4,, and C represent three different numbers from 2 through 5. What is the SMALLEST possible value of the entire expression below?
Show your work.
10 - A B/C

Where the above mean and standard deviation is given, the approximately 47.72% of the years have a snowfall between 31 and 41 inches in this town. Thus the nearest answer is (Option B)

Standardizing the values of 31 and 41 inches, we must use the following formula

Z = (X - μ) / σ

Where -  

For 31 inches -  

Z1 = (31 - 41) / 5 = -2

For 41 inches  -

Z2 = (41 - 41) / 5 = 0

The probability of the snowfall being   less than or equal to 31 inches is the same as the probability ofthe Z-score being less than or equal to -2, which is approximately 0.0228.

P  (31 ≤ X ≤41) = P(X ≤ 41) - P (X  ≤ 31)

= 0.5 -0.0228

= 0.4772

Finally, we convert this probability to a percentage by multiplying by 100  -

Percentage = 0.4772 * 100

= 47.72%

Hence , approximately 47.72% of the years have a snowfall between 31 and 41 inches in this town.

Learn more about mean:
https://brainly.com/question/20118982
#SPJ1

The surface area of the figures are

Pyramid = 96 ft²

Square base prism = 552 ft²

Cube = 216 ft²

Total surface area = 756 ft²

To find the surface area of different shapes, you can use specific formulas depending on the shape.

Here are the formulas used for each shape:

Pyramid:

Surface Area = Base Area + (1/2 × Perimeter × Slant Height)

Base Area =  6² = 36 ft²

Perimeter = 4(6) = 24 ft

Slant Height = √3² + 4² = √9 + 16 = √25 = 5 ft

Surface Area = 36 + (1 / 2 × 24 × 5) = 96 ft²

Square base prism:

Surface Area = 2(Base Area) + (Perimeter of Base × Height)

Base Area = 36

Perimeter of Base = 4(6)= 24

Height = 20

Surface Area = 2(36) + (4 * 6) * 20 = 552 ft²

Cube

The surface area of the cube  = 6 x length² = 6 × 6² = 6 × 36 = 216 ft²

Total surface area

Total surface area = 96  ft² + 552  ft² + 216  ft²= 864 ft²

corrected total surface area = 864 ft² - 36 ft²  - 36 ft² - 36 ft² = 756 ft²

Learn more about surface area at

https://brainly.com/question/16519513

#SPJ1

The function g(x) = x + 3 is a component of the composite function.

In this question we find the case of a composite function, of which one of its components must be deducted. This can be done by means of algebra properties. First of all, the composition of functions is defined below:

f ° g (x) = f [g(x)]

First, write the entire function:

√(x + 5)

Second, derive the expression g(x):

√(x + 5)

√[(x + 3) + 2]

f(x) = √(x + 2), g(x) = x + 3

To learn more on composition of functions: https://brainly.com/question/30660139

#SPJ1

Answer:

the answer is 16 please give me brainlest

a. The factored form of the expression x² - 3x - 28 is (x - 7)(x + 4).

b. The factored form of the expression x² + 3x - 28 is (x - 4)(x + 7).

c. The factored form of the expression x² + 12x - 28 is (x + 14)(x - 2).

d. The factored form of the expression x² - 28x - 60 is (x - 30)(x + 2).

a. To factorize the expression x² - 3x - 28, we can use the factoring method. We look for two numbers that multiply to give the constant term (-28) and add up to the coefficient of the linear term (-3). In this case, the numbers are -7 and 4.

