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Problem 15: The answer is choice A
cos(angle) = adjacent/hypotenuse
cos(B) = BC/AB
cos(B) = 12/13
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miss Roberts simplified this ratio 2:6 explain how you know she is incorrect can you tell where she might have made a mistake
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Do you go to k12 btw ?
add or subtract.
[tex] \binom{7 \sqrt{2} }{2} - \binom{ \sqrt{8} }{2} [/tex]
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This is the fraction of 5*sqrt(2) all over 2
"sqrt" is shorthand for "square root"
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Work Shown:
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{8}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{4*2}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{\sqrt{4}*\sqrt{2}}{2}[/tex]
[tex]\frac{7\sqrt{2}}{2}-\frac{2*\sqrt{2}}{2}[/tex]
[tex]\frac{7\sqrt{2}-2*\sqrt{2}}{2}[/tex]
[tex]\frac{5\sqrt{2}}{2}[/tex]
the least common denominator of 2 fractions is 12 if you add the two denominators their sum is 7 what are the denominators
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it would be 3 and 4 since they are the only two in here that have the least common denominate of 12. 5 isn't divisible by 12, 7 isn't either, so that only leaves 3 and 4 and they worked since 3*4 does equal 12.
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile.
Pick one;
1.2 miles
1.8 miles
2.5 miles
4.2 miles
(Ps: I can't copy the picture but its a right triangle.)
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We know:
Length of the sides of the triangle
We want to know:
Length of the hypotenuse
Using the Pythagorean theorem we have:
[tex]d = \sqrt{3^2 + 3^2} [/tex]
Rewriting the expression we have:
[tex]d = \sqrt{2(3^2)} [/tex]
[tex]d = 3\sqrt{2} [/tex]
[tex]d = 4.2 miles [/tex]
Then, the distance that he would have saved if he travels directly is:
[tex]3 + 3 - 4.2 = 1.8 miles [/tex]
Answer:
he would have saved:
1.8 miles
Answer:
1.8 miles
Step-by-step explanation:
50 students live in a dormitory. the parking lot has the capacity for 30 cars. if each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars?
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To find the probability that there won't be enough parking spaces for all the cars, we can use the binomial distribution formula and calculate the probability of having more than 30 cars in a sample of 50. The probability is approximately 0.9999999999.
Explanation:To find the probability that there won't be enough parking spaces for all the cars, we need to find the probability that the number of cars exceeds the capacity of the parking lot. The number of cars follows a binomial distribution with a probability of success of p = 0.12 and a sample size of n = 50. We can use the binomial probability formula to calculate this probability:
P(X > 30) = 1 - P(X ≤ 30)
where P(X ≤ 30) is the probability that the number of cars is less than or equal to 30. We can use a binomial calculator or software to find this probability:
P(X > 30) ≈ 0.9999999999
19.21 is 113% of what number
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19.21 is 113% of 17
(113/100)x = 19.21
(1 13/100)x = 19.21
19.21 divides by 1 is the same value l
13/100 x = 19.21
Divide both sides by 13/100 or 0.13 to find the answer.
In 2015, the price of a business math text rose to $150. This is 8% more than the 2014 price. What was the old selling price?
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150=1.08x
x=$138.88
Answer: old selling priceof businesss math text rose = $138.89
Explanation:
In year 2015, Price of business math text rose = $150
Suppose privious price (year 2014)= x dollars
Previous price is 8% less than the price in 2015 because given that $150 is 8% more than previous year price.
Now write the linear equation for the given information:
x + 8% of x = 150
Solve for x
x + [tex] \frac{8}{100} [/tex]x = 150
x + 0.08x = 150
1.08x = 150
divide 1.08 both the side
x = [tex] \frac{150}{1.08} [/tex]
x = $138.89
Old selling price = $138.89
You are wearing a pair of cargo pants with six pockets. You've put $10 in one of the pockets, but you cannot remember which one. After checking two pockets without success, what is the probability that the money will be in the next pocket you check? NextReset
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The total number of ways left over is 4 for your next try
The number of pockets that will be successful is 1
Since there are 6 pockets all together. And you checked two of them and neither of them had the $10. so you cannot forget those 2 when figuring this out, and now there are 4 pockets left unchecked
The probability that the money will be in next pocket is 0.25.
We have a pair of cargo pants with six pockets and $10 in one of the pockets.
We have to find out the probability that the money will be in the next pocket you check after checking two pockets without success.
What is the formula to calculate the probability of an event ?The formula to calculate the probability of an event is -
[tex]P(A) = \frac{Total\;number\;of\;favorable\;outcomes}{Total\;number\;of\;outcomes\;in \;sample\; space} =\frac{n(A)}{n(S)}[/tex]In the question it is given -
Total money = $10
Total no. of pockets = 6 = n(S)
After two unsuccessful check in two pockets, new sample space =
n(S') = n(S) - 2 = 4
Hence, the probability that the money will be in the next pocket you check is -
P(A) = [tex]\frac{1}{4} = 0.25[/tex]
Hence, the probability that the money will be in next pocket will be 0.25.
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In a probability experiment, Craig rolled a six-sided die 57 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
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36:21 →12:7
The ratio of rolls greater than three to rolls less than or equal to three is 36:21, which simplifies to 12:7 after dividing both terms by the greatest common divisor of 3.
Since Craig rolled the die 57 times, and it landed on a number greater than three 36 times, then it landed on a number less than or equal to three the remaining number of times. Subtracting the number of greater rolls from the total rolls:
Total rolls: 57
Rolls greater than three: 36
Rolls less than or equal to three = 57 - 36 = 21
Now, we can establish the ratio of rolls greater than three to rolls less or equal to three:
Ratio = Rolls greater than three : Rolls less than or equal to three = 36 : 21
And if needed, we can simplify this ratio by dividing both sides by their greatest common divisor, which is 3:
Simplified Ratio = 12 : 7
1. Solve w=x+y/z for y.
2. Solve the equation above for z.
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Answer:
y = z(w -x)z = y/(w -x)Step-by-step explanation:
As in any "solve for ..." problem, you reverse (undo) the operations done to the variable of interest. Generally, you do that in reverse order.
1. y is divided by z then the quotient added to x. To solve for y, we subtract x, then multiply by z.
... w - x = y/z . . . . . . . subtract x from the given equation
... z(w -x) = y . . . . . . . multiply by z
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2. To solve for z, it is more convenient to start with the equation for y that is the result of the first question. We divide that by the coefficient of z.
... z = y/(w -x)
From w=x+y/z, the value of y = z(w - x)
w=x+y/z
This is changing the subject formula. The first thing to do is to subtract x from both sides. This will be:
w - x = x + y/z - x
w - x = y/z
Then, we cross multiply
z(w - x) = y
Therefore, y = z(w - x)
Since y = z(w - x)
Then, to get the value of z goes thus:
z = y/(w - x)
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What is the value of x?
Enter your answer in the box.
_____ units
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Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: The value of x is 28 units.
Step-by-step explanation:
Since we have given that
DC ║ PA
So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.
So, it becomes,
[tex]\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28[/tex]
Hence, the value of x is 28 units.
The length of a rectangular prism is 4 feet, and the width is 3 feet. The volume of the prism is 9 cubic feet. In inches, what is the height of the prism?
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Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 16 and its height is 6 ?
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base 8, height 12
base 4, height 24
base 2, height 48
base 1, height 96
base 32, height 3
base 48, height 2
base 96, height 1
Which trinomial is the product of the expression below ? (2R-3) (R+12)
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2R^2 + 21R - 36
Explanation:
To answer this question, we will follow these steps:
1- expand the brackets
2- gather like terms
Steps are as follows:
(2R-3)(R+12) = 2R(R) + 2R(12) - 3(R) - 3(12)
= 2R^2 + 24R - 3R - 36
= 2R^2 + 21R - 36
Hope this helps :)
(2R-3) (R+12)---------- > 2R*R+12*2R-3*R-3*12---------- > 2R²+24R-3R-36
2R²+24R-3R-36---------------> 2R²+21R-36
the answer is 2R²+21R-36
which of the following values of x makes the rational expression below equal to zero? 2x+16/x+5
a. 5
b. -5
c. 8
d. -8
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For this case what you should know is that an indefinite expression are those in which mathematically no numerical value can be obtained.
We have then that a division between zero causes an expression to be undefined.
For x = -5 we have:
(2 (-5) +16) / ((- 5) +5)
(-10 + 16) / (- 5 + 5) = 6/0 (undefined)
Answer:
x = -5
b. -5
Answer:
d. -8
Step-by-step explanation:
Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:
2x+16=0
2x=-16
x=-16/2
x=-8
So in order to make the expression equal to 0 x needs to be equal to -8,
How would you write the following phrase as a number expression eight more than triple a number
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Simplify this equation.
(equation and choices in image)
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b.)x³-7x²+3x+36
(x-4)(x²-3x-9)
Distribute x and -4 to x²-3x-9
=x²(x)-3x(x)-9(x)+x²(-4)-3x(-4)-9(-4)
=x³-3x²-9x-4x²+12x+36
Combine all liked terms
=x³-7x²+3x+36
The purchase price of an IPad is 650. What is the total price oif the sales tax rate is 8%
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total price = $702
One-third the sum of 6 and 3 (u get 10 points)
Hurry
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Final answer:
The sum of 6 and 3 is 9, and one-third of this sum is 3 when you divide 9 by 3.
Explanation:
In mathematics, a sum is the result of adding two or more numbers or quantities together. It represents the total or aggregate of those quantities. The process of finding this total is called addition.
Thus,
To calculate one-third the sum of the numerals 6 and 3, we first find the sum of 6 and 3, which is 9.
Then, we need to take one-third of 9.
To find one-third of a number, you divide the number by 3.
So one-third of 9 is 9 divided by 3, which equals 3.
Therefore, one-third the sum of 6 and 3 is 3.
In a survey, 60 baseball fans were asked whether they thought the designated hitter rule should be changed. Forty-one fans thought the rule should be changed. WHat percent of the fans surveyed said that the designated hitter rule should be changed.
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How was triangle A translated?
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A tree 24 feet tall casts a shadow 12 feet long.Brad is 6 feet tall. How long is Brads shadow
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Answer: 6
Step-by-step explanation:
thiss is for a challenge
Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and Charlie in that order. Each customer buys more scones than the last and the increase is the same number in each case. Robbie and Cameron’s combined total number of scones is three sevenths of the total of Louis, Tom and Charlie. How many scones does each boy buy?
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Robbie: 6
Cameron: 9
Louis: 12
Tom: 15
Charlie: 18
Explanation:
1) Assume that Rachel sold all the cones: 60
2) Call x the amount that Robbie bought and d the constant increase on the purchse.
3) That means that the number of cones bought by each one is:
Robbie: x
Cameron: x + d
Louis: x + d + d = x + 2d
Tom: x + 2d + d = x + 3d
Charlie x + 3d + d = x + 4d
The sum of that is: x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 5x + 10d = 60
5x + 10d = 60 may be simplified by dividing each side by 5 => x + 2d = 12.
Equation (1) x + 2d = 12
4) Robbie and Cameron’s combined total number of scones is three sevenths of the total of Louis, Tom and Charlie
=> x + (x + d) = [3/7] [ (x + 2d) + (x + 3d) + (x + 4d) ]
=> 2x + d = [3/7] (3x + 9d)
=> 7(2x + d) = 3 (3x + 9d)
=> 14x + 7d = 9x + 27d
=> 14x - 9x = 27d - 7d
=> 5x = 10d
=> x = 2d
Equation (2) x = 2d
5) Now you just have to solve this simple system of equations:
x + 2d = 12
x = 2d
Subitituing x for 2d in the first equation: x + x = 12 => 2x = 12 => x = 6
Now replace x = 6 in any of the two equations and you get the value of d.
For example, from x = 2d => d = x / 2 = 6 /2 = 3.
6) Finally, calcualte the number of cones of each:
Result
Robbie: x 6
Cameron: x + d 6 + 3 = 9
Louis: x + d + d = x + 2d 9 + 3 = 12
Tom: x + 2d + d = x + 3d 12 + 3 = 15
Charlie x + 3d + d = x + 4d 15 + 3 = 18
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Total 6 + 9 + 12 + 15 + 18 = 60
HELP MEEE!!! PLEASE!!!
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Determine the equation for the parabola graphed below.
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f (x) = ax ^ 2 + bx + c
To verify the equation of the parabola you need three points:
f (x) = ax ^ 2 + bx + c
We choose the points:
(x, y) = (- 1,7)
7 = a (-1) ^ 2 + b (-1) + c
7 = a - b + c
(x, y) = (0,5)
5 = a (0) ^ 2 + b (0) + c
5 = c
(x, y) = (- 2,5)
5 = a (-2) ^ 2 + b (-2) + c
5 = 4a - 2b + c
We solve:
c = 5
5 = 4a - 2b + 5
7 = a - b + 5
Rewriting
b = 2a
a-b = 2
Substituting:
a-2a = 2
a = -2
b = -4
The equation of the parabola is:
f (x) = - 2x ^ 2 -4x + 5
A section in a stained glass window is shaped like a trapezoid. The top base is 1 centimeter and the bottom base is 1.5 centimeters long. If the area of the section of glass is 5.5 square centimeters, how tall is the section?
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Which equation could be the equation of this parabola?
A. y = -2x^2
B. x = -2y^2
C. x = 2y^2
D. y = 2x^2
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Parabolas in the form of [tex]\sf x=y^2[/tex] open to the left or to the right.
Since this parabola opens upward, we know it must be in the form of [tex]\sf y=x^2[/tex]. Also, if the coefficient of 'x' is positive, it opens upward, but if it is negative, it opens downward. This parabola opens upward, so we know that the coefficient of 'x' must be positive. Therefore, our answer must be D, [tex]\sf y=2x^2[/tex]
A car traveled 48.36 miles in one hour. What was it's average speed per minute?
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0.806 miles per minute
Step-by-step explanation:There are 60 minutes in an hour, so replace the unit "hour" by 60 minutes and recompute.
... 48.36 mi/h = 48.36 mi/(60 min) = (48.36/60) mi/min = 0.806 mi/min
The car's average speed was calculated by dividing the total distance of 48.36 miles by the total time of 60 minutes, resulting in an average speed of 0.806 miles per minute.
Explanation:To compute the car's average speed per minute, we need to divide the total distance covered by the total time in minutes. This is because speed is defined as the rate at which an object covers distance. The distance travelled by the car is 48.36 miles (the total distance), and the time is 1 hour. To transform this hour into minutes, we multiply by 60, as there are 60 minutes in an hour. So,
1 hour = 60 minutes
Therefore, to find the average speed, we take the total distance and divide by the total time in minutes. Using this, we find:
Average speed = Total distance / Total time
Average speed = 48.36 miles / 60 minutes = 0.806 miles per minute.
Therefore, the car's average speed was approximately 0.806 miles per minute.
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Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg smartphone survey). if 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
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Using the binomial probability formula, sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings, which will give you the total probability for fewer than 3.
Explanation:The subject of this question appears to be probability theory, a branch of mathematics that studies the likelihood of different outcomes. The problem presented involves calculating the probability of a certain number of smartphone users behaving in a specified way. In this case, it's about finding the likelihood that fewer than 3 out of 12 selected individuals use their smartphones in meetings or classes.
To solve this, we'll use a binomial probability formula: P(X=r) = (nCr) * p^r * (1-p)^(n-r), where:
n is the number of trials (in this case, 12 smartphone users),r is the desired number of successful outcomes,p is the probability of success on a single trial (54%), andnCr is the combination of n items taken r at a time.
You will need to sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings or classes to get the total probability for fewer than 3.
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Va doctor prescribes 10 mg of cough syrup. available is 5 mg/5 ml. how many teaspoons would you give?
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ans: 2 teaspoons