The formula that represents the volume of water in the tank in terms of the number of minutes since the water began draining is v = 40 - 1.5t.
This can be seen by realizing that the volume of water in the tank decreases by 1.5 gallons per minute, so after t minutes the volume will be 40 - 1.5t. The graph of this formula is a straight line with a slope of -1.5 and an intercept of 40. This means that the graph starts at the point (0,40), which represents a tank that is full of water, and decreases linearly as the number of minutes increases.
The statement "The graph of v in terms of t represents all possible values of v and t" is true. This is because the formula v = 40 - 1.5t is defined for all possible values of t, and the graph of this formula includes all possible pairs of (v, t) values that satisfy the formula.
The statement "The point (7.5,35.75) conveys that when the tank has been draining for 7.5 minutes, it has 35.75 gallons of water remaining" is false. This is because the point (7.5,35.75) does not lie on the graph of the equation v = 40 - 1.5t. The correct point on the graph that represents the volume of water in the tank after 7.5 minutes would be (7.5,26.25), which can be found by substituting t = 7.5 into the equation v = 40 - 1.5t.
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x, 3, 1, 12, 8 if x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers? (1) x > 6 (2) x is greater than the median of the 5 numbers.
if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers
What is a median in math?The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
How do you find the median?Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.
(1) x must be higher than one or three. It will be the median if it is 8 or fewer.
Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.
The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.
insufficient
(2) According to the aforementioned findings, x must be at least 9.
Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.
The median and mean expressions are the same, regardless of whether order is appropriate:
Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):
The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.
This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).
insufficient
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Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i. E. , divides the line from ian's house to joe's house in a 1:1 ratio). What are the coordinates of the diner?.
(7, 5) are the required coordinates of the diner.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
You do the reverse to determine a point's coordinates in a coordinate system.
Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there.
To find the y-coordinate, repeat the previous step while adhering to a horizontal line.
So, we must discover the halfway point between Lan's house and Joe's house in order to get the diner's coordinates.
The following equation will determine the midway between any two points:
M(x1 + x2/2, y1 + y2/2)
There are (4, 4), the point, and the point replaces the specified values:
M(4+10/2, 4+6/2)
M(7, 5)
Therefore, (7, 5) are the required coordinates of the diner.
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In triangle LMN, the measure of angle L is 50° and the measure of angle M 70°. What is the measure of the exterior angle to angle N?
Answer:
120°
Step-by-step explanation:
The 3 angle measures of a triangle will always equal 180.
Since we've already got two angles, all we need to do is a simple equation to get our missing angle:
180-(50+70)=60
Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:
180-60=120
And there's your answer, 120°
There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!
A rose cost $3.40 . How much will it cost to buy a dozen roses?
Answer:
$40.8
Step-by-step explanation:
You would do 3.40 * 12 because a dozen is 12 roses.
So 3.40 × 12 = 40.8
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Find a number so that 100% of it is 26.
Answer:
would it not be 26? I honestly don't know
Determine the distance covered by a car traveling 80 km/h each unit and given time round answers to the nearest unit.
A. Kilometers in on hour?
B. Meters in one hour?
C. Meters in one minute?
D. Meters in one second?
Determine the distance covered by a car traveling 80 km/h for each unit and time given. The answer should be in meter in one hour.
What is a kilometer?
1,000 meters is one metric unit of measurement (approximately 0.62 miles).
The car is travelling at the speed of 80 kilometers per hour.
One hour is 60 minutes.
So car will travel in ideal conditions 80 kilometers in one hour which is 60 minutes.
So just convert the kilometers into meters.
1 kilometer = 1000 meters,
Thus,
80 kilometers = 80,000 meters.
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Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
Answer:
Irrational, rational, rational, rational, rational.
Step-by-step explanation:
√23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.
104.42 this is a rational number! An irrational number has repeating values or just random numbers after the decimal point.
Here's an example...
Tell, does this number look rational?
4.2359712309458730495870192354870394587234098657293085412364781236409584790853467923456790324785098234570923845702398547 (and it goes on forever...and ever...and ever......)
√64 is a rational number. As we know that √64 = 8, a rational number.
49.396 with the 6 repeating is rational because we can express 49.39 as:
49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with
49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.
10.97846727460 is rational because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
An organic food company needs to paint its new silo. The silo is a cylinder with a height of 24 yards and a base 3 yards in diameter. The paint the company has selected will cover 150 square feet per gallon. How many gallons of paint will be needed to paint the top and lateral surface of the silo?
Applying the formula of the lateral surface area of a cylinder, the number of gallons needed to paint the top and the lateral surface is: 314,901 gallons.
What is the Lateral Surface Area of a Cylinder?The lateral surface area of a cylinder = 2πrh, where h is the height, r is the radius of the cylinder.
Given the following:
Height of the cylinder (h) = 24 yardsDiameter = 3 yardsRadius (r) = 1/2(diameter) = 1/2(3) = 1.5 yardsLateral surface area of the cylinder = 2 × π × 1.5 × 24 = 226.19 yards²
Area of the top = area of circle = πr² = π(1.5²) = 7.07 yards²
Area to be painted = 226.19 + 7.07 = 233.26 yards²
Convert square yards to square feet:
1 square yard = 1 square feet
233.26 square yards = 2099.34 square feet
Gallons of paint needed = 2099.34 × 150 = 314,901 gallons.
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blackhawk tech gives four presidential scholarships. if there are 58 nominees, in how many ways can the scholarships be awarded?
If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =
[tex]=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270[/tex]
Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
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Write an equation in point-slope form of the line that passes through the given point and with the given slope (-7,2); m =7
Answer:
Y = 7x + 51
Step-by-step explanation:
Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.
Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\
Hope this helps!
Enlarge the triangle by scale factor -3 with centre (3,3)
Dilating a triangle by - 3 with vertices (3, 4), (3, 5), and (5, 5) will be
(- 9, - 12), (- 9, - 15) and (- 15, - 15).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A triangle with vertices (3, 4), (3, 5) and (5, 5).
Now dilating by a scale factor of - 3 will have every point multiplied by - 3 and the new vertices will be (- 9, - 12), (- 9, - 15) and (- 15, - 15).
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five cards are darwn from a standard deck of cards. how many different hands consist of four queens and one king
2,598,960 many different hands consisting of four queens and one king.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
To choose 4 kings, there is only one way, and to choose a queen, there are four.
Thus, there are 4 different methods to draw the 5 cards as instructed.
The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.
= 52!/(47!)(5!) = 2,598,960.
Hence, 2,598,960 many different hands consisting of four queens and one king.
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Find the Base & Height of the triangle
Area =42 in^2
Answer:
Height: 6
Base: 14
Step-by-step explanation:
Area=42 in^2
height=x-1
base=2x
bh/2=42
Substitute in the values:
2x(x-1)/2=42
The 2s cancel out each other.
x(x-1)=42
x^2 - x =42
x^2 - x - 42=0
When we factor that, we get:
(x-7)(x+6)=0
x=7 or x=-6
We will take the positive answer.
height= x-1 = 7-1 = 6
base= 2x = 2(7) = 14
Now let's double check if we are correct.
6(14)/2
=84/2
=42
We are correct!
Answer:
Base: 14 and height: 6 OR Base: -12 and height -7
Step-by-step explanation:
First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.
[tex]\frac{2x(x-1)}{2}=\frac{42}{1}[/tex] Next, cross multiply. This involves taking the numerator of
one side (top) and multiplying it by the denominator
(bottom) of the other side.
84=2x(x-1) 42*2=84 and anything multiplied by 1 equals itself. Next,
distribute (multiply) the 2x by each term in the
parentheses.
84=2[tex]x^2[/tex]-2x 2x*x=2[tex]x^2[/tex]. 2x*-1=-2x. Next, subtract 84 from both sides.
0=2[tex]x^2[/tex]-2x-84 Now, you can simplify this by dividing by 2 on both sides.
0=[tex]x^2[/tex]-x-42 This is a quadratic equation, which means you have to
factor or use the quadratic formula. In this case, you can
factor by using product and sum. You have to find what
multiplies to -42 and adds to -1. Those numbers would be
-7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have
x-7 and x+6
0=(x-7)(x+6) Next, solve each equation with each binomial set equal
to 0. For x-7=0, x=7 because you add 7 to both sides. For
x+6=0, x=-6 because you subtract 6 from both sides.
x=7 x=-6
You can check if these values work by plugging them into the formula.
[tex]\frac{2x(x-1)}{2}- > \frac{2*7(7-1)}{2}- > \frac{14(6)}{2}- > \frac{84}{2}- > 42[/tex]. x can be 7.
[tex]\frac{2x(x-1)}{2}- > \frac{2*-6(-6-1)}{2}- > \frac{-12(-7)}{2}- > \frac{84}{2}- > 42[/tex] x can be -6
The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.
what types of problems can be solved using the greatest common factor?what type of problems can be solved using the least common multiple
The GCF can be applied to problems requiring the division of something into equal groups or an equal number of groups, as well as problems requiring the simplification of a fraction.
The LCM can be used to solve problems involving the overlap of two activities or something similar, as well as problems involving the addition of two or more fractions with different denominators.
What is the GCF?The greatest common factor of two or more integers that are not all zero in mathematics is the largest positive integer that divides each of the integers.
A set's greatest common factor (GCF) is the largest factor that all of the numbers share.
For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, so the GCF of 12, 20, and 24 is 4. The LCM, or smallest common multiple, is the smallest common number or multiple of any two numbers. The least common multiple of 3 and 5 is 15, for example.
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HELP!! WILL GIVE BRAINIEST
For the function, [tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex], the value of h(4) is h(4) ≈ 8.7
Evaluating a functionFrom the question, we are to determine the value of h(4) in the given function.
The given function is
[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]
To determine the value of h(4), substitute 4 for x in the given function
[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8e^{-0.9(4)} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8e^{-3.6} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8(0.0273237) }[/tex]
[tex]h(4) = \frac{50}{5.5 + 0.21859 }[/tex]
[tex]h(4) = \frac{50}{5.71859 }[/tex]
h(4) = 8.7434
h(4) ≈ 8.7
Hence, the value of h(4) is 8.7
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true or false: the most common level of confidence used in creating confidence intervals is 90%. group of answer choices true false
It is true, that the most level of confidence used in creating confidence intervals is 90%.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
We have given,
Given n = 93, u =24, x' = 23, α=5.5
z = x'- u / α(/√n) = 1.645
Hence the answer choice is true.
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(9 * 6) * 1 = 3 operations
Answer:
53
Step-by-step explanation:
PEMDAS
Parenthesis
multiply the numbers
Divide
Add
Subtract
due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit?
Due to construction, approximately 5 minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit.
Given that,
length of highway is 8 miles
Reduced length is 55 miles
Hours taken is 35 miles per hour.
Let t₁ is time taken is 55 mph
t₁ = 8/55
Let t₂ is time taken is 35 mph
t₂ = 8/35
Difference in time = 8/35 - 8/55
= 8 × 20 / (35 * 55) hour
= 160 × 60 / (35 × 55) mins
= 4.7
= 5 minutes (approximately)
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A particle of mass mm moves in the plane with coordinates ( x ( t ) , y ( t ) )(x(t),y(t)) under the influence of a force that is directed toward the origin and has magnitude k / \left( x ^ { 2 } + y ^ { 2 } \right)k/(x 2 +y 2 )—an inverse-square central force field.
An inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
From Newton's second law of motion,
mass × acceleration = Force acting on the mass
Resolving the force F along x and y directions and applying Newton's second law of motion,
Using,
[tex]r = \sqrt{x^2+y^2}[/tex]
Therefore,
[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and cosθ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]
Similarly using,
[tex]r = \sqrt{x^2+y^2}[/tex]
we get,
[tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]
[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]
Where [tex]r = \sqrt{x^2+y^2}[/tex]
and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]
Therefore we showed that holds
[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]
Hence the answer is an inverse-square central force field is [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].
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how is the year 2029 written as a roman numeral?
The year 2029 written as a roman numeral is MMXXIX.
What are Roman numerals?Roman numerals are mathematical representations of numbers in the Roman alphabet. Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers in Europe until the late Middle Ages.
Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which stand for 1, 5, 10, 50, 100, 500, and 1,000, respectively.
In this case, it should be noted that 2029 is MMXXIX.
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help me with this i cant figure out the second part
The value of c that will make the expression x² + 24x + c a perfect trinomial is 144.
The perfect squared trinomial as a perfect binomial is (x + 12)²
How to find the value of c in the expression?An expression obtained from the square of the binomial equation is a perfect square trinomial.
In other words, perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.
If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if it satisfies the condition b² = 4ac.
Therefore,
x² + 24x + c
where
a = 1b = 24c = ?Therefore,
b² = 4ac
24² = 4 × 1 × c
4c = 576
divide both sides by 4
c = 576 / 4
c = 144
Therefore,
c = 144
The perfect squared trinomial as a perfect binomial is as follows:
x² + 24x + 144
x² + 12x + 12x + 144
x(x + 12) + 12(x + 12)
(x + 12)(x + 12)
(x + 12)
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what is the largest integer that is a divisor of $(n 1)(n 3)(n 5)(n 7)(n 9)$ for all positive even integers $n$? (a) 3 (b) 5 (c) 11 (d) 15 (e) 165
The largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) for all positive even integers is 15
The correct answer is an option (d)
In this question, we need to find the largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) for all positive even integers n.
We can observe that (n + 1), (n + 3), (n + 5), (n + 7) and (n + 9) are 5 consecutive odd integers
In every 5 consecutive odd positive integers, one of them is always divisible by 3 and one of them is always divisible by 5.
This means, (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5
i.e., (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15 (3 * 5 = 15)
Therefore, the largest integer that is a divisior of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) = 15
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pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. a small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively
The mean is a measure of location which tells us the average of observation.
Standard deviation tells us how dispersed a data is or how much variation our data contains.
According to question,
The population size : N = 1500
Number of fraudulent in a month : 28
Population proportion : P = 28/1500
=> P = 0.0187
Sample size: n = 180
Sample proportion : p = 28 / 180
=> p = 0.156
Therefore The mean of sampling distribution for the sample size 28,
μ = P
=> μ = 0.0187
The standard deviation will be
=> σ = [tex]\sqrt{\frac{p(1-p)}{n}}[/tex]
Substituting the value,
=> σ = [tex]\sqrt{\frac{0.0187(1-0.0187)}{180}}[/tex]
=> σ = 0.010
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The values for random variables in a Monte Carlo simulation area. selected manually.b. generated randomly from probability distributions.c. taken from forecasting analysis.d. derived secondarily using formulas.
The values for random variables in a Monte Carlo simulation area that were chosen at random from probability distributions are the right answer.
What is Monte Carlo Simulation ?
The Monte Carlo Method, also referred to as the Monte Carlo Simulation or a multiple probability simulation, is a mathematical method for predicting potential outcomes of an uncertain event. To help people make better decisions when faced with uncertainty, John von Neumann and Stanislaw Ulam developed the Monte Carlo Method during World War II.
Therefore, the values for random variables in a Monte Carlo simulation area that were generated at random from probability distributions are the right answer.
