Write an inequality that
represents the graph below.
50 51 52 53 54 55 56 57 58 59

Answer:

A stratified random sampling involves dividing the entire population into homogeneous groups called strata (plural for stratum). Random samples are then selected from each stratum. ... A random sample from each stratum is taken in a number proportional to the stratum's size when compared to the population.

Answer:

Sampling that is used to represent different groups depending on their different qualities.

Hope that helps. x

The volume of the cylinder will increase by a factor of 4 if the radius of the cylinder doubles.

Volume is the amount of space occupied by a three-dimensional object or region of space and expressed in cubic units.

To get the volume of a cylinder, multiply the area of the circular base with the height:

V = \(\pi r^{2} h\)

where

r is the radius of the base (circle) of the cylinder

h is the height of the cylinder

Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius

So if the radius of the cylinder doubles,

V = \(\pi (2r)^{2}h\)

V = \(\pi (4r^{2}) h\)

V = \(4\pi r^{2} h\)

Then, the volume will increase by a factor of 4.

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Answer:

there was a total of 954 people at the pool

Step-by-step explanation:

Answer: 246

Step-by-step explanation:

Answer:

The numbers that you gave are ordered weird on my screen, but it should be the second answer - 18.4 glue and 9.2 glitter

Step-by-step explanation:

Just multiply all the numbers by 4

4.6 x 4 = 18.4

4 + 4 + 4 + 4 = 16

16 + 0.6 + 0.6 + 0.6 + 0.6 = 18.4

2.3 x 4 = 9.2

2 + 2 + 2 + 2 = 8

8 + 0.3 + 0.3 + 0.3 + 0.3 = 9.2

The answer must be a whole number because for example how are you suppose to fit half a child on a bus that can hold 44 people when it already holds that amount.

It will always be a whole number because if there are several left over students they will be put in another bus with more empty seats.

B) The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The alpha value of the reliability coefficient, also known as Cronbach's alpha, measures the internal consistency of a questionnaire. It indicates how well the items on the questionnaire are related to each other and form a consistent measure of the concept being assessed. A high alpha value indicates that the items on the questionnaire are measuring the same underlying concept and that the questionnaire is reliable.

Correlation between the score on the questionnaire and another measure of the same concept (Option A) and consistency by which multiple subjects are able to complete the questionnaire without error (Option D) can also provide information about the reliability of a questionnaire.

The alpha value of the reliability coefficient is one way to establish the validity of a questionnaire.

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Answer:

x = 3

Step-by-step explanation:

you need to set them equal to each other since all sides of a square are the same.

5(4x-3) = 5x+30

distribute

20x - 15 = 5x + 30

combine like terms

15x = 45

divide

3

8t + 7 means 8 times a number plus 7.

The quotient (2x^4 - 3x³-5x²+ 3x + 8) of  divided by x-2 is (2x^3+x^2-3x-3)and remainder is 2.

Long division is a method for getting a number by dividing two numbers. The number which we get from dividing are known as factors.

How to divide number?

We have been given two expressions and we have to divide an expression by another.

here, we have,

Expression 1: (2x^4 - 3x³-5x²+ 3x + 8)

Expression 2: x-2

now,

We know that,

Dividend=Divisor*Quotient +remainder

(2x^4 - 3x³-5x²+ 3x + 8) =(x-2)*(2x^3+x^2-3x-3)+2

If we compare both the equations we can find that quotient is equal to (2x^3+x^2-3x-3) and remainder is equal to 2.

We can check our calculations by solving the right side of the equation.

If it comes equal to left side then our calculations are right.

Hence the quotient of (2x^4 - 3x³-5x²+ 3x + 8) divided by (x-2) is (2x^3+x^2-3x-3)  & remainder is 2.

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Answer:

D. y = 1/2x - 7

Step-by-step explanation:

y = 1/2x + b

-5 = 1/2(4) + b

-5 = 2 + b

-7 = b

Answer:

  50.8°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between side lengths and trig functions for a right triangle. Here, you are given the short side and the hypotenuse, and asked for the largest acute angle.

__

The short side is adjacent to the largest acute angle, so the relevant relation is ...

  Cos = Adjacent/Hypotenuse

  cos(β) = (2√6)/(2√15) = √0.4

The angle measure is found using the inverse cosine function:

  β = arccos(√0.4) ≈ 50.8°

The larger acute angle is about 50.8°.

The distance between Points A and B is 12 units. If we were to draw a number line with Point A at -5 and Point B at 7, we could count the number of units between them.

In order to determine the distance between points A and B on a number line, we need to know the values of each point and then calculate the absolute value of the difference between them.

Point A has a value of -5 and Point B has a value of 7. The absolute value of the difference between -5 and 7 is 12.

Therefore, the distance between Points A and B is 12 units. If we were to draw a number line with Point A at -5 and Point B at 7, we could count the number of units between them.

However, it is more efficient to simply subtract the values of the two points and take the absolute value of the result.

This gives us the distance between the two points, regardless of which one is greater or smaller. In this case, the distance between Points A and B on the number line is 12 units.

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Answer:

3 series I believe

Step-by-step explanation:

7-4=3 this is what I got I believe it's right

f(x) = x(x − 4)3, in this equation the critical numbers of f are x = 4 and x = 3, the intervals on which f is increasing or is decreasing ( 1, 4), (-∞ , 1) and (4,∞), the local maximum of f(x) occurs at x = 3,  Concave up on the entire real line, and the inflection point of f(x) is x = 4.

(a) To find the critical numbers of f, we need to find the values of x where the derivative of f is zero or undefined.

f(x) = x(x - 4)^3

f '(x) =3(x-4)^3 + x(x-4)^2

if we assume that  f '(x) = 0, we get:

3(x-4)^3 + x(x-4)^2 = 0

(x-4)^2(3(x-4) + x) = 0

x-4)^2(4x - 12) = 0

Thus the above equation gives us the critical number(s) of x = 4 and x = 3.

(b) To find the intervals where f is increasing or decreasing, we need to examine the sign of the derivative of f.

f'(x) = (x-4)^3 + 3x(x-4)^2

Whenx<1, f '(x) is negative.

When 1 < x < 4, f '(x) is positive.

When x > 4, f '(x) is negative.

Therefore, the interval on which f is increasing is ( 1, 4) and the interval on which f is decreasing is (-∞ , 1) and (4,∞).

(c) To find the local minimum and maximum values of f, we need to find the critical points.

From above the critical points of f(x) are x = 4, and x = 1.

we need to determine whether these critical points correspond to a local minimum or maximum. to find it we need to,

Taking the second derivative of f(x), we get:

f''(x) = 6(x-4) + 2x(x-4)

At x = 4 f''(4) = 6(4-4) + 2(4)(0) = 0

At x = 3

f''(3) = 6(3-4) + 2(3)(-1) = -6

At x = 4, the second derivative is zero, so the test fails and we cannot determine whether it is a local minimum or maximum.

At x = 3, the second derivative is negative, so f(x) has a local maximum at x = 3.

Therefore, the local maximum of f(x) occurs at x = 3.

(d) To the interval(s) on which f(x) = x (x - 4 )^3 is concave up or concave down, we need to find the second derivative and check the sign:

f(x) = x(x-4)^3

f '(x) = 4x(x-4)^2

f''(x) = 4(x-4)^2 + 8x(x-4)

Simplifying f''(x) by factorial 4(x-4), we get:

f''(x) = 4(x-4)(x+2)

Need to find where f''(x) changes sign, it occurs at x = 4 and x = -2. The values divide the real line into three intervals:

Interval 1: x < -2 ,Interval 2: -2 < x < 4 ,Interval 3: x > 4

by testing each interval by picking a test point and checking the sign of f''(x) at that point

at Interval 1: taking x = -3

f''(-3) = 4(-7)(-1) = 28

at  Interval 1 sign of f''(x) is positive. So f(x) is concave up

at Interval 2: taking x = 0

f''(0) = 4(16)(0+2) = 128

at  Interval 2 sign of f''(x) is positive. So f(x) is concave up

at the Interval 3: taking x = 5

f''(5) = 4(1)(5-4) = 4

at  Interval 2 sign of f''(x) is positive. So f(x) is concave up

Therefore, f(x) is concave up on the entire real line, since it is always concave up on each interval.

(e) To find the inflection points of the function f(x), we need to find where the concavity of the function changes. The concavity of the function changes when the second derivative of the function changes sign.

the second derivatives of f(x):

f(x) = x(x-4)^3

f '(x) = (x-4)^3 + 3x(x-4)^2

f''(x) = 6(x-4)^2 + 6x(x-4) + 3(x-4)^2

set f''(x) = 0 to find the values of x at which the concavity changes:

6(x-4)^2 + 6x(x-4) + 3(x-4)^2 = 0

9(x-4)^2 + 6x(x-4) = 0

3(x-4)(3x-8) = 0

x = 4 or x = 8/3

To determine the concavity of f(x) around these values of x we need to assign the values of x between the two inflection points into the second derivative and see if it is positive or negative.

when:

x < 8/3, f''(x) is positive, it indicates that f(x) is concave up.

x > 8/3, f''(x) is positive again, indicating that f(x) is concave up.

Therefore, x = 8/3 is not an inflection point.

when:

x < 4, f''(x) is negative, indicating that f(x) is concave down.

x > 4, f''(x) is positive, indicating that f(x) is concave up.

Therefore, the inflection point of f(x) is x = 4.

