Answer:
x = − 8 and y = 5 or (-8, 5)
Step-by-step explanation:
In the Itty Bitty High School, there are 85 students. There are 27 students who take French, 51 who take Geometry and 38 who take History. There are 10 that take Geometry and French, 7 that take History and French and 15 that take Geometry and History. There are 2 students who take all 3 and 5 that take none of these subjects.
Answer:
58 students
Step-by-step explanation:
Given
[tex]Total = 85[/tex]
[tex]French = 27[/tex]
[tex]Geometry = 51[/tex]
[tex]History = 38[/tex]
[tex]None = 5[/tex]
[tex]All = 2[/tex]
Required
Students that take only 1 subjects
The attached image illustrates the question.
For French only (x), we have:
[tex]x + 7 -2+10-2+2=27[/tex]
[tex]x + 15=27[/tex]
Collect like terms
[tex]x =- 15+27[/tex]
[tex]x =12[/tex]
For Geometry only (y), we have:
[tex]y+10-2+15-2+2=51[/tex]
[tex]y+23=51[/tex]
Collect like terms
[tex]y=-23+51[/tex]
[tex]y=28[/tex]
For History only (z), we have:
[tex]z +15-2+7-2+2=38[/tex]
[tex]z +20=38[/tex]
Collect like terms
[tex]z =-20+38[/tex]
[tex]z =18[/tex]
Students with one subject is then calculated as:
[tex]1\ subject = x+y+z[/tex]
[tex]1\ subject = 12 + 28 + 18[/tex]
[tex]1\ subject = 58[/tex]
Plz help me well mark brainliest if correct....???.
Answer:
C.18
Step-by-step explanation:
In the chart it shows that 18 boys like to read science fiction. Hope this helps :)
help I don't know the answer
the slope of the line joining points (3 ;2) and (0;a) is-1 determine the value of a
Given:
The slope of the line joining points (3,2) and (0,a) is -1.
To find:
The value of a.
Solution:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope of a line is:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line joining points (3,2) and (0,a) is -1. So,
[tex]\dfrac{a-2}{0-3}=-1[/tex]
[tex]\dfrac{a-2}{-3}=-1[/tex]
Multiply both sides by -3.
[tex]a-2=-1(-3)[/tex]
[tex]a-2=3[/tex]
[tex]a=3+2[/tex]
[tex]a=5[/tex]
Therefore, the value of a is 5.
What is the volume of a sphere with a diameter of 32,5 m, rounded to the
nearest tenth of a cubic meter?
Answer:
V≈17974.16
Step-by-step explanation:
Using the formulas
V=4
3πr3
d=2r
Solving for V
V=1/ 6πd^3=1/ 6·π·32.53≈17974.16422
What is 5.8 written as a percentage?
A)
0.58%
B)
5.8%
o
58%
D)
580%
Answer:
D) 580%
Step-by-step explanation:
you move the decimal to the right twice.
5.8 ---> 580%
hope this helps :)
please help. no links. need answers for all questions :))
Answer:
1. The surface area of the cube is 324 square units
The volume of the cube 360 unit cube
2. The surface area of the cylinder is approximately 169.65 square units
The volume of the cylinder is approximately 169.65 unit cube
3. The surface area of a square pyramid is 360 square units
The volume of the square pyramid is 400 unit cube
4. The surface area of a cone is approximately 452.39 square units
The volume of the cone is approximately 50.27 unit cube
5. The surface area of the triangular prism is 240 square units
The volume of the triangular prism is 180 unit cube
6. The surface area of the sphere is approximately 804.25 square units
The volume of the sphere is approximately 2.144.66
7. The surface area of the composite figure is approximately 653.46 square units
The volume of the composite figure is approximately 1,474.45 unit cube
Step-by-step explanation:
1. The surface area of the figure, SA = 2 × (w·h + l·w + h·l)
Where;
w = The width of the figure = 6
l = The length of the figure = 12
h = The height of the figure = 5
We get;
SA = 2 × (6 × 5 + 12 × 6 + 5 × 12) = 324
The surface area of the figure, SA = 324
The volume of the figure, V = l × w × h
∴ V = 12 × 6 × 5 = 360
The volume of the figure, V = 360
2. The surface area of a cylinder, SA = 2·π·r² + 2·π·r·h
The radius of the given cylinder, r = 3
The height of the given cylinder, h = 6
∴ SA = 2×π×3² + 2×π×3×6 ≈ 169.65
The surface area of the cylinder, SA ≈ 169.65
The volume of a cylinder, V = π·r²·h
∴ V = π×3²×6 ≈ 169.65
The volume of the cylinder, V ≈ 169.65
3. The surface area of a square pyramid, SA = b² + 4·(1/2)·b·√((b/2)² + h²)
Therefore, for the given square pyramid, we have;
SA = 10² + 4×(1/2)×10×√((10/2)² + 12²) = 360
The surface area of a square pyramid, SA = 360
The volume of a square pyramid, V = (1/3) × Area of Base × Height
Therefore, or the given pyramid we have;
V = (1/3) × 10² × 12 = 400
The volume of the square pyramid, V = 400
4. The surface area of a cone, SA = π·r·(r + l)
Where;
The radius of the cone = r
The slant height of the cone, l = 10
The height of the cone, h = 6
∴ The radius of the cone, r = √(10² - 6²) = 8
∴ SA = π×8×(8 + 10) ≈ 452.39
The surface area of a cone, SA ≈ 452.39
The volume of the cone, V = (1/3) × π·r·h
∴ V = (1/3) × π × 8 × 6 ≈ 50.27
The volume of the cone, V ≈ 50.27
5. The surface area of the triangular prism, SA = 2 × (1/2)× b·h + b·w + h·w + w·l
Where;
b = The base length of the triangular surfaces = 5
h = The height of the triangular surfaces = 12
w = The width of the triangular prism = 6
l = The slant length of the prism = 13
Therefore;
SA = 2 × (1/2)× 5 × 12 + 5 × 6 + 12 × 6 + 6 × 13 = 240
The surface area of the triangular prism, SA = 240
The volume of a triangular prism, V = (1/2)·b·h·w
V = (1/2) × 5 × 12 × 6 = 180
The volume of the triangular prism, V = 180
6. The surface of a sphere, SA = 4·π·r²
Where;
r = The radius of the sphere = 8
∴ SA = 4 × π × 8² ≈ 804.25
The surface area of the sphere, SA ≈ 804.25
The volume of a sphere, V = (4/3)·π·r³
∴ V ≈ (4/3)×π×8³ ≈ 2,144.66
The volume of the given sphere, V ≈ 2.144.66
7. The figure is a composite figure made up of a cone and an hemispher
The surface area of the cone shaped part of the figure, SA = π·r·l
Where;
r = The radius of the cone = 8
l = The slant height of the cone = 10
∴ SA₁ = π × 8 × 10 ≈ 251.34
The surface area of the cone shaped part of the figure, SA₁ ≈ 251.34
The volume of the cone, V₁ = (1/3)·π·r²·h
Where;
h = The height of the cone = √(10² - 8²) = 6
∴ V₁ = (1/3) × π × 8² × 6 ≈ 402.12
The volume of the cone, V₁ ≈ 402.12
The surface area of the hemisphere, SA₂ = 2·π·r²
∴ SA₂ = 2 × π × 8² ≈ 402.12
The surface area of the hemisphere, SA₂ ≈ 402.12
The volume of a hemisphere, V₂ = (2/3)·π·r³
∴ V₂ = (2/3) × π × 8³ ≈ 1072.33
The volume of a hemisphere, V₂ ≈ 1,072.33
The surface area of the composite figure, SA = SA₁ + SA₂
∴ SA = 251.34 + 402.12 = 653.46
The surface area of the composite figure, SA ≈ 653.46
The volume of the composite figure, V = V₁ + V₂
∴ V = 402.12 + 1,072.33 = 1,474.45
The volume of the composite figure, V ≈ 1,474.45.
Help!!!!!!!!! Help help help help
Can someone please help me with this question please (sorry for bad photo quality)
Answer:
a) (-1/2,3/2)
Step-by-step explanation:
-3x = x + 2
4x + 2 = 0
4x = -2
x = -1/2
y = -3(-1/2) = 3/2
YOUR ASSIGNMENT: Difference of 10 Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers is greater than 10, then Nita wins. Use the information in the interactive and what you know about absolute value inequalities to better understand the game. Your Player 1. Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select
Answer:
[tex]|x - y| > 10[/tex] ---- Nita wins
[tex]|x - y| < 10[/tex] --- Eric wins
Step-by-step explanation:
The complete instruction is to determine the range at which Erik or Nita wins.
To start with, let
[tex]x \to[/tex] Erik's score
[tex]y \to[/tex] Nita's score
If the difference is greater than 10, the Nita wins.
This implies that:
[tex]|x - y| > 10[/tex] ---- Nita
If less than 10, then Eric wins
This implies that:
[tex]|x - y| < 10[/tex] --- Eric wins
Now, assume that Nita chose 5.
For Nita to win, we have:
[tex]|x - y| > 10[/tex]
[tex]|x - 5| > 10[/tex]
Remove the absolute symbol
[tex]-10 > x - 5 > 10[/tex]
Split
[tex]-10 > x - 5\ or\ x - 5 > 10[/tex]
Solve for x
[tex]5 -10 > x \ or\ x > 10 + 5[/tex]
[tex]-5> x \ or\ x > 15[/tex]
Rewrite as:
[tex]x< -5 \ or\ x > 15[/tex]
x cannot be negative.
So:
[tex]x > 15[/tex]
x cannot exceed 20.
So:
[tex]15 < x \le 20[/tex]
Multiply. (2x-1)(3x+5)
ANSWER
6x² + 7x - 5
Step-by-step explanation:
(2x-1)(3x+5)
= 6x² + 10x - 3x - 5
= 6x² + 7x - 5
Answer:
6x² + 7x - 5
Step-by-step explanation:
FOIL method
Multiply the First terms
2x * 3x = 6x²
Then the Outer terms
2x * 5 = 10x
Inner terms
-1 * 3x = -3x
Last terms
-1 * 5 = -5
--------------------------
All together
6x² + 10x - 3x - 5
Combine like terms
6x² + 7x - 5
Mr. Harris had 35 players try out for the softball
team, but he cut some players from the team.
By the end of tryouts, the team still had more
than 25 players. (Use p as a variable.)
Answer:
35-P=25
Step-by-step explanation:
P= Number of players he cut
Select all ratios equivalent to 10:5.
110:55
24:2
14:6
Answer:
110:55
Step-by-step explanation:
first, let's simplify all our options
110:55=10:5
the first one works!
(to check if you're not sure, ratios are fractions. using the numerator to divide, you can divide the numerator by the denominator. in this case, the numerator happens to be greater. 110/55=2. 10/5=2. they both equal to 2! they are equivalent. you can use this to solve other problems!!)
24:2= 12:1
this does not work
14:6= 7:3
this does not work
the only one that works is 110:55
hope this helped <33333
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table.
A 4-column table with 3 rows. Column 1 has entries in band, not in band, total. Column 2 is labeled play a sport with entries a, d, g. Column 3 is labeled do not play a sport with entries b, e, h. Column 4 is labeled total with entries c, f, i.
Which of the following correctly represents the given data in the problem?
a = 24, g = 48, h = 22, i = 80
a = 22, c = 80, d = 24, i = 48
a = 24, b = 48, c = 22, i = 48
a = 24, c = 48, e = 22, i = 80
Answer:
yes
Step-by-step explanation:
mark me brainlist please
Answer:
the answer is d
Step-by-step explanation:
[tex] \sf \red{Help \: help \: help \: help \: I'm \: desperate - . - }[/tex]
Step-by-step explanation:
1)
7x+20°+3x=180°{straight angle}
10x=180-20
x=160/10
x=16°
again,
y=7x+20{vertically opposed angle r equal}
7×16+20132°stay safe healthy and happy.Answer:
1. x = 20
y = 120
2. x = 263
Step-by-step explanation:
•••
As AOB is a line,
( 7x - 20 ) + 3x = 180
7x - 20 + 3x = 180
10x - 20 = 180
10x = 180 + 20 = 200
10x = 200
x = 200/10 = 20
Then, as COD is a line,
y + 3x = 180
y + 3(20) = 180
y + 60 = 180
y = 180 - 60 = 120
•••
2. Draw a parallel line AB and CD.
Then,
Angle BAE + Angle y = 180 [Co-interior angles]
56 + y = 180
y = 180 - 56 = 124
Angle DCE + Angle z = 180
41 + z = 180
z = 180 - 41
z = 139
Now, z + y = 139 + 124 = 263
[tex][/tex]
What is the area of the figure?
A. 54 cm2
B. 42 cm2
C. 54 cm
D. 42 cm
Answer
The area is 54cm² To get the area i split the shape into two shape both having a length of 9in and a width of 3in. I calculate the area for one by using lxw=area and get 27 and times that by two to get 54.
When calculating the area for this object you get 54 and you add the ²symbol because its area is not one dimensioned it is two dimensioned or length times width not just length, so you use the ² symbol to show that.
Answer:
the answer is
b.)42cm2
Step-by-step explanation:
if u add all the figures together u will get ur answer
WHATS THE ANSWER?? answer ASAP
Five friends take a maths test
Adam, Brandon, Chen together together scored 200 marks
Brandon, Chen and Damion together scored 215
Chen, Damion, Erica together scored 224
Damion and Erica scored more than Chen
The five of them together scored 350 marks
What are their individual scores
Answer:
Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.
Step-by-step explanation:
Since five friends took the maths test, and Adam, Brandon, and Chen together together scored 200 marks; Brandon, Chen and Damion together scored 215; Chen, Damion and Erica together scored 224; and Damion and Erica scored more than Chen; While the five of them together scored 350 marks, to determine what are their individual scores the following calculations must be performed:
Adam + Brandon + Chen = 200
Damion + Erica = 150
Brandon + Chen + Damion = 215
Adam + Erica = 135
Chen + Damion + Erica = 224
Adam + Brandon = 126
Adam + Brandon = 126 + Chen = 200
Chen = 200 - 126
Chen = 74
Damion and Erica scored more than Chen
Chen + Damion + Erica = 224
74 + Damion + Erica = 224
Damion + Erica = 150
Damion = 75
Erica = 75
Brandon + Chen + Damion = 215
Brandon + 74 + 75 = 215
Brandon = 215 - 74 - 75
Brandon = 66
Adam = 350 - 75 - 75 - 74 - 66
Adam = 60
Therefore, Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.
(05.02)A farmer has decided to divide his land area in half in order to plant soy and corn Calculate the area of the entire area so he knows how much soil is needed. SOY #6 yards 6 yards CORN 2.5 yards 6.5 yards Each bag of soil covers 15 Square yards. How many bags should the farmer purchase? 0 1 bag O2 bags O 3 bags 4 bags
9514 1404 393
Answer:
4 bags -- the correct answer is marked
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
where b is the base length and h is the height.
Here, the base is the sum of lengths 2.5 yd and 6.5 yd. The height is given as 6 yd. So, the area is ...
A = (2.5 yd + 6.5 yd)(6 yd) = 54 yd²
At 15 yd² per bag, the farmer will need ...
(54 yd²)/(15 yd²/bag) = 3 3/5 bags
Assuming the farmer can purchase only whole bags, the farmer should purchase 4 bags of soil.
PLEASE HELP MEEEEEE!!!
Answer:
100
Step-by-step explanation:
Mandy is shopping for plates. She is trying to decide between the three packages below. If Mandy is looking for the best deal for each individual plate, which package should she buy
Answer:
Package 3
Step-by-step explanation:
Package 1,
No. of plates = 5
Cost = $38.75
Cost of 1 plate = [tex]\dfrac{38.75}{5}=\$7.75[/tex]
Package 2,
No. of plates = 8
Cost = $58
Cost of 1 plate = [tex]\dfrac{58}{8}=\$7.25[/tex]
Package 3,
No. of plates = 14
Cost = $94.5
Cost of 1 plate = [tex]\dfrac{94.5}{14}=\$6.75[/tex]
The cost of 1 plate in package 3 is the least. It means she should buy package 3.
In
any
School there are 7000
students 45%. are boys. How many
boys are there? How
many girls
are there
Answer: there are 3150 boys and 3850 girl
Step-by-step explanation:
45÷100×7000= 3150 and 7000- 3150 = 3850
Hope this helps!!
properties of parallelograms
PLEASE HELP
Answer:
m∠Q = 109°
m∠QRT = 109°
x = 4
Step-by-step explanation:
1). "Opposite angles of a parallelogram are equal"
By this property,
m∠Q = m∠S = 109°
2). "Opposite sides of a parallelogram are parallel and equal in measure"
By this property,
RQ║ST and diagonal RT is a transversal line.
m∠QRT = ∠SRT = 30° [Alternate interior angles]
3). "Opposite sides of a parallelogram are parallel and equal in measure"
RS = QT
2x = 8
x = 4
David has 55% ownership of a company. If there are 1,300,000 stocks, how many stocks
loes he own?
Answer:
715000
Step-by-step explanation:
1300000 • 55%,
55% = 0.55
1300000 • 0.55 = 715000
Pls help! I need to show my work!
Answer:
Step-by-step explanation:
68 frefq4gtrhrsahhrhshrr
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 : Suppose a sample of 292 tenth graders is drawn. Of the students sampled, 240 read above the eighth grade level. Using the data, construct the 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer:
The 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.149, 0.207).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Suppose a sample of 292 tenth graders is drawn. Of the students sampled, 240 read above the eighth grade level.
So 292 - 240 = 52 read below or at eight grade level, and that [tex]n = 292, \pi = \frac{52}{292} = 0.178[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.28\sqrt{\frac{0.178*0.822}{292}} = 0.149[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.28\sqrt{\frac{0.178*0.822}{292}} = 0.207[/tex]
The 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.149, 0.207).
How do you solve this problem ?
Answer: 2y124√y12
How to: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Have a great day and stay safe !
9514 1404 393
Answer:
[tex]2\cdot y^{\frac{5}{8}}[/tex]
Step-by-step explanation:
The applicable rules of exponents are ...
[tex](a^b)^c=a^{bc}\\\\(ab)^c=a^c\cdot b^c\\\\\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]
__
So, the given expression can be rewritten to ...
[tex](4\sqrt[4]{y^5})^{\frac{1}{2}}=(4^{\frac{1}{2}})(y^{\frac{5}{4}})^{\frac{1}{2}}= 2\cdot y^{\frac{5}{4}\cdot\frac{1}{2}}=\boxed{2\cdot y^{\frac{5}{8}}}[/tex]
_____
k = 2; n = 5/8
a rectangle of side 48cm by 60cm is divided into squares of side x cm.find the greatest value of x and find the area of the area.
Answer:
greatest value of X = 12
Area of square = 144 cm²
Step-by-step explanation:
The greatest value of X will be the highest common factor of 48 and 60 since we are told that the rectangle is divided into squares.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The highest common factor between both factors of 48 and 60 is 12.
Thus,
greatest value of X = 12
Area of square = 12 × 12
Area of square = 144 cm²
Is (1, 2) solution for this system of inequalities ?
Answer:
MAYBE
Step-by-step explanation:
2(x+4)-6 = 2(x-8)+1
plz show work because if I don't have it then I can't pass
Answer:
no solution
Step-by-step explanation:
Given
2(x + 4) - 6 = 2(x - 8) + 1 ← distribute and simplify both sides
2x + 8 - 6 = 2x - 16 + 1
2x + 2 = 2x - 15 ( subtract 2 from both sides )
2x = 2x - 17 ( subtract 2x from both sides )
0 = - 17 ← not possible
This indicates the equation has no solution