallon. the gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). after filling the gas tank, the driver got on a highway and drove for a while. how many gallons are left in the tank when the car has traveled the following distances on the highway?
a. 90 miles
b. 246 miles
The car consumes 3 gallons and 8.2 gallons of fuel respectively.
Milage:
Divide the distance traveled by the amount of gas used. For example, driving 100 miles with a full tank and 5 gallons of gas is 10mpg. When it comes to fuel economy, it's important to know how much your car is costing you each time we drive it.
According to the Question:
The gas mileage is the number of miles that can be covered by a car for a particular amount of fuel.
We are given that the gas mileage of the car is 30 miles per gallon, that means that the car consumes 1 gallon of fuel for each 30 miles covered.
The amount of fuel needed to cover the following distance is:
a) For 90 miles, let x represent the number of gallon of fuel. Hence:
Distance covered / amount of fuel = 30 miles per gallon
90/x = 30
⇒ x = 90/30
⇒ x = 3 gallons
b) For 246 miles, let x represent the number of gallon of fuel. Hence:
Distance covered / amount of fuel = 30 miles per gallon
⇒ 246/x = 30
⇒ x = 246/30
⇒ x = 8.2 gallons
Therefore, the car consumes 3 gallons of fuel for 90 miles and 8.2 gallons for 246 miles.
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shane made a scale drawing of a house and its lot. the scale of the drawing was 11 millimeters : 7 meters. if the lawn in the backyard is 66 millimeters long in the drawing, how long is the actual lawn?
Each piece of room or house length and width should be inverted to be scaled. For instance, a rectangle measuring 66" by 7" might be used to depict a dresser that is 5' by 2' at a scale of 14" = 1'.
A table that is 4' by 4' would also be 1" by 1" in size. [7] When measuring furniture that isn't square or rectangular, make the smallest square or rectangle the item might possibly fit and then use those dimensions. For instance, to represent a wingback chair that is 2' 6" wide and 2' deep, use a 5/8" by 1" rectangle.
Next, draw a rough outline of the chair inside the rectangle. On a piece of graph paper that is blank, draw the furnishings. Use graph paper without the room's floor plan drawn on it.
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steve wants to download a selection of new music. how many ways can steve select three rock songs, five alternative songs, and six rap songs from a list of five rock songs, six alternative songs, and nine rap songs?
Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.
1. To select three rock songs from a list of five, use the formula for combinations: nCr = 5Cr = 5!/ (3!*2!) = 10
2. To select five alternative songs from a list of six, use the formula for combinations: nCr = 6Cr = 6!/ (5!*1!) = 6
3. To select six rap songs from a list of nine, use the formula for combinations: nCr = 9Cr = 9!/ (6!*3!) = 84
4. To find the total number of selections, multiply the individual combinations: 10 x 6 x 84 = 11,250
Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.
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A ball was thrown up into the air and allowed to bounce until it came to a halt.
At which of the following intervals did the height of the ball increase and then decrease?
O 0 < x < 4
O 2 < x < 2
Ο 5 < x < 7
O 7 < x < 9
At the interval of 0 to 4, the ball was thrown up into the air and allowed to bounce until it reached its peak height. Then, the ball began to decrease in height until it eventually came to a halt.
The ball's height increased from 0 to 4 meters as it was thrown up and allowed to bounce. Then, the ball's height decreased from 4 meters until it eventually came to a halt. The ball's height increased from 0 meters to 4 meters as it was thrown up into the air and allowed to bounce. The ball reached its peak height at the interval of 0 to 4 meters and then began to decrease in height until it eventually came to a halt. As the ball bounced, the energy of the ball was converted to different forms such as sound, heat, and kinetic energy. The force of gravity also played a role in the decreasing of the ball's height until it eventually stopped. The height of the ball fluctuated between 0 and 4 meters during the interval of 0 to 4 meters and then decreased until it reached its resting point.
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