if sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............
Solve using double angle trigonometric functions​

Answer:

What is the question or image?

Step-by-step explanation:

Need it to solve

Check the picture below.

so as we can see, the focus point is above the directrix, meaning the parabola opens upwards, and since the vertex is halfway between the directrix and focus point, that means the vertex is at (0 , 1), and distance from the vertex to either the focus or directrix is 2, namely p = 2, and is positive since is opening upwards, thus

\(\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(4(\stackrel{p}{2})(y-\stackrel{k}{1})=(x-\stackrel{h}{0})^2\implies 8(y-1)=x^2 \\\\\\ y-1=\cfrac{x^2}{8}\implies \boxed{y=\cfrac{1}{8}x^2+1}\)

Answer:

525

Step-by-step explanation:

i really dont know what it asking

Answer:

69

Step-by-step explanation:

Answer:  

7/15

Step-by-step explanation:

You have 120 bags and 64 of them in total do not contain buttons 120 - 64 = 56 now =you have 56 bags with buttons.

Hope This Help :) Lol

Let us take the determinant of the given matrix\(\[\mathbf{A}=\left[\begin{array}{ccc} k+1 & 2 & 1 \\ 0 & 3 & k \\ 1 & 1 & 1 \end{array}\right]\]\)as follows:

\(\[\mathbf{A}=\left[\begin{array}{ccc} k+1 & 2 & 1 \\ 0 & 3 & k \\ 1 & 1 & 1 \end{array}\right]\] \[=\begin{aligned}\left| \begin{array}{ccc} k+1 & 2 & 1 \\ 0 & 3 & k \\ 1 & 1 & 1 \end{array} \right|&=\left| \begin{array}{cc} 3 & k \\ 1 & 1 \end{array} \right|-\left| \begin{array}{cc} 0 & k \\ 1 & 1 \end{array} \right|+\left| \begin{array}{cc} 0 & 3 \\ 1 & 1 \end{array} \right|\\ &=3-0-3\\ &=0\end{aligned}\]\)

The determinant is zero for any value of k. Therefore, we can say that the possible values of k are infinite.

The above result is true as the third row is equal to the sum of the first two rows, which makes the rows linearly dependent and the determinant is 0.

Moreover, by expanding the determinant along the third row, we get\(\[\left|\begin{array}{ccc} k+1 & 2 & 1\\ 0 & 3 & k\\ 1 & 1 & 1 \end{array}\right|=k\left|\begin{array}{cc} 2 & 1 \\ 1 & 1 \end{array}\right| - \left|\begin{array}{cc} 2 & 1 \\ 3 & k \end{array}\right| + \left|\begin{array}{cc} k+1 & 2 \\ 0 & 3 \end{array}\right| = k-5k-3-6+3k = -2k - 9\]\)

Now the determinant is zero\(,\[-2k-9=0\]\[\Rightarrow -2k=9\]\)

Therefore, the only possible value of k is\(\[\frac{-9}{2}\]\)

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The cost of tuition and fees in the academic year of 2023–2024 would be = $12,600

Tuition fees is the amount of money that a student pays to be taught in a school such as university or college.

The tuition and fees charged in the academic year of 2014–2015 = $9200

The tuition and fees charged in the academic year of 2019–2020 = $10,900

The difference between the two given years = 4 years

The difference between the fees for those years = 10,900- 9200 = 1,700.

The difference between academic year of 2019–2020 and 2023–2024 is also 4years.

Therefore the estimated cost of tuition fees would be =

10,900+ 1,700 = $12,600.

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The volume of the given solid bounded by the cylinders is 88r³/3

The integral of the top curve less the bottom curve is used to define the space between two curves. Three dimensions can be added to this concept. The double integral of the top surface less the bottom surface is how we described the volume between two surfaces. The Fubini's Theorem can be used to formally express this.

The dimensions of cylinders are x² + y² = 4r² ⇒ x² = 4r² - y²

y² + Z² = 4r² ⇒ z² = 4r² - y²

So, the volume of the give solid

V = ∫r -r∫√(4r² - y²) -√(4r² - y²) 2√(4r² - y²)dx dy

⇒ V = 2∫r -r [ x√(4r² - y²)]√(4r² - y²) -√(4r² - y²) dy

⇒ V = 2∫r -r [(4r² - y²) - {-(4r² - y²)}] dy

⇒ V = 2∫r -r [(4r² - y²) + (4r² - y²)] dy

⇒ V = 2∫r -r [2(4r² - y²)] dy

⇒ V = 4∫r -r (4r² - y²) dy

⇒ V = 4[4r²y - y³/3] r -r

⇒ V = 4[4r²(r+r) - (r³+r³)/3]

⇒ V = 4[4r²*2r - 2r³/3]

⇒ V = 8[4r³ - r³/3]

⇒ V = 8[(12r³ - r³)/3]

⇒ V = 8[11r³/3]

⇒ V = 88r³/3

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a)On Monday, 120 apple tarts were made.

b) The lower bound of the probability that the tart taken at random on Tuesday is a lemon tart is approximately 0.267.

a) To determine the number of apple tarts made on Monday, we can set up a proportion based on the sample of 15 tarts and the known proportion of apple tarts.

Let x be the number of apple tarts made on Monday.

The proportion of apple tarts in the sample is given by:

\(6/15 = x/300\).

Cross-multiplying and solving for x, we get:

\(6 * 300 = 15 * x,\)

\(1800 = 15x\),

\(x = 1800/15\),

\(x = 120\).

b) To find the lower bound of the probability that the tart taken at random on Tuesday is a lemon tart, we need to consider the minimum number of lemon tarts needed in the quality checks sample.

The number of lemon tarts needed is 4 (correct to the nearest whole number).

To calculate the lower bound of the probability, we assume that exactly 4 lemon tarts were needed, meaning the remaining 11 tarts in the sample are apple tarts.

The probability of selecting a lemon tart from the 300 tarts made on Tuesday is:

\(4/15 ≈ 0.267\) (rounded to three decimal places).

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Answer:1. 1.0 1.0 1.4

Step-by-step explanation:

The  length of the sides are given by the 45°–45°–90° triangle theorem.

Correct responses:

The 45°–45°–90° triangle theorem states that the ratio of the lengths of

the sides of triangles having interior angles of 45°, 45°, 90° is 1 : 1 : √2

The lengths of the legs of an isosceles triangle are equal.

The legs of the given isosceles right triangle are AB and AC

Therefore;

AB = AC

Taking the lengths of AB as 1 unit, we have;

AB = 1 = AC

According to Pythagorean theorem, we have;

\(\overline{BC}^2 = \mathbf{\overline{AB}^2 + \overline{AC}^2}\)

Which gives;

\(\overline{BC}^2 = 1^2 + 1^2 = \mathbf{ 2}\)

Therefore;

BC = √2

Therefore, by setting the length of AB = AC = 1, we have;

The above values are in the ratio 1 : 1 : √2, which corresponds with the

45°-45°-90° triangle theorem.

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Yes, One of them must be even and this is because Pigeonhole Principle.

What is Pigeonhole Principle?

According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.  As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

From series {1,2......2n},  we need to select 'n+1' integers.

Even integers series from above series is {2,4,6..........2(n-1), 2n}

Odd integers series from above series is {1,3,5......2(n-2), 2n-1}

We can choose only n odd integers from the series. Therefore, if we choose n+1 integers, at least one of them must have to be even integer.

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Answer:

151 is your answer of this question

Step-by-step explanation:

first youvshoud divide ()and multiply by 5

I think your teacher meant to say Reflexive property instead of reflection. The reflexive property is the idea that any segment is the same length as itself. It seems like a trivial idea, but it's useful to be able to pull triangles apart like in this problem here.

Note: when naming a segment, the order of the endpoints listed doesn't matter. So that's why EU is the same as UE.

If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Answer:

x^2 -12x+36

Step-by-step explanation:

(x - 6)^2

(x-6)(x-6)

FOIL

x^2 - 6x-6x+36

Combine like terms

x^2 -12x+36

Answer: 60%

Step-by-step explanation:

Answer:

The probability that the counter  was blue is \(\mathbf{\frac{2}{5}}\)

Step-by-step explanation:

Number of black Counters = 5

Number of blue Counters = 4

Number of white Counters = 1

We need to write down the probability that the counter  was blue.​

First find Total Counters

Total Counters = Number of black Counters + Number of blue Counters + Number of white Counters

Total Counters = 5+4+1

Total Counters = 10

Now, we need to find probability that the counter taken was blue

The formula used is:

\(Probability= \frac{Number\:of\:favourable\:outcomes}{Total\:outcomes}\)

There are 4 blue counters in the back, so Favourable outcomes = 4

\(Probability= \frac{Number\:of\:favourable\:outcomes}{Total\:outcomes}\\Probability= \frac{4}{10}\\Probability= \frac{2}{5}\)

The probability that the counter  was blue is \(\mathbf{\frac{2}{5}}\)

For the function transformation form of f(x), \(g(x) = a f(\frac{1}{b} x - h) + k \), we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.

