Find the exact value of cos(77°)cos(58°) - sin(77° )sin(58°) Enter answers in exact form, i.e. use sqrt(5) for √5 Next Question Solve sin(2x) cos(7x) – cos(2x) sin(7x) = – 0.4 for the smallest positive solution
X =

Answer:

11 units

Step-by-step explanation:

Answer:

10?

Step-by-step explanation:

Answer:

Observation

Step-by-step explanation:

He walked around seeing if every fifth person bought lunch

Survey - Requires asking questions

Simulation - Needs prior data to make an estimation

Experiment - Testing something

Observation - Just observing and watching

Study - Looking up data

The method he used to collect his data is observational method.

Observational study is usually chosen when the researches the system is likely to produce different result if interfered.

Sample survey is done if the population is too big to analyze or destructible as the analysis occurs.

Controlled experiment is done manually, specifically to deduce conclusions. Its steps are fixed.

Random experiment is done specifically to deduce conclusions, but it is done in a random manner.

We are given that;

He saw every fifth person in cafeteria

Now,

An observational study is a method of collecting data by observing and recording the behavior or characteristics of individuals or groups without interfering or manipulating any variables. Nico did not ask any questions or change any conditions, he just observed whether every fifth person in the cafeteria bought lunch or brought their own.

Therefore, by sampling the answer will be observational method.

Learn more about sampling here:

https://brainly.com/question/9724150

#SPJ7

Answer:

Yes

Step-by-step explanation:

Yes, this is a numerical expression because x represents a number.  This number is unknown, so x = 1 --- 5x (1) + 2 is equivalent to 5x + 2.  5x (1) +2 is a numerical expression, SO that means that 5x + 2 is a numerical expression.  

Note that the area under the curve - f(x) = x² + 2 between a and b using the right-hand sum with the given number of intervals is 460.

Given f( x) = x ² + 2, and

a = 0

b = 10 and

n = 5 intervals

Δx = h = b-a/n

= 10 - 0/5

= 2

Now, let's calculate the right-hand sum approximation:

Approximation = Σ((xi)² + 2) * Δx) from i = 1 to n

We'll evaluate f(x) = x² + 2 at the right endpoint of each subinterval and sum up the areas of the rectangles.

For i = 1:

xi = a + (i * Δx) = 0 + (1 * 2) = 2

f(xi) = f(2) = 2² + 2 = 6

Area of rectangle = f(xi) * Δx = 6 * 2 = 12

For i = 2:

= 0 + (2 * 2) = 4

f(xi) = 18

Area of rectangle

= 18 x 2 = 36

For i = 3:

xi = 6

f(xi)  = 38

Area of rectangle = 76

For i = 4:

xi =  8

f(xi) = 66

Area of rectangle = 132

For i = 5:

xi == 10

f(xi) = f(10) = 102

Area of rectangle  = 204

Summing  up the areas of all the rectangles we have -

Approximation = 12 + 36 + 76 + 132 + 204

= 460

Learn more about Area under the curve:
https://brainly.com/question/15122151
#SPJ1

Answer:

if jhonny had one apple how many apple does the chicken have in the basement across the road in his house under the bed??

Step-by-step explanation:

Answer:

You can either choose B or D.

The value of the contour surface passing through the point (1, 0, 2) is ψ(1, 0, 2) = 1^2 + 2e^0 = 1 + 2 = 3.

To find the points on the curve where the tangent is horizontal, we need to determine the values of t that satisfy the condition for a horizontal tangent, which is when the derivative of y with respect to t is equal to 0.

Given the parametric equations:

x = 2t^3 + 3t^2 - 12t

y = 2t^3 + 3t^2 + 1

Taking the derivative of y with respect to t:

dy/dt = 6t^2 + 6t

Setting dy/dt equal to 0 and solving for t:

6t^2 + 6t = 0

t(6t + 6) = 0

From this equation, we have two possible solutions:

t = 0

6t + 6 = 0, which gives t = -1.

Therefore, the points on the curve where the tangent is horizontal are (0, y(0)) and (-1, y(-1)). To find the corresponding y-values, substitute the values of t into the equation for y:

For t = 0:

y(0) = 2(0)^3 + 3(0)^2 + 1 = 1

For t = -1:

y(-1) = 2(-1)^3 + 3(-1)^2 + 1 = -2 + 3 + 1 = 2

Hence, the points on the curve where the tangent is horizontal are (0, 1) and (-1, 2).

