Using the Pythagorean Theorem, 12² + 5² = 169 = ✓169 = 13
What is Pythagoras theorem?This is simply the way that one can find the missing length of a right angled triangle.
In this case, it should be noted that the theorem is in the form of:
a² + b² = c²
c = hypothenuse
a and b are the other sides
Based on the information given, this will be:
5² + 12²
= 25 + 144
= 169
Now the square root of 169 is ✓169 = 13.
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A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 4800 kilograms have already been loaded into the container. What is the greatest number of 40-kilogram crates that can be loaded into the shipping container?
The greatest number of 40-kilogram crates is 517.5.
From the question, we have
Weight of the crate = 40 kg
Greatest weight that the container can load = 25500 kilograms
Weight of the other shipments on the container = 4800 kg
So the greatest number of 40 kg crates = c
Therefore, the weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container
4800 + 40c ≤ 25500
40c ≤ 25500 - 4800
40c ≤ 20700
c ≤ 517.5
Hence, the greatest number of 40-kilogram crates is 517.5.
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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The number of members on the basketball team
increased from 9 to 12. What was the percent
increase?
I may be incorrect.
Answer: 33.333333333333%
Step-by-step explanation:
The difference is 1/3. Twelve by three is four. Nine by three is three. The different from 9 to 12 is 1/3.
Terry deposits a principal amount of $500 in a savings account that earns an annual rate of simple interest. If he makes no deposits or withdrawals, he will earn $40 in simple interest in 4 years. What is the annual rate of simple interest?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r[/tex]
Write an equation in point-slope form of the line that passes through the point (1, 0) with slope -1/4
Answer:
y = -1/4(x-1)
Step-by-step explanation:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) From the point given [tex]y_{1}[/tex] = 0 and [tex]x_{1}[/tex] = 1
m = slope -1/4 Plug these in and get
y - 0 = -1/4(x - 1) y-0 is just y
help me quick pls/....................
Answer:
A
Step-by-step explanation:
First off, "A" is the only one that even has "x cubed minus one" in it. The y squared divided by twenty-four is also present.
2[tex]2\frac{5}{7} +4\frac{9}{14}[/tex]
Round 57.183 to the nearest whole number tenth and hundredth
Answer:
Step-by-step explanation: 57.183= to the whole number= 58.183
Tenth= 57.180
Hundredth= 57.200
Answer:
Nearest Whole Number: 57
Nearest Tenth: 57.2
Nearest Hundredth: 57.18
*Note: When rounding to a place value the number after the place value you want determines whether the place value number says the same or goes up by 1. In order for the place value number to stay the same the number after has to be less than 5 and in order for the place value number to go up by 1 the number after has to be greater than or equal to 5.
A random sample of 85 printers discovered that 35 of them were being used in small businesses. Find the 99% confidence interval for the population proportion of printers that are used in small businesses
The 99% confidence interval for the population proportion of printers that are used in small businesses, using the z-distribution, is of:
(0.2743, 0.5493)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the equation presented next:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the point estimate of the parameter.z is the critical value of the z-distribution.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
(the critical value can be found either with the z-table or with a z-distribution calculator).
The sample size and the estimate are listed as follows:
[tex]n = 85, \pi = \frac{35}{85} = 0.4118[/tex]
The lower bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 - 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.2743[/tex]
The upper bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 + 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.5493[/tex]
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Given the shape, find the length AD (x)
The length of AD is 8.58 units
Here triangle CDE and triangle CAB are similar triangles.
We know that the corresponding sides of similar triangles are in proportion.
CD/CA = CE / CB = DE/AB
Consider, CD/CA = DE/AB
15/(15 + x) = 7/11
15 * 11 = 7 * (15 + x)
165 = 105 + 7x
7x = 165 - 105
7x = 60
x = 8.58 units
Therefore, the length of AD is 8.58 units
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Given the parent function y=x. Find the equation of a second line that has a negative y intercept and a positive slope.
