How many different 7-digit numbers can be formed using the digits in the number 5,474,575?
6nsquared - 5nsquared + 7nsquared simplify the expression
What is the value of s and the length of side BC if ABCD is a rhombus?
Step 1
Find the value of s
we know that
In a Rhombus all sides are congruent
so
[tex]AB=BC=CD=DA[/tex]
[tex]AB=9s+29\\CD=10s-16[/tex]
equate AB and CD
[tex]9s+29=10s-16\\[/tex]
Combine like term
[tex]10s-9s=29+16\\[/tex]
[tex]s=45\ units[/tex]
The answer Part a) is
the value of s is [tex]45\ units[/tex]
Step 2
Find the value of side AB
[tex]AB=9s+29[/tex]
substitute the value of s
[tex]AB=9*45+29=434\ units[/tex]
Remember that the sides are congruent
[tex]AB=BC=CD=DA[/tex]
therefore
the answer Part b) is
The length of the side BC is [tex]434\ units[/tex]
The value of s is 45 and the length of side BC is; 434.
What is a Rhombus?A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.
Hence,
AB = BC = CD = DATo determine the value of s;
10s - 16 = 9s + 2910s-9s = 29+16s = 45.The length of side BC = CD = 10(45) - 16 = 450 - 16
The length of side BC = 450 -16 = 434
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Precalc: Vector word problem:
A channel flows from north to south at a rate of 15 mph.
A sailboat heads at an angle of 30 degrees upstream at 40 mph.
A strong wind blows towards northwest at 30 mph.
a. Write each vector in component form.
A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.
Assuming that; [tex]\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.[/tex]
For the channel:
Rate, r = 15 mph.The vector representing the flow from North to South is given by:
[tex]15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)[/tex]
Vector = 0, -15
For the sailboat:
Rate, r = 40 mph.Angle = 30 degrees upstream.The vector representing the sailboat is given by:
[tex]40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15[/tex]
Vector = [tex]15\sqrt{3} ,\;15[/tex]
For the strong wind:
Rate, r = 30 mph.The vector representing the strong wind blowing towards northwest is given by:
[tex]30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}[/tex]
Vector = [tex]-15\sqrt{2},\;15\sqrt{2}[/tex]
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what is 2500g converted to kg
Ace Hardware sells boxes of wrenches ($ 100) and hammers ($300). Howard ordered 40 boxes of wrenches and hammers for $ 8,400. How many boxes of each are in the order.
Answer:
18 boxes of wrenches and 22 boxes of hammers.
Step-by-step explanation:
what is the axis of symmetry of y=3x^2+6x+5
1 2 3 4 5 6 7 8 9 10 TIME REMAINING 58:03 The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the standard form of the equation for this line?
The standard form of the equation for the line passing through (-5, -1) and (10, -7) is y = x - 17.
Explanation:The standard form of the equation for the line passing through the points (-5, -1) and (10, -7) can be found using the point-slope form given, which is y + 7 = (x - 10).
First, let's convert this equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Subtracting 7 from both sides of the equation, we get y = x - 17.
This is the standard form of the equation for the line passing through (-5, -1) and (10, -7).
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Given that 3^x = 4^y = 12^z, show that z = (xy)/(x+y).
Final answer:
To show that z = (xy)/(x+y) given that 3^x = 4^y = 12^z, logarithms and the properties of exponents are used to simplify and solve for z.
Explanation:
The problem given is to show that if 3^x = 4^y = 12^z, then z = (xy)/(x+y). To solve this, we can use logarithms or equate the expressions to a common variable. Since 12 = 3 × 4, it means that 12^z = (3^z)(4^z).
Remember that the original equations given were 3^x = 12^z and 4^y = 12^z.
Substituting z into these equations we have 3^x = 3^z × 4^z and 4^y = 3^z × 4^z.
Taking logarithms, we find
[tex]log(3^x) = log(3^z) + log(4^z) and log(4^y) = log(3^z) + log(4^z).[/tex]
Applying the power rule of logarithms, the equations simplify to
[tex]x log(3) = z log(3) + z log(4)[/tex]and [tex]y log(4) = z log(3) + z log(4).[/tex]
Dividing these equations by log(3) and log(4) respectively gives
[tex]x = z + z(log(4)/log(3))[/tex] and [tex]y = z + z(log(3)/log(4)).[/tex]
Adding these equations, we get
[tex]x + y = 2z + z[(log(4)/log(3)) + (log(3)/log(4))],[/tex]
which simplifies to x + y = 2z because [tex](log(4)/log(3)) + (log(3)/log(4)) = 1.[/tex]Finally, solving for z gives z = (xy)/(x+y) as desired.
