Add boys and girls together for total students:
40 + 16 = 56 total students
Girls to total students is 16/56
Divide both numbers by 8 to get 2/7
The ratio is 2/7
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
There are 40 boys and 16 girls in a class of students. ⠀⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀What is the ratio of girls to students?⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
In a class,
boys=40
girls =16
So,
The students of the class =
boys+girls 40+1656According to the question,
we have to find the ratio of girls to the total students
ratio=[tex]\sf{\dfrac{girls}{students} }[/tex] ratio=[tex]\sf{\dfrac{16}{56} }[/tex] ratio=[tex]\sf{\dfrac{\cancel{16}}{\cancel{56}} }[/tex]ratio=[tex]\sf{\dfrac{2}{7} }[/tex] ratio=[tex]\sf{2:7 }[/tex]⠀⠀⠀⠀
[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
⠀⠀⠀⠀
Hence,the ratio of girls to students is 2:7
⠀⠀⠀⠀
If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
A. 13
B. 52
C. 208
D. 104
Answer:
D. 104
Step-by-step explanation:
[tex]y \: \alpha \: \frac{1}{ {x}^{2} } \\ \\ y = \frac{k}{ {x}^{2} } [/tex]
when y is 26, x is 4:
[tex]26 = \frac{k}{ {(4)}^{2} } \\ k = 416[/tex]
when x is 2:
[tex]y = \frac{416}{ {x}^{2} } \\ \\ y = \frac{416}{ {(2)}^{2} } \\ y = 104[/tex]
Answer:
D; 104
This is the correct answer
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW. THIS IS NOT A TEST OR AN ASSESSMENT!!!. Please help me with these math questions. Chapter 10 part 2
3. How do solving for solving to a rational function differ from solving for solutions to a rational inequality? How they are similar?
4. How is the difference quotient of a function determined? And how is the difference quotient related to the secant line? Is there a pattern for the difference quotient of linear functions?
9514 1404 393
Answer:
3. sign changes in the denominator need to be taken into account
4. difference quotient: (f(x+h) -f(x))/h; It is the slope of the secant line. For linear functions, the slope is constant, as is the difference quotient.
Step-by-step explanation:
3. When solving the equation f(x) = 0, where f(x) is a rational function, only the numerator zeros need to be considered.
When solving the inequality f(x) ≤ 0, or f(x) < 0, both numerator and denominator zeros need to be considered. As with solving any inequality, multiplying or dividing by a negative number changes the sense of the comparison.
Example
f(x) = x/(x-2) changes sign at both x=0 and x=2. Then three regions need to be considered when solving f(x) < 0. Those are x < 0, 0 < x < 2, and 2 < x.
__
4. The difference quotient is defined as ...
dq = (f(x +h) -f(x))/h
The difference quotient is essentially the average slope between (x, f(x)) and (x+h, f(x+h)). That is, it is the slope of the secant line between those two points.
For linear functions, the slope is a constant. The difference quotient is a constant equal to the slope of the line.
Example
f(x) = ax +b . . . . . a linear function with a slope of 'a'
The difference quotient is ...
(f(x+h) -f(x))/h = ((a(x+h)+b) -(ax+b))/h = (ax+ah+b -ax -b)/h = ah/h = a
The difference quotient is the slope of the line.
Mini wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
2) Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
I think scheme c Rs48,000 is the answer
14. The data below show the average ages and number of volunteer hours for five randomly chosen persons. Given the equation of the regression line is y' = 9.309x - 167.012, predict the number of hours a person will volunteer if her age is 27.5 years. Age, x Volunteer Hours, y 24.9 66.5 25.6 70.0 26.1 74.8 27.3 89.6 27.0 82.6
The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.
Given equation is,
→ [tex]\hat{y}=9.309x - 167.012[/tex]
Her age,
→ x = 27.5 years
By substituting the value of "x" in the given equation, we get the predicted time,
hence,
→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]
[tex]= 255.9975- 167.012[/tex]
[tex]=88.9855 \ months[/tex]
Thus the above is the right answer
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Combine like terms to simplify the
equation below.
Answer:
4a+6b
Step-by-step explanation:
4a -2a +6b +2a
Combine like terms
4a-2a+2a+6b
4a+6b
Answer:
4a + 6b
Step-by-step explanation:
4a - 2a + 6b + 2a
= 4a + 6b
(because -2a and +2a get cancelled by each other)
HELP SOMEONE FOR 20 POINTS
A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
700 miles driven in a day
Step-by-step explanation:
Create an equation to represent the situation, where x is the number of miles.
