If in a triangle ABC, right angle is at C, BA is hypotenuse, the length of side BC is 5√7 units.
In a right triangle, the hypotenuse is the longest side and is opposite the right angle. Therefore, in triangle ABC, side BA is the longest side, and it is also the hypotenuse.
Using the Pythagorean theorem, we can find the length of the third side BC. The theorem states that the square of the hypotenuse (BA²) is equal to the sum of the squares of the other two sides (BC² + CA²).
BA² = BC² + CA²
16² = BC² + 9²
256 = BC² + 81
BC² = 256 - 81
BC² = 175
BC = √175
BC = 5√7
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At a middle school, 3 out of 4 students ride a bus to school. There are 600 studenta at the school. How many students ride a bus to school
Answer:
450 students ride a bus to school.
Step-by-step explanation:
If 3 out of 4 middle school students attend class by bus, it could be stated that 75% of the students use this means of transport to get to class (3/4 = 0.75).
Therefore, if this school has a total of 600 students, and 75% of them use the bus, it could be stated that 450 students attend school using this means of transport (600 x 75/100 = 450).
Answer:
450 students
Step-by-step explanation:
1/4 = 0.25
3/4 = 0.75
600 x 0.75 = 450 students
Hope this helps!
Help please
Driving on the highway, you can safely drive 70 miles per hour. Which of the following functions could be used to find how far you can drive in ‘h’ hours?
A.) D= 70/h. B.) D=70h. C.)h/70. D.)70+h
Answer:
B
Step-by-step explanation:
How much money would you have to invest at 9% compounded semiannually so that the total investment has a value of $2,090 after one year?
Answer:
Im just doing this for points .,.
Step-by-step explanation:
Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−15, 3), (−15, −6), and (25, −6)?
(−6, 25)
(−25, −3)
(6, −25)
(25, 3)
The missing fourth vertex needed to create a rectangle is (25, 3) option D.
Define the term vertices?Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.
Here, the width of one side of the rectangle;
⇒ +3 - (-6) = 9 unit (left side y-coordinates)
Similarly the length of the rectangle;
⇒ 25 - (-15) = 40 unit (up-side x-coordinates)
Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)
So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:
⇒ (25, -6+9) = (25, 3)
⇒ (-15+40, 3) = (25, 3)
Therefore, the missing fourth vertex is (25, 3)
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what is the standard notation of 5.8x10²
Move the decimal point to the right 2 places:
\(5.8\times10^2=580\)Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
1+2i, 1+√5
The other zeros are
(Use a comma to separate answers.)
Answer:
The other zeros are:
1 - 2i, 1 - √5
O. A water jug is filled with 128 fluid ounces. Anna
pours out 3 pints of liquid from the jug. How
many pints remain?
A. 5 pints
B. 6 pints
C. 8 pints
D.
11 pints
Answer:11
Step-by-step explanation:
what is the approximate solution of the linear system represented by the graph below
The approximate solution of the linear system represented by the graph is, (5, 6)
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Given that,
A graph in which two lines are intersecting each other,
basically solution of linear system means where both the lines will intersect,
So, in the graph it can be seen that lines are intersecting around x coordinate 5 and y coordinate 6,
Therefore, the solution is (5, 6)
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Pls help step by step (special right triangles)
Value of base and hypotenuse of triangle are 9√3 and 18 respectively.
Define right triangleA right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem, that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Height of triangle=9
Base of triangle=y
Hypotenuse of triangle=x
Using trigonometric ratio
Sin30°=Height/Hypotenuse
½=9/x
x=18
Cos30°=Base/hypotenuse
√3/2=y/18
y=9√3
Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.
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Consider a function f defined as follows: f(x)=(x-3)^2, x belongs to [1,2]. Is f invertible in the domain [1,2]? If yes, find the inverse of the function.
(Looking for an complete explanation on how to prove invertible, probably by showing the function is one-to-one and then determining the inverse. )
The inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
What is a function?A relation is a function if it has only One y-value for each x-value.
Let us consider the function f(x)=(x-3)²
Where x belongs to [1, 2]
f(x)=x²+9-6x
y=x²+9-6x
Interchange the variables.
x=y²+9-6y
y=3+√18+x
y=3-√18+x
Relace y with f⁻¹(x)
f⁻¹(x)=3+√18+x, 3-√18+x
Hence, the inverse of the function is f⁻¹(x)=3+√18+x, 3-√18+x
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Find a value for x that makes the equation true.f. -0.5x + 1.1 = -2.9
ANSWER
x = 8
EXPLANATION
We have to find the value of x for which:
-0.5x + 1.1 = -2.9
To do this, first we have to collect like terms:
-0.5x = -2.9 - 1.1
=> -0.5x = -4.0
Divide through by -0.5:
=> x = -4.0 / -0.5
x = 8
That is the value of x.
What is the length of the line segment JK?
