Work out length AC.

10 cm
Not drawn
accurately

120
7 cm

Step-by-step explanation:

As the points A, B, C and D lie on a circle, So, ABCD is a cyclic quadrilateral...

As, Sum of opp. ∠s in a cyclic quadrilateral = 180°

∴ ∠ADC + ∠ABC = 180°

=> ∠ADC + 100° = 180° => ∠ADC = 80°

Now,

Sum, of all angles in a traingle = 180°

In ΔACD, ∠CAD + ∠ADC + ∠ACD = 180°

=> ∠CAD + 80° + 40° = 180°

=> ∠CAD = 180° - 80° - 40° = 60°

As CT is tangent to the circle at the point C and CD is a chord of the circle, So

∠DCT = ∠CAD........(∠s in alternate segments are equal,,So ∠CAD = 60°)

=> ∠DCT = 60°

Answer:

See below ~

Step-by-step explanation:

∠ADC

∠DCT

Answer:

The focus (or foci).

Step-by-step explanation:

The focus of a hyperbola are equidistant from the center of the hyperbola. They can be found with the formula c²= a² + b². The points for the foci being

(-c, y) and (c, y).

In this illustration, the foci are the points in blue.

Answer:

\( \boxed{\bf A. \: x - 2}\)

Step-by-step explanation:

\( \sf ( x + 1)^2-9/ x + 4 \)

First, we need to factor the expressions that are not already factored.

Now, let's Cancel out x+4 in both numerator and denominator.

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

The ending balance in accumulated other comprehensive income on December 31, 2019, is $10,200 (credit balance).

To determine the ending balance in accumulated other comprehensive income on December 31, 2019, we need to analyze the changes in comprehensive income and other comprehensive loss. The net income of $12,000 and other comprehensive loss of $3,000 (net of tax) for the year ended December 31, 2020, indicate that the comprehensive income for the year is $9,000 ($12,000 - $3,000).

The ending balance in accumulated other comprehensive income can be calculated by adding the comprehensive income for the year to the beginning balance in accumulated other comprehensive income. Given that the ending balance on December 31, 2020, is $6,800 (credit balance), we can derive the beginning balance in accumulated other comprehensive income on December 31, 2019, by subtracting the comprehensive income for the year ($9,000) from the ending balance on December 31, 2020. Therefore, the ending balance in accumulated other comprehensive income on December 31, 2019, is $10,200 (credit balance).

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Answer:

vhvjh648585869786

Step-by-step explanation:

Answer:the answer is c :))

Step-by-step explanation:

Answer:THE CORRECT ANSWER IS D)

Step-by-step explanation:

We can determine that the necessary angle ∠a is 15° using the provided secant line.

A secant crosses a circle at precisely two points in a case of a circle.

Mathematicians refer to a line that cuts through the points P and Q of any arbitrary curve whose equation is y=f as a secant, from the Latin term secant, which means to cut (x).

So, we know that:

c = 55° and b = 25°

And, the formula is:

∠a = c - b/2

Now, substitute values as follows:

∠a = c - b/2

∠a = 55 - 25/2

∠a = 30/2

∠a = 15°

Therefore, using the given secant line, we know that the required angle ∠a is 15° respectively.

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Complete question:

Answer:

\( 5^{-3} = \dfrac{1}{125} \)

Step-by-step explanation:

Rule of negative exponents:

\( a^{-n} = \dfrac{1}{a^n} \)

This problem:

\( 5^{-3} = \dfrac{1}{5^3} = \dfrac{1}{5 \cdot 5 \cdot 5} = \dfrac{1}{125} \)

Answer:

\(\boxed{\frac{1}{125}}\)

Step-by-step explanation:

\(5^{-3}\)

Apply rule:

\(\displaystyle a^{-b}=\frac{1}{a^b}\)

\(\displaystyle 5^{-3}=\frac{1}{5^3}= \frac{1}{125}\)

On solving the provided question, we cans ay that sum of co-exterior angles are 180 so, 180-73 = x => x = 7

An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.

here,

angle x and 73 are co-exterior angles

so, sum of co-exterior angles are 180.

so, 180-73 = x => x = 7

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Answer: 112i + 85.8j

Step-by-step explanation:

Answer:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

Step-by-step explanation:

To find the components of a vector given its magnitude and direction, use the following formula:

\(\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}\)

where:

Given:

Substitute the given values into the formula:

\(\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)\)

\(\vec{H}=\left(-32.1, 79.6\right)\)

Therefore:

\(\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}\)

The Chi-square test is a statistical test used to determine if there is a significant difference between observed and expected frequencies in categorical data. In this example, the test is used to assess whether there is a significant difference in the mean breaking strengths of two types of cables.

