2. Billie purchased a Jeep for $12,480. Her down payment was $3,600. If she paid the remainder in 48 monthly payments (excluding interest), what would be her monthly payment? (1) $165 (2) $175 (3) $185 (4) $195 (5) $205 ​

On solving the provided question we can say that ordinary number the answer is  1.495 x 10^0

An ordinary number, also known as a standard form number or a decimal number, is a number that is written in the familiar base-10 format, with a whole number part and a fractional part separated by a decimal point.

A) 5.1 x 10¹ as an ordinary number is 51.

B) To work out the value of (1.7 x 10¹) × (8.5 x 10-²), we first need to multiply the two numbers:

(1.7 x 10¹) × (8.5 x 10-²) = 1.7 x 8.5 x 10¹ x 10-² = 14.95 x 10-1

To express the answer in standard form, we need to move the decimal point to the left so that there is only one non-zero digit to the left of it. 14.95 x 10-1 is 1.495 x 10^0. So the answer is 1.495 x 10^0

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An equation for a parabola with​ x-intercepts (-3,0) and (4,0) which passes through the point (2,-40) is 5(x+3)(x-4)

Quadratic equations are equation that has a leading degree of 2. The standard quadratic equation is given as:

y = a(x-a)(x-b)

where a and b are the x-intercepts of the function

Given the​ x-intercepts (-3,0) and (4,0), the equation will below:

y = a(x-(-3)(x-4))

y = a(x+3)(x-4)

If the curve pass through the y-intercept (2,-40)

-40= a(2+3)(2-4)

-40 = a(4)(-2)
-40 = -8a

a = 5

Substitute the value of a into the resulting function to have:

y = 5(x+3)(x-4)

This gives the required quadratic equation.

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the probability that preparation is within 2 minutes of the mean time is 0.134.

An illustration of a probability distribution shows the anticipated results of potential values for a specific data generation procedure.

Axiomatic, theoretical and experimental are the three types of probability.

P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)

Using cumulative functi0n we get

P(35-2<X<35+2)= P(33<X<37)= P(X<37)-P(X<32)

=\(\frac{37-20}{50-20}-\frac{33-20}{50-20}\\ =0.567-0.433\\=0.134\)

Thus the probability that preparation is within 2 minutes of the mean time is 0.134.

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Answer:

A bar graph

Step-by-step explanation:

It would be the best way to represent it properly,because,the bar graph can show day by day,or week by week.(the 2 weeks)

The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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Answer:

$0.05 per oz.

Step-by-step explanation:

2.39/48=0.049...... which is 0.05 to the nearest tenth. Money is never the unit rate so that is why you divide money by the measurement, in this case, ounces.

Answer:

251+7,76+946-97*

Step-by-step explanation:

61664634*96*49

Answer:

261

Step-by-step explanation:

PEMDAS

Parentheses

Exponents

Multiply

Divide

Add

Subtract

Answer:

AB = 38.6metres

Step-by-step explanation:

Given the right angled triangle ABC with hypotenuse AB and ∠CAB to be 75°, the opposite side of the triangle will be the side facing the angle ∠CAB directly and this is side BC. The adjacent side of the triangle will be side CA.

To get the length of the hypotenuse AB, we will use the trigonometry identity SOH, CAH, TOA.

According to CAH;

Cos∠CAB = adjacent/hypotenuse = CA/AB

Substituting CA = 10 metres and ∠CAB = 75° into the equation;

Cos75° = 10/AB

AB = 10/cos75°

AB = 10/0.2588

AB = 38.6metres

Hence the length of the hypotenuse AB is 38.6metres.

Answer:

38.6 m

Step-by-step explanation:

The daily constraints that the plan places on the company are 150 to 220.

A business constraint can be anything that's stopping a company from achieving its goals.

Analysis

f0 \(\leq\) x = 130

50 ≤ y ≤110

150 ≤ x+y=220

This is a linear planning question.

In the figure on the right, any point of the shadow part meets the Constraints.

Constraints can be business or technical in nature and are defined as restrictions or limitations on possible solutions.

