Answer:
P(prize)= 2/7
Step-by-step explanation:
The probability of getting a prize can be found by dividing the number of favorable outcomes by the total number of outcomes.
P (prize) = favorable / total
The favorable outcome is a prize and there are 10 prizes.
P (prize) = 10 / total
There are 10 prizes and 25 blanks. Add 10 and 25.
10 prizes + 25 blanks= 35 total outcomes
P (prize)= 10/35
This fraction can be simplified. Both the numerator and denominator can be evenly divided by 5.
P(prize)= (10/5) / (35/5)
P(prize) = 2 / (35/5)
P(prize)= 2/7
The probability of receiving a prize is 2/7
In total, Amy and Jack had $1377. Amy spent 0.8 of her money and Jack spent 1/3 of his. They spent the same amount of money.
A) What was the ratio of Amy's money to Jack's money?
B) How much did Jack have at first?
Answer:
Ratio = 5/12
Jack had = $972
Step-by-step explanation:
Given:
Total money $1377Amy had = xJack had = yAmy spent = 0.8xJack spent = 1/3yPart ASince they spent same amount of money:
0.8x = 1/3y8/10x=1/3yx/y = 10*1/8*3 = 5/12The ratio was 5/12
Part BSum of money:
x + y = 1377As per ratio, x = 5/12y, substituting x in above equation:
5/12y + y = 137717/12y = 1377y = 1377*12/17y = 972Jack had $972
Mason purchased Texas Instruments for $45.23 per share and plans to sell the shares when the stock price rises 25%. If Texas Instruments is currently selling for $52.00, what percent increase above the current does Mason need to issue the sell order?
Answer:
8.726%
Step-by-step explanation:
Purchase price = $45.23
Current selling price of stock = $52.00
Intended increase before sale = 25%
25% of purchase price :
100% + 25% = 125%
125% of $45.23
1.25 × 45.23 = $56.5375
$56.5375 is the price at which Mason intends to sell the stock after purchase.
If current price = $52.00;
What percentage increase above the current price is $56.5375.
Let the percentage increase = p
Therefore,
p% of $52 = $56.5375
(p/100) * 52 = 56.5375
52p/100 = 56.5375
52p = 5653.75
p = 5653.75 / 52
P = 108.72596
Therefore p = 108.72596% - 100%
The percentage increase above the current price is thus :
8.72596%
= 8.726%
A woman had less than 1,100 with her when she went to the market.She spent all her money and used a certain number 50.00notes and twice as many as 20.00 notes.Find the maximum number of 50.00 notes she used
Answer:
12
Step-by-step explanation:
Let x = number of 50.00 notes.
They are worth 50x
Then, 2x = number of 20.00 notes.
They are worth 2x * 20 = 40x
50x + 40x < 1100
90x < 1100
9x < 110
x < 12.2
Answer: 12
Check:
x = 12 (number of 50.00 notes)
2x = 24 (number of 20.00 notes)
12 * 50 + 24 * 20 = 1080
If she used one more 50.00 note, she'd go over 1,100, so 12 is correct.
Find the measure of b. A. 126 B. 31.5 C. 27 D. 63
Answer:
D. 63°
Step-by-step explanation:
a = 27°
b = 180° - (a + 27°)
b = 180° - (27° + 27°)
b = 180° - 54°
b = 126°
By inscribed angle theorem:
c = 1/2 b = 1/2 * 126°
c = 63°
The measure of angles a, b, and c in the given figure are 27°, 126°, and 63°, respectively.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
In the triangle ORQ, the two sides of the triangle OR and OQ are the radius of the triangle, therefore, the length of the two sides will be.
Since the two sides of the triangle are equal, therefore, the triangle will be an isosceles triangle, with the angle opposite to the same length measuring the same. Therefore,
∠OQR = ∠ORQ
a = 27°
Now, in a triangle, the sum of the measure of all the angles is equal to 180°. Therefore, we can write,
∠OQR + ∠ORQ + ∠QOR = 180°
a + 27° + b = 180°
27° + 27° + b = 180°
b = 180° - 27° - 27°
b = 126°
Further, In a circle, the measure of the angle formed by the chord in the centre of the circle is twice the measure of the angle formed by the same chord on any point in the circle. Therefore,
∠QOR = 2∠QPR
b = 2 × ∠QPR
126° = 2 × ∠QPR
∠QPR = 126° / 2
∠QPR = 63°
Hence, the measure of angles a, b, and c in the triangle are 27°, 126°, and 63°, respectively.
