Recall that (a + b)² = a² + 2ab + b².
Let a = x² and b = y². Then
(x² + y²)² = (x²)² + 2x²y² + (y²)²
⇒ x⁴ + y⁴ = (x² + y²)² - 2 (xy)²
Given that x² + y² = 13 and xy = 6, we have
x⁴ + y⁴ = 13² - 2×6² = 97
A class consists of 60 boys and 40 girls. If two students are chosen at random, what is the probability that i) both are boys ii) both are girls iii) one boy and one girl?
(i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848 are the probabilities.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
A class consists of 60 boys and 40 girls.
To find the probability if two students are chosen at random:
The probability is ¹⁰⁰C₂.
(i) Both are boys,
The probability is ⁶⁰C₂ ÷ ¹⁰⁰C₂.
⁶⁰C₂ ÷ ¹⁰⁰C₂ = 60! / {2! x (60-2)!} ÷ 100! / {2! x (100-2)!}
⁶⁰C₂ ÷ ¹⁰⁰C₂ = 30 x 59 / 50 x 99
⁶⁰C₂ ÷ ¹⁰⁰C₂ =0.3575757576
(ii) Both are girls,
The probability is ⁴⁰C₂ ÷ ¹⁰⁰C₂.
⁴⁰C₂ ÷ ¹⁰⁰C₂ = 40! / {2! x (40-2)!} ÷ 100! / {2! x (100-2)!}
⁴⁰C₂ ÷ ¹⁰⁰C₂ = 20 x 39 / 50 x 99
⁴⁰C₂ ÷ ¹⁰⁰C₂ =0.1575757576
(iii) one boy and one girl,
The probability is ⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂.
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂ =
40! / {1! x (40-1)!}x 60! / {1! x (60-1)!} ÷ 100! / {2! x (100-2)!}
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂ = 40x60 / 50 x 99
⁴⁰C₁ × ⁶⁰C₁ ÷ ¹⁰⁰C₂=0.48484848
Therefore, the probabilities are (i) Both are boys = 0.3575757576, (ii) Both are girls = 0.1575757576 and (iii) one boy and one girl = 0.48484848
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Select the correct answer. you have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answer:
E. 5,040
Step-by-step explanation:
For plato users
Measure of the following
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle BIG=90^{\circ}[/tex] since the lines are perpendicular, meaning that [tex]m\angle HIG=90-30-25=\boxed{35^{\circ}}[/tex]
Find the surface area of the composite figure. 4 cm 3 cm 5 cm 3 cm 4 cm 5 cm 6 cm 4 cm If you'd like, SA = [ ? ] cm2 you can use a calculator.
The surface area of the composite figure is 144 square cm after calculating separately.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is the name given to this novel 3D object.
We have a composite figure made up of a triangular prism and a cuboid
First we calculate the surface area of the triangular prism:
= 2(area of one triangle) + area of three rectangles
= 2[(1/2)6×4] + 3×5 + 3×5
= 24 + 15 + 15
= 54 square cm
Surface area of rectangle(with three faces) = 2(4×3 + 4×6) + 3×6
= 2(12 + 24) + 18
= 72 + 18 = 90 square cm
Total surface area of figure = 54+ 90 = 144 square cm
Thus, the surface area of the composite figure is 144 square cm after calculating separately.
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what is the answer to this? i've been stuck on it forever
Answer:
42 degrees.
Step-by-step explanation:
70 = 3x + 33 + 5x + 13
70 = 8x + 46
8x = 24
x = 3
m∠ABC = 9 + 33 = 42 degrees.
HELP ME PLEASE ON MATHEMATICS!!
Answer:
1)526 kw
2)1943 m³
3) 33
4) 43 m³
5) 5010 kw
Step-by-step explanation:
1) 7675-7149= 526
2) 462+ 1481= 1943
3) 168-135 = 33
4) 1499 -l456= 43
5) 4945+65= 5010
What is the mean absolute deviation of the data set? Round to the nearest hundredth if necessary.
The mean absolute deviation, rounded to the nearest hundredth, is: 11.67 calories.
How to Find the Mean Absolute Deviation?To find the mean absolute deviation, find the mean of the data then find the average distance of each data point from the mean.
Given the data, 61, 42, 52, 27, 35, 23:
Mean = (61 + 42 + 52 + 27 + 35 + 23)/6
Mean = 240/6
Mean = 40
Mean absolute deviation = [(61 - 40) + ( 42 - 40) + ( 52 - 40) + ( 27 - 40) + ( 35 - 40) + ( 23 - 40) 6 = (21) + (2) + (12) + (13) + (5) + (17)] / 6 = 70/6
Mean Absolute Deviation = 11.67 calories.
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Please help me on this
Answer:
4
Step-by-step explanation:
16/4
If the slope of the line that goes through the points (2, 7) and (5, a) is -3, what is the value of a?
Answer:
a = -2
Step-by-step explanation:
I graphed the given point (2,7) and then I used that point and plugged the point and the slope into the point-slope formula, which is (y-y₁)=m(x-x₁). Then, I just looked for where x=5 on the line and it was -2
Yesterday a car rental agency rented 4 vehicles, of which 2 were pickup trucks. what is the experimental probability that the first vehicle rented today will be a pickup truck?
Using it's concept, it is found that the experimental probability that the first vehicle rented today will be a pickup truck is of 0.5 = 50%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, we have that out of 4 vehicles, 2 are pickup trucks, hence the experimental probability is given by:
p = 2/4 = 1/2 = 0.5.
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4. Factor:
j) x(x+2) + y (x + 2) - 5(x + 2)
k) 5y2 - 10y3
l) ax + ay + az
5. Factor:
m) yx(y+1) + 4x(y + 1) - 5(y + 1)
n) 6p2 - 3p3
o) 4x4 + 2x
The results of factoring are presented below for each algebraic expression.
x(x-3)+y(x+2)-105y²(1-2y)a(x+y+z)y(xy +5x-5)-13p²(2-p)[tex]2x(2x^3+1)[/tex]FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: y²-y= y(y-1), where y is a common term.
You should apply the factor out a common term for solving the question.
Exercise 4 - letter jx(x+2) + y (x + 2) - 5(x + 2)
x²+2x+xy+2y-5x-10
x²-3x+xy+2y-10
x(x-3)+y(x+2)-10
Exercise 4 - letter k[tex]5y^2 - 10y^3[/tex]
5y²(1-2y)
Exercise 4 - letter lax+ay+az
a(x+y+z)
Exercise 5 - letter myx(y+1) + 4x(y + 1) - 5(y + 1)
xy²+xy+4xy+4-5y-5
xy²+5xy-1-5y
y(xy +5x-5)-1
Exercise 5 - letter n[tex]6p^2 - 3p^3[/tex]
3p²(2-p)
Exercise 5 - letter o[tex]4x^4 + 2x[/tex]
[tex]2x(2x^3+1)[/tex]
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Find f¹(x) for the function
f(x) = -4.
2
f¹(x) = [?]x + [ ]
Answer:
[tex] {f}^{ - 1}(x) = 2x + 8[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{x}{2} - 4 \\ \\ y = \frac{x}{2} - 4 \\ \\ y = \frac{x - 8}{2} \\ \\ x = 2y + 8 \\ \\ {f}^{ - 1} (x) = 2x + 8[/tex]
Over what interval is the function in this graph constant?
OA. -3≤x≤2
B. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The interval of the function for which the given graph is constant is when the value of x is less than -2 and when the value is greater than -4. Therefore, we can write this interval as -4< x < -2.
Hence, the correct option is B.
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If the grain pile has a diameter of 30 feet and a height of 16 feet, what is the volume of the grain pile? In terms of TT.
Answer: 75TT
(When you answer in terms of pi, don’t multiply pi but leave it in your answer)
Step-by-step explanation:
assuming the grain pile is a pyramid, V=1/3 TT r^2
(1/3) (TT) (15^2). Remember radius is 1/2 of diameter
(1/3) (225) TT
Answer 75TT
Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Show all steps.
!BRAINLIEST AND 5 STARS TO BEST ANSWER AND FULL
EXPLANATION ONLY!
The coordinate of point P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 is [tex](-\frac{22}3, \frac{23}6)[/tex]
How to determine the coordinates of P?The given parameters are:
A = (-9,3)
B = (1, 8)
m : n = 1 : 5
The coordinate of point P is then calculated using:
[tex]P = \frac{1}{m + n} (mx_2+nx_1,my_2+ny_1)[/tex]
Substitute known values
[tex]P = \frac{1}{1 + 5} (1 * 1 + 5 * -9, 1 * 8 + 5 * 3)[/tex]
Evaluate
[tex]P = \frac{1}{6} (-44, 23)[/tex]
Evaluate the product
[tex]P = (-\frac{22}3, \frac{23}6)[/tex]
Hence, the coordinate of point P is [tex](-\frac{22}3, \frac{23}6)[/tex]
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The graph of a linear function is given below.
f(x)
-8
8
What is the zero of the function?
OA. -3
OB. -
OC.
-
-2
6
6 +
2
2
6
N
a
00
X
The zero of the linear function is -2
How to determine the zero of the function?This is the point where the line of the equation crosses the x-axis
From the attached figure, the line cross the graph at:
x = -2
Hence, the zero of the function is -2
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23.21
Which equation represents the relationship between the number of liters, x, and the number of liquid pints, y?
O y = x + 5.55
Oy=x-5.55
O y = 2.11x
O Y - 211
The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
How to determine the equation?The attached table of values represents the missing piece in the question.
Start by calculating the rate of change using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (14.77 - 10.55)/(7- 5)
Evaluate
m = 2.11
The equation is then calculated using:
y = m(x - x1) + y1
This gives
y = 2.11(x - 5) + 10.55
Evaluate
y = 2.11x - 10.55 + 10.55
y = 2.11x
Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x
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Is this congruent yes or no and explain why
Answer:
Yes, it is because the triangles are about the same shape.
Step-by-step explanation:
Answer: Yes, it is because the triangles are about the same shape. So I think they are congruent.
Which of the following functions best models the data represented by the scatterplot shown below?
A: y=160x-100
B: y=2^x+12
C: y=8x^2+10
D: y=25x+20
Answer:
C: y = 8x^2 + 10.
Step-by-step explanation:
It looks close to being a parabola so I think it is probably a function in x^2.
Try 8x^2 + 10
Checking against the plot
When x = 5 , y = 8(5)^2 + 10 = 210 , and on graph its 200
Calculating y for other values:
When x = 7, y = 8(7)^2 + 10 = 402, and on graph y = 400.
When x = 11, y = 978 , and on graph = 1000.
When x = 17, y = 2322, and on graph y = about 2350.
Ali is about 2,760,000 minutes old. Write this age as a number multiplied by a power of 10. Use ^ to represent an exponent (power)
Answer:
27600x10^10
Step-by-step explanation:
Jenny wants to start an after-school club, so she decides to survey the student body to determine which club would be the most popular: French Club, Architecture Club, or Anime Club. She decides (with Mrs. Howell's permission) to survey the first 25 students who show up to her class one day.
Does her survey comprise an accurate representation of the Reach student body? Why or why not?
Answer:
no because it just reaches one class, not the student body
Step-by-step explanation:
A scientist has two solutions, which she has labeled solution a and solution b. each contains salt. she knows that solution a is 65% salt and solution b is 90% salt. she wants to obtain 110 ounces of a mixture that is 70% salt. how many ounces of each solution should she use?
Answer:
All
Step-by-step explanation:
I done this question before
If f(x) = 2(3x) + 1, what is the value of f(2)
Answer:
x=−2 in the formula for F(x) . Therefore, F(−2)=3(−2)2+1=3(4)+1=13 .
In which two of these numbers does the digit
6 have a value of 0.6?
16.7
61.28 14.63 28.16 96.77 85.62
Answer:
Step-by-step explanation:
In this numbers:
14.63
85.62
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
To determine in which two numbers the digit 6 has a value of 0.6, we need to examine the place value of 6 in each number.
Let's go through each number:
1. 16.7: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
2. 61.28: The digit 6 is in the ones place, so its value is 6 (not 0.6).
3. 14.63: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
4. 28.16: The digit 6 is in the hundredths place, so its value is 6 * 0.01 = 0.06.
5. 96.77: The digit 6 is in the tens place, so its value is 6 * 10 = 60 (not 0.6).
6. 85.62: The digit 6 is in the tenths place, so its value is 6 * 0.1 = 0.6.
The two numbers where the digit 6 has a value of 0.6 are 14.63 and 85.62.
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Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. How much fabric will he need?
A square pyramid with a base of 4 meters by 4 meters and triangular side heights of 3 meters.
The area of a 2D form is the amount of space within its perimeter. The total surface area of the square pyramid is 40 meters².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Henri built a lantern in the shape of a square pyramid. He wants to cover the entire pyramid with fabric. Therefore, the amount of fabric that Henri will need is equal to the total surface area of the square pyramid.
Total surface area = Area of the base + 4(Area of the triangle)
= (4m × 4m) + 4(0.5×4m×3m)
= 16 meters² + 24 meters²
= 40 meters²
Hence, the total surface area of the square pyramid is 40 meters².
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a parallelogram has an area of 153
cm and height of 17 cm what is the length of the base
Answer:
9 cm
Step-by-step explanation:
Formula :
Area (parallelogram) = Base × Height
=========================================================
Given :
⇒ Area = 153 cm²
⇒ Height = 17 cm
===========================================================
Solving :
⇒ 153 cm² = 17 cm × Base
⇒ Base = 153/17
⇒ Base = 9 cm
Answer:
Base = 9 cm
Step-by-step explanation:
Given dimensions:
Area of the parallelogram: 153 cm^2 ( It should be cm^2 not cm )Height of the parallelogram: 17 cmTo Find:
The baseSolution:
This question is a bit tricky.Usually,the height and the base are given. We'll use the formula of area of parallelogram , then substitute/plug the values of height and area of parallelogram, with the exception of base as it's not given.
So recall the formulae of area of parallelogram:
[tex] \rm \: Area_{(Parallelogram)} = b \cdot{h}[/tex]
Here,b = baseh = heightPlug/substitute the values of area of parallelogram & height:
[tex]\rm \: 153 \: cm ^2 =b \cdot17 \: cm[/tex]
We created an equation.Solve it now.
Transpose 17 cm to the LHS:[tex] \implies \rm \cfrac{153 \: cm^2}{17 cm} = base[/tex]
Cancel 153/17 by 17:[tex] \implies \rm9 \; cm = \: base[/tex]
[tex] \implies \rm \: Base = 9\; cm[/tex]
Yes! We're done!
Hence,the base is 9 cm of the parallelogram.
[tex] \rule{225pt}{2pt}[/tex]
Type the correct answer in each box. use numerals instead of words. what are the x-intercept and vertex of this quadratic function? g(x) = -5(x-3)^2 write each feature as an ordered pair: (a,b). the x-intercept of function g is . the vertex of function g is .
Considering the given quadratic function, we have that:
The x-intercept is (3,0).The vertex is (3,0).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is given by:
g(x) = -5(x - 3)²
Hence h = 3, k = 0, and the vertex is (3,0).
What are the x-intercepts of a function g(x)?They are the values of x for which g(x) = 0, hence:
-5(x - 3)² = 0
(x - 3)² = 0
Applying the root to both sides:
x - 3 = 0.
x = 3.
The x-intercept is (3,0).
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any help is great find the missing length?
Answer:
3Step-by-step explanation:
Similar = proportional
solve with an equation
12 : 9 = 4 : x
x = 4 * 9 : 12
x = 3
lmk if u can figured it out
Answer:
see explanation
Step-by-step explanation:
since the triangles are congruent , then corresponding sides and angles are congruent.
(1)
Δ HIJ ≅ Δ LMN
sides angles
--------- -----------
HI ≅ LM ∠ H ≅ ∠ L
HJ ≅ LN ∠ I ≅ ∠ M
IJ ≅ MN ∠ J ≅ ∠ N
(2)
Δ XYZ ≅ Δ JKL
sides angles
-------- ------------
XY ≅ JK ∠ X ≅ ∠ J
XZ ≅ JL ∠ Y ≅ ∠ K
YZ ≅ KL ∠ Z ≅ ∠ L
Answer:
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N.2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.Step-by-step explanation:
I believe it's asking to list the corresponding sides and pairs of angles in the congruent triangles.
Look at the order of the letters HIJ and LMN. There are 3 letters, which represent 3 sides and 3 angles. The first, second, and third letters of the first triangle correspond to the first, second, and third letters of the second triangle.
1. ΔHIJ ≅ ΔLMN
sides: HI ≅ LM, IJ ≅ MN, HJ ≅ LN.angles: ∠H ≅ ∠L, ∠I ≅∠M, ∠J ≅∠N. (these can also be written as ∠HIJ ≅ ∠LMN, ∠HJI ≅ ∠LNM, ∠IHJ ≅ ∠MLN... but it depends on what the instructor wants really).2. ΔXYZ ≅ ΔJKL
sides: XY ≅ JK, YZ ≅ KL, XZ ≅ JL.angles: ∠X ≅ ∠J, ∠Y ≅∠K, ∠Z ≅∠L.You sold a combined total of 25 of item A and item B. You made $88.
Item A: 3$
Item B: 4$
How much of each item did you sell?
Answer:
x = 25 - y = 2
Step-by-step explanation:
Let x represent the number of item A that you sold.
Let y represent the number of item B that you sold.
The total number of item A and item B sold is 25. This means that
x + y = 25
The cost of item A is $3, the cost of item B is $4 and if the total amount of money made is $88, this implies
3(x) + 4(y) = 88 (Substitute x = 25 - y)
→ 3(13 - y) + 4y = 88
→ 39 - 3y + 4y = 88
→ 39 + y = 16
→ y = 23
If y = 23, then x = 25 - y = 2