19. Prove that: (b) cos(A + B).cos(A-B) = cos B-sin²A = cos²A-sin-B​

Answer:

Part A: To create an expression to represent the amount of canned food collected so far by the three friends, we need to add up their individual contributions. Therefore, the expression would be:

Amount collected = (3x² - 2) + (x²) + (2xy + 5)

Amount collected = 4x² + 2xy + 3

Part B: To find the expression that represents the number of cans the friends still need to collect to meet their goal, we need to subtract the amount collected from their goal expression. Therefore, the expression would be:

Cans still needed = 6x² - 2xy + 8 - (4x² + 2xy + 3)

Cans still needed = 2x² + 5

Answer: We do not have enough information to provide an answer for Part C as we need to know the value of x to evaluate the expression 6.02.

Answer:

its aaaaaaaaaaaaaa letter d

d. 0.2628

H0:μ≤116 Ha:μ>116 The value of the test statistic z=1.12. Find the p-value is0.8869. The correct answer is option c. 0.8869.

To find the p-value, we need to use the standard normal table or a calculator with a normal distribution function. The p-value is the probability of observing a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true.

In this case, we are looking for the probability that z is greater than or equal to 1.12, given that the null hypothesis is true.

Using a standard normal table, we can find the area to the left of z=1.12, which is 0.8686. However, we are interested in the area to the right of z=1.12, which is 1 - 0.8686 = 0.1314.

This is the p-value for a one-tailed test. However, the hypothesis test in the question is a two-tailed test, so we need to double the p-value to get the final answer. The p-value for a two-tailed test is 2 * 0.1314 = 0.2628.

Therefore, the correct answer is option c. 0.8869.

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Answer:

In Explanation

Step-by-step explanation:

To convert grams to pounds, we need to first convert grams to kilograms, and then kilograms to pounds.

Given that 1 gram = 0.001 kilograms, we can convert 23,000 grams to kilograms as follows:

23,000 grams = 23,000 * 0.001 kilograms = 23 kilograms

Now, given that 1 kilogram ≈ 2.2 pounds, we can convert 23 kilograms to pounds as follows:

23 kilograms * 2.2 pounds/kilogram = 50.6 pounds

Therefore, 23,000 grams is equivalent to 50.6 pounds.

(Please give brainlist)

One euro is equivalent to $1.2 in dollars thanks to the $1.2/euro conversion rate. The EUR/USD exchange rate is another name for this rate.

A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia. We can multiply the quantity of euros by the conversion rate to convert 160 euros to dollars:

1 euro Equals $1.22; 160 euros = $192.

Hence, 160 euros are equal to $192.

We can divide the amount in dollars by the conversion rate to convert $76.80 to euros:

64 euros are equal to $76,80 at the exchange rate of $1 to the euro.

Hence, 64 euros are equal to $76.80.

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The value of n in the n-sided polygon, with sides AC and AD, where the external angle formed at the point the decagon touches the n-sided polygon is 60° is; n = 15

A polygon is a planar shape with three or more straight sides.

The sum of angles at a point property indicates that, the sum of angles at the point A can be presented as follows;

∠BAC + ∠CAD + ∠DAB = 360°

Angle ∠BAC = 60°

Angle ∠DAB is an interior angle of a 10-sided regular polygon, (a decagon),  therefore, the measure of angle ∠DAB is 144°

Plugging in the values of the measures of the angles ∠BAC and ∠DAB, in the equation, ∠BAC + ∠CAD + ∠DAB = 360°, we get;

+ ∠CAD + 144° = 360°

∠CAD = 360° - (144° + 60°) = 156°

∠CAD = 156°

The formula for finding the measure of the interior angle of an n-sided polygon, θ, can be presented as follows;

θ = (n - 2) × 180°/n

Where the interior angle, θ = 156°, which is the measure of ∠CAD, in the n-sided polygon, we get;

156° = (n - 2) × 180°/n

156·n = 180·n - 360

360 = 180·n - 156·n = 24·n

n = 360/24 = 15

The number of sides in the n-sided polygon is 15, therefore, AC and AD are adjacent to a 15-sided polygon

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The positive solution for x in the equation log_x(1)/256 = -4/3 is x = 4.57

To solve the logarithm problem for the positive solution for x, we can use the following steps:

1. First, we can rewrite the equation in exponential form:
x^(-(4)/(3)) = 1/256

2. Next, we can raise both sides of the equation to the power of -(3)/(4) to isolate x:
(x^(-(4)/(3)))^(-(3)/(4)) = (1/256)^(-(3)/(4))

3. Simplify the left side of the equation:
x = (1/256)^(-(3)/(4))

4. Simplify the right side of the equation:
x = 256^((3)/(4))

5. Take the fourth root of both sides of the equation:
x = (256^((3)/(4)))^(1/4)

6. Simplify the right side of the equation:
x = 256^((3)/(16))

7. Simplify the exponent:
x = 256^(3/16)

8. Calculate the value of x:
x ≈ 4.57

Therefore, the positive solution for x is approximately 4.57.