To find the points on the curve where the tangent is vertical, we need to determine the values of t that satisfy the condition for a vertical tangent, which is when the derivative of x with respect to t is equal to 0.

Taking the derivative of x with respect to t:

dx/dt = 6t^2 + 6t - 12

Setting dx/dt equal to 0 and solving for t:

6t^2 + 6t - 12 = 0

t^2 + t - 2 = 0

(t + 2)(t - 1) = 0

From this equation, we have two possible solutions:

t + 2 = 0, which gives t = -2

t - 1 = 0, which gives t = 1.

Therefore, the points on the curve where the tangent is vertical are (x(-2), y(-2)) and (x(1), y(1)). To find the corresponding x-values and y-values, substitute the values of t into the equations for x and y:

For t = -2:

x(-2) = 2(-2)^3 + 3(-2)^2 - 12(-2) = -16 + 12 + 24 = 20

y(-2) = 2(-2)^3 + 3(-2)^2 + 1 = -16 + 12 + 1 = -3

For t = 1:

x(1) = 2(1)^3 + 3(1)^2 - 12(1) = 2 + 3 - 12 = -7

y(1) = 2(1)^3 + 3(1)^2 + 1 = 2 + 3 + 1 = 6

Hence, the points on the curve where the tangent is vertical are (20, -3) and (-7, 6).

For more questions like Tangent click the link below:

https://brainly.com/question/27021216

#SPJ11

Answer:

7

(

x

−

2

)

−

7

x

−

14

=

0

7

(

x

−

2

)

−

7

x

−

14

=

07

(

x

−

2

)

−

7

x

−

14

=

0

Step-by-step explanation:

Answer: 0 = 0

Step-by-step explanation: i showed the steps with these screen shots

Given:

The number of times coin flipped is N = 60.

The number of heads is n(H) = 42.

The number of tails is n(T) = 18.

The objective is to find the theoretical probability of coin landing heads up.

Explanation:

The general probability of coin landing heads is,

On plugging the given values in equation (1),

To obtain the percentage of probability,

Hence, the probability of the coin landing heads up is 70%.

Answer:

Step-by-step explanation:

nth root of a number 'a' is represented by the expression,

\(\sqrt[n]{a}\)

In this expression 'n' = Index of of the radical

\(\sqrt[4]{16}\) is called the 4th root of 16.

In \(\sqrt[4]{16}\), the index is 4 and the radicand is 16.

4th root of 16 can be represented by \(\sqrt[4]{16}\)

\(\sqrt[4]{16}=(16)^{\frac{1}{4}}\)

       \(=(2^{4})^{\frac{1}{4}}\)

       = 2

Answer:

4c + 3f + 2s + 20

Step-by-step explanation:

\(c + f + 2f + 3c + s + s + 20\)

\(4c + 3f + 2s + 20\)

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

Similar question here:

https://brainly.com/question/29181688?referrer=searchResults

#SPJ11

Answer: a=

−1

3

b+3

Step-by-step explanation:

Answer:

Im in 7th grade and im in 12 too :) I turn 13 in June 21st

Step-by-step explanation:

The answer is 1/12. 5+3+4=12 So 1/12 propabilty.

P.S. My favorite color is red

If this was helpful, please mark it as brainliest! :D

Answer:

the answer will be close to 50% so maybe like 48% or 49%

Step-by-step explanation:

The reasoning behind this is that the are 11 marbles total and half of 11 is 5 and a half. There are 5 red marbles which means that the chances are close 50% but because 5 isn't exactly half of 11 this means that your answer will need to be close to 50% but not exactly 50% which is why i gave the choices 49% or 48%.

The probability that the other child is a boy given that the shorter child is a boy is approximately 0.56 or 56%.

The problem can be solved using Bayes' theorem, which states that:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are events, P(A|B) is the conditional probability of event A given event B has occurred, P(B|A) is the conditional probability of event B given event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

Let A be the event that both children are boys, and B be the event that the shorter child is a boy. We are given that P(B|A') = 1/2, since the gender of the taller child is equally likely to be a boy or a girl.

We are also given that P(A') = 3/4, since there are three equally likely possibilities for the gender of the two children: boy-girl, girl-boy, and girl-girl. Finally, we are given that in 89% of families consisting of one son and one daughter the son is taller than the daughter, which means that P(B|A) = 0.89.

Using Bayes' theorem, we can calculate the probability that the other child is a boy given that the shorter child is a boy:

P(A|B) = P(B|A) * P(A) / P(B)

      = 0.89 * (1/4) / [(1/2) * (3/4) + 0.89 * (1/4)]

      ≈ 0.56

To learn more about probability click on,

https://brainly.com/question/12629667

#SPJ4

The co-terminal angle to 5π/6 in the unit circle is C. 17π/6

Co-terminal angles in a unit circle are angles that share the same terminal point

Given the angle 5π/6, we desire to find the angle that shares the same terminal point in the unit circle. We proceed as follows.

We know that x = 5π/6 + 2π

Taking the L.C.M which is 6, we have that

x = (12π + 5π)/6

x = 17π/6

So, the angle is C. 17π/6

Learn more about co-terminal angle in unit circle here:

https://brainly.com/question/27828444

#SPJ1

Answer:

Either a or d

Step-by-step explanation:

Because they show the data correctly it is A trust me

Answer: Scatterplot A

Step-by-step explanation:

edGE 23

Answer:

1/2

Step-by-step explanation:

Let the total pie be 2

She ate 1/6

Her brother ate 1/3

If she gave her Friend the remaining, the fraction of the amount her friend collected is expressed as:

1-(1/6+1/3)

= 1-((1+2)/6)

= 1-3/6

= 1 - 1/2

=1/2

Hence the fraction she gave her friend is 1/2

To create a validation rule in Salesforce that automatically selects grade A when the percentage is set to 90, you can use the ISPICKVAL function. This function allows you to check the selected value of a picklist field and perform actions based on the value. By using ISPICKVAL in the validation rule, you can ensure that the grade field is populated with A when the percentage field is set to 90.

To implement this validation rule, follow these steps:

Go to the Object Manager in Salesforce and open the Student object.

Navigate to the Validation Rules section and click on "New Rule" to create a new validation rule.

Provide a suitable Rule Name and optionally, a Description for the rule.

In the Error Condition Formula field, enter the following formula:

AND(ISPICKVAL(Percentage__c, "90"), NOT(ISPICKVAL(Grade__c, "A")))

This formula checks if the percentage field is selected as 90 and the grade field is not set to A.

In the Error Message field, specify an appropriate error message to be displayed when the validation rule fails. For example, "When percentage is 90, grade must be A."

Save the validation rule.

With this validation rule in place, whenever a user selects 90 in the percentage field, the grade field will automatically be populated with A. If the grade is not set to A when the percentage is 90, the validation rule will be triggered and display the specified error message.

To learn more about percentage visit:

brainly.com/question/29541337

#SPJ11

Answer:

A) x = 15

Step-by-step explanation:

4x - 30 = 2x

subtract 2x from each side of the equation:

2x - 30 = 0

add 30 to each side:

2x = 30

x = 15

Answer:

\( \displaystyle A) {15}^{ \circ} \)

Step-by-step explanation:

remember that,

when a transversal crosses two parallel lines then the Alternate interior angles are equal that is being said

\( \displaystyle 4x - 30 = 2x\)

cancel 2x from both sides:

\( \displaystyle 2x - 30 = 0\)

add 30° to both sides:

\( \displaystyle 2x = 30\)

divide both sides by 2:

\( \displaystyle x =15\)

hence

our answer is A)

Answer:

slope of st is -0.25

slope of tu is 1

slope of us is -0.25

slope of sv is 1 so it is a parallelogram. the slope of the parallel lines needs to be the same to be a parallelogram. to find the slope, you need to find the change from the points of the referenced line, for example, slope of st you would label each point as x1, y1 and x2,y2. it does not matter which one you label and you can change them for each different line. you would then find the difference by subtracting (y2-y1) divided by (x2-x1) so 4-3=1 and 1-5 is -4. you then divide 1/-4 is -0.25. you the follow the steps for each line. is the parallel lines have the same slope, it is a parallelogram

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)

\(r'(1) = f'(g(1))\times g'(1)\) from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

To learn more about derivative check the link below:

https://brainly.com/question/23819325

#SPJ4

Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

(a) To normalize the wavefunction, we need to determine the value of C.

The wavefunction should satisfy the normalization condition:

\(∫(|Ψ(x,0)|^2)dx = 1\)

Considering the given wavefunction \(Ψ(x,0)\), we can find its squared magnitude:

\(|Ψ(x,0)|^2 = |C*a/(2x)|^2 = (C^2 * a^2)/(4x^2), for a ≤ x ≤ b\)

\(|Ψ(x,0)|^2 = 0, for 0 ≤ x ≤ a and x > b\)

To normalize, we integrate \(|Ψ(x,0)|^2\)over the entire range and set it equal to 1:

\(∫((C^2 * a^2)/(4x^2)) dx = 1\)

Integrating with respect to x, we get:

\((C^2 * a^2/4) * (ln(x)|_a^b) = 1\)

Solving for C, we have:

\(C^2 = 4 / (a^2 * (ln(b) - ln(a)))\)

Taking the square root on both sides, we find the value of C:

\(C = 2 / (a * sqrt(ln(b) - ln(a)))\)

(b) Sketching \(Ψ(x,0)\) and \(|Ψ(x,0)|^2\):

The sketch of \(Ψ(x,0)\) will be a piecewise function with two parts:

For a ≤ x ≤ b, it will have the form C*a/(2x).

For 0 ≤ x ≤ a and x > b, it will be zero.

The sketch of \(|Ψ(x,0)|^2\)will also be a piecewise function:

For a ≤ x ≤ b, it will have the form \((C^2 * a^2)/(4x^2).\)

For 0 ≤ x ≤ a and x > b, it will be zero.

(c) The particle is most likely to be found at t = 0 where the squared magnitude \(|Ψ(x,0)|^2\) is the highest. In this case, it occurs at x = a.

(d) The probability of finding the particle between xa can be calculated by integrating \(|Ψ(x,0)|^2\)over the range xa to b:

P(x > a) = \(∫(|Ψ(x,0)|^2)\) dx from xa to b

P(x > a) = \(∫((C^2 * a^2)/(4x^2))\) dx from xa to b

(e) The expectation value of x (⟨x⟩) can be calculated by integrating\(x * |Ψ(x,0)|^2\) over the entire range:

⟨x⟩ = \(∫(x * |Ψ(x,0)|^2)\) dx from 0 to ∞

⟨x⟩ = \(∫(x * (C^2 * a^2)/(4x^2))\) dx from 0 to ∞

Comparing the answer from (c) to the expectation value of x will give insight into the particle's most likely position and the average position.

Learn more about wavefunction from this link:

https://brainly.com/question/31390478

#SPJ11

One drink of an alcoholic beverage contains approximately 100 to 150Kcal. That is option D

An alcoholic beverage is a type of beverage that contains ethanol which is also a type of alcohol.

The three main types of alcoholic beverage are beer, wine and spirits.

Alcoholic drinks contain a lot of kilojoules and have no nutritional benefits

One drink of an alcoholic beverage contains approximately 100 to 150Kcal.

Learn more about alcohol here:

https://brainly.com/question/13614186

#SPJ4

Answer:

BC = 6 units

Step-by-step explanation:

given that B is between A and C , then

AB + BC = AC ( substitute values )

3x + 4x - 2 = 12

7x - 2 = 12 ( add 2 to both sides )

7x = 14 ( divide both sides by 7 )

x = 2

Then

BC = 4x - 2 = 4(2) - 2 = 8 - 2 = 6

Answer:

6

Step-by-step explanation:

from the question, since point B is between Ac

AC = AB + BC

12 = 3X+4X -2

3X+4X-2 = 12

7X = 12+2

7X = 14

dividing bothsides by 7

7X/7 = 14/7

X = 2

the length BC = 4X-2 = 4(2)-2 = 8-2= 6

length of BC = 6

Answer: 5x + 95= 180

Step-by-step explanation:

Supplementary simply means the two angles sum to 180.

Answer:

Linda car will use 13.5 gallons

Step-by-step explanation:

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

For more questions on Angle .

https://brainly.com/question/31615777

#SPJ8

Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

h(4)=2w+3

4=2w+3

Collect like terms (c. I. T)

4-3=2w

1=2w

Divide both sides by 2(d.b.s)

1/2=2w/2

0.5=w

h=0.5w