Triangle ABC measures are as follows; Angle A measures 30 degrees, angle B measures (3x-9) degrees and angle C measures 29 degrees. What is the value of x?

Answer: d=2√13  

Step-by-step explanation:

You need to use the distance formula or pythagorean.  Pythagorean is simpler. Let's use that.

c²=a²+b²

c= distance

a = how far point went in x direction =4

b=how far went in y direction =6

plug in:

d²=4²+6²

d²=16+36

d²=52                     take square root of both sides

d=√52                    

d=√(4*13                4 and 13 are factors of 52

d=2√13                   take square root of 4

There is evidence to support the claim that brand B gasoline yields a higher mean mpg than brand A gasoline under identical conditions.

Now, For test whether the mpg of brand B is significantly better than that of brand A, we can perform a two-sample t-test,

Here, assuming normality and using a significance level of 5%.

The null hypothesis states that there is no significant difference between the mean mpg of brand A and brand B, while the alternative hypothesis states that the mean mpg of brand B is significantly greater than that of brand A.

the t-value:

t = (xB - xA) / √(Sp/nB + Sp/nA)

where xB = 20.2, xA = 19.6,

Sp = ((nB - 1) sB + (nA - 1) sA) / (nA + nB - 2),

nB = nA = 16, and sB = 0.6, sA = 0.4.

Plugging in the values, we get:

Sp = ((16 - 1) 0.6 + (16 - 1) 0.4) / (16 + 16 - 2)

= 0.0804

Hence,

t = (20.2 - 19.6) / √√(0.0804/16 + 0.0804/16)

t = 3.64

The critical t-value for a two-tailed test with 30 degrees of freedom and a significance level of 5% is ±2.045.

Since the calculated t-value (3.64) is greater than the critical t-value, we can reject the null hypothesis and conclude that the mean mpg of brand B is significantly better than that of brand A.

Therefore, we can conclude that there is evidence to support the claim that brand B gasoline yields a higher mean mpg than brand A gasoline under identical conditions.

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To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.

The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".

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The table marked 3 in the accompanying figure has a rules value of is "void".

The explanation behind this is that Table 3 in the figure does not have any specified rules value. Therefore, it is considered void. In conclusion, the rules value for Table 3 is "void".


The given question provides a table marked as "Table 3" with values A, B, C, D, E, F, G, H, and I. However, the question asks for a "rules value" which is not provided or explained in the context. Therefore, it is impossible to determine a specific value or any relation among the given terms.

Due to the lack of information and context, the answer to the question regarding the rules value of Table 3 is void.

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Answer:

Step-by-step explanation:

Given, 12 / (-4) * 3 + 5

Here we can use the BODMAS rule and solve this problem.

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Now, let’s solve this by applying the BODMAS rule.

In the given sum we can find the Brackets in (-4).

12 / -4 * 3 + 5

There is no Of in this sum.

Let’s gust ignore it.

12 / -4 * 3 + 5

In this sum we can Divide 12 and -4.

-3 * 3 + 5

In this sum we can Multiply -3 and 3.

-9 + 5

In this sum we can Add -9 and 5.

-4

Answer: Slope is 3

Step-by-step explanation:

Answer:

5n - 10 = 15.

Step-by-step explanation:

If the number is n then 5 times it is 5n.

10 less than this is 5n - 10.

So, the equation is

5n - 10 = 15.

The triangle ABC has a surface area of 17.7 square units. Rounding to the nearest tenth of a square unit,

Heron's Formula can be used to calculate the triangle ABC's area. The equation reads as follows:

A = √[s(s-a)(s-b)(s-c)]

Where s is one-half of the triangle's circumference and a, b, and c are its three sides.

By summing the triangle's sides, we can determine the perimeter:

P = a + b + c

The formula below is used to get the other half of the perimeter.

s = P/2

For the triangle ABC, we have the sides a=3, b=5, and c=4.

Therefore, half of the perimeter is s = 8.

Now, Heron's formula can be used to determine the triangle ABC's surface area:

A = √[s(s-a)(s-b)(s-c)]

= √[8(8-3)(8-5)(8-4)]

= √[8(5)(3)(4)]

= 17.7 square units

Therefore, the triangle ABC has a surface area of 17.7 square units, Rounding to the nearest tenth of a square unit.

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Answer:

V = 942mm^3

Step-by-step explanation:

To find the volume of a cone you have to use this equation:

\(V = (\pi r^{2}h)/3\)

V = [(3.14)(10^2)(9)] /3

V = [(3.14)(100)(9)] /3

V = [2826] /3

V = 942mm^3

Answer:

the ratio equalevent for 1:2

7:21

The solutions to the equation \(x^{\frac{2}{3} } -2x^{\frac{1}{3} } -8=0\) are x = 64 and x = -8.

In Mathematics and Geometry, an exponent is a mathematical operation that is commonly used in conjunction with an expression, so as to raise a given quantity to the power of another.

Mathematically, an exponent can be modeled by this mathematical expression;

bⁿ

Where:

the variables b and n are numerical values, letters, or an expression.

n is known as a power.

By applying the law of indices for powers to the given equation, we would have the following simplified expression:

\(a^{\frac{n}{m} }=a^{(\frac{1}{m})n }\\\\x^{(\frac{1}{3} )2} -2x^{\frac{1}{3} } -8=0\\\\n^2 -2n - 8=0\)

n² - 4n + 2n - 8 = 0

n(n - 4) + 2(n - 4) = 0

(n + 2)(n - 4) = 0

n = -2 or n = 4.

Now, we can solve for x as follows;

\(x^{\frac{1}{3} }=4\\\\x = 4^3\)

x = 64.

\(x^{\frac{1}{3} }=-2\\\\x = -2^3\)

x = -8.

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Answer:

10x=y

Step-by-step explanation:

Divide your outputs by your inputs. In other words, divide 20 by 2, 50 by 5, and 70 by 7. These all equal 10. Therefore, 10 times x will equal y.

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

\(C = \frac{5}{9} (F- 32)\)

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

Answer:

y = \(\frac{11}{6}x+\frac{53}{2}\)

Step-by-step explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Slope of the line passing through \((x_1,y_1)\) and \((x_2,y_2)\) is represented by,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

If two points given in the bale are (-9, 10) and (3, 32),

Slope 'm' = \(\frac{32-10}{3-(-9)}\)

               = \(\frac{22}{12}\)

               = \(\frac{11}{6}\)

Therefore, equation of the line passing through (3, 32) and slope = \(\frac{11}{6}\) will be,

y - 32 = \(\frac{11}{6}(x - 3)\)

y = \(\frac{11}{6}x-\frac{11}{2}+32\)

y = \(\frac{11}{6}x+\frac{53}{2}\)

Answer:

140

Step-by-step explanation:

7/20 = 0.35 = 35% of the 20 players made all five baskets.

If this trend holds up, then we should expect 35% of the 400 people to make all five baskets.

35% of 400 = 0.35*400 = 140

We expect about 140 people will make all five baskets.

Note how 140/400 = 0.35 = 35%

-------------

Through another alternative method, we can solve like this

7/20 = x/400

7*400 = 20*x ... cross multiply

2800 = 20x

20x = 2800

x = 2800/20 ... dividing both sides by 20

x = 140 which is the same result as before

it's going to be 150 baskets made

Answer:

Draw a right triangle and name it ABC- C is your right angle. A is the angle above C and B is the angle on the side of C. AC=12 and CB=5, you have to find AB using the Pythagorean Theorem.

Step-by-step explanation:

Using the Pythagorean Theorem you say:

AB²=AC²+CB²

AB²=12²+5²

AB²=144+25

AB²=169

AB=√169

AB= 13

This is about understanding the line of best fit.

Option C is Correct

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Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

Answer:

13

Step-by-step explanation:

Use the distance formula and plug in both points

Answer:

its either 11 or 13 im not sure

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

h(-3)= -3(3)^3+5(-3)

=81-15= 66

g(h(-3))= x-4 : substitute h(-3) in g(x)

=66-4

=62

Answer:

$ 14.65 million

Step-by-step explanation:

The question requires you to add the profits obtained from the two years to get the net profit for the two years.

Profit in the first year of business = $ 6.25 million

Profit in the second year of business = $8.4 million

Net profits the last two years : $6.25 + $ 8.4 = $14.65 million

The function you're referring to is likely a periodic function, as Fourier series expansions are typically used for periodic functions.

The convergence of the Fourier series expansion depends on the properties of the function, such as its continuity and differentiability.

If the function is continuous and piecewise smooth, then the Fourier series will converge to the function itself.

However, if the function is not continuous or not piecewise smooth, then the Fourier series may not converge uniformly.

In some cases, the Fourier series may converge to a different function altogether, known as a Fourier series of the function.

Therefore, to determine the value at which the Fourier series converges, you would need to analyze the properties of the function itself.

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Answer:

8(2A+3P)  40 bags

Step-by-step explanation:

(2A+3P)/ (1/8)          8(2A+3)

2 pounds of almonds (2A) + 3 pounds of peanuts(3P) = 5pounds of the mix

5/1 divided into 1/8 , that is  the same as 5/1 multiplied be 8/1

5/1 x 8/1 =40

Answer:

The x-intercepts are reflecting zero-profit: (0, 0) and (6, 0).

The maximum value of the graph is at vertex (3, 120): maximum profit when the price is $3.

The function is increasing until the vertex, between x-value of 0 to 3 and is decreasing once it reached the vertex, between x-value of 3 to 6.

In the first interval the sale and profit increases, in the second interval the sale and profit decreases.

Average rate of change from x = 3 to x = 5 is:

This represents the profit drop of $30 per $1 price increase when price changes from $3 to $5.

0.135 or 13.5%  is the probability that he had 3 âhits

The probability that the player had 3 hits in 5 at-bats can be calculated using the binomial probability formula, which is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where:
- P(x) is the probability of getting x hits
- n is the number of at-bats (in this case, 5)
- x is the number of hits we want to find the probability for (in this case, 3)
- p is the probability of getting a hit in one at-bat (in this case, 0.343)
- (1-p) is the probability of not getting a hit in one at-bat (in this case, 0.657)

Plugging in the values, we get:

P(3) = (5C3) * 0.343^3 * 0.657^(5-3)
P(3) = (10) * 0.039304527 * 0.4305961
P(3) = 0.134912947

Therefore, the probability that the player had 3 hits in 5 at-bats is approximately 0.135 or 13.5%.

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Answer:

3

Step-by-step explanation:

3 times 4 equals 12

hope I got it right

Step-by-step explanation:

they would each get 4 pencils

Final Answer: All Real Numbers

Steps/Reasons/Explanation:

Question: Solve for a. \(4(a + 3)=12 + 4a\).

Step 1: Expand.

\(4a + 12 = 12 + 4a\)

Step 2: Cancel \(4a\) on both sides.

\(12 = 12\)

Step 3: Since both sides equal, we would have infinitely many solutions.

~I hope I helped you :)~

Answer:1

Step-by-step explanation:1