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The height of a right cone is 42 units.

The area or volume occupied by a right circular cone is referred to as the right circular cone's volume. A three-dimensional solid object called a right circular cone has a pointed end on one side and a circle on the other. The vertex of the cone is another name for the sharp end. A cone with a right circular shape is one whose axis is parallel to the base plane.

Here, we have

Given: The volume of a right cone is 2016\piπ units^3. If its diameter measures 24 units

Height of the cone = Volume of a cone ÷ 1/3(πr²)

Where:

π = 22/7

r = radius = diameter / 2 = 24 / 2 = 12 units

h = height

2016π÷ (1/3 x π x 12²) = 42 units

Hence, the height of a right cone is 42 units.

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In this context, we will explore the benefit and step of budgeting on home pay. By creating a budget and sticking to it, She (Henley) can ensure that she is effectively managing her income and achieving her financial goals.

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Answer: x-14

Step-by-step explanation:

The fourth point has coordinates (-17, 0).

The x-coordinate of A remains constant but the sign of the y-coordinate changes if A is mirrored over the x-axis to form A'. Hence, if Has a coordinates (a, b), A' must also have coordinates (a, -b).

Given that A and A' are the corners of a rectangle that are opposite one another, the other two corners of the rectangle must be on a horizontal line that passes through A and A"s midpoint (a, 0). Since (a, 0) and the fourth point (let's call it C) are separated by 2|b|, the distance between A and A' is also 2|b|. This indicates that depending on which side of the line AA' C is on, it has coordinates of (a + 2|b|, 0) or (a - 2|b|, 0).

In this instance, the coordinates of A are (3, 5) and those of A' are (3, -5). The intersection of A and A' is (3, 0). A and A' are separated by 2|5|, which equals 10.

The fourth point, C, thus, has coordinates of either (3 + 2(10), 0) = (23, 0) or (3 - 2(10), 0) = (-17, 0).

The right response is (3 - 2(10), 0), which can be deduced from the graph since the rectangle is symmetric about the y-axis (-17, 0).

The fourth point therefore has coordinates (-17, 0).

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I may be wrong but, i think it may be C. due to how the question  states the answers and questions, Although it may also be B.

The given function will have a minor and major axis with length 6 and 8, respectively. The correct answer is B.

The given equation is (x²)/(9) - (y²)/(16) = 1 is in the form of (x²)/(a²) - (y²)/(b²) = 1. This is the equation of a hyperbola with a horizontal transverse axis.

The length of the major axis is 2a, and the length of the minor axis is 2b.

In this case, a = 3 and b = 4.

So, the length of the major axis is 2a = 2(3) = 6, and the length of the minor axis is 2b = 2(4) = 8.

Therefore, the correct answer is option b. 6,8.

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The domain of y = x + 6 - 7 is the set of all real numbers

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

y = x + 6 - 7

The domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined

There is no restriction on the input values, x

So, the domain of y = x + 6 - 7 is all real numbers, since there is no restriction on the input (x).

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Answer: The mean increases by 1.6°.

Step-by-step explanation:

The mean is the average or the sum of all the data divided by the amount of data.

58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57 = 965

There are 12 data points so...

965 / 12 ≈ 80.4

To find the new mean add 101 to 965, then divide by 13.

965 + 101 = 1066

1066 / 13 = 82

The mean increases by 1.6°.

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The domain is -7, 1, 3, 7 and the range is 2, 8

Determine if this is a function or not, find the domain, and find the range. {(7,8),(3,2),(1,8),(-7,2)} Is this a function or not? (type yes or no) What is the domain? (list the numbers in increasing order, seperated by a comma ) What is the range? (list the numbers in increasing order, seperated by a comma )

Yes, this is a function. The domain is -7, 1, 3, 7 and the range is 2, 8.

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The sum of a series whose nth term is 3(2x+1) can be calculated using the formula: S = (n/2)(3a + 3d + a), where a = the first term of the series and d = the common difference between the terms. In the given series, the first term is 3(2x+1), and the common difference is 3. Therefore, the sum of the series is: S = (n/2)(3(2x+1) + 3(3) + (2x+1)) = (n/2)(9x + 10)

The measures of those two angles are, 20° and 110°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Two angles of a quadrilateral measure 180° and 50°.

