Answer:
P(Success1) =1/6
P(Success2) =1/6
P(2Success) =1/6 × 1/6 = 1/12
Question is attached
Answer:
D) - 11-----------------------------
Given three consecutive terms of a GP:
4, x + 3, 16The middle term is the geometric mean of the other terms. Therefore:
(x + 3)² = 4*16(x + 3)² = 64x + 3 = ± √64x + 3 = ± 8x = - 3 ± 8x = - 11 and x = 5The matching choice is D.
If a salesman sells a watch at 90% of the cost price, the watch will be sold at $108. At what price must he sell the watch if he wants to make $30?
Answer:
$150
Step-by-step explanation:
Let's call the cost price of the watch C. The salesperson sells the watch at 90% of the cost price, so they sell the watch for 0.9 * C dollars.
We know that 0.9 * C = 108 dollars, so C = 108 / 0.9 = <<108/0.9=120>>120 dollars.
The salesperson wants to make a profit of $30, so they need to sell the watch for 120 + 30 = <<120+30=150>>150 dollars.
All work must be shown for full credit to be earned. Watch your signs!
1) Combine Like Terms
-8w + 16x + 20w – 40x
2) Apply the distributive property to simplify
the expression
8(12x – 20)
3) Add 7w – 12 and -15w + 60
4) Subtract 2w + 4 from 3w – 6
5) Solve for x:
7.2 + x = 18.1
6) Solve for x:
x – 25 = -3
Answer:
See below.
Step-by-step explanation:
1) Combine Like Terms
-8w + 16x + 20w – 40x
= -24x + 12w
2) Apply the distributive property to simplify
the expression
8(12x – 20)
= 96x - 160
3) Add 7w – 12 and -15w + 60
= -8w + 48
4) Subtract 2w + 4 from 3w – 6
= 3w - 6 - (2w + 4)
= 3w - 6 - 2w - 4
w - 10
5) Solve for x:
7.2 + x = 18.1
x = 10.9
6) Solve for x:
x – 25 = -3
x = 22
Answer:
Step-by-step explanation:
1. Combine Like Terms
[tex]\tt -8w + 16x + 20w - 40x[/tex]
[tex]\tt 12w+16x-40x[/tex]
[tex]\boxed{\tt 12w-24x}[/tex]
2) Apply the distributive property to simplify:-
[tex]\tt 8\left(12x-20\right)[/tex]
[tex]\tt 8\times \:12x-8\times \:20[/tex]
[tex]\boxed{\tt 96x-160}[/tex]
3. Add 7w – 12 and -15w + 60:-
[tex]\tt 7w-12+ (-15)w+60[/tex]
[tex]\tt 7w-15w-12+60[/tex]
[tex]\tt -8w-12+60[/tex]
[tex]\boxed{\tt -8w+48}[/tex]
4. Subtract 2w + 4 from 3w – 6:-
[tex]\tt 2w+4-3w-6[/tex]
[tex]\tt 2w-3w+4-6[/tex]
[tex]\tt -w+4-6[/tex]
[tex]\boxed{\tt -w-2}[/tex]
5. Solve for x:-
[tex]\tt 7.2+x=18.1[/tex]
[tex]\tt x+7.2=18.1[/tex]
[tex]\tt x+7.2-7.2=18.1-7.2[/tex]
[tex]\boxed{\tt x=10.9}[/tex]
6) Solve for x:
[tex]\tt x - 25 = -3[/tex]
[tex]\tt x=-3+25[/tex]
[tex]\boxed{\tt x=22}[/tex]
_________________
Hope this helps you!
Have a nice day!
A football field is 100 yds from end-to-end what is the length of a football field in feet
Example 2. Find each measure.
The measure of angle ∠C = 35°, 2x = 50° and x = 25°.
What are angles?In Euclidean geometry, an angle is made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively.
Angles can be formed by two rays in the plane where they are placed.
Additionally, when two planes overlap, angles are created.
Dihedral angles are what they are called.
So, m∠ABC:
We know that ∠C in triangle ABC = 180 - 145 = 35°
Now, the measure of m∠ABC:
95 + 35 + 2x = 180
130 + 2x = 180
2x = 180 - 130
2x = 50°
x = 50/2
x = 25°
Therefore, the measure of angle ∠C = 35°, 2x = 50° and x = 25°.
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Area of a solid box in the shape of a cube with side length 9cm
Answer:
486
Step-by-step explanation:
area of a cube =6x²
length= 9
area=6×9²
=6×81
=486
Which of the following best describes the domain and range of the relation in the graph?
