What are the domain and range of the function f(x) = 2x^3/4 respectively?​

The confidence intervals for this problem, using the t-distribution, are given as follows:

a) 80% confidence level, n = 13: (106.24, 113.76).

b) 80% confidence level, n = 26: (107.42, 112.58).

c) 98% confidence level, n = 13: (102.56, 117.44).

d) These intervals could not be computed if the population had not been normally​ distributed, as the sample size is less than 30.

The t-distribution is used when the standard deviation for the population is not known, and 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 critical values, using a t-distribution calculator, for the two-tailed 95% intervals, are given as follows:

The mean and the standard deviation are given as follows:

[tex]\overline{x} = 110, s = 10[/tex]

For item a, with n = 13, the bounds of the interval are given as follows:

For item b, with n = 26, the bounds of the interval are given as follows:

For item c, with n = 13, the bounds of the interval are given as follows:

The Central Limit Theorem states that the intervals can be obtained for non-normal populations only if the sample size is equal or greater than 30.

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When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The quadratic equation in the factored form is written as

y = a ( x − ℎ )^2 + k

This equation shows the coordinates of the vertex which is v(h, k)

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" helps to determine if the curve opens upwards or downwards. when a is:

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We can find the linear equation by using the given graph, the equation is:

y = 4.8*x + 24

On the graph we can see the best fit line, remember that a linear equation is of the form:

y = m*x + b

Where m is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is at y = 24, then:

y = m*x + 24

Now, notice that when x = 5, the value of y is 48, replacing these values we get:

48 = m*5 + 24

48 -24 = m*5

24/5 = m

4.8*m

The linear equation is:

y = 4.8*x + 24

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The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)

To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.

Here,

We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor

Now,

-7 is a zero of f(k)

i.e. (x+7) is a linear factor of f(k)

now,

we will find out the linear factor of f(c)

so,

f(c)=4x^3+19x^2-58x+35

f(c)=4x^3-4x^2+23x^2-23x-35x+35

f(c)=(x-1)(4x^2+23x-35)

f(c)=(x-1)(4x^2+28x-5x-35)

f(c)=(x-1)(4x(x+7)-5(x+7))

f(c)=(x-1)(x+7)(4x-5)

Hence,

The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)

Thus,

the linear factor of given polynomial is (x-1)(x+7)(4x-5)

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The percentage discount of 40% from the regular price of shoes and  the $73.5 Gwen saves indicates that the regular price of each pair of shoe she buys is $61.25

A percentage is the expression of a proportion based on a scale of 100. A percentage can be described as a fraction that has 100 as the denominator.

The percentage discount = 40%

The amount Gwen saves = $73.50

The number of shoes she buys = 3

The discount on each shoe = $73.5 ÷ 3 = $24.5

Let x represent the regular price of each shoe, from the information in the question, we have;

40% of x = $24.5

40% × x = $24.5

The regular selling price is therefore the ratio of $24.5 and 40% as follows;

The regular selling price = $24.5 ÷ 40% = $61.25

Each pair of shoe regularly costs $61.25

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Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

An outlier, to put it simply, is a data point in a data graph or dataset you're dealing with that is abnormally high or abnormally low in comparison to the nearest data point and the rest of the nearby coexisting values.

The vocabulary term is explained as,

1.Outlier - Extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

2. Cluster - An identifiable cluster of values in a numerical variable's distribution that is close to one another and appears notably more frequently than values on either side of them.

3. Positive linear association - When the variable on the x-axis grows as the variable on the y-axis increases, a positive linear connection exists. An upward-sloping linear regression line demonstrates this.\

4. Negative linear association - A negative linear correlation exists when one variable rises while the other falls. An upwardly sloping straight regression line illustrates this.

5.No association - There is a "negative correlation" when one variable rises while the other one falls. The points in the scatterplot have no connection if there is no correlation between the variables.

6. Non-linear association - When two variables have a nonlinear relationship, the slope of the curve illustrating the relationship alters when the value of one of the variables varies. Any curve whose slope alters when one of the variables' values changes is said to be nonlinear.

