Answer:
Linear equation to represent the total cost:
Let x be the number of kgs of tomatoes Mail bought, and y be the number of kgs of potatoes Mail bought. The cost of x kgs of tomato at Rs. 50 per kg is 50x, and the cost of y kgs of potato at Rs. 20 per kg is 20y. Therefore, the total cost of the vegetables is:
Total cost = 50x + 20y
Substituting the value of total cost as Rs. 200, we get:
50x + 20y = 200
This is the required linear equation to represent the total cost.
Finding the value of x:
Let's assume that Mail bought x kgs of tomato and 2.5 kgs of potato. Using the equation derived above:
50x + 20(2.5) = 200
Simplifying the equation:
50x + 50 = 200
50x = 150
x = 3
Therefore, Mail bought 3 kgs of tomato.
Finding the point at which the graph of 5x+2y=20 cuts x-axis:
To find the point at which the graph of 5x+2y=20 cuts the x-axis, we need to set y = 0 in the equation and solve for x:
5x + 2(0) = 20
5x = 20
x = 4
Therefore, the point where the graph of 5x+2y=20 cuts the x-axis is (4,0).
x = 35, x2 = 250, n= 5 then standard deviation of distribution is a. 1 b. 99 c. 3.1254 d. 9.9498
The correct answer is d. 9.9498.
To find the standard deviation of a distribution, we use the formula:
Standard deviation = √[(∑(x - mean)2)/n]
First, we need to find the mean of the distribution. The mean is the sum of all the values divided by the number of values. In this case, the mean is:
mean = (35 + 250)/5 = 57
Next, we need to find the sum of the squared differences between each value and the mean. This is:
∑(x - mean)2 = (35 - 57)2 + (250 - 57)2 = 485 + 37249 = 37734
Finally, we divide this sum by the number of values and take the square root to get the standard deviation:
Standard deviation = √(37734/5) = √7546.8 = 9.9498
So the standard deviation of the distribution is 9.9498.
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59 points
Use the table below to calculate the average percent change in population in California from 2000-2009.
If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first term is 2.
Answer:
0.03125
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex](r)^{n-1}[/tex]
[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{(7-1)}[/tex]
[tex]a_{7}[/tex] = (2)[tex]\frac{1}{2} ^{6}[/tex]
[tex]a_{7}[/tex] = 0.03125
Helping in the name of Jesus.
Question 1.
Which of the following describes the domain of the piecewise function g of x is equal to the piecewise function of the quantity x squared plus 4 times x end quantity over the quantity x squared plus 2 times x minus 8 end quantity for x is less than 4 and the function log in base 3 of the quantity x plus 5 end quantity for x is greater than or equal to 4 question mark
A. (–∞, 2) ∪ (2, 4) ∪ (4, ∞)
B. (–∞, –4) ∪ (–4, 2) ∪ (2, ∞)
C. (–∞, 2) ∪ (2, ∞)
D. (–∞, ∞)
The domain of the piecewise function g of x is all real numbers, except for x = 2, which is the point at which the two functions overlap. Therefore, the domain is (–∞, 2) ∪ (2, ∞).
What is domain?A domain is a collection of computers and devices connected to one another through a network. It is a logical grouping of computers and devices, such as a local area network (LAN) or a wide area network (WAN). Each device within the network is assigned a unique address, allowing it to communicate with other devices within the network. Domains can also be used to control access to resources, such as files, folders, printers, and databases. Domains can be used to authenticate users and set permissions, which determine the type of access a user has to the domain’s resources. This is commonly used in businesses and organizations to ensure that only authorized personnel have access to sensitive information.
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Translate the shape by the vector
Y₁
9
8
7
6
5
4
3
2
1
O
1
2 3 4 5 6 7
5
89
X
Answer: Your welcome!
Step-by-step explanation:
14
13
12
11
10
9
8
7
6
O
6
7 8 9 10 11 12 13
10
1415
The answer is 14, 13, 12, 11, 10, 9, 8, 7, 6, O, 6, 7, 8, 9, 10, 11, 12, 13, 10, 14, 15. This is the result of translating the shape by the vector (5, 4). The original shape was shifted 5 units to the right and 4 units down, resulting in the new shape.
HELP PLS BRAINLIEST AND FIVE STAR IF YOU GET TWO OF THESE ARE CORRECT
a)√(x^2-14x+49)=x-7
b)√(4x^2-20x+25)=5-2x
(also the answer is most likely NOT all real numbers or no solutions)
(URGENT) PLEASE PLEASE ANSWER THE QUESTION I WILL GIVE YOU THE BRAINLIEST PLEASE ANSWER THE QUESTION.
Find a polynomial function with the following properties: It has a triple zero at x = 1, double zero at x = 3, and has a y-intercept (0.27)
This confirms that our polynomial function has the correct y-intercept.
To find a polynomial function with the given properties, we can use the fact that the zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times that zero appears as a factor in the polynomial.
Since we are given a triple zero at x = 1, this means that (x - 1)^3 is a factor of the polynomial. Similarly, since we are given a double zero at x = 3, this means that (x - 3)^2 is a factor of the polynomial.
To find the y-intercept, we can set x = 0 and solve for y. Since the y-intercept is given as (0, 27), this means that the constant term of the polynomial is 27.
Putting all of this information together, we can write the polynomial function as:
f(x) = 27(x - 1)^3(x - 3)^2
This is a polynomial function that satisfies the given properties. It has a triple zero at x = 1, a double zero at x = 3, and a y-intercept of (0, 27).
We can check our answer by plugging in the values of x and seeing if the function equals zero:
f(1) = 27(1 - 1)^3(1 - 3)^2 = 0
f(3) = 27(3 - 1)^3(3 - 3)^2 = 0
Both of these values equal zero, which confirms that our polynomial function has the correct zeros. Additionally, when we plug in x = 0, we get:
f(0) = 27(0 - 1)^3(0 - 3)^2 = 27
This confirms that our polynomial function has the correct y-intercept.
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Answer this easy geometry question. And no links, please.
Answer:
x = 10
Step-by-step explanation:
Since KL is parallel to HI
m∠JKL = m∠JHI
m∠JLK = m∠LIH
For the two triangles JKL and JHI, we have the common angle J and two angles equal to the corresponding two angles
Therefore the triangles are similar
Ratio of the sides to the corresponding sides must be equal
Hence
[tex]\dfrac{JH}{JK} = \dfrac{JI}{JL}\\[/tex]
JH = JK + KH = 28 + 20 = 48
JI = JL + JL = 14 + x
Therefore
[tex]\dfrac{JH}{JK} = \dfrac{JI}{JL}\\\\= > \dfrac{48}{28} = \dfrac{14 + x}{14}[/tex]
[tex]\dfrac{48}{28} = \dfrac{12}{7}[/tex] by dividing numerator and denominator by 4
Hence
[tex]\dfrac{48}{28} = \dfrac{14 + x}{14}\\\\\rightarrow \quad \dfrac{12}{7} = \dfrac{14 + x}{14}\\\\[/tex]
Multiply both sides by 14:
[tex]14 \cdot \dfrac{12}{7} = 14 \cdot \dfrac{14 + x}{14}\\\\2 \cdot 12 = 14 + x\\\\24 = 14 + x\\\\\text{Subtract 14 both sides:}\\\\24 - 14 = x\\\\or\\\\x = 10\\\\[/tex]
Worksheet 8.1 geometric mean just having a difficult time doing it
The lengths of the sides of the of the right triangles are found using the Pythagorean Theorem as follows;
ΔABN ~ ΔTBA ~ ΔTANx = 20x = 16x = 2·√7x = 15·√5124·√33·√(15)124·√(10))√(77)2·√55·√216·316x = 5·√3, y = 10·√3, z = 10x = 3·√3, y = 6, z = 6·√3x = 6·√5, y = 12, z = 12·√5GH = 2·√(46), HK = 2·√(174)The lake is 9 kilometers longWhat is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the legs of the right triangle.
