Chrissy currently has a credit card that charges 15% interest. She usually carries a balance of about $500. What will her total annual interest be with her current card?

Answer:

12 + -6i

a=12

b=-6

Step-by-step explanation:

( -4 + 3i ) ( -3 - 2i )

-4 * -3 = 12

3i * -2i= -6i

12 + -6i

Answer:

(See explanation below for further detail/Véase la explicación abajo para mayores detalles)

Step-by-step explanation:

(This exercise is written in Spanish and explanations will be held in such language)

a) Las temperaturas quedan representadas a continuación:

Quito - Temporada Fría

Intervalo

[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada fría)

Conjunto

[tex]C = \{\forall t \in \mathbb {R}| 5 \leq t \leq 18\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada fría)

Quito - Temporada Cálida

Intervalo

[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex] (Este intervalo indica si el dato puede pertenecer a la temporada cálida)

Conjunto

[tex]H = \{\forall t \in \mathbb {R}| 4 \leq t \leq 30\}[/tex] (Este conjunto acumula todo el registro de las temperaturas de la temporada cálida)

b) La temperatura de la ciudad de Quito pertenece esencialmente a dos intervalos:

Intervalo de Temporada Fría:

[tex]5 ^{\circ}C \leq t \leq 18^{\circ}C[/tex]

Intervalo de Temporada Cálida:

[tex]4 ^{\circ}C \leq t \leq 30^{\circ}C[/tex]

c) Toda temperatura mayor o igual que 4 °C y menor o igual que 30 °C.

d) Temperaturas mayores o iguales a 5 °C y menores o iguales a 18 °C.

e) Temperaturas mayores o iguales a 4 °C y menores o iguales a 30 °C.

Answer:

f(4) =2

Step-by-step explanation:

f(x) = 2х^2 - 30,

Let x=4

f(4) = 2 (4)^2 -30

     = 2*16 -30

       =32-30

      = 2

Answer:

22,203 ft^2

Step-by-step explanation:

The area of a triangle with angle ∅ and two sides a and b is;

Area A = 1/2 × absin∅ ......1

The park is in the shape of a triangle, with two sides and an angle given;

Given;

a = 190 ft

b = 235 ft

∅ = 84°

Substituting the values into equation 1;

Area of the park;

A = 1/2 × 190 × 235 × sin84°

A = 22,202.70131409 ft^2

A = 22,203 ft^2 (to the nearest whole number)

Area of the park is 22,203 ft^2

Answer:

Step-by-step explanation:

Answer:

S = ⅙ π (65^³/₂ − 5^³/₂)

Step-by-step explanation:

z = x² + y², 1 < z < 4

Surface area is:

S = ∫∫√(1 + (fₓ)² + (fᵧ)²) dA

where fₓ and fᵧ are the partial derivatives of f(x,y) with respect to x and y, respectively.

fₓ = 2x, fᵧ = 2y

S = ∫∫√(1 + (2x)² + (2y)²) dA

S = ∫∫√(1 + 4x² + 4y²) dA

For ease, convert to polar coordinates.

S = ∫∫√(1 + 4r²) dA

S = ∫∫√(1 + 4r²) r dr dθ

At z = 1, r = 1.  At z = 4, r = 4.

So 1 < r < 4, and 0 < θ < 2π.  These are the limits of the integral.

S = ∫₀²ᵖⁱ∫₁⁴√(1 + 4r²) r dr dθ

To integrate, use u-substitution.

u = 1 + 4r²

du = 8r dr

⅛ du = r dr

When r = 1, u = 5.  When r = 4, u = 65.

S = ∫₀²ᵖⁱ∫₅⁶⁵√u (⅛ du) dθ

S = ∫₀²ᵖⁱ (⅛ ∫₅⁶⁵√u du) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ u^³/₂ |₅⁶⁵) dθ

S = ∫₀²ᵖⁱ (¹/₁₂ (65^³/₂ − 5^³/₂)) dθ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) θ |₀²ᵖⁱ

S = (¹/₁₂ (65^³/₂ − 5^³/₂)) (2π)

S = ⅙ π (65^³/₂ − 5^³/₂)

The correct answer is C. Kelli put 6 red marbles and 5 blue marbles in a bag. The probability of selecting a red marble is 6 /11

Explanation:

Theoretical probability occurs as you calculate the probability of a specific outcome in a situation, without experimenting or observing it. Because of this, the probability is theoretical rather than experimental. Also, you can know this, if you divide the number of specific favorable outcomes by the total of possible outcomes.

Option C shows a theoretical probability because this is the only case the probability has not been observed or experimented. Also, expressing the probability as 6/11 is completely correct because 6 is the total of red marbles(possible desired outcomes), while 11 is the total marbles (possible outcomes).

Answer:  r_max = 1.75m

Step-by-step explanation:

Below is a rather brief analysis to solving this problem.

The phone starts sliding when along incline,

when F_net = m g sin(theta) - fs_max = 0  

and fs_max = us N = us m g cos(theta)

m g sin(theta) - us m g cos(theta) =

us = tan(theta) = tan38 = 0.781  

On merry - go - round,

fs_max = us N = us m g

Using F = m a

fs_max = m w^2 r_max and w = 2pi / T

us m g = m (2 pi / T)^2 (r_max)

0.781 x 9.81 = (2 pi / 3)^2 (r_max)

r_max = 1.75 m

cheers i hope this helped !!

Answer:

a) x = 30°

b) mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

(a) If mRS = x, then write an equation that could be used to solve for x

and find the value of x.

(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Answer:

The critical value is T = 2.2622.

The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622, which is the critical value.

The margin of error is:

M = T*s = 2.2622*0.64 = 1.448

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 1.448 = 1.352 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 1.448 = 4.248 pounds

The 95% confidence interval for the mean waste recycled per person per day for the population of Florida is between 1.352 pounds and 4.248 pounds.

Answer:

The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.

The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.

Step-by-step explanation:

Answer:

The expected completion time of this project from now is 2.5 months.

Step-by-step explanation:

To find the expected completion time for the project, we multiply each projection by it's probability.

We have that:

0.4 = 40% probability it takes 2 months to complete the project.

0.3 = 30% probability that it takes 2.5 months to complete the project.

0.2 = 20% probability it takes 3 months to complete the project.

0.1 = 10% probability it takes 3.5 months to complete the project.

What is the expected completion time (in months) of this project from now?

E = 0.4*2 + 0.3*2.5 + 0.2*3 + 0.1*3.5 = 2.5

The expected completion time of this project from now is 2.5 months.

Answer:

  $1741.44

Step-by-step explanation:

The discounted amount is 100% -10% = 90% of the original. The amount of the discount is 10% of the original, or 1/9 of the discounted amount:

  10% = 90% × 1/9

The discount was ...

  $15,673/9 = 1,741.44

_____

Check

The original is the sum of the discounted amount and the discount:

  original price = $15,673.00 +1,741.44 = $17, 414.44

10% of that value is 1,741.44, as shown above.

Here is the full question.

The average finishing time among all high school boys in a particular track event in a certain state is 5 minutes 17 seconds. Times are normally distributed with standard deviation 12 seconds.

A.  The qualifying time in this event for participation in the state meet is to be set so that only the fastest 5% of all runners qualify. Find the qualifying time in seconds (round it to the closest second). (Hint: Convert minutes to seconds.)  

B. In the western region of the state the times of all boys running in this event are normally distributed with standard deviation 12 seconds, but with mean 5 minutes 22 seconds. Find the proportion of boys from this region who qualify to run in this event in the state meet. (Hint: normalcdf)

Answer:

a. x ≅ 337 seconds.

b. P(x > 337 )  = 0.1056

Step-by-step explanation:

A.

Given that ;

Mean [tex]\mu =[/tex] 5 minutes 17 seconds =( (60× 5)+17  ) seconds  = 317 seconds   ( since 60 seconds make 1 minute.

Standard deviation: [tex]\sigma[/tex] = 12 seconds.

Only the fastest 5% of all runners qualify

The objective is to determine the qualifying time in seconds

Let's look for the Z-score of 0.95;

The Z-score is 1.645 from the tables

[tex]x= ( \sigma * z ) + \mu[/tex]

[tex]x = ( 12 * 1.645 ) + 317 \\ \\x = 336.74[/tex]

x ≅ 337 seconds.

B. Given that the standard deviation = 12 seconds

Mean = 5 minutes 22 seconds = (5 × 60 + 22 )seconds = 322 seconds

he objective is  to find P(x > 337 )   i.e the proportion of boys from this region who qualify to run in this event in the state meet.

we are using command normalcdf   (SEE THE ATTACHED FILE BELOW FOR THE COMPUTATION)

we have  P(x > 337 )  = 0.1056

Answer:

$71.59

Step-by-step explanation:

43.25+26.25

=69.5

69.5×103/100

=71.585

Answer:

b. 0.25

c. 0.05

d. 0.05

e. 0.25

Step-by-step explanation:

if the waiting time x follows a uniformly distribution from zero to 20, the probability that a passenger waits exactly x minutes P(x) can be calculated as:

[tex]P(x)=\frac{1}{b-a}=\frac{1}{20-0} =0.05[/tex]

Where a and b are the limits of the distribution and x is a value between a and b. Additionally the probability that a passenger waits x minutes or less P(X<x) is equal to:

[tex]P(X<x)=\frac{x-a}{b-a}=\frac{x-0}{20-0}=\frac{x}{20}[/tex]

Then, the probability that a randomly selected passenger will wait:

b. Between 5 and 10 minutes.

[tex]P(5<x<10) = P(x<10) - P(x<5)\\P(5<x<10) = \frac{10}{20} -\frac{5}{20}=0.25[/tex]

c. Exactly 7.5922 minutes

[tex]P(7.5922)=0.05[/tex]

d. Exactly 5 minutes

[tex]P(5)=0.05[/tex]

e. Between 15 and 25 minutes, taking into account that 25 is bigger than 20, the probability that a passenger will wait between 15 and 25 minutes is equal to the probability that a passenger will wait between 15 and 20 minutes. So:

[tex]P(15<x<25)=P(15<x<20) \\P(15<x<20)=P(x<20) - P(x<15)\\P(15<x<20) = \frac{20}{20} -\frac{15}{20}=0.25[/tex]

Answer:

x= 0, 2, -6

Hope this helps!

Answer:

10 square inches

Step-by-step explanation:

cost of a plain t-shirt = $10

cost of 1 square inch of design addition = $1.50

let there be x square inches of design

then cost of x square inches of design = x*cost of 1 square inch of design

                                                                 = 1.50*x = 1.5x

Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design   = 10 + 1.5 x

It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only

Thus,

10 + 1.5 x = 25

=> 1.5x = 25-10 = 15

=> x = 15/1.5 = 10

Thus, Makeeya can  put 10 square inches of design on her T-shirt.

Answer:

-3 ( x+2i) (x-2i)

Step-by-step explanation:

-3x^2-12

Factor out a -3

-3(x^2 +4)

Rewrite

-3 ( x^2 - -4)

-3 ( x^2 - (-2i)^2)  This is the difference of squares ( a^2 -b^2 ) = (a-b)(a+b)

-3 ( x- -2i) (x+2i)

-3( x+2i) (x-2i)

Answer:

Four-fifths

Step-by-step explanation:

As we know that

By multiplying the function by a constant, we may expand or shrink the function in the y-direction.

