Which angles are adjacent?

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

8x + 1 = 7

y - x = 1

y = 1 + x

sub 1 + x in eqtn i

8x + 1 = 7 { 1 + x }

8x + 1 = 7 + 7x

8x - 7 = 7 - 1

x = 6

y - 6 = 1

y = 1 + 6

y = 7

So,

8x = 8 x 6 = 48

7y = 7 x 7 = 49

My present years is 48

Next year i will be 49

Multiple can be defined as a number that is the product of a given number and some other natural number. For example when we multiply 7 × 3=21 or 8×3 =24

Therefore my present age is 48 and next year will be 49

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Solving a system of equations we wll see that there are  are 24 women, and the other 15 students are men in foruth grade.

We know that there are 39 students in fourth grade, we know that:

3/4 of the women went

2/3 of the men went

And this leaves 11 students at the school, then we can write the equation:

(3/4)*W + (2/3)*M + 11 = 39

Where W and M are the number of women and men respectively.

(3/4)*W + (2/3)*M = 39 - 11  = 28

(3/4)*W + (2/3)*M = 28

And we also know that the total number is 39, then:

M + W = 39

So we can write the system of equations:

(3/4)*W + (2/3)*M = 28

M + W = 39

M = 39 - W

REplacing that on the other equation we get:

(3/4)*W + (2/3)*(39 - W) = 28

(3/4)*W - (2/3)*w + 26 = 28

(3/4)*W - (2/3)*W = 28 - 26 = 2

(9/12)*W - (8/12)*W = 2

(1/12)*W = 2

W = 2*12 = 24

There are 24 women, and the other 15 students are men.

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Answer:

it is D

Step-by-step explanation:

Step-by-step explanation:

Answer:

N/A

Step-by-step explanation:

Vertical lines do not have a slope, unlike horizontal lines, which have a slope of 0

According to the given information, f(125) is equal to 48479.

What is function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To find f(125), we need to apply the recursive formula for f(n) when n is a positive integer divisible by 5. Since 125 is divisible by 5, we can use the formula:

f(125) = f(125/5) + 3(125)²

f(125/5) = f(25) = f(25/5) + 3(25)²

f(25/5) = f(5) = f(5/5) + 3(5)²

f(5/5) = f(1) = 4

Now we can substitute the values back into the formula and simplify:

f(5) = f(5/5) + 3(5)² = 4 + 75 = 79

f(25) = f(25/5) + 3(25)² = 79 + 3(625) = 2054

f(125) = f(125/5) + 3(125)² = 2054 + 3(15625) = 48479

Therefore, f(125) is equal to 48479.

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Answer:

\(t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923\)

The degrees of freedom are

\(df=20+20-2=38\)

And the p value is given by:

\(p_v =2*P(t_{38}>2.923) =0.0058\)

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\(\sigma^2_1 =\sigma^2_2 =\sigma^2\)

And the statistic is given by this formula:

\(t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\)

Where t follows a t distribution with \(n_1+n_2 -2\) degrees of freedom and the pooled variance \(S^2_p\) is given by this formula:

\(S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}\)

The system of hypothesis on this case are:

Null hypothesis: \(\mu_1 = \mu_2\)

Alternative hypothesis: \(\mu_1 \neq \mu_2\)

We have the following data given:

\(n_1 =20\) represent the sample size for group 1

\(n_2 =20\) represent the sample size for group 2

\(\bar X_1 =43.5\) represent the sample mean for the group 1

\(\bar X_2 =40.1\) represent the sample mean for the group 2

\(s_1=4.1\) represent the sample standard deviation for group 1

\(s_2=3.2\) represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

\(\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525\)

And the deviation would be just the square root of the variance:

\(S_p=3.678\)

The statistic is givne by:

\(t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923\)

The degrees of freedom are

\(df=20+20-2=38\)

And the p value is given by:

\(p_v =2*P(t_{38}>2.923) =0.0058\)

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

At the null hypothesis, it is tested if there is no difference, that is:

\(H_0: \mu_1 - \mu_2 = 0\)

At the alternative hypothesis, it is tested if there is a difference, that is:

\(H_a: \mu_1 - \mu_2 \neq 0\)

For each sample, we have that they are given by

\(\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168\)

\(\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155\)

Hence, for the distribution of differences, the mean and the standard error are given by:

\(\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163\)

It is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis, hence:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{3.3 - 0}{1.163}\)

\(t = 2.84\)

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of \(|z^{\ast}| = 2.0244\).

Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.

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The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.

To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.

Given:

Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.

Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.

No information is provided about the defect rate of the third plant.

To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.

Let's calculate the overall probability:

Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)

Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)

To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:

Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)

Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)

Overall probability of selecting a defective MP3 player is given by:

Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)

Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%

Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.

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For parallel lines, gradients (slope) must be the same.

The lines given in multiple choice, no line with the same gradient/slope as line y = 3x - 2.

Step-by-step explanation:

From y = 3x - 2,

The slope = 3

Let's check slopes of lines from multiple choice:

From first line

4x + 2y = 5

2y = -4x + 5 (dived 2 both sides)

y = - 2x + 5/2

The slope = -2

Continue with remaining three equations you get slopes: -1/2, -4 and 4.

Hence no equations above represent parallel equation to y = 3x - 2

Answer: 110 degrees

Step-by-step explanation: If we have a triangle with an exterior line sticking out, we can determine the measure of the exterior angle by applying the Exterior Angle Theorem. According to the theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

In this case, the two known interior angles are 65 degrees and 45 degrees. To find the measure of the exterior angle, x, we add these two angles:

x = 65 degrees + 45 degrees

x = 110 degrees

\(\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -\)

we have given ,

★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.

➝ ∠ A + ∠ B + ∠ C = 180°

➝ 65° + 45° + ∠ C = 180°

➝ 110° + ∠ C = 180°

➝ ∠ C = 180° - 110°

➝ ∠ C = 70°

Now,

★ Calculating for x :-

↝ ∠ C + x = 180°

↝ 70° + x = 180°

↝ x = 180° - 70°

↝ x = 110°

Hence, The value of x will be 110°.

The smallest to the largest side is SQ, RS, QR, the correct option is B.

A triangle is a polygon with three sides, angles, and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides, as obtuse, acute and right-angled triangle and scalene, isosceles and equilateral triangle.

The measure of angle of the triangle is 56°, 83°, and 41°.

From the property of the triangle, the side opposite the bigger measure angle is the largest.

The measure of angle QRS is 41°, angle RQS is 56°, and angle QSR is 83°.

The smallest side will be the side opposite to QRS, i.e. SQ,

The largest side will be the side opposite to QSR, i.e. QR

The side in order from the smallest to the largest, SQ, RS, QR.

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Answer: Kavitha is 18 and Lizzy is 27

Step-by-step explanation: 8 years ago, Kavitha was 10 and Lizzy was 19.

10 × 2 = 20

20 - 1 = 19

Kavitha is 9 years younger than Lizzy because 27 - 9 = 18

9514 1404 393

Answer:

  Kavitha is 19 and Lizzy is 28

Step-by-step explanation:

Let k and l represent the current ages of Kavitha and Lizzy.

  k = l -9 . . . . . Kavitha is 9 years younger

  l -8 = 2(k -8 -1) . . . . 8 years ago, Lizzy was 2 times as old as Kavitha was 9 years ago

  l -8 = 2(l -9 -9) . . . . substitute for k

  l -8 = 2l -36 . . . . . . eliminate parentheses

  28 = l . . . . . . . . . . . add 36 - l

  k = 28 -9 = 19

Kavitha is 19; Lizzy is 28.

Let's consider the relationship between the circumference and the radius:

 ⇒ first, consider the equation for finding the circumference

      \(Circumference = 2\pi *radius\)

Let's consider the known information

Let's plug the known information to find the radius:

  \(Circumference = 2\pi *radius\\36\pi =2\pi *radius\\radius = 18\)

Thus the radius is 18 cm

Answer: 18 cm

Hope that helps!

There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

Answer:

3rd one

Step-by-step explanation:

Answer: Pair of angle 56 and angle 34 are both complementary

Step-by-step explanation:

Complementary angles are angles that add up to 90°

Answer:

Jeremiah travels at 26.667 mi/hr and Ermias travels at 18.667 mi/hr.

Step-by-step explanation:

Say Ermias' speed is 's' and Jeremiah's is 'v'

distance = rate * time

distance = ( v * time) + ( s * time)

v = s + 8

240mi = ( (s+8) * 8 ) + ( s + 8)

240 = (8s +64) + s + 8

240 = 9s + 72

240 - 72 = 9 s

168 = 9 s

18.6666667 = s

v = 18.6666667 + 8

v = 26.6666667

The equation of the relationship is f(200) = 0.75 * 200

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

Total number of drinks = 200

Cost of each drink = 0.75

Using the above as a guide, we have the following:

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

Substitute the known values in the above equation, so, we have the following representation

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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Answer\(2pq^{3} (7p^{2} r^{2} +q)\)

Step-by-step explanation:

When we factor something we try to pull out as much as possible. When looking at the 2 parts, we see that we can pull out a 2 as the largest coefficient. We also see that both parts have a p, so we pull out 1 p. We see that both sides have q^3, so we will pull that out. Only 1 side has r, so we cannot pull that out.

Hopefully this helps!

The value of angle 1 given the value of angle 4 as 47° will be 133°

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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Answer:

C: EAF Is the correct answer

Weight is in Olivia's backpack is 5/6 pound.

As in the given problem olivia's  history book weights 1/2 of a pound and

her lunch weighs 2/3 of a pound.

As both the units are same,

Thus total weight must be summation of both history book and her lunch  box.

total weight is =1/2 +2/3 pound

= (3+2)/6

that is equal to 5/6 pound.

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Answer:

\( {a}^{2} + 2ab + {b}^{2} \)

Step-by-step explanation:

\((a + b) {}^{2} = (a + b)(a + b) = {a}^{2} + ab + ab + {b}^{2} = {a}^{2} + 2ab + {b}^{2} \)

Hi!

___________________________________________________________

\(\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup\)

a^2+2ab+b^2

\(\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup\)

Remember the rule for expanding a binomial squared.

\(\twoheadrightarrow\sf (a+b)^2=a^2+2ab+b^2\)

So we square the first term, then multiply the product of the two terms times 2.

\(\twoheadrightarrow\sf a^2+2ab+b^2\)

This is our answer.

--

Hope that this helped! Best wishes.

\(\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}\)

--

The triangles given are similar; therefore, the ratio of their side lengths must be the same.

This means

therefore,

cross multipication gives

Dividing both sides by 4 gives

which is our answer!

\(f(g(13)) = f( \alpha ) \\ where \: \alpha = g(13)\)

As shown in the output of g when we want to input 13 is shown in the second figure.

\( \alpha = g(13 )= 16\)

Now we want to solve for f(g(13)),now that we know what g(13) is

\(f(g(13)) = f( \alpha ) = f(16) = 32\)

Answer:

C=32

Step-by-step explanation:

This mapping is both one to one mapping and onto mapping

f(g(13))=f(ã)

since we know that g(13),we proceed to the codomain of g which is g(16)

That will be

f(16)=32