the equation of a circle given the center (–4, 4) and raduis r = 5.

The closest point is (3.5, 1.9) and the distance is 1.96 units

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

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P( A Student participates in Both sports and Drama) =0.07

The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that a student participates in both sports and drama:

Let

A =Student  participate in Sport

B = Student  participate in Drama

Thus we have:

P(A) = 0.42

P(B) = 0.25

and

P(Ac and B or A and Bc) =0.53

P(Ac and B ) + P( A and Bc) =0.53

P(B) - P(A and B) + P(A) - P(A and B) = 0.53

0.25 - P(A and B )  +  0.42 - P(A and B) = 0.53

0.25+0.42 - 2 * P( A and B) = 0.53

0.67 - 2 * P(A and B) = 0.53

0.67 - 0.53  = 2* P(A and B)

0.14  =  2 * P(A and B)

0.14 / 2  = P( A and B)

0.07 = P( A and B)

that is:

P( A and B) = 0.07

P( A Student  participate in Both sports and Drama) =0.07.

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The probability that a student participates in both sports and drama is [tex]0.14[/tex].

If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].

We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].

By the above formula, we obtain:

[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]

Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].

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Answer:

B) 9:35

Step-by-step explanation:

the travel time we get by dividing the distance by the speed

distance / distance/time = time

so,

60 / 80 = 6/8 = 3/4 = 0.75 hours or 45 minutes.

since she arrived 20 minutes late, that means at 10:20 am, she left home 45 - 20 = 25 minutes before 10:00am.

and that is 9:35 am.

Utilizando la distribución binomial, la probabilidad de resolver un problema de n problemas propuestos, es p^n.

La fórmula es:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

La probabilidad de que todos los problemas sean resolvidos es dada por P(X = n), asi:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = n) = C_{n,n}.p^{n}.(1-p)^{n-n}[/tex]

P(X = n) = p^n

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The equation that can be used to find the cost of each binder n in dollars is 861=7n.

Given that the cost of 7 binders is $8.61.

We are required to form an equation that represents the total cost of each binder n in dollars.

Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.

Suppose the cost of 1 binder is n dollar.

We know that the total cost is basically the product of price of 1 unit and number of quantities of units.

Total cost=Price of 1 unit* number of units

8.61=n*7

8.61=7n

Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.

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Answer:

c,d

Step-by-step explanation:

The voltage of the circuit is 8 + i .  Option C

From the information given, we have that;

E = IZ

Where;

We have that;

I = 3 + 2i

Z = 2 - i

Substitute into the formula

E = IZ

E = ( 3 + 2i) ( 2 - i)

Making the product of complex numbers we have:

E = ( 3 × 2 - i ) + ( 4i - 2i²)

E = ( 6 - 3i ) + ( 4i - 2 ( -1) )

E = ( 6 + 2) + ( 4 - 3 ) i

E = 8 + i

Thus, the voltage of the circuit is 8 + i .  Option C

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Answer:

It's C

Step-by-step explanation:

Answer:

This questions seems to be incomplete but generally tan with x is expressed as

tan(x) =

The value of the expression 2n - 1 when n = 7 is 13.

2n - 1

when n = 7

2n - 1

= 2(7) - 1

= 14 - 1

= 13

Mathematical expression is an expression which involves the combination of numbers and variables in a valid way, in a function of addition, subtraction, multiplication, division and exponentiation

Therefore, the value of the expression 2n - 1 when n = 7 is 13.

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Answer:

What is this?

Can't understand anything!

Answer : what is this question?

First, I will subtract 53 from 697.

697 - 53 = 644

Next, I will divide the total by 2.

644 / 2 = 322.

This means the cost of the garden table is 322.

I will add 53 back to the total.

322 + 53 = 375.

The cost of the bench is $375.

Answer:

second option

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Since the two triangles ABE and ADE are congruent, their corresponding sides and angles are equal.

After observing all the options, we can conclude that :

Only angle AED and angle AEB are angles of given triangles and are actually equal.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The price at which equilibrium is achieved is $20.

The equilibrium point is the point where the lines of the demand and supply functions meet.

From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).

Also from the question, the lines intersect at point (15, 20).

The y-coordinate of the intersection point is 20 in this scenario.

Hence, the price at which equilibrium is achieved is $20.

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Answer:

b

Step-by-step explanation:

The value of x when the secants intersect is 4

A secant of a circle is a line that connects two distinct points on a curve.

The secant touches two sides of the circumference of a circle.

Therefore, using secant rule,

4(x + 2 + 4) = 5(x - 1 + 5)

Hence,

4(x + 6) = 5(x + 4)

Hence, open the brackets

4x + 24 = 5x + 20

Therefore, subtract 4x from both sides

4x - 4x + 24 = 5x - 4x + 20

24 = x + 20

subtract 20 from both sides

24 - 20 = x + 20 - 20

x = 4

Therefore, the value of x is 4.

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Answer: 30%

Step-by-step explanation:

the first 2 bars < or = to 650 add up to ~29% roughly, cant be 25%, 68%, or 99%. Therefore the only answer available is 30%

Answer:

30%

Step-by-step explanation:

For Connexus students its 30% :)

Answer:

8

Step-by-step explanation:

-32/-4 the minus takes out the second minus then we are left with 32/4which makes the answer a positive 8

[tex]{ \red{ \bold{cos \: y \: }}}[/tex]

Step-by-step explanation:

[tex]{ \green{ \tt{ \frac{1 \: + \: \cos \: y \: }{1 \: + \: \sec \: y \: }}}} \: → {eq}^{n} (1)[/tex]

But, as you know that

[tex]{ \blue{ \tt{sec \: y \:}}} = { \green{ \tt{\frac{1}{ \ \cos \: y }}}} [/tex]

Then the equation (1) becomes

[tex]{ \green{ \tt{ \frac{1 \: + \: cos \: y }{1 \: + \: \frac{1}{cos \: y} }}}} \: [/tex]

Multiply Numerator and Denominator by [tex] \frac{cos \: y}{cos \: y} [/tex]

then,

[tex]{ \green{ \tt{( \frac{cos \: y}{cos \: y})}}} \: { \green{ \tt{ \frac{1 \: + \: cos \: y}{1 \: + \: \frac{1}{cos \: y}}}}} [/tex]

[tex] = { \green{ \tt{ \frac{cos \: y \: + \: {cos}^{2} \: y }{cos \: y \: + \: 1 }}}}[/tex]

take cos y as common, then

[tex]{ \green{ \tt{cos \: y}}} \: { \green{ \tt( \frac{1 \: + \: cos \: y}{cos \: y \: + \: 1} )}}[/tex]

Here, (1+cos y/cos y + 1) gets cancelled.

Then the remaining answer is cos y.

Answer:

Step-by-step explanation:

deleted

Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

According to thermodynamics, heat is a type of energy that crosses a thermodynamic system's border due to a temperature differential across the barrier. In a thermodynamic system, heat is not present.

But the phrase is also frequently used when referring to the thermal energy that makes up a system's internal energy and is reflected in the system's temperature. Heat is a type of energy in both senses of the word. Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

Therefore, heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

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Answer:

[tex]t = \cfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]4(t+\cfrac{1}{4})=3[/tex]

Divide both sides by 4:

[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]

Subtract 1/4 from both sides:

[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]

[tex]t = \cfrac{2}{4}[/tex]

Simplify:

[tex]t = \cfrac{1}{2}[/tex]

Answer:

[tex]t = \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]4(t + \frac{1}{4} ) = 3[/tex]

Divid the whole equation by 4.

[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]

[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]

[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]

Take 1/4 to right side.

[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]

[tex]t= \frac{2}{4} [/tex]

To simplify the answer more divide the numerator and denominator by 2.

[tex]t = \frac{1}{2} [/tex]

The expression representing the given statement is 7×(6+3)-(4÷2). Option A is correct.

Given the statement is Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2.

Firstly, we will break the statement in two parts that is Multiply 7 by the sum of 6 and 3 and second part is subtract the quotient of 4 and 2.

Multiply 7 by the sum of 6 and 3 means there is addition sign between 6 and 3 and the addition of 6 and 3 is multiply with 7, we get

7×(6+3)    ......(1)

subtract the quotient of 4 and 2 means 4 is divisible by 2 and this is subtract means there is a minus sign, we get

-(4÷2)   .....(2)

Combine equation (1) and (2), we get

7×(6+3)-(4÷2)

Hence, the expression which represents the given statement Multiply 7 by the sum of 6 and 3, and then subtract the quotient of 4 and 2 is 7×(6+3)-(4÷2).

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An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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Steve's expected win from the lottery ticket purchase is $3 because his chance of winning the $300 prize is only 1%.

The expected winnings for Steve are a function of the probability of some predictable outcomes.

In this situation, the predictable outcome is the size of the lottery prize.

The probability that Steve will win the prize is 1% (1/100), depicting his chance of winning.

Sale price per ticket = $5

Lottery prize = $300

Value of lottery prize to Steve if he wins = $295 ($300 - $5)

Probability of winning = 1% (1/100 x 100)

Expected win = $3 ($300 x 1%)

Thus, Steve's expected win is $3, which outweighs the cost of a ticket.

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The equivalent expression of  2x√44x - 2√11x  is 2x√11x

An equivalent expression can be find when simplified or factorised.

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

The expression equivalent to 2x√44x - 2√11x is as follows:

2x√44x - 2√11x

factorise

2x√44x - 2√11x = 2(x√44x - √11x³)

Hence,

2(x√44x - √11x) = 2(x√4 × 11x  - √11x³)

2(x√4 × 11x  - √11x) =  2(2x√11x  - x√11x)

Therefore,

2(2x√11x  - x√11x) = 4x√11x - 2x√11x

4x√11x - 2x√11x = 2x√11x

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1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.

2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.

3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.

4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.

Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.

Affordability can be measured as a Debt To Income (DTI) ratio.

Current monthly income = $3,500

Monthly mortgage payment = $900

Monthly student loan payment = $350

Total monthly debt payment = $1,250

Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)

Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.

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The answer to the questions of volumes are given as follows

a) [tex]v=128 \pi[/tex]

b) [tex]v=\frac{128}{3} \pi[/tex]

 c)[tex]v=\frac{1024}{5} \pi[/tex]

d)[tex]V=\frac{13568}{15} \pi[/tex]

Generally, the questions are  mathematically solved below

[tex]y=\sqrt{x}, y=4, x=0[/tex]

a) x-axis

if $y=4, x=16, x=0$

Using disk method

[tex]} v=\pi \int_{0}^{16}(\sqrt{x})^{2} d x \\[/tex]

[tex]v=\pi\left(\frac{x^{2}}{2}\right)_{0}^{16} \\[/tex]

[tex]v=\frac{\pi}{2} \times 16 \times 16 \\[/tex]

[tex]v=128 \pi[/tex]

b)  line y=4

if x=0, y=0 ;

[tex]y=\sqrt{x} \Rightarrow x=y^{2}[/tex]

Using shell method

[tex]v = \int_{0}^{4} 2 \pi(4-y) \cdot y^{2} d y \\[/tex]

[tex]v=2 \pi \int_{0}^{4}\left(4 y^{2}-y^{3}\right) d y[/tex]

[tex]v=2 \pi\left[\frac{4 y^{3}}{3}-\frac{y^{4}}{4}\right]_{0}^{4} \\[/tex]

[tex]v=\frac{2 \pi}{12}[1024-768] \\[/tex]

[tex]v=\frac{512 \pi}{12} \\[/tex]

[tex]v=\frac{128}{3} \pi[/tex]

c) y-axis

0 ≤ y ≤ 4

x=y^2

Using disk method

volume

[tex]v=\pi \int_{0}^{4} y^{4} d y$[/tex]

[tex]v=\pi\left(\frac{y 5}{5}\right)_{0}^{4} \\[/tex]

[tex]v=\frac{1024}{5} \pi[/tex]

d) line x=-1

y=√x, y=4, x=0

0 ≤ x ≤ 6

Using shell method

volume is

[tex]V=\int_{0}^{16} 2 \pi(1+x) \sqrt{x} d x$[/tex]

[tex]V=2 \pi\int_{0}^{16}(x^{1 / 2}+x^{3 / 2}\right) )d x\right. \\[/tex]

[tex]V=2 \pi\left[\frac{x^{3 / 2}}{3 / 2}+\frac{x^{5 / 2}}{5 / 2}\right]_{0}^{16} \\[/tex]

[tex]V=2 \pi\left[2 / 3 \cdot\left(4^{2}\right)^{3 / 2}+2 / 5\left(4^{2}\right)^{5 / 2}\right] \\[/tex]

[tex]V=4 \pi / 3 \cdot 4^{3}+4 \pi / 5 \cdot 4^{5} \\[/tex]

[tex]V=4 \pi\left(\frac{1}{3}+\frac{4^{2}}{5}\right)[/tex]

[tex]V=\frac{256}{15}(5+48) \pi \\[/tex]

[tex]V=\frac{256 \times 53}{15} \pi \\[/tex]

[tex]V=\frac{13568}{15} \pi[/tex]

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Answer:

(2+n)-3

That's how you write if that is what you want.

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

In this problem we have a cubic equation and the nature of their roots must be inferred according to a algebraic method.

Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, there is a method to infer the nature of the roots of such polynomials: The discriminant from Cardano's method, an analytical method used to solve polynomials of the form a · x³ + b · x² + c · x + d = 0.

The discriminant is described below:

Δ = 18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d²      (1)

Where:

If we know that a = 1, b = 2, c = 4 and d = 8, then the nature of the roots is:

Δ = 18 · 1 · 2 · 4 · 8 - 4 · 2³ · 8 + 2² · 4² - 4 · 1 · 4³ - 27 · 1² · 8²

Δ = - 1024

The cubic equation f(x) = x³ + 2 · x² + 4 · x + 8 has one real root and two complex roots.

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Answer:

  none

Step-by-step explanation:

The domain of the equation can be found by looking at the requirements ...

For n+2 ≥ 0, we find ...

  n ≥ -2 . . . . . . . . subtract 2 from both sides

For -16-5n ≥ 0, we find ...

  -16 ≥ 5n . . . . . add 5n

  -3.2 ≥ n . . . . . divide by 5

Together, these domain restrictions require that ...

  n ≥ -2

  n ≤ -3.2

These intervals do not overlap, so there are no values of n that can satisfy this equation.

__

Additional comment

The solutions would appear on the attached graph as points where the curves intersect above the x-axis. They do not intersect, hence the equation has zero solutions.

__

If we were to solve this without regard to domain restrictions, we would square both sides to get ...

  (n +2)² = -16 -5n

  n² +9n +20 = 0 . . . . . put in standard form

  (n +4)(n +5) = 0 . . . . . factor

  n = {-5, -4} . . . . . . . . . both are extraneous solutions.

These "solutions" do not satisfy the requirement that the square root be positive.