Domain: {1 < x ≤ 9}
Range: {0 ≤ y ≤ 9}
B
Domain: {4 ≤ x ≤ 9}
Range: {1 ≤ y ≤ 9}
C
Domain: {0 ≤ x ≤ 9}
Range: {1 < y ≤ 9}
D
Domain: {5 < x ≤ 9}
Range: {4 < y ≤ 9}
Answer:
A
Step-by-step explanation:
Option A is the only Option with the correct domain.
A bag contains 2 blue, 1 red, and 3 green marbles. You choose one marble. Without
putting it back, you choose a second marble.
What is the probability that you first choose a green marble and then a blue marble?
P(green then blue) = 1/15
P(green then blue) = 1/5
P(green then blue) = 1/6
P(green then blue) = 2/5
The probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.
What is probability?
Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given:
A bag contains 2 blue, 1 red, and 3 green marbles.
So, the total marbles are 2 + 1 + 3 = 6
The probability of selecting a green marble is:
P(Green) = 3/6
Now, there are 5 marbles left.
The probability of selecting a blue marble is:
P(Blue) = 2/5
The required probability is:
P = 3/6 * 2/5 = 6/30 = 1/5
Hence, the probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.
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I’m in a rush please hurry!
After the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.
What is the system of equation?One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given system of the equation,
x = 3y - 17 {equation 1}
2x + 3y = -7 {equation 2}
Substitute the value of x from the equation 1 to equation2,
2 (3y - 17) + 3y = -7
Therefore, after the substitution 2(3y - 17) +3y = -7 is the answer of the system of equation.
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HELP PLEASE! THIS IS DUE TOMORROW! GIVING OUT 20 PTS!
Lucy's grade for her science class will be the average of her Unit 1 and Unit 2 tests and
her Unit 3 project. If she got a 91 on her Unit 1 test and an 88 on her Unit 2 test, what must
she score on her project to earn a 90 average?
Answer:91
Step-by-step explanation:
Formula for average is: (Unit 1 + Unit 2 + Unit 3) / 3
If we plug the values in we get
(91 + 88 + x) / 3 = 90
(179 + x) / 3 = 90
*3 *3
179 + x = 270
x = 91
6.
Technology required. A 6 oz cylindrical can of tomato paste needs to have a volume of
178 cm. The current can design uses a radius of 2.75 cm and a height of 7.5 cm. Use
graphing technology to find a cylindrical design that would have less surface area so
each can uses less metal.
The required parameters of a smaller surface area and a smaller amount of metal per can are a radius of 3.05 cm and a height of 6.09 cm.
What is surface area?The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. A three-dimensional shape's surface area is the sum of all of its faces. Finding the area of each face and adding them together gives us the surface area of a form.
Here,
V=πr²h
178=πr²h
πrh=178/r
S=2πr²+2πrh
S=2πr²+2*(178/r)
S=2πr²+356/r
S'=4πr-356/r²
S'=0
4πr=356/r²
r³=356/4π
r³=28.343
r=3.05 cm
h=178/πr²
h=178/(3.14*3.05*3.05)
h=178/29.23
h=6.09 cm
The dimensions needed for less surface area so each can uses less metal is radius as 3.05 cm and height as 6.09 cm.
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Hello Factor this with steps please
Answer:
[tex](2x-3)(4x^2+6x+9)[/tex]
Step-by-step explanation:
Given expression:
[tex]8x^3-27[/tex]
Rewrite 8 as 2³ and 27 as 3³:
[tex]\implies 2^3 \cdot x^3-3^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=(ac)^b[/tex]
[tex]\implies (2x)^3-3^3[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of Cubes Formula}\\\\$a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)$\\\end{minipage}}[/tex]
Apply the Difference of Cubes Formula.
Therefore:
a = 2xb = 3[tex]\implies (2x-3)((2x)^2+2x \cdot 3+3^2)[/tex]
[tex]\implies (2x-3)(4x^2+6x+9)[/tex]
3x² = 20 - 7х ?????????????????
x=5/3
x=-4
This is simple just rearrange and sub into quadratic formula. The formula will spit out two answers and those are your final answers. Enjoy!
For the function h(x) = -5x, determine h(4).
A) -20
B) 9
Answer: A.-20
Step-by-step explanation:
Since x=4
substitute in and solve
h(4)=-5(4)
h(4)=-20
Answer:
Step-by-step explanation:
when x=4, then h(x)=-5 * 4=-20
Therefore, choose A
[tex]67\pi *7=?[/tex]
The value of the given expression, 67π × 7, is 1473.4
Evaluating an expressionFrom the question, we are to determine the value of the given expression.
From the given information,
The given expression is
67π × 7
To determine the value of the expression, we will evaluate the expression step-wisely.