1) The location of the angles and the congruent 90° angle and a second congruent angle indicates;
ΔABN ~ ΔTBA ~ ΔTAN
The missing values of x can be obtained using Pythagorean Theorem as follows;
2) AB = √(10² + 5²) = √(125) = 5·√5
[tex]\overline{AB}[/tex]² = (5 + x)² - [tex]\overline{AN}[/tex]²
[tex]\overline{AN}[/tex]² = (5 + x)² - [tex]\overline{AB}[/tex]²
[tex]\overline{AN}[/tex]² = 10² - x²
10² + x² = (5 + x)² - [tex]\overline{AB}[/tex]²
10² + x² = (5 + x)² - 125
[tex]\overline{AB}[/tex]² = (5 + x)² - (10² + x²) = 10·x - 75
10·x - 75 = (5·√5)² = 125
10·x - 75 = 125
10·x = 125 + 75 = 200
x = 200/10 = 20
x = 20
3) The hypotenuse side of the right triangle with sides 8 and 4 can be found as follows;
Length of the hypotenuse = √(8² + 4²) = 4·√5
Length of the leg of the larger right triangle is, length = √(8² + x²)
Therefore;
(x + 4)² = (8² + x²) + (4·√5)²
(x + 4)² - (8² + x²) = (4·√5)²
8·x - 48 = 80
8·x = 80 + 48 = 128
x = 128/8 = 16
x = 16
4) The leg of the larger right triangle = (12 + 2)² - x² = 14² - x²
14² - x² - 12² = x² - 2²
2·x² = 14² - 12² + 2² = 56
x² = 56/2 = 28
x = √(28) = 2·√7
x = 2·√7
5) The length of the shorter leg of the larger right triangle can be found as follows;
Length of the shorter leg = (20 + 25)²- x²
x² - 25² = (20 + 25)²- x² - 20²
2·x² = (20 + 25)² + 25² - 20² = 2250
x² = 2250/2 = 1125
x = √(1125) = 15·√5
x = 15·√5
6) x² - 4² = (32 + 4)² - x² - 32²
2·x² = (32 + 4)² + 4² - 32² = 288
x² = 288/2 = 144
x = √(144) = 12
x = 12
7) Let x represent the length of the right tringle and let h represent the altitude of the right triangle
(PR)² = 16² - x²
16² - x² - 12² = x² - 4²
2·x² = 16² - 12² + 4² = 128
x² = 128/2 = 64
x = √(64) = 8
The length of the short leg is; x = 8
Length of the longer leg, PR = √(16² - x²)
PR = √(16² - 8²) = 8·√3
Length of the longer leg = 8·√3
The square of the altitude = 16² - x² - 12²
Length of the altitude = √(16² - 64 - 12²) = 4·√3
8) Let x represent the length of the shorter leg, we get;
(PR)² = 18² - x²
The square of the altitude, (PS)² = 18² - x² - 15² = x² - 3²
2·x² = 18² - 15²+ 3² = 108
x² = 108/2 = 54
x = √(54) = 3·√6
Length of the shorter leg, x = 3·√6
PR = √(18² - 54) = 3·√(30)
Length of the longer leg, PR = 3·√(30)
Length of the altitude, PS = √(54 - 3²) = 3·√(15)
9) Let PQ = x, we get;
(QR)² = 30² - x²
30² - x² - (30 - 6)² = x² - 6²
2·x² = 30² - (30 - 6)² + 6² = 360
x² = 360/2 = 180
x = √(180) = 6·√5
PQ = x = 6·√5
(QR)² = 30² - 180 = 720
QR = √(720) = 12·√5
QS = √(720 - (30 - 6)²) = 12
The altitude, QS = 12
The geometric mean of 2 numbers is the square root of the product of the numbers;
10) The geometric mean of 5 and 8 = √(5 × 8) = 4·√10
11) 7 and 11
The geometric mean = √(7 × 11) = √(77)
12) 4 and 5
The geometric mean is; √(4 × 5) = 2·√5
13) 2 and 25
The geometric mean is; √(2 × 25) = √(50) = 5·√2
14) 6 and 8
The geometric mean is; √(6 × 8) = √(48) = 16·√3
15) 8 and 32
The geometric mean is; √(8 × 32) = 16
16) (15 + 5)² - y² = z²
15² + x² = y²
x² + 5² = z²
Therefore;
(15 + 5)² - 15² - x² = x² + 5²
2·x² = (15 + 5)² - 15² - 5² = 150
x² = 150/2 = 75
