Jack made $200 for working 40 hours. Saida made $242 for 44 hours of work. Are the pay rates proportional?

[tex]P(x)[/tex] has degree 3, so it takes the general form

[tex]P(x)=ax^3+bx^2+cx+d[/tex]

It has a root [tex]x=1[/tex] of multiplicity 2, which means [tex](x-1)^2[/tex] divides [tex]P(x)[/tex] exactly, and it has a root of [tex]x=-3[/tex] of multiplicity 1 so that [tex]x+3[/tex] also is a factor. So

[tex]P(x)=a(x-1)^2(x+3)[/tex]

Expanding this gives

[tex]P(x)=a(x^3+x^2-5x+3)=ax^3+ax^2-5ax+3a[/tex]

[tex]\implies\begin{cases}a=b\\-5a=c\\3a=d\end{cases}[/tex]

The [tex]y[/tex]-intercept occurs for [tex]x=0[/tex], for which we have

[tex]P(0)=d=2.1[/tex]

Then

[tex]3a=d\implies a=0.7[/tex]

[tex]a=b\implies b=0.7[/tex]

[tex]-5a=c\implies c=-0.14[/tex]

So we have

[tex]\boxed{P(x)=0.7x^3+0.7x^2-0.14x+2.1}[/tex]

Answer:

4

Step-by-step explanation:

on edge.

Step-by-step explanation:

Given equation of circle is,

[tex] {x}^{2} + {y}^{2} - 6y - 12 = 0 \\ by \: compairing \: it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\2 g = 0 \: or \: g = 0 \\ 2f= - 6 \\ or \: f= - 3 \\ c = - 12[/tex]

again the another form of circle is,

[tex] {x}^{2} + {(y - k)}^{2} = 21 \\ or \: {x}^{2} + {y}^{2} - 2ky + {k}^{2} - 21 = 0 \\ by \: compairing \:it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\ g = 0 \\f = - k \\ c = {k}^{2} - 21[/tex]

now equating the values of f in both equations,

-k=-3

i.e. k=3

therefore k=3

A class consists of ten individuals. The instructor selects three kids to accompany her to the library. It makes no difference in whatever sequence they are picked. There are 120 options for selecting pupils.

A permutation is a process of putting items or pieces in a certain order. Combinations are a method of picking things or pieces from a set of objects or collections when the order of the objects is irrelevant.

No of student=10

Students to be choosen=3

The ways are there to choose the students are found with the help of combination as;

If n is the number of the ways:

n= 10C₃

[tex]\rm nCr = \frac{n!}{r!(n-r)!}\\\\[/tex]

Where n is the total of students and r is the teacher to be chosen:

[tex]\rm 10 C_3= \frac{10 !}{3!7!}\\\\ 10 C_3= \frac{3628800}{30240} \\\\ n=120[/tex]

Hence, there is 120 no of ways are there to choose a student.

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Answer: A class consists of ten individuals. The instructor selects three kids to accompany her to the library. It makes no difference in whatever sequence they are picked. There are 120 options for selecting pupils.

Step-by-step explanation:

Answer:

B. (-3, 0) and (-6,0)

Step-by-step explanation:

x intercept when y = 0

so x^2 + 9x + 18 = 0

Factor

(x + 6)(x + 3) = 0

x+6 = 0; x = -6

x+3 = 0; x = -3

Answer

B. (-3, 0) and (-6,0)

Answer: Option B.

Step-by-step explanation:

The graph of the quadratic equation is a parabola.

The parabola intercepts the x-axis when [tex]y=0[/tex].

Then, you need to substitute [tex]y=0[/tex] into the equation:

[tex]y=x^2+9x+18\\0=x^2+9x+18[/tex]

Factor the quadratic equation: find two number that when you add them you get 9 and when you multiply them you get 18. In this case these numbers are 6 and 3. Then:

 [tex]0=(x+6)(x+3)\\\\x_1=-6\\x_2=-3[/tex]

Therefore, the x-intercepts are:

(-3,0) and (-6,0)

Answer:

3

Step-by-step explanation:

The assumed frequency of defects is 2/16.

When we apply this rate to 24, (2/16)*24, we get 3.

Therefore, we can assume around 3 defective boxes tomorrow.

Answer:

197,500

Step-by-step explanation:

200500*25-184000/6.25-2560.43=4980499.57 Which rounds to 197,500.

Allison owes approximately $1,380.50 in prorated taxes and interest for the property she's closing on September 17.

To calculate the prorated taxes and interest that Allison owes, we need to break down the calculation into two parts: prorated property taxes and prorated interest.

1. **Prorated Property Taxes:**

  - Allison is closing on September 17, which means she will own the property for 106 days of the year (September 17 to December 31).

  - The seller has already paid $2,560.43 in property taxes for the entire year.

  - To calculate Allison's portion of the property taxes, we need to divide the seller's payment by the number of days in the year and then multiply by the number of days Allison will own the property.

Prorated Property Taxes = Seller's Property Tax Payment/

Days in Year × Days Allison Owns the Property

 [tex]\[ \text{Prorated Property Taxes} = \frac{2,560.43}{365} \times 106 \][/tex]

 [tex]\[ \text{Prorated Property Taxes} = \frac{2,560.43}{365} \times 106 = 741.12 \][/tex]

2. **Prorated Interest:**

  - Allison is taking out a 25-year fixed-rate mortgage for $185,000 at 6.25% interest.

  - To calculate the prorated interest, we need to find out how much interest Allison will owe for the remaining days of September.

 Daily Interest Rate [tex]$=\frac{\text { Annual Interest Rate }}{\text { Days in Year }}=\frac{6.25 \%}{365}$[/tex]

  Prorated Interest for September = [tex]Loan Amount $\times$ Daily Interest Rate $\times$ Number of Days in September[/tex]

  [tex]\[ \text{Prorated Interest for September} = 185,000 \times \frac{6.25\%}{365} \times 14 \][/tex]

 [tex]\[ \text{Prorated Interest for September} \approx 639.38 \][/tex]

Now, let's add up the prorated property taxes and prorated interest:

[tex]\[\text{Total Prorated Taxes and Interest} = \text{Prorated Property Taxes} + \text{Prorated Interest for September}\][/tex]

[tex]\[\text{Total Prorated Taxes and Interest} = 741.12 + 639.38\][/tex]

[tex]\[\text{Total Prorated Taxes and Interest} = 1380.50\][/tex]

So, Allison will owe approximately $1,380.50 in prorated taxes and interest.

The required value of the wall after the window is made is 32 cubic feet.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The total number of cubic feet in the wall before the window is made is,

6 feet (height) × 6 feet (width) = 36 cubic feet.

The window is 2 feet high and 2 feet wide, so its area is:

2 feet (height) × 2 feet (width) = 4 square feet.

To find the number of cubic feet removed to make the window, we simply multiply the area of the window by the depth of the wall, which is 1 foot:

4 square feet × 1 foot = 4 cubic feet.

Therefore, the total number of cubic feet in the wall after the window is made is,

36 cubic feet - 4 cubic feet = 32 cubic feet.

So the value of the wall after the window is made is 32 cubic feet.

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Answer: 1 and 3, means the first one and the third one

Step-by-step explanation:

So just do the equations and you know you will get the right answer.

Fun Fact:

To get the right answer just solve all the equations, even the one in the question. And match the one that is equivalent.

Note:

If you are reading this, please let me know if you need to know anything else.

Mark BRAINLIEST

Answer:

1.28 is the amount you get off

Step-by-step explanation:

Answer: C: $1.28

Step-by-step explanation: took test

Check the picture below.

Answer:

540

Step-by-step explanation:

9✖️6= 54

This means that there are 54 square feet in the garden

Since there are 10 flowers in each foot then you would have to multiply

54✖️10= 540

This means that there are 540 flowers in the garden

Hope this helps! :3

The probability that it will be a clear day in San Antonio in May is 0.57 or 57%, calculated by dividing the number of clear days (17) by the total number of days in May (30).

In order to determine the probability of a clear day in San Antonio in May, we need to use the given data. From option OA, it is stated that there are 17 clear days out of 30. Probability is calculated by dividing the number of favorable outcomes (clear days) by the total number of outcomes (total days in May).

So, if we divide 17 (the number of clear days) by 30 (the total number of days in May), we get the probability as 0.57 after rounding to two decimal places which matches option OA.Therefore, the probability that it will be clear in San Antonio in May is 0.57 or 57%.

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Because 6 of the 30 days were Clear, The probability is 0.2

The probability of A given B is defined as ;

Hence, Probability of being clear given you're in San Antonio ;

Now we have ;

P(Clear n SA) = 6 / 30 = 0.2

Hence, the correct option is D.

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30 is the value of x given of above quertion

Answer:

30°

Step-by-step explanation:

x + 2x + 3x = 180°

30° + 60° + 90° = 180°

x = 30°

Answer:

8.48 I believe that is the correct answer

Step-by-step explanation:

Answer:

8.48

Step-by-step explanation:

Answer:

[tex]x=t[/tex]

[tex]y=\pm\sqrt{3t-t^2}[/tex]

Step-by-step explanation:

The given polar equation is;

[tex]r=3\sin \theta[/tex]

We multiply  both sides by r

[tex]r^2=3r\sin \theta[/tex]

The corresponding rectangular equation is

[tex]y^2+x^2=3x[/tex]

[tex]y^2=3x-x^2[/tex]

[tex]y=\sqrt{3x-x^2}[/tex]

Let x=t,

Then;

[tex]y=\pm \sqrt{3t-t^2}[/tex]

Answer: Usain Bolt

Step-by-step explanation:

Answer:

The horse ran like a jaguar trying to feed.

Step-by-step explanation:

Answer:

D 70/3

Step-by-step explanation:

5 /3 * 2/3 * 21

10/9 * 21/1

210/9

We can divide by 3 on the top and bottom

70/3

the final product is 70/3, making the correct answer D).

The question asks to find the product of the numbers (5/3), (2/3), and 21. To solve this, we will multiply these numbers step by step.

So, the final product is 70/3, making the correct answer D).

Y=-2/5x -1 is the answer I believe, if anything check Photomath, that should be the right slope double check the y-intercept by plugging it in with your points provided to u

Answer:y = -2x + 7

Step-by-step explanation:

The equation of a straight line when two points are given is y - y1 = m(x - x1) but m is gradient which is y2 - y1 / x2 - x1

Substitute the points (3 ,1 ) and (7 , -7)

To the gradient equation and solve for the gradient which is m = -2 .Now with the gradient and the first point (3 , 1) solve for the equation

:• y - 1 = -2(x -3 )

y - 1 = -2x +6

. y = -2x + 7

Answer:

1.) What percent of girls don't wear makeup? [30%]

2.) What percent of the people surveyed were girls? [50%]

3.) What percent of people don't have an opinion? [23.3%]

4.) What percent of boys boys prefer girls who don't wear make up? [33.3%]

5.) What percent of boy have no opinon? [10%]

I hope this helps!!!

[tex]\boxed{h=\frac{6}{b}}[/tex]

Solving for [tex]h[/tex] is the same as isolating it. In this problem, we have the following equation:

[tex]6=bh[/tex]

So we need to do the following steps:

Step 1: Interchange the order of the equation:

[tex]bh=6[/tex]

Step 2: Divide the whole equation by [tex]b[/tex]:

[tex]\frac{1}{b}bh=\frac{1}{b}6[/tex]

Step 3: Simplify

[tex]h=\frac{6}{b}[/tex]

Finally, this h is in term of b and is:

[tex]\boxed{h=\frac{6}{b}}[/tex]

The product of c and 7 is less than or equal to -28  is  7c≤-28.

A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.

solving this we will get the valve of Y if x is given.

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Answer:

[tex]\large\boxed{\sqrt{27y^8}=3y^4\sqrt3}[/tex]

Step-by-step explanation:

[tex]\sqrt{27y^8}=\sqrt{9\cdot3\cdot y^{4\cdot2}}\\\\\text{Use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ (a^n)^m=a^{nm}\ \text{and}\ \sqrt{a^2}=a\\\\=\sqrt9\cdot\sqrt3\cdot\sqrt{(y^4)^2}=3\cdot\sqrt3\cdot y^4=3y^4\sqrt3[/tex]

Answer:

I believe that the reciprocal of -1

Hope this helps

Step-by-step explanation:

In order to find the reciprocal of a number, we should just flop it over, like so:-

[tex]\sf{The~reciprocal~of~a~is~\frac{1}{a}}[/tex]

Flop it over:-

[tex]\sf{-\displaystyle\frac{1}{1} }[/tex]

There's something you should notice about this number.

No matter how we flop it over, we're going to end up with -1.

Hence, the reciprocal of -1 is:-

[tex]\boxed{-1}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

D. Inscribed angle

An inscribed angle has a vertex on the circumference. For any arc, every inscribed angle is exactly half of the central angle. In other words, if the central angle is [tex]x^{\circ}[/tex] and the inscribed angles is [tex]y^{\circ}[/tex], then it is true that:

[tex]y^{\circ}=\frac{x^{\circ}}{2}[/tex]

In this problem [tex]y^{\circ}=36^{\circ}[/tex], then the central angle is [tex]x^{\circ}=2y^{\circ} \ \therefore x^{\circ}=2(36^{\circ}) \therefore x^{\circ}=72^{\circ}[/tex]

Answer:

Option D.

