the difference between the highest and lowest observation is known as​

The partial sum S_n of the arithmetic sequence are

a)S_26=910,

b) S_1780=3596 and

c) S_15=168.75.

1. The formula for the partial sum of an arithmetic sequence is:

S_n = (n/2)(2a + (n-1)d)

where a is the first term, d is the common difference, and n is the number of terms given.

Substituting the given values of a, d and n into the formula:

S_26 = (26/2)(2(-2) + (26-1)(25))

S_26 = 13(48 + 625)S_26 = 910

2. The formula for the nth term of an arithmetic sequence is:

a_n = a + (n-1)d

where a is the first term, d is the common difference, and n is the number of terms given.

Substituting the given values of a and d into the formula, and solving for n:

3596 = 5 + (n-1)(2)

3596 - 5 = 2(n-1)

3591 = 2n - 2

3590 = 2n

1780 = n

So, 1780 terms must be added to get a value of 3596.

3. To find the common difference, we use the formula for the nth term:

a_n = a + (n-1)d

Substituting the given values of a and n into the formula, and solving for d:

d = (a_n - a)/(n-1)d = (10.5 - 9)/(5-2)d = 0.5

To find the partial sum, we use the formula:S_n = (n/2)(2a + (n-1)d)

Substituting the given values of a, d, and n into the formula:

S_15 = (15/2)(2(9) + (15-1)(0.5))

S_15 = 7.5(18 + 7(0.5))

S_15 = 7.5(22.5)

S_15 = 168.75

Learn more about Arithmetic Sequence at

https://brainly.com/question/3512500

#SPJ11

Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

BE = x+23

EC = x+41

Therefore:

\(\frac{x+23}{x+41} = 0.5\)

Now we can solve by multiplying both sides by x+41 to eliminate the fraction:

\(x+23=0.5(x+41)\)

Now we multiply out the brackets and move the terms to different sides:

\(x+23=0.5x+20.5\)

\(0.5x = -2.5\)

\(x = -5\)

And if we substitute the -5 into the equations:

-5+23 = 18

-5 + 41 = 36

We will see that -5 does indeed give us the same ratio between the lengths:

18/36 = 0.5

Hope this helped!

Answer is 6|x+2|+2

Please check the attached image of answer to clear the doubt.

By Benjemin ☺️

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

Learn more about confidence interval here

brainly.com/question/24131141

#SPJ4

Answer:

x + y = 29

5x + 2y = 100

Step-by-step explanation:

y = 15

x = 14

Answer:

The answer is A

Answer:

I think it is C maybe I'm wrong correct me in the comments. SRY

Step-by-step explanation:

Force is simply the pull or push of an object.

The information needed by the student is the direction and the source of the force

First, we look at what balanced and unbalanced forces mean

Unbalanced forces simply mean that different magnitudes of forces act on an object.

Take for instance,

Assume forces of 2 newtons and 3 newtons act in different directions, on a ball.

Such forces are unbalanced forces

Balanced forces mean that the same magnitude of forces act on the object in opposite directions.

Take for instance,

Assume forces of 2 newtons and 2 newtons act in opposite directions, on a ball.

Such forces are balanced forces, because they are equal, and they act in opposite direction.

Having explained what both forces are:

The student must determine where the force is coming from.

The text "where the force is coming from" means that, the student must determine the direction of the force (i.e. right, left, up, down or whatever direction) and the source of the force

Hence, option (b) is correct.

See attachment for illustrations of both forces

Read more about balanced and unbalanced forces at:

https://brainly.com/question/11914965

The  T-test, product-moment correlation, Chi-square are available for analyzing the results of an experiment with just one independent variable

Depending on the type of data and research issue being investigated, statistical tests such as the t-test, product-moment correlation, and chi-square can be used to examine the outcomes of an experiment with only one independent variable.  A frequent statistical test for comparing the means of two groups is the t-test. It may be used to compare the means of two groups, such as a control group and an experimental group, in an experiment with one independent variable.

A statistical method for determining the degree and direction of a linear relationship among two continuous variables is product-moment correlation, sometimes referred to as Pearson correlation. When looking at the relationship between two continuous variables, it may be utilized to analyse outcomes of an experiment using a single independent variable. A statistical technique which is chi-square test examines if there is a meaningful correlation between two category variables. When analysing connection among two categorical variables, it may be used to evaluate outcomes of an experiment using a single independent variable.

Read more about independent variable on:

https://brainly.com/question/82796

#SPJ4

Answer:

1-a) 78+x+16+x+24=180°

118+2x=180

2x=62

so x=31

Step-by-step explanation:

thats a

Answer:

1a) x = 31

1b) x = 12

2) angle A = 60 degrees

3) x = 40 degrees

Step-by-step explanation:

Answer:

Square and Rhombus

Sorry for being late

The equation that describes the hanger is y = x + 1.b-This line will represent the equation y = x + 1.c. The equation for the first hanger is y = x + 1.

Equation is a mathematical statement that expresses the equality of two expressions by using symbols. It typically consists of an equals sign (=) and two expressions that are related by the equals sign. Equations are used to describe the relationship between different variables, such as the area of a circle or the speed of a moving object. Equations are also used to solve problems, to make predictions, or to reveal patterns or trends.

a. The equation that describes the hanger is y = x + 1. This equation states that the y-coordinate (height of the hanger) is always 1 unit greater than the x-coordinate (width of the hanger).

b. To find x, I will draw more hangers to represent each step of the process. For the first hanger, I will draw a line with a y-intercept of 1 and a slope of 1. This line will represent the equation y = x + 1.

For the second hanger, I will draw a line with a y-intercept of 1 and a slope of 2. This line will represent the equation y = 2x + 1.

For the third hanger, I will draw a line with a y-intercept of 1 and a slope of 3. This line will represent the equation y = 3x + 1.

The reason I chose to draw each hanger with a y-intercept of 1 is to represent the constant value of 1 in each equation. The slope of each hanger is increased by 1 from the previous hanger to represent the coefficient of x in each equation.

c. The equation for the first hanger is y = x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 1.

The equation for the second hanger is y = 2x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 2.

The equation for the third hanger is y = 3x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 3.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1

The equation of the exponential function is 2ˣ with the given properties.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

An exponential function of base e has the form f(x) = \(ae^{(bx)}\), where a and b are constants.

The horizontal asymptote of this function is at y=1, which means that a=1.

The y-intercept is the point where the graph crosses the y-axis, which is at x=0. The value of f(0) is the y-intercept of the graph, and since it is less than 2, we have \(f(0) = 1\times e^{(b\times0)}\) = 1 < 2.

The graph also contains the point (-1, 2), which means that f(-1) = 2. Substituting the values we have found for a and f(0) into the equation for f(x), we get \(f(-1) = 1\times e^{(b\times(-1))}\) = 2.

Solving this equation for b, we find that b = ln(2).

Substituting this value for b into the equation for f(x), we get f(x) = \(e^{(ln(2)x)} = 2^x\).

This is the equation of the exponential function with the given properties.

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ1

Answer:

d is vertical so its 70 b c and a combined is also vertical to e so we have 110

Step-by-step explanation:

Answer:

  2mn

Step-by-step explanation:

The expanded form of the square can be found using the distributive property.

__

  (m -n)² = (m -n)(m -n) = m(m -n) -n(m -n) . . . use the distributive property

  = m² -mn -nm +n² . . . . use it again

  = m² -2mn +n² . . . . . . combine like terms

The missing term is 2mn.

The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

To learn more about hours click here brainly.com/question/29121756

#SPJ11

Answer:

A. SAS

Step-by-step explanation:

- SAS is side, angle, side.

- when both triangle are compared, both triangles are similar in their: (the point face upward)

• left-side (one line)

• upper angle

• base / down-side (two lines)

Answer:

122

Step-by-step explanation:

calculations attached

Answer:

B. 5

Step-by-step explanation:

Step 1: Rewrite the equation a bit

\(\frac{7^\frac{3}{4}}{7^\frac{x}{8}}=\sqrt[8]{7}\\7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\)

Step 2: Place a logarithm base 7 on both sides

\(7^\frac{3}{4}^-^\frac{x}{8}=7^\frac{1}{8}\\log_77^\frac{3}{4}^-^\frac{x}{8}=log_77^\frac{1}{8}\\(\frac{3}{4}-\frac{x}{8})log_77=\frac{1}{8}log_77\\(\frac{3}{4}-\frac{x}{8})1=\frac{1}{8}1\\\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\)

Step 3: Solve for x

\(\frac{3}{4}-\frac{x}{8}=\frac{1}{8}\\\frac{6}{8}-\frac{x}{8}=\frac{1}{8}\\-\frac{x}{8}=-\frac{5}{8}\\\frac{x}{8}=\frac{5}{8}\\x=5\)

Neat exponent question :)

Given:

In circle O, m∠R = 30.8°.

To find:

The m∠NOQ

Solution:

Central angle theorem: According to this theorem, the central angle is always twice of subtended angle on the same arc.

Angle NOQ and angle NRQ are on the same arc but ∠NOQ is the central angle and ∠NRQ is the subtended angle on the arc NQ.

Using central angle theorem, we get

\(m\angle NOQ=2\times m\angle NRQ\)

\(m\angle NOQ=2\times m\angle R\)

\(m\angle NOQ=2\times 30.8^\circ\)

\(m\angle NOQ=61.6^\circ\)

Therefore, \(m\angle NOQ=61.6^\circ\).

Answer:

40

80

160

Step-by-step explanation:

The function f(x) = xlnx is decreasing on the open interval (0, e^-1).

To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.

Using the product rule of differentiation, we can find the first derivative of f(x) as

f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)

Now, we need to find the values of x where f'(x) < 0

1 + ln(x) < 0

ln(x) < -1

x < e^-1

Therefore, f(x) is decreasing on the interval (0, e^-1).

Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.

Learn more about product rule here

brainly.com/question/27072366

#SPJ4

Answer:

Y= -21

Step-by-step explanation:

Answer: b) 4lb

Step-by-step explanation:

Answer:Your answer is B

Step-by-step explanation:

64 oz is= to 4 lb

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

For more questions on: combinations

https://brainly.com/question/29595163

#SPJ8                  

Answer:

Rhombuses have…

The only way it could be a rhombus is if it is a square

Try to draw it out, if it is a square this is true

Answer:

Letter B

9.16

...........

.

Answer:

Sometimes, not always.

Step-by-step explanation:

The LCM is the lowest common number between 2 numbers, sometimes it can represent the product of the 2 numbers, but sometimes it doesn't.

2 Examples:

2: 2, 4, 6, 8, 10.

3: 3, 6, 9, 12, 15.

6 is the least common multiple of 2 and 3 and it does represent the product between both numbers.

17: 17, 34, 51, 68, 85.

34: 34, 68, 102, 136, 170.

34 is the least common multiple of 17 and 34 and it does not represent the product between both numbers, the product is represented as 578.

We can prove that sometimes the LCM is the product between 2 numbers, and sometimes not.

a) The height of the frisbee each second it is in the air are 5, 29, 45, 53, 53, 45, 29, 5, -27 and -67.

b) The frisbee is in the air for a total of 8 seconds.

To find the height of the frisbee each second it is in the air, we need to substitute different values of t into the equation \(h = -16t^2 + 40t + 5\) and calculate the corresponding height.

a) Let's substitute t = 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 into the equation:

When t = 0: \(h = -16(0)^2 + 40(0) + 5 = 5\)

When t = 1: \(h = -16(1)^2 + 40(1) + 5 = 29\)

When t = 2: \(h = -16(2)^2 + 40(2) + 5 = 45\)

When t = 3: \(h = -16(3)^2 + 40(3) + 5 = 53\)

When t = 4: \(h = -16(4)^2 + 40(4) + 5 = 53\)

When t = 5: h = \(-16(5)^2 + 40(5) + 5 = 45\)

When t = 6: h = \(-16(6)^2 + 40(6) + 5 = 29\)

When t = 7: h = \(-16(7)^2 + 40(7) + 5 = 5\)

When t = 8: h = \(-16(8)^2 + 40(8) + 5 = -27\)

When t = 9: h =\(-16(9)^2 + 40(9) + 5 = -67\)

b) The frisbee is in the air as long as its height is greater than 0. From the calculations above, we can see that the frisbee is in the air from t = 0 to t = 7, inclusive.

Note: The table you provided shows the height of the frisbee at each second it is in the air, but it seems to be cut off. However, based on the calculations above, the height values at each second should be as follows:

0 seconds: 5 feet

1 second: 29 feet

2 seconds: 45 feet

3 seconds: 53 feet

4 seconds: 53 feet

5 seconds: 45 feet

6 seconds: 29 feet

7 seconds: 5 feet

For more such questions on height

https://brainly.com/question/28990670

#SPJ8