MAKING AN ARGUMENT In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In this exercise, you're required to describe the score which this ski jumper must earn on the second jump to beat his or her competitor. Therefore, let x represent the score of his or her second acrobatic ski jump.
Based on the competitor's score of 119.8 in the second jump, this ski jumper must earn the following score represented by this inequality:
x > 119.8
Who is correct?From the table (see attachment), we can logically deduce that the competitor's score in the first ski jump is equal to 117.1. This ultimately implies that, the ski jumper's score can be modeled by this inequality:
x > 117.1
In this context, we can reasonably infer and logically deduce that both the coach and the teammate are correct because a score of "118.4" and "117.5" are greater than a score of "117.1."
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Complete Question:
MAKING AN ARGUMENT
In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.
a. Describe the score that you must earn on your second jump to beat your competitor.
b. Your coach says that you will beat your competitor if you score 118.4 points. A teammate says that you only need 117.5 points. Who is correct? Explain.
100 students are interviewed to see which of biology, chemistry or physics they prefer.
39 of the students are girls. 21 of the girls like biology best.
16 of the boys prefer physics.
11 out of the 34 who prefer chemistry are girls.
What percentage of the students prefer biology?
.
Answer:
43%
Step-by-step explanation:
There are 39 girls. 21 of them like biology. 11 out of 34 who like chemistry are girls.
No. of girls who prefer biology = 21
There are (100-39) boys. 16 of them like physics. (34-11) of them like chemistry.
No. of boys who prefer biology = 100-39-16-34+11
= 22
Percentage of students who prefer biology = [tex]\frac{21+22}{100}[/tex] × 100%
= [tex]\frac{43}{100}[/tex] × 100%
= 43%
There are 270 calories in 5 ounces of a certain ice cream how many calories are there in 2 pounds
1 pound = 16 ounces (general knowledge)
270 calories divided 5 ounces
1 ounce= 54 calories
2 pounds = 32 ounces
32 ounces × 54 calories = 1728
2 pounds = 1728 calories
A cyclist travels 21 miles in 45 minutes.
What is his average speed in mph?
Answer:
28 mph
Step-by-step explanation:
1h = 60m
45m --- 21 miles
60m --- [tex]\frac{60}{45}[/tex] × 21 miles = 28 miles
Thus, his average speed is 28 mph.
help what does 2 1⁄3 ÷ 1 1⁄2 =
Answer:
[tex]1\frac{5}{9}[/tex]
Step-by-step explanation:
This is the answer because:
1) Reduce the expression, if possible, by cancelling the common factors.
2) You can also find the reciprocal of 1 1/2 = 3/2 while dividing the expression:
1. Convert both fractions into improper fractions:
[tex]2\frac{1}{3} = \frac{7}{3}[/tex]
[tex]1\frac{1}{2} = \frac{3}{2}[/tex]
2. Divide both fractions:
[tex]\frac{7}{3}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{7}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{14}{9}[/tex] = [tex]1\frac{5}{9}[/tex]
Therefore, the answer is [tex]1\frac{5}{9}[/tex]
Hope this helps! :D
What are the coordinates for a dilated triangle, A'B'C', if
the scale factor for the dilation is 0.75?
Answer:
3
Step-by-step explanation:
Answer: Answer is D
Step-by-step explanation:
I just did the question
Which point lies on the circle x^2+y^2=100
A (0,-100)
B (10,-10)
C (25,75)
Answer:
NOT a single ordered pair satisfies the equation.
Step-by-step explanation:
Given the equation
[tex]x^2+y^2=100[/tex]
Let us substitute all the given ordered pairs to find which ordered pair satisfies the equation.
For (0, -100)
[tex]x^2+y^2=100[/tex]
substitute x=0 and y=-100
[tex]0^2+\left(-100\right)^2=100[/tex]
[tex]10000=100[/tex]
FALSE
Thus, the ordered pair (0, -100) does NOT satisfy the equation.
For (10, -10)
[tex]x^2+y^2=100[/tex]
substitute x=10 and y=-10
[tex]10^2+\left(-10\right)^2=100[/tex]
[tex]200=100[/tex]
FALSE
Thus, the ordered pair (10, -10) does NOT satisfy the equation.
For (25, 75)
[tex]x^2+y^2=100[/tex]
substitute x=25 and y=75
[tex]25^2+\left(75\right)^2=100[/tex]
[tex]6250=100[/tex]
FALSE
Thus, the ordered pair (25, 75) does NOT satisfy the equation.
Therefore, NOT a single ordered pair satisfies the equation.
\left|\left|x-5\right|+2\right|\le 3
Answer:= x +27 Solve for x x = 326 = 8 32 ≈ 8.666666667
Find the compound interest on ₹ 31,250 at 12% pa for 2 1/2 years
pls give step by step explanation
Answer:
42,183
Step-by-step explanation:
We will use the Continuous Compounding Interest since a regular interval was not stated.
P(t) = Pe^(rt)
We will plug in the variables to the formula
P(t) = 31250 * e^(.12 * 2.5)
We can simplify and evaluate the compound interest.
P(t) = 42183.08
Which function of x has the least value for the y-intercept?
A
y=-4x+ 15
Х
B
Х
4
3
2
1
-4-3-2-1
-1
-3
-
С
y=2x-3
D
x
Answer:a
Step-by-step explanation:
pls help me
1. If y = 24 when x = 2, find y when x is 9.
2. If y = 18 when x = 25, find y when x is 30.
3. If y = 10 when x = 1, find y when x is 20.
4. If y = 10 when x = 21, find x when y is 35
9514 1404 393
Answer:
direct: 108; inverse: 16/3direct: 108/5; inverse: 15direct: 200; inverse: 1/2direct: 147/2; inverse: 6Step-by-step explanation:
We cannot tell what kind of proportionality to assume here.
If x and y are directly proportional, multiplying one by a factor will multiply the other by the same factor.
If x and y are inversely proportional, multiplying one by a factor will divide the other by the same factor.
__
1. Given (x, y) = (2, 24). Direct: y = 9/2(24) = 108.
Inverse: y = 2/9(24) = 16/3
__
2. Given (x, y) = (25, 18). Direct: y = 30/25(18) = 108/5.
Inverse: y = 25/30(18) = 15.
__
3. Given (x, y) = (1, 10). Direct: y = 20/1(10) = 200.
Inverse: y = 1/20(10) = 1/2.
__
4. Given (x, y) = (21, 10). Direct: x = 35/10(21) = 147/2.
Inverse: x = 10/35(21) = 6.
30% of all Skittles are supposed to be purple.
a) If there are 84 skittles in a pack, how many should be purple? (Response area)
b) What percentage or skittles are not purple? (Response area)
c). Assuming that there are 18 purple Skittles in a pack, then how many total Skittles are there? (response area)
Answer:
a) 25
b) 59
c) Too lazy
Step-by-step explanation:
If 30% were to be a decimal, it would be 0.3 because 30% of 1 is 0.3. We will use this to figure out how many purple skittles there are.
A) To find the amount of purple skittles we must multiply the total number of skittles by the percent (in this case 0.3). Equation = (84*0.3=25.2) You can't really have 0.2 of a skittle so we would round down to the whole number (25).
B) Knowing the number of purple skittles, finding the number of non-purple skittles is straightforward. All you have to do is subtract the # of purple skittles from the total amount of skittles (84-25=59).
C) Kinda forgot how to do this but good luck
Find d²y/dx² in terms of x and y.
y^5 = x^7
d²y/dx² =????
Answer: [tex]\frac{14y}{25x^2}[/tex]
====================================================
Work Shown:
First calculate [tex]\frac{dy}{dx}[/tex] through the use of implicit differentiation.
Don't forget about the chain rule.
[tex]y^5 = x^7\\\\\frac{d}{dx}\left[y^5\right] = \frac{d}{dx}\left[x^7\right]\\\\5y^4\frac{dy}{dx} = 7x^6\\\\\frac{dy}{dx} = \frac{7x^6}{5y^4}\\\\[/tex]
Go back to line 3, shown above, and apply the derivative to both sides.
You'll be using the product rule.
[tex]5y^4\frac{dy}{dx} = 7x^6\\\\\frac{d}{dx}\left[5y^4\frac{dy}{dx}\right] = \frac{d}{dx}\left[7x^6\right]\\\\\frac{d}{dx}\left[5y^4\right]*\frac{dy}{dx}+5y^4*\frac{d}{dx}\left[\frac{dy}{dx}\right] = 42x^5\\\\20y^3*\frac{dy}{dx}*\frac{dy}{dx}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]
Use substitution and isolate [tex]\frac{d^2y}{dx^2}[/tex] to get the following:
[tex]20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\20y^3*\left(\frac{7x^6}{5y^4}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5y^5}+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5x^7}+5y^4\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]
[tex]\frac{196x^5}{5}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\5y^4*\frac{d^2y}{dx^2}=42x^5-\frac{196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{210x^5-196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{14x^5}{5}\\\\[/tex]
[tex]\frac{d^2y}{dx^2}=\frac{14x^5}{5}*\frac{1}{5y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5}{25y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5*x^2}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14x^7}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y^5}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y}{25x^2}\\\\[/tex]
Write the augmented matrix for the following system of equations.
-2z=-4y-9x
0=4x+6z+2
2z=2+3y
The augmented matrix for the system of equations is given as follows:
[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]
What is a system of equations?A system of equations is when multiple variables are related, and equations are constructed to find the values of each variable. There are multiple ways to solve a system, and one of the most usual is in a matricial way, as the augmented matrix of the system is constructed.
In standard notation, the system is given by:
9x + 4y - 2z = 0.4x + 0y + 6z = -2.0x - 3y + 2z = 2.The augmented matrix for a system with variables x, y and z is constructed as follows:
The first column contains the coefficients of x.The second column contains the coefficients of y.The third column contains the coefficients of z.The fourth column contains the results of the operations.Hence for this system, the matrix is given by:
[tex]\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right][/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
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The question is on the picture
Answer: slope is 5/4 and y intercept is -7
Y=mx(slope)+b(y-intercept)
What expressions are equal to -5
Tyler has a ramp for his skateboard that measures 17 feet long. The vertical height is 8
feet from the ground to the top of the ramp. What is the horizontal distance from the base
of the ramp to the support? (Hint: draw a picture)
Answer:
15
Step-by-step explanation:
Hypotenuse: 17ft long
Height: 8ft long
17^2 = 8^2 + b^2
b^2 = 17^2 - 8^2
b = √225
b = 15
Which of the following is a factor of 32x + 4? (1 point)
O 2x -1
O 4x-4x + 1
O 4x²- 2x + 1
O Nonc of thc abovc
Answer:
2x-1
Step-by-step explanation:
hope you get help from me
state if the triangle is a right triangle.
a²+b²=c²
4²+ 8\sqrt 2²=12²
16+11.3=144
27.3=144
this answer in the back says that this triangle is supposed to be a right triangle so could you help me if you see an errors that I made. I'm pretty sure I did in regards to the square root section.
Yes, it is a right-angled triangle.
A right triangle, sometimes known as a right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle or two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.Use the Pythagorean theorem.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.a² + b² = c²(4)² + (8√2)² = (12)²16 + (64*2) = 14416 + 128 = 144144 = 144The left hand side is equal to the right hand side.Hence, it is a right angled triangle.To learn more about the Pythagorean theorem, visit :
https://brainly.com/question/14930619
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Which graph represents the solutions to the inequality |2x - 6 < 4? (5 points)
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
9
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1
0 1 2 3 4 5 6 7 8 9
Answer:
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Step-by-step explanation:
Given the expression
[tex]|2x\:-\:6|\:<\:4[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-4<2x-6<4[/tex]
[tex]2x-6>-4\quad \mathrm{and}\quad \:2x-6<4[/tex]
condition 1
[tex]2x-6>-4[/tex]
Add 6 to both sides
[tex]2x-6+6>-4+6[/tex]
[tex]2x>2[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}>\frac{2}{2}[/tex]
[tex]x>1[/tex]
condition 2
[tex]2x-6<4[/tex]
Add 6 to both sides
[tex]2x-6+6<4+6[/tex]
[tex]2x<10[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{10}{2}[/tex]
[tex]x<5[/tex]
combine the intervals
[tex]x>1\quad \mathrm{and}\quad \:x<5[/tex]
Merging overlapping intervals
[tex]1<x<5[/tex]
Thus,
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Which expression is equivalent to (3x-2)(x+3) ?
A. 4x^2 + 4x + 1
B. 3x^2 + 11x + 6
C. 3x^2 + 7x - 6
D. 4x + 1
Answer: C. 3x^2 + 7x - 6
Step-by-step explanation:
3x^2 + 9x -2x -6
3x^2 + 7 - 6
Hope you got it.
Mark me as Brainliest Please.
Step 2 of the Coefficient Method involves blank x-term and y-term coefficients.
Answer:
Dividing
Step-by-step explanation:
In an equation, y varies directly as x varies. If y = 72 when x = 12 what is the value of x when y = 48?
Answer:
8
Step-by-step explanation:
y=kx where k is a constant.
72=12k
k=72/12=6
y=6x
48=6x
x=48/6=8
Darien could swim 30 laps an
hour last year. This year he can
swim 36 laps an hour. Determine the
percent change
Answer:
D
Step-by-step explanation:
If the percent change is 30 to 36 you can already see that it is an increase
here is the work
36 - 30
30
x 100% = 20%
Answer:
20% increase, which corresponds to the light
Step-by-step explanation:
(y - x)/x * 100
(36 - 30)/30 * 100
(6 * 100)/30
600/30
20% increase
if a bag has 22 orange 18 red and 8 blue marbles what is the probability, that I draw blue marble, keep it, then draw another blue marble?
Answer:
The probability is 8/48
Step-by-step explanation:
There is a total of 48 marbles and 8 of them are blue.
Yesterday 3. Hali was making a bouquet of flowers. 60% of her bouquet was made up of roses. Show much of her bouquet was made up of roses on the model below. Write the fraction and decimal equivalent to 60%. h 441
Answer:
0.6, 3/5
Step-by-step explanation:
60%=
100% * 60/100=
1*60/100=
60/100=6/10=0.6
6/10=3/5
A car traveled 180 miles at a constant rate.
Part 1. Complete the table to show the rate at which the car was traveling if it completed the same distance in each number of hours.
travel time (hours) rate of travel (miles per hour)
(5:
1040)
(4.5:
520)
(3:
360)
(2.25:
180)
Answer 1:
1040
Answer 2:
520
Answer 3:
360
Answer 4:
180
A school has 109 students signed up for a science workshop. The school will buy every student attending the workshop a pencil, a folder, and an eraser. A package of 12 erasers is $0.75. Only whole packages of erasers can be bought. Folders are $0.10 each. A package of 8 pencils is $0.50. Only whole packages of pencils can be bought. How much will the school spend?
Answer:
The amount is $25.4
Step-by-step explanation:
There are 109 students to attend the science workshop.
Number of erasers needed is 109, but whole packages of erases can be bought which consist 12 erasers. The total packages of erasers needed would be 10.
The cost of 10 packages of erasers = $0.75 x 10
= $7.5
The cost of 109 folders = 109 x $0.10
= $10.9
Number of pencils needed is 109, but whole packages of pencils can be bought which consist 8 pencils. The total packages of pencils needed would be 14.
The cost of 14 packages of pencils = $0.50 x 14
= $7.0
Total cost = $7.5 + $10.9 + $7.0
= $25.4
The amount that would be spent by the school is $25.4
Answer:
25.4
Step-by-step explanation:
pls help i need the answer
Answer:
(3,22.50)
(6, 33)
Rise/Run using two points
33-22.50/ 6-3
10.5/3
Rate = 3.5
Describe and correct the error in using the diagram to find the value of x.
Hi there!
The error in using the diagram to find x in the solving is that they only picked two angles and equated to 180° which is wrong. You'll find out that their final value for x contains a decimal point which should never be in angles.
The above diagram is a revolution (360°) or angle at a point, so all the angles have to be considered and equated to 360° and NOT 180°
Below is the corrected solving.
[tex]13x + 45 + 12x - 40 + 19x + 3 + 6x + 2 = 360[/tex]
(reason: angles at a point = 360°)
Collect like terms, and make x the subject of formula.
[tex]⟹50x + 10 = 360[/tex]
[tex]⟹50x = 360 - 10[/tex]
[tex]⟹50x = 350[/tex]
Now, divide both sides by 50 to find the value of x.
[tex] \frac{50x}{50} = \frac{350}{50} [/tex]
Therefore:
[tex]x = 7[/tex]