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The correct response is the set of values for random variables in a Monte Carlo simulation region that were randomly selected from probability distributions.
In order to represent uncertainty in a model that represents a real system and computes the values of model outputs, a Monte Carlo technique is used. During World War II, John von Neumann and Stanislaw Ulam created the Monte Carlo Method to aid people in making better judgments when faced with uncertainty.
As a result, the correct response is the random values for random variables that were produced using probability distributions in a Monte Carlo simulation area.
Can someone please help me with, best answer will be marked brainiest.
A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.
The value of x is 47
The value of y is 10.6
The four angles for the given quadrilateral are,
96, 94, 76, and 94.
What is quadrilateral?A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.
We have,
A an isoceles trapezium.
Where one pair of sides are equal and parallel.
Two angles are equal.
Now,
94 = 2x
x = 47
Now,
The four angles sum is 360.
94 + 94 + 96 + 3y + 44 = 360
328 + 3y = 360
3y = 360 - 328
3y = 32
y = 32/3
y = 10.7
Now,
3y + 44 = 3 x 10.7 + 44 = 32 + 44 = 76
Thus,
The four angles for the given quadrilateral are,
96, 94, 76, and 94.
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the area of trapezoid $abcd$ is $60$. one base is $4$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
The length of the median of the trapezoid ABCD is 12 .
In the question ,
it is given that ,
the area of the trapezoid ABCD is = 60 ,
the height of the trapezoid ABCD is = 5 ,
let one base of the trapezoid ABCD be = a ,
So, b = a + 4 ,
Substituting the value in the formula for Area of the trapezoid = A =(a+b)h/2
(a + a + 4)5/2 = 60
(2a + 4)5 = 120
2a + 4 = 120/5
2a + 4 = 24
2a = 24 - 4
2a = 20
a = 20/2
a = 10 units
and other base = 10 + 4 = 14 units
So , the length of the median will be = (10 + 14)/2
= 24/2 = 12 units
Therefore , the length of median is = 12 .
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Elouise and Marcus are 20km apart.
There is a lake due west of Elouise that is also 10√3 km due north of Marcus.
Work out the bearing of Marcus from Elouise
Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.
At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.
Given that,
Elouise and Marcus are 20 km apart (AB)
There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)
Now, according to a Pythagoras theorem,
(AC)² + (AB)² = (BC)²
or, (AC)² = (BC)²- (AB)²
or, (AC)² = (10√3)² - (20)²
or, AC = [tex]\sqrt{500}[/tex]
or, AC = 22.36 km
So, distance bearing of Marcus from Elouise is 22.36 km.
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It is -4 in Iceland at 7 am. The temperature then
increases by 6 Degrees. What is the new temperature?
Answer:
Step-by-step explanation:
kakaka
Answer: 2 degrees.
Step-by-step explanation: If it is -4 degrees in Iceland at 7 am and the temperature increases by 6 degrees, the new temperature would be -4 + 6 = 2 degrees.
1.5 times 4/5 in fraction form
Answer: 1 1/5
Step-by-step explanation: you can write it as 1.5/1 times 4/5.
multiply by numerator and denominator so 1.5*4 which is 6
and 1*5 which is 5.
Now you have 6/5
6 can go into 5 once and you have 1 extra so 1 1/5
an english reading list has 9 american novels and 7 english novels. a student must read 4 from the list, and at least 2 must be american novels. in how many different ways can the 4 books be selected?
The total ways in which the student can readd the books are 1512 ways.
What is Combination?
A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).
Solution:
Since reading 2 american novels is compulsory
The student therefore needs to read only two more novels
It can be either American Novels or English Novels
Ways to read American Novel = 7C2
Ways to read English Novel = 7C2
Total Ways = 9C2 * (7C2 + 7C2)
Total Ways = 36 * (42)
Total Ways = 1512 ways
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