The probability that the sum of two dice is 7 given that the purple die landed on 6 is 1/6, as only one outcome from the green die (rolling a 1) will achieve this sum.
Explanation:The question is about calculating the conditional probability of rolling a sum of 7 on two dice, given that the purple die has already landed on 6. Since we know the outcome of the purple die, we only need to determine the probability that the green die will land on a 1 to make the sum 7 (6 from the purple die and 1 from the green die).
There are 6 possible outcomes when rolling a six-sided die. Since only one of these outcomes (rolling a 1) will result in the sum of 7 when the purple die is a 6, the conditional probability is 1/6.
Seventy-five 6 th-grade students chose to watch a movie on the last day of school. This is 25% of the 6 th-grade class. How many total students are in the 6 th grade?
The total number of students in the 6th grade is 300.
What is a percentage?A percentage is a number or ratio expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
For the given situation,
25% of the 6th-grade class students is 75
Let x be the total number of students, say 100%.
⇒ [tex]25\%=\frac{1}{4}[/tex]
Here, 1 part is 25% then 4 parts are 100%
Thus 1 part = 75, then
⇒ [tex]4 parts = 4(75)[/tex]
⇒ [tex]4 parts = 300[/tex]
Hence we can conclude that the total number of students in the 6th grade is 300.
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What is -5d+(-6)u-3?
Answer:-5d-6u-3
Step-by-step explanation:
-5d+(-6)u-3
-5d-6u-3
The set of life spans of an appliance is normally distributed with a mean 48 and a standard deviation 8 months. What is the z-score of an appliance that stopped working at 64 months?
Answer:
2
Step-by-step explanation:
The value of z-score of an appliance that stopped working at 64 months is,
⇒ 2
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The set of life spans of an appliance is normally distributed with a mean 48 and a standard deviation 8 months.
We know that;
Z- score = (X - μ) / σ
Here, We have;
μ = 48
σ = 8 months
X = 64 months
Hence, We get;
z - score = (64 - 48) / 8
z - score = 16 / 2
z - score = 2
Thus, The value of z-score of an appliance that stopped working at 64 months is,
⇒ 2
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How many solution does the equation 5x+8=2x-1 wil have.
Answer:
1 solution. Solution is -3.
Step-by-step explanation:
First subtract 8 from both sides. This gives you 5x=2x-9.
Then subtract 2x from both sides. This gives you 3x= -9
Next divide both sides by 3. This would give you that x = -3.
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Final answer:
The equation 5x + 8 = 2x - 1 is solved by isolating x to find that it has one solution, x = -3.
Explanation:
The equation 5x + 8 = 2x - 1 can be solved for x to determine how many solutions it has. To do this, we first rearrange the equation to bring all terms involving x on one side and the constants on the other. Subtract 2x from both sides to obtain 3x + 8 = -1. Next, subtract 8 from both sides to get 3x = -9. Finally, divide both sides by 3 to isolate x, which yields x = -3. Therefore, the equation has one solution: x = -3.
the product of twice a number and four. *
Answer: 20
Step-by-step explanation:
8 times 2 = 16
16 plus 4 = 20
Answer:
2x * 4
Step-by-step explanation:
A property had been a rectangular 100-by-200-ft parcel. The new zoning map
changed the boundaries so that the property is now shaped like a parallelogram.
The landowner complained that this represents a loss of area. Do you agree? If
so, what is the loss in square feet?
Answer:
Yes there is a loss of area
The loss is 5,858 ft²
Step-by-step explanation:
Kindly find attached rough sketch of the problem for your reference.
