Please help me solve ma

Answer:

Distributive property

Step-by-step explanation:

In this problem, you are distributing the 5 to both the \(\sqrt{3}\) and the 2. Therefore, the answer is the distributive property

Answer: Distributive property.

Step-by-step explanation: The initial terms are being multiplied by 5 into both terms and they are equivalent by the distributive properly.  

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these are three ways to describe graphs in slope

Step-by-step explanation:

(1) Verbally slope indicates the steepness of a line (the sign indicates direction and the absolute value describes the steepness -- the larger the absolute value the steeper the graph.) This is related to the grade of a hill or the pitch of a roof.

(2) Algebraically slope is typically represented by m: for instance the equation of a line can be written as y=mx+b where m represents the slope. Also the slope formula where m=(y_2-y_1)/(x_2-x_1)  . However, some linear functions use other letters for the value that is the slope of the graph such as a direct variation y=kx where k is the constant of proportionality.

(3) Graphically slope is often represented as rise over run, or (Delta y)/(Delta x)  , or the ratio of the change in the vertical direction to the change of the horizontal.

The isosceles triangle of the maximum area is also an equilateral triangle.

Given, an isosceles triangle ABC is inscribed in a circle with center D and radius r.

We can obtain the side a in function of r and α by applying Law of Sines to triangle BCD,

a/sin(2α) = r/sin β

Since, 2α + β + β = 180°

2α + 2β = 180°

α + β = 90°

β = 90° - α

a = r(sin 2α/sin(90°-α))

a = r(2 sinα cosα)/cosα

a = 2r sinα

a = 4r sin(α/2) cos(α/2)

We can obtain the height h in function of r and α,

tan(α/2) = (a/2)/h

h = a/2tan(α/2)

Replacing with the value of a,

h = [4r sin(α/2) cos(α/2)/2][cos(α/2)/sin(α/2)]

h = 2r cos2(α/2)

Now, find the area of the triangle in function of a and r,

Area, A = (base)(height)/2

A = [4r sin(α/2) cos(α/2)][2r cos2(α/2)]/2

A = 4r2sin(α/2) cos3(α/2)

Now, take the derivative to find the maximum or minimum of the area of the triangle.

dA/dα = [4r2cos(α/2)(1/2)cos3(α/2)] + [4r2sin(α/2) 3cos2(α/2)(-sin(α/2))(1/2)]

On simplification,

= [2r2cos4(α/2)] - 6r2sin2(α/2) cos2(α/2)

Taking out common terms,

= 2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)]

Equating the derivative to zero, we get

2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)] = 0

2r2cos2(α/2) = 0

cos2(α/2) = 0

Thus, α/2 = 90°

α = 180°

Also, cos2(α/2) - 3sin2(α/2) = 0

cos2(α/2) = 3sin2(α/2)

[sin2(α/2)/cos2(α/2)] = 1/3

tan2(α/2) = 1/3

tan(α/2) = 1/√3

So, α/2 = 30°

α = 60°

This implies that ∠B = ∠C = 60°

Thus, the isosceles triangle of the maximum area that can be inscribed in a circle of radius r. is also an equilateral triangle.

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Answer:

\(\huge\boxed{x=12sin80=11.8}\\\huge\boxed{y=12cos80=2.1}\)

Step-by-step explanation:

Because sine = opposite over hypotenuse, simply multiply both sides by the hypotenuse to get:

hypotenuse * sinθ = opposite

Do the same thing with cos to get:

hypotenuse * cosθ = adjacent

Hope it helps :) and let me know if you want me to elaborate.

The function (g+h)(n-4) is the sum of the function g(n-4) and h(n-4) will be written as (g+h)(n-4) = n² - 7n + 9.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

g(n) = n² + 4n

h(n) = - 3n - 3

The function (g+h)(n) is calculated as,

(g+h)(n) = g(n) + h(n)

(g+h)(n) = n² + 4n - 3n - 3

(g+h)(n) = n² + n - 3

Put n = n - 4, then we have

(g+h)(n-4) = (n - 4)² + (n - 4) - 3

(g+h)(n-4) = n² + 16 - 8n + n - 4 - 3

(g+h)(n-4) = n² - 7n + 9

The function (g+h)(n-4) will be (g+h)(n-4) = n² - 7n + 9.

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Answer:

Step-by-step explanation:

no because 6 , 7 and 10 doesn't add up to 180 so it is not

A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.

To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:

a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.

In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.

The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.

The sum of 36 kilometers and 49 kilometers is 85 kilometers.

The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.

Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.

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Answer: 310

Step-by-step explanation:

1.Find your constant difference of the sequence by subtracting from left to right which is 9

2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5

3. T(35)=9n-5=9(35)-5=310

By elimination, the solution of the system of equations, 5x - 2y = -19 and 2x + 3y = 0, is (-3 , 2).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

First, multiply the first equation by 3 and the second equation by 2.

5x - 2y = -19 ⇒ 15x - 6y = -57     (equation 1)

2x + 3y = 0 ⇒ 4x + 6y = 0     (equation 2)

Adding the two equations will eliminate the variable y.

15x - 6y = -57     (equation 1)

4x + 6y = 0     (equation 2)

19x        = -57

x = -3

Substitute the value of x to any of the two equation and solve for y.

2x + 3y = 0     (equation 2)

2(-3) + 3y = 0

3y = 6

y = 2

Hence, the solution of the system of equations is (-3 , 2).

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The carnival committee should expect to pay $218.70 for prizes at the booth.

We can start by calculating the expected number of students who win each prize:

Stuffed toy: 22% of 150 students = 0.22 x 150 = 33 students

Jump rope: 16% of 150 students = 0.16 x 150 = 24 students

T-shirt: 6% of 150 students = 0.06 x 150 = 9 students

No prize: 100% - (22% + 16% + 6%) = 56% of 150 students = 0.56 x 150 = 84 students

Next, we can calculate the total amount of money that the carnival committee should expect to pay for prizes at the booth:

Stuffed toy: 33 students x $3.60 per toy = $118.80

Jump rope: 24 students x $1.20 per rope = $28.80

T-shirt: 9 students x $7.90 per shirt = $71.10

Total cost of prizes = $118.80 + $28.80 + $71.10 = $218.70

Therefore, the carnival committee should expect to pay $218.70 for prizes at the booth.

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The expression (6u + 7v) · V simplifies to 42 + 14v · V.

First, let's find the value of (6u + 7v) · V using the given information:

Since ||v|| = 2, we know that v · v = ||v||^2 = 2^2 = 4.

Similarly, ||u|| = 7, so u · u = ||u||^2 = 7^2 = 49.

Now, let's expand the expression (6u + 7v) · V using the dot product properties:

(6u + 7v) · V = (6u · V) + (7v · V)

Since u · y = 3, we can substitute it in the equation:

(6u · V) + (7v · V) = (6(3) + 7v · V) = 18 + 7v · V

Finally, we need to simplify the expression 7v · V. Using the dot product properties, we have:

v · V = ||v|| * ||V|| * cos(θ)

Since ||v|| = 2 and ||V|| = 2 (from ||v|| = 2), and cos(θ) is the cosine of the angle between v and V, which can range from -1 to 1, we can simplify the expression to:

v · V = 2 * 2 * cos(θ) = 4 * cos(θ)

Therefore, the final simplified expression is:

(6u + 7v) · V = 18 + 7(4 * cos(θ)) = 18 + 28cos(θ) = 42 + 14v · V.

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Only if I'm right of course...

Answer:

Step-by-step explanation:

This is a right triangle trig problem. The base of the right triangle is the distance that Donna if from the flagpole; the flagpole is the side opposite the reference angle which was given as 26, and we are looking for the height of the flagpole, h. The trig ratio that uses the side opposite over the side adjacent is the tangent ratio, specifically:

\(tan26=\frac{h}{123}\) and

123tan(26) = h so

h = 60.0 rounded to the nearest tenth. But that is only the height from her line of vision and up, not the whole height. In order to find the whole height, we have to add in her height up to her line of vision which is 5.3 feet. Therefore, the height of the flagpole is

60.0 + 5.3 = 65.3 feet.

Answer:

Step-by-step explanation:

To solve for the variable n in the equation 1/3 = n + 3/4, you can follow these steps:

Subtract 3/4 from both sides of the equation to isolate the variable n on one side:

1/3 - 3/4 = n

Find a common denominator for 1/3 and 3/4, which is 12. Multiply the numerator and denominator of 1/3 by 4 to get 4/12, and multiply the numerator and denominator of 3/4 by 3 to get 9/12:

4/12 - 9/12 = n

Simplify the expression on the left side of the equation by subtracting the numerators:

-5/12 = n

Rewrite the solution as a fraction or mixed number in simplest form:

n = -5/12

Therefore, the solution to the equation 1/3 = n + 3/4 is n = -5/12.

Answer:

5y

Step-by-step explanation:

because there are no other terms with a y

Answer:

0.01364

Step-by-step explanation:

It is given that,

A store sells a 33-pound bag of oranges for $3.60 and a 55-pound bag of oranges for $5.25.

Price per pound of 33 pound bag is 3.60/33 = 0.10909 price per pound

Price per pound of 55 pound bag of oranges is 5.25/55 = 0.09545 price per pound

Difference between price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges is :

D = 0.10909 - 0.09545

D = 0.01364

Therefore, this is the required solution.

Sure! Here's the 99.5% confidence interval for the true population mean textbook weight: (49.433, 60.567) ounces.

To construct a confidence interval for the true population mean textbook weight, we can use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √(sample size))

Given the information provided:

- Sample mean = 55 ounces

- Population standard deviation = 11.4 ounces

- Sample size = 32 textbooks

First, we need to find the critical value corresponding to a 99.5% confidence level. Since the sample size is relatively small (32 textbooks), we can use a t-distribution instead of a normal distribution.

The degrees of freedom for a t-distribution are given by (sample size - 1). In this case, the degrees of freedom will be (32 - 1) = 31.

Using a t-table or a statistical calculator, we find the critical value for a 99.5% confidence level and 31 degrees of freedom is approximately 2.750.

Now, we can calculate the confidence interval:

Confidence Interval = 55 ± 2.750 * (11.4 / √32)

Confidence Interval = 55 ± 2.750 * (11.4 / 5.657)

Confidence Interval = 55 ± 5.567

Therefore, the 99.5% confidence interval for the true population mean textbook weight is approximately (49.433, 60.567) ounces.

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The observed data indicates that the null hypothesis should be rejected at a rejection criterion of 0.05. This means that the data supports the researcher's hypothesis that ants show handedness, and that they are more likely to turn into the right or left arms of a T-maze.

The researcher is interested in determining if ants show handedness.

The researcher is hypothesizing that if ants show handedness, they will be more likely to turn into the right or left arms of a T-maze.The researcher placed 20 ants into the maze and observed that 16 of the ants walked into the right arm and 3 into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). The probability that exactly 16 of the ants enter the right arm when the null hypothesis is true is 0.368. This is calculated using the binomial formula, P(x=16) = (20 choose 16) * (0.5)^16 * (0.5)^4, where 0.5 is the probability of each ant turning into either arm.Outcomes that are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true include: 17R, 3L; 18R, 2L; 19R, 1L; and 19R, OL.The probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true are: 0.246 for 17R, 3L; 0.127 for 18R, 2L; 0.052 for 19R, 1L; and 0.026 for 19R, OL.The probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true is 0.451. This is calculated by adding up the probabilities associated with each of the outcomes identified in Problem 5 (0.368 for 16R, 4L, 0.246 for 17R, 3L, 0.127 for 18R, 2L, 0.052 for 19R, 1L, and 0.026 for 19R, OL).

The observed outcome does not indicate that the null hypothesis should be rejected at a rejection criterion of 0.05 since the P value for the binomial test (0.451) is greater than 0.05. Therefore, we cannot reject the null hypothesis and conclude that ants do not show handedness.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

Check the picture below.

\(\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches\)

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Step-by-step explanation:

straight south is 180°.

so it is 180° 20'.

straight west is 270°.

so, it is 270° 0' 30".

If a random sample of 36 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon, then the 90% "confidence-interval" is  (6.3426 , 7.4174).

The sample mean of x is (x') = $6.88,

the sample standard-deviation (σ) = $1.96,

the sample size (n) is = 36,

The z value for the 90% confidence interval is = 1.645,

So, the margin of error(E) is = (z×σ)/√n = (1.645×1.96)/√36 ≈ 0.5374,

So, the interval will be = (x' ± E),

Substituting the values,

we get,

⇒ (6.88 - 0.5374 , 6.88 + 0.5374),

⇒ (6.3426 , 7.4174)

Therefore, the required 90% confidence interval is (6.3426 , 7.4174).

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The given question is incomplete, the complete question is

In the third week of July, a random sample of 36 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.96 per 100 pounds.

Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop.

Answer:

b is the intercept of the graph. When x is 0, b is the y-value.

b affects the y-values, rather than the x-values. That means that it translates the graph up or down the y-axis by b units.

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The values in decreasing order is 64, 13. 5, √170 , 13, 7 , 6

From the information given, we need to determine the order on the basis of their values from greatest to least value

Given the values;

64 7 √170, 13.5, 6, 13​

Let's convert the surd form to decimal

√170 = 13. 0

In decreasing order, that is, from greatest to least, we have;

64, 13. 5 , 13. 0, 13, 7, 6

Thus, the values in decreasing order is 64, 13. 5, √170 , 13, 7 , 6

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Answer:

12 edges, 6 faces, and 7 vertices.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

I say 12 edges because there are 12 meeting points, and an open shape.

6 faces because there are 6 highlighted points on what looks like an unfolded shape.

8 vertices because you add 2 to the number of edges and subtract by the number of faces, 6.

a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:

74.5 - 17.34 = 57.16 Mbps

b. To find the number of standard deviations, divide the difference by the standard deviation:

57.16 / 20.79 = 2.75

So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.

Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.

It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.

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