Evaluate 67π
67π = 210.4867
Multiply by 7
210.4867 × 7
= 1473.4069
≈ 1473.4
Hence, the value is 1473.4
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A box contains 512 grams of cereal. one serving of cereal is 56 grams. How many servings of cereal does the box contain
Answer:
9.14 servings
Step-by-step explanation:
The question is asking how many servings of cereal does the box contain, or in other words, how many groups of 56 grams can you make from 512 grams.
To find out how many groups of 56 you can make, you need to divide 512 by 56:
512 ÷ 56 = 9.14
Slopes of parallel and perpendicular lines
Answer:
The slope of both equations is 7. Yes, since the slopes are the same, the lines are parallel.
Step-by-step explanation:
For both equations, as the x increased by 1, the y increased by 7.
Iri’ checking account pay a imple interet at 2% per year. She ha $175 in her account. Write a linear function to model the amount of money in her checking account at any time
The required linear function to model the amount of money in Iri's account at any time t using the simple interest formula is 185 + 5.55t.
What is interest?An expense associated with borrowing money or other assets is interest.
The principal is the amount borrowed, and the interest is calculated as a percentage of the principal for a specific period of time.
If someone borrowed $1,000 at 2% interest and accumulated $100 in interest, the interest for that year would be $22.
It's because interest is paid on a total of $1100, which includes the principal ($1000) and accrued interest ($100). 2% of $1100 is $22.
So, in this situation, the checking account offers simple interest at a rate of 3% annually. Her account has $185 in it.
The total balance of the account will always be:
= 185 + (PRT/100)
P = principal
R = rate
T = time
Then,
= 185 + [(185 × 3 × t)/100]
= 185 + 5.55t
185 + 5.55t is the function.
Therefore, the required linear function to model the amount of money in Iri's account at any time t using the interest formula is 185 + 5.55t.
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Correct question:
Iris's checking account pays simple interest at 3% per year. She has $185 in
her account. Write a linear function to model the amount of money in her
checking account at any time t.
Donald buys a pack of 9 chocolate bars.
The pack costs £2.50
Donald sells all 9 chocolate bars for 45p each.
Work out Donald's percentage profit.
Answer:220%
Step-by-step explanation:
a. DVDs can be made in a factory in New Mexico at the rate of 20 DVDs per $3, but the factory costs $80,000 to build. If they make 1 million DVDs, what is the unit cost per DVD? Pls I need help this is due at 12:00 pm!!!!
Answer:
$1
Step-by-step explanation:
To find the unit cost per DVD, you need to calculate the total cost of producing 1 million DVDs and divide that by the number of DVDs produced.
First, you need to find the cost of producing 1 DVD. You can do this by dividing the cost of building the factory by the number of DVDs produced per dollar spent on the factory:
cost of 1 DVD = $80,000 / (20 DVDs/$3) = $1
Then, you can multiply this cost by the number of DVDs produced to find the total cost of producing 1 million DVDs:
total cost = (cost of 1 DVD) * (number of DVDs) = $1/DVD * 1,000,000 DVDs = $1,000,000
Finally, you can divide the total cost by the number of DVDs produced to find the unit cost per DVD:
unit cost per DVD = total cost / number of DVDs = $1,000,000 / 1,000,000 DVDs = $1/DVD.
So, the unit cost of producing 1 DVD is $1.
Answer:
Step-by-step explanation:
I think you should divide
a_1 = 8 and a_n = 3a_n-1 then find the value of a_4
In the series of a value of a(4)=216
What do the terms sequence and series mean?
Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of the elements in a sequence, which is a group of arranged elements that follow a pattern. The formulas for the nth term and the sum are typically included in the sequence and series formulas.
Given that:
a(1) = 8
a(n)= 3a(n-1)
so a(4) = 3a(3) = 72*3 = 216
a(3)= 3a(2) = 24*3 = 72
a(2)= 3a(1) = 3*8 = 24
Hence a(4) = 216
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Write the equation of the line perpendicular to y = 1/3x + 12 that contains the point (- 9, - 1).
Answer:
y = - 3x - 28
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{3}[/tex] x + 12 ← is in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (- 9, - 1 ) into the partial equation
- 1 = 27 + c ⇒ c = - 1 - 27 = - 28
y = - 3x - 28 ← equation of perpendicular line
Pls answers fast quick quick quick
Congruence is a property between two or more shapes that proves that they are equal in all respect. The required proof in the given question is shown below:
Two or more figures are said to be congruent if and only if they have equal length of sides, or measure of interior angles.
A triangle is a plane shape bounded by three straight sides, with three interior angles. The series properties can be used to classify the types of triangles with respect to their sides and angles. Some types of triangles are; equilateral, isosceles, right angled, acute angles scalene etc.
Thus to prove that: ΔADE ≅ Δ CDF
ΔBDE ≅ ΔBDF
AD ≅ DC (congruent property of similar figures)
AE ≅ CF (similarity property)
DE ≅ DF (congruent property of similar figures)
Thus,
ΔADE ≅ ΔCDF (SSS congruent property)
Also,
EB ≅ FB (congruent property of similar figures)
BD (common side of congruent figures)
DE ≅ DF (congruent property of similar figures)
So that,
ΔBDE ≅ ΔBDF (SSS congruent property)
This implies that,
i ΔADE + ΔBDE = ΔABD
ii. ΔCDF + ΔBDF = CBD
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What are the solutions to the equation
The solution of the quadratic equation 2x² - 5x = - 3 will be 3/2 and 1. Then the correct option is B.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]
The quadratic equation is given below.
2x² - 5x = - 3
Simplify the equation, then we have
2x² - 5x + 3 = 0
Then the roots of the equation are given as,
x = [-(-5) ± √((-5)² - 4 × 2 × 3)] / (2 × 2)
x = [5 ± √(25 - 24)] / 4
x = (5 ± 1) / 4
x = (5 + 1) / 4, (5 - 1) / 4
x = 6 / 4, 4 / 4
x = 3/2 and 1
The solution of the quadratic equation 2x² - 5x = - 3 will be 3/2 and 1. Then the correct option is B.
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Mai claims that the equation representing the relationship between feet and inches is y=12x, while Noah claims that the equation is y=x/12
Who is correct? Note: There are 12 in. in 1 ft.
A. Mai
B. Noah
C. Both
D. Neither
Both equations relate dimensions in feet with dimensions in inches (one is the inverse of the other) so the correct option is C.
Who is correct?
Mai and Noah tried to find an equation that relates dimensions in feet to equivalent dimensions inches.
Remember that the relation between inches and feet is:
1 feet = 12 inches.
Then, the number in inches in x feet, is 12 times that amount, so:
y = 12*x
That is the equation for Mai.
While the number of feet in x inches, is given by:
y = x/12
That is Noah's equation.
So, technically, both of them are correct. Both of their equations relate dimensions in feet with equivalent dimensions in inches.
So the correct option is C.
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find the measure of each angle indicated
A $1,000 TR Global bond at 80. 5 pays 6% interest. Find the interest. (Hint: Remember that a bond price of 90 on a $1,000 bond means that the bond sells for 90% of $1,000, or $900. )
The required interest as calculated from the given data equals $48.3 .
Given,
A $1,000 TR Global bond at an interest rate of 80.5 pays 6%.
A bond price of 90 on a $1,000 bond indicates that the bond will sell for $900, or 90% of $1,000.
Because we provided a $1,000 TR Global bond at 80.5 pays
means that 80% of $1,000 is used to fund the bond.
80.5% of $1,000 is equal to frac80.5100*1000=805.
The true cost is $805.
Currently, actual interest is 6%.
6% of $805= 6*100*805*0.06*805
=48.3
Final interest equals $48.3
Interest is calculated as Interest Rate * Balance or Principal.
Choosing the appropriate interest rate is frequently the more challenging part of calculating interest. The APR is typically used to denote the interest rate, which is frequently stated as a percentage.
The APR, however, frequently does not take compounding into account.
The actual rate of interest to be paid is expressed instead using the effective yearly rate.
To determine the appropriate interest earned over a specific period, an annual rate must frequently be converted.
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Suppose y varies directly with x. When x is 3, y is 18. What is x when y is 24?
Answer:
4
Step-by-step explanation:
If I'm reading it correctly, x is multiplied by 6 to equal y.
So, 3(x) x 6 = 18(y)
Therefore, 24/6 = 4 OR, 4(x) x 6 = 24(y)
NEED HELP PLSSS
Just need to explain why is it wrong
please help much appreciated!
The equation of the inequality graph with dashed line
y > 2x - 4The equation of the inequality graph with solid line
y ≥ -x + 4How to derive the equationsUsing the slope intercept form of the straight line which is of the form
y = mx + c
The slope, m is the ratio of the change in the output to the change in the input. This is given by the formula
m = (y₀ - y₁) / (x₀ - x₁)
Slope calculation using the points (0, -4) and (2, 0)
m = (-4 - 0) / (0 - 2)
m = 2
y intercept, c from the graph
c = -4
applying inequality representations
shading above the line is greater than and dotted lines means it does not have equal to
hence y > 2x - 4
for the solid line graph
the slope, m calculating using the points on the graph (0, 4) and (4, 0)
m = (4 - 0) / (0 - 4)
m = (4) / (-4)
m = -1
y intercept, c from the graph
c = 4
The equation of the line is y = -x + 4
Solid lines indicate an equality in the inequality, while shading over the line indicates a greater than
hence y ≥ -x + 4
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