Thus, extreme values that significantly deviate from the dataset's or graph's normal distribution are known as outliers.

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Answer:Equivalent expressions Calculator Get detailed solutions to your math problems with our Equivalent expressions step-by-step calculator. Practice your math skills and learn step by step.

Answer:

Answer:Equivalent expressions Calculator Get detailed solutions so your math problems with ur Equivalent expressions

Step-by-step explanation:

The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

What are fractions?

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.

A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.

In the given question, we have:

6 persons for 40 dresses;

So, here

The numerator is 6;

and,

The denominator is 40;

So, The fraction that will be formed is: [tex]\frac{6}{40}[/tex]

In order to simplify to the simplest form, we have to divide it by the common divisor of 6 and 40.

So,

The fraction formed in the lowest form is [tex]\frac{3}{20}[/tex]

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Answer:

[tex] \huge{ \boxed{y = - 52x - 49}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = -52

In order to find c we substitute the points (−1,3) into the equation and find c

We have

[tex]3 = ( - 52)( - 1) + c \\ 3 = 52 + c \\ c = 3- 52 \\ c = -49[/tex]

We have m and c now so we substitute it into the main equation

We have the final answer as

[tex] \bold{y = - 52x - 49}[/tex]

Hope this helps you

Using the initial amount of the radioactive substance, in 1 gram 913.28 hours remaining.

In the given question;

The half- life of the radioactive substance is

[tex]t_{1/2}[/tex]=14days

For changing this into hours we have to multiply 24 in 14 because in 1 day have 24 hours.

[tex]t_{1/2}[/tex]=14*24

[tex]t_{1/2}[/tex]=336 hours

Initial amount of the radioactive substance is:

N(0)=6.58g

Now here we use the radioactive substance formula

[tex]N(t)=N(0)(\frac{1}{2})^{t/t_{1/2}}[/tex]

Where; N(t)= the radioactive substance after t hours

N(0)= Initial amount of the radio active substances

[tex]t_{1/2}[/tex] = Half lie

t=time (in hours)

Now put the value in formula

N(t)=6.58[tex](\frac{1}{2})^{t/336}[/tex]

N(t)=6.58[tex](0.5)^{t/336}[/tex]

By the question we know

N(t)=1

1=6.58[tex](0.5)^{t/336}[/tex]

Divide by 6.58 on both side, we get

1/6.58=[tex](0.5)^{t/336}[/tex]

[tex](0.5)^{t/336}[/tex]=1/6.58

Now taking the log on both side:

log [[tex](0.5)^{t/336}[/tex]]=log [1/6.58]

t/336 log[0.5]=log[1/6.58]

The formula of log used here, is as follows: Log(m^b)=blog(m)

Multiply by 336 on both side,we get

t*log[0.5]=336 log[1/6.58]

t=(336 log[1/6.58])/ log[0.5]

t=913.28hours

Hence, In 1 gram 913.28 hours remaining.

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The value of expression a²-b is 12 and value of equation -a+√-4+b id 10+2i where a is -2 and b is 8.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

if a = -2 and b = 8

a²-b=(-2)²-8

=-4

-a+√-4+b=-(-2)+2i+8

=10+2i

The equation a²-b has a value of 12 and the expression -a+-4+b has a value of 10+2i, where a is -2 and b is 8.

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Based on the z-score value, Latisha earned a higher IQ score.

In order to determine the person who earned a higher IQ score, we would have to calculate the z-score for the two IQ tests that Felix and Latisha took.

Mathematically, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

For Felix, we have the following:

Z-score = (130 - 105)/10

Z-score = 25/10

Z-score = 2.5.

For Latisha, we have the following:

Z-score = (120 - 95)/5

Z-score = 25/5

Z-score = 5.0.

Therefore, Latisha had the higher score because she has a higher z-score than Felix.

