Step-by-step explanation:
Here,
No. Of total =600
Let,
no. Of boy=3x
no. Of girls = 5x
By the question,
Number of boys and number oof girls =600
or,3x +5x=600
or, 8x =600
or, x= 600/8
or, x= 75
Again,
No. Of boys =3x
Or, 3 * 75
=225
No. Of girls = 5x
Or, 5 * 75
= 375
A line goes through the point (−4, 1) and goes through the origin. Which of the following is the correct equation of the line?
y= -4x
y= 4x
y= -1/4x
y= -1/4x+1
y= x-4
Find the values of a and b such that x² + 2x - 7 = ( x + a )² + b
Answer:
a = 1 ; b = - 8
Step-by-step explanation:
x² + 2x - 7 = (x² + 2x + 1) - 1 - 7 = (x + 1)² - 8
a = 1
b = - 8
Answer:
a = 1 , b = -8
Step-by-step explanation:
(x+1)^2 = x^2+2x+1
x^2+2x+1-8 = x^2+2x-7
Kinsley went rock climbing at red river gorge at noon she was at an elevation of 76 feet then she climbed 28 feet higher to reach the peak what was kinsley elevation at the peak
Answer:
104 feet
Step-by-step explanation:
Answer:
104
Step-by-step explanation:
6 Use the Distributive Property to simplify.
7(x-3)
Answer:
7x-21
Solution:
7 times x and 7 times negative 3
Answer:
[tex]\huge\boxed{\sf{7x-21}}[/tex]
Step-by-step explanation:
Hello.
The Distributive property states that
a(b+c)=ab+ac
Where
a, b, and c = variables/constants
Now, simplify the expression:
7(x-3)
Multiply x and 3 times 7 and subtract the products:
7x-21
I hope it helps & have an outstanding day.
[tex]\boxed{imperturbability}[/tex]
HELP ME ASAP!!
Write a rule for the nth term of the geometric sequence using the given information: a1= 5 and r=2
Answer:
[tex] \huge A (n) = 5 ({2})^{n - 1} \\ [/tex]
Step-by-step explanation:
The nth term of a geometric sequence is given by
[tex]A(n) = a _ 1( {r})^{n - 1} [/tex]
a1 is the first term
r is the common ratio
From the question we have the final answer as
[tex]A (n) = 5 ({2})^{n - 1} [/tex]
Hope this helps you
Rhombus ABCD has the following vertices:
A(-8,11)
B(-1, -13)
C(14,7)
D(7,31)
Is rhombus ABCD a square, and why?
Answer: No because BC is not perpendicular to AB.
Step-by-step explanation:
Yes, rhombus ABCD is a square as all four angles of the rhombus are right angles.
A square is a special type of rhombus where all four sides have the same length and all four angles are right angles.
In this case, we can see that all four sides of the rhombus have the same length by calculating the distance between each pair of vertices. For example, the distance between A and B is:
distance = [tex]\sqrt{[/tex] [tex]((-8 - (-1))^2[/tex] + [tex](11 - (-13))^2[/tex])
distance = [tex]\sqrt{[/tex] ([tex]7^2[/tex] + [tex]24^2[/tex])
distance = [tex]\sqrt{[/tex] (625) = 25
The distance between each other pair of vertices is also 25, so all four sides of the rhombus have the same length.
We can also see that all four angles of the rhombus are right angles by calculating the angles between each pair of adjacent sides. For example, the angle between sides AB and BC is:
angle = arctan((13 - (-13))/(-8 - (-1)))
angle = arctan(26/7)
angle = 78.6°
The angle between each other pair of adjacent sides is also 78.6°, so all four angles of the rhombus are right angles.
Therefore, rhombus ABCD is a square.
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GIVING BRAINLIESTT!!!!!!
Answer:
136
Step-by-step explanation:
the two base pairs angles add up to equal 44
subtract 44 from 180 to get the missing angle
you get 136
Answer:
c
Step-by-step explanation:
Solve 8^(x+2)=5 by taking logs of both sides. Please write a step by step guide.
Answer: x=−1.226024
Step-by-step explanation: Let's solve your equation step-by-step.
8x+2=5
Solve Exponent.
8x+2=5
log(8x+2)=log(5)(Take log of both sides)
(x+2)*(log(8))=log(5)
x+2=
log(5)
log(8)
x+2=0.773976
x+2−2=0.773976−2(Subtract 2 from both sides)
x=−1.226024
Do dis pls and don’t be toxic and take points
According to the National Telecommunication and Information Administration, 51% of U.S. households had Internet access in 2001.
a. If we select four U.S. households at random (with replacement), what is the probability that all four had Internet access in 2001?
b. What is the probability that at least one of four randomly selected U.S. households had Internet access in 2001?
Answer:
a
[tex]P(X = 4 ) = 0.0677 [/tex]
b
[tex]P(X \ge 1 ) = 0.9424 [/tex]
Step-by-step explanation:
From the question we are told that
The probability of a US household having an internet access in 2001 is p = 0.51
The sample size is n = 4
Generally the distribution of the number of US household with internet access at 2001 follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that all four had Internet access in 2001 is mathematically represented as
[tex]P(X = 4 ) = ^{4}C_4 * (0.51)^4 (1- 0.51)^{4-4}[/tex]
=> [tex]P(X = 4 ) = 0.0677 [/tex]
Generally the probability that at least one of four randomly selected U.S. households had Internet access in 2001 is mathematically represented as
[tex]P(X \ge 1 ) = 1 - P(X < 1 ) = 1- P(X = 0 )[/tex]
=> [tex]P(X \ge 1 ) = 1- [^{4}C_0 * (0.51 )^0 * (1- 0.51 )^{4-0 } ][/tex]
=> [tex]P(X \ge 1 ) = 1- [1 * 1 * (0.49 )^{4 } ][/tex]
=> [tex]P(X \ge 1 ) = 0.9424 [/tex]
Khalid purchases flower bulbs from a catalog for 2$ each, plus a 4$ shipping charge for the entire order. He spends $20 on flower bulbs. Which model can be used to determine the number of bulbs Khalid can order?
Answer:
n,mjnj,nj,n
Step-by-step explanation:
m, ,m,mn
Khalid can order 8 flower bulbs for $ 20.
Given that Khalid purchases flower bulbs from a catalog for 2 $ each, plus a 4 $ shipping charge for the entire order, and he spends $ 20 on flower bulbs, to determine the number of Khalid can order bulbs the following calculation must be performed:
4 + 2X = 20 2X = 20 -4 X = 16/2 X = 8
Therefore, Khalid can order 8 flower bulbs for $ 20.
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what is the value of 3.85+0.004+0.117?
Answer: 3.971
Step-by-step explanation: first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:
3.85
0.004
0.117
+————-
Then you add vertically and you get your answer of 3.971
Your welcome :)
The value of the given expression ( 3.85+0.004+0.117 ) is 3.971.
What is summation?
The process of increment of any number of quantities or the process of integrating small parts to make a big part is called summation.
first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:
3.850
0.004
0.117
+————-
3.971.
Then you add vertically and you get your answer of 3.971.
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Given the sequence, 26, 13, 6.5, ..... find a) the 10th term and b) the sum of the first 18 terms X Clear * Undo Redo
Answer:
[tex]T_{10} = 0.05078125[/tex]
[tex]S_{18} = 51.9998016358[/tex]
Step-by-step explanation:
Given:
Sequence = 26, 13, 6.5 ....
Solving (a): The 10th term
The sequence is a geometric progression and the nth term will be solved using:
[tex]T_n = ar^{n-1}[/tex]
In this case:
[tex]n = 10[/tex]
[tex]r = \frac{T_2}{T_1}[/tex] --- Common Ratio
[tex]r = \frac{13}{26}[/tex]
[tex]r = 0.5[/tex]
[tex]a = 26[/tex] --- First term
So, [tex]T_n = ar^{n-1}[/tex] becomes
[tex]T_{10} = 26 * 0.5^{10-1}[/tex]
[tex]T_{10} = 26 * 0.5^{9}[/tex]
[tex]T_{10} = 26 * 0.001953125[/tex]
[tex]T_{10} = 0.05078125[/tex]
Solving (b): The sum of first 18 terms
This will be calculated using:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
Substitute values for n, a and r
[tex]S_{18} = \frac{26 * (1 - 0.5^{18})}{1 - 0.5}[/tex]
[tex]S_{18} = \frac{25.9999008179}{0.5}[/tex]
[tex]S_{18} = 51.9998016358[/tex]
Hence, the sum of first 18 terms is 51.9998016358
On weekdays, a bakery sells 240 cupcakes per day. If the bakery sells 330 cupcakes per day on weekends, by what percent do the sales increase?
Answer:
Percentage increase= 37.5%
Step-by-step explanation:
Giving the following information:
Sales on weekdays (Q0)= 240 units
Sales on weekends (Q1)= 330 units
To calculate the percentage increase, we need to use the following formula:
Percentage increase= [(Q1/Q0) - 1]*100
Percentage increase= [(330/240) - 1]*100
Percentage increase= 37.5%
HELP Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f
Step-by-step explanation:
hope this helps, happy learning
Two vertical asymptotes exist. The leftmost one's equation is, x = -6, and the rightmost one's equation is, x = 6.
What is oblique asymptotes?An asymptote along a line is called an oblique or slant asymptote. Oblique asymptotes are formed when the degree of the denominator of a rational function is one less than the degree of the numerator. For example, the function has a vertical asymptote at the line and an oblique asymptote about the line. (-, -6) U (-6, 6) U Domain: (6, )On the f(x) graph, there are two vertical asymptotes. The equation for the left one is x = -6, and the equation for the right one is x = 6.Because there are vertical asymptotes at x=-6 and x=6, the domain of f is (-infinity -6) U (-6,6) U.Domain: ,(-∞, -6) U (-6, 6) U (6, ∞)
There are two vertical asymptotes on the f(x) graph. The leftmost one's equation is:
x = -6
and the equation of the rightmost one is:
x = 6
Part B
The vertical asymptotes at x=-6 and x=6 define the domain of f as follows:
(-∞, -6) U (-6, 6) U (6, ∞)
Therefore, Two vertical asymptotes exist. The leftmost one's equation is x = -6, whereas the rightmost one's equation is x = 6.
The complete question is:
Identify any vertical, horizontal, or oblique asymptotes in the graph of y=f(x). State the domain of f. Identify any vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. There is only one vertical asymptote. Its equation is (Type an equation.)OB. There are two vertical asymptotes. The equation of the leftmost one is and the equation of the rightmost one is (Type an equation.)OC. There are no vertical asymptotes.
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How much does Kelly make an hour if she worked 35 hours and made $323.75 this
week?
Answer: $9.25 an hour
Step-by-step explanation:
if a(2x-3)=bx+5 then the solution for x in terms of a and b is
Answer:
x=(3a+5)/(2a-b)
Step-by-step explanation:
first we distribute the a to the 2x and -3
2ax -3a=bx+5
we move the -3a over by adding 3a
2ax=bx+5+3a
then we move the bx over
2ax-bx=5+3a
we can now group the left side like this
x(2a-b)=5+3a)
to find x all we must do is divide both sides by (2a-b)
x=(3a+5)/(2a-b)
PLEASE PLEASE PLEASE ANSWER THIS.
Hi there!
[tex]\large\boxed{53) \text{ } KL = 31}\\\\\large\boxed{54) \text{ } { } DC = 3}[/tex]
53)
The altitude of a triangle is always perpendicular to the base, therefore:
5x° must equal 90°.
Solve for x:
5x = 90
5x / 5 = 90 / 5 ----> x = 18
KL is equal to 2x - 5, so plug the value of x into the equation:
KL = 2(18) - 5
KL = 36 - 5 ---> KL = 31
54)
A median bisects the base, therefore:
AD ≅ DC
Set both equations equal to each other:
3x = 2x + 1
Subtract 2x from both sides:
x = 1
Plug in the value of x into the equation for DC:
2(1) + 1 = 3.
DC = 3.
A) Two angles are adjacent if their measures add up to 90°.
B) Two angles are supplementary if they share a side.
True or false
Answer:
A) False
B) False
Step-by-step explanation:
A. Two angles whose measures add up to 90° are said to be complementary, while two angles are adjacent when formed beside each other. So, adjacent angles might be complementary or supplementary. Thus, the answer to the first part of the question is false.
B. When two angles share a side, they are said to be adjacent to each other. But supplementary angles add up to [tex]180^{o}[/tex]. Since adjacent angles might be complementary or supplementary, then the answer to the second part of the question is false.
subtract 2x³-4x²+3x+5 from 4x²+x²+x+6
Answer:
(-2x^3)+(9x^2)
Step-by-step explanation:
Answer is above. Hope it helps!
Find all solutions of the equation in the interval [0, 2).
sin
x +
3
+ sin
x −
3
= 1
Answer:
x = 30 0 <= x < 2
Step-by-step explanation:
senx +3 + sex -3 = 1
2senx = 1
senx =1/2
x = arcsen(1/2)
x = 30
x = 8 is a solution for the equation x/2 = 4
Answer:
x = 8 is a solution for the equation
Water flows through a pipe at a rate of 4 quarts per month.Express this rate of flow
in gallons per day. Round your answer to the nearest hundredth.
The rate of flow of water through a pipe is gallons per day is 3.333%.
Given that, water flows through a pipe at a rate of 4 quarts per month.
We need to express this rate of flow in gallons per day.
How many quarts make a gallon?4 quarts will make a gallon.
Now, according to the question, 1 gallon of water flows through a pipe per month.
We know that number of days in a month is equal to 30 days.
Per day=1 gallon of water/Number of days in a month
=1/30 gallons of water.
The rate of flow in gallons per day=1/30 × 100
=3.3333%≈3.333%
Therefore, the rate of flow of water through a pipe is gallons per day is 3.333%.
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A function _______ is a rule that pairs each element in one set with exactly one element from a second set.
Answer:
relation
Step-by-step explanation:
First of all, all functions are relations, but not all relations are functions.
A function is a relation where one element in the domain is paired exactly with one element of the range.
A relation assigns one element of the domain to one or more elements of the range.
The range is any set of ordered pairs, while the function is a set where the group of pairs do not share the same first coordinate.
You roll a die and it comes up a "6" three times in a row.
What is the probability of rolling a "6" on the next toss?
Answer:
1/6
Step-by-step explanation:
there are 6 sides on a die and they each have equal chances of being rolled
Help pleaseeeeeeeeeeeeeeeee
Answer: 0.92 feet (choice B)
You're close but not quite there. To get the answer, you divide 29.44 over 32
If you had 32 feet of banner and 32 students, then each student would get 32/32 = 1 foot. Since the length of the banner is smaller than the number of students, this means each student only gets a fraction of a foot. This fraction value is fairly close to 1 because 29.44 is close to 32.
Answer:
B: 0.92
Step-by-step explanation:
Divide the banner length by the amount of students
[tex]\frac{29.44}{32}[/tex]
What’s the product of 1,243x8
Answer:
9944
Step-by-step explanation:
Calculator. Was there anything else you needed help on while I'm at it?
Answer:
9944
Explaination:
Typed it into a calculator
Two numbers have a difference of 3. The sum of their square is 89
Answer:
I just know additional
Step-by-step explanation:
HELP THIS IS URGENT FIND THE AREA OF THE SHAPE SHOWN BELOW
Answer:
uuhh sorry
Step-by-step explanation:
17. Find m2 USW if m_ USW = 7x - 34 and m2 TSR = 4x + 29.
Answer:
Step-by-step explanation:
Find the diagram attached. From the diagram, we can see that;
<USW = <TSR (vertically opposite angles)
Given
<USW = 7x-34
<TSR = 4x+29
Equate
7x-34 = 4x+29
7x-4x = 29+34
3x = 63
x = 63/3
x = 21°
Find <USW
<USW =7x-34
<USW =7(21)-34
<USW = 147-34
<USW = 113°
Hence the measure of <USW is 113°