The model represents the factorization of 2x2+5x+3.
What are the factors of the polynomial?
'O
tx
+X
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
AX​

Answer:

the answer is 9

Step-by-step explanation:

Given:

The base of the given figure = 23.8 ft

Height of the parallelogram = 15 ft

To find the area of the shaded region.

Formula

where, [tex]A[/tex] be the area of the shaded region

[tex]A_{1}[/tex] be the area of the parallelogram.

[tex]A_{2}[/tex] be the area of the triangular part.

Now,

Putting, Base = 21, Hypotenuse = 23.8 we get,

[tex]Height^{2} = 23.8^{2}-21^{2}[/tex]

or, [tex]Height = \sqrt{566.44-441}[/tex]

or, [tex]Height = 11.2[/tex]

Therefore,

Area of the parallelogram [tex]A_{1} = (23.8)(15)[/tex] sq ft = 357 sq ft

Area of the triangle [tex]A_{2}[/tex] = [tex]\frac{1}{2}(11.2)(21)[/tex] sq ft = 117.6 sq ft

So,

The area of the shaded part = (357-117.6) sq ft = 239.4 sq ft

Hence,

The area of the shaded part is 239.4 sq ft.

Answer:

5

Step-by-step explanation:

Figuring the short side, it becomes a nice 3, 4, 5 triangle

so the short side is 5 units.

Hope this helped

:)

Final answer:

The length of the shortest side of the triangle is the length of side BC, which is calculated to be 5 units using the distance formula.

Explanation:

To find the length of the shortest side of the triangle with the given vertices, we will calculate the length of each side using the distance formula √((x2-x1)² + (y2-y1)²) and then determine the shortest one.

Therefore, the length of the shortest side is the length of side BC, which is 5 units.

The ground speed of the plane is approximately 116.88 km/h, and its bearing is about 83.44°, given an airspeed of 134 km/h on a 78° bearing and a 21 km/h wind from 225°.

The plane's ground speed is approximately 116.88 km/h, and its bearing is roughly 83.44°. This calculation incorporates the plane's airspeed of 134 km/h at a bearing of 78° and a wind speed of 21 km/h from a bearing of 225°.

First, we decompose the velocities into horizontal and vertical components. For the plane's airspeed, the horizontal component is about 27.81 km/h, and the vertical component is around 131.04 km/h. Similarly, for the wind, the horizontal and vertical components are approximately -14.85 km/h each. By adding the horizontal components of the airspeed and wind, we get 12.96 km/h. Likewise, adding the vertical components yields 116.19 km/h.

Using these components, we calculate the resultant velocity vector's magnitude, approximately 116.88 km/h, using the Pythagorean theorem. The direction, or bearing, is computed to be approximately 83.44° using the inverse tangent function.

Therefore, the plane moves at a speed of about 116.88 km/h, slightly northeast of east, due to the combined effect of its airspeed and the wind.

1 is union so all all the numbers inside the circles:

{8,9,14,15,16,17}

2 is intersection so the numbers where the circles cross each other

{14,17}

3. A’ is any number not included with A

There are 10 total numbers.

7 are not associated with A

Probability would be 7/10 = 0.70

The error interval for y is 7.8 ≤ y < 7.9.

The error interval is determined by the decimal digits that will determine the value of y. Since the calculator display shows 7.8, y will be between 7.8 and the next smallest number, which will be 7.9. Therefore, the error interval for y is:

7.8 ≤ y < 7.9

https://brainly.com/question/31950158

#SPJ12

The error interval for y is [7.8, 7.9).

To find the error interval for y, we need to consider the decimal place immediately after the given value on Sarah's calculator display. Since the given value is 7.8, we look at the digit after the decimal point, which is 0. If this digit is 5 or greater, we round up the previous digit. In this case, 0 is not greater than 5, so we do not round up. Therefore, the error interval for y is [7.8, 7.9).

https://brainly.com/question/31950158

#SPJ3

at maximum. dt/dh=0

if you differentiate you will get

-32t=-100

t=3.125

Answer:

The correct answer is x [tex]\geq[/tex] 106, where x is the marks score by Jose in his remaining test, n.

Step-by-step explanation:

Jose scored 544 points in his math test.

Jose needs minimum of 650 points to get an A.

Let Jose scores x in the remaining test, n.

Jose needs to score an A. So, to reach 650 points, Jose need to score a minimum of 650 - 544 = 106 points.

Thus the value of x must be greater than of equal to 106, in his remaining test, n, to ensure that Jose gets an A.

⇒ x [tex]\geq[/tex] 106.

Answer:

Correct answers is

[tex] \frac{1}{216} [/tex]

Step-by-step explanation:

Given: The chances of striking the bull's-eye each time of throw =\frac{1}{6}

Since, if we throe dart on dart board , each event will be independent of the other.

Then, If we throw 3 times, what is the probability that we will strike the bull's-eye all 3 times is given by :-

[tex]p(strike \: bulls \: eye \: ) = \frac{1}{6} x \frac{1}{6} x \frac{1}{6} = \frac{1}{216} [/tex]

Hence, the probability that we will strike the bull's-eye all 3 times is 1/216

Answer:

1/216

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

sue your math professor that professor is evil

Answer:

75%

Step-by-step explanation:

Here, we are asked to calculate the percentage of a trip that has been completed by Leigh.

Firstly, we identify the total length of the trip, this is 1470km. She stopped 370km from her destination. The length of the distance traveled is 1470km - 370km = 1100km

Now we proceed to calculate what percentage of the journey is this.

We calculate this by placing it over the total length multiplied by 100%

That would be

1100/1470 * 100 = 74.82 approximately 75%

Answer:

Net worth is defined as:

Assets - Liabilities.

Assets are what you own.

Liabilities are what you have to pay.

So, home + truck + investments are assets.

Likewise, mortgage + student loans + credit cards are liabilities.

Doing the math, Susan's net worth is

Assets - Liabilities

$143,392.90 - $98,077.12 =

$45,315.78

Susan's net worth is $45,315.78

Good luck!

Susan's net worth is calculated by subtracting her total liabilities (mortgage, student loans, and credit card debt) from her total assets (home, truck, and investments). Therefore, Susan's net worth is $45,315.78.

The question is about calculating Susan's net worth. Net worth is calculated by subtracting the total liabilities from total assets. In Susan's case, her assets include her house, truck, and investments, which total to $143,392.90 ($128,318.74 for the house, $10,615.00 for the truck, and $4,459.16 for her investments). Her liabilities include her mortgage, student loans, and credit card debt, which sums up to $98,077.12 ($93,987.74 for the mortgage, $2,874.46 for the student loans, and $1,214.92 for the credit card debt). To calculate Susan's net worth, subtract total liabilities from total assets. Therefore, Susan's net worth is $45,315.78 ($143,392.90 - $98,077.12).

https://brainly.com/question/36453917

#SPJ12

Answer:

[tex]11[/tex]

Step-by-step explanation:

[tex] \frac{90}{360} \times 2 \times \pi \times 7 \\ \frac{1}{4} \times 2 \times \frac{22}{7} \times 7 \\ = 11[/tex]

Answer:

11

Step-by-step explanation:

[tex] = \frac{1}{2} \pi \: r \\ = \frac{1}{2} \times \frac{22}{7} \times 7 \\ = \frac{1}{2} \times 22 \\ = 11[/tex]

Answer:

The system of equations are

x+y=557

[tex]\frac35x+\frac56 y=407[/tex]

The total pages in shorter book is 245

The total pages in longer book is 312

Step-by-step explanation:

Given that,

Scott has read 407 of the total number of 557 pages, which [tex]\frac35[/tex] of the shorter book and [tex]\frac56[/tex] of longer book.

Total number of pages of shorter book be x and longer book be y.

Then,

[tex]\frac35[/tex] page of the shorter book  [tex]=\frac35 x[/tex]

[tex]\frac56[/tex] pages of the longer book = [tex]\frac56y[/tex]

So, he has read [tex]=\frac35x+\frac 56y[/tex]

Total number of pages of both book is = x+y

According to the problem,

x+y=557.........(1)

[tex]\frac35x+\frac56 y=407[/tex].......(2)

We can write equation (2) as

[tex]\frac35x+\frac56 y=407[/tex]

[tex]\Rightarrow \frac{18x+25y}{30}=407[/tex]

[tex]\Rightarrow {18x+25y}=407\times 30[/tex]

[tex]\Rightarrow {18x+25y}=12,210[/tex]......(3)

Now 18 times of equation (1) subtract from equation (3)

   18x+25y=12210

   18x+18y=10026

-        -        -

_______________

        25y-18y=12,210-10,026

     ⇒7y=2,184

     [tex]\Rightarrow y=\frac{2184}{7}[/tex]

     ⇒y= 312

Plug y=312 in equation (1)

x+312=557

⇒x=557-312

⇒x=245

The total pages in shorter book is 245

The total pages in longer book is 312

The system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is

3 / 5 x + 5 / 6 y = 407

x + y = 557

Scott has read 407 of the total number of 557 pages, which is  3 / 5 of the shorter book and 5 / 6 of longer book.

x = number of pages in the shorter book

y = number of pages in the longer book

Therefore, the system of equation that can be used to determine the total number of pages in the shorter book x, and the total number of pages in the longer book, y is as follows;

3 / 5 x + 5 / 6 y = 407

x + y = 557

learn more on system of equation here: https://brainly.com/question/27631842

#SPJ5

Answer:

3.49

Step-by-step explanation:

5-1.51=3.49

Answer:

3.49 meters long

Step-by-step explanation:

5-1.51 = 3.49

- If you need this further explained please let me know. I would be glad to help.

Answer:

-5

Step-by-step explanation:

The minimum is at the vertex.  This is at (1, -5)

The minimum value is -5

Answer:

2.54648 ft

Step-by-step explanation:

r = 8/π (ft.) Therefore, the radius of the circle when its circumference is 16 feet is r ≈ 2.54648 ft. C = 2 (3.14159) (2.54648) ft :)

Answer:

  5 1/4

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by its inverse.

  (3 3/4)/(5/7) = (15/4)/(5/7) = (15/4)·(7/5) = 21/4 = 5 1/4

_____

Many graphing calculators (and some scientific calculators) will do this mixed-number arithmetic for you.

Answer:

The area of frame is 180 square meters.

Step-by-step explanation:

We are given the following in the question:

Dimension of rectangular painting:

Length, l = 20 cm

Width, w = 16 cm

Dimension of frame:

Length, L = 25 cm

Width, W = 20 cm

We have to find the area of frame.

Area of rectangle =

[tex]A = l\times w[/tex]

Area of frame =

[tex]A-a\\=(L\times W)-(l\times w)\\=(25\times 20)-(20\times 16)\\=180\text{ square meters}[/tex]

Thus, the area of frame is 180 square meters.

Answer: They must hire 12 Counselors and 18 Aides

Step-by-step explanation: The most important factor here is the fact that they need to minimize hiring costs. The math camp can afford to hire up to 45 members of staff and can as well run properly with 30 members of staff.

The camp must have at least 10 aides (simply put, any number above 10 will do). Also they may have up to 3 aides for every 2 counselors, that is the ratio of counselor to aide has been given as;

2 : 3

If the math camp decides to hire the minimum required in order to minimize cost, they would be hiring 30, and that would be divided according to the following ratio;

(Counselor):

30 x 2/5 = 12

(Aide):

30 x 3/5 = 18

Hence they would be hiring 12 counselors at a cost of

2400 x 12 = 28800

And 18 Aides at a cost of

1100 x 18 = 19800

Therefore the total (minimum) cost of hiring staff is $48,600

The problem is a mathematical optimization problem, solved using systems of inequalities. The camp's optimal hiring strategy can be obtained by satisfying a set of constraints and minimizing a cost function.

This problem can be solved using systems of inequalities in mathematics. Let's let C represent the number of counselors and A represent the number of aides. Here are the constraints you need to consider:

Also, keep in mind that the camp wants to minimize costs, and the average monthly salary is $2400 for counselors and $1100 for aides, so you need to minimize the total cost function: 2400C + 1100A. By solving this system of inequalities and minimizing the cost function, the camp will have an optimal hiring strategy.

https://brainly.com/question/32199704

#SPJ3

Final answer:

After converting the chain length from feet to inches, Tony will have 6 inches of gold chain left after making three necklaces, each requiring 16-inch pieces.

Explanation:

Tony needs to determine how much gold chain he will have left after making three necklaces, each requiring 16-inch pieces. First, we need to convert the total chain length from feet to inches. Since 1 foot equals 12 inches, 4.5 feet would be 4.5 × 12 inches, which equals 54 inches. Now, we can calculate the total length of chain needed for the necklaces by multiplying the length of one necklace (16 inches) by the number of necklaces (3), which is 16 × 3 = 48 inches.

Subtracting the total chain used for the necklaces (48 inches) from the total length of chain available (54 inches) gives us the remaining length of chain. So, 54 inches - 48 inches = 6 inches of chain leftover after making the three necklaces.

Answer:

False.

Step-by-step explanation:

it is an angle formed by 2 adjacent sides inside the polygon.

Answer:

False

Step-by-step explanation:

Interior angle is formed by 2 adjacent sides

Answer:

452 cm^3

Step-by-step explanation:

The volume of a cilinder is [tex]\pi (radius^{2})(height)[/tex]

The diameter of the cup is 8cm, the formula of the radius is [tex]\frac{diameter}{2}[/tex]

So the radius would be [tex]\frac{8}{2}[/tex] = 4cm

We change variables in the formula of the volume [tex]\pi(4^{2})(9)[/tex] = 144[tex]\pi[/tex] = 452cm^3

Answer:

i needed the same thing woa

Answer:

the tires are 42 dolars

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

25% × 56 =

(25 ÷ 100) × 56 =

(25 × 56) ÷ 100 =

1,400 ÷ 100 =

14

Answer:

[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]  

[tex]p_v =P(z<-0.309)=0.379[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=115 represent the adults with the medication was effective

[tex]\hat p=\frac{115}{180}=0.639[/tex] estimated proportion of adults with the medication was effective

[tex]p_o=0.65[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:  

Null hypothesis:[tex]p \geq 0.65[/tex]  

Alternative hypothesis:[tex]p < 0.65[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

[tex]p_v =P(z<-0.309)=0.379[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Answer:

H0: p = 0.65

Ha: p < 0.65

Sample proportion  = 115 / 180 = 0.6389

Test statistics

z =  - p / sqrt( p( 1 -p ) / n)

= 0.6389 - 0.65 / sqrt ( 0.65 * 0.35 / 180)

= -0.31

Critical value at 0.05 level = -1.645

Since test statistics falls in non-rejection region, do not reject H0.

We conclude at 0.05 level that we fail to support the claim.

Step-by-step explanation:

Answer:

A. [tex]h(x) = 3^{x+1}[/tex]

Step-by-step explanation:

Stretching means that original function is multiplied by a constant, which is equal to 3 in this case:

[tex]h(x) = 3 \cdot g (x)[/tex]

[tex]h(x) = 3\cdot 3^{x}[/tex]

[tex]h(x) = 3^{x+1}[/tex]

The answer is A.

Answer:

A

Step-by-step explanation:

Answer:

3/20 of the students play soccer

Step-by-step explanation:

1. Divide the amount of students that play sports, 3/4 by the amount of those that play soccer, 1/5

2. 3/4 divided by 1/5= 3/20

Answer:

3/20

Step-by-step explanation:

Answer:

No real Solution

Step-by-step explanation:

Plug a=14, b=9, and c=10 into the quadratic formula, and you'll get

[tex]x=(-(9)±\sqrt{-479})/ 28[/tex]

since -479 is negative, you'll get an imaginary number.

Answer:

0.75 is the probability of selecting a CD that is not comedy.

Step-by-step explanation:

We are given the following in the question:

Number of comedy CD = 4

Number of science CD = 5

Number of adventure CD = 7

Total number of CD,n = 16

We have to find the probability for selecting a random CD that is not comedy.

Formula:

[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]

P( Non-Comedy CD) =

[tex]=\dfrac{\text{n(Non-Comedy)}}{n}\\\\=\dfrac{5+7}{16} = \dfrac{12}{16}=\dfrac{3}{4}= 0.75 = 75\%[/tex]

Thus, 0.75 is the probability of selecting a CD that is not comedy.