x = √(75) = 5·√3
x = 5·√3
z² = x² + 5²
z² = 75 + 25 = 100
z = √(100) = 10
z = 10
15² + x² = y²
15² + 75 = 300 = y²
y = √(300) = 10·√3
y = 10·√3
17) 12² - y² = z²
z² - 9² = x²
z² = 9² + x²
x² + 3² = y²
12² - x² - 3² = z²
12² - x² - 3² = 9² + x²
2·x² = 12² - 3² - 9² = 54
x² = 54/2 = 27
x = √(27) = 3·√3
x = 3·√3
z² = 9² + x²
z² = 9² + 27 = 108
z = 6·√3
x² + 3² = y²
y² = x² + 3²
y² = 27 + 3² = 36
y = √(36) = 6
y = 6
18) x² - 6² = y²
z² - 24² = y²
(6 + 24)² - x² = z²
Therefore; x² - 6² = z² - 24² = (6 + 24)² - x² - 24²
x² - 6² = (6 + 24)² - x² - 24² = 30² - x² - 24²
x² - 6² = 30² - x² - 24²
2·x² = 30² + 6² - 24² = 360
x² = 360/2 = 180
x = √(180) = 6·√(5)
x = 6·√(5)
z² = (6 + 24)² - x²
z² = (6 + 24)² - 180 = 720
z² = 720
z = √(720) = 12·√5
z = 12·√5
z² - 24² = y²
y² = 720 - 24² = 144
y² = 144
y = 12
19) Let x represent GH, we get;
32² - x² = (HK)²
32² - x² - (32 - 8)² = x² + 8²
2·x² = 32² - (32 - 8)² - 8² = 384
x² = 184
x = √(184) = 2·√(46)
GH = x = 2·√(46)
GH = 2·√(46)
(HK)² = (32 - 8)² + (x² - 8²)²
(HK)² = (32 - 8)² + (184 - 8²) = 696
HK = √(696) = 2·√(174)
HK = 2·√(174)
20) Let x represent the length of the lake, we get;
x² + 6² = (x + 4)² - (4² + 6²) = x² + 8·x - 36
x² + 6² = x² + 8·x - 36
8·x = 6² + 36 = 72
x = 72/8 = 9
The length of the lake, x = 9 km
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in the diagram what is the measure of angle one to the nearest degree
Answer: D
Step-by-step explanation:
7x + 4 = 88
x = 12
angle 1 = 180 - 7(12) + 2
angle 1 = 98
So it's D
Answer: The angle measure for angle 1 would be 98 degrees.
Step-by-step explanation: First, you set 88 equal to (7x+4) since they are vertical angles. (Vertical angles are congruent.) Then you solve and find that x=12. You then plug 12 in to the second equation, (7x-2) and get 82. Since angle 1 is supplementary to the angle that measures 82 degrees, you would take 180-82= Angle 1.
Question 11 Exercise. Suppose P(x) is a polynomial presented as a product: P(x)=(2x+5)(5x-2)^(2)(x+7)Q(x) where Q(x) is an unspecified polynomial of degree 6 . What is the degree of P(x) ?
The final answer is degree of P(x) is 10.
The degree of a polynomial is the highest power of x that appears in the polynomial.
In the case of P(x), we can find the degree by multiplying the degrees of each factor together.
The degree of (2x+5) is 1,
the degree of (5x-2)^(2) is 2,
the degree of (x+7) is 1,
and the degree of Q(x) is 6.
Therefore, the degree of P(x) is 1*2*1*6 = 12.
However, we need to subtract 2 from the degree because (5x-2)^(2) is raised to the power of 2.
So the degree of P(x) is 12-2 = 10.
Therefore, the degree of P(x) is 10.
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a. 180mm side length
b. a 125 angle
c a 55 angle
d. a 55 mm side length
Answer:
C. a 55 degree angle
Step-by-step explanation:
180 degrees-125 degrees=55.
20% tip, 8% tax sales, total is $23. 04, what is the pretax price?
The pretax price of the item is $18. The tip is $3.60 (0.20 * 18) and the tax is $1.44 (0.08 * 18), which when added to $18 gives us a total cost of $23.04.
For a 20% tip, 8% tax sales. Total $23. 04, we can say that The pre-tax cost is $19.20.
Let x be the pre-tax cost of the sales. Then we can set up the equation:
x + 0.20x + 0.08x = 23.04
Simplifying and solving for x, we get:
1.28x = 23.04
x = 23.04 / 1.28
x = 18
The pretax price is the amount charged for a product or service before any taxes are added. It is the price that a customer would pay for a product or service without any additional charges imposed by the government. In most countries, taxes such as sales tax, value-added tax (VAT), or goods and services tax (GST) are added to the pretax price to determine the final price that a customer pays.
Pretax prices are important for businesses to determine their profit margins and pricing strategies. It is also useful for customers to compare prices between different products or services before taxes are added. However, it is important to note that the final price paid by the customer may vary based on the applicable tax rate.
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Complete Question: -
Need help on math You have a meal at a restaurant. The sale tax is 8% . You leave a tip for the waitress that is 20% of the pretax price . You spend $23.04 . What is the pretax price of the meal?
I NEED heLP ON THIS ASAP!!!
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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Find the solution to the following equation: 4(x + 3) = 44
Answer:
x = 8
Step-by-step explanation:
4(x + 3) = 44 ( divide both sides by 4 )
x + 3 = 11 ( subtract 3 from both sides )
x = 8
How do you find the scale factors with fractions
To find the scale factors with fractions, you first need to understand what scale factors are. Scale factors are the ratios of corresponding lengths in two similar figures. They tell you how much larger or smaller one figure is compared to another.
To simplify fractions, you need to find the greatest common factor (GCF) of the numerator and denominator and divide them by it.
For example, if we have the fraction 6/12, we can simplify it by finding the GCF of 6 and 12, which is 6. Then, we divide both the numerator and denominator by 6:
6/12 = (6 ÷ 6) / (12 ÷ 6) = 1/2
So, 6/12 simplifies to 1/2.
If the fraction is already in its simplest form, then there is no need to simplify it further.
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The complete question i:
How do you find the scale factors with fractions? Give example.
NEED HELP DUE FRIDAY!!!!!!!!!
If the coordinates of point I are (9, 12), what is the value of cos(G), sin(G), and tan(G) for triangle GHI? Explain your reasoning.
Answer:
cos G = 3/5
sin G = 4/5
tan G = 4/3
Step-by-step explanation:
I(9, 12)
GH = 9
HI = 12
(GI)² = 9² + 12²
GI = 15
For <G:
opp = HI = 12
adj = GH = 9
hyp = GI = 15
cos G = adj/hyp = 9/15 = 3/5
sin G = opp/hyp = 12/15 = 4/5
tan G = opp/adj = 12/9 = 4/3
Step-by-step explanation:
remember the triangle in a circle, when you learned about sine, cosine and the other trigonometric functions ?
this looked the same way, just that the circle was the norm-circle with radius 1.
here, now, the radius is larger, so every function line is also multiplied by the actual radius.
but the principles are the same.
sine is the up/down leg of the right-angled triangle.
cosine is the left/right leg.
tangent is sine/cosine.
I = (9, 12)
so, Pythagoras gives us the radius (line GI) :
GI² = GH² + HI² = 9² + 12² = 81 + 144 = 225
GI = sqrt(225) = 15
sin(G) × GI = HI
sin(G) × 15 = 12
sin(G) = 12/15 = 4/5 = 0.8
cos(G) × GI = GH
cos(G) × 15 = 9
cos(G) = 9/15 = 3/5 = 0.6
tan(G) = sin(G)/cos(G) = 4/5 / 3/5 = (4×5)/(5×3) =
= 4/3 = 1.333333333...
Suppose sin θ = - 3/5, sin ɸ = 20/29 Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. Find the following. sin(θ + ɸ) = ____ cos(θ + ɸ) = ____
sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
Suppose sin θ = -3/5, sin ɸ = 20/29. Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. We can find sin(θ + ɸ) and cos(θ + ɸ) by using the following formulas: sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ and cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ.
First, we need to find cos θ and cos ɸ. Since θ is in Quadrant IV, cos θ is positive. We can use the Pythagorean identity, sin² θ + cos² θ = 1, to find cos θ:
cos² θ = 1 - sin² θ
cos² θ = 1 - (-3/5)²
cos² θ = 1 - 9/25
cos² θ = 16/25
cos θ = √(16/25)
cos θ = 4/5
Similarly, since ɸ is in Quadrant l, cos ɸ is also positive. We can use the Pythagorean identity to find cos ɸ:
cos² ɸ = 1 - sin² ɸ
cos² ɸ = 1 - (20/29)²
cos² ɸ = 1 - 400/841
cos² ɸ = 441/841
cos ɸ = √(441/841)
cos ɸ = 21/29
Now we can plug in the values of sin θ, sin ɸ, cos θ, and cos ɸ into the formulas for sin(θ + ɸ) and cos(θ + ɸ):
sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ
sin(θ + ɸ) = (-3/5)(21/29) + (4/5)(20/29)
sin(θ + ɸ) = -63/145 + 80/145
sin(θ + ɸ) = 17/145
cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ
cos(θ + ɸ) = (4/5)(21/29) - (-3/5)(20/29)
cos(θ + ɸ) = 84/145 + 60/145
cos(θ + ɸ) = 144/145
Therefore, sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
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Using the p-value given, are the results significant at a 1% level? p-value = 0. 802
No, the result is not significant at 1 percent level for the p-value of 0.802.
Results are significant at a certain level,
Compare the p-value to the significance level (known as alpha).
The significance level is typically set at 0.05 or 0.01.
Here, the p-value is 0.802, which is much larger than 0.01.
This implies here we cannot reject the null hypothesis at a 1% significance level.
Or , the result is not statistically significant at a 1% level.
If the significance level was 5% that is equal to 0.05.
The result would not be significant at 5% level either.
If the significance level was 10% which is equal to 0.10.
Then the result would be significant as the p-value is less than 0.10.
Therefore, for the given p-value 0.802 result is not significant at 1%.
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PLSSSS HELP IF YOU TURLY KNOW THISSSS
Answer: 1
Step-by-step explanation:
3(x-2) = 4x+2
3x-6 = 4x+2
To move 3x, deduct it on both sides of the equation.
3x - 6 - (3x) = 4x + 2 - (3x)
0 - 6 = [1]x +2
Given:-
[tex] \tt \: 3( x - 2 ) = 4x + 2[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: 3( x - 2 ) = 4x + 2[/tex][tex] \: [/tex]
[tex] \tt \: 3x - 6 = 4x + 2[/tex][tex] \: [/tex]
[tex] \tt \: -6 = 4x - 3x + 2[/tex][tex] \: [/tex]
[tex] \tt \: -6 = 1x + 2 [/tex][tex] \: [/tex]
[tex] \tt \: -6 = 3x[/tex][tex] \: [/tex]
[tex] \tt \: \cancel\frac{ - 6}{3} = x[/tex][tex] \: [/tex]
[tex] \boxed{\tt \green{- 2 = x}}[/tex][tex] \: [/tex]
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hope it helps ⸙
9.
Choose the best answer.
A bag contains 16 purple, 12 blue, 14 white, and 6 brown marbles. You select a marble at random and then put it back into the bag. You then select another marble.
Find (not purple, white).
Probability of selecting a marble at random and then put it back into the bag will be [tex]\frac{7}{36}[/tex]
What is ProbabilityThe likelihood that something will occur is known as the probability. Because we don't know how something will turn out, we might talk about the probability of one result or the potential for several outcomes. The study of events that fit into a probability distribution is known as statistics. The best example for understanding probability is flipping a coin:
There are two possible outcomes—heads or tails.
Given;Number of purple marble=16
Number of blue marble=12
Number of white marble=14
Number of brown marble=6
The Probability is =[tex]\frac{12+14+6}{16+12+14+6}[/tex] × [tex]\frac{14}{16+12+14+6}[/tex]
=[tex]\frac{32}{48}[/tex] × [tex]\frac{14}{48}[/tex]
=[tex]\frac{7}{36}[/tex]
Hence, Probability of selecting a marble at random and then put it back into the bag will be [tex]\frac{7}{36}[/tex].
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Susie and Jenny are 25 miles apart. Susie sights a hot-air balloon at a 30 degree angle of elevation east of where she is standing. Jenny sights the same hot-air balloon at a 40 degree angle of elevation west of where she is standing. How far is the balloon from Jenny? (Round to the nearest thousandth.)
The distance of the hot-air balloon from Jenny is approximately 12.500 miles
To find the distance of the hot-air balloon from Jenny, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle. In this case, the triangle is formed by Susie, Jenny, and the hot-air balloon.
Let the distance from Susie to the hot-air balloon be x, and the distance from Jenny to the hot-air balloon be y. Using the Law of Sines, we can write the following equation:
(x/sin(40)) = (y/sin(30)) = (25/sin(110))
Now, we can cross multiply and solve for y:
(y)(sin(110)) = (25)(sin(30))
y = (25)(sin(30))/(sin(110))
y = 12.500
Therefore, the distance of the hot-air balloon from Jenny is approximately 12.500 miles.
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Pls asnwer
due in 10 mins
give simple working
Answer:
:-)
Step-by-step explanation:
Straight line=180 so 180-75-50=55
Since angles in a triangle=180 and since a=55 and c=50 b must =75
According to alternate angle theorem since angle next to a =50 angle c equals 50.
d=50 because the opposite angle theorem states that d=c and c=50
a catapult is trying to destroy a 40 foot wall that is 120 feet away from it by firing rocks at it the rock launches out of the catapult reaching its maximum height of 50 feet 75 feet away from the catapult the rock then comes down from the maximum height to smash the wall 8 feet from the top a write an equation that models the pathology of the rock
To model the path of the rock, we can use a quadratic equation of the form y = ax^2 + bx + c, where y is the height of the rock, x is the distance from the catapult, and a, b, and c are constants.
We can use the given information to find the values of a, b, and c.
First, we know that the rock launches out of the catapult at a height of 0 feet, so when x = 0, y = 0. This means that c = 0.
Next, we know that the rock reaches its maximum height of 50 feet when it is 75 feet away from the catapult, so when x = 75, y = 50. We can plug these values into the equation and simplify:
50 = a(75)^2 + b(75) + 0
50 = 5625a + 75b
Finally, we know that the rock hits the wall 8 feet from the top when it is 120 feet away from the catapult, so when
x = 120, y = 40 - 8 = 32. We can plug these values into the equation and simplify:
32 = a(120)^2 + b(120) + 0
32 = 14400a + 120b
We now have a system of two equations with two unknowns:
5625a + 75b = 50
14400a + 120b = 32
We can use substitution or elimination to solve for a and b. Using elimination, we can multiply the first equation by -1.6 to eliminate the b term:
-9000a - 120b = -80
14400a + 120b = 32
Adding the two equations together gives:
5400a = -48
Solving for a gives:
a = -48/5400 = -0.00888888889
We can then plug this value of a back into one of the original equations to solve for b:
5625(-0.00888888889) + 75b = 50
-50 + 75b = 50
75b = 100
b = 100/75 = 1.33333333333
So the equation that models the path of the rock is:
y = -0.00888888889x^2 + 1.33333333333x + 0
Or, rounding to three decimal places:
y = -0.009x^2 + 1.333x
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Bookwork code: 597
This is a new version of the question. Make sure you start new workings.
The cylinder below has a curved surface area of 408 m² and a length of 17 m
< Back to task
Work out the total surface area of the cylinder.
Give your answer to 3 s.f.
curved surface area = 408m m²
17 m
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Answer >
The total surface area of the cylinder is 548.13 square meters.
How to calculate curved surface area?The curved surface area of a cylinder can be calculated using the formula:
CSA = 2πrh
where CSA is the curved surface area, r is the radius, and h is the height or length of the cylinder.
We are given that the curved surface area of the cylinder is 408 m² and the length is 17 m.
