Is a quadrilateral a square?

The measure of the angle ∠P is given by the law of sines and ∠P = 46°

Given data ,

Let the triangle be represented as ΔMNP

Now , the measure of side MP = 46

The measure of side MN = 34

And , the measure of ∠MNP = 78°

Now , from the law of sines , we get

So , a / sin A = b / sin B = c / sin C

On simplifying , we get

34 / sin P = 46 / sin 78°

Multiply by sin P on both sides , we get

sin P ( 46 / 0.97814760073 ) = 34

sin P = 0.72297866

Taking inverse on both sides , we get

sin⁻¹ ( 0.72297866 ) = 46.30°

Hence , the measure of angle is P = 46°

To learn more about law of sines click :

https://brainly.com/question/13098194

#SPJ1

The standards that use 2.4 GHz are:

A wifi standard defines two characteristics of the wi-fi network, which are speed and frequency.

Such that there are two common frequencies, 2.4 GHz (usually with larger speed) and 5 GHz (usually with lower speed)

The standards that use 2.4 GHz are:

If you want to learn more about wifi:

https://brainly.com/question/6947486

#SPJ11

Answer: C

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the smaller triangle is the larger triangle divided by 4 so 16÷4 is 4.

Answer:

uuuummmmmm go to khanacademy but i think 140

Step-by-step explanation:

Answer:

Sentence Fram: I found x-intercept by substitute y by 0 and I found y-intercept by substitute x by 0

x-intercept = (6, 0), y-intercept = (0, -3) ⇒ C

Step-by-step explanation:

∵ The equation of the graph is 6x - 12y = 36

→ Equate y by 0 to find x

∵ y = 0

∴ 6x - 12(0) = 36

∴ 6x - 0 = 36

∴ 6x = 36

→ Divide both sides by 6 to find x

∴ x = 6

∴ The x-intercept = (6, 0)

→ Equate x by 0 to find y

∵ x = 0

∴ 6(0) - 12y = 36

∴ 0 - 12y = 36

∴ -12y = 36

→ Divide both sides by -12 to find y

∴ y = -3

∴ The y-intercept = (0, -3)

∴ Sentence Fram: I found x-intercept by substitute y by 0 and I found

   y-intercept by substitute x by 0

∴ x-intercept = (6, 0), y-intercept = (0, -3)

The translated formula is 59 = 23 + v, where v represents Vidya's height.

To translate the sentence "59 is the sum of 23 and Vidya's height" into an equation using the variable v to represent Vidya's height, we can use the following formula:

59 = 23 + v

Here, we are saying that the number 59 is equal to the sum of 23 and Vidya's height (which we are representing with the variable v).

To summarize, we can say that we have translated the given sentence into an equation using the formula 59 = 23 + v, where v represents Vidya's height.

What is the mathematical variable?

a symbol (often a letter) used in algebra to represent a variable with an undetermined numerical value. The following variables are frequently used: t (time), r (radius), s (arc length), x and y (real-number unknowns), and z (complex-number unknowns).

For more questions on equation

https://brainly.com/question/29174899

#SPJ8

Evaluated value of the given integral -x^2021(1/2022)cos(x^2022) + (1/2022)sin(x^2022) + C

To evaluate ∫x^2021sin(x^2022)dx, we can use substitution.

Let u = x^2022, then du/dx = 2022x^2021, which implies dx
u = x^2021 (du = 2021x^2020 dx)
dv = sin(x^2022) dx (v = -(1/2022)cos(x^2022))

Integration by parts formula:

∫udv = uv - ∫vdu

So, ∫x^2021sin(x^2022)dx = -x^2021(1/2022)cos(x^2022) + (1/2022)∫2021x^2020cos(x^2022)dx

Now, let w = x^2022. Then, dw = 2022x^2021 dx.

The integral becomes:

(1/2022)∫2021x^2020cos(x^2022)dx = (1/2022)∫cos(w)dw

Integrating cos(w) with respect to w, we get:

(1/2022)∫cos(w)dw = (1/2022)sin(w) + C

Substituting w back:

(1/2022)sin(x^2022) + C

Now, combine the two parts:

-x^2021(1/2022)cos(x^2022) + (1/2022)sin(x^2022) + C

So, the final answer is:

-x^2021(1/2022)cos(x^2022) + (1/2022)sin(x^2022) + C

Visit here to learn more about indefinite integral:

brainly.com/question/30721617

#SPJ11

Answer:

54 inches

Step-by-step explanation:

To find the surface area you have to multiply the base x height

Base: 9in

Height: 6in

9x6=54 inches

The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

Learn more about ratio here

https://brainly.com/question/13419413

#SPJ4

The Confidence interval for the mean is (491.7, 480.3), rounding all values to the nearest tenth.

A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.

Given:

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating from high school seniors.

The study examined the scores of a random sample of 223 graduating seniors and found the mean score to be 486 with a standard deviation of 89.

\(\bar x\) = 486, z = 0.95, s = 89 and n = 223

So,

The confidence interval,

= \(\bar x\) ± z(s/√n)

= 486 ± (0.95)(89/√223)

= 486 ± 5.61

= (491.67, 480.33)

Therefore, the confidence interval is (491.67, 480.33).

To learn more about the confidence interval;

https://brainly.com/question/24131141

#SPJ1

Answer:

The amount of initial investment was $3,949.60.

Step-by-step explanation:

Since Jimmy invests a sum of money in a savings account with a fixed annual interest rate of 3% compounded 10 times per year, and after 10 years, the balance reaches $ 5,329, to determine what was the amount of initial investment, the following calculation has to be done:

X x (1 + 0.03 / 10) ^ 10x10 = 5,329

X x 1.003 ^ 100 = 5,329

X x 1.3492 = 5,329

X = 5,329 / 1.3492

X = 3,949.60

Therefore, the amount of initial investment was $3,949.60.

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

for such more questions on matrix

https://brainly.com/question/1279486

#SPJ8

Answer:

the answer is 16

Answer:16

Step-by-step explanation: im not sure to be honest

Answer:

You will only be able  to go 29 months

Step-by-step explanation:

To calculate the amount of carpentry needed for your bedroom, you should find the area of the bedroom. The answer is A. Area.

When we talk about the amount of carpentry required for a room, we are talking about the number of square feet that need to be covered with carpet. As a result, we'll need to calculate the area of the room to figure out how much carpet we'll need.The area is the amount of space that a two-dimensional object takes up. To calculate the area of a rectangle, multiply the length by the width. The formula for calculating the area of a rectangle is:A = l × wWhere A is the area, l is the length, and w is the width of the rectangle.

For example, if the length of your room is 10 feet and the width is 12 feet, the area of your room will be: A = 10 × 12

= 120 square feet.

To calculate the amount of carpentry needed for your bedroom, you should find the area of the room by multiplying the length by the width.

To know more about area, visit

https://brainly.com/question/1631786

#SPJ11

Answer:

72w + 81x - 90

Step-by-step explanation:

9(8w + 9x – 10)

9 * 8w = 72w

9 * 9x = 81x

9(-10) = -90

Combined:

72w + 81x - 90

Answer:

D

Step-by-step explanation:

I just took the quiz

The value for x is 7π/6 and 11π/6.

sin2xsecx+2cosx=0

(2sinxcosx)(1/cosx)+2cosx=0

sinxcosx/cosx+2cosx=0

So,

2sinx+2cosx=0

2(sinx+cosx)=0

(2(sinx+cosx))²=0

4(sin²x+cos²x+2sinxcosx)=0

hence,

(sin²x+cos²x+2sinxcosx)/4=0/4

sin2x+cos2x+2sinxcosx=0

1+sin2x=0

sinx=−1/2

=7π/6 and 11π/6

Know more about trigonometry at:

https://brainly.com/question/20519838

#SPJ4

The Reflexive property of congruence can be used to prove

ΔPQR≅ΔPSR .

Given:

∠QPR≅∠SPR

∠PQR≅∠PSR

What is Reflexive property of congruence ?

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

We learned that the reflexive property of equality means that anything is equal to itself. The formula for this property is a = a. This property tells us that any number is equal to itself. For example, 3 is equal to 3.

PR≅PR (Reflexive property of congruence)

If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.(AAS theorem)

Hence, ΔPQR≅ΔPSR.

Learn more about Reflexive property of congruence at:

https://brainly.com/question/8741371

#SPJ1

Answer:

By the Substitution property, the measure of angle ABC is equal to GHI.

Step-by-step explanation:

According to the Question,

Since we have,

On substituting the value of from equation (1) to equation (2)

We get, ∠ABC = ∠GHI ∴ ∠ABC ≅ ∠GHI

Thus, By the Substitution property  

The measure of angle ABC is equal to angle GHI.

The perimeter of the polygon is found as the 42 cm.

For the shown polygon:

Points A, B, C and D are tangents on the circle.

Thus, these tangent will subtend equal length from the points.

So,

AB = 3 + 4 = 7 cm

BC = 4 + 5 = 9 cm

As, ∠B ≅ ∠D, sides must also be equal.

CD = 5 + 4 = 9 cm

DA = 4 + 3 = 7 cm

Perimeter = AB + BC + BC + BC

                 = 7 + 9 + 9 + 7

Perimeter = 42 cm

Thus, the perimeter of the polygon is found as the 42 cm.

To now more about the perimeter of the polygon, here

https://brainly.com/question/27083382

#SPJ1

The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

Learn more about standard deviation

brainly.com/question/23907081

#SPJ4

The ordered triple (2, -3, 4) is not a solution of the system, while the ordered triple (-2, 3, -4) is a solution of the system.

Let's assume the given system of equations is:

Equation 1: 2x - 3y + 4z = 0

Equation 2: -2x + 3y - 4z = 0

Ordered Triple (2, -3, 4):

Substituting the values into the equations:

Equation 1: 2(2) - 3(-3) + 4(4) = 4 + 9 + 16 = 29 (not equal to 0)

Equation 2: -2(2) + 3(-3) - 4(4) = -4 - 9 - 16 = -29 (not equal to 0)

Since both equations are not satisfied when substituting the values of the ordered triple (2, -3, 4), this ordered triple is not a solution of the given system.

Ordered Triple (-2, 3, -4):

Substituting the values into the equations:

Equation 1: 2(-2) - 3(3) + 4(-4) = -4 - 9 - 16 = -29 (equal to 0)

Equation 2: -2(-2) + 3(3) - 4(-4) = 4 + 9 + 16 = 29 (equal to 0)

Since both equations are satisfied when substituting the values of the ordered triple (-2, 3, -4), this ordered triple is a solution of the given system.

To learn more about ordered triple : brainly.com/question/13019297

#SPJ11

Answer:

-10

Step-by-step explanation:

Answer: 3x

verry eazy just subtract and keep the x

Explanation

if you know 2 points of a line you can easily find the slope using

Let

P1(-1,5)

P2(7,1)

replace,

I hope this helps you

Answer:

true

Step-by-step explanation:

if you rewrite \(sec\left(\frac{\pi }{2}\:-x\right)\) with trigonometric identities:

\(sec\left(\frac{\pi }{2}\:-x\right)\)    \(=\frac{1}{\sin \left(x\right)}\)

\(\frac{1}{\sin \left(x\right)}\)  \(=\csc \left(x\right)\)

so, yes,  \(sec\left(\frac{\pi }{2}\:-x\right)\)  \(=\csc \left(x\right)\)

hope this helps!!

Answer:

25

Step-by-step explanation:

5^2 means 5 multiplied by itself 2 times, so therefore: 5x5

5x5 = 25 so 5^2=25

Hope this helped!

Answer:

Step-by-step explanation:

\(5^2 = 5\times 5\\=25\\\)

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( \(e^{(-λ)\) * \(λ^k\)) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = (\(e^{(-72.8)\)* \(72.8^(70)\)) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

\(Z = (X - mean) / \sqrt{(variance)\)

Fοr X = 70, we have:

Z = (70 - 1.4) / \(\sqrt{(1.4)\) ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

To learn more about Probability from given link.

brainly.com/question/30034780

#SPJ1

The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

a. the mean of the sampling distribution of the sample proportion is 0.46

b. the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. he sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. the standard deviation of the sampling distribution by a factor is 0.0704

a. The mean of the sampling distribution of the sample proportion, denoted as μp^, is equal to the population proportion, which in this case is 46%.

μp^ = p = 0.46

the mean of the sampling distribution of the sample proportion is 0.46

b. The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

Where p is the population proportion (0.46) and n is the sample size (100).

σp^ = √((0.46 * (1 - 0.46)) / 100) = 0.0498

the standard deviation of the sampling distribution of the sample proportion is 0.0498

c. The sampling distribution of p^ is approximately normal due to the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n ≥ 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. Since the sample size is 100 in this case, we can assume that the sampling distribution of p^ is approximately normal.

d. To find the probability that more than 60 households will own VCRs, we need to calculate the probability of getting a sample proportion greater than 0.6. We can standardize this value using the z-score formula:

z = (x - μp^) / σp^

Substituting the values, we have:

z = (0.6 - 0.46) / 0.0498 = 2.811

the probability of having a z-score greater than 2.811 is equal to 1 - 0.9974 = 0.0026, or 0.26%.

e. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion (σp^) would be multiplied by a factor of √(2), which is approximately 1.414. Therefore, the standard deviation would become:

New σp^ = σp^ * √(2) = 0.0498 * 1.414 = 0.0704

the standard deviation of the sampling distribution by a factor is 0.0704

Learn more about Standard Deviation here

https://brainly.com/question/29115611

#SPJ4

The mean of the sampling distribution of the sample proportion is 0.46. The standard deviation of the sampling distribution of the sample proportion is approximately 0.0498. The sampling distribution of p^ is approximately normal when the sample size is large enough. The probability that more than 60 households will own VCRs is approximately 0.0024. If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution would be multiplied by a factor of approximately 1.4142.

In statistics, a sampling distribution is the probability distribution of a given statistic based on a random sample. The sampling distribution of the sample proportion, denoted as p^, is the distribution of the proportions obtained from all possible samples of the same size taken from a population.

The mean of the sampling distribution of the sample proportion is equal to the population proportion. In this case, the population proportion is 46% or 0.46. Therefore, the mean of the sampling distribution of the sample proportion, denoted as μp^, is also 0.46.

The standard deviation of the sampling distribution of the sample proportion, denoted as σp^, is determined by the population proportion and the sample size. It can be calculated using the formula:

σp^ = √((p * (1 - p)) / n)

where p is the population proportion and n is the sample size. In this case, p = 0.46 and n = 100. Plugging in these values, we get:

σp^ = √((0.46 * (1 - 0.46)) / 100) = √((0.46 * 0.54) / 100) = √(0.2484 / 100) = √0.002484 = 0.0498

The sampling distribution of p^ is approximately normal when the sample size is large enough due to the Central Limit Theorem. This theorem states that the sampling distribution of a sample mean or proportion becomes approximately normal as the sample size increases, regardless of the shape of the population distribution. In this case, the sample size is 100, which is considered large enough for the sampling distribution of p^ to be approximately normal.

To calculate the probability that more than 60 households will own VCRs, we need to use the sampling distribution of p^ and the z-score. The z-score measures the number of standard deviations an observation is from the mean. In this case, we want to find the probability that p^ is greater than 0.6.

First, we need to standardize the value of 0.6 using the formula:

z = (x - μp^) / σp^

where x is the value we want to standardize, μp^ is the mean of the sampling distribution of p^, and σp^ is the standard deviation of the sampling distribution of p^.

Plugging in the values, we get:

z = (0.6 - 0.46) / 0.0498 = 2.8096

Next, we need to find the probability that z is greater than 2.8096 using a standard normal distribution table or a calculator. The probability is approximately 0.0024.

If the sample size is decreased from 100 to 50, the standard deviation of the sampling distribution of the sample proportion would be multiplied by a factor of:

√(n1 / n2)

where n1 is the initial sample size (100) and n2 is the final sample size (50). Plugging in the values, we get:

√(100 / 50) = √2 = 1.4142

About sampling distribution here:

https://brainly.com/question/31465269

#SPJ11

                     "