How would the function change if the base of the exponent were 1?.

The probability that it appears five times exactly is 0.3472, or 34.72%.

Binomial distribution of probabilities;

P(X = x)  = C(n,x).pˣ.(1 - p)ⁿ⁻ˣ

C(n,x) = n1/ x1(n - x)!

The variables are:

In this issue:

Three dices are made, hence n is equal to 3.

Since one of its six sides is a five, therefore, p = 1/6 = 0.1167.

P(X = 1) is the chance that the number five appears exactly once, so;

P(X = x)  = C(n,x).pˣ.(1 - p)ⁿ⁻ˣ

P(X = 1)  = C(3,1).0.1167¹.(0.8333)³

P(X = 1)  = 0.3472

Thus, the probability that it appears five times exactly is 0.3472, or 34.72%.

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The difference between an angle that measures 5π/3 radians and an angle that measures 5/3 radians is 204.51 degrees

An angle measure of 5π/3 radians is converted to degree using the proportion

angle in degrees, d / 180 = angle in radian /  π

d / 180 = 5π/3 / π

d = 180 * 5/3

d = 300

For 5/3 radians

d / 180 = 5/3 / π

d = 180 * 5/3π

d = 95.49

The difference

= 300 - 95.49

= 204.51 degrees

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A point estimate is a single approxmate value of some parameters.

A point estimate for difference in average means is the difference between the sample means .

Point estimator :

In statistics, point estimation uses sample data to compute a single value, called a point estimate, to identify a point in a given parameter space.

Estimator Properties:

Point Estimate of Difference in Average Sales:

Point Estimate of Population Mean The calculation is the sum of all samples divided by the number of values .

Suppose we want to compare the means of two different populations . Each population has a mean and a standard deviation. Take a random sample from Population1 and label the resulting sample statistic with Index1 . Draw a sample from population2 and label its sample statistic with index 2, without reference to the first sample.

It is denoted by " μ1-μ2 " .

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The ratio of the empty bags to the total bags is found as 7/11.

As the stated question-

Total bags = 55

Empty bags = 35

Brand new nags = 20

Ratio = Empty bags/ Total bags

Ratio = 35/55

Ratio = 7/11

Thus, the ratio of the empty bags to the total bags is found as 7/11.

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Answer:  The correct results are shown below by plugging in the values.

f(x)=[tex]3^{x}[/tex]

 X       Y  

  -2     1/9

  -1      1/3

   0       1

   1        3

   2       9

Step-by-step explanation:  Confirmed correct.

Please remember to vote this answer as Brainliest if I earned it!

The sample proportion of the random sample of 50 students is 64% or 0.64.

Given:

the college administrator was only able to survey a random sample of 50 students.

she finds that 32 of these students report having a full- or part-time job.

we are asked to determine the sample proportion = ?

Based on the given conditions, we formulate:

32÷50

simplify:

16/25

= 64% or 0.64

hence we get the required sample proportion.

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If the function be f(x) = 4x - 2 then the value of f(3) exists 10.

An expression, rule, or law that establishes a connection between an independent variable and a dependent variable.

In mathematics, a variable is referred to as the alphabetic symbol used to represent a number or numerical value. An unknown quantity is represented by a variable in algebraic equations.

In mathematics, a function is a relationship where the values of one or more independent variables determine the values of a single dependent variable. The term "function" denotes that the independent variable influences the dependent variable.

Let the function be f(x) = 4x - 2

substitute the value of x = 3, then

f(3) = 4 × 3 - 2

simplifying the above equation, we get

f(3) = 10

Therefore, the value of f(3) exists 10.

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Services are usually produced and consumed at the same time, so they follow empty marketing channels such as haircuts and doctor visits.

Hence, Services are usually produced and consumed at the same time, so they follow empty marketing channels such as haircuts and doctor visits.

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Answer:

van can carry 15 people

Bus can carry 30 people

Step-by-step explanation:

we can make a system of equation for these 2 schools

15v+16b=705

8v+6b=300

isolate a variable

8v+6b=300

-8v.       -8v

6b=300-8v

/6.  /6.   /6

b=50-8/6v

Now substitute

15v+16(50-8/6v)=705

15v+800-21 1/3v=705

-6 1/3v+800=705

         -800.  -800

-6 1/3v=-95

/19/3.    /-19/3

    v=-95*3/-19

v=-285/-19

v=15

Now fill in v to find b

8(15)+6b=300

120+6b=300

-120.      -1#0

6b=180

/6.  /6

b=30

Hopes this helps please mark brainliest

Answers to be filled are rectangle, [tex]2\pi[/tex] , equal, [tex]2\pi r^2[/tex].

Given,

In the question:

Suppose the bottom surface, or base, of a cylinder is divided into 16 congruent sectors. then the sectors are rearranged as shown.

Open this GeoGebra activity to divide the circle into even more sectors and rearrange the sectors for yourself.

To complete the statement to compare the areas of the two figures and find the area of the base of the cylinder.

Now, According to the question:

To complete the statements

A circle of radius 'r' and rearranged figure out of sectors of the same circle.

When the sectors of the circle are rearranged , they are close to forming a rectangle with a length of 2[tex]\pi[/tex]r units and a width of r units.

The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2[tex]\pi r^2[/tex] sq. units

Hence, Answers to be filled are rectangle, [tex]2\pi[/tex] , equal, [tex]2\pi r^2[/tex].

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When the sectors of the circle are rearranged, they are close to forming a

rectangle with a length of 2*pi*r units and a width of r units. The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2*pi*r square units.

Sydney will spend $19.48 on fruit.

Price of strawberries = $1.68 per pound

Price of raspberries = $2.98 per pound

Sydney wants to buy 8.4 pounds of strawberries and 1.8 pounds of raspberries.

Therefore,

Price of 8.4 pounds strawberries = 8.4*Price per pound

Price of 8.4 pounds strawberries = 8.4*1.68 = $14.112

Price of 1.8 pounds raspberries = 1.8*price per pound

Price of 1.8 pounds raspberries = 1.8*2.98 = $5.364

Total spent on fruit = Price of 8.4 pounds strawberries + Price of 1.8 pounds raspberries

Total spent on fruit = $14.112 + 5.364 = 19.48

Rounding off to nearest hundredth;

Total spent on fruit = $19.48

Therefore, Sydney will spend $19.48 on fruit.

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All the correct options that apply to the given dot plot are;

A dot plot is a simple plot that displays data values as dots above a number line.

5 students spent 2 hours on homework.

Dot plots show the distribution of the data.

A dot plot is defined as a simple plot that displays data values as dots above a number line. Dot plots show the frequency with which a specific item appears in a data set and also shows the distribution of the data.

From the given dot plot, we can interpret the following parameters;

Number of students that spent 1 hour on homework = 1 person

Number of students that spent 2 hours on homework = 5 persons

Number of students that spent 3 hours on homework = 6 persons

Number of students that spent 4 hours on homework = 4 persons

Number of students that spent 5 hours on homework = 1 person

Number of students that spent 6 hours on homework = 1 person

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Using the slope line formula,

The slope of line y = mx is 1.0315.

We have given that,

parabola equation is y = 5x - 3x²

line passing through origin is in the form of y = mx

==> mx = 5x - 3x²

==> 3x²+ mx - 5x = 0

==> 3x² + x(m -5) = 0

==> x(3x + (m -5)) = 0

==> x = 0 , x = (5 -m)/3

The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3

Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108

==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108

==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108

==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108

==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108

==> (5 -m)³/18 - (5 -m)³/27 = 125/108

==> (5 -m)³/54 = 125/108

==> (5 -m)³ = 125/2

==> (5 -m) = 3.9685

==> m = 5 - 3.9685

==> m = 1.0315

Hence slope of line = 1.0315

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To answer this question where An investigator wishes to determine whether alcohol consumption we need to know the sample sizes for each group and the standard deviation for each group.

The spread or dispersion of a set of data values is measured by standard deviation. It is calculated as the square root of variance, which is the average of the squared deviations from the mean. In other words, it is a measurement of how widely apart a group of numbers are from one another. A low standard deviation implies that the data are closely grouped around the mean, whereas a large standard deviation suggests that the data are more scattered or spread out. outliers or anomalies in a dataset and to estimate the degree of variation or uncertainty in a population. It is a helpful tool for comparing and measuring.

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The mean and standard deviation of the number of people with blood type a-positive in 100 randomly selected is μ=85, σ=3.5707

The standard deviation is a statistic that measures the amount of variation or dispersion of a group of values.

Standard deviation is usually abbreviated SD and is most commonly represented in mathematical texts and equations by the lower case Greek letter (sigma) for population standard deviation or the Latin letter s for sample standard deviation.

A low standard deviation indicates that the values are close to the mean of the set (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a broader range.

Given, The population proportion of success is p=0.85

And also given that the sample size is n=100

b) The population mean is:

μ=np

μ=100(0.85)

μ=85

Therefore, mean=85

And the population standard deviation is:

σ=√np(1-p)

σ=√100(0.85)(1-0.85)

σ=3.5707

Therefore, standard deviation=3.5707

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The complete question is:

" Rh - positive blood appears in 85% of the population in the USA. a) Verify that it's possible to use the normal approximation to binomial distribution if a sample size is 100 randomly selected people. b) Find the mean and standard deviation of the normal distribution."

The factor and levels in the scenario is,

Factor = dip flavor. Levels = strawberry, orange, and banana.

What is popsicles?

A frozen treat on a stick made of liquid is known as an ice pop. An ice pop is "quiescently" frozen, or frozen when at rest, and turns into a solid block of ice, unlike ice cream or sorbet, which are churned while freezing to prevent ice crystal formation. It is held by the stick, which serves as a handle.

There is only one factor (independent variable) involved in above case, i.e. dip flavor is only factor mentioned in given case.

We can see that dip flavor has three categories or levels, i.e. strawberry, orange, and banana

Therefore, we have

factor = dip flavor and levels = strawberry, orange, and banana.

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(50.56; 71.44) constructed a 95% confidence interval for the mean savings in dollars for bringing a television to the doctor instead of making an office visit because the population is roughly symmetric.

Using these data, we can use the following formulas to determine the mean and deviation:

the sample mean, represented by the X  at 61, is

Mean population for μ (variable of interest)

the sample standard deviation is s=65.89.

The sample size is n = 20

The formula provides the mean's confidence interval We must first determine the degrees of freedom, given by: in order to calculate the critical value tα.

Now that everything is in place, we can replace formula (1) as follows:

61 – 2.09*65.89/root of 20 = 61 – 10.44 = 50.56

61 + 2.09*65.89/root of 20 = 61 + 10.44 = 71.44

The 95% confidence interval in this instance would therefore be provided by (50.56;71.44)

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To prove that  h be a subgroup of g. and suppose h is the only subgroup of g of order(h) h is normal in g is that it is proven by homomorphism .

This is a small contribution, however in reaction to a remark above, you may additionally clear up this with out the use of any homomorphism properties. Assume the subgroup H has order n and select out g∈g. Then, for any [tex]h∈H: = (ghg^-1)^n ghg^-1.ghg^1/n time.\\= gh^n g^-1 = geg ^-1 = geg ^-1 = gg ^-1 = e[/tex]

Since H has order n. The above holds for all h∈H, so the subgroup gHg−1 has order n, so it's miles identical to H through assumption. Then each h∈H has a few h∈H such that ghg−1=h′, implying gh=h′g, so gH=H

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The exponential function of f with base b is defined by​ f(x) = bˣ, b>0

and b≠1. Using interval​ notation, the domain of this function is (−∞, ∞)

and the range is (0, ∞).

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.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

According to the given question, the required solution would be as:

The exponential function of f with base b is defined by​ f(x) = bˣ, b>0

and b≠1. Using interval​ notation, the domain of this function is (−∞, ∞)

and the range is (0, ∞).

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The expression -2x³ + 13x² + 3x + 50 is equivalent to 10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²

An algebraic expression is an expression which consists of variables, coefficients, constants, and mathematical operators such as addition, subtraction, multiplication and division. Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged in the expression, both the expressions give the same result.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

In the given expression;

10 - (2x³ + 11x² - 2x - 35) + (x + 5) + 6(4x²); this can be reduced or simplified to -2x³ + 13x² + 3x + 50

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It only produces favorable results. |3x - 6| = -5, etc., will not have solutions for x. |4x - 2| = -6 has a negative value of -6. Therefore, there is no answer to the equation |4x - 2| = -6.

Result of an equation with no solutions 4x-2 =-6 equations without answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.

There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If an equation has no solutions, you can tell.

[tex]5x+7 \s= 3x+4+2x\s5x+7[/tex]

=[tex]5x+4[/tex]

meld the phrases 3x and 2x together.

[tex]7 \s= 4[/tex]

Take 5 times off of each side.

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2. Critical numbers of a function h(t) = t^(3/4) - 3t^(1/4) are (1/16 , -1/16).

A number is critical if it makes the derivative of the expression equal 0.

Critical numbers are values of a function where the function's tangent lines are either horizontal or vertical.

Given function is,

h(t) = t^(3/4) - 3t(1/4)

We have to find critical points.

For this we will take derivative and set it with 0

Therefore

h'(t) = (3/4)t^(-1/4) - 3(1/4)t^(-3/4) = 0

3/4[t^(1/4)] = 3/4[t^(3/4)]

4t^(3/4) = t^(1/4)

4 = 1/√t

t = 1/16 and t= -1/16.

Therefore critical points are (1/16 , -1/16).

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The step-by-step method of mean deviation given below.

What is the mean deviation method?

When calculating the average departure from the mean value of a particular data set, statisticians employ a measure known as the mean deviation. Following the steps below will make it simple to determine the mean deviation of the data values.

In statistics, the term "deviation" refers to the discrepancy between the observed value of a data point and its expected value. As a result, mean deviation, also known as mean absolute deviation, is the typical departure of a data point from the mean, median, or mode of the data collection.

MAD = (∑ f1 |xi - x⁻|) / ∑ f1

fi is the frequency of repetition xi, xi of denotes the mid-value of the class interval.

Example,  Say your data set is: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4.

The Mean is: 9 + 2 + 5 + 4 + 12 + 7 + 8 + 11 + 9 + 3 + 7 + 4 + 12 + 5 + 4 + 10+ 9 + 6 + 9 + 4. Over 20. That equals 104 over 20 = 7.

Statistics refers to deviation as the difference between the observed value of a data point and the expected value. The average deviation of a data point from the mean, median, or mode of the data collection is known as the mean deviation, sometimes known as the mean absolute deviation. Mean deviation is indicated by the acronym MAD.

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The value of the greater integer is 9

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero

From the question, we were told that;

An integer is subtracted from 5 times the next consecutive odd integer, the difference is 38

Represent the integer with x

So, we have the following representation

x is subtracted from 5 times the (x + 2), the difference is 38

When represented as an equation, we have

5(x + 2) -x = 38

Open the brackets

5x + 10 - x = 38

Evaluating the like terms

4x = 28

Divide both sides of the equation by 4

x = 7

The next odd integer is x + 2

So, we have x + 2 = 7 + 2

Evaluating x + 2 = 9

Hence, the solution is 9

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The solution for the code is can be followed by breaking the loop twice.

Given,

After running which of the following code segments would the robot end up in the same place facing the same direction as after running the code segment below;

Below is the trace that robot takes ,

|   -  <---

          |

--->      |

This means it moves forward twice and rotate left and this repeat for 3 times.

Same steps can be followed by breaking the loop twice which is being done by,

REPEAT 2 TIMES

{

MOVE_FORWARD ( )

}

ROTATE_LEFT ( )

REPEAT 2 TIMES

{

MOVE_FORWARD ( )

}

ROTATE_LEFT ( )

REPEAT 2 TIMES

{

MOVE_FORWARD ( )

}

ROTATE_LEFT ( )

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a) The 90% confidence interval for the average salary of an entry-level computer engineer is of: (16.28, 83.72).

b) The sample contains the value 80, hence it does not give sufficient evidence that the average salary of all entry-level computer engineers is different from $80,000.

c) The 90% confidence interval for the standard deviation of entry level salaries is of: (6.67, 389.86).

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample in this problem is given as follows:

30, 50, 70.

Hence the values of the parameters are given as follows:

[tex]\overline{x} = 50, s = 20, n = 3[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 3 - 1 = 2 df, is t = 2.92.

Then the lower bound of the interval is of:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 50 - 2.92\frac{20}{\sqrt{3}} = 16.28[/tex]

The upper bound of the interval is of:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 50 + 2.92\frac{20}{\sqrt{3}} = 83.72[/tex]

The bounds of the confidence interval for the standard deviation are given as follows:

[tex]\frac{(n - 1)s^2}{\chi^2_\frac{\alpha}{2}} \leq \sigma \leq \frac{(n - 1)s^2}{\chi^2_{1 - \frac{\alpha}{2}}}[/tex]

The critical values of the chi-square distribution with a confidence level of 90% and 2 df are given as follows:

[tex]\chi^2 = 0.1026, \chi^2 = 5.9915[/tex]

Hence the lower bound of the interval is of:

2 x 20/5.9915 = 6.67.

The upper bound of the interval is of:

2 x 20/0.1026 = 389.86.

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Compared to the distance between Earth and Mars, the distance between Jupiter and Saturn is much larger. (Option B)

Planetary distance is the measure of distance between two planets which vary based on the placement of the planet in an orbit. An orbit is the path where planets revolve around the Sun in the solar system. The planets’ orbits form an elliptical shape. To measure the distance between two planets in the solar system an astronomical measure used is astronomical unit (AU). An Astronomical Unit (AU) is the average distance between Earth and the Sun and is used to measure distances within our solar system. The distance between Mars from Earth is equivalent to 0.52 AU while the distance between Jupiter and Saturn is 4.32 AU. Hence, compared to the distance between Earth and Mars, the distance between Jupiter and Saturn is much larger.

Note: The question is incomplete as it is missing options which are a) much smaller b) much larger c) about the same d) just slightly less.

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Sinθ = ±5/[tex]\sqrt{106}[/tex]

Given in the Question:

[tex]\cos 2\theta=\dfrac{28}{53}[/tex]

Trigonometric Identity for

Cos2θ = Cos²θ-Sin²θ -(i)

Sin²θ+ Cos²θ=1 -(ii)

Then  Sin²θ=1-Cos²θ

Replacing  Sin²θ with 1-Cos²θ in equation (i)

Then

Cos2θ= Cos²θ -(1-Cos²θ )

Cos2θ= Cos²θ - 1 + Cos²θ

Cos2θ= 2Cos²θ - 1

Putting values

28/53= 2Cos²θ-1

28/53+1=2Cos²θ

28+53/53=2Cos²θ

81/52=2Cos²θ

81/53 X 1/2 =Cos²θ

81/106 =Cos²θ

Then Cosθ=[tex]\sqrt{\frac{81}{106} }[/tex]

Where,

 81 = 9X9 =9²

106 =   53X2

Cosθ= ±9/[tex]\sqrt{106}[/tex]

From the identity (ii)

Sin²θ + Cos²θ=1

Putting value

Sin²θ+ 81/106=1

Sin²θ = 1- 81/106

Sin²θ = 106 - 81/53

Sin²θ = 25/106

Then Sinθ = [tex]\sqrt{\frac{25}{106}}[/tex]

Since 25 = 5X5 = 5²

Sinθ = ±5/[tex]\sqrt{106}[/tex]

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I think that this is a great phrase! I defiently agree that we should all be thankful for what we have and because atleast we have somthing rather than us having nothing.

Answer:Yes I agree you should be grateful.

Step-by-step explanation:You should be grateful and thankful for what you have. Never be ungrateful.

The transformations that would map the polygon ABCD onto polygon A'B'C'D' is

dilation followed by a translation

The original coordinate of the polygon, from the graph using a position as an instance

A (1. -1)

There was a dilation with a scale factor of 2, transformation rule for dilation is

(x, y) for a scale factor of r → (rx, ry)

followed by a translation three units down, the transformation rule for translation 3 units down is

(x, y) → (x, y - 3)

following similar procedure for the given problem we have

preimage                           image (dilation)               image (translation)

A (1, -1)   → (1 * 2, -1 * 2) →   A' (2, -2) → (2, -2 - 3) →   A'' (2, -5)

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