Let h(x)=[tex]\sqrt{x+3}[/tex] and k(x)=2x+7

Find the value of h(k(3))

Answer:

a)  10

b)  Number of hours of phone support (per month).

c)  Total bill (per month).

d)  y = 35x + 10

e)  2.5 hours

Step-by-step explanation:

The company bills you at a rate of:

The fixed cost (the constant) is the cost per month ⇒ $10.

The independent variable is the variable that is not affected by any other variables.

Therefore, the independent value (variable x) is the number of hours of phone support per month.

A dependent variable is the variable that is affected by the other variable.

Therefore, the dependent value (variable y) is the total bill (in dollars) per month.

The equation that describes the given situation is:

To calculate how many hours of phone support was needed for a bill of $97.50, substitute y = 97.5 into the equation from part d and solve for x.

[tex]\implies 35x+10=97.5[/tex]

[tex]\implies 35x+10-10=97.5-10[/tex]

[tex]\implies 35x=87.5[/tex]

[tex]\implies \dfrac{35x}{35}=\dfrac{87.5}{35}[/tex]

[tex]\implies x=2.5[/tex]

Therefore, 2.5 hours of phone support was needed last month.

You ran 1/8 of miles more today than yesterday.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

Miles you ran yesterday is three fourths of a mile.

Let 1 mile be M.

Miles you ran yesterday = 3/4 M

Today you ran seven-eighths of a mile.

Miles you ran today = 7/8 M

Difference of miles = 7/8 M - 3/4 M

3/4 is same as 6/8.

Difference of miles = 7/8 M - 6/8M

                                = 1/8 M

Hence you ran 1/8 of miles more than yesterday.

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Answer: An equation of a line that is parallel to another line has the same slope as the original line. The slope of a line can be found by rearranging the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To find the equation of a line that is parallel to the line x - 5y = 15 and passes through the point (-5,7), we can first rearrange the equation of the original line in slope-intercept form:

x - 5y = 15

y = (1/5)x - 3

The slope of this line is (1/5). To find an equation of a line that is parallel to this line and passes through the point (-5,7), we can use the point-slope form of a line:

y - y1 = m(x - x1)

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

Substituting in the values given in the question, we get:

y - 7 = (1/5)(x - (-5))

y - 7 = (1/5)x + 1

y = (1/5)x + 1 + 7

y = (1/5)x + 8

Therefore, the equation of the line that is parallel to the line x - 5y = 15 and passes through the point (-5,7) is y = (1/5)x + 8.

Step-by-step explanation:

Answer: x=(y+9)5−32 simplified

Step-by-step explanation:

The short leg of a 30-60-90 triangle is 1/2 the length of the hypotenuse. 30-60-90 triangle is the half of an equilateral triangle.

Right triangles with 30-60-90 interior angles are called special right triangles.

A 30-60-90-degree triangle is a special right triangle and its side lengths are always consistent with each other. The ratio of the sides follows the 30-60-90 triangle ratio: 1: 2: [tex]\sqrt{3}[/tex] .

Short side (opposite the 30° angle) = x

Hypotenuse (opposite the 90° angle) = 2x

Long side (opposite the 60° angle) = x√3

30-60-90 Triangle Theorem:

These three properties can be examined by the 30-60-90 triangle theorem and are unique to these special right triangles:

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The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.

Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10

= 73

Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.

There are on one event is where 5 athletes are, that is 8th grade baseball players.

So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

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the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65

They need at least $1,150

They have already saved $700

They are selling shirts with a profit of $7.00 per shirt

If they sell n number of shirts, they will earn n times $7.00

Since they have already 700, they will earn a total of 700 + 7n

If this quantity has to be equal or greater to 1,150, we can write:

1150 <= 700 + 7n

if we solve this inequality for n:

1150 <= 700 + 7n

1150 - 700 <= 7n

450 <= 7n

450/7 <= n

64.28 <= n

Since the number of shirts has to be an integer (you can not sell "part" of a shirt)

n >= 65

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More than one applies to the slope.

The non-negative value of a real number x without regard to its sign is known as its absolute value or modulus in mathematics and is indicated by the symbol |x|. Specifically, display style |x|=x and |x|=-x for positive and negative numbers, respectively, and display style |0|=0 for zero.

The slope of the parent function from any point to the vertex is either 1 or -1. The points in the issue are (-2, 3), and (–1, 0)

The slope is m = 0 - 3 / (-1 - (-2)) between the two sites.

m = 3

It is steeper than one.

As a result, a scale factor other than 1 has been used to dilate the graph.

The complete question is : The graph of an absolute value function has a vertex at (–2, 3) and passes through the point (–1, 0). Using transformations of the parent function, has the graph been dilated by a scale factor other than 1? Explain.

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Answer:

[tex]y=\sqrt{10}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]y=\sqrt{(2)(5)}=\sqrt{10}[/tex].

A. The net of a triangular prism is a flattened version of the prism that shows all the faces of the prism.

The prism's base is a right triangle with a base of 3 units and a height of 4 units. The prism is six units tall. The net of the triangular prism would look like a rectangle with a length of 3 units and a width of 4 units. On top of this rectangle, there would be two smaller triangles, each with a base of 3 units and a height of 6 units.

B. To calculate the surface area of the prism, we need to add the area of all the faces.

The base of the prism is a right triangle with an area of (1/2) (3 units) (4 units) = 6 square units.

The two triangular faces have an area of (1/2) (3 units) (6 units) = 9 square units each.

The rectangular face has an area of (3 units) (6 units) = 18 square units.

So, the total surface area of the prism is:

6 square units (base) + 9 square units (triangular face) + 9 square units (triangular face) + 18 square units (rectangular face) = 42 square units.

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Answer:

208

Step-by-step explanation:

60 percent of 520 is 312

520 subtract 312 is 208

Answer:

208

Step-by-step explanation:

(520)-60% of 520

(520)-3×104

520-312

=208

Hope it helps you

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The score interval that is within one standard deviation of the mean is

(70 , 80).

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

Some of the properties of the standard deviation are:

1. It cannot be negative

2. It is only employed to calculate the spread or dispersion around a data set's mean

3. It displays the degree of deviation  from the mean value

4. The larger the spread, the more standard deviation, with data of about the same mean.

Given,

 The mean of the test μ = 75

The standard deviation σ = 5

We are asked to find the scores within one standard deviation of the mean.

This means that the scores should be in the interval ( μ - σ , μ + σ )

μ - σ = 75 - 5 =70

μ + σ = 75 + 5 = 80

Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.

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The sine of an acute angle in a right triangle is the ratio of the angle of the triangle to the opposite side of the hypotenuse.

Trigonometric ratios:

Trigonometric ratios are the ratios of the lengths of the sides of a triangle. These ratios in trigonometry relate the aspect ratio of a right triangle to each angle. A basic trigonometric ratio is the ratio of sin, cos, and tan, or the ratio of sin, cos, and tangent. Other important trigonometric ratios cosec, sec, and cot can be derived from sin, cos, and tan, respectively.

Acute Sine Ratio:

The tangent function examines the ratio of his two legs of a right triangle. You can also use the ratio of leg length divided by hypotenuse length.

In a right triangle, each angle has an opposite side and an adjacent side. And there is always a hypotenuse. On the opposite side and the hypotenuse we are dealing with the sine ratio. The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

Let's examine some properties of the sine ratio using the Pythagorean theorem. For a right triangle, let the lengths of the triangle be a, b, and c. where a is the length of the other side of A and b is the length of the other side of B.

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Answer:

Converting from degrees to radians is actually very simple, it is a one step unit conversion.All we need to know to solve this is that (π)radians=(180)degrees Therefore 135degrees⋅(π)radians180degrees=(135180)π radians =3π4 radians

Step-by-step explanation:

hope this helps

The speed of Mark riding the bike is 16 miles/hour. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.

Speed tells us how quickly or slowly an object is moving. While distance, as the name suggests, refers to the amount of space between two points, time refers to the period of time separating two events.

Given,

Distance travelled= 6 miles

time taken = 30 minute =0.5 hour

[tex]speed = distance/time\\speed=8/0.5\\speed= 16 miles/hour[/tex]

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Answer: An increase of a population doubling every year can be modeled using repeated multiplication. The expression for the increase after five years would be:

2 * 2 * 2 * 2 * 2 = 2^5 = 32

This can also be written as an exponential expression, with 2 as the base and 5 as the exponent:

2^5 = 32

This notation expresses that 2 is multiplied by itself 5 times to get 32, which represents the population size after 5 years with the rate of doubling every year.

It's also worth mentioning that exponential notation is used to represent the quantity of growth (doubling every year) , and using exponents makes it easy to see how much the population has grown over a certain period of time.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2^5= 32

=2 x 2 x 2 x 2 x 2

= 2^5

= 32

The basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, section, and segment.

the surface or circumference of a circle, ball, and other object measured in a straight line The radius and diameter of a circle are equal. The length of such a line. whatever radiating or radial component. A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.

Here,

given

The letter "C" should be in the center.

radius=r=AC=CB

Diameter=d=2r=AB.

Therefore , the solution to the given problem of circle comes out to be ,the basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, sector, and segment.

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When we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

So, we have:
[tex]$$\int_0^1 \int_x^z e^{\frac{x}{y}} d y d x$$\\[/tex]

Here:  [tex]z=\sqrt{x}[/tex]

Next, reverse the sequence:

[tex]$$\int_0^1 \int_m^y e^{\frac{x}{y}} d y d x$$ $m=y^2$$$\\\\\begin{aligned}\\& \int_{=0}^1\left(e^{\frac{x}{y}} y\right) \| \begin{array}{l}y \\y^2\end{array} d y \\& \int_{=0}^1(e y)-\left(e^y y\right) d y\end{aligned}$$[/tex]

The following section uses integration by parts,

[tex]$$\begin{aligned}& \mathbf{u}=\mathbf{y}, \\& d v=e^y\end{aligned}$$$$\mathrm{d} u=1$$$$v=e^y$$$$\begin{aligned}& =\left(\left(\frac{e y^2}{2}\right)-\left(y e^y\right)\right)||_0^1+\int_0^1 e^y d y \\& = \\& =\frac{e}{2}-e+e-1=\frac{e}{2}-1\end{aligned}$$[/tex]

Therefore, when we reverse the integration and evaluation orders, we obtain: [tex]\frac{c}{2}-1[/tex]

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Correct question:

Evaluate the integral by reversing the order of integration.

8 0 2 3ex4 dx dy 3 y

The equivalent values to the given expressions are -

2/3 and 3/7 respectively.

Given are two expressions as -

1/3 + 1/3

5/7 - 2/7

The given expression are -

1/3 + 1/3

(1 + 1)/3

2/3

5/7 - 2/7

(5 - 2)/7

3/7

Therefore, the equivalent values to the given expressions are -

2/3 and 3/7 respectively.

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Three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color is 0.8824 or 88.24%

The likelihood or chance that a specific event will occur is represented by a probability.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportion with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given that three cards are chosen from a pack of 52 cards.

There are 26 cards of each color (i.e. 26 cards are red color and 26 cards are of black color)

The probability of drawn first card of any one color is

P(1)= 26/52 = 1/2

The probability of drawn second card of same color is

P(2)= 25/51

The probability of drawn third card of same color is

P(3)= 24/50 = 12/25

The probability of having three cards are same color is

P = P(1)*P(2)*P(3)

P = 1/2 * 25/51 * 12/ 25

P = 6/51

So the probability that three cards are not all the same color is

P' = 1 - P

P' = 1 - 6/51

P' = (51-6)/51

P' = 45/51 = 15/17

P' = 0.8824

The likelihood that the three cards are not all red is roughly 0.8824, or 88.24%,

.

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The minimum value of the expression 3x² + 6x + 6 is 3.

Therefore the answer is 3.

A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.

Minimum value of a quadratic equation of form ax² + bx + c is when

x = -b/ 2a

Then minimum value is

a( -b/ 2a )² + b( -b/ 2a ) + c

= (b²a + -2ab² + 4a²c)/ 4a²

= ( - b² + 4ac)/ 4a

= c - b²/4a

In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is

= 6 - 6²/ (4×3)

= 3

--The question is incomplete, answering  to the question below--

"What will be the minimum value of the expression 3x² + 6x + 6?"

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Answer:

Step-by-step explanation:

A^2 + B^2 = C^2

12^2 + B^2 = 18^2

144 + B^2 = 324

Subtract 144 from both sides

B^2 = 324 - 144

B^2 = 180

[tex]\sqrt{180}[/tex] = 13.416

B^2 = 13.4

The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

What is the average rate of change?

The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval, divided by the difference in the x-values of the endpoints.

In this case, the function is h(x) = -x² + 8x, the interval is 0 ≤ x ≤ 5, and we want to find the average rate of change over that interval.

So, we can use the following formula:

Average rate of change = (h(5) - h(0)) / (5 - 0)

Now we have to substitute the values into the equation:

h(5) = -5^2 + 85 = -25 + 40 = 15

h(0) = -0^2 + 80 = 0

Average rate of change = (15 - 0) / 5 = 3

Hence, The average rate of change of the function h(x) = -x² + 8x over the interval 0 ≤ x ≤ 5 is 3.

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The total surface area of the hemisphere is 108 pi cm^2.

Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.

The surface area of a sphere with the radius r is 4 pi r^2

The surface area of a hemisphere with the radius r = 2 pi r^2 +   pi r^2

where pi r^2 represents the area of the circular base of the hemisphere of radius r.

The surface area of a hemisphere sphere with the radius r is 3 pi r^2

For radius r=6cm

TSA of  the hemisphere is 3 pi (6x6) cm^2

TSA = 108 pi cm^2

108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.

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Answer:

Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)

Step-by-step explanation:

Let's reorganize the given expression:

(1/3x+2x−5/3x)−(−1/3x+5)

1/3x+2x−5/3x + 1/3x-5       [Expand the parentheses]

2/3x+2x−5/3x -5       [Combine like terms]

-3/3x+2x -5

-x + 2x - 5

x - 5                       One of the equivalent expressions

The option 4x-5-3x also reduces to x - 5

Column A and B matching the results with the operations

The expression that represents the perimeter of the rhombus is 2d√17

How to determine the expression that represents the perimeter of the rhombus?

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

The length of one diagonal of a rhombus is 4 times the length of the other diagonal.

This means that

Length 1 = 4 * Length 2

From the question, we have

Let d be the length of the shorter diagonal.

This means that

Length 1 = 4d

Length 2 = d

The perimeter of the rhombus from the diagonals is calculated as

P = 2√(Length 1² + Length 2²)

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

P = 2√((4d)² + d²)

Evaluate the exponents

P = 2√(16d² + d²)

So, we have

P = 2√(17d²)

Evaluate the exponents

P = 2d√17

Hence, the perimeter is 2d√17

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40 percent price of the ring gone down due to a clearance sale

In mathematics, percent implies a relative value of any quantity. Generally, percent value expresses the hundredth parts of any given quantity. Sometimes, operator % is used to indicate a percent value.

From a given percent value we can determine the real value and percent value is calculated from the original data.

given, the original price of the emerald ring = $1730

after a clearance sale, the price of ring became = $1038

difference in price = $(1730-1038) = $ 692

hence, the price of the ring that gone down = $692

now, percent value of the price gone down = $692/$1730 × 100

                                                                          = 40%

hence, forty percent of the ring price gone down.

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If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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