For the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
What is the slope-intercept form of a line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula y = mx + b. (0, b). The y value of the y-intercept point is represented by b in the formula.
For the given parent function y = x.
Comparing with the slope-intercept form y = mx + c, we get
slope(m) = 1, and the y-intercept is c = 0;
So we can make one line such that it has a negative y-intercept and a positive slope.
y = mx + c, where c < 0 and m > 0.
Hence, for the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
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The velocity v of an object rolled down an inclined plane is given by the formula v= √48d, where d is the distance the object has rolled. Solve the formula for d
d=(Simplify your answer. Use integers or fractions for any numbers in the expression.)
The formula for d is d = v/√48
What is a formula?
In science, a formula is a compact manner of symbolically describing information, such as a mathematical formula or a chemical formula. In physics, the phrase formula refers to the general construct of a connection between given quantities. In mathematics, a formula is an identity that equates one mathematical statement to another, the most significant of which are mathematical theorems. A formula (also known as a well-formed formula) is a logical object that is produced utilizing the symbols and formation rules of a specific logical language. For example, calculating the volume of a sphere necessitates extensive use of integral calculus or its geometrical equivalent, the method of exhaustion.
The equation is given as v= √48d
Hence, the formula for d is, d = v/√48
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Find the value of the expression (3x – 12) – (1/2xy-10) for x = 3 and y = 6.
-2
Answer:
When x = 3, y = 6,
[tex][3(3)- 12]-[(\frac{1}{2}(3)(6)) -10] = (9-12)-(9-10)[/tex]
[tex]= (-3)-(-1)[/tex]
[tex]= -3+1[/tex]
[tex]=-2[/tex]
I would like to be walked through this and see if my answer is correct as well as how to do it
Answer:
perimeter = 16 ft
Step-by-step explanation:
You want the perimeter of an isosceles triangle with side length 5 ft and altitude 4 ft.
Base lengthThe side lengths being equal mean the triangle is isosceles. That also means altitude PS bisects the peak angle and segment QR. Once we find the length QS using the Pythagorean theorem, we can double that measure to find QR.
The Pythagorean theorem tells us ...
QS² +PS² = QP²
QS² +(4 ft)² = (5 ft)²
QS² = (25 ft²) -(16 ft²) = 9 ft² . . . . . evaluate squares, subtract 16 ft²
QS = √(9 ft²) = 3 ft
Now we know the base length is ...
QR = 2·QS = 2(3 ft) = 6 ft
PerimeterThe perimeter is the sum of the outside edge lengths:
Perimeter = PQ +QR +RP
Perimeter = (5 ft) +(6 ft) +(5 ft) = 16 ft
The perimeter of ∆PQR is 16 feet.
__
Additional comment
With some practice, you can learn to recognize a 3-4-5 right triangle. That is the triangle used here for each of the right triangles that make up ∆PQR. Once you identify the long side as 4 and the hypotenuse as 5, you know immediately the short side is 3.
The set {3, 4, 5} is called a "Pythagorean triple." Other triples commonly seen in high school problems are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. Legs of these lengths form a right triangle. Knowing any two (or their ratio) tells you immediately the value of the third. Of course, these triples can be scaled by any factor. (3, 4, 5) scaled by 2 is (6, 8, 10), another commonly seen triple.
There are no isosceles right triangles that have integer values for both the legs and the hypotenuse. If the legs are both 4, the hypotenuse will be 4√2 ≈ 5.657... (an irrational number), not 5.
Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.
The number of candies bought = 10
The number of pretzels bought = 8
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let,
x = number of candies bought
y = number of pretzels bought.
The equations that describe the given problem are:
4.75 x + 3.5 y = 75.50..........(1)
x + y = 18
x = 18 - y.................(2)
Substitute equation 2 in equation 1,
4.75 (18 - y) + 3.5 y = 75.50
85.5-4.75y+3.5y=75.50
85.5-1.25y=75.50
1.25y=85.5-75.50=10
y=8
Substitute y=8 into x = 18 - y.
x=18-8=10
The number of candies bought is 10, and the number of pretzels bought is 8.