A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,

We have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, \(g(x) = a f(\frac{1}{b} x - h) + k \), now see the graph carefully.

Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.

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Complete question:

The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k

replacing which variable with what number will result in the transformation displayed in the graph?

a) b is replacing by 1/2

b) k is replacing by -1/2

c) h is replacing by -2

d) a is replacing by 2

For series (a), the series converges for |z| ≤ 1, and for series (b), the series converges for |z| ≤ 1.

For series (a), ∑_{1}^{∞} n!z^n, we can determine the values of z for which the series converges by using the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Using the ratio test, we have:

lim_{n}^{∞} |{(n+1)!z^{(n+1)} / (n!z^n)|

= lim_{n}^{∞} |(n+1)z} / (z^n)|

=lim_{n}^{∞} |(n+1) / {z^{(n-1)}}|

For the series to converge, we need this limit to be less than 1. Let's consider two cases:

1. If |z| > 1, then as n approaches infinity, the absolute value of the ratio |(n+1)/z^{(n-1)}| will tend towards infinity. Therefore, the series diverges.

2. If |z| ≤ 1, then as n approaches infinity, the absolute value of the ratio |(n+1)/z^{(n-1)}| will tend towards zero. Therefore, the series converges.

For series (b), ∑_{1}^{∞} n!z^n, we can use the ratio test in a similar way to determine the values of z for which the series converges.

Using the ratio test, we have:

lim_{n}^{∞} |{(n+1)!z^{(n+1)²} / (n!z^{n²})|

= lim_{n}^{∞} |{(n+1)z^{(2n+1)}} / (z^{n²})|

= lim_{n}^{∞} |{(n+1)z^{(2n-1)}} / {z^{n²}}|

Again, we consider two cases:

1. If |z| > 1, then as n approaches infinity, the absolute value of the ratio|{(n+1)!z^{(n+1)²} / (n!z^{n²})|  will tend towards infinity. Therefore, the series diverges.

2. If |z| ≤ 1, then as n approaches infinity, the absolute value of the ratio |{(n+1)z^{(2n-1)}} / {z^{n²}}| will tend towards zero. Therefore, the series converges.

In summary, for series (a), the series converges for |z| ≤ 1, and for series (b), the series converges for |z| ≤ 1.

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For series (a), the series converges for |z| ≤ 1, and for series (b), the series converges for |z| ≤ 1.

For series (a), \(\sum_{1}^{\infty} n!z^n\), we can determine the values of z for which the series converges by using the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges.

Using the ratio test, we have:

\(\lim_{n \to \infty}| \frac {(n+1)!z^{(n+1)}}{(n!z^n)} |\)

\(= \lim_{n \to \infty} |\frac {(n+1)z}{(z^n)}|\)

\(= \lim_{n \to \infty} |\frac {(n+1)}{z^{(n-1)}}|\)

For the series to converge, we need this limit to be less than 1. Let's consider two cases:

1. If |z| > 1, then as n approaches infinity, the absolute value of the ratio \(|\frac{(n+1)}{z^{(n-1)}}|\) will tend towards infinity. Therefore, the series diverges.

2. If |z| ≤ 1, then as n approaches infinity, the absolute value of the ratio \(|\frac{(n+1)}{z^{(n-1)}}|\) will tend towards zero. Therefore, the series converges.

For series (b), \(\sum_{1}^{\infty} n!z^n\), we can use the ratio test in a similar way to determine the values of z for which the series converges.

Using the ratio test, we have:

\(\lim_{n \to \infty} |\frac{(n+1)!z^{(n+1)^2}}{(n!z^{n^2})}|\)

\(= \lim_{n \to \infty} |\frac{(n+1)z^{(2n+1)}}{(z^{n^2})}|\)

\(= \lim_{n \to \infty} |\frac{(n+1)z^{(2n-1)}}{z^{n^2}}|\)

Again, we consider two cases:

1. If |z| > 1, then as n approaches infinity, the absolute value of the ratio \(|\frac {(n+1)!z^{(n+1)^2}}{(n!z^{n^2})}|\)  will tend towards infinity. Therefore, the series diverges.

