Write an expression to represent "triple a
number more than four"

Answer:

The correct answer is option A.

Step-by-step explanation:

Hi! Nice to meet you and have a great day.

Answer:

The answer is B.

Step-by-step explanation:

The probability of getting 3 is P(A) = 1/216. The probability that sum being 3 is 1 / 216.

When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. A dice can show a minimum of one and a maximum of six dots, for a total of six sides, giving it a total of 6 * 6 * 6 = 216 possible outcomes.

:When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. The probability can be calculated as follows:

Let A be the event that the sum is 3. The number of ways to get 3 is 1, i.e., (1, 1, 1). The total number of possible outcomes is 6³,

since each die can have 6 possible outcomes.

Therefore, the probability of getting 3 is P(A) = 1/216.

In conclusion, the probability that sum being 3 is 1 / 216.

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

The limit as x approaches one is infinity.

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} =\infty\)

The limit of a function, f(x) as x approaches a given value b, is define as the value that the function f(x) attains as the variable x approaches the given value b.

From the given question, as x approaches 1,

substituting x into 1 - x,

the denominator of the function approaches zero, because 1 - 1 = 0 and thus the function becomes more and more arbitrarily large.

Thus, the limit of the function as x approaches 1 is infinity.

Therefore,

The limit (as x approaches 1)

\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} = \infty \)

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The amount of cars that have been sold more this year compared to the previous year is given as follows:

3,600 cars.

The amount of cars that have been sold more this year compared to the previous year is obtained applying the proportions in the context of the problem.

The amount of cars sold this year is given as follows:

11/13 x 27300 = 23,100 cars.

The amount of cars sold on the previous year is given as follows:

15/21 x 27300 = 19,500 cars.

Hence the difference is given as follows:

23100 - 19500 = 3,600 cars.

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Answer: A

Step-by-step explanation: A

Answer:f

Step-by-step explanation: none.

To test the claim that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is not equal to 0.50, we can use a hypothesis test.

Let p be the true proportion of teenagers who receive all the recommended doses of the HPV vaccine.

Our null hypothesis is that the true proportion is equal to 0.50, i.e. H0: p = 0.50. Our alternative hypothesis is that the true proportion is not equal to 0.50, i.e. Ha: p ≠ 0.50.

We can use a normal approximation to the binomial distribution to perform the hypothesis test. Under the null hypothesis, the sample proportion of teenagers who received all the recommended doses of the HPV vaccine follows a normal distribution with mean 0.50 and standard deviation σ = √((0.50)(1-0.50)/200) = 0.05.

Using the sample data, the test statistic is:

z = (p' - p) / σ = (0.55 - 0.50) / 0.05 = 1.00

where p' = 110/200 = 0.55 is the sample proportion.

The p-value for a two-sided test with a test statistic of 1.00 is approximately 0.32. Since the p-value is greater than the significance level of α = 0.05, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the proportion of teenagers who receive all the recommended doses of the HPV vaccine is different from 0.50 at the 5% significance level.

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The radius of convergence,R, of the series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\) is (1, ∞)

We know that for a power series ∑an (x - p)^n

if |x - p| < R then the series converges,

and if |x - p| > R then the series diverges.

Here, the number R is called the radius of convergence.

We have been given a series \(\[ \sum_{n=1}^{\infty} ~9(-1)^n~ nx^n \]\)

We need find the radius of convergence.

We use ratio test.

We know for \($\lim_{x\to\infty}~ | \frac{a_{n+1}}{a_n}|=L\)

if L < 1, then the series converges

and If \($\lim_{x\to\infty}~a_n \neq 0\) then \(\sum a_n\) diverges.

Using ratio test for given series,

\($\lim_{x\to\infty}~ | \frac{9(-1)^{n+1}~ (n+1)x^{n+1}}{9(-1)^n~ nx^n}|\\\\\\\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x^{n+1}}{nx^n}|\)

= \($\lim_{x\to\infty}~ | \frac{(n+1)x}{n}|\)

\(=|x| $\lim_{x\to\infty}~ | \frac{n+1}{n}|\)

= |x|

This means, the series is convergent for |x| < 1.

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To determine the time it takes for light to travel a distance of 9.2 × 10^7 miles, we need to divide the distance by the speed of light. The correct answer, written in scientific notation and rounded to the hundredths place, is option D: 49.5 × 10^3 seconds.