0.8x + 120 = 0.9x + 50
Solve for x:
120 = 0.1x + 50
70 = 0.1x
700 = x
So, the rental costs will be the same at 700 miles driven in a day.
A prism and two nets are shown below: Prism 1 E 3 Net A Net Part A: Which is the correct net for the prism? Explain your answer. (2 points) Part B: Write the measurements of Sides AB. BC, and CD of the correct net. (4 points) Part C: What is the surface area of the prism? Show your work. (4 points)
Answer:
A) Net A (see explanation)
B) AB = 3 in. | BC = 5 in. | CD = 7.2 in.
C) SA = 98.4 in²
Step-by-step explanation:
Part A
Net A is the correct net for the prism. If you look at the way the folds are, the flaps on the top and bottom would fold up to make the side of the prism. On net B, the flaps wouldn’t fit the shape correctly.
Part B
AB = This is the height of the prism.
= 3 in.
BC = This is the slant on the front of the prism.
= 5 in.
CD = This is the length of the prism.
= 7.2 in.
Part C
* First we’ll solve for the two triangles. They are the same shape and size, so we just need to solve one then duplicate it.
One triangle:
A = 1/2bh
= 1/2 (4) (3)
= 6 in²
Back rectangle:
A = bh
= 7.2 (3)
= 21.6 in²
Front rectangle:
A = bh
= 7.2 (5)
= 36 in²
Bottom rectangle:
A = bh
= 7.2 (4)
= 28.8 in²
Total:
A = 6 + 6 + 21.6 + 36 + 28.8
= 98.4 in²
· f(x)= x2 - 49
Identify the number of zeros of the polynomial function
Answer:
x = -7, x = 7
Step-by-step explanation:
Firstly, you are going to set the equation to 0, and then factor it.
Set equation to 0 -----> f(x)= x^2 - 49 will become x^2 - 49 = 0
Now, you're going to factor the equation.
You'll get (x-7) (x+7) upon factoring.
Thirdly, you will set (x-7)(x+7) equal to 0 and also solve for x.
Keep in mind that you'll be treating them as two separate equations
So, ----> (x-7) = 0 (x+7) = 0
When you solve for the x, you'll find out that x is equal to 7 and -7 ---> these are your zeros.
Please I need the answer ASAP!!!!
Step-by-step explanation:
D
*not sure about this answer pls tell me i ak right or wrong
Graph the function g(x) = 3^x + 3 and give its domain and range using interval notation.
When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.
The domain and the range of the given function are:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex](3,\infty)[/tex]
The given function is:
[tex]g(x) = 3^x + 3[/tex]
First, we plot the graph of g(x)
To do this, we need to generate values for x and g(x). The table is generated as follows:
[tex]x = 0 \to g(0) = 3^0 + 3 = 4[/tex]
[tex]x = 1 \to g(1) = 3^1 + 3 = 6[/tex]
[tex]x = 2 \to g(2) = 3^2 + 3 = 12[/tex]
[tex]x = 3 \to g(3) = 3^3 + 3 = 30[/tex]
[tex]x = 4 \to g(4) = 3^4 + 3 = 84[/tex]
The generated values in tabular form are:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ g(x) & {4} & {6} & {12} & {30} & {84} \ \end{array}[/tex]
Refer to the attached image for graph of g(x)
To determine the domain, we simply observe the x-axis.
The curve stretches through the x-axis, and there are no visible endpoints on the axis. This means that the curve starts from [tex]-\infty[/tex] to [tex]+\infty[/tex]
Hence, the domain of the function is: [tex](-\infty,\infty)[/tex]
To determine the range, we simply observe the y-axis.
The curve of g(x) starts at y = 3 on the y-axis and the curve faces upward direction. This means that the curve of g(x) is greater than 3 on the y-axis.
Hence, the range of the function is: [tex](3,\infty)[/tex]
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Function: [tex]g(x) = 3^{x} + 3[/tex]. Domain: [tex]Dom \{g(x)\} = \mathbb{R}[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex], respectively.
In Function Theory, the domain of a function [tex]f(x)[/tex] represents the set of values of the independent variable ([tex]x[/tex]), whereas the range of the function is the set of values of the dependent variable.
The Domain of the Function represents the set of values of [tex]x[/tex] (horizontal axis), whereas the Range it is the set of values of [tex]y[/tex] (vertical axis). After analyzing the existence of Asymptotes, we complement with graphic approaches and conclude where domain and range (in Interval notation) are.
Analytically speaking, the domain of exponential functions is the set of all real numbers and the range of [tex]g(x)[/tex] is any number between [tex]\lim_{x \to -\infty} g(x)[/tex] and [tex]\lim_{x \to +\infty} g(x)[/tex]. In a nutshell, we get the following conclusions in interval notation:
Domain: [tex]Dom \{g(x)\} = (-\infty, +\infty)[/tex], Range: [tex]Ran \{g(x) \} = (3, +\infty)[/tex]
Lastly, we proceed to complement this analysis by graphing function with the help of a graphing tool.
According to the image, domain and range coincides with outcomes from analytical approaches.
What are the measures of Angles a,b, and c? show your work and explain your answers.
Answer:
a=35
b=55
c=110
Step-by-step explanation:
a=35
Opposite angles which are non-adjacent angles formed by two intersecting lines are equal
b+35+90=180 sum of interior angle of a triangle equal to 180
b=180-125
=55
c+70=180 Angles on a straight line add up to 180°
c=180-70
=110
add 10 and g, then subtract f from the result
Answer:
(10+g) -f
Step-by-step explanation:
Add 10 and g
10 +g
Subtract f from the result
(10+g) -f
Which of the following equations is of a parabola with a vertex at (1, 2)?
O y = (x - 1) 2 - 2
Oy= (x - 1)2 + 2
O y = (x + 1)2 - 2
O y = (x + 1)2 + 2
Answer:
the second option: (x-1)squared +2
Explanation:
The x value of the vertex can be found in the parenthesis after the x. However, you have to do the opposite value of it. So, since the paranthesis has (x-1) then that means that the vertex's x-value has to be 1.
For the y-value of the vertex, that can be found after the paranthesis. This value will not be used as the opposite like with the x-value. So, we know that in (x-1)^2 +2 the "+2" indicates the y-value to be 2.
3/4 of the households in a rural area have pets. how many households have pets in this area if there are 1500 total households
Answer:
1,125 households would have pets in the area.
Step-by-step explanation:
We have 1,500 total households. We also know that 3/4 (or 0.75) of these households have pets. We would multiply 1,500 by 0.75 (which is equal to 3/4), resulting in 1,125. Therefore, 1,125 households would have pets in the area.
Answer:
1125 households
Step-by-step explanation:
3/4 of total households in area = # of households that have pets in the area
3/4 of 1500 = # of households that have pets in the area
3/4 · 1500 = # of households that have pets in the area
75/100 · 1500 = # of households that have pets in the area
0.75 · 1500 = 1125
1125 households
Change the following to percentages:
a) 83 out of 100
b) 24 out of 50
c) 9 out of 25
d) 7 out of 20
e) 6 out of 10
f)72 out of 200
g)12 out of 40
h)36 out of 60
Answer:
a.83%
b. 48%
c.36%
d.35%
e.69%
f.36%
g.30%
h.69%
-7x-17=2x+10
Show work
-7x-17=2x+10
2x+7x= -17 -10
9x= - 27
x = – 27/ 9
x= –3
I hope I helped you^_^
what is the value of g
Answer:
the value of g is gram .
may this answer is helpful for you
I need help with these questions
9514 1404 393
Answer:
17. 25 mile per gallon
18. Eduardo did should have divided by -4.
Step-by-step explanation:
17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...
(450 mi)/(18 gal) = 25 mi/gal
__
18. The appropriate method for solving this inequality is ...
-4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)
x < -30
The step Eduardo took of adding 4 will give ...
-4x +4 > 124 . . . . . puts him one step farther away from a solution
Eduardo chose an operation to perform that did not get him closer to a solution.
Choose the slope-intercept form of 3x + 2y = 5.
3.
у==x
5
2.
O
O y=-x+
5
0
5
v=-x+
O
yox
5
3
Answer:
y = -3x/2 + 5/2
Step-by-step explanation:
Well, basically what you do is modify it so that y is on one side.
3x+2y = 5
2y = 5-3x
y = (5-3x)/2
y = 5/2 -3x/2
So, the answer is the second option.
Answer:
B
Step-by-step explanation:
3x + 2y = 5
Our goal is this form:
y = mx + b
- move 3x to right anc change its sign
2y = -3x + 5
- divide each member by 2
y = -3/2 x + 5/2
find an odd natural numbers x such that LCM (x, 40) = 1400
Answer:
175
Step-by-step explanation:
so, the LCM is the combination of the longest chains of the prime factors in every number.
40 : 2, 2, 2, 5
1400 / 40 = 35
35 : 5, 7
but LCM(35, 40) = 2×2×2×5×7 = 280
and not 1400.
what is missing ?
1400 / 280 = 5
aha, another prime factor 5 is missing to get 1400.
x : 5, 5, 7
so, x = 5×5×7 = 175
LCM(175, 40) = 2×2×2×5×5×7 = 1400
if i pay 15300 interest capital on a loan for 25 years how much will i pay?
Answer:
i dont know soory
Step-by-step explanation:
Angles 1 and 2 form a linear pair and the measure of angle two is 22 more than 4 times of the measure of angle 1. What degrees is angle 2
Answer:
m<2= 148.4
Step-by-step explanation:
A linear pair means that both angles add to 180.
m<2 = 4*m<1 +22
Together
m1 + m2 = 180
Put the value for m<2 into the above equation
m<1 + 4*m<1 + 22 = 180 Combine like terms\
5m<1 + 22 = 180 Subtract 22
5m<1 = 180 - 22
5m<1 = 158 Divide by 5
m<1 = 158/5
m<1 = 31.6
m<2 = 4*31.6 + 22
m<2 = 138.4
Need the value of P please
Answer:
B. 35°
Step-by-step explanation:
First, find the two interior angles that are adjacent to angles 90° and 125° respectively.
Thus:
Interior angle 1: 180° - 90° = 90° (linear pair)
Interior angle 2: 180° - 125° = 55° (linear pair)
P + 90° + 55° = 180° (sum of interior angles in a triangle)
P + 145° = 180°
Subtract 145° from each side
P = 180° - 145°
P = 35°
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 10 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses.
What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.
The probability that the hacker guesses the password on his first try is:
P = 1/(62^10) = 1.19*10^(-18)
We know that the password is 10 characters long.
In each one of these, we can put.
One lower case letter (26 of these)
One upper case letter (26 of these)
one numerical digit (10 of these)
So, for every single digit, we have a total of:
26 + 26 + 10 = 62 options
Now we can find the total number of different passwords, which will be equal to the product between the number of options for each one of the characters.
We know that for each character we have 62 different options.
And we have 10 characters.
Then the product between the numbers of options is:
C = 62^10
Then if the hacker does a random guess, the probability that the random guess is correct is one over the total number of possible combinations.
P = 1/C = 1/(62^10)
The probability that the hacker guesses the password on his first try is:
P = 1/(62^10) = 1.19*10^(-18)
If you want to read more about probability, you can read:
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Given f (x) = 3x - 5 find f (x - 2)
Answer:
3x-11
Step-by-step explanation:
f (x) = 3x - 5
f(x-2)
Replace x in the function with x-2
f (x-2) = 3(x-2) - 5
=3x-6 -5
=3x-11
Please answer and explain :)
Write an example for each of the following:
equation notation
set notation
interval notation
solution graph
Answer:
set notation _ A set is denoted or represented by a capital letter and enclosed in a curly bracket For example {A,B,P,Q}.
Twice a certain number is subtracted from 9 times the number. The result is 21. Find the number.
Answer:
3
Step-by-step explanation:
Let x represent the number.
Create an equation to represent the situation, and solve for x:
9x - 2x = 21
7x = 21
x = 3
So, the number is 3.
Which graph represents the given equation? y=3/2x^2+4x-2
Answer:
y=3/2x^2+4x-2
Hope it helps
Solve the inequality is it a,b,c,d?
Answer:
B
Step-by-step explanation:
-2/3x<31/3
x>-31/2
x>-15 1/2
Answer:
x > - 15 1/2
Step-by-step explanation:
-2/3 x -10 < 1/3
Multiply each side by 3
3(-2/3 x -10 < 1/3)
-2x -30 < 1
Add 30 to each side
-2x-30+30 <1+30
-2x < 31
Divide by -2 remembering to flip the inequality
-2x/-2 > 31/-2
x > -31/2
x > - 15 1/2
