How many positive integers less than 1000 have the sum of their digits equal to 4

Answer:  the ball reaches a maximum height of 76 ft, and it takes 2 seconds to reach the highest point.

Step-by-step explanation: The acceleration induced by gravity is estimated to be approximately -32 ft/s^2, with the negative value indicating its downward direction.

At the apogee of the ball's trajectory, its vertical velocity experiences a momentary cessation.

The duration required for the ball to attain its maximum height can be determined through employment of the equation t = Vf / a, in which Vf denotes the attained final velocity (which is zero in the present scenario) and a denotes the gravitational acceleration. Upon substitution of the given numerical values, the resulting value of t is determined to be equal to 2 seconds, achieved through the utilization of the equation t = 64 / 32.

The determination of the maximum height achieved by the ball can be achieved through utilization of the formula h = hi + Vit + 1/2at^2, with hi denoting the initial height (12 ft), Vi representing the initial velocity (64 ft/s), a signifying the acceleration due to gravity (-32 ft/s^2), and t representing the time it takes for the ball to reach the apex of its trajectory (2 seconds). Upon entering the provided numerical values into the formula, the resulting value for the height of the object can be determined as h = 12 + 64(2) + 1/2(-32)(2)^2, which equates to 76 feet.

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Answer:

36°

Step-by-step explanation:

angle a= 180-117

angle a=63°. because angles on straight line add to 180°

angle b= 180-81-63

angle b=36°. because angles in triangle add to 180°

Answer:9/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

3 x 3/8 = 1 1/8

The correct options are- B. x = –4 – √2 and D. x = –4 + √2 are the roots of the given quadratic equation.

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

Given quadratic equation:

x² – 8x + 16 = 2

This can be written as:

x² – 2*4x + 4² = 2

(x + 4)² = 2

Taking square root both sides:

√(x + 4)² = √2

(x + 4) = ±√2

x = ±√2  - 4

Or x = -4 + √2 and x = -4 - √2

Thus, the roots of the quadratic equation found by using the method of completing the square are - x = -4 + √2 and x = -4 - √2

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Complete question:

Use completing the square to solve this quadratic equation. Check all that apply. x² – 8x + 16 = 2

A. x = 4 –√2

B. x = –4 – √2

C. x = 4 + √2

D. x = –4 + √2

Answer:

The Correct answer is C

y>7

Step-by-step explanation:

Area of a kite = D1 × D2/2

D1 = 6.9 + 13.8 = 20.7m

D2 = 9.2 + 9.2 = 18.4m

Area =. 20.7 × 18.4

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

2

= 190.44m²

The balance in this account has grown because of the interest earned on the account, which is compounded annually. Each year, the interest is calculated based on the beginning balance for the year, which includes the previous year's balance plus any new deposits made at the beginning of the year. The interest rate is then applied to this balance, and the resulting interest is added to the balance. This process is repeated each year, causing the balance to grow over time. Additionally, in this particular example, new deposits were made in the first year, which further increased the balance and contributed to its growth.

Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

In addition, ratios can be used to compare components of an ensemble, such as the ration of a circle's surface area to its circumference. As it is a linear correlation that cannot be reduced, the ratio in this instance is not simplified. In mathematics, science, economics, and many other disciplines, ratios are frequently employed to explain and study the quantitative relationships between various values.

given

The ratio is:

[tex]4x^5 / (2x^3)[/tex]

We can divide the numerator by the denominator to simplify the quotient.

By dividing 4x5 by 2x3, we obtain:

[tex](4x^5) / (2x^3) = 2x^(5-3) = 2x^2[/tex]

Hence, the quotient is [tex]2x^2[/tex] in its simplest form as the numerator by the denominator to simplify the quotient.

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Let's use the variables w and l to represent the current ages of the wool and linen tapestries, respectively.

