Solve each triangle. Round answers to the nearest tenth.

Answer:

∠MGN = 24°

∠NGO = 24°

Step-by-step explanation:

⭐What is an angle bisector?

Thus, ∠MGN ≅ ∠NGO.

To solve for ∠MGN and ∠NGO, we need to:

1. Create an equation about their relationship:

If ∠MGN ≅ ∠NGO, then...

\(5x-6 = 11x -42\)

2. Solve for "x":

\(5x - 6 = 11x -42\)

\(42 - 6 = 11x - 5x\)

\(36 = 6x\)

\(6 = x\)

3. Substitute "x" back into the equations to find the angle measures:

\(< MGN = 5x - 6\)

\(< MGN = 5(6) - 6\)

\(< MGN = 30 - 6\)

\(< MGN = 24\)

❗❗❗At this point, you could write that ∠MGN and ∠NGO = 24°, as they are congruent, but you should still substitute "x" into  ∠NGO to make sure "x" is correct.❗❗❗

\(< NGO = 11x - 42\)

\(< NGO = 11(6) - 42\)

\(< NGO = 66 - 42\)

\(< NGO = 24\)

∴ ∠MGN = 24°

∴ ∠NGO = 24°

The computed value of the test statistic is 2.94.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

Answer:

Try -6/7

Step-by-step explanation:

it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

To know more about MATLAB related question visit:

https://brainly.com/question/30763780

#SPJ11

A symmetrical distribution of exam scores in a college course indicates that the student's scores are evenly distributed across the entire range of scores. This suggests that about an equal number of students had relatively high and relatively low scores.

Correct answer will be b) About an equal number of students had relatively high and relatively low scores.

And that there is no single group that overwhelmingly outperformed or underperformed the others. Furthermore, it indicates that there were a substantial number of students who achieved high scores, as well as a substantial number who achieved low scores.

This type of even distribution of scores is often seen when students are equally prepared, and when the exam is designed to be neither too difficult nor too simple.

In conclusion, a symmetrical distribution of exam scores suggests that the students were similarly prepared and that the exam was appropriately challenging.

know more about symmetrical distribution here

https://brainly.com/question/28285791#

#SPJ11

Answer:

b) y

Step-by-step explanation:

joannes speed = 250/2.5 =100km/h

francois speed = 100-10 = 90km/h

after 5h, francois would have travelled 450

Answer:

THE OTHER PERSON IS WRONG IT IS D/4x3(x2 − 5x − 9)

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

Step-by-step explanation:

Answer:

49/4

Step-by-step explanation:

⇒ x2 + 7x +49/4 = 4 + 49/4

⇒ {4x2 + 28x + 49}/4 = {16 + 49} /4

⇒ {4x2 + 28x + 49} = 16 + 49

⇒ (2x + 7)2 = 65 [since a2+ 2ab + b2 = (a + b)2]

⇒ (2x + 7)2 = (√65)2

a) The least square estimator is 2.785221.  b) The coefficient of determination is 0.9960514.  c) We would reject the null hypothesis at the 5% significance level.

To calculate the least squares estimators of the slope, the y-intercept, and the variance, we can use the method of simple linear regression.

(a) First, let's calculate the least squares estimators:

Step 1: Calculate the mean of the temperature (x) and maltose sugar content (y):

X = (155 + 160 + 165 + 170 + 175 + 180 + 185 + 190 + 195 + 200 + 205 + 210) / 12 = 185

Y = (25 + 28 + 30 + 31 + 31 + 35 + 33 + 38 + 40 + 42 + 43 + 45) / 12 = 35.333

Step 2: Calculate the deviations from the means:

xi - X and yi - Y for each data point.

