Prove that cos²(A-B)-sin²(A+B)=cos2Acos2B

Answer:

B chose b im sure

Step-by-step explanation:

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

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:

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: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

There is six sides die :

So, the number of outcomes will be

1,2,3,4,5,6.

There is a card with numbers :

1,2,3,4,5,6,7,8,9,10.

We need to find the event corresponds to exactly one outcome of the experiment.

According to options:

A)Both numbers are 5s.

So, there is exactly one event regarding both numbers are 5's. i.e. (5,5).

B) Neither number is a 5.

There is more than one event having not a 5.

Like (1,1),(1,2) ..........

C) The sum of the numbers is 3.

It can be (1,2),(2,1).

so, there is having two events regarding the sum of the numbers is 3.

D) One of the numbers is a 3.

It can be (3,1), (3,2), (3,4)......

So, we can see that there is more than one event corresponds to one of the numbers is a 3.

Hence, Option 'A' is correct.

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:

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:

0

Step-by-step explanation:

You can't construct any triangles with those angles. Because when you add all the angles of a triangle, it has to add up to 180. But when we add 50,70, and 100, it equals 220. So you can't construct any triangles.

Hope this helps. (If it does, please mark me brainliest)

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:

Since April 2020 wow

Step-by-step explanation:

Answer:

x^2 + (y-8)^2 = 16

Step-by-step explanation:

1. Start with the formula for a circle:

(x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius

2. Plug in values for the center coordinates and the radius:

(x-0)^2 + (y-8)^2 = 4^2

3. Simplify:

x^2 + (y-8)^2 = 16

Answer:

Step-by-step explanation:

Given p(2) = 14 and p(-3) = 0, according to factor theorem, if a polynomial p(x) is divided by a function x+c where c is a constant, then x+c is said to be a factor of p(x) if p(-c) = 0 i.e if the remainder is zero after the division.

According to the question, it can be seen that p(-3) = 0. This means that the function x+3 is said to be factor if the remainder of the polynomial is zero when divided the polynomial because the reminder leaves zero after division where c = 3

Answer:

70%

Step-by-step explanation:

To solve this problem, you simply divide 7 by 10.

7 ÷ 10 = .7

.7 is the decimal form of 70%. This means that you have a 70% chance of winning this round.

Answer:16x+1 = y

Step-by-step explanation:

2x squared is basically 2x times 2x which is 4x. So now that you eliminated that you have 4x+12x+1 = y . Now you have to group like terms. 4x+12x= 16x. So now you have 16+1 = y.

Answer:

D. 1,350

Step-by-step explanation:

150x3= 450

450+900=1,350

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:

[tex]\frac{72}{96} =\frac{36}{48}=\frac{18}{24} =\frac{9}{12} =\frac{3}{4}[/tex]

Step-by-step explanation:

All are correct, but only the first is unmodified, and probably the one you want to use.

72 is out of the number, so it is on top.

The number is out of 96, so it is on the bottom.

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:

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:

False

Step-by-step explanation:

The downpayment is the first payment you make, an initial deposit.

Answer:

1. ∠ O

2. ∠ QOP

3. ∠ POQ

Step-by-step explanation:

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:

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]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:

C

Step-by-step explanation:

i got it right

Answer:

C

Step-by-step explanation:

Edge 2021 assignment:)

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:

[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:

B, D, E

Step-by-step explanation:

I am assuming that the equation is y = [tex]\frac{1}{3}[/tex] * x and not y = [tex]\frac{1}{3x}[/tex].

Using y = (1/3)x, we can transpose the x, so that now we have y/x = 1/3.

Take note that the given options are in the format of (x, y). You can simply plug all the values, and whichever gave you a result of 1/3 is your answer.

B.) 2/6 = 1/3

D.) 5/15 = 1/3

E.) -1/-3 = 1/3

The ordered pairs that satisfy the equation y = 1/3x are B (6,2), D (15,5), and E (-3,-1). Ordered pairs are verified by substituting the x-value into the equation to see if the resulting y-value matches the pair.

To determine which ordered pairs satisfy the given linear equation y = 1/3x, we need to substitute the x-value of each ordered pair into the equation to see if the corresponding y-value is correct.

So the ordered pairs that satisfy the equation y = 1/3x are B (6,2), D (15,5), and E (-3,-1).

https://brainly.com/question/14107548

#SPJ2

Answer:

6

Step-by-step explanation: