The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39. 48, 56, 95, 81 and 75. Find the

Range of the marks obtained

Mean marks obtained by the group

Answer:The answer is B

Step-by-step explanation:

The formal is A = a+b/2 time h

You just substitute the variables and get the answer

Answer:

256 text

Step-by-step explanation:

Let's call the number of text messages Sarah sends in a month as "x".
So, the total cost of the text messages is $0.25 * x.

The total cost of the phone service and text messages is $35 + $0.25 * x = $99.

So, $35 + $0.25 * x = $99.

Subtracting $35 from both sides, we have:$0.25 * x = $99 - $35 = $64

Dividing both sides by $0.25, we have:x = 256

So, Sarah sent 256 text messages in one month.

Answer:

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

Given that f(x) = 7x + 5 and g(x) = 6x - 8, we can substitute these values into (f - g) (x):

(f - g) (x) = (7x + 5) - (6x - 8)

(f - g) (x) = 7x + 5 - 6x + 8

(f - g) (x) = x + 13

So, the answer is (f - g) (x) = x + 13

To find how many more texts were sent this week than last week we use,

(f − g)(x) = x + 13.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

From the given information, The number of more texts sent this week than last week is the difference between the functions f(x) - g(x).

= (f - g)x.

= (7x + 5) - (6x - 8).

= 7x + 5 - 6x + 8.

= x + 13.

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The length of AC from the given triangle ABC is 10 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, in the right triangle ABC below, DE is parallel to AC, and DE is perpendicular to CB at E.

The length of AB is 26 units, the length of DE is 5 units, and the length of BE is 12 units.

Consider ΔABC and ΔBDE

∠BDE=∠BAC=90°

∠ABC=∠DBE (Reflexive property)

By AA similarity, ΔABC is similar to ΔBDE.

By midpoint line segment theorem,

AC=2DE

AC=2×5

AC=10 units

Therefore, the length of AC is 10 units.

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One solution exists for the following system of equations. In this question, correct answer is option (5) which states the solution is point

(3 , 2).

There are many various ways to define an equation. The definition of an equation in algebra is a mathematical statement that illustrates the equality of two mathematical expressions.

As we know that when the system of equations are given in graph form ,

then the solution to them is the number of points they intersect each other.

Now in the given question,

In the given graph it can be clearly seen that graphs of equations meet at one point. The point at which the graph meets is (3 , 2).

We can see that option (5) is correct.

So the given system of equations have one solution.

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The sample space for choosing one card is S={V, S, I, D, I, I, N, O}.

What is a sample space?

A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S". Events are a subset of the potential outcomes of an experiment. The results in a sample area could vary depending on the experiment.

Given that, a set of eight cards were labeled D, I, V, I, S, I, O, and N.

All the possible outcomes should be included in the sample space.

Here, the sample space will be { D, I, V, I,S, I, O, N}

Elements in the order will be

S={V, S, I, D, I, I, N, O}

Therefore, the sample space for the given set of cards is

S={V, S, I, D, I, I, N, O}.

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The estimated percentage of states with an average per capita income greater than 32.5 k  is:we need to use the ogive (cumulative frequency curve) to determine the percentage of states with an average per capita income greater than 32.5k.

Assuming that the ogive is a continuous curve, we can estimate the percentage by finding the value on the horizontal axis corresponding to the 50% mark on the vertical axis, and then subtracting it from 100%. From the graph, we can see that the 50% mark corresponds to a value of around 30 k, which is between the values for Oklahoma and Pennsylvania. To get a more accurate estimate, we can use linear interpolation between these two data points.

Let's assume that the values for Oklahoma and Pennsylvania are

(x₁,y₁) = (25k,40%) and (x₂,y₂) = (35k,60%)

respectively. Then the equation of the straight line connecting these two points is:

(y-y₁) =(y₂-y₁) / (x₂-x₁) * (x-x₁)

Substituting in the values gives:

y - 40 = (0.6 - 0.4)/(35 - 25) * (x - 25)

y - 40 = 0.02(x - 25)

y = 0.02x - 0.5

To find the value of x that corresponds to the 50% mark, we can set y = 50% and solve for x:

50 = 0.02x - 0.5

0.02x = 50.5

x = 2525

So the estimated value for x is 25.25k. Therefore, the estimated percentage of states with an average per capita income greater than 32.5k is:

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Copy code

100% - 40% - (10% * (32.5 - 25.25)/(30 - 25))

= 50.5%

Therefore, we estimate that about 50.5% of the states have an average per capita income greater than 32.5k.

