Consider this equation.

cos(0) = 4/41

If 0 is an angle in quadrant IV, what is the value of sin(0)

Answer:

side xy = 9.41 cm

Step-by-step explanation:

Answer:

side xz is 78°

90+12=102

180-102

Answer:

\(z = 1.06\)

Step-by-step explanation:

Given

\(\bar x = 519\) -- Mean

\(\sigma = 104.7\) --- Standard Deviation

\(x = 630\) --- Time

Required

Determine the standardized value (z)

The standardized value (z) is calculated using:

\(z = \frac{x - \bar x}{\sigma}\)

This gives:

\(z = \frac{630 - 519}{104.7}\)

\(z = \frac{111}{104.7}\)

\(z = 1.06017191977\)

\(z = 1.06\) --- approximated

Given:

Consider the below figure attached with this question.

In circle A below, chord BC and diameter DAE intersect at F.

The arc CD = 46° and arc BE = 78°.

To find:

The measure of angle BFE.

Solution:

According to intersecting chords theorem, if two chords intersect inside the circle then the angle on the intersection is the average of intercepted arcs.

Using intersecting chords theorem, we get

\(m\angle BFE=\dfrac{1}{2}(m(arcCD)+m(arcBE))\)

\(m\angle BFE=\dfrac{1}{2}(46^\circ+78^\circ)\)

\(m\angle BFE=\dfrac{1}{2}(124^\circ)\)

\(m\angle BFE=62^\circ\)

Therefore, the measure of angle BFE is 62°.

Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

42 1/6 square inches

Step-by-step explanation:

253=6x

x=42 1/6

42 1/6 square inches

:]

\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)

Answer:

2^3 = 8

Step-by-step explanation:

I'm not sure what you mean, but I'll try.

2^3 is the same as \( 2^3 \),

and it means a multiplication of 3 factors of the base, 2.

That means \(2^3 = 2 \times 2 \times 2 = 4 \times 2 = 8\)

Answer:

x = 6, y = -2, z = 0

Step-by-step explanation:

To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.

Answer:

6, -2, 0

Step-by-step explanation:

Answer:

You can think percentages as fractions by always using the denominator as 100 and the percentage as the numerator. For example, 10% would be 10/100 or 1/10 and 25% as 25/100 or 1/4 and 75% as 75/100.

After solving, the maximum height of the ball is 90.25 feet.

In the given question,

A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.

The quadratic function

h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.

We have to find the maximum height of the ball.

Height is given that;

h(t) = -16t^2+52t + 48

Now comparing the given equation by the standard equation ax^2+bx+c=0

Here b = 52, a = -16

For maximum height put t= -b/2a

t = -52/2(-16)

t = 52/32

t = 1.625

Maximum height

h(1.625) = -16(1.625)^2+52(1.625) + 48

h(1.625) = -42.25+ 84.5 + 48

h(1.625) = 90.25 feet

The maximum height of the ball is 90.25 feet.

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Answer:

700

Step-by-step explanation:

175 divided by 3 is 58.3 and then you multiply 58.3 by 12 and get 700

The equivalent expression 2/3 × 42 is 28. The equivalent expression 5/12 × 26 is \(10\frac{5}{6}\).

What is an equivalent expression?

Expressions that are similar in value or worth but differ in appearance are called equivalent expressions. At least two expressions are required to determine whether two expressions are equivalent. Equivalent expressions are used and required on numerous occasions in math. The distributive property makes it simple to write an expression without parentheses around it. Equivalent expressions are used frequently in algebra in mathematics.

Given numbers are 2/3 × 42 and 5/12 × 26.

Now simplify 2/3 × 42:

(2/3) × (42/1)

= (2×42)/(3×1)

= 2×14        [Divide denominator and numerator by 3]

=28

Now simplify 5/12 × 26:

(5/12) × (26/1)

= (5×26)/(12×1)

= (5×13)/(6×1)       [Divide denominator and numerator by 3]

= 65/6

Convert improper fraction to mixed fraction:

= (60/6) + (5/6)

= \(10\frac{5}{6}\)

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

See attachment for plot

Step-by-step explanation:

Given

\(l = 4h\)

Required

Represent the scenario on a graph

When h = 0

\(l = 4h= 4 * 0 = 0\)

When h = 1

\(l = 4 * 1 = 4\)

When h = 2

\(l = 4 * 2 = 8\)

When h = 3

\(l = 4 * 3 = 12\)

When h = 4

\(l = 4 * 4 = 16\)

When h = 5

\(l = 4 * 5 = 20\)

So, we have:

\((h,l) = (0,0)\)

\((h,l) = (1,4)\)

\((h,l) = (2,8)\)

\((h,l) = (3,12)\)

\((h,l)= (4,16)\)

\((h,l)= (5,20)\)

See attachment for plot

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

y=1x+3

Step-by-step explanation:

y=kx + m

k= y2-y1 / x2- x1

pick two of them, so for example (-2,5) and (0,3)

k=(3-5)/(0-2)= -2/-2= 1

Now we want to know the m . That is by inserting a point in the equation . y=kx+m.

so I'll pick (0,3)

3=1×0+m

m=3

Try with another one to see if you get the same answer.

this time I'll pick (-2,5)

5=1×-2+m

m=3

We can try with (2,5) so that it get used too.

5=1×2+m

m=3

The right equation will therefor be

y=1x+3

Answer:

y=|x|+3

Step-by-step explanation:

The point-slope form of the equation that represents the data set is y - 56 = -5(x - 6), or y = -5x + 86.

We are given two points: (6,56) and (12,26) from the data set. We can use the point-slope form of a linear equation to find an equation that represents the data set.

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

To find the slope, we use the two given points:

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

m = (26 - 56) / (12 - 6)

m = -30 / 6

m = -5

Now that we have the slope, we can use one of the given points, say (6, 56), to write the point-slope equation:

y - y1 = m(x - x1)

y - 56 = -5(x - 6)

y - 56 = -5x + 30

y = -5x + 86

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The expression equivalent to 30÷(3+x) is 30 divided by (x+3).

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6. Complex riddles are solved using mathematical expressions.

Given:

30÷(3+x)

Now, we know the fraction form of is written as x/y, where x is numerator and y is denominator.

So,  Numerator = 30

Denominator = (3+x)

Hence, the expression 30/ (3+ x)

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Answer:

22/22X22-22+22= 22÷5 =4.5

33/33X33-33+33=33÷5=6.6

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer: 5=49, 6= 131

Step-by-step explanation:

The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

The Lower limit is 0.745 and the Upper limit is 0.976.

In data, an easy random sample is a subset of people (a pattern) chosen from a larger set (a population) wherein a subset of individuals are selected randomly, all with identical possibilities. it is a system of choosing a pattern in a random manner. In SRS, each subset of okay individuals has the identical chance of being chosen for the sample as every other subset of okay individuals. An easy random pattern is an independent sampling approach. simple random sampling is a fundamental sort of sampling and may be an element of other extra complicated sampling strategies.

In statistics, an easy random pattern is a subset of individuals (a pattern) selected from a bigger set (a population) in which a subset of individuals are chosen randomly, all with identical chances. it's far a manner of choosing a pattern in a random way. In a random sample, every subset of okay people has the identical possibility of being chosen for the pattern as any other subset of okay individuals. An easy random pattern is an impartial sampling approach. simple random sampling is a fundamental type of sampling and can be an issue of other extra complex sampling strategies.

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The total change in the weight after 4 months is given as follows:

+2.5 lb.

The total change in the weight after 4 months is obtained adding the change in the weight for each month.

From the table given by the image at the end of the answer, the changes for each month are given as follows:

Hence the total change is given as follows:

2.25 - 1.5 - 0.875 + 2.625 = 2.5 lb.

The table is given by the image presented at the end of the answer.

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Answer:

Area = 12a m²

Step-by-step explanation:

Given information,

→ Length = 4a m

→ Width = 3a m

Now we have to,

→ find the area of rectangular park.

Formula we use,

→ Area = L × W

Then the area of rectangle is,

→ L × W

→ 4a × 3a

→ (4 × 3)a

→ 12a m²

Therefore, the area is 12a m².

Answer:

$29.90

Step-by-step explanation:

Can you only buy paint by the gallon?  That is what I am thinking.  

She is painting 4 walls.  I am thinking that she is not painting the floor or the ceiling.

The area of the four walls would be:

(11.6 x 10) = 116

(11.6 x 10) = 116

10.6 x 10) = 106

(10.6 x 10) = 106

This totals 444 square feet.  Since a gallon can only paint 400 square feet, she will need to buy 2 gallons for 29.90

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150