Donna DePaul is raising money for the homeless. She discovers that every church group requires two hours of letter writing and one hour follow up while every labor union. She needs two hours of letter writing in three hours to follow up. Donna can raise $125 from each church group and $200 from each union local and she has a maximum of 20 hours of letter writing in a box mama 14 hours a follow up available per month determine the most profitable mixture of groups she should contact in the most money she can raise in a month.
a) 2 letters to church and 4 letters to union
b) $ 1000
what is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given data:
Letter writing time for church = 2 hours
Follow up required for church = 1 hour
Letter writing time for labor union = 2 hours
Follow up required for labor union = 3 hour
Funds from church = $ 100
Funds from union = $ 200
now, let 'x' be the number of letters written to church
and let 'y' be the number of letters written to labor union
According to the given conditions
maximum timing for letter writing = 12 hours
So,
2x + 2y ≤ 12 hours
x + y ≤ 6 hours
Now, maximum time for follow up = 14 hours
1x + 3y ≤ 14 hours
on solving the both the equations
x + y = 6
- ( 1x + 3y = 14 )
----------------------
0 - 2y = -8
y = 4 hours
and, x + 4 = 6
x = 2
Now,
money raised = (2 × $ 100) + (4 × $ 200)
= $ 1000
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Can someone help plsss it’s due in 2 days
Answer:
20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
10% of 200 is 20 :)
HELP PLEASE!!
NEED ANSWER ASAP!!!
A farmer in China discovers a mammal
hide that contains 54% of its original
Find age of the mammal hide to the nearest year.
amount of C-14
N=N0e^-kt
N = Noe
No = inital amount of C-14 (at time t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
6163.2 years
Step-by-step explanation:
A_t=A_0e^{-kt}
Where
A_t=Amount of C 14 after “t” year
A_0= Initial Amount
t= No. of years
k=constant
In our problem we are given that A_t is 54% that is if A_0=1 , A_t=0.54
Also , k=0.0001
We have to find t=?
Let us substitute these values in the formula
0.54=1* e^{-0.0001t}
Taking log on both sides to the base 10 we get
log 0.54=log e^{-0.0001t}
-0.267606 = -0.0001t*log e
-0.267606 = -0.0001t*0.4342
t=\frac{-0.267606}{-0.0001*0.4342}
t=6163.20
t=6163.20 years
PLEASE MARK BRAINLY
HELP WITH C
5mph buffer what is the new function and graph?
The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The coordinate points from the graph are (10, 550) and (30, 200).
Here, slope = (200-550)(30-10)
= -350/20
= -35/2
= -17.5
Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get
550=-17.5(10)+c
c=550+175
c=725
So, the equation is y= -17.5x+725
Thus, f(n)= -17.5n+725
a) The fine at every speed should go up by $10.
So, the coordinates are (10, 560) and (30, 210)
New slope (m)= (210-560)(30-10)
= -350/20
= -35/2
= -17.5
Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get
560=-17.5(10)+c
c=550+175
c=735
So, the equation is y= -17.5x+735
Thus, f(n)= -17.5n+735
b) The fine at every speed should be doubled in construction zones.
So, the coordinates are (20, 550) and (60, 200)
New slope (m)= (200-550)(60-20)
= -350/40
= -8.75
Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get
550=-8.75(10)+c
c=550+87.5
c=637.5
So, the equation is y= -8.75x+637.5
Thus, f(n)= -8.75n+637.5
Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.
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Jenna worked at an ice cream shop for 4.5 hours on Friday and 5.5 hours on Saturday. She made a total of $77.50. How much does Jenna get paid per hour?
Answer:
$7.75 per hour
Step-by-step explanation:
Write 13/3
as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answer:
4.333...
Step-by-step explanation:
There is a group of five children, where two of the children are twins. How many ways can I distribute 16 identical pieces of candy to the children, if the twins must get an equal amount of candy?
Answer:
you give 1 1/5 to each child?
How much would 3 computers, 6printers, and 30 cd’s cost ?
The total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.
What is cost?Cost is the amount of money that must be paid for goods or services. It can refer to the price of a single item, the total expense of a purchase, or the amount of money paid for a particular service. Cost is an important factor in calculations such as profit, budgeting, and pricing. It is also a factor in determining the value of goods and services when comparing different providers.
The total cost of 3 computers, 6 printers, and 30 CD's would depend on the type of products you are looking to purchase. Computers will vary in price depending on the make and model, as well as the features included. For example, a basic laptop might cost anywhere from $200 to $400, while a high-end gaming laptop could cost upwards of $2,000. Similarly, printers also vary in price depending on the features and type, ranging from $50 to $500. CDs can cost anywhere from $0.50 to $7.00 each, depending on the type and quality.
Therefore, the total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.
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Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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BOOMER GENERATION: At 84%, Boomers are the highest amongst all the generations that want to shop in-store. In a sample size of 75 people in the Boomer Generation, estimate how many of them prefer to shop in-store.
In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.
What is proportion?Proportion shows the relative number of objects or people in the whole.
Proportions are ratios equated to each other.
They are expressed as fractional values, in decimals, percentages, and fractions.
The percentage of Boomers who want to shop in-store = 84%
The sample size of the Boomer Generation = 75
The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)
Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.
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60 is 20 percent more than what number
PLEASE GIVE BRAINLIEST :)
Answer:
50
Step-by-step explanation:
If 60 is 20% more than x, then we can write it as:
x + 0.2x = 60
Simplifying the left side:
1.2x = 60
Dividing both sides by 1.2:
x = 50
Therefore, 60 is 20% more than 50.
fill in the blanks to find x line ab is a straight line(Please show your work)
Statement Reason
1. m<AOB = 180 degrees Angle on a straight line
2. m<AOE + m<EOF + m<FOB = m<AOB supplementary angles
3. x + 2x + 34° + 20° = 180 degrees Substitution
4. x = 42 degrees Algebra
How to solve for the missing angle xx + 2x + 34° + 20° = 180 degrees - supplementary angles
3x + 54 = 180
3x = 180 - 54
3x = 126
x = 126 / 3
x = 42 degrees
What is angle on a straight line?
This refers to angle formed by a straight line which is equal to 180 degrees.
What are supplementary angles?
This refers to angles whose sum is equal to 180 degrees. Sum of angles on a point on a straight line is equal to 180 degrees
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The starting salaries of individuals with an undergraduate degree from UC Riverside are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000?
Answer:
The probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000 is 0.7699.
Step-by-step explanation:
Let X denote the starting salaries of individuals with an undergraduate degree from UC Riverside.
It is provided that, \(X\sim N(\$40,000,\ \$5,000^{2})\)
Compute the value of P (34000 < X < 46000) as follows:
\(P (34000 < X < 46000)=P(\frac{34000-40000}{5000}<\frac{X-\mu}{\sigma}<\frac{46000-40000}{5000})\\\\=P(-1.2<Z<1.2)\\\\=P(Z<1.2)-P(Z<-1.2)\\\\=0.88493-0.11507\\\\=0.76986\\\\\approx 0.7699\)
Thus, the probability that a randomly selected individual with an undergraduate degree from UC Riverside will have a starting salary of $34,000 to $46,000 is 0.7699.
During a snowstorm, the temperature drops from 0°F to -8°F in 2 hours. On
average, by how many degrees is the temperature changing per hour?
A. -8°F
B. 10°F
C. -6°F
D. -4°F
Help pls no links :()
Answer: D. -4F
Step-by-step explanation:
Let's use simple math. 1 - 5 = -4 or -8 divided by 2 = -4, right?
Same idea, so now lets apply it.
If it decreases -8F in only two hours you just simply divide the temperature by the hour.
Looking at problem A that just would not make sense, how could it decrease while staying at the same number?
Problem B also wouldn't make sense because a negitive plus negitive equals a negitive, same with subtracting. So 10 is inncorrect
Problem C also is inncorrect because 8 divided by 2 = 4, not 6
So, D is correct because -8 divided by 2 equals = -4
Hope this helps!
A company that makes cartons finds that the probability of producing a carton with a puncture is 0.03, the probability that a carton has a smashed corner is 0.08, and the probability that a carton has a puncture and has a smashed corner is 0.002. Answer parts (a) and (b) below. (a) Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive? Explain. A. No, a carton cannot have a puncture and a smashed corner. B. No, a carton can have a puncture and a smashed corner. Your answer is correct.C. Yes, a carton cannot have a puncture and a smashed corner. D. Yes, a carton can have a puncture and a smashed corner. (b) If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner. The probability that a carton has a puncture or a smashed corner is nothing.
Answer:
(a) Having a smashed corner need to now not depend on whether or not the carton had a puncture or not,
so these occasions have to be independent.
One manner to check it the usage of the given probabilities:
If P(A)P(B) = P(A and B), then the events are independent.
Here we have : (0.05)(0.08) which is 0.004, that is P(A and B), so the events are independent.
(b) P(A or B) = P(A)+P(B)-P(A and B) = 0.05 + 0.08 – 0.004 = 0.126
Step-by-step explanation:
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Janet wants to purchase a new car. At the car dealership, a salesperson tells her she can choose from 10 car models, 7 exterior
colors, and 9 interior colors.
How many ways can Janet customize a car? Enter your answer as a whole number, like this: 425
evious
Janet has 630 options to customize a car based on the given features.
How to solve the question?
To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:
10 car models x 7 exterior colors x 9 interior colors = 630
Thus, Janet has 630 options to customize a car based on the given features.
It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.
Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.
In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.
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f(x)=2|5x+7|−1, evaluate f(−4)
Answer:
Step-by-step explanation:
f(x) = 2 |5(-4)+7| -1
= 2 |(-20)+7| -1
= 2 | -13 | -1
= 26 - 1
= 25
A function assigns the value of each element of one set to the other specific element of another set. The value of the function f(-4) is 25.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The value of f(-4) can be evaluated by substituting the value of x as -4 in the given function, therefore, the value of f(-4) can be written as,
f(x) = 2|5x+7| − 1
f(-4) = 2|5(-4)+7| − 1
= 2|-20 + 7| - 1
= 2|-13| - 1
= 2(13) - 1
= 26 - 1
= 25
Hence, the value of the function f(-4) is 25.
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Bonnie has 3 rolls of wallpaper border. Each roll has 10 4/5 feet she will need 40 1/3 of border. how much more border does she need?