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The graph shows the function g(x) as

\(g(x)=x^{1/3}-3\)

Given, that the function f(x)

\(f(x)=x^{1/3}\)

the graph shows a function g a transformation of f(x).

As, the graph of f(x) shifted 3 units downwards to get this function in the graph.

we know, that when a graph of a function is shifted 'a' units upwards or downwards then we add or subtract 'a' to the function respectively.

because the graph is shifted 3 units downwards.

Hence, the function g(x) can be defined as

\(g(x)=x^{1/3}-3\)

So, the graph shows the function g(x) as

\(g(x)=x^{1/3}-3\)

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Answer: let me explain!

Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P

So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!

It’s 20!

So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)

So that answer would be 8x*twenty twos*

Which is…*drumroll please*

8,388,608
I even double checked!

And for the briefcase skeleton thing

She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!

Hope this helps :P

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Answer:

So first y intercept

SO the first part where the line hits the Y axis is 2

So the y intercept is 2 Which leaves 2 choices .

Now from that y-intercept or from any point, find the slope by just rising or running till you reach a point which in this case would be

Y=1/2x+2

Answer:

Step-by-step explanation:

A

Answer:

7*(5)^0,5

:D hope it helps

Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.

Total interest is determined by the addition of all the interest payments.

United bank offers mortgage at an APR of 4.2%

APR means annual percentage rate.

mortgage is offered for the period of 15 years.

initial principal amount of Marcy = $120000

we need to determine the monthly payment from United bank.

at first, we will determine the rate of interest per month.

monthly interest rate = (4.2) / (100 × 12) = 0.0035

1 year = 12 months

15 years = 15×12 = 180 months

monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal

monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000

                          = $1207.70

from united bank monthly payment = $1207.70

Now we calculate the monthly payment from Capitol bank.

APR for capitol bank = 4.5%

number of years for which mortgage is issued = 25 years

number of months = 12×25 = 300.

monthly interest rate = (4.5) / (100×12) = 0.00375

monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000

                 = 1834.62

monthly payment from Capitol bank = $1834.62

total interest from Capitol bank = principal money × yearly interest rate × time period.

Total interest = 120000 × 4.5/100× 25

                        = $135000 for the Capitol bank

Total interest from United bank = principal amount × yearly interest × time period

            = 120000× 4.2/100 × 15

total interest from united bank   = $75600

United bank has lower total interest.

difference in monthly payment = 1834.62 - 1207.70

                                                   = 626.92 dollars

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Answer:

Step-by-step explanation:

Total students in the class=18

Girls=10

Boys=8

a.  Pr(Girl, Girl)= 10/18*9/17=90/306.

b.   Pr ( at least one is a boy) = BG* BB* GB*GGB*BBG*BBB*BGG*GBG*GBB*BGB*

Answer:

Question 1  : 0.44

Question 2: 0.853

Step-by-step explanation:

We should use combinatorics to solve this problem

Combinations

The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed

The formula for finding the number of ways you can pick r items from a set of n items where duplicates are eliminated is given by the combinations formula:

\(C(n,r) = \dfrac{n!}{( r! (n - r)! )}\)

where the ! stands for the factorial of the number

Let's take simple example to illustrate this

Suppose we have 3 books labeled A, B. C and we are asked to randomly pick 2 books in one shot. There are 3 possible picks:

AB, AC, BC

Note that though there are six possible arrangements of 2 items from a set of 3, we have to eliminate duplicates because AB is the same as BA.

In the above case, r = 2, n = 3 so using the formula we get

\(C(3,2) = \dfrac{3!}{( 2! (3 - 2)! )}\\\\= \dfrac{3!}{2! \times 1! }\\\\\\= \dfrac{3 \times 2 \times 1}{(2 \times 1)(1)}\\\\\\= 3\\\\\)

Now to the actual problem

There are a total of 18 students in the class

Number of ways of picking 3 students is
\(C(18,3) = \dfrac{18!}{( 3! (18 - 3)! )}\\\\= \dfrac{18!}{3! \times 15! }\\\\\\=816\)

So there are 816 possible ways to pick 3 students from 18 students

There are calculators to perform this gruesome task so I will omit the actual steps and just show the result

Let's consider the first question
Out of the 3 students picked 2 are girls. That means the other one is a boy

Number of ways of picking 2 girls out of 10 is C(10, 2)

C(10, 2) = 45

Then we have to consider the lone boy. Number of ways of picking 1 boy out of 8 is

C(8, 1) = 8

Total number of ways of picking 2 girls and 1 boy

= 45 x 8 = 360

Therefore P(2 girls, 1 boy) :

\(\dfrac{360}{816} = 0.44\)

Second question
To find the number of ways that at least 1 boy can appear in the group is the sum of the number of ways 1, 2 or 3 boys can appear in the group.

Rather than do this, let's approach it in a easier fashion

The probability of at least 1 boy appearing in the group is the complement of no boys on the group, i.e. all volunteers are girls

Number of ways of selecting a volunteer group of all 3 girls:

C(10, 3) = 120

P(no boys in group) = P(all 3 girls in group)
\(=\dfrac{120}{816} = 0.147\)

Therefore P(at least 1 boy) = 1 - P(no boys)

= 1-0.147

= 0.853

Could you please let me know if correct? This is a tough subject area for me too :)

The function g(x) is a transformation of the parent function f(x) is Horizontal or vertical stretch.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The function g(x) is a transformation of the parent function f(x).

Vertical Stretch :

g(x) = a f(x)

Horizontal Stretch :

g(x)= f(ax)

Vertical reflection:

g(x) = -f(x)

Horizontal reflection:

g(x) = f(-x)

Vertical shift:

g(x) = f(x) + k

Horizontal shift:

g(x) = f(x+ k)

The reflection of the point (x,y) across  the line y = x is the point (y, x).

By the given tables we can see that, g(x)= 1/9 f(x).

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Answer:

Much larger than 1 for both of them

Step-by-step explanation:

The most common bottom numbers are "4, 8, and 16". A further explanation is provided below.

The bottom numeral indicates the type of remark to measure. That seems to be, if whether measures should be counted as quarterly notes, 8th or 16th notes.

As nothing more than a result, the only quantities you'll see as the bottom amount relate to note value systems:

You could keep going with 32 or 64, although presumably, you won't have to because it becomes a little cumbersome after a time.

Thus the aforementioned response is appropriate.

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The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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The survey method which will produce the best representative sample is option B.  survey 3 randomly selected students from every homeroom.

Sampling methods are methods used to select a sample using specific methods. This includes various types of probability sampling and non probability sampling methods.

Here given that,

a middle school principal wants to change the lunch menu at the school.

It is impossible to survey the whole students in school.

In order for the survey results to be the best representative of the whole school, it is important to survey students representing each class and group.

So when we survey every fifth student who rides in a car to school, survey will be biases to only the students who travels in car.

When the survey only done to seventh grade students, it is also biased.

When the survey is done in art and music classes, again the survey will be biased since only the music students takes place.

If students from every homeroom is selected, it will represent the whole school.

Hence the best method is option B.

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A middle school principal wants to change the lunch menu at the school. The principal surveys the students to determine how the students would feel about the changes. Which survey method will produce the best representative sample? A: survey every fifth student who rides in a car to school B: survey 3 randomly selected students from every homeroom C: survey every tenth seventh grade student during lunch D: survey 5 randomly selected students from every art, drama, and music class

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Answer:

D

Step-by-step explanation:

RISE/RUN = slope

This slope will be POSITIVE because it rises in quadrant 1.

Rise=2, run=3

Slope= 2/3

Hope that helps

A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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If \(f^{-1}(x)\) is the inverse of \(f(x)\), then

\(f\left(f^{-1}(x)\right) = x\)

Given

\(f(x) = 3x-9\)

composing with the inverse function gives

\(f\left(f^{-1}(x)\right) = 3f^{-1}(x) - 9 = x\)

Solve for the inverse:

\(3f^{-1}(x)-9 = x \\\\ 3f^{-1}(x) = x+9 \\\\ \boxed{f^{-1}(x) = \dfrac x3 + 3}\)

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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