Now we have

[tex]y=a(b^{x})[/tex]

if [tex]a> 1[/tex]  > the function would enlarge

if [tex]0< a < 1[/tex] > the function would shrinks

Now

For case A

[tex]a = \frac{4}{5}[/tex]

[tex]0 < (\frac{4}{5} )< 1[/tex] ....... > the function would shrinks

For case B

[tex]a = \frac{5}{4}[/tex]

[tex](\frac{5}{4} )>1[/tex] .......> the function would enlarge

For case C

[tex]a = \frac{3}{2}[/tex]

[tex](\frac{3}{2} )>1[/tex] .........> the function would enlarge

For case D

[tex]a = \frac{7}{4}[/tex]

[tex](\frac{7}{4} )>1[/tex] .........> the function would enlarge

Therefore the second option is correct

Answer: 4/5

Step-by-step explanation: E2020

Answer:

10 and 2

Step-by-step explanation

Nitesh is currently 10 and Ravi is currently 2

(2 times 5 is 10)

in 2 years Nitesh will be 12 and Ravi will be 4

(4 times 3 is 12)

Hey there! :)

Answer:

Price per cup: $3.5

Price for 18 cups: $63.

Step-by-step explanation:

To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.

30x = 105

Divide both sides by 30:

x = $3.5.

To find the cost of 18 cups, simply multiply this price by 18:

18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.

Answer:

As  [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex]  and as  [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]

Step-by-step explanation:

Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards  minus infinity).

As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)

Answer:

[tex]\frac{56}{96}[/tex] is your answer

Step-by-step explanation:

[tex]\frac{7}{12}[/tex]=[tex]\frac{x}{96}[/tex]

to get to 96 you must multiply by 8

and since you did that for the bottom then you need to do the same for the top,

[tex]\frac{56}{96}[/tex] is your answer

Answer:

mean:12

Step-by-step explanation:

The population mean or sample mean as indicated in the given samples is 14

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mathematically,

Mean = Sum of the observations/number of observations

Now the given sample is,

17, 11, 8, 12, 22

So, Number of sample = 5

Thus, Mean = Sum of the sample /number of sample

Mean = (17 + 11 + 8 + 12 + 22) / 5

⇒ Mean = 70/5

⇒ Mean = 14

Thus, the population mean or sample mean as indicated in the given samples is 14

To learn more about mean :

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Answer:

Circle

Step-by-step explanation:

r = 2 cos θ

Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular.

x² + y² = 2x

x² − 2x + y² = 0

Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

This is a circle with center (1, 0) and radius 1.

The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

Given function is r = 2 cos θ

Now, Multiply both sides by r.

r² = 2r cos θ

Convert to rectangular form;

x² + y² = 2x

x² − 2x + y² = 0

Using Complete the square.

x² − 2x + 1 + y² = 1

(x − 1)² + y² = 1

Hence, This is a circle with a center (1, 0) and radius of 1.

Learn more about circle here;

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Answer:

(12x2-2x+2)

Step-by-step explanation:

(12x)(x)+(5)(x)+-7x+2

12x2+5x+-7x+2

(12x2)+(5x+-7x)+(2)

12x2+-2x+2

Step-by-step explanation:

a. It would provide a quantitative data

b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.

c. 44% of the respondents strongly agree

d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.

Answer:

19.51% probability that none of them voted in the last election

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

42% of Americans voted in the previous national election.

This means that [tex]p = 0.42[/tex]

Three Americans are randomly selected

This means that [tex]n = 3[/tex]

What is the probability that none of them voted in the last election

This is P(X = 0).

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

[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]

19.51% probability that none of them voted in the last election

Answer:

Step-by-step explanation:

[tex](x-3)^2=49[/tex]

<=>

[tex](x-3)^2-49=0\\\\<=> (x-3)^2-7^2=0\\\\<=> (x-3-7)(x-3+7)=0\\<=> (x-10)(x+4)=0\\<=> x -10=0\ or \ x+4=0\\<=> x = 10 \ or\ x = -4[/tex]

solutions are -4 and 10

do not hesitate if you need further explanation

if you like my answer, tag it as the brainliest :-)