The Chi-square test of significance is employed when dealing with categorical or nominal data. It compares the observed frequencies with the frequencies that would be expected if the variables were independent. In this case, the breaking strengths of the two cables are the variables of interest.

To perform the test, the first step is to define the null hypothesis (H0) and the alternative hypothesis (Ha). In this example, H0 assumes that there is no difference in the mean breaking strengths of the two cables, while Ha suggests that there is a difference.

Next, the test statistic, denoted by X2 (chi-square), is calculated using the formula X2 = Σ[(O - E)²/E], where O represents the observed frequencies and E represents the expected frequencies under the assumption of independence.

To determine the expected frequencies, we need to estimate the means and variances of the breaking strengths. Here, x = 1925 and sigma = 40 for the first cable, and x = 1905 and sigma = 30 for the second cable.

Once the test statistic is calculated, it is compared to a critical value from the Chi-square distribution with degrees of freedom equal to (r - 1)(c - 1), where r is the number of rows and c is the number of columns in the contingency table. The significance level of 0.01 determines the critical value.

If the calculated X2 value is greater than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the mean breaking strengths of the two cables. Conversely, if the calculated X2 value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant difference.

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The correct answer to the multiple-choice question is B) 0.2294. To answer this question, we need to use the properties of the normal distribution.

We know that the distribution of scores is normal with a mean of 560 and a standard deviation of 90. We want to find the percentage of examinees who score between 600 and 700.

To do this, we first need to standardize the scores using the formula z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. For a score of 600, the standardized score is z = (600 - 560) / 90 = 0.44. For a score of 700, the standardized score is z = (700 - 560) / 90 = 1.56.

Next, we look up the percentage of examinees who score between these two standardized scores using a standard normal distribution table or a calculator. The percentage of examinees who score between 0.44 and 1.56 is approximately 0.2294 or 22.94%.

Therefore, the correct answer to the multiple-choice question is B) 0.2294.

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Answer:

-7

Step-by-step explanation:

We are given the following sequence:

\( \displaystyle \large{6,5,4,3,2,...}\)

Checking if the sequence is arithmetic by using the following formula:

\( \displaystyle \large{a_{n + 1} - a_n = d}\)

where d is a common difference. Common Difference means that these sequences must have same difference.

Let's check!

5-6 = -1

4-5 = -1

3-4 = -1

2-3 = -1

Since they are the same, the sequence is arithmetic.

General Term of Arithmetic Sequence

\( \displaystyle \large{a_n = a_1 + (n - 1)d}\)

We know that a1 is 6 since 6 is the first term.

d is -1.

Our goal is to find a14. Therefore,

\( \displaystyle \large{a_{14} = 6 + (14 - 1)( - 1)} \\ \displaystyle \large{a_{14} = 6 + (13)( - 1)} \\ \displaystyle \large{a_{14} = 6 - 13} \\ \displaystyle \large{a_{14} = - 7}\)

Therefore, the 14th term of sequence is -7.

Answer:

I also searched it before.

Answer: A

Step-by-step explanation:

because 145 is on the outside and is a supplementary line so the angle next to it would be 180-145 = 35

now for 85, the angle next to it would be 180-85 = 95

we now know to angles in the triangle 35 and 95

there is 180 degrees in a triangle

A = 180 - 35 + 95

A = 50

Answer:

50 degrees

Step-by-step explanation:

using the outside angles, 180 - 85, and 180-145, to get the inner angles. then subtracting them from 180. 180-35-95=50

Answers:

Please read the disclaimer below.

=============================================

Explanation:

Disclaimer: The issue is that without the coordinate values, it's impossible to determine the regression line. It's not clear where some (or most) of the red points are located. Often that's why a table is needed. I would ask your teacher for clarification.

With that said, I'll still give it a shot.

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

Part 1

The blue regression line appears to go through the two points (0,30) and (50,50). Let's find the slope through this line

m = (y2-y1)/(x2-x1)

m = (50-30)/(50-0)

m = 20/50

m = 0.40

The y intercept is b = 30 since the blue line appears to cross the y axis at this location.

So y = mx+b turns into y = 0.40x+30

Replace x with n and replace y with b

We go from y = 0.40x+30 to b = 0.40n+30 which is the regression line.

Again this is all based on the assumptions that the blue line goes through (0,30) and (50,50).

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

Part 2

Assuming we have the correct regression equation, we can immediately see that each extra call costs $0.40 which is the same as 40 cents. So it's 40 cents per call. This is the slope value, which is the rate of change. Each time n goes up by 1, b goes up by 0.40

Because the regression line estimates the actual observed values, we won't always land on a red point. But the goal is to get as close as possible.

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

Part 3

Again assuming we have the correct regression equation, we plug in n = 34 and evaluate to determine the bill

b = 0.40*n + 30

b = 0.40*34 + 30

b = 43.60

Pete would pay $43.60 if he made 34 calls.

Answer:

18c - 30d + 36

Step-by-step explanation:

6(3c - 5d + 6) ← multiply each term in the parenthesis by 6

= 18c - 30d + 36

Answer:

18c - 30d + 36

Step-by-step explanation:

6(3c - 5d + 6)

= (6 × 3c) + (6 × 5d) + (6 × 6)

= 18c - 30d + 36

The pressure of the gas at the volume of 900 litres will be 32 kilopascals.

Boyle’s law states that the pressure of compressed gas is inversely proportional to its volume. It means that the product of the pressure and volume of the gas is constant when the temperature of the gas is constant.

Given that the pressure of a certain sample of gas is 16 kilopascals when its volume is 1,800 litres.

The pressure of the gas at the volume of 900 litres will be calculated as;-

P₁V₁ = P₂V₂

( 16 x 1800 ) = P₂ x 900

P₂ = ( 16 x 1800 ) / 900

P₂ = 16 x 2

P₂ = 32 Kilopascal

Hence, the pressure will be 32 kilopascals.

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Answer: 6 liters

Step-by-step explanation:

24 liters

He sells 75%

24 x 0.75 = 18 liters

24 - 18 = 6

He still has 6 liters left

Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.

The result of the each of the following set is

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

The given values are

A = {1, 3, 5, 7, 9}

B = {3, 6, 9}

C = {2, 4, 6, 8}

Then find the each given terms in set roaster notation

Union of the set, intersection of the set  and the difference of the set are the basic operations of set

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

Therefore, all the given terms has been found

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Answer:

? =8.77

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite side/ hypotenuse

sin 20 = 3 / ?

? = 3/ sin 20

? = 8.7714132

To the nearest hundredth

? =8.77

Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

The solution of an inequality is the set of numbers that make the inequality true.

In this case, you know that:

Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is

10 + 0.70x <34.50

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Answer:

The first and last option.

Explanation:

You said quick soooo... brainliest?

Explanation

let x represents 140 of the original price

Step 1

if

as the proportion is the same

To estimate the mean per capita income for a major city in California with an error of at most $0.56 at the 85% confidence level, the economist needs to determine the required sample size.

To calculate the required sample size, we can use the formula: \(n = \left(\frac{{Z \cdot \sigma}}{{E}}\right)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level (in this case, for 85% confidence level, \(Z \approx 1.44\)), \(\sigma\) is the known standard deviation (\$6.6), and \(E\) is the desired margin of error (\$0.56). Plugging in the values, we have \(n = \left(\frac{{1.44 \cdot 6.6}}{{0.56}}\right)^2 \approx 52\). Therefore, a sample size of approximately 52 would be required to estimate the mean per capita income with an error of at most $0.56 at the 85% confidence level.

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For the upper bound, we can simplify the expression by ignoring the smaller terms. In this case, the dominant term is 2nlogn. We can drop the constant factor 2 and write it as O(nlogn).

This represents the upper bound, indicating that the function grows no faster than a multiple of nlogn.

For the lower bound, we consider the dominant term. Here, the dominant term is also 2nlogn. Again, ignoring the constant factor, we have Ω(nlogn) as the lower bound. This means the function grows no slower than a multiple of nlogn.

Combining the upper and lower bounds, we can conclude that T(n) = 2nlogn + logn is in the Big Theta runtime class Θ(nlogn). It means the function's growth rate is tightly bounded by nlogn, with both an upper and lower bound.

Note that the smaller term logn does not affect the overall complexity class since it is overshadowed by the dominant term 2nlogn. Therefore, we can disregard it in the Big Theta analysis.

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The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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