Answer:
The probability that the student scored an A is : 0.778
Step-by-step explanation:
There are 55% boys and 45% girls
So, No of boys is: 55/100
No of girls is: 45/100
So, total no of girls are: 45
Since 35% of the girls scored A on test
No of girls who scored A on test = 35
The probability that the student scored an A is: 35/45
The probability that the student scored an A is : 0.778
Answer:
[tex]P(A | B)=\frac{7}{9}=0.778[/tex]
Step-by-step explanation:
Let's call B the event that consists of the selected student being a girl
Call A to the event in which the selected student obtained an A.
Then we look for the probability that A will occur given that B. That is, we look for P(A | B)
This is a conditional probability and is calculated using the following formula
[tex]P(A | B)=\frac{P(A\ and\ B)}{P(B)}[/tex]
In this case
[tex]P(B)=0.45\\P(A\ and\ B)=0.35[/tex]
So
[tex]P(A | B)=\frac{0.35}{0.45}[/tex]
[tex]P(A | B)=\frac{7}{9}=0.778[/tex]
what are natural number less than 5
Answer:
Natural numbers = {1,2,3,4,5…} Answer 1: A is the set of Natural numbers between 1 and 5 inclusive. Answer 2: A is the set of Natural numbers less than 6.
Step-by-step explanation:
Answer:
n = 1, 2, 3, 4
Step-by-step explanation:
Natural numbers are any integers (whole numbers) that are positive.
In this case, all natural number (n) is less than (<) 5
n < 5 is your equality, but in reality it looks like: 0 < n < 5
The numbers that can fit into your problem is n = 1 , 2, 3, 4
n = 1, 2, 3, 4 is your answer.
~
CraftWork rents a storage space that measures 200 ft x 300 ft x 30 ft.
CraftWork pays $1500 for the storage space each month. What is the cost
per cubic foot?
O
A. $0.008
O B. $0.0002
O C. $0.0015
O D. 50.00083
Answer:
0.00083
Step-by-step explanation:
200*300*30=1800000
1500/1800000=0.00083
The cost per cubic foot of the storage space is approximately $0.00083 per cubic foot. Hence the correct option is D.
To find the cost per cubic foot of the storage space, we need to calculate the total cubic footage of the space and then divide the monthly cost by that number. The storage space measures 200 ft x 300 ft x 30 ft, so the total volume is:
Total Volume = length times width times height
= 200 ft x 300 ft x 30 ft
= 1,800,000 cubic feet
Now, we calculate the cost per cubic foot:
Cost Per Cubic Foot = Total Monthly Cost / Total Volume
= $1500 / 1,800,000 cubic feet
= $0.00083 per cubic foot (rounded to five decimal places).
i need help please can someone help
Answer:
x = 8Step-by-step explanation:
[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]
[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]
A number cube has 6 faces, numbered from 1 to 6. If the cube
is rolled six times, what is the probability that a face with a 6
comes up exactly once?
[tex]|\Omega|=6^6\\|A|=6\cdot 5^5\\\\P(A)=\dfrac{6\cdot5^5}{6^6}=\dfrac{5^5}{6^5}=\dfrac{3125}{7776}\approx40.2\%[/tex]
The probability that a face with a 6 comes up exactly once will be 0.40.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A number cube has 6 faces, numbered from 1 to 6.
If the cube is rolled six times.
Then the probability that a face with a 6 comes up exactly once will be
The total number of the event will be
Total event = 6⁶
Total event = 46656
Favorable event = 6 x 5⁵
Favorable event = 18750
Then the probability will be
P = 18750 / 46656
P = 3125 / 7776
P = 0.40
More about the probability link is given below.
https://brainly.com/question/795909
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What is the value of p?
Answer:
D. 35 degrees.
Step-by-step explanation:
125 = p + 90 (by the external Angle of a Triangle theorem).
p = 125 - 90
p = 35 degrees (answer).
Answer:
35 degrees
Step-by-step explanation:
Ok so that angle that has the 125 degree is adjacent to an angle inside the triangle. These adjacent angles are actually supplementary because they are formed by a straight-edge. So the angle inside adjacent to the 125 degree angle is 180-125=55 degrees.
Same logic applies to angle adjacent to the 90 degree angle. The angle adjacent to the 90 degree angle is also supplementary to the 90 degree angle. So 180-90=90 degrees for the other inside angle next to the 90 degree angle.
So the figure formed here is a triangle. The angles in this triangle should add up to be 180 degrees. So we have the equation 90+55+p=180.
Let's solve this by first simplifying the 90+55 part!
145+p=180
Subtract 145 on both sides:
p=180-145
Simplify.
p= 35 degrees
Here is the histogram of a data distribution.
Which best describes the shape of this distribution?
Answer:
B. Unimodal-Skewed
Step-by-step explanation:
A distribution is called unimodal if it has only one hump in the histogram.
A symmetric distribution is equally divided on both sides of the highest hump.
The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.
So the correct answer is:
B. Unimodal-Skewed ..
Answer:
B. Unimodal Skewed
Step-by-step explanation:
The Histogram given in figure has one peak and it is skewed to the right So, it is Right Skewed Unimodal Histogram.
Moreover, Unimodal means the distribution has one peak, Skewed means this peak is present in either the left or right side of the center of the distribution.
Option A is incorrect because the given histogram is not symmetric, it is skewed distribution.
Option C can't be taken because uniform means the size of bars is approximately same for the given distribution.
Options D & E is not correct because the given distribution is not Bimodal it has only one peak.
Lucy Furr must supply 2 different bags of chips for a party. She finds 10 varieties at her local grocer. How many different selections can she make?
Answer:
she can make 50 different selections!
Step-by-step explanation:
To find the different selections that can be made, we use the formula:
nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen
In this case:
'n' equals 10 and 'r' equals 2. Therefore:
[tex]10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50[/tex]
So she can make 50 different selections!
Answer: 45
Step-by-step explanation:
The combination of n things taking r at a time is given by :-
[tex]C(n;r)=\dfrac{n!}{(n-r)!}[/tex]
Given : Lucy Furr must supply 2 different bags of chips for a party.
She finds 10 varieties at her local grocer.
Then the number of different selections she can make is given by :-
[tex]C(10;2)=\dfrac{10!}{2!(10-2)!}\\\\=\dfrac{10\times9\times8!}{2\times8!}=\dfrac{90}{2}=45[/tex]
Hence, the number of different selections she can make= 45
What is the order of rotational symmetry for the figure
Answer:
Order of symmetry = 1
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
The given shape, when rotated will only have the shape like original shape after one complete rotation so the order of symmetry is one ..
On a quiz worth 5 points, eight students earned a 5, two students earned a 4, five students earned a 3, six students earned a 2, five students earned a 1, and zero students earned a zero. Find the class average on this quiz.
Express your answer rounded to the tenths place.
Answer:
Step-by-step explanation:
[tex]\frac{8(5)+2(4)+5(3)+6(2)+5(1)}{26}[/tex]
Now we simplify:
[tex]\frac{80}{26}[/tex]
[tex]\frac{40}{13}[/tex]
Now we divide:
[tex]3.1[/tex]
8. A right cone has a volume of 8,579 m3 and a radius of 16 m. Find its altitude.
A. 32.0 m
B. 27.6 m
C. 2.7 m
D. 64.2 m
Answer:
Option A is correct.
Step-by-step explanation:
The formula used for finding the volume of right cone is:
Volume of Right cone = (1/3)π.r².h
We need to find altitude i.e h
Volume of cone=V = 8579 m^3
Radius=r = 16m
Altitude =h =?
Putting values,
8579 = (1/3) * 3.14 * (16)^2*h
8579 = 1/3 * 3.14 * 256 *h
8579 = 267.95 * h
=> h = 8579/267.95
h = 32.0 m
So, Altitude of right cone is 32.0 m
Option A is correct.
What is the domain of the function y=^3 sqrt x-1
Answer:
Domain is all real numbers also known as [tex](-\infty,\infty)[/tex] in interval notation.
[tex]f(x)=\sqrt[3]{x-1}[/tex]?
Step-by-step explanation:
If your function is [tex]f(x)=\sqrt[3]{x-1}[/tex] then the domain is all real numbers because you can cube root any real number.
If x is a real number, then x-1 is a real number.
So if you cube root (x-1) for any x then you still get a real number back.
Now if it was a square root, that is when we can run into some problems.
Answer: -infinity and positive infinity
Step-by-step explanation: It's either a on your test or two zero's that look twisted :)
Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7.
f(x) = −one twenty fourth(x − 1)2 − 5
f(x) = one twenty fourth(x − 1)2 − 5
f(x) = −one twenty fourth(x + 5)2 + 1
f(x) = one twenty fourth(x + 5)2 + 1
Answer:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Explanation
The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.
Such parabola has equation of the form,
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is the midway from the focus to the directrix
The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).
The y-value of the vertex is
[tex]y = \frac{ 7 + - 5}{2} [/tex]
[tex]y = \frac{ 2}{2} = 1[/tex]
The equation of the parabola now becomes
[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]
p is the distance from the focus to the vertex which is p=|7-1|=6
Substitute the value of p to get:
[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]
[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]
We solve for y to get:
[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]
Answer:
f(x) = −one twentyfourth (x + 5)2 + 1
Step-by-step explanation:
12. A fruit basket contains oranges and grapefruits. One-third of the orange
and one-fourth of the grapefruits were spoiled. You threw away 4 oranges
and 7 grapefruits. How many pieces of fruit were in the basket?
Answer:
There were 12 + 28 = 40 pieces of fruit in the basket.
Step-by-step explanation:
Suppose there were x oranges and y grapefruit.
Then we have
1 /3 x = 4
x = 4*3 = 12.
1/4 y = 7
y = 7*4 = 28.
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 26.47 units²
B. 28.53 units²
C. 33.08 units²
D. 27.28 units²
Answer:
Option B [tex]28.53\ units^{2}[/tex]
Step-by-step explanation:
The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let
a,b,c be the lengths of the sides of a triangle.
The area is given by:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
p is half the perimeter
[tex]p=\frac{a+b+c}{2}[/tex]
step 1
Find the area of triangle ABD
we have
[tex]a=AB=2.89\ units[/tex]
[tex]b=BD=8.59\ units[/tex]
[tex]c=DA=8.6\ units[/tex]
Find the half perimeter p
[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]
Find the area
[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]
[tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex]
[tex]A=\sqrt{149.89}[/tex]
[tex]A=12.24\ units^{2}[/tex]
step 2
Find the area of triangle ADC
we have
[tex]a=AC=4.3\ units[/tex]
[tex]b=AD=8.6\ units[/tex]
[tex]c=DC=7.58\ units[/tex]
Find the half perimeter p
[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]
Find the area
[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]
[tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex]
[tex]A=\sqrt{265.35}[/tex]
[tex]A=16.29\ units^{2}[/tex]
step 3
Find the total area
[tex]A=12.24+16.29=28.53\ units^{2}[/tex]
Answer:
B.) 28.53 units²
Step-by-step explanation:
I got it correct on founders edtell
QUIZ
ALU
0 2 O) A 5 OU
Which shows the four-term polynomial and factored form of x2 + 6x-27?
O x2 + 3x – 9x - 27 = (x + 3)(x -9)
O x2 + 6x – 3x-27 = (x + 6)(x – 3)
O x2 + 9x -3x – 27 = (x + 9)(x – 3)
O x2 + 3x – 6x-27 = (x + 3)(x-6)
Answer:
C
Step-by-step explanation:
O x² + 9x -3x – 27 = (x + 9)(x – 3)
x² + 6x - 27 = (x + 9)(x - 3)
Find the value of y for the following system of equations. -x - y = 7 x - y = 9
Answer:
y = -8
Step-by-step explanation:
It is given that,
-x - y = 7 ---(1)
x - y = 9 ---(2)
To find the solution
Add eq (1) and eq(2) we get
-x - y = 7 ---(1)
x - y = 9 ---(2)
0 - 2y = 16
y = 16/(-2) = -8
Substitute the value of y in eq(1)
-x - y = 7 ---(1)
-x - -8 = 7
-x + 8 = 7
x = 8 - 7 = 1
Therefore x = 1 and y = -8
What is the solution to the equation 9-3x = 7?
Answer:
x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given
9 - 3x = 7 ( subtract 9 from both sides )
- 3x = - 2 (divide both sides by - 3 )
x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\huge{\boxed{x=\frac{2}{3}}}[/tex]
Add [tex]3x[/tex] on both sides. [tex]9=7+3x[/tex]
Subtract 7 from both sides. [tex]2=3x[/tex]
Divide both sides by 3. [tex]\boxed{\frac{2}{3}}=x[/tex]
-12=f-7 help please
Answer:
f=-5
Step-by-step explanation:
1) Add 12 to both sides
2) You should get f=-5
Answer:
[tex]\huge \boxed{F=-5}\checkmark[/tex]
Step-by-step explanation:
First, switch sides.
[tex]\displaystyle F-7=-12[/tex]
Then, add by 7 from both sides of equation.
[tex]\displaystyle F-7+7=-12+7[/tex]
Simplify, to find the answer.
[tex]\displaystyle -12+7=-5[/tex]
[tex]\huge \boxed{F=-5}[/tex], which is our answer.
Graph the linear equations in three points: -x-2y=-10
Answer:
Step-by-step explanation:
Rewrite -x-2y= -10 as -2y= x - 10 and then as y = (-1/2)x + 5.
Then choose any 3 x values and find the corresponding y values using this formula. For example:
x y = (-1/2)x + 5 (x, y)
----- -------------------- ---------
0 5 (0, 5)
-4 (-1/2)(-4) + 5 = 7 (-4, 7)
6 (-1/2)(6) + 5 = 2 (6, 2)
Plot these three points and then draw a line through them.
Answer:
0,5 2,6 4,7
Step-by-step explanation:
You have to solve the equation by keeping y on its own. The equation is
y=-1/2x-5
Coordinates are:
0,5 2,6 4,7
he
5) A banker learned that $842.40 is withheld from his monthly check for taxes and insurance. If
this represents 18% of his total pay, find the total pay.
A triangle has two sides of lengths 7 and 9. What value could the length of the third side be?
Answer:
The length of the third side could be all real numbers greater than 2 units and less than 16 units
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
so
Applying the triangle inequality theorem
Let
x ------> the length of the third side
we have
First case
1) 7+9 > x
16 > x
Rewrite
x< 16 units
Second case
2) 7+x > 9
x > 9-7
x > 2 units
therefore
The solution for the third side is the interval
(2,16)
All real numbers greater than 2 units and less than 16 units
A cierta hora del dia los rayos solares forman un angulo de 60° con el suelo. ¿Que sombra dara el arbol de 7 m de altura? Auxilioooooo por favorecer help!!
Answer:
4.04 m
Step-by-step explanation:
El arbol y el suelo forman un angulo de 90°. Son los catetos de un triangulo rectangulo.
Los rayos solares forman un angulo de 60° con el suelo y forman la hipotenusa del triangulo.
Se tiene un triangulo rectangulo de angulos de 30°-60°-90°.
En este genero de triangulo, el cateto mayor mide [tex] \sqrt{3} [/tex] veces el cateto menor.
cateto menor = [tex] \dfrac{7}{\sqrt{3}} [/tex]
[tex] = \dfrac{7\sqrt{3}}{3} [/tex]
[tex] = 4.04 ~m [/tex]
The length of the shadow of the tree would be -
s = {7/√3}.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that at a certain time of day the sun's rays make an angle of 60° with the ground.
Assume that the length of the shadow is [x] meters. Using the trigonometric ratios, we can write -
tan (60) = (height of tree {h})/(length of shadow {s})
sin(60)/cos(60) = (height of tree)/(length of shadow)
(√3/2)/(1/2) = {7/s}
√3/2 x 2 = 7/s
√3 = 7/s
s = {7/√3}
Therefore, the length of the shadow of the tree would be -
s = {7/√3}.
To solve more questions on functions, expressions and polynomials, visit the link below -
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{The question in english is -
At a certain time of day the sun's rays make an angle of 60° with the ground. What shade will the 7 m tall tree cast?}
Its for a test i need to take and this is a review question just need to know how to solve it
A high school coach needs to buy new athletic shorts for the 15 members of the basketball team. The coach must spend less than $200 and needs to determine how much he can spend per pair of shorts. Write and solve an inequality to determine the maximum price for each pair of shorts. What does the solution represent?
Answer:
15x < 200; x < 13.33; the maximum price for a pair of shorts
Step-by-step explanation:
1. Set up the inequality
Let x = price of a pair of shorts. Then
15x = price of shorts for the team
You have one condition:
15x < 200
2. Solve the inequality
[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]
3. Meaning of solution
The solution represents the maximum price the coach can pay for a pair of shorts.
If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.
Answer: The coach may spend up to $13.33 per pair of shorts.
Step-by-step explanation:
Hi, to answer this question we have to write an inequality with the information given:
Number of shorts: 15 (for 15 members) Budget: $200So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)
That cost must be equal or less to 200.
Mathematically speaking
15 x ≤ 200
Solving for x
x ≤200/15
x ≤ 13.33
This solution represents that the coach may spend up to $13.33 per pair of shorts.
Feel free to ask for more if needed or if you did not understand something.
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75%, percent of the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut?
Choose 2 answers
Answer:
.75
Step-by-step explanation:
If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.
Answer:
Area = [tex]3y^2 - 4y - 4[/tex] units square.
Perimeter = 8y units.
Step-by-step explanation:
Area of a rectangle = length * width.
Perimeter of a rectangle = 2*(length + width).
It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.
Area = length * width = (y-2)*(3y+2).
Expanding the expression gives:
Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.
Similarly,
Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.
Therefore, the expression for the area and the perimeter of the given rectangle is ([tex]3y^2 - 4y - 4[/tex]) units square and (8y) units respectively!!!
if you lose 3 1/2 pounds the first week of your diet and 2 2/3 pounds the second week, how many pounds do you still need to lose to reach your goal of losing 10 pounds?
Answer:
3 5/6
Step-by-step explanation:
3 1/2 plus 2 2/3 equals 6 1/6. 10 minus 6 1/6 equals 3 5/6. So they still need to lose 3 5/6 pounds to reach their go of losing 10 pounds.
let's firstly convert the mixed fractions to improper fractions, and then subtract.
[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{goal}}{10}-\stackrel{\textit{first week}}{\cfrac{7}{2}}-\stackrel{\textit{second week}}{\cfrac{8}{3}}\implies \cfrac{10}{1}-\cfrac{7}{2}-\cfrac{8}{3}\implies \stackrel{\textit{using an LCD of 6}}{\cfrac{(6)10-(3)7-(2)8}{6}} \\\\\\ \cfrac{60-21-16}{6}\implies \cfrac{23}{6}\implies 3\frac{5}{6}[/tex]
which of the following is the quotient of the rational expressions shown below 2x/4x+3 divided x-1/2x
Answer:
4x^2/4x^2-x-3
Step-by-step explanation:
boomchakalaka
The quotient is 4x²/4x²-x-3.
What's known as a quotient?
In mathematics, a quotient is a quantity produced with the aid of the department of numbers.
How do you discover a quotient?The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.
Learn more about quotient here: brainly.com/question/629998
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Check each set that includes the number shown 5/9 a. natural numbers b.whole numbers c.integers d. rational numbers e.irrational numbers f.real numbers
Answer:
5/9 from these categories can only be classified as rational and real.
Step-by-step explanation:
Natural numbers are counting numbers. People don't ever say the number 5/9 when counting people. So 5/9 is not natural.
Whole numbers are counting numbers plus also including 0. So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.
Integers are whole numbers plus the opposite of the whole numbers. 5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.
Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.
Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.
Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.
Answer:
d. Rational Numbers
f. Real Numbers
Step-by-step explanation:
The number shown is 5/9
Let us see the options one by one
a. Natural numbers
Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.
b. Whole numbers
Whole numbers is the set of natural numbers along with zero so it is also not the right answer.
c. Integers
Integers are combination of negative and positive whole numbers hence it is also not correct.
d. Rational numbers
Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.
e. As the number is rational, it cannot be irrational
f. Real numbers
As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..
A boy is flying a kite. The length of the string is 61 meters and the
horizontal distance between the boy and the kite is 60 meters. Assuming
there is no slack in the string, find the height of the kite from the ground.
Answer:
11 meters
Step-by-step explanation:
Using the Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + 60^2 = 61^2
a^2 + 3600 = 3721 (subtract 3600 from both sides)
a^2 = 121 (square root both sides so a^2 becomes a)
a = 11
Answer:
11 meters.Step-by-step explanation:
This problem models a right rectangle, where the hypothenuse is the length of the string, and the legs are the height and the horizontal distance. So, to find the answer, we just have to use the pythagorean theorem
[tex]a^{2}=b^{2}+c^{2}[/tex]
Where
[tex]a=61;b=60;c=x[/tex]
Replacing and solving for [tex]x[/tex], which is the height
[tex]a^{2}=b^{2}+c^{2}\\61^{2}=60^{2}+x^{2} \\x^{2}=61^{2}-60^{2}\\x=\sqrt{3721-3600}=\sqrt{121}=11[/tex]
Therefore, assuming there is no slack in the string, the height of the kite from the ground is 11 meters.