From the problem, we know that:

w = l + 32 (the wool tapestry is 32 years older than the linen tapestry)

w - 20 = 2(l - 20) (twenty years ago, the wool tapestry was twice as old as the linen tapestry)

We can simplify the second equation by distributing the 2:

w - 20 = 2l - 40

Now we can substitute the first equation into the second equation to eliminate w:

(l + 32) - 20 = 2l - 40

Simplifying this equation, we get:

l + 12 = 2l - 40

Adding 40 to both sides:

l + 52 = 2l

Subtracting l from both sides:

l = 52

Now we can use the first equation to find w:

w = l + 32 = 52 + 32 = 84

Therefore, the present age of the wool tapestry is 84 years old, and the present age of the linen tapestry is 52 years old.

So the answer is option (b) 84, 52.

Answer:

Step-by-step explanation: X=1

Answer:

p = 1 or p = 7

So first number line is the answer we are looking for.

Step-by-step explanation:

|8-2p| = 6

To do that, we need to get rid of the brakes and rewrite equation in two forms:

8 - 2p = 6

or

8 - 2p = -6

For the first state:

8 - 2p = 6

- 2p = -2

2p = 2

p = 1

Now, the second state:

8 - 2p = -6

- 2p = -14

2p = 14

p= 7

The equation of the line is

To find the equation of the line passing through the points (2,2) and (-2,0), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where

m is the slope of the line, and

(x1, y1) are the coordinates of one of the points on the line.

First, we need to find the slope of the line. The slope is given by:

m = (0 - 2) / (-2 - 2) = -1/2

substituting the points

y - 2 = (-1/2)(x - 2)

Expanding the right side and simplifying, we get:

y - 2 = (-1/2)x + 1

y = (-1/2)x + 3

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The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.

given

The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.

Calculating the sample proportion is necessary:

The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:

P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031

Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:

[tex]z = (0.476 - 0.34) / 0.031 = 4.39[/tex]

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

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Answer:

Step-by-step explanation:

The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹

Exponents are a way of expressing the repeated multiplication of a number by itself.

Here are the rules of exponents:

Here we have

The expression (x³y⁴)⁻²/(x⁻²y)  

The above expression can be simplified as follows

Using the above exponent rules

=>  (x³y⁴)⁻²/(x⁻²y)                  

=>  (x³⁽⁻²⁾y⁴⁽⁻²⁾) /(x⁻²y)                 [ By the Power Rule: (aᵇ)ⁿ = aᵇⁿ ]

=>  (x⁻⁶y⁻⁸) /(x⁻²y)              

=>  (x⁻⁶ · x² · y⁻⁸ · y⁻¹)                 [ By the Quotient Rule:  aᵇ / aⁿ = a⁽ᵇ⁻ⁿ⁾ ]

=>  (x⁻⁶⁺² y⁻⁸⁻¹)                           [ By the Product Rule: aᵇ × aⁿ = a⁽ᵇ⁺ⁿ⁾ ]

=>  (x⁻⁴y⁻⁹)  

Therefore,

The expression (x³y⁴)⁻²/(x⁻²y) is the same as x⁻⁴y⁻⁹

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Answer:

Hibah's store developed a leak in the roof during a rainstorm, causing a circular puddle to form on the sales floor. The radius of the puddle increased by 0.1 cm per minute. The rain stopped by 7 am, when the morning shift arrived and discovered the puddle. The employees cleaned up the puddle and placed a bucket under the leak.

I hope that's what your looking for :)

The range of a function refers to the set of all possible output values that the function can produce for its corresponding input values. In this case, the function is:

f(x) = 6x / (x^2 - 9)

To find the range of this function, we need to consider the restrictions on the denominator (x^2 - 9) that would make the function undefined.

The denominator (x^2 - 9) can be factored as a difference of squares:

x^2 - 9 = (x + 3)(x - 3)

So, the function is undefined when the denominator is equal to zero, i.e., when:

(x + 3)(x - 3) = 0

This occurs when x = -3 or x = 3.