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Two objects were lifted by a machine. One object had a mass of 2000 grams, and was lifted at a speed of
2 m/sec. The other had a mass of 4000 grams and was lifted at a rate of 3 m/sec.
a. Which object had more kinetic energy while it was being lifted?
Answer:
The second object (4000 grams) had more kinetic energy
Step-by-step explanation:
Use the equation KE = 0.5mv², where m is the mass and v is the velocity.
Find the kinetic energy of the first object:
KE = 0.5(2000)(2 m/s)²
KE = 4000 J
Find the kinetic energy of the second object:
KE = 0.5(4000)(3 m/s)²
KE = 18000 J
So, the second object (4000 grams) had more kinetic energy.
The second object of mass 4000 grams will have more kinetic energy than the first mass.
What is kinetic energy?The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
Use the equation KE = 0.5mv², where m is the mass and v is the velocity.
The kinetic energy of the first object:
KE = 0.5(2000)(2 m/s)²
KE = 4000 J
The kinetic energy of the second object:
KE = 0.5(4000)(3 m/s)²
KE = 18000 J
Therefore, the second object (4000 grams) had more kinetic energy.
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When a number of oranges is divided among six girls, each gets four
oranges. How many oranges would each girl get if there were eight girls ?
Answer:
3
Step-by-step explanation:
ok first multiply 6 and 4 it becomes 24 then we divide 24 with 8.
A truck traveled 130 miles using 4 gallons of diesel fuel. What distance would the same truck cover using 6.7 gallons of diesel fuel?
Answer:
217.75
Step-by-step explanation:
Divide the distance traveled by the gallons used. This will give you the distance that can be traveled using one gallon.
130/4 = 32.5
Now, multiply this value by 6.7 to find the distance that can be covered.
6.7 × 32.5 = 217.75
ts
The triangles shown in the graph are congruent. Based
on the graph, determine which congruency statement
is correct.
O AXYZ ALGM
O AZYX ALGM
O AXZY ALGM
Answer:
C.) ΔXZY ≅ ΔLGM
Step-by-step explanation: I got it right on Edge
The correct congruency statement is: [tex]\triangle XZY \cong \triangle LGM[/tex]
From the graph, we have the following corresponding points
Point X and point LPoint Z and point GPoint Y and point MThe above highlights mean that:
Triangle XZY corresponds to triangle LGM
Hence, the correct congruency statement is: [tex]\triangle XZY \cong \triangle LGM[/tex]
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I want to buy 4 tickets to go to Disney World. They are currently on sale for with a 12% discount. Write the SIMPLIFIED expression to represent this scenario. *
Answer:
The simplified expression to represent the scenario is Y = 4·X - 0.48·X
Step-by-step explanation:
The given parameters are;
The number of tickets required = 4
The amount of discount offered = 12%
Let the selling price = X
Therefore the amount paid for each ticket = X - X×12 %
Which gives;
The amount paid for each ticket = X - X×0.12
The amount paid for the four tickets = 4 × (X - X×0.12) = 4·X - 4×0.12·X = 4·X - 0.48·X
Whereby the amount paid for the four tickets = Y, we have;
Y = 4·X - 0.48·X
Which gives, the simplified expression to represent the scenario as Y = 4·X - 0.48·X.
Aluminum is a highly reactive metal that oxidizes when exposed to air. Which of these would be a good first step in balancing this reaction? Al + O2 → Al2O3
Answer:
first step to balance the equation is :
multiply AL by 2 to match the amount of aluminum on the other side
balanced equation : 4 Al +3O2 → 2 ALO3
Step-by-step explanation:
Al + O2 → Al2O3
first step to balance the equation is :
multiply AL by 2 to match the amount of aluminum on the other side
but then you have to deal with the amount of O from both sides, we need to find the least common multiple between 2 and 3 which is 6
the best thing to balance the equation is to multiply O2 by 3 and O3 by2, then deal with the amount of AL which is 4 on the other side. last step is to multiply AL by 4 to balance the equation.
What is the degree (highest exponent) of
a quadratic?