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The value of  (tan20° + tan40°)/(1 - tan20°tan40°) is √3.

tan(A + B) = (tanA + tanB)/(1 - tanA.tanB).

Given, tan 20 degrees + tan 40 degrees/1-tan 20 degrees tan 40 degrees

which is,

= (tan20° + tan40°)/(1 - tan20°tan40°).

= tan(20 + 40)°.

= tan60°.

= √3.

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Answer:

1.875 years or 1.9 if rounded to nearest tenth

Step-by-step explanation:

8% simple interest of $800 is $64. you know that 1% will be $8 per year and that 2 years of 8% simple interest will be $128. If you subtract 8 from 128, it is $120. So it will take him 1.875 years or [tex]1\frac{7}{8}[/tex]

Answer:

  2 points: b, d

Step-by-step explanation:

Given the graph of a cubic function, you want to know the number of relative extreme points.

A point is a relative extreme if the points on either side of it are both less than or both greater than the extreme point. A relative extreme is a peak point or valley point on a graph, a point where the slope is zero, and changes sign from one side of the point to the other.

The relative extremes on the given graph are labeled 'b' and 'd'. There are two relative extremes.

__

Additional comment

Point 'b' is a relative minimum, where the slope changes from decreasing to increasing, and adjacent points are more positive. Point 'd' is a relative maximum, where the slope changes from increasing to decreasing, and adjacent points are more negative.

An "absolute extreme" is a relative extreme such that no points anywhere on the graph are more extreme.

The number of relative extremes a polynomial graph may have is 1 less than the degree of the polynomial. This can help you determine the degree from the number of extremes, or the number of extremes from the degree.

Answer:

$1742.12

Step-by-step explanation:

I'm assuming it would be compounded annually so,

A = 1300(1 + 0.05)^6

A = 1742.12

Answer:

Q1: 13 :)

Q2: 9 :)

Q3: 5 :)

Q4: 1 :)

Step-by-step explanation:

For functions, we must replace the x with the value given in the table and solve from there! :D

Question 1:

y = -2(-2) + 9

y = 4 + 9

y = 13

Question 2:

y = -2(0) + 9

y = 0 + 9

y = 9

Question 3:

y = -2(2) + 9

y = -4 + 9

y = 5

Question 4:

y = -2(4) + 9

y = -8 + 9

y = 1

Have an amazing day!!

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The simplified exponential expression (z^9z^(-3))^(-2) is given as follows:

1 over z raised to the twelfth power.

The expression for this problem is given as follows:

(z^9z^(-3))^(-2)

The parenthesis takes precedence, hence the first term to be simplified is:

z^9z^(-3)

We have the multiplication of two terms with the same base and different exponents, hence the base z is kept and the addition of the exponents 9 and -3 is of:

9 - 3 = 6.

Hence the simplified part is of:

z^6

Then the expression is:

(z^6)^(-2).

Now we have the power of power rule, in which the base z is kept and then the exponents 6 and -2 are multiplied, as follows:

6 x (-2) = -12.

Then the simplified expression is:

z^(-12).

A negative exponent means that the number can be written into the denominator with a positive exponent, hence:

1/(z^12) = 1 over z raised to the twelfth power.

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Answer:

80/44 = 1.81

The unit rate is $1.81

Answer:

Step-by-step explanation:

y= 1/4x+2

y=-2x-7

Graphs below

The effective tax rate for a taxable income of $75,400 is 24%.

The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate.

WE have Given that;

Marginal Tax Rate           Chart Tax Bracket

$0 –$10,275                                  10%

$10,276 –$41,175                           12%

$41,176 –$89,075                          22%

$89,076 –$170,050                      24%

$170,051 –$215,950                      32%

$215,951 –$539,900                     35%

> $539,901                                     37%

Hence, the effective tax rate for income of $95, 600 lies in the range of a marginal tax rate of; 24%.

thus, the effective tax rate;

= 72,026/ 95600

= 24 %

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Answer:

4,416.90

Step-by-step explanation:

12% tax bracket: $38,520 - 10,725 = 27795(0.12) = 3335.4

1027.50+3335.4 = 4416.90

Answer: option a

Step-by-step explanation:

The length of the line segment is 18 units. option B is the correct answer.

We know that

The distance(D) between two points (x₁ , y₁) and (x₂, y₂) is

D = √( y₂ - y₁)² + (x₂ - x₁)²

From the question, we have

Two endpoints of the line segment are (-10, 9) and (5, -1).

D = √( y₂ - y₁)² + (x₂ - x₁)²

D = √(-1 - 9)² + (5 - (-10))²

D = √100 + 225

D = √325

D = 18 units (approx.)

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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Answer: 18 units

Step-by-step explanation: I got it right on the quiz

The probability that the hat was blue or was from Manufacturer B is 0.8677.

The P[tex](red)^{c}[/tex] is 0.6985.

The P(manufacturer B and Red) is 0.1640.

The P(Manufacturer B or Red) is 0.8456.

Probability is used to determine the odds that a random event would happen. The odds that the random event happens range from 0 to 1.

The probability that the hat was blue or was from Manufacturer B = (number of blue hats / total number of hats) + (number of hats from manufacturer B / total number of hats)

The probability that the hat was blue or was from Manufacturer B = (44 / 136) + (74 / 136) = 118/136 = 0.8677

The P[tex](red)^{c}[/tex] = complement of red = hats that are not red = (number of black hats + number of blue hats) / total number of hats

The P[tex](red)^{c}[/tex] = (51 + 44) / 136

The P[tex](red)^{c}[/tex] = 95 / 136

The P[tex](red)^{c}[/tex] = 0.6985

The P(manufacturer B and Red) = (number of hats produced by manufacturer B / total number of hats) x (number of red hats / total number of hats)

(74 / 136) x (41 / 136) = 0.1640

The P(Manufacturer B or Red) =  (number of hats produced by manufacturer B / total number of hats) + (number of red hats / total number of hats)

(74 / 136) + (41 / 136) = 115 / 136 = 0.8456

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The third number so that the three numbers form a right triangle,

1)40

2)84

Therefore, we can form a right triangle with 9,41,40 and 13,85,84

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

1) By applying Pythagorean theorem,

a²+b²=c²

x²+9²=41²

x²=41²-9²

x²=1681-81

x²=1600

x=√1600

x=40

Therefore, the third number is 40

2) x²+13²=85²

x²=85²-13²

x²=7225-169

x²=7056

x=√7056

x=84

Therefore, the third number is 84

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The expected value of your third punch is 5660.

What is probability?

A linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100% expresses the likelihood that a specific event (or series of events) will occur.

Given that,

This is the third and last punch and also there is no removal of prizes after each punch. Hence, the expected value would be equal to the mean of all the possibilities available.

E(third punch) = Σ  x  p(x)

=  100× (5/50) + 250 × (10/50) + 500 × (10/50) + 1000 × (10/50) + 2500 ×(8/50) + 5000 × (4/50)     + 100000 × (2/50) + 25000 × (1/50)

=  5660

Let us find the median of the given possibilities,

5 100's, 10 250's, 10 500's, 10 1000's, 8 2500's, 4 5000's, 2 100000's, 1 25000

There is a total of 50 possibilities and hence the median will be the average of the 25th and 26th terms.

25th term = 500

26th term = 1000

Median = (500 + 1000) / 2 = 750

The next available possibility greater than 750 is 1000.

Probability of getting more than 1000 in third punch = P (x > 1000) = (No. of terms greater than 1000) / Total no. of possible outcomes                                                                                                         = 15 / 50 = 0.3

Probability of getting less than 1000 in third punch = P (x > 1000) = (No. of terms lesser than 1000) / Total no. of possible outcomes                                                                                                                

= 25 / 50 = 0.5

Hence, in the second chance of punch, 1000 or anything greater than 1000 is preferred because the probability of getting more than 1000 in the next chance is less than the probability of getting less than 1000.

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