Deviation for each temperature (x):

155 - 185 = -30

160 - 185 = -25

165 - 185 = -20

170 - 185 = -15

175 - 185 = -10

180 - 185 = -5

185 - 185 = 0

190 - 185 = 5

195 - 185 = 10

200 - 185 = 15

205 - 185 = 20

210 - 185 = 25

Deviation for each maltose sugar content (y):

25 - 35.333 = -10.333

28 - 35.333 = -7.333

30 - 35.333 = -5.333

31 - 35.333 = -4.333

31 - 35.333 = -4.333

35 - 35.333 = -0.333

33 - 35.333 = -2.333

38 - 35.333 = 2.667

40 - 35.333 = 4.667

42 - 35.333 = 6.667

43 - 35.333 = 7.667

45 - 35.333 = 9.667

Step 3: Calculate the sum of the products of the deviations:

Σ(xi - X)(yi - Y)

(-30)(-10.333) + (-25)(-7.333) + (-20)(-5.333) + (-15)(-4.333) + (-10)(-4.333) + (-5)(-0.333) + (0)(-2.333) + (5)(2.667) + (10)(4.667) + (15)(6.667) + (20)(7.667) + (25)(9.667) = 1433

Step 4: Calculate the sum of the squared deviations:

Σ(xi - X)² and Σ(yi - Y)² for each data point.

Sum of squared deviations for temperature (x):

(-30)² + (-25)² + (-20)² + (-15)² + (-10)² + (-5)² + (0)² + (5)² + (10)² + (15)² + (20)² + (25)² = 15500

Sum of squared deviations for maltose sugar content (y):

(-10.333)² + (-7.333)² + (-5.333)² + (-4.333)² + (-4.333)² + (-0.333)² + (-2.333)² + (2.667)² + (4.667)² + (6.667)² + (7.667)² + (9.667)² = 704.667

Step 5: Calculate the least squares estimators:

Slope (b) = Σ(xi - X)(yi - Y) / Σ(xi - X)² = 1433 / 15500 ≈ 0.0923871

Y-intercept (a) = Y - b * X = 35.333 - 0.0923871 * 185 ≈ 26.282419

Variance (s²) = Σ(yi - y)² / (n - 2) = Σ(yi - a - b * xi)² / (n - 2)

Using the given data, we calculate the predicted maltose sugar content (ŷ) for each data point using the equation y = a + b * xi.

y₁ = 26.282419 + 0.0923871 * 155 ≈ 39.558387

y₂ = 26.282419 + 0.0923871 * 160 ≈ 40.491114

y₃ = 26.282419 + 0.0923871 * 165 ≈ 41.423841

y₄ = 26.282419 + 0.0923871 * 170 ≈ 42.356568

y₅ = 26.282419 + 0.0923871 * 175 ≈ 43.289295

y₆ = 26.282419 + 0.0923871 * 180 ≈ 44.222022

y₇ = 26.282419 + 0.0923871 * 185 ≈ 45.154749

y₈ = 26.282419 + 0.0923871 * 190 ≈ 46.087476

y₉ = 26.282419 + 0.0923871 * 195 ≈ 47.020203

y₁₀ = 26.282419 + 0.0923871 * 200 ≈ 47.95293

y₁₁ = 26.282419 + 0.0923871 * 205 ≈ 48.885657

y₁₂ = 26.282419 + 0.0923871 * 210 ≈ 49.818384

Now we can calculate the variance:

s² = [(-10.333 - 39.558387)² + (-7.333 - 40.491114)² + (-5.333 - 41.423841)² + (-4.333 - 42.356568)² + (-4.333 - 43.289295)² + (-0.333 - 44.222022)² + (-2.333 - 45.154749)² + (2.667 - 46.087476)² + (4.667 - 47.020203)² + (6.667 - 47.95293)² + (7.667 - 48.885657)² + (9.667 - 49.818384)²] / (12 - 2)

s² ≈ 2.785221

(b) The coefficient of determination (R²) is the proportion of the variance in the dependent variable (maltose sugar content) that can be explained by the independent variable (temperature). It is calculated as:

R² = 1 - (Σ(yi - y)² / Σ(yi - Y)²)

Using the calculated values, we can calculate R²:

R² = 1 - (2.785221 / 704.667) ≈ 0.9960514

(c) To conduct an upper-sided model utility test for the slope parameter at the 5% significance level, we need to test the null hypothesis that the slope (b) is equal to zero. The alternative hypothesis is that the slope is greater than zero.

The test statistic follows a t-distribution with n - 2 degrees of freedom. Since we have 12 data points, the degrees of freedom for this test are 12 - 2 = 10.

The upper-sided critical value for a t-distribution with 10 degrees of freedom at the 5% significance level is approximately 1.812.

To calculate the test statistic, we need the standard error of the slope (SEb):

SEb = sqrt(s² / Σ(xi - X)²) = sqrt(2.785221 / 15500) ≈ 0.013621

The test statistic (t) is given by:

t = (b - 0) / SEb = (0.0923871 - 0) / 0.013621 ≈ 6.778

Since the calculated test statistic (t = 6.778) is greater than the upper-sided critical value (1.812), we would reject the null hypothesis at the 5% significance level. This suggests that there is evidence to support a positive linear relationship between mashing temperature and maltose sugar content in this data set.

To learn more about least square estimator here:

https://brainly.com/question/31481254

#SPJ4

Answer:

7.85

Step-by-step explanation:

Using the formulas

C=2πrd=2r

Solving forC

C=πd=π·2.5

Answer:

\(2.5\pi\)

Step-by-step explanation:

Since we know the diameter (d), we can find the radius (r):

\(r = \frac{1}{2} \times d = \frac{1}{2} \times 2.5 = 1.25\)

And not we can find the circumference:

C=\(2\pi \times r = 2 \times \pi \times 1.25 = 2.5\pi\)

Answer:

17.6

Step-by-step explanation:

Answer:

Parte 1

a) {0, 1, 2, 3, 4}

b) {11, 13, 17, 19}

c) {12, 24, 36, 48, 60}

d) Conjunto A = {4, 5, 6, 7, 8, 9, 10, 11}

Conjunto B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Parte 2

a) {x ∈ Z / x > 10}

{11, 12, 13, 14, 15, ....}

b) {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c) {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d) {x ∈ N / x < 10}

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} o {1, 2, 3, 4, 5, 6, 7, 8, 9}

e) {x ∈ Z / 2x < 15}

{2, 4, 6, 8, 10, 12, 14}

Step-by-step explanation:

Parte 1

a.) El conjunto de enteros no negativos menos de cinco.

Los enteros son números enteros. Los enteros no negativos son enteros positivos y 0 (0 es un entero neutral ya que es un número entero)

{0, 1, 2, 3, 4}

b.) El conjunto de números primos entre 10 y 20.

Los números primos son números divisibles por solo 1 y ellos mismos.

{11, 13, 17, 19}

c.) El conjunto de múltiplos de 12 que son menores de 65.

Los múltiplos de 12 son números que surgen cuando 12 se multiplica por números enteros.

{12, 24, 36, 48, 60}

d.) A = {x ∈ Z / 3 < x < 12}. y. B = {x / x es un número de un dígito}.

El conjunto A se refiere a todos los números enteros entre 3 y 12 (no incluido)

Conjunto A = {4, 5, 6, 7, 8, 9, 10, 11}

El conjunto B es un conjunto de todos los números de un dígito.

Conjunto B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Parte 2

a. El conjunto de enteros mayores que diez.

El conjunto variará de 11 a infinito.

Se escribirá como {x ∈ Z / x> 10}

{11, 12, 13, 14, 15, ....}

b.) El conjunto de enteros pares.

El conjunto de enteros pares comenzará desde 2 e incluirá todos los números pares hasta el infinito.

Se escribirá como {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c.) El conjunto {1, 2, 3, 4, 5}.

Este es un conjunto de enteros entre 1 y 5 (inclusive)

Se escribirá como {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d.) El conjunto de números naturales menores de 10.

Los números naturales son números de conteo.

Se escribirá como {x ∈ N / x < 10}

Algunos casos incluyen 0 como número natural y otros no.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} o {1, 2, 3, 4, 5, 6, 7, 8, 9}

e.) El conjunto de múltiplos de 2 que son menores que 15.

Se puede escribir como {x ∈ Z / 2x <15}

{2, 4, 6, 8, 10, 12, 14}

¡¡¡Espero que esto ayude!!!

In English

Part 1

a. The set of nonnegative integers less than five.

Integers are whole numbers. Non-negative integers are positive integers and 0 (0 is a neutral integer as it is a whole number)

{0, 1, 2, 3, 4}

b. The set of prime numbers between 10 and 20.

Prime numbers are numbers divisible by only 1 and themselves.

{11, 13, 17, 19}

c. The set of multiples of 12 that are less than 65.

Multiples of 12 are numbers that arise when 12 is multiplied by whole numbers.

{12, 24, 36, 48, 60}

d. A = {x ∈ Z / 3 < x < 12}. and. B = {x / x is a one-digit number}.

Set A refers to all integer numbers between 3 and 12 (non-inclusive)

Set A = {4, 5, 6, 7, 8, 9, 10, 11}

Set B is a set of all the one digit numbers.

Set B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Part 2

a. The set of integers greater than ten.

The set will range from 11 to infinity.

It'll be written as {x ∈ Z / x > 10}

{11, 12, 13, 14, 15, ....}

b. The set of even integers.

The set of even integers will start from 2, and include all the even numbers till infinity.

It'll be written as {x ∈ Z / 2x}

{2, 4, 6, 8, 10, 12, ....}

c. The set {1, 2, 3, 4, 5}.

This is a set of integers between 1 and 5 (inclusive)

It'll be written as {x ∈ Z / 1 ≤ x ≤ 5}

{1, 2, 3, 4, 5}

d. The set of natural numbers less than 10.

Natural numbers are counting numbers.

It'll be written as {x ∈ N / x < 10}

Some cases include 0 as a natural number and some others do not.

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} or {1, 2, 3, 4, 5, 6, 7, 8, 9}

e. The set of multiples of 2 that are less than 15.

It can written as {x ∈ Z / 2x < 15}

{2, 4, 6, 8, 10, 12, 14}

Hope this Helps!!!

Answer:

\(15^{12}\)

Step-by-step explanation:

assuming you mean

\((15^3)^{4}\)

using the rule of exponents

\((a^m)^{n}\) = \(a^{mn}\) , then

\((15^3)^{4}\)

= \(15^{3(4)}\)

= \(15^{12}\)

Answer:

Step-by-step explanation:

3.3%

B's efficiency is 1/60th of the work per day, which means B can complete 1/60th of the work in one day.

Hence, B will take 60 days to complete the whole work alone.

Let's assume that A's efficiency is represented by the variable 'x' (meaning A can complete 1/xth of the work per day), and B's efficiency is represented by the variable 'y' (meaning B can complete 1/yth of the work per day).

According to the given information:

1. A and B together can complete the work in 30 days.

  So, their combined efficiency is 1/30th of the work per day:

  x + y = 1/30   -- Equation 1

2. A works for 16 days and B finishes the remaining work alone in 44 days.

  In 16 days, A completes 16x of the work.

  The remaining work is (1 - 16x), which B completes alone in 44 days.

  So, B's efficiency is (1 - 16x)/44th of the work per day:

  y = (1 - 16x)/44   -- Equation 2

To find how many days B will take to complete the whole work alone, we need to determine the value of 'y' when the entire work is done (which is equivalent to 1).

To solve the system of equations (Equations 1 and 2), we can substitute Equation 2 into Equation 1 and solve for 'x':

x + (1 - 16x)/44 = 1/30

Multiplying through by the common denominator 44*30 = 1320:

1320x + 30(1 - 16x) = 44

1320x + 30 - 480x = 44

840x = 14

x = 14/840 = 1/60

Now, substitute the value of 'x' back into Equation 2 to solve for 'y':

y = (1 - 16(1/60))/44

  = (1 - 4/15)/44

  = (15/15 - 4/15)/44

  = 11/660

  = 1/60

Therefore, B can finish 1/60th of the work in a day because of his efficiency of 1/60th of the job every day.

As a result, B will need 60 days to do the entire project by himself.

Learn more about variable on:

https://brainly.com/question/28248724

#SPJ11

Answer:

I think what you are asking for is an example.

Step-by-step explanation:

Standard form equation

8x-4y = 20

1. move 8x to the other side

-4y=20-8x

2. divide both sides by -4

\(\frac{-4y}{-4} = \frac{20-8x}{-4}\)

3. Solve for this...

y=2x-5

Answer:

x < -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

Step 2: Divide both sides by 4.

Therefore, the answer is x < -3.

The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth.

1. The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth. These factors have led to numerous challenges, including increased traffic congestion, inadequate infrastructure, and strain on public services. The city's population is growing at a rapid pace, resulting in overcrowding, housing shortages, and environmental concerns.

2. To mitigate the present traffic jam situation in Dhaka City, a restructuring of the population can be pursued through various strategies. One approach is to promote decentralization by developing satellite towns or encouraging businesses and industries to establish themselves in other regions. This would help reduce the concentration of population and economic activities in the city center. Additionally, improving public transportation systems, including expanding the metro rail network, introducing dedicated bus lanes, and enhancing cycling and pedestrian infrastructure, can provide viable alternatives to private vehicles. Encouraging telecommuting and flexible work arrangements can also help reduce the number of daily commuters. Moreover, urban planning should focus on creating mixed-use neighborhoods with residential, commercial, and recreational spaces to minimize the need for long-distance travel.

By implementing these measures, the population of Dhaka City can be restructured in a way that reduces the strain on transportation systems, alleviates traffic congestion, and creates a more sustainable and livable urban environment.

Learn more about Urbanization here:

brainly.com/question/30663968

#SPJ11

Answer:

8

Step-by-step explanation:

Finding a square root is finding what times what rises to that number. Finding a solid shape root is finding what times what times what approaches that number. For instance, the square foundation of 64 is 8, since 8 x 8 = 64. In any case, the 3D shape foundation of 64 is 4, since 4 x 4 x 4 = 64.

Answer: Angle 4 shows Angle EHD

Step-by-step explanation:

The two angles are vertically opposite angles so that’s why they are equal

a) The perimeter of the figure is given as follows: 44 ft.

b) The area of the figure is given as follows: 24 ft².

The perimeter of the figure is obtained as the sum of the outer side lengths of the figure.

The side lengths are given as follows:

Hence the perimeter is of:

P = 2 x (16 + 6)

P = 44 ft.

The area of the figure is given as half the multiplication of the base of 16 ft by the height of 3 ft, hence:

A = 0.5 x 16 x 3

A = 24 ft².

More can be learned about perimeter and area at https://brainly.com/question/24571594

#SPJ1

Answer:

I'm getting stuck by

\( = lim \: \: \: \: \: \: \frac{ {h}^{ \frac{1}{5} } }{h} \\ h > 0\)

Sorry I can't help you out, if you find the answer through FP lmk

Answer:

What's the complex name

Pd(co2) (me3p)2

The exact probability of at least one person being chosen more than once in a sample of 1000 from a population of 1 million is approximately \(\[-\left(\frac{999}{1000}\right)^{1000}\]\). The approximate probability is around 31.62% based on the formula \(\[ \sqrt{\frac{n}{k}} \]\), where n is the population size and k is the sample size.

The exact probability that at least one person will get chosen more than once in a random sample of size 1000 from a population of size 1 million, with replacement and with equal probabilities, is:

P(at least one duplicate) = 1 - P(no duplicates)

The probability of no duplicates is:

\(\begin{equation}P(\text{no duplicates}) = \left(\frac{999}{1000}\right)^{1000}\)

Therefore, the exact probability of at least one duplicate is:

\(\begin{equation}P(\text{at least one duplicate}) = 1 - \left(\frac{999}{1000}\right)^{1000}\)

This probability can be approximated using the following formula:

\(\begin{equation}P(\text{at least one duplicate}) \approx \sqrt{\frac{n}{k}}\)

where n is the population size and k is the sample size.

In this case, n = 1 million and k = 1000, so the approximate probability of at least one duplicate is:

\(\begin{equation}P(\text{at least one duplicate}) \approx \sqrt{\frac{1000000}{1000}} = 31.62\)

As you can see, the exact probability is slightly lower than the approximate probability. This is because the exact probability takes into account all of the possible ways that duplicates can occur, while the approximate probability only considers the most likely way.

To know more about the exact probability refer here,

https://brainly.com/question/5008594#

#SPJ11

Answer:

The slope of AB = slope of CD and slope of BC = slope of DA

Hope this helps!

Step-by-step explanation:

Step-by-step explanation:

numbers that can not be written as a fraction

Answer:

I also don't know good luck girly