Answer:
Step-by-step explanation:
Probability of a 2 = 1/6
Probability of a 4 = 1/6
probability of a 2 or 4 = 1/6 + 1/6 = 2/6 = 1/3
[tex]\text{We need to find the probability of rolling a 2 or 4}\\\\\text{Rolling a 2 or 4 is our intended outcome}\\\\\text{Therefore, it would be 2 outcomes in our probability}\\\\\text{We also know that there are a total of 6 sides in a number cube}\\\text{This represents our total amount of outcomes}\\\\\text{With the information above, we would write our probability as:}\frac{2}{6}\\\\\text{You can simplify it by dividing by 2}\\\\\boxed{\frac{1}{3}}[/tex]
Part A The circumference of a dinner plate is 19.5 inches. What is its radius? ( use π=3.14 ) Round your answer to the nearest hundredth. inches.
Circumference = PI x diameter
FInd the diamter:
19.5 = 3.14 x diameter
Divide both sides by 3.14:
Diameter = 19.5 / 3.14
Diameter = 6.21019108 inches.
Radius = diameter / 2
Radius = 6.21019108 / 2
Radius = 3.10509554 inches
Rounded to the nearest hundredth = 3.11 inches.
When a cycle is sold allowing 10% discount on its marked
price a seller gains 5% and allowing 5% discount the profit is
Rs 351. Find the cost price of the cycle. (Ans: Rs. 3240)
The cost price of the cycle is Rs.3240
Represent the cost price of the cycle with x and the selling price with y
A gain of 5% when the marked price is at a discount of 10% implies that:
[tex]5\%=\frac{(1 - 10\%)y-x}{x}[/tex]
Express 10% as decimal
[tex]5\%=\frac{(1 - 0.10)y-x}{x}[/tex]
[tex]5\%=\frac{0.90y-x}{x}[/tex]
Express 5% as decimal
[tex]0.05=\frac{0.90y-x}{x}[/tex]
Cross multiply
[tex]0.05x=0.90y-x[/tex]
Collect like terms
[tex]x + 0.05x=0.90y\\[/tex]
This gives
[tex]1.05x=0.90y[/tex]
Make y the subject of the formula
[tex]y = \frac{1.05x}{0.90}[/tex]
Also, when the discount is 5% and the profit is 351, we have:
[tex]351=(1 - 5\%)y -x[/tex]
Express 5% as decimal
[tex]351=(1 - 0.05)y -x[/tex]
This gives
[tex]351=0.95y -x[/tex]
Make y the subject
[tex]0.95y = 351 + x[/tex]
Substitute [tex]y = \frac{1.05x}{0.90}[/tex]
[tex]0.95 \times \frac{1.05x}{0.90} = 351 + x[/tex]
[tex]\frac{0.9975x}{0.90} = 351 + x[/tex]
Subtract x from both sides
[tex]\frac{0.9975x}{0.90} -x= 351[/tex]
Take LCM
[tex]\frac{0.9975x - 0.9x}{0.90}= 351[/tex]
[tex]\frac{0.0975x}{0.90}= 351[/tex]
Multiply both sides by 0.90
[tex]0.0975x= 315.9[/tex]
Divide both sides by 0.0975
[tex]x= 3240[/tex]
Hence, the cost price of the cycle is Rs.3240
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4/7 of the students in a classroom are boys. If there are twelve girls in the class, how many total students are there?
Answer:
28 students total.
Step-by-step explanation:
Let's use a ratio:
boys : girls
4 : 3
16 : 12
To find the total, we need to add 16 and 12 which equals 28
Answer:
28 students
Step-by-step explanation:
If 4/7 of the students are boys,
then 1- 4/7 = girls
7/7 -4/7 = 3/7
total students *3/7 = girls
total students * 3/7 = 12
Multiply each side by 7/3
total students * 3/7 *7/3 = 12*7/3
total students = 28
Four students were asked to write an expression which has terms that have a greatest common factor of 8c.
the expressions provided by the students are shown below.
Tanya
32C+16cd
Wyatt
8c-48cd
Xavier
36c-24c yang. 8c+40
Which student wrote the correct expression?
Answer:
Wyatt
Step-by-step explanation:
Tanya: 32c+16cd=16c(2+d)
The GCD of the terms is 16cWyatt : 8c-48cd=8c(1-6d)
The GCD of the terms is 8cXavier :36c-24c =12c(3-2)
The GCD of the terms is 12cYang: 8c+40=8(c+5)
The GCD of the terms is 8Since the expression is required to have a GCD of 8c, Wyatt wrote the correct expression.
Answer:
wyatt answered correctly
Step-by-step explanation:
What is the solution to the inequality 1/4+x<5/6
Answer:
x < 7/12
Step-by-step explanation:
1/4+x<5/6
Multiply each side by 12 to get rid of the fractions
12*1/4+12x<5/6*12
3 + 12x < 10
Subtract 3 from each side
3+12x-3 < 10-3
12x < 7
Divide by 12
12x/12 < 7/12
x < 7/12
Answer:
A
Step-by-step explanation:
Which sentence describes a benefit that short-term disability insurance offers a policyholder? A. It provides 30% to 40% of the policyholder's income for up to one year. B. It provides 10% to 25% of the policyholder's income for up to two years. C. It provides 50% of the policyholder's income for up to one year. D. It provides 40% to 60% of the policyholder's income for up to one year.
Answer:
D. It provides 40% to 60% of the policyholder's income for up to one year.
Step-by-step explanation:
Insurance is a risk sharing device where the risk is shared between the policyholder and the insurance company through regular periodic payment called premium. What Short term disability insurance does is to make do with the income of a person that has to leave his/her place of work as a result of sickness or injury. It provides financial assistance while the individual convalesces at home. The employee are liable to receive 40 to 60 % of their gross weekly income pending on the premium paid. This coverage period is 9 to 52 weeks, (i.e 2.25 to 12 months).
Answer:
D. It provides 40% to 60% of the policyholder's income for up to one year.
Step-by-step explanation:
What is the Solution?
Answer: w=2 and 2=6
Step-by-step explanation:
If you substitute 6 and 2 in for w they both work, making c the correct answer
Answer:
w = 2 and w = 6
Step-by-step explanation:
Given
[tex]\frac{w}{2w-3}[/tex] = [tex]\frac{4}{w}[/tex] ( cross- multiply )
w² = 4(2w - 3) ← distribute
w² = 8w - 12 ( subtract 8w - 12 from both sides )
w² - 8w + 12 = 0 ← in standard form
(w - 2)(w - 6) = 0 ← in factored form
Equate each factor to zero and solve for w
w - 2 = 0 ⇒ w = 2
w - 6 = 0 ⇒ w = 6
A number cube is rolled 12 times and lands on 3 four times and on 5 three times. Find the experimental probability of landing on three.
Answer:
the answer is 27
Step-by-step explanation:
because you have to multiply 3x4 and 5x3 which will give you 15 and 12 which equals 27
Find the surface area of the prism.
Answer:
9x4x5= 180cm
You would do length x width x hight
Answer:
A=202
Step-by-step explanation:
Length: 9
Width: 4
Height: 5
Formula: L*W*H
Hope this helps
Selecting 5 out of the 13 students will ride in a car instead of a van.
A) Permutation
B) Combination
C) Circular permutation
Answer:
combination
Step-by-step explanation:
permutation is when there is a specific order, whereas combination is when they are not in any specific pattern (in this case, 5/13 students, not in any particular order. just 5.
I don't want to explain circular permutation right now (it's difficult to explain), but it's not it from my knowledge
The number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.
The way of selecting 5 out of the 13 students will ride in a car instead of a van is evaluated by the combinations.
We consider the group of 5 students can be selected to ride in a car instead of a van.
Thus, for selecting a random group of the data from the universal data, we have to apply combinations to evaluate it.
