A picture frame has a perimeter of 62 inches. The difference between the
length and twice the width is 1 inch. What are the length and width of the
frame?

Answer:

79

Step-by-step explanation:14+11+2(12) = 24 + 14 + 11 = 79

Answer:

49

Step-by-step explanation:

14+11+2(12)

14+11+24

25+24

49

Answer

-6

Step-by-step explanation:

3x-12=-2x-42

(Collect like terms together:)

3x+2x=-42+12

(when the number crosses the equal sign it changes signs)

5x/5=-30/5

(We devided by 5 cause we looking for x not 5x)

Answer:

a)1400 + 300x ≤ 5000

b) x ≤ 12 days

Step-by-step explanation:

a) Since the grocery store owner wants to stay within budget then, this means he would be spending at most $5,000

The word at most is represented by the inequality sign ≤ = Less than or equal to

Let x = Number of days

Hence,

Our inequality equation is

$1400 + 300× x ≤ $5000

1400 + 300x ≤ 5000

b) Solving for x

1400 + 300x ≤ 5000

300x ≤ 5000 - 1400

300x ≤ 3600

x ≤ 3600/300

x ≤ 12 days

Answer:

The momentum for the truck and cargo is 150000 kg·km/h

Step-by-step explanation:

p = mv

p = (2000 kg + 1000 kg)(50 km/h)

p = (3000 kg)(50 km/h)

p = 150000 kg·km/h

Answer:

a. 12 sides

b. Not possible

Step-by-step explanation:

a.

\(d=\frac{1}{2} n(n-3)\)

\(\frac{1}{2}n^{2}-\frac{3}{2} n=54\)

multiply by 2

\(n^{2} -3n=108\)

equation

\(n^{2} -3n-108=0\)

factor

\((n-12)(n+9)\)

\(n-12=0\\n=12\)

b.

\(n^{2} -3n=33\)

\(n^{2} -3n-33=0\)

The roots of the equation are decimal numbers

The number of sides must be integer

So there is no polygon with 33 diagonals.

Hope this helps

Answer

50/1    6/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

PS =5 because PS's line is parallel to 5 the line.

So now all that is left is the angle one

m∠Q =105° we can come to this conclusion because 105° is parallel to m∠Q

If you are still confused please, let me know! :)

The number of students attending the charter school t years after 2005 is given by -50t + 350

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Let N(t) represent the number of students after t years, hence:

Since the population has decreased by 100 students every two years:

N(t) = -(100)/2 * t + 350 = -50t + 350

The number of students attending the charter school t years after 2005 is given by -50t + 350

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Answer: 75

Step-by-step explanation:

Answer:

take lowest common factor

Step-by-step explanation:

Answer:

Find the least common denominator for both fractions and set up the fractions so they can both contain that same denominator.

Step-by-step explanation:

For example, let's say you want to add the fractions \(\frac{3}{4}\) and \(\frac{2}{7}\).

First, you will want to find the least common demoninator.  Write out the multiples for both denominators originally given, in this case 4 and 7.  Let's go up to 4*10 and 7*10:

4: 4,8,12,16,20,24,28,32,36,40

7: 7,14,21,28,35,42,49,56,63,70

Se which number in both sets is the first number to be the same in both sets.  That will be your least common denominator.  In this case, the least comon denominator is 28.

To set the fractions right, you would need to multiply the first fraction, 3/4, by 7/7: \(\frac{3}{4}*\frac{7}{7}=\frac{21}{28}\)

Then, you would need to multiply the second fraction, 2/7, by 4/4: \(\frac{2}{7}*\frac{4}{4}=\frac{8}{28}\)

Now, since both fractions have a common deonminator now, you can add them togther and simplify afterwards if you need to:

\(\frac{21}{28}+\frac{8}{28}=\frac{29}{28}=1\frac{1}{28}\)

And that's it.

Answer: I think it’s the first choice. Foreign Language, Math/CS, and social studies

Step-by-step explanation:

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Answer: Refer to the images attached.

Step-by-step explanation:

The Q3 means the third quartile which is 16

Answer: 5 - 20 i

Step-by-step explanation:

To determine for which values of x the power series ∑ (-1)^k (x-5)^k converges, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Let's apply the ratio test to the given power series:

a_k = (-1)^k (x-5)^k

We calculate the ratio of consecutive terms:

|a_(k+1)| / |a_k| = |(-1)^(k+1) (x-5)^(k+1)| / |(-1)^k (x-5)^k|

                 = |(-1)^(k+1) (x-5)^(k+1)| / |(-1)^k (x-5)^k|

                 = |(-1)(x-5)|

To ensure convergence, we want the absolute value of (-1)(x-5) to be less than 1:

|(-1)(x-5)| < 1

Simplifying the inequality:

|x-5| < 1

This inequality represents the interval of convergence. To find the specific interval, we need to consider the endpoints and check if the series converges at those points.

When x-5 = 1, we have x = 6. Substituting x = 6 into the series:

∑ (-1)^k (6-5)^k = ∑ (-1)^k

This is an alternating series that converges by the alternating series test.

When x-5 = -1, we have x = 4. Substituting x = 4 into the series:

∑ (-1)^k (4-5)^k = ∑ (-1)^k (-1)^k = ∑ 1

This is a constant series that converges.

Therefore, the interval of convergence is [4, 6]. The series converges for values of x within this interval, and we have checked the endpoints x = 4 and x = 6 to confirm their convergence.

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A person heart beats is 4.2 x 10∧7

there are 7,600,000,000= 7.6 x 10∧9

the heartbeats for all the people here on earth= 4.2 x 10∧7 x 7.6 x 10∧9

choosing like terms

4.2 ×7.6×10∧7×10∧9

31.92x10∧(7+9)

31.92×10∧16

a=31.92

b=16

Answer:

\(3.192*10^1^7\)

Step-by-step explanation:

To find this value, multiply the two values given:

4.2x10^7 = 4.2 x ( 10 x 10 x 10 x 10 x 10 x 10 x 10) = 42000000

42000000 x 7600000000 = 319200000000000000

Then convert 319200000000000000 into scientific notation:

319200000000000000 = 3.19200000000000000

Cut off all the zeroes and I moved the decimal 17 places to the left, so the exponent will be positive:

\(3.192*10^1^7\)

Answer:

y= - 1/6x + 2

Step-by-step explanation:

I know you need it quick

In order to generalize about a population using data from a sample, researchers should employ appropriate sampling techniques to ensure representative and unbiased results.

By using random sampling methods and ensuring an adequate sample size, researchers can increase the likelihood of accurate population generalization.

When researchers want to make inferences about a population based on data collected from a sample, it is crucial to use proper sampling techniques. Random sampling is widely considered the best approach to achieve representativeness. By randomly selecting individuals from the population, researchers can minimize bias and increase the likelihood of obtaining a sample that accurately reflects the population's characteristics.

Additionally, the sample size plays a crucial role in generalization. A larger sample size generally provides more reliable estimates of population parameters. With a larger sample, there is a higher chance of capturing the diversity and variability present in the population, reducing the margin of error in the generalizations made.

Furthermore, researchers should consider the sampling frame—the list or source from which the sample is drawn. The sampling frame should be comprehensive and include all members of the population of interest. If the sampling frame is incomplete or biased, it can lead to inaccurate generalizations.

In summary, to generalize about a population using data from a sample, researchers should employ random sampling techniques, ensure an adequate sample size, and use a comprehensive and unbiased sampling frame. These practices increase the likelihood of obtaining representative and reliable results, enabling accurate generalizations about the larger population.

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Answer:

Step-by-step explanation:

Write down the factors for the numerator and the denominator.

Determine the largest factor that is common between the two.

Divide the numerator and denominator by the greatest common factor.

Write down the reduced fraction.

value of n=72

Answer:

∆ABC~DEF

since the side of similar triangle are proportional

\( \frac{AB}{DE} = \frac{BC}{EF} \)

\( \frac{54}{9} = \frac{n}{12} \)

6×12=n

n=72

Given:

The volume of a cube-shaped box is \(\dfrac{1}{8}\) cubic meter.

To find:

The perimeter of each of its faces.

Solution:

Let "a" be the side length of the cube shaped box. Then the volume of the box is:

\(V=(side)^3\)

\(V=a^3\)

It is given that the volume of a cube-shaped box is \(\dfrac{1}{8}\)  cubic meter.

\(a^3=\dfrac{1}{8}\)

Taking cube root on both sides, we get

\(a=\dfrac{1}{2}\)

Now, the perimeter of each face of a cube is:

\(P=4a\)

Where, a is the side length of the cube.

Putting \(a=\dfrac{1}{2}\), we get

\(P=4\times \dfrac{1}{2}\)

\(P=2\)

Therefore, the perimeter of each face of a cube-shaped box is 2 meters.

Answer: It's 2 meters

Answer:

y = -1/2x - 3

Step-by-step explanation:

slope: (y2-y1) / (x2-x1)

(-5 - -2) / (4 - -2)

(-5 + 2) / (4 + 2)

-3 / 6

- 1 / 2

y-intercept: y = mx + b

-5 = -1/2(4) + b

-5 = -2 + b

-3 = b

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The slope is given as,

Slope = (d - b) / (c - a)

Where (a, b) and (c, d) are the two points on the line.

The equation of the line is y = -(1/2)x - 3

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y = mx + c

The line passes through (-2, -2) and (4, -5).

The slope is given as,

Slope = (d - b) / (c - a)

Where (a, b) and (c, d) are the two points on the line.

This means,

Slope = (-5 + 2) / (4 + 2) = -3 / 6 = -1/2

Now,

(-2, -2) = (x, y)

-2 = (-1/2)(-2) + c

-2 = 1 + c

c = -2 - 1

c = -3

Now,

m = -1/2

c = -3

y = (-1/2)x - 3

Thus,

The equation of the line is y = -(1/2)x - 3

Option B is the correct answer.

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Answer:72

Step-by-step explanation:

The probability that, out of a random sample of 10 internet users, 6 are concerned about the privacy of their e-mail can be calculated using the binomial probability formula.

The binomial probability formula allows us to calculate the probability of a specific number of successes (concerned internet users) in a given number of trials (random sample of 10 internet users), given the probability of success in a single trial (95% or 0.95 in this case).

Using the binomial probability formula, we can calculate the probability as follows:

\(P(X = 6) = C(n, x) * p^x * (1 - p)^(n - x)\)

P(X = 6) is the probability of exactly 6 internet users being concerned about privacy,

n is the total number of trials (10 in this case),

x is the number of successful trials (6 in this case),

p is the probability of success in a single trial (0.95 in this case), and

C(n, x) is the number of combinations of n items taken x at a time.

Plugging in the values, we have:

\(P(X = 6) = C(10, 6) * 0.95^6 * (1 - 0.95)^(10 - 6)\)

Calculating this expression will give us the probability that exactly 6 out of the 10 internet users in the random sample are concerned about the privacy of their e-mail.

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Answer:

below

Step-by-step explanation:

Let's evaluate the given expressions for the values of the variables.

3m² + 4

m = 8, so:

     \(3*8^2+4\)

     \(3*64+4\)

     \(192+4\)

     \(\boxed{\sf{196}}\)

b- 8

b = 5, so:

   \(5-8\)

   \(\boxed{\sf -3}\)

Answer:

50x - 99 x =79 + 31 is your answer

Step-by-step explanation: