16. A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden. A. 15m B. 3m C. 12m D. Square root of 12m


17. What is the value of c so that x^2-11x+c is a perfect-square trinomial? A. 121, B. 121/4, C. -11/2, D. 121/2


18. PLEASE HELP ASAP! Solve the equation by completing the square. Round to the nearest tenth. X^2+8x=10 A. 1. 1, 9. 1 B. 1. 1,-9. 1 C. -1. 1,9. 1 D. -1. 1, -9. 1

Answer:

If I understood what you mean properly... 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

30/10x = 3x

Answer:

\(30\div10x\)

Step-by-step explanation:

Using x for the unknown number, "the quotient of thirty and ten times a number" is written as:

\(30\div10x\)

Answer. The correct option is (E). 9.5 and 14.5

Explanation for step 1This is because 95% of the mean weights from samples of size 100 cats from this population will fall between 9.5 and 14.5 pounds. The other answers are incorrect because they do not fall within the range of 95% of the mean weights from samples of size 100 cats from this population

About 95% of the mean weights from samples of size 100 cats from this population would fall between approximately 11.51 pounds and 12.49 pounds.

To determine the range within which 95% of the mean weights from samples of size 100 cats would fall, we can use the concept of the confidence interval.

Given:

Population mean weight (μ) = 12 pounds

Population standard deviation (σ) = 2.5 pounds

Sample size (n) = 100 cats

Since the population distribution is assumed to be approximately normal, the sampling distribution of sample means will also be approximately normal. To calculate the range, we can use the formula for the confidence interval:

Confidence Interval = sample mean ± (z * standard error)

The standard error can be calculated using the formula:

Standard Error = σ / √n

Using a 95% confidence level, the corresponding z-value is approximately 1.96 (obtained from standard normal distribution table).

Plugging in the values:

Standard Error = 2.5 / √100 = 0.25

Confidence Interval = 12 ± (1.96 * 0.25)

Calculating the values:

Lower limit = 12 - (1.96 * 0.25) ≈ 11.51 pounds

Upper limit = 12 + (1.96 * 0.25) ≈ 12.49 pounds

Know more about mean weights here:

https://brainly.com/question/16170417

#SPJ11

Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

The statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true if and only if u is orthogonal to the projection of (v-w) onto the subspace spanned by u.

Since proju(v) and proju(w) are the projections of v and w onto the subspace spanned by u, we can rewrite the statement as "if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u".

Let proj_u(v - w) be the projection of (v - w) onto the subspace spanned by u. We know that (v - w) can be decomposed as (v - w) = proj_u(v - w) + (v - w - proju(v - w)).

Note that (v - w - proju(v - w)) is orthogonal to the subspace spanned by u, since proju(v - w) is the closest vector in the subspace to (v - w). Therefore, (v - w) is orthogonal to u if and only if proju(v - w) = 0, which is equivalent to saying that the projection of (v - w) onto the subspace spanned by u is the zero vector.

Assuming that proju(v) = proju(w), we have:

proju(v - w) = proju(v) - proju(w) = proju(v) - proju(w) = 0

Therefore, (v - w) is orthogonal to u, which implies that the statement "if proju(v) = proju(w) then (v − w) ⊥ u" is true.

In conclusion, we have proven that if the projections of v and w onto the subspace spanned by u are equal, then (v - w) is orthogonal to u.

Learn more about orthogonal

brainly.com/question/2292926

#SPJ11

Answer:

the total distance covered by the train

Step-by-step explanation:

-the direction doesn't matter, a train can go 40 km/h in any direction

-the mass doesn't matter, a heavy or a light train can go 40 km/h

-the time doesn't matter, it can be travelling at 2 am or 9 pm, that doesn't influence the speed.

The formula for velocity in physics is V = S/T (velocity = space divided by time). So space here would be the distance covered, which is the missing component. V = 40km/h, the time will be determined by the distance covered. Ex: if the distance covered is 80 km, then the time will be 2 hours.

The equation of the parabola represented by the graph is y = 9x²

From the question, we have the following parameters that can be used in our computation:

Point = (2, 36)

See attachment for the graph

This means that

(x, y) = (2, 36)

The vertex of the parabola is represented as

(h, k) = (0, 0)

The equation of the parabola is represented as

y = a(x - h)² + k

When the vertices are substituted, we have

y = a(x - 0)² + 0

So, we have

y = ax²

Using the point, we have

a * 2² = 36

So, we have

a = 9

Hence, the equation of the parabola is y = 9x²

Read more about parabola at

https://brainly.com/question/1480401

#SPJ4

Answer: -94

Step-by-step explanation:

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

The probability of rolling a sum less than 0.6366 is therefore 3/36, or 1/12, which is approximately 0.0833.

The numerical value of the area of a circle is given by the formula A = πr^2, where r is the radius of the circle. The numerical value of the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

If the sum of the numbers rolled on the pair of standard dice is s, then the diameter of the circle is s. Therefore, the radius of the circle is s/2.

The inequality A < C can be rewritten as πr^2 < 2πr. Substituting r = s/2, we get:

(π/2) s^2 < πs

Dividing both sides by πs and simplifying, we get:

s < 2/π ≈ 0.6366

Therefore, the sum of the numbers rolled on the dice must be less than 0.6366 for the area of the circle to be less than the circumference of the circle.

To find the probability of this event, we need to find the probability that the sum of the numbers rolled on the dice is less than 0.6366.

There are 36 possible outcomes when rolling two standard dice, each with a value between 1 and 6. To find the probability of rolling a sum less than 0.6366, we need to count the number of outcomes that satisfy this condition.

The only possible sums less than 0.6366 are 2 and 3. There is only one way to roll a sum of 2 (rolling a 1 on both dice) and two ways to roll a sum of 3 (rolling a 1 and a 2, or a 2 and a 1). Therefore, there are three possible outcomes that satisfy the condition.

The probability of rolling a sum less than 0.6366 is therefore 3/36, or 1/12, which is approximately 0.0833.

Learn more about "Probability" : https://brainly.com/question/23417919

#SPJ11

Answer:

3.14

Step-by-step explanation:

area=pi times the square of radius

1^2 = 1 x 3.14=3.14

The solution to the inequality x/6 ≤ -0.5 is x ≤ -3. Since -3 is negative, the answer is negative.

To solve x/6 ≤ -0.5, multiply both sides by 6 to get rid of the denominator:6(x/6) ≤ -0.5 x6. Simplify: x ≤ -3

Therefore, the answer to the inequality x/6 ≤ -0.5 is x ≤ -3.  So the solution to the inequality is x ≤ -3, which means that x is less than or equal to -3.

Since -3 is negative, the answer is negative.

An inequality is a statement that compares two values using inequality symbols such as <, >, ≤, or ≥. For instance, x < 3, y > 5, and z ≤ 1/2 are all examples of inequalities.

For such more question on negative:

https://brainly.com/question/1685227

#SPJ11

Answer:

62,144

Step-by-step explanation:

60,000 x (1 + 2%)^2 : growth in 2 years

+ 750: in migrants

- 410: out migrants

- 620: died

Answer:

62,144

Step-by-step explanation:

\(60,000 \times (1 + 2\%)^{2} \)

➡️ \( = 62,424\)

In-migrants:

➡️ \(750 - 410 = 340\)

now:

\(62,424 + 340 - 620\)

➡️ \( = 62,144\)

So, the present of the municipality is 62,144

Answer:

7.3 hours per day.

Step-by-step explanation:

Just do 58.4 divided by 8 and you get 7.3.

*Hope this helps*

The coordinates of Q between points R and S are (0, 5)

From the question, we have the following parameters that can be used in our computation:

R(-2, 6) and S(4, 3)

We have the partition to be

m : n = 1 : 2

The coordinate is then calculated as

Q = 1/(m + n) * (m₂ + nx₁, my₂ + ny₁)

Substitute the known values in the above equation, so, we have the following representation

Q = 1/3 * (1 * 4 + 2 * -2, 1 * 3 + 2 * 6)

Evaluate

Q = (0, 5)

Hence, the coordinate of point Q is (0, 5)

Read more about line segment ratio at

brainly.com/question/17374569

#SPJ1

Question

Given the point R(-2, 6) and S(4, 3), the point Q on directed line segment RS that partitions RS into the ratio 1 to 2.

Write down the coordinates of Q​

Probability samples have the advantage of providing a more representative sample of the population over non-probability samples.

Each member of the population has a known and non-zero chance of being chosen for the sample in probability sampling. This means that every member of the population has an equal chance of being chosen, which aids in reducing selection bias.

As a result, probability samples are more likely to accurately reflect population characteristics and can provide more reliable and valid population inferences.

Non-probability samples, on the other hand, lack this property and may not accurately reflect the population. In a convenience sample, for example, people are chosen simply because they are easily accessible, which may not accurately reflect the population as a whole.

To learn more about probability.

https://brainly.com/question/29750701

#SPJ4

20

10÷1/2

≈10/1÷1/2

KFC

10/1×2/1

=20/1=20

Hope this helped- have a good day, cya)

Answer:

5x - 10 = 2(2x + 2)

5x - 10 = 4x + 4

x = 14

Middle Segment of a Triangle:

Triangles are geometric figures with three sides and three internal angles. We can find different types of lines inside a triangle; one of them is the middle segment. The middle segment of a triangle is a line parallel to one of the sides and bisecting the other two sides. Let L be the line of the middle segment and AC the side parallel to the line L, then the formula of the middle segment is:

L = AC/2

We are given a diagram:

Our objective is to find the missing length of RQ.

We can see that the RQ line divides the ST and UT lines in equal parts. Moreover, the SU and RQ lines are parallel; therefore, we can conclude that the RQ line is the middle segment of the STU triangle. So:

RQ = SQ/2

→2x+2 = (5x-10)/2

→2(2x+2) = 5x-10

→4x+4 = 5x-10

→ 5x-4x = 10+4

x = 14

and RQ = 30

and SU = 60

Answer:

what.....................

Answer:

muchas gracias por los puntos

que tengas un buen dia

Answer:

42$

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

Scale factor = 10/45 = 2/9

A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

Learn more about Probability:

https://brainly.com/question/26203207

#SPJ4

The probability of selecting red balls from a bag containing both red and blue balls is equal to the number of red balls divided by the total number of balls. In this example, let's assume there are 10 red balls and 10 blue balls, so the probability of selecting a red ball would be 10/20 or 1/2, or 50%.

To explain further, the probability is the likelihood of an event occurring and is expressed as a number between 0 and 1, or a percentage between 0% and 100%. A probability of 0 means the event will never happen, while a probability of 1 means it will always happen. The probability of selecting a red ball in this example is 50%, meaning that it is equally likely to select either a red ball or a blue ball.

In other words, if the bag contained 10 red balls and 10 blue balls and you randomly selected one ball from the bag, there is a 50% chance that the ball will be red and a 50% chance that the ball will be blue.

If the number of red balls or blue balls changes, the probability of selecting a red ball would also change. For example, if the bag contained 6 red balls and 10 blue balls, the probability of selecting a red ball would be 6/16 or 3/8, or 37.5%.

Know more about Probability here :

https://brainly.com/question/13604758

#SPJ11

No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.

Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.

To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.

However, both of these jugs are larger than 3 gallons.

This means that it is impossible to measure 3 gallons of water using these jugs.

To measure 4 gallons of water, we can follow these steps:

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 2 gallons of water in jug A.

Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.

Fill jug A to the top with water.

Pour the water from jug A into jug B until jug B is full.

This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.

Thus, we can measure 4 gallons of water using these jugs.

For such more questions on gallons

https://brainly.com/question/28274339

#SPJ8

The derivative of log x is 1/x because log x represents the inverse operation of taking the exponential of x, and the derivative of the exponential function is 1/x.

1. Take the natural log of both sides (ln):

ln(x) = log x

2. Take the derivative of both sides with respect to x:

d/dx ln(x) = d/dx log x

3. Use the chain rule and the derivative of the natural log function (1/x):

d/dx ln(x) = (1/x) * d/dx x

4. Simplify:

d/dx ln(x) = (1/x) * (1)

5. Final answer:

d/dx ln(x) = 1/x

The derivative of log x is 1/x because it is the inverse operation of taking the exponential of x, and the derivative of the exponential function is 1/x. The chain rule is used to take the derivative of both sides, which results in a final answer of 1/x.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

Answer:

\(\frac{6}{35}\)

Step-by-step explanation:

To find the ' middle ' add the 2 fractions and divide by 2 ( average )

\(\frac{1}{5}\) + \(\frac{1}{7}\) ( change denominators to 35 , the LCM of 5 and 7 )

= \(\frac{7}{35}\) + \(\frac{5}{35}\)

= \(\frac{12}{35}\)

midway = \(\frac{12}{35}\) ÷ 2 = \(\frac{6}{35}\)

The fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

Sometimes you need to find the point that is exactly midway between two other points. For instance, you might need to find a line that bisects (divides into two equal halves) a given line segment. This middle point is called the "midpoint".

According to the question

The fraction is exactly midway between 1/5 and 1/7

Now ,

To find midway between 1/5 and 1/7

Step1 : Add fraction 1/5 and 1/7

= \(\frac{1}{5} +\frac{1}{7}\)

= \(\frac{12}{35}\)

Step2 : Divide the sum by 2 or multiply by 1/2

= \(\frac{12}{35}\) * \(\frac{1}{2}\)

= \(\frac{6}{35}\)

Hence, the fraction is exactly midway between 1/5 and 1/7  is  \(\frac{6}{35}\) .

To know more about midway here:

https://brainly.com/question/511147

#SPJ3

Answer:

0.67

Step-by-step explanation:

correct

Answer:

y=-8x-2

Step-by-step explanation:

Answer:

100,000

Step-by-step explanation:

The 9 is in the hundredth thousand place

The slope of the line that passes through the points (-9, 0) and (−17,4) is -2

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

The formula to calculate slope is -

m = x2 - x1 / y2 - y1

(-9, 0) and (−17,4)

m = -17 + 9 / 4 - 0

m = -8/4

m = -2

To learn more about the slope of the equation from give link

https://brainly.com/question/3493733

#SPJ9