Therefore, the ways can be formulated as:
[tex]^{13}C_5=\dfrac{13!}{5! \times 6!}\\=1287\;\rm{ways}[/tex]
Thus, the number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.
To know more about the combinations, please refer to the link:
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What is the surface area?
10 cm
8 cm
10 cm
12 cm
10 cm
square centimeters
Step-by-step explanation:
surface area = (2*0.5*12*8) + (2*10*10) + (12*10)
= 96 + 200 + 120
= 416 cm^2
2 Points
What is the surface area of the cube below?
A. 96 units2
B. 64 units2
C. 80 units2
D. 120 units2
Answer:
A
Step-by-step explanation:
The cube has 6 surfaces with side lengths 4 by 4. Each of the faces has area 4*4=16 units, and multiplying this by 6 yields 96 units, or answer choice A. Hope this helps!
The surface area of the given cube is 96 square units, option A is correct.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The formula to find the surface area of cube is 6s²
Where s is the side length of cube
s=4 from the given cube
Plug in the value of s in surface area formula
surface area = 6(4)²
=6×16
=96 square units
Hence, the surface area of the given cube is 96 square units, option A is correct.
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Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π.
The sphere's radius is 6.
Answer:
V≈904.78
Step-by-step explanation:
You have to multiply
6*3.14
Answer:
288π
Step-by-step explanation:
Question 3- Please help. Find the area of the sector for the image below:
Answer:
The answer is 16.8 cm^ 2.
Someone please help me with the answer. ASAP
option a is the answer you are which class same question is there for me
6 divided 2 (1+2) and 9 - 3 divided by 1/3 +1
Answer:
1
Step-by-step explanation:
Work between parenthesis first, so distribute the 2 into both digits within the parenthesis then add the together.
Now divide that number by the 6 at the beginning of the problem to get your first answer.
Now you work on the second part, divide 3 by 1/3 which would give you 9.
9-9=0
0+1=1
1 is your overall answer
Answer:
1 ; 18/4
Step-by-step explanation:
6/ 2(1+2) ; 9 - 3/(⅓ + 1)
6/ 2(3) ; 6/ (4/3)
6/6 ; 6 / (4/3)
1; (6×3)/4
1 ; 18/4
What is the solution to the system of linear equations graphed below?
5
4 3
2
1
1
2 3
4
5
x
Answer: -5,-1
Step-by-step explanation:
Answer:
-5,-1
Step-by-step explanation:
Fill in the blanks:-
The product of a number and its reciprocal is __________ .
PLEASE HELP.....I NEED TO SUBMIT IT NOW
Answer:
The product of a number and its reciprocal is 1.
For i.e : 4/3 and its reciprocal 3/4, 4/3 x 3/4 = 1
Hope this helps!
:)
Which expressions have a value of 15 when
S = 15
what are the answer choices?
The expression S/3 + 10 has the value of 15 when S = 15. Then the correct option is A.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let's check all the options, then we have
A. S/3 + 10
If S = 15, then we have
⇒ 15 / 3 + 10
⇒ 5 + 10
⇒ 15
B. S/2 + 10
If S = 15, then we have
⇒ 15 / 2 + 10
⇒ 10 + 10
⇒ 20
C. S + 10
If S = 15, then we have
⇒ 15 + 10
⇒ 15 + 10
⇒ 25
D. - S/3 + 10
If S = 15, then we have
⇒ -15 / 3 + 10
⇒ -5 + 10
⇒ 5
The expression S/3 + 10 has the value of 15 when S = 15. Then the correct option is A.
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The missing options are given below.
A. S/3 + 10
B. S/2 + 10
C. S + 10
D. - S/3 + 10
please Help it’s urgent
Answer:
Angle IAJ
Step-by-step explanation:
X idea again. They are opposite to each other in the immediate area around them.
Find the resultant (sum) of the complex numbers. Express in rectangular form a plus b i.
3 - 12 i, -7 + 2 i
Answer:
he trigonometric ( or polar) form of z= a+bi is z = r(cosθ+isinθ) .
So for Part 3 3 - 3i we have r = √(3^2 + (-3)^2) = 3√2 and θ= arctan(3/-3) = arctan (-1) = -π/4.
So the answer is 3√2(cos(-π/4) + isin(-π/4).
Part 1. 3 = 3(cos 0 - i sin 0).
Part 2. -6i = 6(cos (-π/2) - isin -(π/2)
Step-by-step explanation:
Solve this Inequality, show work if you can, Thanks!!
Answer:
28 is less than or equal to x
Step-by-step explanation:
20 is less than or equal to x - 8
20 + 8 is less than or equal to x - 8 + 8
You add to cancel out the 8 to isolate x.
28 is less than or equal to x
What is the area of this figure?
Answer: 50
Step-by-step explanation:
Base: 8
Height: 5
The formula for the area of a triangle is base times height divided by two. Add the area of the rectangle to the triangles and BOOM there’s your answer.!.
For the parrallelogram, if measure of angle 2= 5x-28 and measure of angle 4= 3x-10, Find x.
Answer:
x = 9
Step-by-step explanation:
Unfortunately you didn’t provide the figure however we can use the picture below to work on:
from a property of the parallelogram (opposit angles) we know that angle 2 and 4 are equal in measure
then
5x - 28 = 3x - 10
then
5x - 3x = 28 - 10
then
2x = 18
then
x = 18/2
= 9
Rocky has 7 bottles of water. He will buy bottles of water from the store. The store has 8 cases in stock and each case contains 24 bottles of water. The store will not sell partial cases. The function that models the number of bottles of water Rocky will have after his purchase is F(c) = 24c +7, where c is the number of cases of water he buys.
What is the theoretical domain of the function?
A)
All Real Numbers
B)
All Real Numbers From 1 To 8, Inclusive
C)
{31, 55, 79, 103, 127, 151, 175, 199}
D)
All Integers From 1 To 8, Inclusive
Answer:
A)
All Real Numbers
Step-by-step explanation:
Every integer is a real number.
A building in a downtown business area casts a shadow that measures 88 meters along the ground. The straight-line distance from the top of the building to the end of the shadow it creates is at a 32° angle with the ground. What is the approximate height of the building? Round your answer to the nearest meter. The building is meters high.
The height of the building with a shadow of 88 feet is 55 feet.
Trigonometric ratioTrigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the building, hence using trigonometric ratios:
tan(32) = h / 88
h = 88 * tan (32) = 55 feet
The height of the building with a shadow of 88 feet is 55 feet.
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Answer: 55
Step-by-step explanation: The building is 55 meters high
. You deposit $600 in an account that earns simple interest. The difference between the total interest earned after 5 years and the total interest earned after 3 years is $24. What is the annual interest rate?
Answer:
The answer is .007874989
Step-by-step explanation:
Can someone please help me? I keep losing points...
CORRECT ANSWERS ONLY PLEASE!!!!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent.
Answer:
$14,000
Step-by-step explanation:
i = prt
i= ($70,000)(.04)(5)
i = $14,000
Answer:
$14000
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 70000 × 4/100 × 5
I = $14000
How fast was a driver going if it left skid marks that were 63 feet long on wet concrete? (The coefficient of friction is 0.97)?
Answer:
Step-by-step explanation:
Let m be the mass of the vehicle
frictional force = μ mg
μ is coefficient of friction ,
deceleration = μ g
= .97 x 32
a = - 31.04 ft /s
v² = u² - 2 a s
0 = u² - 2 a s
u² = 2 a s
= 2 x 31.04 x 63
= 3911.04
u = 62.54 ft / s
Answer:
43mph
Step-by-step explanation:
Took the test
the number of subscriptions to an interior design magazine was 16,450 in 1996. Since then, the number of subscriptions has increased by 9.2% each year. find the approximate number of subscriptions in 2018.
Answer:
49,744.8 so round up to 49,745
Step-by-step explanation:
