Two students are selected at random from the class this can be done in 45 ways.
It is necessary for there to be one girl and one boy this is done in 24 ways.
In a given class there are six( 6 ) girls and four( 4 ) boys.
In this case, there are given two cases that two students are selected at random from the class, In how many ways can this be done
And the other case is it necessary for there to be one girl and one boy, how many ways are possible
To solve the two cases we use Combinations;
Total number of students in a class = 6 + 4 = 10
For case ( 1 ):
Two students are selected at random from the class this can be done by;
A = ¹⁰C₂
A = [tex]\frac{10!}{2!*(10-2)!}[/tex]
A = 45
For case ( 2 ):
It is necessary for there to be one girl and one boy thus is done by;
B = ⁶C₁ ˣ ⁴C₁
B = [tex]\frac{6!}{1!*(6-1)!} \\[/tex] ×[tex]\frac{4!}{1!*(4-1)!}[/tex]
B = 6 × 4
B = 24
Two students are selected at random from the class this can be done in 45 ways.
It is necessary for there to be one girl and one boy this is done in 24 ways.
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Find the y-intercept of the quadratic function: g(x)=2(x+3)^2+8
x-intercept:
(−3,0)
y-intercept:
(0,118098)
A store owner mixes 2 Ib of candy that costs x dollars per pound with 3 Ib of candy that costs $1.50 per pound. She sells the mix for $2.50 per pound.
On solving the linear equation 12.5 = 2x + 4.5, we find that cost of first type of candy is $4 per pound
What is an linear equation in one variable?Linear equation is an equation containing one unknown variable with power one and constants.
The standard form of an linear equation in one variable x is :
ax + b = 0 , where a, b are constants
x= -b/ a is solution if this equation or we can solve this equation by adding or subtracting, multiplying, dividing same number to both sides.
Given that there are two types of candies one is of x dollars per pound
and one is of $1.50 per pound
Cost of 2lb of candy that costs x dollars per pound = 2 × x = $ 2x
Cost of 3lb of candy that costs $1.50 per pound = 3 × 1.5 = $ 4.5
2lb of one type of candy and 3lb of other type of candy are mixed to form a mix of weight 2lb + 3lb = 5lb
The cost of one pound of mixture = $2.50
The cost of 5lb of such mixture = $ 5× 2.50 = $ 12.5
Cost of 5lb mix = Cost of 2lb candy of first type + Cost of 3lb candy of second type
⇒ 12.5 = 2x + 4.5
Subtract 4.5 from both sides,
⇒ 12.5 - 4.5 = 2x
⇒ 8 = 2x
Divide both sides by 2
⇒ 4 = x
Therefore, the cost of first type of candy is $ 4 per pound
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The boca grande causeway in florida is about 1 4/9 times as long as the golden gate bridge in san francisco golden gate bridge is about 9000 feet long about how long is the boca grande causeway
The length of the Boca Grande Causeway = 13,000 feet.
When do we use multiplication ?Repeated addition of the same number is made easier by multiplying the numbers. When we need to merge groups of similar sizes, we employ it. For instance, if there are 5 baskets, each containing 4 apples, we can use multiplication to get the total number of apples, which is 5 x 4 = 20 apples.
We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group.
Given: The boca grande causeway in florida = 1 4/9 times golden gate bridge
Length of the Golden Gate Bridge = 9000 feet
Thus the length of the Boca grande causeway = 1 4/9 × 9000
= 13/9 × 9000
On further solving we get
= 13 × 1000
= 13,000 feet .
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Question 2
What is the definition of
congruence?
A) If two figures have the same shape, then they are congruent.
B) If two figures have the same area, then they are congruent.
C) If there is a sequence of transformations taking one figure to another, then they are congruent.
D) If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.
Next Question
Answer:
A. If two figures have the same shape, then they are congruent.
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly: StartFraction 2 Over x squared minus 36 EndFraction minus StartFraction 1 Over x squared + 6 x EndFraction = StartFraction 2 Over (x + 6) (x minus 6) EndFraction minus StartFraction 1 Over x (x + a) EndFraction. = StartFraction b x Over (x + 6) (x minus 6) x EndFraction minus StartFraction x minus c Over (x + 6) (x minus 6) x EndFraction. = StartFraction d x minus x + e Over (x + 6) (x minus 6) x EndFraction. = StartFraction x + f Over (x + 6) (x minus 6) x EndFraction. = StartFraction g Over x (x minus 6) EndFraction
Answer:
6, 2, 6, 2, 6, 6, 1
Step-by-step explanation:
a = 6
b = 2
c = 6
d = 2
e = 6
f = 6
g = 1
Answer: 6, 2, 6, 2, 6, 6, 1
Step-by-step explanation:
Twenty students participated in a psychology experiment which measured their heart rates in two different situations.
Which situation shows greater variability?
Twenty students participated in a psychology experiment which measured their heart rates in two different situations.[75,100] situation shows greater variability.
f(75)=1
f(80)=4
f(90)=5
f(95)=4
f(100)=1
The measure of center should be median as the data is a bit scattered whereas the measure of variability should be the range of it.
Mean should be the measure of center as the data is concentrated in the middle the most whereas the standard deviation should be the measure of variability.
How far apart points are from one another and from the center of a distribution or a data collection is shown by variability. Spread, scatter, and dispersion are other terms for variation.
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one of the longest commercial aircraft in use today is 144 feet in length. another airplane manufacturer decides to build an airplane that is approximately 41% of this length. use compatible numbers to estimate the length of the plane built by the other manufacturer.
The length of the other aircraft is 59.04ft.
Percentage of NumberTo solve this problem, we simply need to find the certain percentage of the length of aircraft which is given as 144ft.
let's calculate 41% of 144
[tex]41\% of 144[/tex]
This is given as
[tex]\frac{41}{100} = \frac{x}144}\\ 0.41 = \frac{x}{144} \\x = 0.41 * 144\\x = 59.04ft[/tex]
The length of the plane built by the other manufacturer is 59.04 ft.
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Determine which integer(s) from the set S:{−40, 2, 20, 42} will make the inequality three eighths m minus three is less than one fourth m plus 2 false.
Answer:
{-40, 2}
Step-by-step explanation:
Part A: -40/8 x 3/8 would be
120/8 but then we have to subtract it from 3
that would be 117/8 then we simplify it 14 -5/8.
Part B: first it would be 2 plus 2 and that's 4 and then make 4 into a fraction
4/4 we simplify that 1 0/4.
14 -5/8 < 1 0/4.
Hope This Helped!
Question 6(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation MC)
How many times larger is 8 x 105 than 4 x 10³?
2,000
200
20
2.0
8 × [tex]10^5[/tex] is 200 times greater than 4 × [tex]10^3[/tex] as according to multiplying and dividing as per the scientific notation of multiplication and division.
What is scientific notation?A kind of representation of number which is some power of 1/10 can also be expressed in as easily in scientific notation.
1/10 = [tex]10^{-1[/tex] (“ten to the minus one power”)
More generally, the expression “[tex]10^{-n[/tex]” (where n is a whole number) means (1/10) n. Thus
[tex]10^{-3[/tex] = [tex]\frac{1}{10}^{-3}[/tex]
= 1/1000
[tex]10^{-8[/tex] = [tex]\frac{1}{10}^{-8[/tex]
= 1/100,000,000
Scientific notation was invented to help scientists (and science students) deal with very large and very small numbers, without getting lost in all the zeros.
Herein this question
8 × [tex]10^5[/tex] can also thus be written as 2 x 4 × [tex]10^5[/tex]. On dividing with 4 × [tex]10^3[/tex] we get 2 x [tex]10^2[/tex]. Thus, it is 2 x [tex]10^2[/tex] i.e., 200 times larger than 4× [tex]10^3[/tex].
The expression “10n”, where n can be stated as a whole number, simply means that “10 is raised to the nth power,” or in other words, a number that is got by using 10 as a factor n times.
You can also notice that the number of zeros that are present in the ordinary decimal expression is absolutely equal to the power to which thus 10 is raised.
If any kind of number is expressed in words, first we have to write it down as an ordinary decimal number and then we have to convert it. Thus, the value “ten million” becomes 10,000,000. There are a total of seven zeros, so in powers of ten notation ten million is written [tex]10^7[/tex].
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Jose will spend at most $20 on gifts. So far, he has spent $12 . What are the possible additional amounts he will spend?
Answer:8 dollars
Step-by-step explanation:
20-12=
At an important meet Hassan won the mens 800 meters in 106.72 seconds Hassan ran at an average of blank meters per second
To find the average rate at which Hassan ran in meters per second, divide the distance of 800 meters over the 106.72 seconds that it took for Hassan to run that distance:
[tex]\frac{800m}{106.72s}=7.496251874...\frac{m}{s}\approx7.50\frac{m}{s}[/tex]Therefore, Hassan ran at an average of 7.50 meters per second.
Here is an inequality: 7x+6<3x+2
Select all values that are solutions
x=1
x=0
x=-1
x=-2
x=-8
Answer:
x < -1
Step-by-step explanation:
7x + 6 < 3x + 2
7x - 3x + 6 < 2
7x - 3x < 2 - 6
4x < -4
x < -4 / 4
x < -1
how do i multiply this and simplify (2x+6)^2
Answer:4x^2+24x+36
Step-by-step explanation:
when you have it squared it turns into (2x+6) (2x+6) then you distribute it which gives you 4x^2+12x +12x+36 when you simplify that you et 4x^2+24x+36
Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
in the market for canadian dollars measured in us dollars, if the price of a us dollar is 1.10 canadian dollars, a canadian dollar is a.1.10 us dollars b.1 us dollar c.0.99 cents us d.0.91 cents us
The price of one canadian dollar in US dollars is 91 cents or 0.91 US dollars.
It is given that the price of a US dollar is 1.10 Canadian dollars in the market.
Thus we can say that,
1.10 Canadian Dollar = 1 US Dollar
∴ 1 Canadian Dollar = [tex]\frac{1}{1.10}[/tex] US Dollars
⇒ 1 Canadian Dollar = 0.91 US Dollars
Now we know that 1 US Dollar = 100 cents
∴ 0.91 US Dollars = 0.91 x 100 = 91 cents
Hence the value of 1 Canadian Dollar is 0.91 US Dollars or 91 cents.
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Question 8 (1 point)
Identify the slope as POSITIVE, NEGATIVE, ZERO, OR UNDEFINED.
Answer:
Step-by-step explanation:
i think its undefined
72=6x
What is x equal to?
Answer:
12
Step-by-step explanation:
72:6=12
1x=12
hope ut help
The graph of the function p(x)=x^3+x^2+4x+4 is shown below
Find all real and complex roots of the function. The Zeros are:
List the zeros as complex numbers. Separate answers by commas as needed.
Answer:
1 ; -2·i ; 2·i
Because x = -1 is a real root, you can divide
(x^3 + x^2 + 4·x + 4)/(x + 1) = x^2 + 4
Roots of x^2 + 4 are
x^2 + 4 = 0
x^2 = -4
x = ± 2·i
All real and complex roots are
1 ; -2·i ; 2·i
O LINEAR EQUATIONS
Finding the dimensions of a rectangle given its perimeter and a...
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 64 yd, find its length and width.
length: yd
width: yd
X
Answer: width=8, length=24
Step-by-step explanation:
2(x+3x)=64
2x+6x=64
x=8
width (x)=8
length (3x)=24
perimeter=2(x+3x)=64
pls help my mom is mad at me Tyler was making a meal for his family. For every 3/4 pound of beef, the recipe calls for 9/8 cups of broccoli. How many cups of broccoli would be needed for a pound of beef?
Group of answer choices
1 and ½ cup of broccoli per beef
1/2 cup of broccoli per beef
2/3 pound of broccoli per beef
5/4 cup of broccoli per beef
Answer:
1 1/2
Step-by-step explanation:
for divide 3 for 9/8 and 3/4 so 9/8 divide 3 so 3/8
So there is 3/8 for each 1/4. Then time 4 so one pound is 12/8 and you simplify your answer is 3/2 or 1 1/2
Pls give brainliest
-4 + (-5) =
1 + (-4) =
Answer:
-9,-3
Step-by-step explanation:
-4+-5 = -9
1+-4 = -3
Think about a number line to help you
Answer: -4 + (-5) = -9
1 + (-4) = -3
Step-by-step explanation: Subtract -4 and -5 and u get -9. Subtract 4 and 1 to get -3
A square has a perimeter of 40 m what is the length of each side
Answer:
10m
Step-by-step explanation:
Perimeter means adding up all of the sides of a shape.
One property of a square is that all lengths of a square are the same.
We also know squares have 4 sides.
Lets set up an expression to solve the length for each side with variable S representing the length of a side:
4 * S = 40
Divide each side by 4:
S = 10
Therefore, each side of the square has a length 10m
If * = 8 units, y= 13 units, and h= 11 units, then what is the area of the parallelogram shown above?
The area of the figure shown below is equivalent to 88 square units.
Properties of a parallelogramA parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
The opposite sides of a parallelogram are congruent and the sum of their adjacent side is equivalent to 180 degrees.
The formula for calculating the area of a parallelogram is expressed as;
Area = length * breadth
Area = x * h
Area = 8 * 11
Area = 88 square units
Hence the area of the parallelogram above is 88 square units.
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Greta is opening a savings account. She starts with $100 and plans to add $50 each week. How do you write an equation she can use to calculate the amount of money she have after any number of weeks. How much money will she have after 1 year?- what is the unit rate of change for this situation
Answer:
100+50n
n stands for the number of weeks
There are about 52 weeks in a year, so
100+50(52) = 2700
Greta would have $2700 after 1 year
Exterior angle, theorem, and triangle, some theorem
Answer:
? = 94°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
143° is an exterior angle of the triangle , then
? + 49° = 143° ( subtract 49° from both sides )
? = 94°
4) A group entering a zoo purchased 33 admission tickets for a total of $139.50. Adult tickets (x) cost $7.50 and
tickets for children (y) cost $3.50. How many of each type of ticket were purchased?
/5 points
The number or children tickets are 24 and adults tickets are 9.
How to illustrate the information?Adult tickets (x) cost $7.50 and tickets for children (y) cost $3.50. The equation will be:
7.5x + 3.5y = 139.5
There are 33 tickets. This will be:
x + y = 33
x = 33 - y.
Recall 7.5x + 3.5y = 139.5
Substitute for x.
7.5(33 - y) + 3.5y = 139.5
247.5 - 7.5y + 3.5y = 139.5
-4.5y = 139.5 - 247.5
4.5y = 108
y = 108/4.5
y = 24
Number of children ticket = 24
Adult tickets = 33 - 24 = 9
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Un laboratorio está diseñando una nueva bacteria que se supone ayude a limpiar los ríos contaminados. Cada hora que pasa, el número de bacterias se duplica, por lo que se requiere una expresión que permita determinar ese número. Expresa la cantidad de bacterias que habrá después de "x" horas como una potencia. Seleccione una:1. 2x 2. 2x3. x² 4. 2X
From the statement, we know that the bacteria population doubles every x hours. We write the population as a function of x as:
[tex]P(x)=P_0\cdot2^x.[/tex]Where:
• P₀ = initial population,
,• x = time in hours.
If we consider P₀ = 1, we get the following formula:
[tex]P(x)=2^x.[/tex]Answer[tex]2^x[/tex]Help pleaseeeeee (ignore the part that says explain math mistake)
Check the picture below.
Tom walked a total of 15 kilometers by making 5 trips to school. Later on, he walked 33
kilometers during 11 trips. How many kilometers does Tom walk per trip?
Write the ratio 9:4 in the form n: 1
The ratio 9:4 in the form n:1 is 2.25:1.
The given ratio is 9:4.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
We need to write the given ratio in the form n:1
Divide the given ratio by 4
9/4 : 4/4
⇒ 2.25:1
Therefore, the ratio 9:4 in the form n:1 is 2.25:1.
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