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3d ÷ (d*d*d/4c) as one fraction
Answer: (3/4c*d*d)
Step-by-step explanation:
First, get rid of the denominator by multiplying the numerator by it.
so d*d*d*4c*.
Then now its 3d/d*d*d*4c, you can eliminate a d from the numerator and denominator, and now it's (3/4c*d*d)
What is the slope of the function y = -5/4x+1
Answer:-5/4
Step-by-step explanation:
the slope is the number next to the letter X.
Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.
Answer:
x^2(3x-2) cubic inches OR in^3
OR
3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS
-
NOTE: '^' MEANS TO THE POWER OF..
-
Volume = v, abc = 3 sides of cube (height, width, length)
Using the formula for volume in a cube,
[tex]v = abc[/tex]
We can solve this.
If one side is (3x-2)in,
(3x-2)(x)(x) = v.... x are the other two sidesx^2(3x-2) = vx^2(3x-2) cubic inches OR in^3
If all sides are (3x-2)in,
Use the formula,
[tex](a - b) ^{3} = {a}^{3} + 3ab(b - a) - {b}^{3} [/tex]
We can solve this.
(3x-2)(3x-2)(3x-2) = v(3x-2)^3 = v.... 3x = a and -2 = b(3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v27x^3 + 18x(2-3x) -8 = v(27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 83x(9x^2 -18x +12) = v... Take 3 as common again in the brackets3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets3x [ 3 [ 3x (x-2) + 4 ]] - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
___
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___
The difference between a two digit number and the reverse of that number is 18
Answer:
64
Step-by-step explanation:
please help me this is geometry
Answer:
RT
Step-by-step explanation:
Hypotenuse is the greatest and since it is obtuse, it will be even longer.
Answer:
RT is the longest segment.
Step-by-step explanation:
If Angle S is 92°, then AngleR and AngleT are both acute angles. So AngleS is the biggest angle, so the side opposite AngleS is the biggest side. RT is the side opposite from AngleS. RT is the biggest side.
sample Response: The sample is from the right population, his customers. However, because he is surveying such a small number of people and only asking his best customers (who are probably the most satisfied, or they would not buy so much from him), the results are going to be biased, most likely positive, and not representative of his entire customer base.
What did you include in your response? Check all that apply.
The sample size is too small.
Only sending the survey to his best customers will yield biased results, most likely in the positive direction.
The sample is not representative of the entire population.
The thing to include in the response regarding the sampling include:
The sample size is too small.Only sending the survey to his best customers will yield biased results, most likely in the positive direction.The sample is not representative of the entire population.What is sampling?Sampling is the process of selecting the group from which you will collect data for your research. For example, if you want to know what students think at your university, you could survey 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.
The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study.
In this case, the sample size wasn't a true reflection of the customers.
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Louis recorded how many times he could jump rope without stopping. Here is
his data:
50 15 102 64 29 55 100 97 48 81 61
Find the median, upper quartile, and lower quartile of his data.
28 divided by x + 4 = 11
Answer:
x= -16/11
Step-by-step explanation:
hope this helps
Answer: x=4
Step-by-step explanation:
28 divided by x+4=11
28 divided by x=7
28/7=4
what is the smallest number 4.36,4.3,4.06,4.306
Answer: its 4.06
Step-by-step explanation:
For which values of A, B,
and C
will Ax+By = C be a vertical line
through the point (9, 3)?
Answer:
See below
Step-by-step explanation:
A vertical line is just x =
so if a = 1 b = 0 and c = 9 would be a vertical line through the point
so you wind up with x = 9
I don't know whether this line is a negative or positive. The line is crossing the origin and is in the 1 quadrant and 3 quadrant. Please help!!
The given line is positive.
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Given that,
The line is crossing the origin and is in the 1 quadrant and 3 quadrant.
This means, the graph of the line starts at the bottom left and goes towards the top right.
If a line has a positive slope, then y always rises when x rises and always falls when x falls (i.e., m > 0). The line's graph thus begins at the bottom left and moves up to the top right.
So, the given line is positive.
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Joseph had 7 1 4 ounces of candy to share with his friends. He gave them 2 4 5 ounces of candy when they came over to play video games. How many ounces of candy does joseph have left?.
Joseph left 469 ounces of candy, according to the given question.
What do you mean by candy?
A sugar-based confection that frequently contains filling and flavoring: a slice of such a confection is called candy. Something that has a lighthearted or frivolous appeal and visual delights.
According to data in the given question,
We have:
Total ounces of candy = 714
Number of candy he shared = 245
Now, we need to determine the candy he has left,
= Total number of candy - Number of shared candy
= 714 - 245
= 469
Therefore, he left 469 ounces of candy.
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Which set of ordered pairs represents a function?
A. {(1, 7), (8, -9), (1, -2), (-6, -1)\}{(1,7),(8,−9),(1,−2),(−6,−1)}
B. {(9, 0), (7, 9), (3, -4), (3, -6)\}{(9,0),(7,9),(3,−4),(3,−6)}
C. {(-2, -6), (-5, -6), (9, -2), (7, 3)\}{(−2,−6),(−5,−6),(9,−2),(7,3)}
D. {(4, 7), (8, 1), (-6, -1), (-6, -5)\}{(4,7),(8,1),(−6,−1),(−6,−5)}
The set of ordered pairs that is a function is (c) {(-2, -6), (-5, -6), (9, -2), (7, 3)}
How to determine the ordered pair that is a function?The list of options represents the given parameter
As a general rule, for an ordered pair to be a function;
The y values on the ordered pair must point to different x values
In (a) the y values -1 and 7 have the same x value of 1
So, it is not a function
In (b) the y values -4 and -6 have the same x value of 3
So, it is not a function
In (c) all the y values have different x values
So, it is a function
In (d) the y values -5 and -1 have the same x value of -6
So, it is not a function
Hence, the ordered pair that is a function is (c)
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Answer:
The answer would be C. {(-2, -6), (-5, -6), (9, -2), (7, 3)\}{(−2,−6),(−5,−6),(9,−2),(7,3)}
Step-by-step explanation:
a university found that of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals). 0.2061 b. compute the probability that exactly will withdraw (to 4 decimals). 0.2182 c. compute the probability that more than will withdraw (to 4 decimals). 0.5886 d. compute the expected number of withdrawals.
The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Compute the probability that 2 or fewer will withdraw,To determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:Then, multiply this quantity by, = 190Which is the number of ways to choose 2 students from the total of 20. Therefore:The probability that exactly 2 students withdraw is Following an process determine that: The probability that exactly 1 student withdraw is The probability that exactly none students withdraw is Finally, the probability that 2 or fewer students will withdraw is,= 0.355Compute the expected number of withdrawals.Hence ,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.hence,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
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Write an equation that makes it easier to find the number of vertices in an
octahedron, which has 8 faces.
Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.
Given:
Octahedron has 8 faces
Let F be the faces of octahedron
Let V be the vertices of octahedron
we know that:
V + F = 14
Given F = 8 substitute
V + 8 = 14
V = 14 - 8
V = 6
Therefore Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.
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A 13 km stretch of road needs repairs. Workers can repair 3 1/2km of road per week.
How many weeks will it take to repair this stretch of road?
The workers would need 3.71 weeks to repair the road.
A generalization of arithmetic in which letters representing numbers are combined using arithmetic rules
Given that the total length of the road is 13km. Workers can repair 3.50 roads per week.
To determine the number of weeks required to repair the road, divide the total by per week. The equation would be:
13 ÷ 3.5
= (13 x 10)/35
= 130/ 35
= 3.71
Therefore the workers would need 3.71 weeks to repair the road.
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