Split the middle term (-3x) using -7x and 4x:

x² - 7x + 4x - 28

Group the terms and factor by grouping:

(x² - 7x) + (4x - 28)

x(x - 7) + 4(x - 7)

Factor out the common binomial (x - 7):

(x - 7)(x + 4)

b. For the expression x² + 3x - 28, we follow a similar process:

Split the middle term (3x) using 4x and -x:

x² + 4x - x - 28

Group the terms and factor by grouping:

(x² + 4x) + (-x - 28)

x(x + 4) - 1(x + 28)

Factor out the common binomial (x + 4):

(x + 4)(x - 7)

c. Moving on to x² + 12x - 28:

Split the middle term (12x) using 14x and -2x:

x² + 14x - 2x - 28

Group the terms and factor by grouping:

(x² + 14x) + (-2x - 28)

x(x + 14) - 2(x + 14)

Factor out the common binomial (x + 14):

(x + 14)(x - 2)

d. Finally, let's factorize x² - 28x - 60:

Split the middle term (-28x) using -30x and 2x:

x² - 30x + 2x - 60

Group the terms and factor by grouping:

(x² - 30x) + (2x - 60)

x(x - 30) + 2(x - 30)

Factor out the common binomial (x - 30):

(x - 30)(x + 2)

By following these steps, we can factorize the given expressions into their respective factored forms.

For more such information on factoring expressions, visit:
https://brainly.com/question/29877882

#SPJ8

Joe made the first mistake in the proof by making the assumption that line l is parallel to AB without providing any evidence or justification for this claim. This suspicion subverts the ensuing thinking and conclusion of the proof.

Joe's first error in his proof was assuming, without any evidence or justification, that line l is parallel to line AB. In order to construct a parallel line, specific information or conditions are required, such as the use of particular construction techniques or predetermined angles.

Joe's proof's subsequent reasoning and conclusions become questionable if the parallel relationship between the lines is not established. For the purpose of establishing that the sum of the interior angles of the triangle equals 180 degrees, the congruence or equality of angles must be demonstrated using the parallel line assumption.

Joe's proof cannot be considered accurate or valid because it lacks a solid logical foundation for the parallel line assumption.

Learn more about triangle's interior angle here:

https://brainly.com/question/7620723

#SPJ4

Answer:  It would be 80

Step-by-step explanation:

Answer:

(f ￮ g)(- 1) = 11

Step-by-step explanation:

to evaluate ( f ￮ g)(- 1) find g(- 1) then substitute the value obtained into f(x)

g(- 1) means what is the value of g(x) when x = - 1

from the table when x = - 1 , g(x) = - 3

now evaluate f(- 3) , which means what is the value of f(x) when x = - 3

from the table when x = - 3 , f(x) = 11

The statistical analysis of the data using a two-sample t-test indicates;

(a) B. Yes, the Meters On data appears to have higher speeds

A. No, there does not appear to be any outlier

(b) H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]

H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]

The P-value for the test is about 0.037

A two-sample t-test is used to determine if there is a difference between the means of two independent groups of data.

(a) The average of the data values are;

Ramp meters on;

[tex]\mu_{on}[/tex] = (29+47+55+38+32+25+42+47+51+36+55+41+43+25+47)/15 ≈ 40.87

[tex]\mu_{off}[/tex] = (25+25+43+35+36+31+48+37+19+29+22+40+36+50+40)/15 ≈ 34.4

The higher average value for the speed with the Ramp meters on indicates;

B. Yes, the Meters On data appears to have higher speeds

The five number summary are;

Ramp Meters On

Min = 25, Max = 55, Q₁ = 32, Q₂ = 42, Q₃ = 47

IQR = 47 - 32 = 15

Outlier = 47 + 1.5 × 15 = 69.5

32 - 1.5 × 15 = 9.5

Therefore, there are no outliers for the Ramp Meters On

Ramp Meters Off

Min = 19, Max = 50, Q₁ = 25, Q₂ = 36, Q₃ = 40

IQR = 40 - 25 = 15

Outlier = 40 + 1.5 × 15 = 62.5

25 - 1.5 × 15 = 2.5

Therefore, there are no outliers for the Ramp Meters Off data

(b) The null hypothesis is; H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]

The alternative hypothesis is; H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]

(c) The two sample t-test, can be obtained using the formula;

[tex]t_{cal} = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} ) } }[/tex]

Where; [tex]\bar{x}_1[/tex] = 40.87

[tex]\bar{x}_2[/tex] = 34.40

s₁ = 9.91

s₂ = 9.20

n₁ = n₂ = 15

Therefore; [tex]t_{cal}[/tex] = 1.8516. The degrees of 15 + 15 - 2 = 28, and the one-tailed hypothesis, indicates, using an online tool;

The p-value is less than 0.05, therefore, the result is significant.