We can use this information to solve for the radius:
CSA = 2πrh
408 = 2πr(17)
r = 408 / (2π × 17)
r ≈ 3.00 m (rounded to 2 decimal places)
Now that we know the radius, we can calculate the total surface area of the cylinder by adding the areas of the two bases and the curved surface area:
Total surface area = 2πr² + 2πrh
Total surface area = 2π(3.00)² + 2π(3.00)(17)
Total surface area ≈ 226.19 + 321.94
Total surface area ≈ 548.13
Therefore, the total surface area of the cylinder is approximately 548.13 square meters.
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brian needs to bake 6 batches of cookies eatch batch calls for 3/4 teaspoons of vanilla how much vanilla will he need altogether
Answer:
4.5 teaspoons of vanilla
Step-by-step explanation:
We can do this by multiplying:
3/4*(6)
18/4
9/2
4.5 teaspoons of vanilla
Find the area of the figure.
Answer:
76 ft²
Step-by-step explanation:
You want the area of a trapezoid with bases 6 ft and 13 ft, and height 8 ft.
TrapezoidThe area formula for a trapezoid is ...
A = 1/2(b1 +b2)h
A = 1/2(6 ft +13 ft)(8 ft) = 76 ft²
The area of the figure is 76 square feet.
__
Additional comment
The length of the longer base on the right is the sum of 6 ft and 7 ft. It is 13 ft.
The area of the figure is 76 square feet.
the area of a trapezoid is: 76 ft².
Here, we have,
from the given figure, we get,
The length of the longer base on the right is the sum of 6 ft and 7 ft. It is 13 ft.
We have to find the area of a trapezoid with bases 6 ft and 13 ft, and height 8 ft.
Trapezoid
The area formula for a trapezoid is
A = 1/2(b₁ +b₂)h
A = 1/2(6 ft +13 ft)(8 ft)
= 76 ft²
so, we get,
The area of the figure is 76 square feet.
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show that T<0,2> (0,1). Is T<0,2> (x,y) = D3 (x,y) a true statement for any point (x,y)? Why or why not.
Answer:
To show that T<0,2> (0,1), we need to evaluate the transformation T at the point (0,1) and check if the result is in the range of T.
T<0,2> (0,1) means that the transformation T takes the point (0,1) in the input space to a point in the output space that has coordinates (0,2).
Let's evaluate T at (0,1):
T<0,2> (0,1) = D3(0,1) + (0,1)
= (0+0, 3+1)
= (0, 4)
The output point (0,4) is not equal to (0,2), which means that T<0,2> (0,1) is false. Therefore, T<0,2> does not map the point (0,1) to (0,2).
To determine if T<0,2> (x,y) = D3 (x,y) is a true statement for any point (x,y), we need to check if the transformation T always equals the function D3.
T<0,2> (x,y) = (x, 3+y)
D3(x,y) = (x,y,3)
Since T and D3 have different ranges (T has a range of R^2 and D3 has a range of R^3), the statement T<0,2> (x,y) = D3(x,y) is not true for any point (x,y).
Therefore, we cannot equate T<0,2> and D3, and the statement T<0,2> (x,y) = D3 (x,y) is false for any point (x,y).
Chose one of two tables below to create your own Question (with solution).
A. If a friend's kid has no curfew, what is the probability that they don't have chores? B. the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3. C. I chose this question because it involves calculating a conditional probability based on a given set of data.
Describe Probability?Probability can also be used to describe more complex events, such as the likelihood of a stock price increasing by a certain amount in a given period of time, or the probability of a medical treatment being effective for a certain disease.
My Conditional Frequency Question is:
If a friend's kid has no curfew, what is the probability that they don't have chores?
Solution:
The conditional probability of a kid not having chores given that they have no curfew can be found using the formula:
P(No Chores | No Curfew) = P(No Chores and No Curfew) / P(No Curfew)
From the table, we can see that the number of kids who have no curfew and no chores is 2, and the total number of kids who have no curfew is 6. Therefore:
P(No Chores | No Curfew) = 2/6 = 1/3
So the probability that a friend's kid doesn't have chores given that they have no curfew is 1/3.
I chose this question because it involves calculating a conditional probability based on a given set of data. This is a common type of question in statistics and probability, and it requires an understanding of the basic concepts of probability such as conditional probability and independence. The table provided gives us the data we need to calculate the conditional probability, and the solution involves applying the formula for conditional probability and simplifying the fraction.
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