Factor each trinomial completely.
4x^2 - 25b^2 and x^2 - 81

Answer:

take the square root of both sides

Step-by-step explanation:

Answer:

The correct first step is to factor x^2-10+3x.

Step-by-step explanation:

x^2−10+3x=0 (move all the terms to one side)

(x−2)(x+5)=0 (factor)

x=2,−5 (solve for x)

Answer:

$13.299 million

Step-by-step explanation:

We need the model from Part A to answer Part B to three decimal places,

The point marked by the blue arrow is clearly an outlier. I ignored it in "eyeballing" the best-fit line.

My line has four points above and five points below the line,

You probably had to use a statistical calculator to get the equation for the line of best fit.

Assume it was

y = 38.9016 - 0.7951x

You would use that equation to predict y when x = 32.2.

y = 38.9016 - 0.7951 × 32.2 = 39.1588 - 25.6022 = 13.299

If a movie brought in $32.2 million on opening night in Tallahassee, it should bring in $13.299 million in Gainesville.

The  expected revenue be for Gainesville is $13.299 million.

here we assume that

y = 38.9016 - 0.7951x

Here that equation to predict y

when x = 32.2.

So,

y = 38.9016 - 0.7951 × 32.2

= 39.1588 - 25.6022

= 13.299

hence, The  expected revenue be for Gainesville is $13.299 million.

Learn more about an equation here: https://brainly.com/question/24595872

Answer:

It goes in order of odds.

Step-by-step explanation:

2+3=5

5+5=10

10+7=17

17+9=26

and so on.

Answer:

D) Add 1 to the term number squared

Step-by-step explanation:

i got it right on edg2021

Answer:

No

Step-by-step explanation:

Step 1:  Determine if linear

It is not linear because it has the x variable to the second power which makes the line bend and turns into a parabola.  A linear line would have the x to the first power or just x.

Answer: No

Graph Below

Answer:

0.3478

Step-by-step explanation:

Given:-

- The number of sophomore, S = 150

- The sophomore and had summer internship, x = 80

- The number of juniors, J = 200

- The junior and had summer internship, y = 150

Find:-

What is the probability that the person is a sophomore given that the person had a summer internship?

Solution:-

- The total sum of sophomore and junior students is N:

                         N = S + J

                         N = 150 + 200

                         N = 350 students.

- We will denote event A as random selection of sophomore from total.

- We will denote event B as random selection of student who had summer internship.

- We are to determine the conditional probability that a person selected is sophomore given that the person had a summer internship. That is the probability of event A given that event B has already occured.

- The conditional probability can be written as:

                        P ( A / B ) = P ( A & B ) / P ( B )

Where,

        P ( A & B ) : The probability the person is a sophomore and had a summer internship.

        P ( B ): The probability that the person selected had a summer internship.

                      P ( A & B ) = x / N

                                        = 80 / 350

                                        = 0.22857143

                     P ( B ) = ( x + y ) / N

                               = ( 80 + 150 ) / 350 = 230/350

                               = 0.65714286

Therefore the required probability is:

                     P ( A / B ) = 0.22857143 / 0.65714286

                                      = 0.3478  ... Answer

Answer:

8/23

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because area = L x w

8 x 10 = 80

C

Answer:

A=80

Step-by-step explanation:

You find the area of rectangle using Length times width. 8 times 10 =80

The decimal 0.5 is equal to the fraction 1/2. To find this answer, you first look at the place value of the decimal. 0.5 is read as 'five tenths'

Answer:

50/100

Step-by-step explanation:

.5 is also known as 1/2 so if you think about 100 50 is half of 1 hundred.

Answer:

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

you take 18-12 wich gives you 6, then you do 18+6 wich equals 24. hope this helps. good luck in the future :)

Answer:

6

Step-by-step explanation:

Answer:

the theoretical probability is 1/5.

the experimental probability is 3/10.

chances are the experimental probobility will approach the theoretical probobility.

Step-by-step explanation:

since blue is one of five equal sizes, the probobility that it will land on blue is 1/5.

the expiromental probobility is the number of times it landed on blue devided by the number of spins. 15/50. this can be simplified by pulling out a 5, leaving us with 3/10.

last it stands to reason that the more times the spinner is spun the closer the experimental probability will model the theoretical probability.

Answer:

[tex]f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2} [/tex]

Step-by-step explanation:

The given quadratic functions are:

[tex]f(x) = - 0.5 {x}^{2} [/tex]

[tex]f(x) = 14 {x}^{2} [/tex]

[tex]f(x) = {x}^{2} [/tex]

We want to order these functions, from the widest to the narrowest.

How wide the graph will open depends on the absolute value of the coefficient of the function.

The smaller the absolute value of the coefficient, the wider the graph.

Since

[tex] | - 0.5| \: < \: |1| \: < \: |4| [/tex]

Therefore from the widest graph to the narrowest graph, we have:

[tex]f(x) = - 0.5 {x}^{2} \to \: f(x) = {x}^{2} \to \: f(x) = 14 {x}^{2} [/tex]

Answer:

She could divide 9.42 by Pi to find the radius, then multiply 9.42 by the radius.

(Last option)

Step-by-step explanation:

We need the formula for the area of a circle:

A = πr²

Remember r² = r × r

So you could rewrite the formula like this:

A = π × r × r

If π × r = 9.42, then the area becomes:

A = 9.42 × r

"Then multiply 9.42 by the radius".

To find "r", divide 9.42 by π.

π × r = 9.42

r = 9.42/π

"Divide 9.42 by Pi to find the radius".

Answer: The answer is the last one

Step-by-step explanation:

Answer:

3.5 Gallons Per Minute or 3.5m

Step-by-step explanation:

Since there is 10.5 Gallons in 3 minutes, do

10.5/3 = 3.5

(please mark brainliest if this helps!)

Final answer:

The flow rate from the faucet is 3.5 gallons per minute. To determine the amount of water that comes out in any number of minutes, we multiply the flow rate by the number of minutes desired.

Explanation:

Given that 10.5 gallons of water are dispensed in three minutes, we can calculate the rate of flow, which will allow us to determine how many gallons of water would come out of the faucet in any other number of minutes.

We start by finding the flow rate per minute by simply dividing the volume of water dispensed by the number of minutes it took. So, the flow rate is 10.5 gallons / 3 minutes = 3.5 gallons per minute. Now, to find out how many gallons flow in any number of minutes, we multiply the flow rate (3.5 gallons per minute) by the number of minutes.

For example, if we want to know how much water comes out in 5 minutes, we calculate it as follows: Flow rate x Time = 3.5 gallons/minute x 5 minutes = 17.5 gallons. Therefore, 17.5 gallons of water would come out of the faucet in 5 minutes.

The congruent relationship between the triangles are;

10. ΔABC ≅ ΔDBC, SSS congruence rule

11. ΔABD ≅ ΔDBC, ASA congruence rule

12. ΔABC ≅ ΔDCB, SSS congruence rule

13. ΔABC ≅ ΔEDC, SAS congruence rule

14. ΔABC ≅ ΔDCB,  SAS congruence rule

15. ΔABC ≅ ΔDCB, SAS congruence rule

16. ΔABC ≅ ΔDBC, ASA congruence rule

17. ΔABC ≅ ΔEDC, LH congruence rule

18. ΔBAC ≅ ΔCDB, SSS, congruence rule

Congruent triangles have the same size and shape.

10. [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] by the reflexive property, [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CD}[/tex] by the definition of midpoint of [tex]\overline{AD}[/tex], therefore;

ΔABC is congruent to ΔDBC by the Side Side Side, SSS, congruence rule

11. ∠ABC is congruent to ∠DBC (definition of bisected angle)

ΔABD is congruent to ΔDBC by the Angle Side Angle, ASA congruence rule

12. The reflexive property indicates that line segment [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex], therefore; ΔABC is congruent to ΔDCB by the Side Side Side, SSS congruence rule

13. The definition of bisected line segments indicates; [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CE}[/tex] and [tex]\overline{BC}[/tex] is congruent to [tex]\overline{CD}[/tex]

∠ECD is congruent to ∠BCA (Vertical angles theorem)

Therefore, ΔABC is congruent to ΔEDC by the Side Angle Side SAS congruence rule

14. [tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] reflexive property, therefore;

ΔABC is congruent to ΔDCB by the Side Angle Side, SAS, congruence rule

15. The alternate interior angles and a facing side of the quadrilateral ABCD are congruent, the location of the angles and the sides indicates that ABCD is a parallelogram

[tex]\overline{BD}[/tex] is congruent to [tex]\overline{AC}[/tex] (Properties of the facing sides of a parallelogram)

ΔABC is congruent to ΔDCB by the Side Angle Side, SAS, congruence rule

16. [tex]\overline{CB}[/tex] is congruent to [tex]\overline{CB}[/tex] (reflexive property)

∠ACB is congruent to ∠DCB and ∠CBA is congruent to ∠CBD (Definition of bisected angles ∠DCA and ∠DBA)

ΔABC is congruent to ΔDBC by the Angle Side Angle, ASA congruence rule

17. [tex]\overline{AC}[/tex] is congruent to [tex]\overline{CE}[/tex], definition of bisected line segment [tex]\overline{AE}[/tex]

ΔABC is congruent to ΔEDC by the Leg Hypotenuse, LH, congruence rule

18. Quadrilateral ABCD is a parallelogram (Definition of a parallelogram)

[tex]\overline{AC}[/tex] is congruent to [tex]\overline{BD}[/tex] and [tex]\overline{AB}[/tex] is congruent to [tex]\overline{CD}[/tex] (Properties of a parallelogram)

[tex]\overline{BC}[/tex] is congruent to [tex]\overline{BC}[/tex] (Reflexive property)

ΔBAC is congruent to ΔCDB by the Side Side Side, SSS, congruence rule

Learn more on congruence rules here: https://brainly.com/question/21474941

#SPJ3

Final answer:

To find the 95% confidence interval for the average cooking time of a 10 pound turkey given a sample mean of 2.9 hours and a standard deviation of 0.24 hours for 19 turkeys, we calculate using the formula and a t-score of 2.101, resulting in an interval between approximately 2.784 hours to 3.016 hours.

Explanation:

To calculate a 95% confidence interval for the average cooking time of a 10 pound turkey, given the sample mean (μm) is 2.9 hours and the sample standard deviation (s) is .24 hours for a sample size (n) of 19 turkeys, we use the formula for the confidence interval for a mean with unknown population standard deviation (since the population standard deviation is not provided).

The formula for the confidence interval is:

CI = μm ± (t* × (s / √n))

Where t* is the t-score from the t-distribution table corresponding to the desired confidence level (95% in this case) and n - 1 degrees of freedom (19 - 1 = 18).

For 95% confidence with 18 degrees of freedom, the t-score (t*) approximately equals 2.101.

So the confidence interval is calculated as:

CI = 2.9 ± (2.101 × (0.24 / √19))

CI = 2.9 ± (2.101 × 0.055)

CI = 2.9 ± 0.116

Thus, the 95% confidence interval for the average cooking time of a 10 pound turkey is approximately 2.784 hours to 3.016 hours.

The 95% confidence interval for the average cooking time of a 10-pound turkey is 2.792 hours, 3.008 hours

The 95% confidence interval for the average cooking time of a 10-pound turkey is given by: [tex]\[ \bar{x} \pm Z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}} \][/tex]

where:[tex]- \( \bar{x} \)[/tex] is the sample mean,

[tex]- \( Z_{\frac{\alpha}{2}} \)[/tex] is the Z-value corresponding to the desired confidence level,

[tex]- \( \sigma \)[/tex] is the population standard deviation,

[tex]- \( n \)[/tex] is the sample size.

Given:

[tex]- \( \bar{x} = 2.9 \)[/tex] hours,

[tex]- \( \sigma = 0.24 \)[/tex] hours,

[tex]- \( n = 19 \)[/tex],

- Confidence level = 95%.

First, we need to find the Z-value that corresponds to a 95% confidence level. For a 95% confidence interval, the alpha value is 0.05, and since the confidence interval is two-tailed, we divide this by 2 to get [tex]\( \frac{\alpha}{2} = 0.025 \)[/tex]. Looking up the Z-value for a two-tailed test with [tex]\( \alpha = 0.025 \)[/tex] in the standard normal distribution table (or using a Z-table calculator), we find that [tex]\( Z_{\frac{\alpha}{2}} = 1.96 \)[/tex].

Now we can calculate the margin of error (ME):

[tex]\[ ME = Z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}} = 1.96 \times \frac{0.24}{\sqrt{19}} \] \[ ME = 1.96 \times \frac{0.24}{\sqrt{19}} \approx 1.96 \times \frac{0.24}{4.359} \approx 1.96 \times 0.055 \approx 0.108 \][/tex]

Finally, we calculate the confidence interval:

[tex]\[ \text{Lower limit} = \bar{x} - ME = 2.9 - 0.108 \approx 2.792 \] \[ \text{Upper limit} = \bar{x} + ME = 2.9 + 0.108 \approx 3.008 \][/tex]

In LaTeX format, the confidence interval is: [tex]\[ \boxed{(2.792, 3.008)} \][/tex]

Answer:

There are 6 classes we find the median by finding the middle number of the 3rd highest class and 4th highest class, even if this is a decimal.

6/3 = 3+ 0.5

The process would be different if some values are the same values already on the chart total of each class.

ie) 20  31  14  22 20 31

small data like this below you can rearrange

14  20  20  22  31 31  

and see that 21 is the correct value

as there are even numbers, so we choose 20 , 22

and select the middle value = 21

Step-by-step explanation:

If there is an even number of numbers locate the two middle numbers so that there is an equal number of values to the left and to the right of these two numbers. Step 3: If there is an odd number of numbers, this middle number is the median. If there is an even number of numbers add the two middles and divide by 2.

Answer:

The answer is in the photo ˚∆˚

Step-by-step explanation:

Answer:

1. ∠ O

2. ∠ QOP

3. ∠ POQ

Step-by-step explanation:

Answer:

W = 72

Step by step explanation:

White = W

Red = R

W + R = 90

Write an equation

W = 5R - 6

Substitute

5R - 6 = 90

Add 6 to both sides of the equation

5R = 90

Simplify

90 ÷ 5 = 18

R = 18

90 - 18 = W

W = 72

Hope this was useful to you!

Final answer:

By setting up an algebraic equation, we determine that there are 74 white marbles in the bag when the total number of marbles is 90 and the white marbles count is 5 times the number of red marbles minus 6.

Explanation:

Calculating the Number of Marbles

To figure out how many white marbles are in the bag, we can set up a simple algebraic equation. Let's define the number of red marbles as x. According to the problem, the number of white marbles is 5 times the number of red marbles minus 6. We can represent this as 5x - 6. Since we know the total number of marbles is 90, we can write the equation as:

x + (5x - 6) = 90.

Combining like terms results in:

6x - 6 = 90.

Adding 6 to both sides gives us:

6x = 96.

Dividing both sides by 6, we get:

x = 16.

So, there are 16 red marbles. Now, to find the number of white marbles, we plug this back into the equation for white marbles:

5(16) - 6 = 80 - 6 = 74.

There are thus 74 white marbles in the bag.

Answer:

w= 3.4

Step-by-step explanation:

.6+w=4

in order to solve for w you have to subtract.6 from both sides leaving w to equal 3.4

W=3.4

Answer:

C

Step-by-step explanation:

i got it right

Answer:

C

Step-by-step explanation:

Edge 2021 assignment:)

Answer:

12/10, 18/15?

Step-by-step explanation:

There are multiple fractions equivalent to it, if you keep multiplying forever, but the simplest are

1 1/5 and 12/10

Answer:

D. 1,350

Step-by-step explanation:

150x3= 450

450+900=1,350

Answer:

2

Step-by-step explanation:

2 for $1

6 for $15

15/6 = 2.5

1/2 = 0.5

Baseball = 1 for $0.5

Basketball = 1 for $2.5

2.5 - 0.5 = 2

Answer:£368.94

Step-by-step explanation:

258*1.43= 368.94

1) The measure needed is the C. Base area,  2) the scenario represents the equation D. 10.5= (1/3)B (4.5)

and 3) the tent will cover C. 7 square feet of the back porch.

Use the appropriate formulas to solve it step-by-step.

The formula for the volume of a cone is:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]

We need to find the base area of the cone (which is a circle) to determine the area covered by the tent on the back porch. The base area (A) of the cone is:

[tex]A = \pi r^2[/tex]

To calculate this, we must first determine the radius (r) of the cone. Let's rearrange the volume formula to solve for the radius (r):

[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]

Simplifying this equation, we get:

[tex]10.5 = \frac{1}{3} \pi r^2 4.5[/tex]

Multiply both sides by 3 to get rid of the fraction:

[tex]31.5 = \pi r^2 4.5[/tex]

Divide both sides by 4.5:

[tex]\frac{31.5}{4.5} = \pi r^2[/tex]

[tex]7 = \pi r^2[/tex]

Divide both sides by π:

[tex]r^2 = \frac{7}{\pi}[/tex]

Taking the square root of both sides, we find the radius (r):

[tex]r = \sqrt{\frac{7}{\pi}}[/tex]

Now we can calculate the base area (A) of the cone:

[tex]A = \pi r^2[/tex]

Substitute r^2 back into the equation:

[tex]A = \pi \left( \frac{7}{\pi} \right) = 7 \text{ square feet}[/tex]

Answer:

[tex]a. \ P(X=5)=0.2417\\\\b. \ P(X\geq 6)=0.3056\\\\c. \ P(X<3)=0.2255[/tex]

Step-by-step explanation:

a. This is a binomial probability  distribution problem expressed as:

[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]

Where:

Given n=10, p=0.47 the probability of exactly 5 is calculated as:

[tex]P(X=5)={n\choose x}p^x(1-p)^{n-x}\\\\={10\choose 5}0.47^5(1-0.47)^5\\\\=0.2417[/tex]

Hence, the probability that exactly 5 adults have very little confidence is 0.2417

b. Given n=10, p=0.47,

-We substitute our values in formula and  the probability of at least 6 is calculated as:

[tex]P(X\geq 6)={n\choose x}p^x(1-p)^{n-x}\\\\\\\ \ \ \ \ \ ={10\choose 6}0.47^6(0.53)^4+{10\choose 7}0.47^7(0.53)^3+{10\choose 8}0.47^8(0.53)^2+{10\choose 9}0.47^9(0.53)^1+{10\choose 10}0.47^{10}(0.53)^0\\\\\\=0.1786+0.0905+0.0301+0.0059+0.0005\\\\\\=0.3056[/tex]

Hence, the probability of at least 6 adults is 0.3056

c. The probability of of less that four adults is calculated as:

[tex]P(X<4)={n\choose x}p^x(1-p)^{n-x}\\\\\\\ \ \ \ \ \ ={10\choose 0}0.47^0(0.53)^{10}+{10\choose 1}0.47^1(0.53)^9+{10\choose 2}0.47^2(0.53)^8+{10\choose 3}0.47^3(0.53)^7\\\\\\=0.0017+0.0155+0.0619+0.1464\\\\\\=0.2255[/tex]

Hence, the probability that less that 4 adults have confidence in the newspapers is 0.2255

The correct probabilities for the given scenarios are:

To solve this problem, we can use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]

(a) For exactly five adults:

[tex]\[ P(X = 5) = \binom{10}{5} (0.47)^5 (0.53)^5 \][/tex]

[tex]\[ P(X = 5) \approx 0.205 \][/tex]

(b) For at least six adults, we sum the probabilities of having six, seven, eight, nine, and ten adults with very little confidence:

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]

[tex]\[ P(X \geq 6) \approx 0.254 \][/tex]

(c) For less than four adults, we sum the probabilities of having zero, one, two, and three adults with very little confidence:

[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]

[tex]\[ P(X < 4) \approx 0.347 \][/tex]

Answer: Part A is the graph with 4 dots for 0, 2 dots for 2, 10 dots for 4, 9 dots for 6, 2 for 7(in between 6 and 8) 1 dot for 8, and 1 dot for 12.

Part B: Answer: Most are clumped together and smaller than 8, with one data point far away from the others.

Part C: Answer; 12 hours seems to much higher than the other data values.

Step-by-step explanation: Hope that helped:) I just did it and checked and it’s correct. Have a good day!