Answer:[tex]x^{2}[/tex]
Step-by-step explanation:
The highest degree is [tex]x^{2}[/tex]
quadratic equations are usually in this form: [tex]ax^{2}[/tex] +bx +c =0 (the signs may be positive or negative depending on the question given)
Alma is 3 years older than liz.
let l =liz's age.
then ? =alma age
Answer:
l+3
Step-by-step explanation:
since Alma is 3 years older than Liz so then she would be l+3
if g^-1(x) is the inverse of g(x) which statements must be true
Answer:
A, B, D, F
Step-by-step explanation:
The domain of a function is the range of its inverse.
The composition of a function and its inverse is an identity.
What is the decimal equivalent of 23/9
Answer:
the ans in decimal will be 2.55 bcz of 2 s.f ( significant figures)
Answer:
2.5555
Step-by-step explanation:23 divided by 9 is 2.5 repeating
plz help ASAP WILL MARK BRAINLIST
Answer: B. The domain is {x|x<0 or x>0} and the range is {y|y>0}
Step-by-step explanation:
f(x)=x^-2
----------------------------
#1 Any negative (-) exponents means the answer will be 1/ the term
- for example, 3^-2=1/3^2=1/9
NOTE: NEGATIVE EXPONENTS DOES NOT MEAN IT IS A NEGATIVE NUMBER, IT IS STILL A POSITIVE NUMBER IF THE BASE IS POSITIVE.
-----------------------
The domain, which will be the value of x.
x can be any real number, except 0, because 0 can't go to negative exponents or else it will be undefined.
{x|x<0 or x>0}
-------------------------------------
The range, which will be the value of y.
Since the x value is being squared, it is always positive
{y|y>0}
Answer:
A. The first choice.
Step-by-step explanation:
[tex] f(x) = x^{-2} [/tex]
Let's rewrite the function in a more familiar way.
[tex] f(x) = \dfrac{1}{x^2} [/tex]
Domain:
We know that a denominator cannot equal zero, so we set the denominator equal to zero to find the values of x that must be excluded from the domain.
x^2 = 0
x = 0
The only value excluded from the domain is x = 0.
The domain is all reals except for zero.
Range:
Now that we know the domain is all real numbers except for 0, we look closely at the denominator.
What happens when you replace x with negative numbers? Since you are squaring x, all denominators will be positive. When you replace x with positive numbers, all denominators will also be positive. For values of x with a large absolute value, for example 1000, -1000, 1,000,000 or -1,000,000, as the absolute value of x increases, f(x) approaches zero. For values of x with a small absolute value, such as 0.0001, -0.0001, -0.00000001, or 0.00000001, as x approaches zero, f(x) approaches positive infinity.
The range is all positive real numbers.
Answer:
Domain: all real numbers except 0.
Range: all positive real numbers.
If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y. 1008 units2 720 units2 624 units2 384 units2
Answer:
The correct option is;
720 unit²
Step-by-step explanation:
The given dimension of square pyramid is given as follows;
The length and width of the square prism = w = 12 units
The height of the square prism = x = 7 units
The base width of the pyramid = w = 12 units
The formula of the area of the square prism = 2 × w² + w × x × 4
∴ The area of the square prism = 2 × 12² + 12 × 7 × 4 = 624 unit²
The area of the square pyramid = w² + 1/2×4×w ×√((w/2)² + y²)
The area of the square pyramid = 12² + 1/2×4×12×√((12/2)² + 8²) = 12² +240 unit²
The formula for the surface area of the figure = The slant surface area of the square prism + The area of the base of the square prism + The slant surface area of the square pyramid
The surface area of the figure = 12² + 12 × 7 × 4 + 1/2×4×12×√((12/2)² + 8²) = 720 unit²
The surface area of the figure = 720 unit².
Answer:
720 units2
Step-by-step explanation:
Hope this helps :)
Problem number 26 of the Rhind Papyrus says: Find a quantity such that when it is added to StartFraction 1 Over 4 EndFraction of itself the result is a 15. The modern day equation that models this problem is x plus StartFraction 1 over 4 EndFraction x equals 15.
Answer:
12
Step-by-step explanation:
x + 1/4 x = 15
4/4 x + 1/4 x = 15
5/4 x = 15
x = 15 * 4/5
x = 12
Answer:
Its 12 trust me just did it
Step-by-step explanation:
Which equation is equivalent to x2 + 36x = 88?
(x + 6)2 = 88
b
(x + 6)2 = 124
с.
(x + 18)2 = 412
d
(x +
+ 18)2 = 1,384
Answer:
The answer is A
Step-by-step explanation:
Please help with this question
Answer:
Step-by-step explanation:
a. 2a(3+7a)
b.2x(x^3+x^4+x^9)
c.3z(z-5)
d i cant see
Answer:
1) 6a + 14a^2
2a(3+7a)
2) 2x^4 + 2x^5 + 2x^10
2x^4(1 + x + x^6)
3) 6z^2 - 15z
3z(2z - 5)
4) 42w^3 - 14w + 77w^2
42w^3 + 77 w^2 - 14 w
7w(6w^2 + 11w - 2)
Step-by-step explanation:
Solve -x2 - 3x = 4 over the set of complex numbers
Answer:
[tex]\bold{x=\dfrac{-3\pm i\sqrt{7}}{2}}[/tex]
Step-by-step explanation:
Given quadratic equation is:
[tex]-x^2 - 3x = 4[/tex]
Rewriting the given equation:
[tex]-x^2 - 3x - 4 = 0[/tex]
OR
[tex]x^2 + 3x + 4=0[/tex]
Solution of a quadratic equation represented as [tex]ax^2+bx+c=0[/tex] is given as:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Comparing the given equation with standard equation:
a = 1
b = 3
c = 4
So, the roots are:
[tex]x=\dfrac{-3\pm\sqrt{3^2-4\times 1 \times 4}}{2\times 1}\\\Rightarrow x=\dfrac{-3\pm\sqrt{9-16}}{2}\\\Rightarrow x=\dfrac{-3\pm\sqrt{-7}}{2}[/tex]
[tex]\sqrt{-7 }[/tex] can be written as [tex]7\sqrt{-1}[/tex]
and [tex]\sqrt{-1} = i[/tex]
So, [tex]\sqrt{-7} = i\sqrt7[/tex]
The numbers containing [tex]i[/tex] in them, are called as complex numbers.
Therefore, the roots of the equation can be written as:
[tex]\Rightarrow \bold{x=\dfrac{-3\pm i\sqrt{7}}{2}}[/tex]
PLEASE HELP!!!
Find the measure of WV¯¯¯¯¯¯¯¯¯. A. 8 B. 6 C. 7 D. 4
Answer:
[tex]\Huge \boxed{\mathrm{B. \ 6}}[/tex]
Step-by-step explanation:
We can apply the Intersecting Secant-Tangent Theorem.
TV is the secant.
VW is the tangent.
VW² = VT × VU
(x+6)² = (5+x+4) × (x+4)
Combine the terms in bracket.
(x+6)² = (x+9)(x+4)
Expand brackets on both sides of the equation.
x²+12x+36=x²+13x+36
Subtract x² from both sides.
12x+36=13x+36
Subtract 12x from both sides.
36=x+36
Subtract 36 from both sides.
0=x
WV = x+6
x=0
WV = 0+6 = 6
The measure of the tangent WV is 6.
The cost C of hiring a lorry is partly constant and partly varies with the time T spent. If it cost ₦850 for 4 hours hire and ₦1300 for 7 hours hire, find the cost for 12 hours.
The cost for 4 hours is 850, the cost for 7 hours is 1300 then the cost for 12 hours will be equal to 1906.8.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Cost for 4 hours = 850
4 × 212.5 = 850
Cost for 7 hours = 1300
7 × 185.7 = 1300
The rate at which it is increasing,
212.5 - 185.7 = 26.8
For 12 hours,
185.7 - 26.8 = 158.9
12 × 158.9 = 1906.8
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Which statement about the stamps is correct?
Karl has stamps in his desk drawer. The possible
combinations of stamps are shown below.
Karl's Stamp Collection
The total number of stamps is 25.
The total value of the stamps is $18.75.
The total number of stamps is 35.
The total value of the stamps is $19.15.
Number of
Number of
45-cent stamps 65-cent stamps
18
17
2015
22
13
10
25
Answer:
The answer is "The total number of stamps is 35".
Step-by-step explanation:
There are many 35 stamps in total. The number of stamps during the first mixture is= 35
Then let the other configurations be checked
[tex]\to 20 + 15= 35 \\\to 22+13 = 35 \\\to 25 + 10 = 35 \\[/tex]
Therefore the correct answer is =35
The total number of stamps is 35. Therefore, the correct answer is option C.
From the given table,
Which ever the combination we choose, we get total number of stamps as 35.
Total cost of stamps in each case is
i) 18×0.45+17×0.65
= $14.65
ii) 20×0.45+15×0.65
= 9+9.75
= $18.75
iii) 22×0.45+13×0.65
= 9.9+8.45
= $18.35
iv) 25×0.45+10×0.65
= 11.25+6.5
= $17.75
Therefore, the correct answer is option C.
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A snake accelerates from 2 m/s to 10 m/s in 4 seconds. What is the snake’s average acceleration?
Acceleration =‘change in speed / time:
Acceleration = (10-2)/4
Acceleration =8/4
Acceleration = 2 m/s^2
please help Which of these numbers is equivalent to 2.4×10 to the 5 power? A. 2,400 B.24, 000 C. 240,000 D. 2,400,000
Answer:
C
Step-by-step explanation:
● 2.4 × 10^5
10^5 is 100000
● 2.4 × 100000
● 240 000
Answer:
C. 240,000
Step-by-step explanation:
This question is about using scientific notation.
In order to solve these types of questions, you move the decimal as many places as indicated by the Exponent ( which is given above the 10).
So in this example, we are given 2.4 x 10 ⁵. This means we would move the decimal 5 places. Since the exponent is positive, we will move the decimal to the right.
2 . 4 .
Which gives us option C. 240,000.
Factor this problem ?
125 +27y^3
Answer:
(5 + 3y)(25 - 15y + 9y²)
Step-by-step explanation:
This is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²), thus
125 + 27y³
= 5³ + (3y)³ with a = 5 and b = 3y
= (5 + 3y)(5² - 5(3y) + (3y)² )
= (5 + 3y)(25 - 15y + 9y²)
At the fair Jenny's friend, Michael buys 3 bags
of chips and 2 bottles of Gatorade for $7.35.
Write the linear model algebraically. If a
gatorade cost $1.80, how much does a bag of
chips cost?
Plzzzz help need help ASAP
Let [tex]y[/tex] be bags of chips and [tex]x[/tex] bottles of Gatorade.
The system of linear equations emerges.
[tex]3y+2x=7.35[/tex]
[tex]x=1.8[/tex]
Insert value of x from second equation into first to get rid of the system and get:
[tex]3y+2(1.8)=7.35[/tex]
Now solve for y.
[tex]y=\frac{7.35-2(1.8)}{3}=1.25[/tex].
A bag of chips costs $1.25.
Hope this helps.
Rewrite the problem below as an equivalent addition expression and evaluate.
10.25 - (3.5)
10.25 + (-3.5) = 6.25
10.25 + (-3,5) = 6.75
10.25 + (3.5) = 13.75
10.25 - (-3.5) = 13.75
Answer:
The correct option is;
10.25 + (-3.5) = 6.75
Step-by-step explanation:
We note that when adding numbers the negative sign is equivalent to the minus sign which is a mathematical operator. Therefore, when we subtract one number from another, it is equivalent to adding the negative of the other number to the first number
The given expression is 10.25 - (3.5)
The result of the given expression is 10.25 - (3.5) = 6.5
Therefore, we have;
10.25 + (-3.5) = 6.75
Graph -7+5y=35. khan acadmy forms of linear equations question. pls show work
The graph is a representation of how the value of the variable y vary.
Given that y is equal to a constant, 8.4, the graph is an horizontal line.
Response:
The graph of the linear equation -7 + 5·y = 35 having one variable is the graph of the horizontal line y = 8.4, attached.Which is the form of the given linear equation?The given equation is; -7 + 5·y = 35
The number of variables in the given equation is one (y), the
power of the variable is also one and the variable is y.
Therefore;
The value of the variable is a constant, in the form; y = c (constant)The graph of a constant y-value is a horizontal lineSolving the equation gives;
-7 + 5·y = 35
5·y = 35 + 7 = 42
[tex]y = \dfrac{42}{5} = \mathbf{8.4}[/tex]
The graph of the equation is the graph of the line, y = 8.4
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What is the image of (-4,-2)(−4,−2) after a reflection over the x-axis?
Answer:
(- 4, 2 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y )→ (x, - y ), thus
(- 4, - 2 ) → (- 4, 2 )
The image of the coordinate after a reflection over the x-axis is (-4, 2).
What is the reflection on x-axis?When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
The given coordinate point is (-4, -2).
The rule of reflection is (x, y)→(x, -y)
Here, (-4, -2)→(-4, -(-2))
= (-4, 2)
Therefore, the image of the coordinate is (-4, 2).
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