And, The other two angles are in a ratio of 2:11.

Since, The other two angles are in a ratio of 2:11.

Hence, ,Measures of both angles are, 2x and 11x.

Now, We know that;

Sum of all interior angles of a quadrilateral are 360°.

Hence, We get;

⇒ 180 + 50 + 2x + 11x = 360

⇒ 230 + 13x = 360

⇒ 13x = 360 - 230

⇒ 13x = 130

⇒ x = 10

Thus, Measures of both angles are,

2x = 2 × 10 = 20°

and 11x = 11 × 10 = 110°

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The solution of the system of equations is (-4, 3).

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Given are two linear equations.

y = -3/2 x - 3

y = 3/4 x + 6

The two equations are in slope intercept form.

The solution of the two equations is the intersection of the two lines.

Equate both the equations.

-3/2 x - 3 = 3/4 x + 6

-3/2 x - 3/4 x = 6 + 3

-9/4 x = 9

-x/4 = 1

x = -4

Substitute x = -4 in y = 3/4 x + 6.

y = -3 + 6 = 3

Hence the solution of the equations are x = -4 and y = 3.

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Answer:

do you have like any picture of a graph?

Answer:

They have large leaves with holes in them that the Toucan can use to reach the fruit inside. The Toucan's beak is also used to break open hard-shelled fruits, such as coconuts. The Toucan's beak is also used for defence against predators, as it can be used to peck and jab at them. The adaptations of the rainforest plants are examples of convergent evolution. Both the Toucan and Monstera Plants have adapted to their environment in order to survive. The Toucan has a large beak that helps it to reach fruit in the canopy, while the Monstera Plant has long, grooved leaves with drip tips that allow water to run off and prevent mould. Both adaptations are beneficial for the survival of the species in the rainforest.

Step-by-step explanation:

If the stove's output is greater than or equal to the estimated BTUs, then it should be large enough to heat her basement.

Cary can determine if a stove is large enough to heat her basement by checking the stove's specifications for its heating capacity or output. Typically, a stove's output is measured in British Thermal Units (BTUs) per hour. She can use the following formula to estimate the BTUs required to heat her basement:

BTUs = (Length x Width x Height of basement) x 5

Once Cary has an estimated BTU requirement, she can compare it to the output of the stove she's considering.

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The total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

To calculate the total miles that all eight vehicles drove, we need to add up the miles driven by the seven vehicles that completed the trip and the miles driven by the eighth vehicle that only completed 50% of the journey.

The seven vehicles that completed the trip each drove 50 miles, so their total mileage is 7 x 50 = 350 miles.

The eighth vehicle only completed 50% of the journey, so it drove 50 x 0.50 = 25 miles.

To find the total miles driven by all eight vehicles, we add the miles driven by the seven vehicles and the miles driven by the eighth vehicle:
350 + 25 = 375 miles

Therefore, the total miles that all eight vehicles drove is 375 miles, and the correct answer is A. 375.

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The probability that a randomly selected school or district uses digital content and uses it as part of its curriculum is 48.6%.

Probability refers to the odds, chance, or likelihood that an expected outcome is obtained out of many possible outcomes.

Probability is a fractional value lying between zero and one based on the degree of certainty.

The percentage of K-12 schools or districts using digital content = 81%

The fractional value of those who use digital content as part of their curriculum = 12/20 = 0.6 or 60%.

Thus, the probability of randomly selecting a school or district using digital content as part of curriculum = 48.6% (81% x 60%).

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1. The value of Z is 1.96 determined from Z-table or a calculator. 2. The confidence interval equation is 161 ± 1.96* (4/√20). 3.The standard error is 0.8944. 4. The margin of error is 1.754. 5. The upper and lower limits are 162.754 and 159.246 respectively. 6. Confidence interval indicate how confident the researchers is that true mean is within the range.

1. For a 95% confidence interval, the value for Z is 1.96. This value is found by looking at a Z-table or using a calculator to find the Z-score that corresponds to a 95% confidence level.

2. The confidence interval equation is:

CI = x ± Z* (σ/√n)

Where x is the sample mean, Z is the Z-score, σ is the sample standard deviation, and n is the sample size.

Plugging in the values from the question, we get:

CI = 161 ± 1.96* (4/√20)

3. The standard error is calculated by dividing the sample standard deviation by the square root of the sample size:

SE = σ/√n = 4/√20 = 0.8944

4. The margin of error is calculated by multiplying the Z-score by the standard error:

ME = Z*SE = 1.96*0.8944 = 1.754

5. The upper and lower limits are calculated by adding and subtracting the margin of error from the sample mean:

Upper limit = x + ME = 161 + 1.754 = 162.754

Lower limit = x - ME = 161 - 1.754 = 159.246

6.  The 95% confidence interval for the mean drug price is between $159.246 and $162.754. This means that we are 95% confident that the true mean price of the drug is within this range.

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The difference quotient [f(x+h)-f(x)]/h for the function f(x)=-5x-1 is -5.

To find and simplify the difference quotient [f(x+h)-f(x)]/h for the function f(x)=-5x-1, we need to substitute (x+h) into the function for x and then simplify.

First, let's substitute (x+h) into the function for x:
f(x+h) = -5(x+h) - 1

Next, let's simplify:
f(x+h) = -5x - 5h - 1

Now, let's subtract f(x) from f(x+h):
[f(x+h) - f(x)] = (-5x - 5h - 1) - (-5x - 1)

Simplifying further:
[f(x+h) - f(x)] = -5h

Finally, let's divide by h:
[f(x+h) - f(x)]/h = -5h/h = -5

Therefore, the difference quotient [f(x+h)-f(x)]/h for the function f(x)=-5x-1 is -5.

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Answer: See attached.

Step-by-step explanation:

     First, we will find the unit rate by dividing.

30 rings / $12 = 2.5 rings per dollar

     Then, we can fill out the other values using this unit rate.

2 dollars * 2.5 rings per dollar = 5 rings

45 tosses / 2.5 rings per dollar = 18 rings

       Lastly, we will use these two equivalent ratios we found above to fill out the table and then plot the points. See attached.

Step-by-step explanation:

10^-3 is equivalent to 1/1000 or 0.001.

We are being informed that the sum of the two numbers is 12 and their difference is 6.

Thus, the two numbers whose sum is equal to 12 and their difference is equal to 6 are 9 and 3 respectively.

Let those two unknown numbers be (a) and (b)

a + b = 12

Their difference;

i.e.

a - b = 6

So, we can equate the two equations together:

i.e.

a + b = 12     --- (1)

a - b = 6        --- (2)

From equation (1); Let a be:

a = 12 - b

Now, Let's replace the value of (a) into equation (2)

12 - b - b = 6

12 - 2b = 6

-2b = 6 - 12

-2b = -6

2b = 6

b = 6/2

b = 3

If b = 3;

Then from equation, we have:

a + b = 12

replace b with 3 from the above equation, we have:

a + 3 = 12

a = 12 - 3

a = 9

Therefore, we can conclude that the sum of the two numbers are 9 and 3. respectively

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A polynomial that represents the distance between the heights of the balls after t seconds. Time t =15/20=0.75 seconds

a. Change of speed versus acceleration and time:

v = u + at

20  =  -16t2 + 30 +16t2 + 20t + 5

20=  20t + 35

20t=35-20=15

b.  We now interpret this polynomial as follows:Δh(t)=[tex]h_{0} -u_{y} t[/tex]

This shows how far apart the two balls are at time t. The two terms can be interpreted as follows: The initial separation between the two balls at time t=0 is represented by the constant term, h0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this issue[tex]h_{0} =30 feet.[/tex] The second ball's initial velocity, which serves as the coefficient of the linear term, [tex]u_{y}[/tex]tells us that the gap between the two balls closes by [tex]u_{y}[/tex] feet every second.

Time t =15/20=0.75 seconds. Time is the continuous pattern of existence and the events that take place in what appears to be an unbroken progression from the past through the present and into the future. It is a component number of various measurements that are used to compare the lengths of events or the pauses between them, to compare the order in which they occur, and to gauge the rates at which certain quantities in the physical world or in conscious experience change.

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So the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

In this problem, you are given a graph of a linear function. The graph shows two points on the line: (-2, 0) and (3, 5).

To find the slope of the line, we can use the formula:

slope = (change in y) / (change in x)

We can use the two points given to find the change in y and the change in x:

change in y = 5 - 0 = 5

change in x = 3 - (-2) = 5

Plugging these values into the formula, we get:

slope = 5/5 = 1

So the slope of the line is 1.

To find the y-intercept of the line, we can use one of the points on the line and the slope we just found. Let's use the point (-2, 0):

y - y1 = m(x - x1)

where (x1, y1) is the point (-2, 0) and m is the slope we just found:

y - 0 = 1(x - (-2))

y = x + 2

Therefore, the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

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