On a cross-country trip, a couple drives 500 mi (miles) in 10h on the first day, and 400 mi in 8h on a second day. the average speed for the whole trip is:
A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to
The value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]
Explanation:Aspirin also known as acetylsalicylic acid, is a medication used to reduce pain, fever, or inflammation. A test statistic is the random variable that calculated from sample data it used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis or not. The test statistic can compare the data with what is expected under the null hypothesis
A survey (a general view, examination, or description of someone or something) claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. the value of the test statistic in this problem is approximately equal to [tex]\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex] where
a = People who indicate that they recommend aspirin = 0.83
b = the actual proportion of doctors who recommend aspirin = 0.9
c = the actual proportion of doctors who not recommend aspirin = 1-0.9 = 0.1
d = a random sample = 100
[tex]\frac{a-b}{\sqrt{\frac{(b)(c)}{d} } } =\frac{0.83-0.9}{\sqrt{\frac{(0.9)(0.1)}{100} } }[/tex]
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Liz is using the distributive property to evaluate the expression 27(36) by using friendlier numbers. Her work is shown below.
Liz’s Work
27(36)
Step 1
27(3 + 12)
Step 2
27(3) + 27(12)
Step 3
81 + 324
Step 4
405
What was the first error that Liz made?
Step 1 should have been 27(6 + 30).
Step 2 should have been 27(3) + 12.
Step 3 should have been 27(30)(12).
Step 4 should have been 16,244.
Answer:
A
Step-by-step explanation:
what is the answer to simplify 10y-7y
what is 802 and 6 hundredths in expanded form
42 out of 96 support a candidate in an office election what percent of the vote is that
divide
42/96 = 0.4375
0.4375*100 = 43.75 percent
round the answer as needed.
a rectangle has a length of 7 meters longer than double the width. the perimeter is 134 meters. find the dimensions of the rectangle.
how do you write 10 X 3 ten's in standard form?
Solve the quadratic equation by completing the square. x^2-14x+42=0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.
Form: ______
Solution: _______
If you choose a card at random from a well shuffled deck of 52 cards, what is the probability that the card chosen is not a heart
The probability that the card chosen is not a heart is 0.75
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Sample space ={13 H + 13 D + 13 S + 13 C}
= 52 cards
The total number of cards in a deck is 52
Number of cards with hearts = 13
Therefore, P(getting one heart) = 13/52 = 1/4
P( getting NO heart) = 1-1/4 = 3/4 = 0.75
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A new surgery is successful 75% of the time. if the results of 10 such surgeries are randomly sampled, what is the probability that fewer than 9 of them are successful
This is a binomial probability problem where we calculate the probability of fewer than 9 successful surgeries out of 10, given a success rate of 75% for each surgery. The probabilities of 0 to 8 successful surgeries are calculated and summed up.
Explanation:The question asks for the probability that fewer than 9 out of 10 surgeries are successful, given that each surgery has a 75% chance of being successful. This is a binomial probability problem since each surgery can result in either success (75%) or failure (25%), and we are dealing with a fixed number of independent trials (10 surgeries).
To solve this, we first calculate the probability of exactly 8 successes, exactly 7 successes, and so on down to 0 successes, then sum these probabilities. The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and nCx is the combination of n items taken x at a time.
However, calculating each probability individually and summing them can be tedious, and tools or calculators designed for binomial distributions are often used to compute this more efficiently. For a result of fewer than 9 successes, we would add the probabilities of getting 8, 7, ..., down to 0 successful surgeries.
Lisa is asked to draw a triangle with the following specifications:
two angles are complementary
the side between the two complementary angles has a length of 10 centimeters
Which of the following statements about this triangle is true?
A.
More than one triangle exists with the given conditions, and all instances must be right triangles.
B.
More than one triangle exists with the given conditions, and all instances must be isosceles triangles.
C.
Exactly one triangle exists with the given conditions, and it must be a right triangle.
D.
Exactly one triangle exists with the given conditions, and it must be an isosceles triangle.
N a poisson probability problem, the rate of errors is one every two hours. what is the probability of at most three defects in four hours
The probability of having at most three defects in a four-hour period is approximately 0.8572.
The Poisson probability distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this problem, the rate of errors is given as one error every two hours. We need to find the probability of having at most three defects in a four-hour period.
To solve this problem, we can use the Poisson probability formula, which is:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) is the probability of having exactly x events occur in the given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! is the factorial of x.
First, we need to calculate the average rate of events in a four-hour period. Since the rate is given as one error every two hours, we can calculate the rate for a four-hour period as follows:
Average rate = (4 hours) / (2 hours/error) = 2 errors
Now, we can plug this average rate (λ = 2) into the Poisson probability formula for x = 0, 1, 2, and 3 to find the probabilities of having at most three defects:
P(0; 2) = [tex](e^{(-2)} * 2^0)[/tex] / 0! ≈ 0.1353
P(1; 2) = ([tex]e^{(-2)} * 2^1[/tex]) / 1! ≈ 0.2707
P(2; 2) = [tex](e^{(-2)} * 2^2)[/tex] / 2! ≈ 0.2707
P(3; 2) = [tex](e^{(-2)} * 2^3)[/tex] / 3! ≈ 0.1805
To find the probability of at most three defects, we sum up these individual probabilities:
P(at most 3 defects) = P(0; 2) + P(1; 2) + P(2; 2) + P(3; 2) ≈ 0.8572
So, the probability of having at most three defects in a four-hour period is approximately 0.8572.
Two buses leave at the same time traveling in opposite directions. One bus travels at 63mph and the other at 62mph. How soon will they be 187.5
miles apart?
A business has $11,080 to spend on new laptops and tablet computers for its salespeople. The laptops cost $515 each. The tablets cost $285 each. The business wants each salesperson to have either a laptop or a tablet. There are 30 salespeople. How many of each type of computer should the business buy?
515x + 285y = 11,080
x + y = 30
Hydraulicists often express rainfall in acre-feet. this is the amount of water required to cover an area of one acre to a depth of one foot. there are 640.0 acres in a square mile, and 5280 feet in one mile. how many cubic feet are there in one acre-foot?
Answer:
1 acre foot = 43560 ft³
Step-by-step explanation:
1 square mile = 640 acres.
5280 feet = 1 mile
5280 x 5280 ft² = 640 acres.
1 acre = 43560 ft².
1 acre foot = 43560 x 1 ft³ = 43560 ft³
1 acre foot = 43560 ft³
The net of a pyramid is shown below. The net of a square based pyramid, with base edges labeled 4 inches and the height of the triangle labeled 8 inches. The surface area of the solid is ____ square inches.
Consider the equation y=2x+5 . Create a table of five ordered pairs that satify the equation. What is the y-intercept of the equation? What is the x-intercept of the equation?
Answer:
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
y intercept is (0,5)
x intercept is (-2.5, 0)
Step-by-step explanation:
y=2x+5
To get 5 ordered pairs , plug in some random number for x and find out y
x y= 2x+5
-2 2(-2) + 5= 1
-1 2(-1) + 5= 3
0 2(0) + 5= 5
1 2(1) + 5= 7
2 2(2) + 5= 9
five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)
When x=0 , the value of y = 5
So y intercept is (0,5)
To find x intercept we plug in 0 for y
y=2x+5
0 = 2x +5
subtract 5 from both sides
-5 = 2x
divide by 2 on both sides
x= -5/2
so x intercept is (-2.5, 0)
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . After how long will it reach its maximum height? Do not round your answer.Time: ___ seconds
The time taken to reach the maximum height = 3 s
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²
The maximum value of the function is obtained if the first derivative of the function h (t) = 0
96-32t = 0
96 = 32t
t = 3 s
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Final answer:
The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.
Explanation:
To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).
To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:
h'(t) = d/dt (96t - 16t²) = 96 - 32t.
Setting the derivative equal to zero:
96 - 32t = 0
32t = 96
t = 96/32 = 3 seconds.
Therefore, the ball reaches its maximum height after 3 seconds.
The half life of cobalt -60 (used in radiation therapy) is 5.26 years ( actual data ).how much of a 200 g sample of cobalt-60 will remain after 26.3 years
The amount of cobalt-60 will decrease with each half-life, which is 5.26 years. After 5 half-lives (26.3 years), the 200g sample will reduce to 6.25g.
Explanation:The subject of the question is the half-life of a radioactive substance, in this case, cobalt-60. Half-life is the time required for half the atoms in a sample to decay. Given that the half-life of cobalt-60 is 5.26 years, and we are interested in a period of 26.3 years, we first classify this period into 'half-life' units, which equals 26.3 / 5.26 = 5 half-lives.
With each half-life, the quantity of cobalt-60 is cut in half. We start with a 200g sample and after 5 half-lives, the amount of cobalt-60 would decrease as follows:
After the 1st half-life = 200/2 = 100g After the 2nd half-life = 100/2 = 50gAfter the 3rd half-life = 50/2 = 25gAfter the 4th half-life = 25/2 = 12.5gAfter the 5th half-life = 12.5/2 = 6.25gTherefore, after 26.3 years, only 6.25g of the original 200g sample of cobalt-60 will remain.
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The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.
What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?
The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.
Explanation:The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.
There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.
Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.
Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.