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Answer: C= 24-4t

Step-by-step explanation: Since four were eaten each dat the blue is getting lower, use -4t to represent it. 24 is the total amount gotten by substitution.

According to the given question,  when m=5 and n=4, the value of the expression 10m + 4n²/4 is 66.

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operations may be add, subtraction, multiply, or divide. An expression's basic components are as follows: (Math Operator, Number/Variable, Expression)

Keep in mind that words can be variables, constants, or coefficients. Therefore, 1+1 is a straightforward example of an expression. This equation has two constant terms and one operation (addition). x³ is another illustration.

To evaluate the expression 10m + 4n²/4 when m=5 and n=4, we substitute these values into the expression and simplify:

10m + 4n²/4

= 10(5) + 4(4^2)/4

= 50 + 4(16)/4

= 50 + 16

= 66

Therefore, when m=5 and n=4, the value of the expression 10m + 4n^2/4 is 66.

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If the measure of ABC = 170°, the measure of QRS is equal to 10°.

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles ABC and QRS are supplementary angles:

m∠ABC + m∠QRS = 180°

Substituting the given parameters into the formula, we have the following;

170° + m∠QRS = 180°

m∠QRS = 180° - 170°

m∠QRS = 10°

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Answer: Ray HF is opposite of Ray FH

Step-by-step explanation:

Answer:104

Step-by-step explanation:

If 1/2 d=52,

d/2=52

Multiply both sides by 2.

Thus, d=52×2= 104.

Hope this helps! :)

B, 222 units, is the correct answer.

There are 4,608 different ways that the class can elect a president, vice president, and secretary.

To find the number of different ways that a class of 18 students can elect a president, vice president, and secretary, we will use the formula for permutations, which is given by -

nPk = n! / (n - k)!

where n is the total number of items and k is the number of items to be selected in a specific order.

In this case, we are given n = 18 students and k = 3 positions.

Thus, the number of different ways to elect a president, vice president, and secretary will be -

18P3 = 18! / (18 - 3)! = 18! / 15! = 18 x 17 x 16 = 4,608

Therefore, there are 4,608 different ways that the class can elect a president, vice president, and secretary.

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Answer:

In the expression -17 + (-b) + (-25), the coefficient is a number that multiplies a variable. In this case, the coefficients are -17, -1 (which multiplies the variable "b"), and -25.

Step-by-step explanation:

The Construction of angle equal to 65 degree is shown below with attached figure.

Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructs.

The steps to draw angle 65 and copy of Angle:

(i) Draw ∠AOB = 65° with the help of protractor.

(ii) Draw a ray O’X.

(iii) With O as center and any radius, draw an arc cutting OA and OB at C and D respectively.

(iv) With O’ as center and with the same radius, draw an arc, cutting O’X at P.

(v) With P as center and radius equal to CD, cut the arc through P at Q.

(vi) Join O’Q and produce it to Y. Then ∠YO’X is the required angle equal to ∠AOB.

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Answer:

CF = 7.2 cm

Step-by-step explanation:

given 2 chords intersecting inside a circle , then the product of the parts of one chord is equal to the product of the parts of the other chord, that is

BF ×FC = DF × EF

10x = 8 × 9 = 72 ( divide both sides by 10 )

x = CF = 7.2 cm

The equivalent to the ratio 1:2 is 2 : 4

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

Ratio = 1 : 2

To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)

Using the above as a guide, we have the following:

Ratio = 2 * 1 : 2 * 2

Evaluate

Ratio = 2 : 4

Hence, the ratio is 2 : 4

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Answer:

30.

Step-by-step explanation:

We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:

y = 42 - (drainage rate) * t

Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:

30 = 42 - (drainage rate) * 2

12 = (drainage rate) * 2

drainage rate = 6 gallons per minute

Substituting this value into the original equation, we get:

y = 42 - 6t

So, the equation that represents the number of gallons of water in the tub after 2 minutes is:

y = 42 - 6 * 2 = 42 - 12 = 30.

Answer:

The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.

Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):

m = (42 - 30) / 2 = 6 gallons per minute

The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:

b = 42 - (6 * 0) = 42

Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:

y = 6t + 42

So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

We have,

In an equilateral triangle,

- all three sides are of equal length

- the altitude drawn from any vertex bisects the opposite side into two equal segments, forming a right triangle.

Let's denote the side length of the equilateral triangle as "s."

When an altitude is drawn, it bisects the base into two equal segments, each measuring "s/2."

The altitude forms a right triangle with the base, where one leg is the altitude (15 m) and the other leg is half of the base (s/2).

So,

Using the Pythagorean theorem, the value of "s":

s² = (s/2)² + 15²

s² = s²/4 + 225

4s² = s² + 900

3s² = 900

s² = 300

s = √300 = 10√3

Now,

Perimeter = 3 * side length

Perimeter = 3 * 10√3

Perimeter = 30√3 meters

Thus,

The equilateral triangle perimeter is 30√3 meters and option C is the correct answer.

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The equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

What is the equation in one variable?

An equation in one variable is a mathematical expression that contains a single variable, typically represented by x. The goal of solving an equation in one variable is to determine the value of the variable that makes the equation true.

To solve the equation -6(x+1)+8x=2(x-3), we can simplify the left-hand and right-hand sides of the equation and then solve for x. Here are the steps:

Distribute the -6 and 2 to the terms inside the parentheses: -6x - 6 + 8x = 2x - 6

Combine like terms on each side of the equation: 2x - 6 = 2x - 6

Subtract 2x from both sides of the equation: -6 = -6

At this point, we have a true statement (-6 = -6), but there is no variable present. This means that the equation has infinitely many solutions, and every real number is a solution to the equation.

Hence, the equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

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The conclusion that can be drawn about the number of trials and the probability is A. The experimental probability is closer to the theoretical probability for group Y than X.

The theoretical probability for picking a heads or tails is 50 % as there are only two outcomes of heads and tails.

The experimental probability for heads is 53 % in Group Y and 47 % for tails. This is close enough to the 50 % theoretical probability.

For group X, the experimental probability for heads for Group x is :

= 33 / 50

= 66 %

This is too far from the theoretical probability.

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Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.

The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.

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Complete Question

sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?

Answer: D

Step-by-step explanation: I can't really see everything well but I think it is D

I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?

Answer:

arc PN = 164°

Step-by-step explanation:

given chords PM and PN are congruent.

• if 2 chords are congruent then the corresponding arcs are congruent

then

arc PN = arc PM = 164°

Answer: A geometric sequence is a sequence of numbers such that the ratio of any two consecutive terms is constant. Let's call the common ratio "r". We can use this property to find "r" and then calculate other terms in the sequence.

Given that t3 = 24 and t9 = 1536, we can use the formula for the nth term in a geometric sequence: tn = t1 * r^(n-1), where t1 is the first term in the sequence.

Since we know t3 and t9, we can find r by dividing t9 by t3:

r = t9/t3 = 1536/24 = 64

Now that we have found "r", we can use it to find t1 by dividing t3 by r^(3-1):

t1 = t3 / r^(3-1) = 24 / 64^(3-1) = 24 / 64 = 3/2

Now that we know t1 and r, we can find any term in the sequence by using the formula: tn = t1 * r^(n-1).

Therefore, there are two possible sequences with two different first terms:

Sequence 1: t1 = 3/2, r = 64

Sequence 2: t1 = -3/2, r = -64

These are the two possible geometric sequences that satisfy the conditions t3 = 24 and t9 = 1536.

Step-by-step explanation:

Answer:

x = 6, y = -3

Step-by-step explanation:

[tex]\frac{x}{y + 1} = -3\\\frac{y}{x-3} = -1[/tex]

x = -3(y+1) - Isolate for x or y (I chose x)

x = -3y -3

Plug in x into y

[tex]\frac{y}{x-3} = -1\\\frac{y}{(-3y -3) - 3} = -1\\\frac{y}{-3y -6} = -1\\y = -1(-3y - 6)\\y = 3y + 6\\-2y = 6\\y = -3[/tex]

Plug y back into equation

[tex]\frac{x}{y+ 1} = -3\\\frac{x}{(-3)+ 1} = -3\\\frac{x}{-2} = -3\\x = -3(-2)\\x = 6[/tex]

The rate of change for Modis building stairwell is 0.68 feet per step.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.

Now, rate = 15/22

= 0.68 feet per step

In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel

Here, rate 7/17

= 0.41 feet per step

Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.

Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.

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