Learn more on two-sample t-test here: https://brainly.com/question/32024330

#SPJ1

The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

Learn more about Pythagoras theorem:https://brainly.com/question/21926466

#SPJ1

Answer: b

Step-by-step explanation:

The order of the functions from least to greatest rates is (a) g(x), h(x), f(x)

From the question, we have the following parameters that can be used in our computation:

f(x) = x² + 2x + 3

x  -1 0  1  2  3

h(x) -7 4 -1 2 5

The interval is given as [0, 2]

For the functions, we have

f(0) = 0² + 2(0) + 3 = 3

f(2) = 2² + 2(2) + 3 = 11

h(0) = 4

h(2) = 2

So, we have the average rates of change at this interval to be

f(x) = (11 - 3)/(2 - 0) = 4

h(x) = (2 - 4)/(2 - 0) = -1

When ordered, we have

h(x), f(x)

Hence, the order is (a) g(x), h(x), f(x)

Read more about average rates of change at

https://brainly.com/question/31965106

#SPJ1

Answer:

[tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]

Step-by-step explanation:

Let [tex]\sin(2\arccos(-\frac{3}{5}))=\sin(2\theta)=2\sin\theta\cos\theta[/tex] and [tex]\theta=\arccos(-\frac{3}{5})[/tex] so that [tex]\cos\theta=-\frac{3}{5}[/tex]. Now we'll need to find [tex]\sin\theta[/tex] having known [tex]\cos\theta[/tex]:

[tex]\displaystyle \cos\theta=\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{-3}{5}\\\\\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{\sqrt{5^2-(-3)^2}}{5}=\frac{\sqrt{25-9}}{5}=\frac{\sqrt{16}}{5}=\frac{4}{5}[/tex]

Therefore, [tex]2\sin\theta\cos\theta=2(\frac{4}{5})(-\frac{3}{5})=2(\frac{-12}{25})=-\frac{24}{25}[/tex], which makes [tex]\sin(2\arccos(-\frac{3}{5}))=-\frac{24}{25}[/tex]

There is no solution for the given Angle measures and side length of the right-angled triangle.

In a right-angled triangle ABC, the given angle measures are:∠A = 40°, ∠C = 90° and AB = 7.5 cm.Law of sines:Sine rule, also known as the law of sines, is a theorem in trigonometry that defines the relationship between the angles and sides of a triangle. This law is generally used in trigonometry when we have a triangle with angle measures and a side length which are known or have been given.

Law of cosines:The law of cosines, also known as the cosine formula or the cosine rule, relates to the lengths of the sides of a triangle to the cosine of one of its angles. In geometry, it is a statement that explains the relationship between the sides and angles of a triangle.Let ∠B = x

We have the side adjacent to ∠A which is AB and the side opposite to ∠B which is BC.For the ∆ABC using sine rule:AB/sin ∠C = BC/sin ∠A=> AB/sin 90 = BC/sin 40=> AB = BC.sin 40⇒ AB = 7.5 sin 40 ≈ 4.83 cmNow we can use cosine rule:AC² = AB² + BC² - 2 AB BC cos ∠C=> AC² = 7.5² + BC² - 2 × 7.5 × BC × 0=> AC² = 7.5² + BC²⇒ AC² = 56.25 + BC²Also, we have the angle opposite to the hypotenuse of the right-angled triangle.

Using the cosine rule:cos ∠C = AB/ACcos 90 = AB/AC=> 0 = AB/AC⇒ AB = 0 (which is not possible)

Therefore, there is no solution for the given angle measures and side length of the right-angled triangle.

For more questions on Angle.

https://brainly.com/question/28394984

#SPJ8

Answer:

a. To find the velocity and acceleration of the rock at time t, we need to take the first and second derivatives of the height equation with respect to time:

s = 28t - 0.8t^2

v = ds/dt = 28 - 1.6t

a = dv/dt = -1.6

So the velocity of the rock at time t is v = 28 - 1.6t m/s, and its acceleration is a = -1.6 m/s^2.

b. To find how long it takes the rock to reach its highest point, we need to find the time at which the velocity is zero. We can set v = 28 - 1.6t = 0 and solve for t:

28 - 1.6t = 0

t = 17.5 seconds

So it takes 17.5 seconds for the rock to reach its highest point.

c. To find the maximum height reached by the rock, we can substitute t = 17.5 seconds into the height equation:

s = 28t - 0.8t^2

s = 28(17.5) - 0.8(17.5)^2

s = 245 meters

So the rock reaches a height of 245 meters.

d. To find how long it takes the rock to reach half its maximum height, we can set s = 245/2 = 122.5 meters and solve for t:

s = 28t - 0.8t^2

0.8t^2 - 28t + 122.5 = 0

t = 7.5 seconds or t = 20 seconds

So it takes the rock 7.5 seconds to reach half its maximum height.

e. To find how long the rock is aloft, we need to find the time at which it returns to the surface. We can set s = 0 and solve for t:

s = 28t - 0.8t^2

0 = 28t - 0.8t^2

t = 35 seconds

So the rock is aloft for 35 seconds.

Answer:D. The graph is stretched horizontally and shifted 1 unit to the right.

Step-by-step explanation: The absolute value function |s| reflects the part of the graph below the x-axis to above the x-axis, resulting in a V-shape. The modification (s - 1)|s| shifts this V-shape 1 unit to the right and stretches it horizontally by a factor of 1. Therefore, option D is the correct answer.

[tex](x - 1)(x - 2)(x - 6) \\ ({x}^{2} - 2x - x + 2)(x - 6) \\ ( {x}^{2} - 3x + 2)(x - 6) \\ {x}^{3} - 6 {x}^{2} - 3 {x}^{2} + 18x + 2x - 12 \\ {x}^{3} - 9 {x}^{2} + 20x - 12 [/tex]

PLEASE GIVE ME BRAINLIEST

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

For more questions on Cyclists .

https://brainly.com/question/3807925

#SPJ8

The trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

Trigonometric identities are equations that contain trigonometric ratios.

Given the trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a, we need to show that Left hand side (L.H.S) equals Right hand side (R.H.S). We proceed as follows

L.H.S =  cos a(2sec a + tan a)(sec a - 2tan a)

Expanding the brackets, we have that

cos a(2sec a + tan a)(sec a - 2tan a) =  cos a(2sec² a -  4tan asec a + tan a sec a - 2tan² a)

= cos a(2sec² a -  3tan a sec a - 2tan² a)

Now using the trigonometric identity 1 + tan² a = sec² a, we have that

cos a(2sec² a -  3tan a sec a - 2tan² a) = cos a(2(1 + tan² a) -  3tan a sec a - 2tan² a)

= cos a(2 + 2tan² a -  3tan a sec a - 2tan² a)

Collecting like terms in the equation, we have that

= cos a(2 + 2tan² a - 2tan² a -  3tan a sec a)

= cos a(2 + 0 -  3tan a sec a)

= cos a(2 -  3tan a sec a)

Expanding the bracket, we have that

= 2cos a -  cos a × 3tan a sec a

=  2cos a -  cos a × 3tan a/cos a  (since sec a = 1/cos a)

= 2cos a - 1 × 3tan a

= 2cos a - 3tan a

= R.H.S

So, since L.H.S = R.H.S,

cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

Learn more about trigonometric identities here:

https://brainly.com/question/29722989

#SPJ1

The value of the integral is [tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