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Answer:

x=1 and y=4/5

Step-by-step explanation:

Given system of equations

3x+5y=7

5x+10y=13

Multiply first equation by 2

2(3x+5y)=2(7)

6x+10y=14

Eliminate y-variable to get "x"

 6x+10y=14

- 5x+10y=13

         x = 1

Substitute x=1 into either equation and find "y"

3x+5y=7

3(1)+5y=7

3+5y=7

5y=4

y=4/5

Therefore, x=1 and y=4/5

The number that was coded is 45.

First, note that if you raise any integer between 1 and 76 to the power 17, the result will be an integer with many digits.

However, since we are reducing the result modulo 77, we only need to consider remainders when dividing this large number by 77.

To compute the remainder when raising a number to a power modulo 77, you can use the repeated squaring algorithm. Here's how it works:

Start with the base number, which is the secret digit you want to code (let's call it x).

Compute \(x^2\) modulo 77.

Compute\((x^2)^2\) modulo 77.

Repeat step 3 a total of 15 times. At this point, you have computed x^16 modulo 77.

Multiply \(x^{16}\) by x modulo 77 to get \(x^{17}\) modulo 77.

Alternatively, you can use a built-in function in most programming languages to compute modular exponentiation.

For example, in Python, you can use the pow() function with three arguments: the base, the exponent, and the modulus. Here's how you can use it:

x = 25  

for i in range(1, 77):

   if pow(i, 17, 77) == x:

       print(i)

       break

This code will print the secret digit that corresponds to the remainder of 25 when raised to the power of 17 and reduced modulo 77, which is 45.

Therefore, the number you coded is 45.

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The radius and height of a cylindrical soda with a volume of 412cm³ that minimize the surface area is 4.03cm and 8.064 cm respectively.

a)To find the radius and height of a cylindrical soda can with a volume of 412 cm³ that minimize the surface area, follow these steps:

b)To compare your answer in part (a) to a real soda can, which has a volume of 412 cm³, a radius of 3.1 ​cm, and a height of 14.0 ​cm, to conclude that real soda cans do not seem to have an optimal design, follow these steps:

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Answer:

.17 per once for the smaller box and .15 for the bigger box

Step-by-step explanation:

El resultado de esta división es 0.010

Para solucionar la operación matemática debemos realizar los siguientes pasos:

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Answer:how long u got to answer the question

Step-by-step explanation:

The area of the preimage is 400units²

Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.

A scale factor shows the relationship between the old shape and new shape.

The scale factor is expressed as ;

scale factor = dimension of the new length / dimension of old length

scale factor = 3/2 = 1.5

old length = x

therefore 1.5 = 30/x

1.5x = 30

divide both sides by 1.5

x = 30/1.5 = 20units

therefore the area of the preimage = l²

= 20²

= 400units²

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An angle bisector is a line that is drawn between the angle, which divides the angle into two equal parts. For example, if we bisect an angle that is 70°, then it will be two angles of 35°

We can draw an angle bisector either by measuring the angle using a protractor or marking the half. But the commonly used method is by using a compass.

Step 1

Draw the angle with vertex a, b, and c

Step 2

Draw a circle with b as the Centre, that intersects with each side of the angle.

Step 3

Draw congruent circles or arcs, centered at each intersection point on the sides of the angle.

Step 4

Use a straight line to connect point b with the intersection of two overlapping circles or arcs.

The properties of angle bisectors are

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The value (4.5, 98) is the outlier in the table which shows the number of hours spent studying for a history final exam and the score on that exam.

An outlier is a data point or observation that significantly deviates from the general pattern or trend of the dataset. It is an observation that is abnormally far from other population or sample values. Outliers can occur in one-dimensional data, such as a single variable, or in multi-dimensional data with multiple variables.

The data is given as

                  hours studied, x        percentile ranking on the test  y

                         1.5                                             65

                         2                                               68

                         3.5                                             71

                         4.5                                             98

                         4.5                                             82

                         6                                             84

                         6.5                                             88

                         7                                             85

                         7                                             80

Based on the plot, we can see that the point (4.5, 98) is significantly distant from the other points. It is much higher in the y-coordinate (exam score) compared to the other values.

Therefore, the value (4.5, 98) is the outlier in the table.

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Answer:

We are given a length of 27 cm and a width of 16 cm and we can also see that our figure is a rectangle.  This means that we are able to use the area formula for the rectangle which is \(A=l*w\).

Therefore, we can just multiply 27 cm by 16 cm and we get \(A = 432\ cm^2\)

Hope this helps!  Let me know if you have any questions

We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.

Let's evaluate f(1) and f(7) to determine their signs:

f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4

f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332

From the calculations, we can see that f(1) = -4 and f(7) = 332.

Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.

According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.

Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.

Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

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The number of freshmen that are students is 738

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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Angle 1 and 2 are equal because of correspondence angle

so , (78-2x) = (89-3x)

x = 89 - 78

x = 11

hence angle 1 = ( 78 - 2*11) = 56

and angle 2 = ( 89-3*11) = 56

So, both of angle is 56

hope it help and your day will full of happiness