This problem bothers on the mensuration of flat shapes, rectangle and parallelogram
Firstly let us calculate initial area of the map, the rectangle
Area = length x width
Area = 200*100
Area = 20,000ft²
Now let us calculate the area of the new zoning map, parallelogram
Area = Base x height
But from the sketch we can solve for the height Applying
SOH CAH TOA
Using SOH
Sinθ= opposite/hypotenuse
Sin θ= h/100
h= sinθ*100
h= sin(45)*100
h= 0.7071*100
h= 70.71ft
We can now solve for the area of the new zoning map
A= 200*70.71
A= 14142ft²
Loss in square feet is
Area of initial map - area of New map
= 20,000-14,142
= 5,858 ft²
Ryan has $0.75 worth of pennies and nickels. He has 3 more nickels than pennies. Determine the number of pennies and the number of nickels that Ryan has.
9514 1404 393
Answer:
10 pennies13 nickelsStep-by-step explanation:
Let n represent the number of nickels Ryan has. Then the number of pennies is n-3, and his coins have a value (in cents) of ...
5n +1(n -3) = 75
6n = 78 . . . . . . . . . collect terms, add 3
n = 13 . . . . . . . . . . number of nickels Ryan has
n-3 = 10 . . . . . . . . number of pennies Ryan has
Ryan has 10 pennies and 13 nickels.
Ryan has 10 pennies and 13 nickels.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
Ryan has $0.75 worth of pennies and nickels.
Let x be the number of nickels Ryan has.
So, the number of pennies be x-3,
Then,
5x +1(x -3) = 75
6x = 78
x = 13
and, x-3 = 10
Hence, Ryan has 10 pennies and 13 nickels.
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Given kite MNOP below, which of the following conjectures, concerning the diagonals of a kite, is most likely true?
(graph attached)
A. The diagonals of a kite bisect the angles.
B. The diagonals of a kite are perpendicular.
C. The diagonals of a kite are perpendicular bisectors of each other.
D. The diagonals of a kite form four congruent triangles.
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
The boxplot below shows salaries for Construction workers and Teachers.
20 25 30 35 40 45 50
Salary (thousands of $)
Teacher
Construction
If a person is making the maximum salary for a construction worker, they are making more than what percentage of Teachers?
They are making more than
% of Teachers.
The construction worker are making more than More than 75% of teachers.
What is box- plot?A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
Let us consider the construction workers is 45000.
So 45,000 represent the third quarter which is 75% of the data.
So, the construction worker are making more than More than 75% of teachers.
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Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has
$3,875.79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?
Compound interest formula: V(t)= P 1-
t = years since initial deposit
n = number of times compounded per year
r= annual interest rate (as a decimal)
P = initial (principal) investment
VO) = value of investment after t years
2 years
9 years
18 years
36 years
Mark this and retum
Save and Exit
Nexs
Answer:
18 years
Step-by-step explanation:
Formula: V(t) = P* (1 + r/2)^(2t)
r = 4% = 0.04
P =$1,900
V(t) = $1,900 *(1 + 0.04/2)^ (2t)
V = 1900 *(1.02)^(2t)
$3,875.79 = 1900 * 1.02^2t
3875.79/1900 = 1.02^ (2t)
2.0398894736842 = 1.02 ^(2t)
ln 2.0398894736842 = ln (1.02^(2t) )
ln 2.0398894736842 = 2*t*ln (1.02)
ln 2.0398894736842 /(2* ln (1.02)) = t
0.71289562682179 / (2 * 0.0198 ) = t
18.00002 years = t
click the correct symbol 2,000 lb 1 T <, > , +
Answer:
>
Step-by-step explanation:
The correct symbol for the unit conversion is given by 2000 lb = 1 T
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the symbol be represented as A
Now , the weight of the object is given by
Let the first weight be p = 2000 lb
Let the second weight be q = 1 Ton
And , from the unit conversion
2000 lb = 1 Ton
So , the value of q = p
Hence , the symbol is equal to and 2000 lb = 1 Ton
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A. David notices that the shape of the Ligersville toxic dumpsite is somewhat like a triangle. He claims that he can approximate the perimeter of the dumpsite without doing any extra measurements. What assumption about side AB of the dumpsite would David need to make in order to justify his claim?
B. Based on the assumption in part A, determine the approximate length of side AB of the dumpsite. Explain your reasoning in at least two sentences.
C. Determine the approximate perimeter of the Ligersville toxic dumpsite. Explain your reasoning.
Answer:
A) AB is approximately straight line
B) 40 yards
C) 96 years
Step-by-step explanation:
A) For the toxic dump site to be traingular, AB must be a straight line to form hypotneuse of the traingle and that the traingle is right angle triangle
B) assuming a right angle triangle, using pythagoras theorem
H²=P²+B²
H²= 24²+ 32²
H= 40 yards
C) Parameter= 24+32+40=96 yards
Answer:
A. Side AB is approximately straight and forms the hypotenuse side of the right triangle
B. 40 yards
C. 96 yards
Step-by-step explanation:
A. The assumption about the curved side AB that David would need to make in order to justify his claim is that the side AB is straight and is the hypotenuse side of the right triangle.
B. The length of AB is thus;
√(24² + 32²) = 40 yard
C. The approximate perimeter is therefore;
24 + 32 + 40 = 96 yards
Esme earns a net salary of $2,400 per month. She already has a savings account that has $100 in it. After paying her expenses every month, she’ll be able to add $100 to her savings account. Esme also plans to purchase a car priced at $20,000 using a no-interest loan. She will make a $300 payment on the loan every month. In how many months will Esme have enough money saved to pay off her loan completely?
A. 44.45 months
B. 45.75 months
C. 47.75 months
D. 49.75 months
E. 50.45 months
Answer:
D. 49.75 months
Step-by-step explanation:
Esme earns a net salary of $2400 per month.
In her saving account she already have a balance of $100.
She saves $100 every month after her monthly expenses.
She plans to buy a car of $20000 using a no interest loan .
She usually make a $300 payment on the loan every month.
The number of months she will save enough money to pay off her loan completely can be calculated below.
let
x = number of months
The amount she saved altogether every month is $300 + $100 = $400.
Recall she already has $100 in her account
Amount of loan to be repaid = 100 + 400x
20000 = 100 + 400x
20000 - 100 = 400x
19900 = 400x
divide both sides by 400
x = 19900/400
x = 49.75 months
Answer:
D.) 49.75 Months
Step-by-step explanation:
Determine the volume of each right prism
A- area of base = 6cm2, height = 4cm
B- Area of base = 20cm, height =2cm
C- Height = 10cm, area of base = 15cm
Step-by-step explanation:
A:24
B:40
C:150
Hope this helped if I was correct
Suppose ACT Reading scores are normally distributed with a mean of 21.4 and a standard deviation of 5.9. A university plans to award scholarships to students whose scores are in the top 9%. What is the minimum score required for the scholarship? Round your answer to the nearest tenth, if necessary.
To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.
Explanation:To find the minimum score required for the scholarship, we need to find the z-score that corresponds to the top 9% of the normal distribution.
Step 1: Convert the top 9% to a z-score using the standard normal distribution table.
Step 2: Use the z-score formula to find the corresponding ACT Reading score.
Step 3: Round the answer to the nearest tenth.
The minimum score required for the scholarship is the score that corresponds to the z-score found in Step 1.
To be in the top 9% for ACT Reading scores, a student needs a minimum score of approximately 29.3.
To determine the minimum ACT Reading score required for the top 9%, we need to find the z-score that corresponds to the 91st percentile in a standard normal distribution. According to z-tables, the z-score for the 91st percentile is approximately 1.34.
Next, we use the z-score formula to find the required ACT score:Formula:⇒ Z = (X - μ) ÷ σ
Given values:⇒ Mean (μ) = 21.4,
⇒ Standard Deviation (σ) = 5.9,
⇒ Z = 1.34
Solve for X:⇒ X = Z × σ + μ
⇒ 1.34 × 5.9 + 21.4 = 7.906 + 21.4
≈ 29.3
Therefore, to be in the top 9%, the minimum ACT Reading score required is approximately 29.3.
2.
Write the ratio of passing scores to all 500 testing scores if there were 25 failing
scores.
Answer:
Simply subtract the fail rate from 100; the resulting number is the pass rate. So, if you know that 6 percent of students failed, you would subtract: 100 - 6 = 94 percent is the pass rate for the test.
Step-by-step explanation:
Answer:
19:20
Step-by-step explanation:
500 test scores
25 failing
500 -25 = 475 = passing scores
passing:all scores
475: 500
Divide each side by 25
475/25:500/25
19:20
If 1,500 students attend the high school, how many students get to school by bus or car?
375 students
750 students
975 students
525 students
Step-by-step explanation:
Simple
The percent of bus and car is 35
So 35% x 1500 = 525
Total bus and car students are 525
Find the arc length of a semicircle
Answer:
28.26
Step-by-step explanation:
What is the measure of angle 4?
Answer:
45 degrees
Step-by-step explanation:
∠1 and ∠4 are on a straight line. Therefore, they are supplementary and add to 180 degrees.
∠1+∠4=180
We know that the m∠1 is 135 degrees. We can substitute 135 in for ∠1.
135+∠4=180
Now we have to solve for ∠4. To do this, we need to get ∠4 by itself. 135 is being added on to ∠4. To undo this, subtract 135 from both sides, because subtraction is the opposite of addition.
135-135+∠4=180-135
∠4=180-135
∠4=45
The measure of ∠4 is 45 degrees.
Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
a.y=(x+8)^2-7
b.y=3(x-8)^2-7
c.y=3(x+8)^2-7
d.y=3(x+8)^2+7
We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.
We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], where point (h,k) represents vertex of parabola.
Let us write equation of parabola using our given information as:
[tex]y=a(x-(-8))^2-7[/tex]
[tex]y=a(x+8)^2-7[/tex]
Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:
[tex]-4=a(-7+8)^2-7[/tex]
[tex]-4=a(1)^2-7[/tex]
[tex]-4=a-7[/tex]
[tex]-4+7=a-7+7[/tex]
[tex]3=a[/tex]
Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex] and option 'c' is the correct choice.
Easy Question, Easy Points
Topic: Volume
Focus on question 12
Answer:
The air is .6m^3
Step-by-step explanation:
The volume of a cube is
V = s^3 where s is the side length
The volume of the tank is
V = 1^3 = 1 m^3
The volume of the water is 1 by 1 by .4
V = l*w*h
= 1 *1*.4
= .4 m^3
The difference must be filled by air
1- .4 = .6 m^3
The air is .6m^3
Answer:
0.4 m³
Step-by-step explanation:
Volume of air:
Base area × height
1 × 1 × 0.4
0.4 m³
What us the surface area of the triangular prism
Answer:
12 inches
Step-by-step explanation:
Because surface area is like a box,it would be the top.
Answer:
A ≈ 374.81
Step-by-step explanation:
SA = bh + (s1 + s2 + s3)H is the formula for SA of a triangular prism. if you plug in all of the digets thats what you get.
Which ordered pair is a to the equation y=6x -2
====================================================
Explanation:
The idea is to plug in each pair of coordinates and see if you get a true equation. Choice A does not work because
y = 6x-2
20 = 6(6)-2 ... plugged in x = 6 and y = 20
20 = 36-2
20 = 34
we have a false equation. So this shows choice A does not work.
--------
However, choice D does work since...
y = 6x-2
28 = 6(5)-2 .... plug in (x,y) = (5,28)
28 = 30-2
28 = 28
Put another way, if we plugged x = 5 into the equation, then we'd get y = 28. Therefore, showing (5,28) is a point on the line y = 6x-2.
To find the ordered pair that satisfies the equation, substitute values for x and solve for y. The ordered pair for the equation y = 6x - 2 is (0, -2).
Explanation:To find the ordered pair that satisfies the equation y = 6x - 2, we need to substitute different values for x and solve for y. Let's start by substituting x = 0. Plugging x = 0 into the equation, we get y = 6(0) - 2 = -2. So the ordered pair is (0, -2). Another way to find more ordered pairs is by using the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 6 and the y-intercept is -2.
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the floor of the truck is 36 inches high and the bottom of the ramp needs to be 323 inches from the truck. how long does Abraham need to make the ramp?
Answer:
About 324.96 inches
Step-by-step explanation:
Pythagorean Triangle Formula: a²+b²=c²
36²+323²=c²
1296+104329=c²
c²=105,598
Square root both sides
c=[tex]\sqrt{105,598}[/tex]
c=324.958459 inches≈324.96 inches
Which equation has x = 4 as the solution? log Subscript 4 Baseline (3 x + 4) = 2 log Subscript 3 Baseline (2 x minus 5) = 2 log Subscript x Baseline 64 = 4 log Subscript x Baseline 16 = 4
Answer:
A. log Subscript 4 Baseline (3 x + 4) = 2
Step-by-step explanation:
I graphed it.
The equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4
What is an equation?An equation is an algebraic expression that is represented by the equality "=" sign
For an equation to have a solution of x = 4, the equation must be true at x = 4
From the options, we have:
[tex]\log_4(3x + 4) = 2[/tex]
Substitute 4 for x
[tex]\log_4(3*4 + 4) = 2[/tex]
[tex]\log_4(16) = 2[/tex]
Express 16 as 4^2
[tex]\log_4(4^2) = 2[/tex]
Apply the law of logarithm
[tex]2\log_4(4) = 2[/tex]
Apply the law of logarithm
[tex]2*1 = 2[/tex]
[tex]2= 2[/tex]
The value of x = 4 is true for [tex]\log_4(3x + 4) = 2[/tex].
Hence, the equation [tex]\log_4(3x + 4) = 2[/tex] has a solution of x = 4
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Find the volume. *
4) height = 9 ft; radius = 3 ft
Volume =
Please help me ASAP
Answer:
B
Step-by-step explanation:
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Which graph represents a line with a slop of -2/3 and a y-intercept equal to that of the line y =2/x -2
Answer:
y = -2/3x - 2
Step-by-step explanation:
The slope of this line is -2/3 and the y-intercept is -2.
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classify each event as simple or compound
spinning a spinner and flipping a coin
picking a marble from a bag
drawing a card from the deck
rolling a number cube twice
Answer:
1. Compound
2. Simple
3. Simple
4. Compound
Step-by-step explanation:
The way I differentiated these was based on the quantitivity of each scenario. I related it to compound and simple sentences. For example, when one act was committed, it was clearly singular & simple. But if there was two actions consecutively, I'd consider that compound.
Answer:
compound
Step-by-step explanation:
hope this helps
An internet company randomly selected 50 of its customers and asked them how many hours per week they use the internet. Of those surveyed, 28 use the internet more than 15 hours per week. Based on the data, if the company has 800 subscribers, how many use more than 15 hours per week?
Answer:
Number of person use more than 15 hours per week from 800 subscribers = 448
Step-by-step explanation:
Given:
Total number of sample = 50
Result = 28 Person use more than 15 hours per week
Find:
How many people use more than 15 hours per week
Computation:
⇒ Probability of Person use internet more than 15 hours per week = 28 / 50
⇒Probability of Person use internet more than 15 hours per week = 0.56
⇒Number of person use more than 15 hours per week from 800 subscribers = 800 × Probability of Person use internet more than 15 hours per week
⇒Number of person use more than 15 hours per week from 800 subscribers = 800 × 0.56
⇒ Number of person use more than 15 hours per week from 800 subscribers = 448
Answer:
448
Step-by-step explanation:
Since 28/50 customers use the internet more than 15 hours per week. 28/50 is our fraction. So we do 28/50x800 which gives you 448.