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

[tex]m<XYZ=\frac{1}{2}(arc\ XZ)[/tex]

In this problem  

The measure of angle XYZ is an inscribed angle

Answer:

108.505 is greater.

Step-by-step explanation:

It is 5 thousandths bigger.

Answer:

Step-by-step explanation:

The formula of a distance between two points (numbers) A and B on the number line:

d = |B - A| = |A - B|

We have A = -13 and B = -4. Substitute:

d = |-13 - (-4)|

Answer:

295245

you can round it yourself

Step-by-step explanation:

10.00 was the markup

Ellen's markup on the rose bushes is calculated by subtracting the wholesale price from the retail price, resulting in a markup of $10.00.

The question asks to calculate the markup of rose bushes that were bought at a wholesale price and then sold at a retail price.

To find the markup, we subtract the wholesale price from the retail price: Retail Price - Wholesale Price = Markup.

In this case, Ellen bought the rose bushes at a wholesale price of $24 and the retail price was $34.

So, the markup calculation would be:

= $34 - $24 = $10.

Therefore, the markup on the rose bushes is $10.00.

The answer is:

It will take 4.5 hours for two bricklayers to lay a total of 3150 bricks.

From the statement, we know that on Monday, bricklayers took 3 hours to lay a total of 4200 bricks.

So, we have that the rate of the four bricklayers is given by the following equation:

[tex]Production=Rate*Time\\\\Rate=\frac{Production}{time}[/tex]

[tex]Rate=\frac{4200bricks}{3hours}=\frac{1400bricks}{hour}[/tex]

Therefore, we have that the rate of the four bricklayers is 1400 bricks per hour, meaning that each bricklayer can lay 350 bricks per hour.

Now, to calculate how many hours it will take to the 2 bricklayers to lay a total of 3150, we need to divide the calculated rate (for bricklayers) by two, since there are only 2 bricklayers working on Tuesday.

So, calculating the time, we have:

[tex]Production=\frac{Rate}{2}*Time[/tex]

[tex]3150bricks=\frac{\frac{1400bricks}{hour}}{2}*Time[/tex]

[tex]3150bricks*2*\frac{1hour}{1400bricks}=Time[/tex]

[tex]6300bricks*\frac{1hour}{1400bricks}=Time[/tex]

[tex]Time=4.5hours[/tex]

Hence, we have that it will take 4.5 hours for two bricklayers to lay a total of 3150 bricks.

Have a nice day!

Given the rate of work from Monday, each bricklayer can lay 350 bricks an hour. Therefore, 2 bricklayers can lay 700 bricks an hour. It will take them approximately 4.5 hours to lay 3150 bricks.

First, we need to find out the rate of work done by each bricklayer. On Monday, 4 bricklayers took 3 hours to lay a total of 4200 bricks. Therefore, each bricklayer can lay 4200 bricks divided by 4 bricklayers divided by 3 hours, which equals 350 bricks per hour. So, one bricklayer can lay 350 bricks an hour.

On Tuesday, there are only 2 bricklayers, and they need to lay a total of 3150 bricks. Since each bricklayer can lay 350 bricks an hour, two bricklayers can lay 700 bricks an hour. To find out the time it will take to lay 3150 bricks, we divide 3150 bricks by the 700 bricks that two bricklayers can lay in an hour. This equals to approximately 4.5 hours.

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Answer:

Final answer is p=2.

Step-by-step explanation:

Given equation is [tex]\frac{4-p}{p-1}=\frac{2}{p-1}[/tex]

Cross multiply

[tex]\left(4-p\right)\left(p-1\right)=2\left(p-1\right)[/tex]

[tex]4p-4-p^2+p=2p-2[/tex]

[tex]4p-4-p^2+p=2p-2[/tex]

[tex]0=p^2-4p+4-p+2p-2[/tex]

[tex]0=p^2-3p+2[/tex]

[tex]0=p^2-1p-2p+2[/tex]

[tex]0=(p-1)(p-2)[/tex]

[tex]0=(p-1)[/tex] or [tex]0=(p-2)[/tex]

[tex]1=p[/tex] or [tex]2=p[/tex]

But p=1 will make denominator 0 and make the problem not defined.

Hence final answer is p=2