2. If |z| ≤ 1, then as n approaches infinity, the absolute value of the ratio \(|\frac{(n+1)z^{(2n-1)}}{z^{n^2}}|\) will tend towards zero. Therefore, the series converges.

In summary, for series (a), the series converges for |z| ≤ 1, and for series (b), the series converges for |z| ≤ 1.

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Geometric solids with circular cross-sections include cylinders, cones, and spheres. Geometric solids with circular cross-sections include cylinders, cones, and spheres. And Cylinders, cones, and spheres can be created by rotating a two-dimensional shape about an axis.

1. Cylinder: A cylinder is a 3-dimensional solid that has two parallel circular bases connected by a curved surface. Cylinders are commonly found in everyday objects like soda cans and water bottles.

2. Cone: A cone is a 3-dimensional solid that has a circular base and a curved surface that tapers to a point. Cones are often used in architecture, like on the top of a church steeple.

3. Sphere: A sphere is a 3-dimensional solid that has a circular shape in all directions. Spheres are found in many natural objects like planets and fruit, as well as in man-made objects like Christmas ornaments.

Geometric solids with circular cross-sections are used in various fields, including architecture, engineering, and science. They are used for creating objects such as cans, pipes, towers, and buildings. These shapes are also used for modeling the natural world, such as the earth, planets, and the stars.

Cylinders, cones, and spheres can be created by rotating a two-dimensional shape about an axis. For instance, a circle that is rotated around its center axis forms a cylinder. Similarly, a triangle that is rotated around one of its sides forms a cone, while a circle that is rotated around its center axis forms a sphere.

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Answer:

Area: 6x+6

Perimiter: 4x+10

Step-by-step explanation: to find the area of something multiply the width times the height. to find the perimeter of something add each side together. use the order of operations (PEMDAS).

Area=3(2x+2)

Area=6x+6

Perimeter=3+3+(2x+2)+(2x+2)

Perimeter=6+4x+4

Perimeter=4x+10

Answer:

Area=length*width

A=3(2x+2)=6x+6 unit squar

Perimeter = 2l+2w

P=2(3)+2(2x+2)

P=6+4x+4

P=10+4x

Given:

f is an even function.

Even function symmetric with respect to y-axis.

b)

function is neither odd nor even.

Its not symmetric.

Answer:

Write the equation of a line passing through point (8, -3 ) and is perpendicular to

−

2

x

+

y

=

9

Step-by-step explanation:

The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

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Answer:

t=1/2u

Step-by-step explanation:

Since t=tens digit and u=units digit, as given in the equation that means that t+u=9. Since the tens digit is one-half the units digit that means: \(t=\frac{1}{2}u\) since it's one half the units digit.

A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

Suppose that the given function is

\(f:X\rightarrow Y\)

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

\(f^{-1}: Y \rightarrow X\)

such that:

\(\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X\)

(and vice versa).

It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'

The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.

Hence, the correct option is A.

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a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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The probability that the article will have no errors is approximately 0.0233.

To solve this problem, we can use the formula for the probability of an event, which is the number of favorable outcomes divided by the total number of outcomes.

Let's first find the probability that the article is typed by the first typist. Since the article is equally likely to be typed by either typist, this probability is 1/2.

Now, we need to find the probability that the article has no errors given that it is typed by the first typist. We know that the average number of errors per article typed by the first typist is 3.5, so the probability that an article typed by the first typist has no errors is given by the Poisson distribution with λ = 3.5:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-3.5) * 3.5^0 / 1 = e^(-3.5) ≈ 0.0302

Similarly, we can find the probability that the article has no errors given that it is typed by the second typist. This probability is given by the Poisson distribution with λ = 4.1:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.1) * 4.1^0 / 1 = e^(-4.1) ≈ 0.0164

Finally, we can use the law of total probability to find the probability that the article has no errors:

P(X = 0) = P(X = 0 | typed by first typist) * P(typed by first typist) + P(X = 0 | typed by second typist) * P(typed by second typist)

= 0.0302 * 1/2 + 0.0164 * 1/2

= 0.0233

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