Now, we need to consider the behavior of the function as x approaches these values. As x approaches -3 or 3 from the left, the function becomes increasingly negative, and as x approaches -3 or 3 from the right, the function becomes increasingly positive. This is because the numerator (6x) remains constant while the denominator approaches zero, resulting in a very large positive or negative value for f(x).

Since the function can approach arbitrarily large positive or negative values as x approaches -3 or 3, respectively, the range of the function is (-∞, ∞), which represents all real numbers except for the values -3 and 3. In interval notation, the range of the function can be written as:

Range of f(x): (-∞, ∞) \ {-3, 3}

The period of the parent cosine function, y = cos(x) is 1

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

The parent cosine function, y = cos(x)

For a parent cosine function, y = cos(x), the period is always 1

This is the general rule of the cosine sinusoidal function

Hence, the period of the parent cosine function, y = cos(x) is 1

The graph of the cosine function is added as an attachment

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a) The only outcome that satisfies both events X and Y is the letter C.

b) The outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

c) The complement of event X is {D, E, F, G}.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The outcomes for each of the following events are:

(a) Event "X and Y": {C}

To satisfy both events X and Y, the letter selected must come before "D" (which includes the letters A, B, and C) and must be one of the letters in the word "CAGE" (which includes only the letter C). Therefore, the only outcome that satisfies both events X and Y is the letter C.

(b) Event "X or Y": {A, B, C, E, G}

The outcomes that satisfy event X are A, B, and C (since they come before "D"), and the outcomes that satisfy event Y are C, A, G, and E (since they are letters found in the word "CAGE"). Therefore, the outcomes that satisfy either event X or event Y are {A, B, C, E, G}.

(c) The complement of event X: {D, E, F, G}

The complement of event X is the set of outcomes that do not satisfy event X. The outcomes that do not satisfy event X are D, E, F, and G (since they come after or are equal to "D"). Therefore, the complement of event X is {D, E, F, G}.

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Answer:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped

Step-by-step explanation:

Hey

So my brother posted this on Yahoo

Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth. A right-angled triangle is formed. Length of side to the water-surface is 5 cm, the hypot is 7 cm.

What you do now is the following:

Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

So θ is approx 44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area ≃ 88.8/360*area of circle - ½*7*7*sin88.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

≃ 13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

b)

volume of water = cross-sectional area * length

≃ 13.5 * 30 cm³

≃ 404 cm³

Hoped it Helped

i. The second angle that will make the 2 angles complementary is 33^o.

ii. The second angle that will make the 2 angles supplementary is 123^o.

Complementary angles are measure of given angles whose addition gives a right angle i.e 90^o. While two or more angles are supplementary when their addition produces 180^o.

a. To find the second angle that will make the 2 angles complementary, we have;

let the second angle be represented by x, then;

x + 57 = 90

x = 90 - 57

  = 33

x = 33^o

b. To find the second angle that will make the 2 angles supplementary, we have;

let the second angle  be represented by y; so that;

y + 57 = 180

y = 180 - 57

  = 123

y = 123^o

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The probability of selecting no Republicans is approximately 0.2102, or about 21.02%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

There are a total of 22 members in the group, consisting of 10 Democrats, 9 Republicans, and 3 Independents.

To find the probability of selecting no Republicans, we need to consider the possible ways in which two members can be selected without any Republicans being chosen.

There are two cases to consider:

The first person selected is not a Republican, and the second person selected is also not a Republican.

The first person selected is a Republican, and the second person selected is not a Republican.

Case 1: The probability of selecting a non-Republican member on the first draw is (10 + 3)/22, since there are 10 Democrats and 3 Independents out of 22 members. After the first member is selected, there are 21 members left, including 9 Republicans. The probability of selecting another non-Republican member on the second draw is (10 + 3 - 1)/(22 - 1), since there is one fewer member in the group after the first draw. Therefore, the probability of selecting no Republicans in this case is:

(10 + 3)/22 * (10 + 3 - 1)/(22 - 1) = 13/77

Case 2: The probability of selecting a Republican member on the first draw is 9/22, since there are 9 Republicans out of 22 members. After the first member is selected, there are 21 members left, including 10 Democrats and 3 Independents. The probability of selecting a non-Republican member on the second draw is (10 + 3)/(22 - 1), since there is one fewer member in the group after the first draw and we cannot select the Republican member again. Therefore, the probability of selecting no Republicans in this case is:

9/22 * (10 + 3)/(22 - 1) = 27/418

The total probability of selecting no Republicans is the sum of the probabilities in the two cases:

13/77 + 27/418 = 0.2102 (rounded to four decimal places)

Therefore, the probability of selecting no Republicans is approximately 0.2102, or about 21.02%.

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The correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

A mathematical object called a function accepts inputs (often represented by the symbol x) and creates outputs (typically represented by the symbol y or f(x)). An equation can be used to describe a function, although a function is not always defined by an equation.

It may incorporate one or more variables, but it does not always indicate how those variables are related.

For instance, even if the equation 2x + 3 = 7 involves the variable x, it does not define a function.

Given the function starts at (-3, 0) and extends upwards and to the right.

Thus, if x approaches negative infinity, the function cannot take on negative values, so the graph approaches the x-axis but never touches or goes below it.

Hence, the correct answer is option A: As x decreases in value, y increases in value. As x increases in value, y increases in value.

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The answer of the given question based on the quadrilateral is , the line segment corresponding to EH⎯ is AD⎯.

A line segment is a part of a line that consists of two endpoints and all the points between those endpoints that are collinear (lying on the same straight line). In other words, a line segment is a straight line that is bounded by two distinct points. A line segment is usually denoted by drawing a line over the two endpoints and labeling it with a single letter representing the segment name or by labeling the endpoints with capital letters and drawing a bar over them to indicate the segment between them.

A line segment has a finite length and can be measured using a ruler or a measuring tape. The length of line segment is distance between its two endpoints.

In the pre-image, the line segment corresponding to EH⎯ is AD⎯.

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Note that the value of C that satisfies the mean value theorem is -11/6

The mean value theorem in mathematics says that for each given planar arc between two end points, there exists at least 1   point where the tangent to the arc   is parallel to the secant between its ends. It is one of the most significant findings in real -  world analysis.

To apply the mean value theorem, we need to check 2 conditions

f(x) is continuous on [-3, -1]

f(x) is differentiable on (-3, -1)

f(x) = (x^2-1/3x) satisfies both conditions.

Now, let's find the value of c that satisfies the mean value theorem:

f(-1) - f(-3) = f'(c)(-1 - (-3))

(2/3) - (-26/3) = f'(c)(2)

f'(c) = -4

To find the value of c, we need to solve for c in f'(c) = -4 ...  

f '(x) = d/d x(x²  -1/3x)

= 2x - 1/3

2c - 1/3 = -4

2c = -4 + 1/3

c = -11/6

So we can state that  the value of c that satisfies the mean value theorem is -11/6

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The volume of the modelled Saturn is 2176.40 cm³.

Eliza made sphere-shaped models of the Earth and Saturn out of playdough for a science project. The model of Earth has a diameter of 4.8 cm and the model of Saturn has a diameter of 45.6 cm.

Therefore, the volume of the spherical Saturn can be found as follows:

volume of the Saturn = 4 / 3 πr³

where

r = radius

Therefore,

r = 45.6 / 2 = 22.8 cm

volume of the Saturn = 4 / 3 × 3.14 × 22.8²

volume of the Saturn = 4 / 3 × 3.14 × 519.84

volume of the Saturn = 6529.1904 / 3

volume of the Saturn = 2176.3968

volume of the Saturn = 2176.40 cm³

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Answer: C

Step-by-step explanation:

your typical equation for varies inversely is y=k/x

here E = k/d² from the wording of problem.  plug in numbers to solve for k.

120=k/20²

k=48000

plug k back in to get generic E equation.  

E=48000/d²