The average rate of change over the interval [4, 10] is 3/2

From the question, we have the following parameters that can be used in our computation:

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The integral expression is given as

[tex]\int\limits^{10}_4 {f(x)} \, dx[/tex]

So, we have

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[5 - 4]} \, dx[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[1]} \, dx[/tex]

Integrate

[tex]\int\limits^{10}_4 {f(x)} \, dx = [x]\limits^{10}_4[/tex]

Expand

[tex]\int\limits^{10}_4 {f(x)} \, dx = 10 - 4[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

Here, we have

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The interval is [4, 10]

So, we have

Average rate = (5 + 4)/(10 - 4)

Evaluate

Average rate = 3/2

Hence, the average rate of change is 3/2

Read more about average rate of change at

https://brainly.com/question/31965106

#SPJ1

To configure the emergency trauma center within the given 1,500 square feet, consider the dimensions of equipment items such as patient beds, medical carts, examination tables, imaging equipment, surgical equipment, workstations, and storage areas.

To configure the emergency trauma center within the given 1,500 square feet, we need to consider the dimensions of the equipment items and plan an efficient layout. Here is a list of equipment items and their dimensions:

Patient beds: These typically have dimensions of around 3 feet by 6 feet. Depending on the number of beds required, we can allocate sufficient space for them, keeping in mind the need for walkways around each bed.

Medical carts: These can vary in size, but a common dimension is around 2 feet by 3 feet. Allocate a designated area or storage space for the medical carts, ensuring easy access and mobility.

Examination tables: These usually have dimensions of approximately 2.5 feet by 5 feet. Plan a separate area for examination rooms where the tables can be placed along with other necessary equipment.

Imaging equipment: Such as X-ray machines or CT scanners, which may require a designated room or area with specific shielding and safety considerations. Ensure enough space for patient accessibility and the equipment's operation.

Surgical equipment: Depending on the specific surgical procedures performed, allocate adequate space for surgical tables, anesthesia carts, surgical instruments, and any required sterilization equipment.

Workstations: Create workstations for medical staff, including computers, desks, and storage areas for paperwork and supplies. Consider the need for privacy and comfortable working conditions.

Storage areas: Allocate space for storing medical supplies, medications, and other equipment that may not be immediately needed but should be easily accessible.

When planning the layout, consider factors such as patient flow, accessibility, and safety regulations. It's essential to create a functional and efficient floor plan that allows for smooth operations and optimal patient care within the given square footage.

For more such question on dimensions. visit :

https://brainly.com/question/28107004

#SPJ8

Vertically stretch the cubic parent function, we multiply the function by the vertical stretch factor, a. The new equation of the function is y = a(x^3).  

If you vertically stretch the cubic parent function, the equation of the new function is y = a(x^3) where a is the vertical stretch factor. A cubic parent function is a polynomial function with a degree of three and an equation of y = x^3.

A vertical stretch is a transformation that increases the distance between each point on a graph and the x-axis. This transformation does not change the shape of the graph, but it affects the height of the graph.

To vertically stretch the cubic parent function, we multiply the function by a vertical stretch factor, a. Therefore, the equation of the new function is y = a(x^3).

For example, let's say we want to vertically stretch the cubic parent function y = x^3 by a factor of 2. To do this, we multiply the function by 2, which gives us y = 2(x^3). This means that the new function is twice as tall as the original function.

On the other hand, if we want to vertically shrink the cubic parent function y = x^3 by a factor of 1/2, we divide the function by 1/2. This gives us y = (1/2)(x^3), which means that the new function is half as tall as the original function.

To learn more about : function

https://brainly.com/question/11624077

#SPJ8

Answer:

a=3, b=2

Step-by-step explanation:

Let's fill in the given solution:

8a - 7b = 10

8b - 7a = -5

To solve, let's eliminate b. To do that, we want equal terms in both equations.

This can be achieved by multiplying the first by 8, the second by 7:

64a - 56b = 80

56b - 49a = -35

If we add the equations, we get:

64a - 49a - 56b + 56b = 80 - 35 =>

15a = 45

a = 3

In the original equation, this gives:

8*3 - 7b = 10 =>

-7b = -14

b = 2

Answer:

? = 113°

Step-by-step explanation:

the chord- chord angle TVU is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, then

∠ TVU = [tex]\frac{1}{2}[/tex] (UT+PS) = [tex]\frac{1}{2}[/tex] (125 + 101)° = [tex]\frac{1}{2}[/tex] × 226° = 113°

Answer:

Car 1: 40 mpg; Car 2: 15 mpg

Step-by-step explanation:

Car 1:

fuel: 20 gal

distance: x

efficiency: a

Car 2:

fuel: 40 gal

distance: y

efficiency: b

x + y = 1400

a + b = 55

efficiency equation:

efficiency in mpg = distance (in miles) / fuel used (in gallons)

Car 1:

a = x/20

Car 2:

b = y/40

We have 4 equations in 4 variables:

a = x/20

b = y/40

x + y = 1400

a + b = 55

20a = x

40b = y

20a + 40b = 1400

a + b = 55

20a + 40b = 1400

20b + 20b = 1100

20b = 300

b = 15

a + b = 55

a + 15 = 55

a = 40

Answer: Car 1: 40 mpg; Car 2: 15 mpg

Answer:

The mean is 22. So, as a percentage its 22%.

I don know what you're trying say for: 10) Ten Atlan h find be t Ex Fin​

The missing measure, h (height), for a right circular cone with a radius of 5 and a volume of 100 is approximately 3.82.

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The volume of a cone is expressed as;

V = (1/3) × π × r² × h

Where r is the radius of the base, h is the height of the cone and π is constant pi.

Given that:

Volume V = 100

Radius r = 5

Height h =?

Plug the given values into the above equation and solve for height h:

V = (1/3) × π × r² × h

100 = (1/3) × π × 5² × h

3 × 100 = 3 × (1/3) × π × 25 × h

300 = π × 25 × h

300 = 25π × h

h = 300 / 25π

h = 12/π

h = 3.82 units

Therefore, the height is approximately  3.82 units.

Learn more on volume of cones here: brainly.com/question/1984638

#SPJ1

Answer:

x = 52.7°

Step-by-step explanation:

To find the value of x in the given right triangle, we can use the tangent trigonometric ratio.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

The unknown angle is x, so θ = x.

The side opposite the angle measures 21 units, so O = 21.

The side adjacent the angle measures 16 units, so A = 16.

Substitute the values into the ratio and solve for x:

[tex]\tan x=\dfrac{21}{16}[/tex]

     [tex]x=\tan^{-1}\left(\dfrac{21}{16}\right)[/tex]

     [tex]x=52.6960517...[/tex]

     [tex]x=52.7^{\circ}\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 52.7°.

The equation for the missing angle is

Tan x = 21 / 16

The problem will be solved using Trigonometry - SOH CAH TOA

SOH for Sin = Opposite / Hypotenuse

CAH for Cos = Adjacent / Hypotenuse

TOA for Tan = Opposite / Adjacent

The given part is

opposite  = 21

Adjacent = 16

using TOA

Tan x = 21 / 16

Learn more on Trigonometry here:

https://brainly.com/question/24349828

#SPJ1

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

Read more about equation

brainly.com/question/29174899

#SPJ1

Answer:

Step-by-step explanation:

The expression 3s + s + 3 represents the total amount Alex and his family will spend to go to the movies. To simplify this expression, we can combine like terms.

The terms 3s and s are like terms because they both have the variable "s" raised to the power of 1. To combine them, we add their coefficients:

3s + s = (3 + 1)s = 4s

Therefore, the simplified expression is 4s + 3, which represents the total amount Alex and his family will spend to go to the movies.