Given that the speed of light is 1.86 × 10^5 miles/second, we want to calculate the time it takes for light to cover a distance of 9.2 × 10^7 miles. To find the time, we divide the distance by the speed of light:

Time = Distance / Speed

Plugging in the given values:

Time = (9.2 × 10^7 miles) / (1.86 × 10^5 miles/second)

To divide these values, we subtract the exponents:

Time = (9.2 / 1.86) × 10^(7-5) seconds
Time = 4.946 × 10^2 seconds

Rounding to the nearest hundredth, we get 49.5 × 10^2 seconds. In scientific notation, this can also be expressed as 49.5 × 10^3 seconds, which matches option D.

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Answer:

Estimate: You can easily know to look at 45 and 32 in the ten thousands place and to add them together, which is 77. So, the answer is going to be around 77,000, but when you look at the entire numbers, you can tell 846 plus 185 is going to be over a thousand. So, if you know 45,000 plus 32,000 is 77,000 and 846 plus 185 is over a thousand, you should add 77,000 and 1,000 together to make an estimate of 78,000.

(This is my way of estimating for this problem, but everyone has different ways of thinking about it!!)

Value: 45,846+32,185=78,031

Since the estimate was only 31 away from the actual answer, you know the estimate was pretty accurate!

Hope this helped you out; have an amazing day!!! :3

Answer:

The amswer is "2,4,9....."

Step-by-step explanation:

\(x=\frac{1}{7}\\\\x_d=0.\overline{142857}\\\\x_h=0.\overline{249}\\\\\)

by leave you to work out the other 7 digits:

\(\to \frac{1}{7}\approx \frac{a}{16}\\\\a= \text{first hex digit}\\\\a=floor(\frac{16}{7})=2\\\\\)  

\(\to \frac{1}{7}- \frac{a}{16}\approx \frac{b}{16^2}\\\\b= \text{second hex digit}\\\\b=floor(\frac{16^2}{7} -16a)=4\\\\\)  

\(\to \frac{1}{7}- \frac{a}{16}-\frac{b}{16^2} \approx \frac{c}{16^3}\\\\c= \text{third hex digit}\\\\c=floor(\frac{16^3}{7} -16^2a-16b)=9\\\\\)  

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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Answer:

...........

2(x + 2) + 2x = 20

Answer:

x(x+2) = 20

Step-by-step explanation:

Perimeter Formulas of rectangle is: Perimeter = 2 × (a + b)

(a) The set of all nxn singular matrices and (c) the set of all nxn skew symmetric matrices are not subspaces, while (6) the set of all nxn upper triangular matrices is a subspace.

In order for a subset of a vector space to be considered a subspace, it must satisfy three conditions: (1) it must contain the zero vector, (2) it must be closed under vector addition, and (3) it must be closed under scalar multiplication. Let's examine each of the given subsets to see if they satisfy these conditions.
(a) The set of all nxn singular matrices: This subset does contain the zero matrix (since the zero matrix is always singular), and it is closed under scalar multiplication (if A is singular and k is any scalar, then kA is also singular). However, it is not closed under addition: the sum of two singular matrices can be invertible (i.e. not singular), so this subset fails to satisfy condition (2). Therefore, this subset is not a subspace.
(b) The set of all nxn upper triangular matrices: This subset contains the zero matrix (which is upper triangular), and it is closed under both addition and scalar multiplication. To see why it is closed under addition, note that if A and B are upper triangular, then so is A+B (since the sum of two upper triangular matrices is still upper triangular). Similarly, if A is upper triangular and k is any scalar, then kA is also upper triangular. Therefore, this subset satisfies all three conditions and is a subspace.
(c) The set of all nxn skew symmetric matrices: This subset contains the zero matrix (which is skew symmetric), and it is closed under scalar multiplication (if A is skew symmetric and k is any scalar, then kA is also skew symmetric). However, it is not closed under addition: the sum of two skew symmetric matrices need not be skew symmetric, so this subset fails to satisfy condition (2). Therefore, this subset is not a subspace.

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Answer:

888.467.789.985.872

Step-by-step explanation:

Answer:

$8.69

Step-by-step explanation:

you divide 52.14 by 6

Given:

The LCM of two numbers is 14 times their HCF.

The sum of LCM and HCF is 600.

One number is 280.

To find:

The other number.

Solution:

Let HCF of two numbers be x.

The LCM of two numbers is 14 times their HCF.

LCM = 14x

The sum of LCM and HCF is 600.

\(14x+x=600\)

\(15x=600\)

\(x=\dfrac{600}{15}\)

\(x=40\)

So, HCF = 40 and the LCM is

\(LCM=14(40)\)

\(LCM=560\)

We know that, if a and b are two numbers, then

\(a\times b=LCM(a,b)\times HCF(a,b)\)

One number is 280.

\(280\times b=560\times 40\)

\(b=\dfrac{560\times 40}{280}\)

\(b=2\times 40\)

\(b=80\)

Therefore, the other number is 80.

Catori traveled for 7/2 hours at 15 mph and 4 hours at 4 mph.

Catori started biking to the mall at 15 mph and it took her x hours to travel y miles.

After x hours, her bike got a flat, so she had to walk the rest of the way. She walked at 4 mph, and it took her z hours to travel the remaining 72 miles to the mall.

Since the total trip to the mall took 7 hours, we can calculate that x + z = 7.

We can also calculate that y + 72 = 72.

Using these two equations, we can solve for x and z.

x + z = 7
y + 72 = 72

Subtract 72 from both sides of the second equation to get:

y = 0

Substitute 0 for y in the first equation to get:

x + z = 7

Solve for z:

z = 7 - x

Substitute 7 - x for z in the second equation to get:

y + (7 - x) = 72

Simplify the equation to get:

y = 72 - 7 + x

Substitute 72 - 7 + x for y in the first equation to get:

x + (7 - x) = 7

Simplify the equation to get:

2x = 7

Divide both sides of the equation by 2 to get:

x = 7/2

Substitute 7/2 for x in the equation y = 72 - 7 + x to get:

y = 72 - 7 + (7/2)

Simplify the equation to get:

y = 72 - (7/2)

Therefore, Catori traveled for 7/2 hours at 15 mph and 4 hours at 4 mph.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

What is this?

Step-by-step explanation:

The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

The missing image is attached below.

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\( \frac{ {x}^{2} + 2x - 8 }{ {x}^{2} - 3x - 10 } \)

let the denominator x² - 3x - 10 is f(x),

• Setting this factor equal to 0,

→ x² - 3x - 10 = 0

• By using Middle term splitting method,

→ x² - 5x + 2x - 10 = 0

→ (x² - 5x) + (2x - 10) = 0

• Taking common,

→ x( x - 5 ) + 2( x - 5 ) = 0

→ ( x - 5 ) ( x + 2 ) = 0

• Again, setting these factors equal to 0,

( x - 5 ) = 0 and ( x + 2 ) = 0

→ x = 5 → x = -2

Hence, the values that would make the fraction undefined is x = 5,-2...

The values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

To find the values that would make the fraction undefined, we need to identify any values of x that would make the denominator equal to zero.

The denominator of the fraction is (\(x^2 - 3x - 10\)). We need to solve the equation:

\(x^2 - 3x - 10 = 0\)

To factorize the quadratic equation, we look for two numbers that multiply to -10 and add up to -3. These numbers are -5 and 2:

(x - 5)(x + 2) = 0

Now, we can set each factor equal to zero and solve for x:

x - 5 = 0 => x = 5

x + 2 = 0 => x = -2

Therefore, the values x = 5 and x = -2 would make the fraction undefined since they would result in a zero denominator.

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point B is located in quadrant II (option B)

Point A: (6, 3) = (x, y)

reflection of point A across the y axis:

The x coordinate will be negative and the y coordinate will remain the same

reflection of point A across the y axis = (-6, 3)

Attaching the graph showing the point after reflection:

Since point B is the reflection of point A.

Hence, point B is located in quadrant II (option B)

Answer:

A small pizza cost $12.99

Answer:

The price of a small pizza is 12.99

Step by step explanation:

15.75 + 17.50 + ? = 46.24

15.75 + 17.50 = 33.25

46.24 - 33.25 = 12.99

Answer:

5

Step-by-step explanation:

12g - 18 > 6g + 12

12g > 6g + 30

6g > 30

g = 5

Have a great day!

Please rate!

Answer:

do you mean y=2+4x?

if it is, it would be the top one.

The side lengths of the given triangle are 3 m, 10 m, and 10 m.

Let's assume the length of the third side of the triangle is x.

According to the given information, the two equal sides of the triangle are each 8 m less than six times the third side. Therefore, the lengths of the two equal sides can be expressed as:

6x - 8

6x - 8

The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 23 m:

x + (6x - 8) + (6x - 8) = 23

Simplifying the equation:

x + 6x - 8 + 6x - 8 = 23

13x - 16 = 23

13x = 23 + 16

13x = 39

x = 39 / 13

x = 3

Now that we have the value of x, we can find the lengths of the two equal sides:

Equal side 1 = 6x - 8 = 6 * 3 - 8 = 10 m

Equal side 2 = 6x - 8 = 6 * 3 - 8 = 10 m

Therefore, the side lengths of the triangle are 3 m, 10 m, and 10 m.

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