Which graph represents the polar curve r = 3 – 2cos(θ)?

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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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 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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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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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:

12 pints

Step-by-step explanation:

[tex]\frac{1}{8}[/tex] = [tex]\frac{8}{96}[/tex]

8 ounces is equal to 1 pint.  8 x 12 = 96, so 1 x 12 is 12

Answer:

Step-by-step explanation:

The price of the car before tax was $18,560.3

Let the price of the car be x. Then,

x + 6% of x = $19,674

106x/100 = $19,674

x = $ 19,673*100/106

with BODMAS, we get

x= $18560.3

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Answer:

Step-by-step explanation:

y= 1/4x+2

y=-2x-7

Graphs below

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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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

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 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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The polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the polynomial is given with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.

Each zero, such as a, corresponds to a linear factor, such as (x a). The repeating of such components is corresponding to multiplicity. The following polynomial thus meets the requirements in our example:

= (x-(-3))³(x-0)¹

=(x³-3x²(-3)+3x(-3)²-(-3)²)(x)

=x³+9x²+27x-9x

=x³+9x²+16x

Thus, the polynomial function with -3 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1 will be x³+9x²+16x.

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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:

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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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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The previous population of the city is 62500

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 3x + 4y = 14, 5x − 4y = 4.

if the previous population is represented by x and the increment by y, then

y= x×28/100

y = 28x/100 equation 1

the new population = previous population+ increment

therefore x+y= 80,000

represent 28x/100 for y in equation 2

x+28x/100= 80000

making the LHS a single fraction

(100x+28x)/100= 80000

128x= 80000×100

divide both sides by 128

x= 8000000/128

x= 62500

therefore the previous population is 62500

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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: option a

Step-by-step explanation:

The slopes and the y-intercepts of two equations are different.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the information provided, we have the following equations:

2x + y = 3       ....equation 1.

−2y = 14 − 6x    ....equation 2.

In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:

2x + y - 2x = 3 - 2x

y = 3 - 2x

y = -2x + 3

Therefore, m = -2 and c = 3.

For the second equation, we would divide both sides by -2 as follows:

−2y/-2 = 14/-2 − 6x/-2

y = -7 + 3x

y = 3x - 7

Therefore, m = 3 and c = -7.

In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.

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Answer:

y = -2x + 3

y = 3x + -7

The slopes and the y-intercepts are different.

The system represents lines that Intersect at one point

Exactly one solution

Step-by-step explanation:

Edge2022

get me brainliest

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 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:

$1742.12

Step-by-step explanation:

I'm assuming it would be compounded annually so,

A = 1300(1 + 0.05)^6

A = 1742.12

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 most equitable way to share the coin between Mai and Jeff is ratio 5:3. Mai will have 5 coins and Jeff 3 coins

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b.

Mai dropped 5 loaves and Jeff 3 loaves. This means that the ratio of brad dropped by Mia and Jeff is 5:3.

The stranger dropped 8coins. the most equitable way to share the coin is to share it in ratio 5:8

Using this ratio, the total ratio is 8

therefore Mia will have 5/8×8=5coins

Jeff will have 3/8×8= 3coins

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