Answer: The hypotenuse are both 13 cm
Step-by-step explanation:
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, in this case:
c^2 = a^2 + b^2
c^2 = 5^2 + 12^2
c^2 = 25 + 144
c^2 = 169
c = √169
c = 13
So the length of the hypotenuse is 13 cm.
Next, we can use the Pythagorean theorem to find the length of the segments into which the bisector of the right angle divides the hypotenuse. Let's call the length of the segments x. Then, the segments form two right triangles with legs of length x and (13-x)/2.
Using the Pythagorean theorem on each triangle, we have:
x^2 + ((13-x)/2)^2 = 13^2
x^2 + (13-x)^2/4 = 169
x^2 + (13^2 - 2x(13) + x^2)/4 = 169
x^2 + (13^2 - 2x(13))/4 = 169
x^2 + (169 - 26x)/4 = 169
x^2 + 169 - 26x = 676
x^2 - 26x + 507 = 0
Now, we can use the quadratic formula to find x:
x = (-b ± √(b^2 - 4ac)) / 2a
a = 1, b = -26, c = 507
x = (26 ± √(26^2 - 4 * 1 * 507)) / 2 * 1
x = (26 ± √(676)) / 2
x = (26 ± 26) / 2
x = 26 / 2
x = 13
So, the lengths of the segments into which the bisector of the right angle divides the hypotenuse are both 13 cm, to the nearest tenth.
Can someone help me thank you
The value of the fractions will be:
1. 4/10 + 2/10 = 6/10
2. 9 /12 + 3/12 = 1
3. 6/10 + 4/10 = 1
4. 2/8 + 3/8 = 5/8
5. 2/7 + 6/7 = 1 1/7
6. 11/9 + 8/9 = 2 1/9
7. 5/13 + 10/13 = 1 2/13
8. 3/5 + 7/10 = 1 3/10
9. 7/8 + 13/16 = 1 11/16
10. 9/30 + 3/5 = 9/10
How to calculate the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
It should be noted that in order to add the numbers it's essential to have a common denominator. For example, 7/8 + 13/16 will be:
= 7/8 + 13/16
= 14/16 + 13/16
= 27/16
= 1 11/16
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the all time leader in career battling average among major league baseball players is ty cobb with a career average of .366. this means he got a hit in 36.6% of his official at-bats. what was cobb's probability of getting atleast one hit in four official at-bats
The greatest positive integer n such that [tex]$2^n$[/tex]divides k is 18.
The product k can be expressed as [tex]$(b - a)_{1 \le a < b \le 20}$[/tex] . Since [tex]$2$[/tex] is the only even number between [tex]$1$[/tex] and [tex]$20$[/tex], the product can be written as [tex]$(2 - 1)_{1 \le a < b \le 20}$[/tex]. Since the product of [tex]$(b - a)$[/tex] is the same for all pairs of integers a and b that satisfy [tex]$1 \le a < b \le 20$, $k$ is equal to $(2 - 1)^{19}$.[/tex]
To determine the greatest positive integer n such that [tex]$2^n$[/tex]divides k, we need to calculate the largest exponent m such that [tex]$2^m$[/tex] is a factor of [tex]$(2-1)^{19}$[/tex]. To do this, we can factor [tex]$(2-1)^{19}$[/tex] using the equation [tex]$(2-1)^{19} = 2^{19} - 1$[/tex]. This equation can be written as [tex]$2^{19} = (2-1)^{19} + 1$[/tex], which can be rewritten as [tex]$2^n(2^{19-n}+1) = (2-1)^{19}$[/tex] for any positive integer n. Since the factor [tex]$(2-1)^{19}$[/tex] is odd, the greatest positive integer n such that [tex]$2^n$[/tex] divides k is 18, since [tex]$2^{19}$[/tex] is the greatest power of 2 that divides [tex]$(2-1)^{19}$.[/tex]
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The relationship between t, a student’s test scores, and d, the student’s success in college, is modeled by the equation d = 0.48t + 75.2. Based on this linear regression model, the correlation coefficient could be?
Based on the linear regression model, the correlation coefficient would be; between 0 and 1
How to find the Correlation Coefficient?The correlation coefficient is defined as a statistical measure of the strength of a linear relationship between two variables.
Now, In positively correlated variables, the value increases or decreases in tandem. In negatively correlated variables, the value of one increases as the value of the other decreases.
Correlation coefficients are expressed as values between +1 and -1. A coefficient of +1 indicates a perfect positive correlation. A coefficient of -1 indicates a perfect negative correlation
In this case, the slope is positive which is 0.48 and as such we can say that it has positive correlation and as a result the correlation coefficient will be between 0 and 1.
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what is the equation for a line that passes through the point (8,-1) and is parallel to the line that passes through points (-2,2) and (6,6)
Answer:y=2x-15
Step-by-step explanation:
First, we find the slope of the first line
Slope equation:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Plug-in values
[tex]\frac{6-2}{6-(-2)}[/tex]
=[tex]\frac{4}{8}[/tex]=[tex]\frac{1}{2}[/tex]
Slope=1/2
Remember that parallel lines have the same slope.
Now, we use the slope to get the y-intercept.
We start from (8,-1)
We go up 1 (rise) and right 2 (run), or the opposite of the slope (-1 rise, -2 run).
We get a y-intercept of -5.
Plug into y=mx+b
y=1/2x-5
If x1 and x2 are solutions to 3x^2+15x+9=0 quadratic equation, then
x1*x2 =
Answer:
x₁ × x₂ = 3
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 (a ≠ 0 )
then the product of the roots = [tex]\frac{c}{a}[/tex]
3x² + 15x + 9 = 0 ← is in standard form
with a = 3 and c = 9 , then
x₁ × x₂ = [tex]\frac{9}{3}[/tex] = 3
divide a by 2 in algebraic expression
Answer: a/2
I believe for this problem all they’re asking is how you would write the expression.
If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T
Answer:
2½ years
Step-by-step explanation:
I =PxRxT
$625=$5000 x 5/100 x T
$ 625= $250 T
625/250=T
T = 2.5
I am smaller than 70. I am a common multiple of 12 and 15. Who am I?
The number is 60.
What are Multiples?A multiple is defined as the the number resulting form the process of multiplication of two numbers.
For example, 6 is a multiple of 2 and 3 since 2 × 3 = 6.
Let x be the number.
x < 70
Multiples of 12 less than 70 = 12, 24, 36, 48, 60
Multiples of 15 less than 70 = 15, 30, 45, 60
Multiple common to 12 and 15 = 60
Hence the number here is 60.
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Lesson 25: Geometric interpretation of the solutions of a linear system
Answer:
h
Step-by-step explanation:
d
how many seating arrangements are possible if fred (a boy) and carrie (a girl) must be seated next to each other?
(n-1) x (n-2)! ways of seating arrangements are possible if Fred (a boy) and Carrie (a girl) must be seated next to each other.
A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.
Let's say there are n seats in total.
Then, there are (n-1) gaps between the seats that Fred and Carrie can be placed in.
If we place Fred and Carrie in one of these gaps, there will be (n-2)! possible arrangements for the rest of the seats.
Therefore, there will be (n-1) x (n-2)! total possible seating arrangements for Fred and Carrie if they must be seated next to each other.
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Pleeeeeeeeeeeaaaaaaaaaaase help me soon
Answer:
third choice in image. √(16³)
the squareroot of 16 to the third power
Step-by-step explanation:
Fractional exponents tell you that you have roots. Could be squareroot or thirdroot, fourth root, fifth root...etc. You know which because you look at the bottom number (denominator) of the fraction. I use the phrase "down and out" to help remember that the bottom number in the fractional exponent is the "outside number" (index) on the radical sign.
The top number (numerator) of the fraction is an exponent. It can be either inside the radical right there on the shoulder of the 16 or it could also be outside the whole entire radical.
16^ (3/2) = √(16³) = (√16)³
the value of the series $4 4x 4x^2 4x^3 \cdots$ is a real number greater than $8$. find all possible values of $x$, giving your answer in interval notation.
The possible values for the given series, the interval notation will be calculated as follows:
Sn is the sum of a geometric series, and a1/(1-r).
R = x a1 = 4 in this mathematical sequence.
If you want the sum to be higher than 8, enter:.
r cannot equal 1 (the equation would have 0 in the denominator) and it cannot be GREATER than one. 8 1/2 Interval notation: (1/2, 1). We must limit it to 1. as the series becomes divergent and lacks a sum if it does.
Interval arithmetic is a general numerical computing technique that automatically generates guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and arithmetic roundoff. Intervals are at the center of this technique.
The definition of intervals also applies to arbitrary totally ordered sets, such as integers or rational numbers. In the special section that follows, the notation of integer intervals is discussed.
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Note that the full question is:
The value of the series 4+4x+4x^2+4x^3... is a real number greater than 8. Find all possible values of x, giving your answer in interval notation.
Find 1+ 1/2+1/6+1/12 , where we alternately multiply by 1/2 and 1/3 to get the next term.
In a certain infinite geometric series, the first term is 1, and each term is equal to the sum of the two terms after it. (For example, the first term is equal to the sum of the second term and third term). If s is the sum of the series and r is the common ratio, find s - r.
Which measurement is equivalent to 1/2 gallon?
8 pints
16 cups
128 fl. oz.
2 quarts
Answer:
the answer is 128 fluid ounce
Step-by-step explanation:
from a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 4.9 hours with a standard deviation of 0.35 hours. what is the 95% confidence interval for the amount of time spent on personal issues?
The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).
Mean time that employees spend on personal issues each week(M) = 4.9 hours
Standard deviation = 0.35 hours
The following formula is used to get the confidence interval for the sample mean and standard deviation given:
μ = M ± t(sM)
where; M = sample mean
t = T-statistic based on confidence interval
Degree of freedom = n - 1
From the question, n = 55
Degree of freedom = 55 - 1
Degree of freedom = 54
(Standard errors)sM = √(s^2/n)
Now putting the value
sM = √(0.352/55)
sM = 0.05
t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)
Now the confidence interval
μ = M ± t(sM)
μ = 4.9 ± 2.005 × 0.05
μ = 4.9 ± 0.095
μ = (4.9 - 0.095, 4.9 + 0.095)
μ = (4.805, 4.95)
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plssssssssssssssssssssssssss
Answer:
C
Step-by-step explanation:
you can use the website desmos and literally type the exact equations in and it will show the graph.
Number 8 please will give brainliest
Answer: X= 90
Step-by-step explanation:
There is a 90-degree symbol. So I think X= 90.
Thank you
a certain identification number is a sequence of seven digits. (a) how many identification numbers are possible? numbers
The answer is A) 10,000,000 seven-digit numbers; B) The number is 20,000 ; C) 5,314,410 identification numbers are possible if no two adjacent digits are the same.
Seven-digit identification number:
A.) The number of possible identifying numbers
Possible digits are 0 up to 9.
Total number of digits: 10
Any of the 10 digits may be used for each;
Hence,
10×10×10×10×10×10×10 equals 10,000,000 potential outcomes.
B.) For it to start begin with either 023 and 003.
- the first digit must be 0 (1 possible value)
- 2nd digit must be 2 or 0 (2 possible values)
- 3rd digit must be 3 (1 possible value)
- 4th and 5th can be filled with any digit (10 × 10 possible values)
Which gives
1×2×1×10×10×10×10 = 20,000
3.) no two adjacent digits are the same that is no two digits that follows each other are the same.
In this case only one digit have 10 possible values.
The other four digits have 9 possible values each.
Which gives:
10×9×9×9×9×9×9 = 10× [tex]9^{6}[/tex] = 5,314,410
The full question:
A certain identification number is a sequence of seven digits. (a) How many identification numbers are possible? (b) How many of them begin with either 023 or 003? (c) How many identification numbers are possible if no two adjacent digits are the same? (For example, 123-4-567 is permitted, but not 123-3-456.).
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The regulations of a paper airplane contest state that any paper airplane in the shape of a trapezoid must be an isosceles trapezoid th
software to sketch a trapezoid, as shown.
Not to scale
The measurement of each diagonal is;
i. DB = 23.32 inches
ii. RY = 25.05 inches
What is a diagonal?A diagonal is a line drawn from one edge of a shape to another, which divides it into two equal shapes produced. Thus a diagonal is not the same as the line of symmetry.
NB: A shape may have more than one diagonal.
In the given question, we can apply Pythagoras theorem to have;
i. From triangle DHB,
/Hyp/^2 = /Opp/^2 + /Adj/^2
DB^2 = DH^2 + HB^2
= 20^2 + 12^2
= 400 + 144
DB^2 = 544
DB = (544)^1/2
= 23.324
DB = 23.32 inches
ii. From triangle HKR,
/Hyp/^2 = /Opp/^2 + /Adj/^2
KR^2 = HR^2 + HK^2
= 16^2 + (8.72)^2
= 256 + 76.0384
KR^2 = 332.0384
KR = (332.0384)^1/2
= 18.2219
KR = 18.22
but,
YR = YK + KR
= 6.83 + 18.22
= 25.05
YR = 25.05 inches
The measurement of the diagonals are: DB = 23.32 inches, and RY = 25.05 inches.
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Madelyn's office recycled a total of 21 kilograms of paper over 3 weeks. After 4 weeks, how many kilograms of paper will Madelyn's office have recycled? Solve using unit rates.
The quantity of kilograms of paper that Madelyn's office would have recycled after 4 weeks would be = 28kg
How to calculate the quantity of recycled paper?The recycling activities of Madelyn's office in weeks is listed below:
The total quantity of paper recycled for 3 weeks = 21 kg
Then, after 4 weeks would be = xkg
To calculate the unit rate is to find out the quantity recycled per week;
That is,
3 weeks = 21 kg
1 week = X
Make X the subject of formula;
X = 21/3
X= 7 kg
Then if 7 kg = 1 week
X kg = 4weeks
X kg = 7×4/1
= 28 Kilograms
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Which expression is NOT equal to 125?
Answer:
A
Step-by-step explanation:
the cost , where is the number of miles driven, of renting a car for a day is $42 plus $0.65 per mile. what is the slope of the linear function and its units?
A linear function is a mathematical function that defines a straight line when plotted on a coordinate plane.
It is defined by an equation of the form:
[tex]$y = mx + b$[/tex]
where [tex]$y$[/tex] is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope of the line is the rate at which the dependent variable changes with respect to the independent variable. In other words, it represents how much the dependent variable will change for each unit change in the independent variable.
In the case of the cost of renting a car for a day, the dependent variable is the cost (C) and the independent variable is the number of miles driven (x). The equation for the cost is:
[tex]$C = 42 + 0.65x$[/tex]
The slope of the line is 0.65, which means that for each additional mile driven, the cost of renting the car will increase by $0.65. The units of the slope are dollars per mile, since it represents the additional cost per mile driven.
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describe all solutions of ax =0 in parametric vector form, where a is row equivalent to the given matrix.1 3 -3 70 1 -4 5
A general solution of matrix to the system Ax = 0 in parametric vector form is given by: X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]
How to find all solutions of Ax = 0 in parametric vector form?
The matrix [2 -1 -4 2 6 -3] can be row-reduced to the row-echelon form [2 -1 -4 0 6 -9], which has a pivot in the first, second and fourth columns. This implies that the columns with zero entries in the row-echelon form correspond to free variables in the solution.
Since there are two free variables in the row-echelon form, the solution to the homogeneous linear system Ax = 0 will be in the form of a parametric vector, where X_2 and X_3 are the free variables and X_1, X_4, and X_5 are expressed in terms of X_2 and X_3.
A general solution to the system Ax = 0 in parametric vector form is given by the matrix
X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]
where X_2 and X_3 are arbitrary constants. This represents a two-dimensional subspace in R^5, which consists of all linear combinations of the two linearly independent vectors [1 0 1 0 0] and [0 1 0 1 0].
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In the expression, 5g3+2, which of the following is a constant? Responses
The constant term for the expression 5g³ + 2 is 2.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given the expression,
5g³ + 2,
a linear equation consists of three terms,
variables, coefficient of variables, and constant.
A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Compared with the given expression,
g is the variable and 5 is the coefficient,
2 is the constant term.
Hence 2 is constant.
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In this regular pentagon, all of the exterior
angles marked f are the same size.
Find the value of f.
Give your answer in degrees (°).
The value of f in the pentagon is 72 degrees.
How to find the angles of a pentagon?A pentagon is a polygon with 5 sides. A regular pentagon is a polygon with 5 sides equal to each other. Therefore, In the regular pentagon, all of the exterior angles marked f are the same size.
Let's find the value of f as follows:
Therefore, the sum of exterior angles of a pentagon is 360 degrees.
Hence,
5f = 360 degrees
divide both sides of the equation by 5
5f / 5 = 360 / 5
f = 72 degrees
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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by 14% per day. Determine the mass of the radioactive sample at the beginning of the 11th day of the experiment.
Answer:
At the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.
Step-by-step explanation:
Let's call the mass of the substance after n days "m". We can calculate the mass for each day using the formula:
m = 1300 * (1 - 0.14)^n
Plugging in n = 11:
m = 1300 * (1 - 0.14)^11
m = 1300 * 0.15572634
m = 201.87 grams
So at the beginning of the 11th day, the mass of the radioactive sample was 201.87 grams.
Help help help please help with the question
Answer: I think the answer is A
Step-by-step explanation: It goes from 128 to 150.
9) show ur equation steps
The system of equations has one solution, it is (-3,-5)
How to solve the system of equations?Here we have the system of equations:
y = -8x - 29
y = 7x + 16
Because y is isolated in both of the equations, we can write:
-8x - 29 = 7x + 16
-29 - 16 = 7x + 8x
-45 = 15x
-45/15 = x
-3 = x
And the value of y is what we get when we evaluate one of the equations in x = -3
y = 7x + 16 = 7*(-3) + 16
= -21 + 16 = -5
The solution is (-3, -5)
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edge joy a question asks: how many steps per day do you walk? what would be the best numerical summary of data from 288 participants' answers about the number of steps per day they walked?
The best numerical summary of data from 288 participants' answers about the number of steps per day they walked would be a combination of median, IQR, and range (B) and number and percent of the total for each response option (C). Hence, option E is the correct answer.
The median represents the middle value of the data set and is not affected by outliers. The IQR (interquartile range) represents the spread of the middle 50% of the data and is a good indicator of variability.
The range represents the difference between the maximum and minimum values in the data set and gives a good idea of the overall variability of the data.
The number and percent of the total for each response option will give an idea of the distribution of the sample and show the frequency of each response.
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The complete question is -
edge joy a question asks: how many steps per day do you walk? what would be the best numerical summary of data from 288 participants' answers about the number of steps per day they walked?
a. mean, standard deviation, and range.
b. median, IQR, and range.
c. Number and percent of the total for each response option.
d. A or B depending on the distribution of the sample.
e. B and C.
An outlier in a data set can significantly affect the value of the mean but not the median.a. Trueb. False
True. An outlier in a data set can significantly affect the value of the mean but not the median.
This is because the median is the middle value in a data set and is not affected by extreme values, while the mean is calculated by adding all the data values and then dividing by the total number of values, which can be significantly affected by extreme values or outliers.
To illustrate this, let's consider the data set {1, 2, 3, 4, 1000}. The median value of this data set is 3, since that is the middle value. The mean of this data set is 205, since it is calculated by adding all the values (1+2+3+4+1000) and dividing by the total number of values (5). The outlier value of 1000 has a significant effect on the mean, changing it from an average of 3.2 (1+2+3+4/4) to an average of 205 (1+2+3+4+1000/5). The median, however, remains unchanged (3). Therefore, it can be concluded that an outlier in a data set can significantly affect the value of the mean but not the median.
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Josiah and Katya are asked to build an accessibility ramp to a building. josiah suggests a triangle with side lengths 6, 8, and 10. katya suggets a triangle with side lengths 4, 9, and 12. which ramp creates a right triangle?