Match the polynomials with their factors. 2a2 + 5a − 3 (a + 1)(2a − 3) 2a2 − a − 3 (a − 1)(2a + 3) 2a2 − 5a − 3 (2a − 1)(a + 3) 2a2 + a − 3 (2a + 1)(a − 3)

AYZ is a right triangle (we're given that YA is perpendicular to XZ). So, we can use the pythagorean theorem to find the missing side:

[tex]YA^2+AZ^2=YZ^2[/tex]

But we're also given [tex]YZ = 2AZ[/tex], so we have

[tex]YA^2+AZ^2=(2AZ)^2=4AZ^2[/tex]

Since AZ is half of YZ, which is 10, we deduce AZ=5.

Solving for YA, we have

[tex]YA^2+AZ^2=4AZ^2 \iff YA^2 = 3AZ^2 \iff YA = AZ\sqrt{3} = 5\sqrt{3}[/tex]

Answer:

[tex]\large\boxed{(x-4)^2+(y+3)^2=25}[/tex]

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (4, -3) and the point on the circle (9, -3).

The length of radius is equal to the distance between a center and an any point on a circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Susbtitute:

[tex]r=\sqrt{(9-4)^2+(-3-(-3))^2}=\sqrt{5^2+0^2}=\sqrt{5^2}=5[/tex]

The center (4, -3) → h = 4, k = -3.

Finally we have:

[tex](x-4)^2+(y-(-3))^2=5^2\\\\(x-4)^2+(y+3)^2=25[/tex]

Answer:

Each CD would be $10.99

Step-by-step explanation:

$48.96-5.00=43.96

43.96/4= 10.99

Answer:

The answer is $12.24 each CD. I just did this for my assessment. Looks like we are in the same online school program :D

Step-by-step explanation:

$48.96/4 = $12.24

you can check your answer by doing

$12.24 x 4

Answer:

Step-by-step explanation:

ax^2+bx+c

-b +- sqaure root of b^2 -4ac/2a

-2 +- square root (2)^2-4(2)(-1)/2(2)

-2 +- square root 4+8 /4

-2 +- 2 square root 3 /4

reduce

-1 +- square root 3/2

Answer:

[tex]\large\boxed{x=\dfrac{-1-\sqrt3}{2}\ or\ x=\dfrac{-1+\sqrt3}{2}}[/tex]

Step-by-step explanation:

The quadratic formula of a quadratic equation:

[tex]ax^2+bx+c=0[/tex]

Discriminant of a Quadratic is [tex]\Delta=b^2-4ac[/tex]

If Δ < 0, then an equation has no real solution (has two complex solutions)

If Δ = 0, then an equation has one real solution [tex]x=\dfrac{-b}{2a}[/tex]

If Δ >0, then an equation has two real solutions [tex]x=\dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

==========================================

We have the equation:

[tex]2x^2+2x-1=0\\\\a=2,\ b=2,\ c=-1[/tex]

Substitute:

[tex]\Delta=2^2-4(2)(-1)=4+8=12>0\\\\\sqrt\Delta=\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3[/tex]

[tex]x=\dfrac{-2\pm2\sqrt3}{(2)(2)}=\dfrac{-2\pm2\sqrt3}{4}[/tex]    simplify by 2

[tex]x=\dfrac{-1\pm\sqrt3}{2}[/tex]

Answer:

1?

Step-by-step explanation:

Answer:

The answer is i

Step-by-step explanation:

[tex] \sqrt{ - 1} = i[/tex]

Answer:

Negatively skewed.

Step-by-step explanation:

In a negatively skewed distribution, the mode is greater then the median, and the median is greater then the mean. Overall, the majority of the data is to the right, which means that the distribution of data is skewed to the left, or negatively skewed.

Answer: Hence, Option 'C' is correct.

Step-by-step explanation:

As we know that if one tail is longer than the other, the distribution is said to be skewed.

And there are two types of skewed  distribution :

1) Negatively skewed

2) Positively skewed

It depends on the direction of the long tail.

If the long tail is to the right , then it is said to be positively skewed distribution.

If the long tail is to the left , then it is said to be negatively skewed distribution.

According to question, the distribution  here is a positively skewed distribution.

Hence, Option 'C' is correct.

Answer: it’s 506

Step-by-step explanation:

The number of cannonballs in the stack exists at 650. Since the stack is in the formation of the square pyramid the total number of balls can be acquired by utilizing the formula for discovering the total number of spheres in the square pyramid.

Find the number of cannonballs in the stack:

Given that the pyramid stands a square pyramid and the numeral of balls that form the side of the square exists 12.

By utilizing the formula of a square pyramid,

n(n+1)(2n+1)/6

12(12+1)(2(12)+1)/6

12(13)(25)/6

2*13*25

=650

Therefore the number of cannonballs in the stack exists at 650.

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Answer:

82

Step-by-step explanation:

49 - 3 + 72/2

= 46 + 36

= 82

For this case we must find the value of the following expression:

[tex]7 ^ 2[/tex]-3 + 9 * 8÷2 =

According to the PEMDAS algebraic order of operations:

P: Perform any calculation within parentheses

E: Simplify any exponential expressions.

MD: Do all the multiplications and divisions, from left to right, as they appear.

AS: Do all the addition and subtraction, from left to right, as they appear.

So:

49-3 + 9 * 8÷2 =

49-3 + 72÷2 =

49-3 + 36 =

46 + 36 =

82

ANswer:

82

Answer:

.72 or .73 which ever one is on your sheet

Step-by-step explanation:

Answer:

0.72 or 0.73

Step-by-step explanation:

8/11 expressed as a decimal is 0.72 or 0.73

Answer:

A because they are opposites.

Step-by-step explanation:

They equal the same they are just swapped the 2 set of numbers are the same but the first set of numbers are different when you add them they become the same number in the end :) hope this helps

B. Addition Property of Equality justified the statement,

"If WX=YZ, then WX+RS=YZ+RS".

Facts regarding any two or more quantities connected by the equal sign are known as properties of equality.

There are four types of properties of equality.

Addition property, when two equal quantities are increased by a common value, the equality is preserved.

Transitive property of equality, entities that are equivalent to one another are also equivalent to one another.

Subtraction property, equality is maintained when a common term is subtracted from two equal terms.

Multiplying by a common term do not alter the equality, according to the multiplication property of equality.

Given, An equation WX = YZ, Now, In this expression WX + RS = YZ + RS

We have added RS to both side of the equation to maintain the equality sign.

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Answer: Option A

A. 0.98

Step-by-step explanation:

Plan A consists of:

Plan A: treat with antibiotics 1. If not effective, treat with antibiotics 2

Antibiotic 1 has a probability P (1) of 0.8 to be effective

Antibiotic 2 has a probability P (2) of 0.9 to be effective.

For a patient to be treated successfully with plan A it can happen that:

The antibiotic 1 works, or that the antibiotic 1 does not work but the 2 antibiotic if it works.

So the probability that plan A works is:

[tex]P = P (1) + P (not\ 1) P (2)\\\\P = 0.8 + (1-0.8) (0.9)\\\\P = 0.8 + 0.2 * 0.9\\\\P = 0.98[/tex]

The probability of a patient being successfully treated under plan A, which involves treatment with antibiotic 1 and then antibiotic 2 if the first fails, is 0.98, or 98%.

The probability that a patient treated under plan A will be successfully treated is calculated by summing the probabilities of success in each step. Initially, the patient is treated with antibiotic 1 which has an 80% success rate. If this fails (which will happen 20% of the time), then the patient is treated with antibiotic 2 which has a 90% success rate. This 90% will only occur, though, for the remaining 20% of patients who failed the initial treatment. Thus, we calculate this like so: Probability(successful treatment under plan A) = (successful treatment with antibiotic 1) + ((failed treatment with antibiotic 1)*(successful treatment with antibiotic 2)) = 0.8 + (0.2*0.9) = 0.98. Therefore, the probability of successful treatment under plan A equals 98% or 0.98, which corresponds to Choice A.

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Answer:

1 hour

8 min

49 sec

Step-by-step explanation:

we know that

1 m=3.281 ft

1 mi=5,280 ft

Convert 26 mi to ft

26 mi=26*5,280=137,280 ft

Convert 137,280 ft to m

137,280 ft=137,280/3.281=41,840.90 m

using proportion

9.87/100=x/41,840.90

x=41,840.90*(9.87)/100

x=4,129.70 sec

Remember that

1 hour=3,600 sec

1 hour=60 min

1 min=60 sec

4,129.70 sec=4,129.70/3,600= 1.147 h

0.147*60=8.82 min

0.82*60=49 sec

therefore

1 hour

8 min

49 sec

John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.

First, we need to convert John's 100-meter dash time into a pace that can be extrapolated over the marathon distance. Given that John ran a 100-m dash in 9.87 seconds, we need to find out how many meters he runs per second. This would be 100 m / 9.87 s = 10.13 meters per second.

Next, we convert the marathon distance from miles to meters. As there are 5280 feet in a mile and 3.281 feet in a meter, there are 5280 / 3.281 = 1609.34 meters in a mile. The marathon distance is therefore 26 miles * 1609.34 meters/mile = 41842.84 meters.

Using John's pace, we can calculate the time it would take to run the marathon: 41842.84 meters / (10.13 meters/second) = 4129.64 seconds.

Finally, we convert the total seconds to hours, minutes, and seconds. There are 3600 seconds in an hour and 60 seconds in a minute:

Therefore, if John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.

Answer:

- 273

Step-by-step explanation:

The n th term of an arithmetic sequence is

• [tex]a_{n}[/tex] = a₁ + (n - 1)d ← substitute in values

[tex]a_{100}[/tex] = 222 + (99 × - 5 ) = 222 - 495 = - 273

Pages Minutes

15 1

45 3

75 5

300 20

600 40

15 x 2= 39

45x 2= 90

75x2=150

30x20=60

600 x 2 = 1,200

There are 2 sides that are 2 x 1 = 2 ft^2 each

2 sides are 1 x 8 = 8 ft^2 each

And 2 sides 2 x 8 = 16 ft^2 each

Total surface area = 2 + 2 +8+ 8 +16 + 16 = 52 ft^2

Answer: [tex]\text{Surface area =}52\text{ ft.}^2[/tex]

Step-by-step explanation:

The surface area of a rectangular prism is given by :-

[tex]S.A.=2(lw+wh+lh)[/tex], where l is length, w is width and h is height of prism.

From the given picture, length =2ft

height = 8 ft.

width = 1 ft

Then , the surface area of prism will be :-

[tex]S.A.=2((2)(1)+(1)(8)+(8)(2))\\\\\Rightarrow\ S.A.=2(26)\\\\\Rightarrow\ S.A.=52\text{ ft.}^2[/tex]

Answer:

16-20

Step-by-step explanation:

Mode is the one that happens the most and 16-20 has the highest bar

The mode is in people of age between 16- 20 , Therefore Option B is the answer.

Mode is the measure of central tendency of data , It is the value that is occurring continuously in a data set.

A histogram is given in the question ,

As from the definition mode is the value which is occurring repeatedly in the data , The mode is in people of age between 16- 20 , Therefore Option B is the answer.

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Answer:

see explanation

Step-by-step explanation:

c = a - 2b

  = < 4, 5, 6 > - 2 < 1, 2, 3 > ← multiply each component by 2

  = < 4, 5, 6 > - < 2, 4, 6 >  ← subtract corresponding components

  = < 4 - 2, 5 - 4, 6 - 6 > = < 2, 1, 0 >

| c | = [tex]\sqrt{2^2+1^2+0^2}[/tex] = [tex]\sqrt{4+1+0}[/tex] = [tex]\sqrt{5}[/tex]

-------------------------------------------------------------------------------------------------

sum the product of corresponding components

u.v = (3 × 2) + (- 2 × - 1) + (4 × - 6) = 6 + 2 - 24 = - 16

For part two using what we already know can you figure out the length of the segment?

answer D) 24

Answer:

C = 20.65 + 0.75M

Step-by-step explanation:

Given in the question that,

standard charge by the rental company = S = 16.95 + 0.60M

insurance charge by the rental company = I = 3.70 + 0.15M

Total charge C = S + I

16.95 + 0.60M + 3.70 + 0.15M = C

20.65 + 0.75M = C

So the equation which represent total charge that includes insurance in terms of M is

Answer:

56,994

Step-by-step explanation: multiply the population by 0.02, round it to the nearest whole number, and then multiply that number by 3 and add it onto 53,768

The population of Oak Forest in three years will be approximately 57,091.

To find the population of Oak Forest in three years, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 is 53,768, r is 0.02 (2% as a decimal), and t is 3. Plugging these values into the formula, we get:

P = 53,768 * (1 + 0.02)3

Simplifying the expression inside the parentheses:

P = 53,768 * (1.02)3

Calculating (1.02)3:

P = 53,768 * 1.0604

Calculating the final population:

P ≈ 57,091

Therefore, the population of Oak Forest in three years will be approximately 57,091.

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Answer:

[tex]\large\boxed{D.\ 8x^2-3x+7}[/tex]

Step-by-step explanation:

[tex](2x^2-7x+5)-(-6x^2-4x-2)\\\\=2x^2-7x+5-(-6x^2)-(-4x)-(-2)\\\\=2x^2-7x+5+6x^2+4x+2\qquad\text{combine like terms}\\\\=(2x^2+6x^2)+(-7x+4x)+(5+2)\\\\=8x^2-3x+7[/tex]

Answer:

8x^2-3x+7

Step-by-step explanation:

By simplifying the expression.

Answer:

(a + c, b)

Step-by-step explanation:

First the easy part... the Y-value.

There's an horizontal line where the P is... that line has a point identified (a,b).  So, the Y-value of P is b.

Now the X-value.  

You see that P is a bit right to c, so it's something more than c, but how much?  If you look, P is as right to C as a is to the origin.  Since we know it's a parallelogram, the line that goes from origin to (a,b) is parallel to the one going from C to P.

So the X-value of point P is: c + a

The probability of picking a 7 and then picking a number greater than 7 is [tex]\dfrac{1}{3}[/tex]  or  [tex]0.\overline{3}[/tex].

Probability shows us the chances of an event occurring.

[tex]\bold{Probability =\dfrac{Desired\ Outcome}{Total\ number\ of\ outcomes\ possible}}[/tex]

Now, given that we have already picked three cards. therefore, 7, 8, and 9.

The number of possible outcomes is 3.

[tex]\bold{Probability(7) =\dfrac{Number\ 7(1)}{Total\ number\ of\ outcomes\ possible (3)}= \dfrac{1}{3}}[/tex]

Now, as card seven is already picked up cards 8 and 9 are the only card left.

therefore, the sample size(possible outcomes) was reduced to 2 only.

Also, cards 8 and 9 both are greater than 7, thus the desired outcome is also 2.

Further the probability of the number greater than 7 occurring,

[tex]\bold{Probability(n>7) =\dfrac{cards\ 8\ and\ 9(2)}{Total\ number\ of\ outcomes\ possible (2)}= \dfrac{2}{2} = 1}[/tex]

The probability of picking a 7 and then picking a number greater than 7

= Probability of card 7 occuring x probability of card 8 and 9 occurring

[tex]=\dfrac{1}{3}\times 1[/tex]

[tex]=\dfrac{1}{3}[/tex]

Hence, the probability of picking a 7 and then picking a number greater than 7 is  [tex]\dfrac{1}{3}[/tex]  or  [tex]0.\overline{3}[/tex].

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Answer:

Answer: yes.

Step-by-step explanation:

x: (x1 + x2)/2 = (-3 + 1)/2 = -2/2 = - 1 So far so good.

y: (y1 + y2)/2 = (1 - 4 )/2 = (-3/2) = -1.5

The midpoint is (-1 , - 1.5)

True

Answer:

f(x) = (x − 3)² − 11

Step-by-step explanation:

To convert to vertex form, complete the square.

f(x) = x² − 6x − 2

f(x) = x² − 6x + 9 − 9 − 2

f(x) = (x − 3)² − 11

We need to complete the square: if we add and subtract 11 from the expression, we have

[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]

Answer:

B.

• x+2y=-6

• x-2y=-6

Step-by-step explanation:

Try the solution in the equations and choose the set of equations that is true.

___

A. -6+0 ≠ 0 . . . not this system

__

B. -6 +2·0 = -6 . . . true

-6 -2·0 = -6 . . . true . . . . . this system has solution (-6, 0)

__

C. -6 -6·0 ≠ 1 . . . not this system

__

D. 4(-6)+3·0 ≠ -18 . . . not this system

yes, if you do 94/9 you get about 10%. this determines that out of all 94 responses, by dividing it by the 9 people who prefer organic food, you get 10.444 percent which is approximately 10%

The pet store owner's conclusion about her customers' preference for organic pet food is not entirely valid due to the small sample size and potential bias in her survey results. For more accurate conclusions, she should get responses from a larger, more diverse group of customers.

The pet store owner's conclusion is not entirely valid because it is based on the assumption that the 94 responses she received are representative of her entire customer base. While 9 out of 94 responses did indicate a preference for organic pet food, this is a small sample size and may not accurately reflect the preferences of all customers. For a more accurate estimate, she would need to collect responses from a larger and more diverse group of customers, to allow the results to be more statistically significant.

A small sample size can lead to inaccuracies or bias in survey results. In addition, because these customers self-selected to respond tot he survey, they may not represent the full spectrum of her customers. This type of bias is known as a self-selection bias.

So, while it's a starting point, further sampling and more robust survey methods would help strengthen the validity of her conclusions about her customers' pet food preferences.

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Answer:

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded.

Step-by-step explanation:

Answer:

4x=45

Step-by-step explanation:

Cross multiply to get a simplified equation.

4/5=9/x

4x=45

x=11.25

Answer:

Step-by-step explanation:

4/5=9/x

cross multiphication

x=9*5/4

x=45/4

Answer:

C

Step-by-step explanation:

Number on top: largest value of k

On the right: the expression for k

Bottom: the first number for k

So,

1. 2³ = 8, but k can not be 3, so it can't be A or B.

2. 8 ÷ 2 = k, which means that the first k should be 4.

So, the answer is C.

Answer:

C

Step-by-step explanation: