The nurse reported that Tricia's daughter had gained 4.2 pounds
since her last checkup and now weighs 31.6 pounds. How much
did Tricia's daughter weigh at her last checkup?

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

Answer:

\(x^{2} + y^{2} - 10\cdot y = 0\)

Step-by-step explanation:

The following expressions are used to transform from polar into rectangular form:

\(r = \sqrt{x^{2}+y^{2}}\)

\(\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}\)

Now, the variables are substituted and equation is finally simplified:

\(\sqrt{x^{2}+y^{2}} = 10\cdot \frac{y}{\sqrt{x^{2}+y^{2}} }\)

\(x^{2}+y^{2} = 10\cdot y\)

The equivalent equation in rectangular coordinates is:

\(x^{2} + y^{2} - 10\cdot y = 0\)

Answer:

Step-by-step explanation:

60 three-digit positive integers can be made from the digits 1, 3, 5, 6, and 8 if repetition is not allowed. This can be calculated by using method of permutation which is explained below.

There are 5 options available for the first digit (1 , 3 ,5 ,6 ,8 ) and there are 4 options left for the second digit when the first digit is chosen as repetition is not allowed. When first two digits are chosen 3 options are left for third digit as repetition is prohibited here

Hence the possible number of three-digit positive integers are-5 x 4 x 3 =60                                

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Answer:

80

Step-by-step explanation:

1 pizza has 8 \(\frac{1}{8}\)ths. 10 pizzas have 10 × 8 = 80 1/8ths. So 80.

Answer:

80 because if one student gets 1/8 that means 8 students get one slice out of the pizza multiply 8 by 10 and it equals 80

Answer: 1.684

Step-by-step explanation:

since sample size (n) is 41

confidence level = 0.90 = 90%

df = n - 1

df = 41 - 1

df = 40

that is For Degrees of Freedom = 40

significance level α = 1 - (confidence level / 100)

Significance Level α = 1 - (90/100 ) =  0.10

using the z-score

critical values of t = 1.684

A graph has been attached to further assist.

The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+45/4=4x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

4x-x=45/4

3x=45/4

x=15/4

x=3.75

x≈4 hours

Therefore, option B is the correct answer.

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If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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Answer: 252.5

Step-by-step explanation:

Add 211+216+256+327= 1,010

Divide 1,010/4= 252.5

The solution of the linear equation  is determined as x = -4.

The solution of the linear equation is calculated by applying the following method as follows;

The given linear equation;

2/x+3 - 1/x = -4/x² +3x

We can start by simplifying the equation and getting rid of the fractions.

Multiplying every term by x will help us achieve that:

2 + 3x - 1 = -4/x + 3x²

Simplifying further:

2 + 3x - 1 = (-4 + 3x²) / x

Combining like terms:

3x + 1 = (-4 + 3x²) / x

(x)(3x + 1) = -4 + 3x²

3x² + x = -4 + 3x²

We can subtract 3x² from both sides:

x = -4

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

Domain: \(All \ real\ numbers\)

Range: \(y\geq -5\)

Function: \(|x|-5=y\)

Step-by-step explanation:

The domain of this function is all real numbers, this is because any real number can be substituted into this function to produce a real output.

The range of this function is (\(y\geq -5\)), this is because all outputs are greater than (-5), rather (-5) is the lowest output that one can have.

The function is \(|x|-5=y\). As one can see, the function as the shape of an absolute value function, the v-shape composed of two (\(y=x\)) lines facing opposite directions. The graph has been shifted downwards by (5) units, one can see this because of the vertex formed by the two intersecting lines.

Answer:

y = -5x + 7

Step-by-step explanation:

Hi there!

We are given the line y=-5x+4

We want to write an equation of the line that passes through the point (1, 2) and is parallel to y = -5x + 4

Parallel lines have the same slope, so let's first find the slope of y = -5x + 4

The equation is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

In this case, -5 is in the place of where m is, so the slope of the line must be -5

It is also the slope of our new line that we are trying to find

As we now know the slope of this line, we can substitute that in as m in y=mx+b

Replace m with -5:

y = -5x + b

Now we need to find b

As the line passes through the point (1, 2), we can use it to help solve for b

Substitute 1 as x and 2 as y.

2 = -5(1) + b

Multiply

2 = -5 + b

Add 5 to both sides

7 = b

Substitute 7 as b into the equation

y = -5x + 7

Hope this helps!

Topic: finding parallel lines

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Answer:

  \(f_{ave}=\dfrac{9\pi}{4}\)

Step-by-step explanation:

You want the average value of f(x) = √(81 -x²) on the interval [0, 9].

The function f(x) defines a quarter circle of radius 9 in the first quadrant on the given interval. Its area is given by the formula in the problem statement:

  A = (1/4)πr² = (π/4)·81

The average value of the function is the area divided by the width of the interval:

  \(f_{ave}=\dfrac{\dfrac{81\pi}{4}}{9}\\\\\\\boxed{f_{ave}=\dfrac{9\pi}{4}}\)

__

Additional comment

You will notice that the average value is π/4 times the radius. This is also true for a semicircle. The attachment shows the rectangle with area equal to that of the quarter circle.

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Answer: Then the surface area that you should report to the hardware store is 15 ft^2.

Step-by-step explanation:

Remember that the area of a rectangle of length L and width W is

A = L*W

In this case, we can think in the door as a rectangle, where:

L = 6ft + 8in

W = 30in

Now, we know that in the hardware store they sell paint by how much covers a square foot, then we must calculate the area of the door in square feet.

Then the first step would be to replace all the units by ft.

We know that:

1ft = 12in.

Then we have that:

(1ft/12in) = 1

Then we have that:

8in = 8in*1 = (8in/12in)*1ft = 0.6... ft

(the 3 dots means that the 6 repeats infinitely)

And;

30in = 30in*1 = 30in*(1ft/12in) = 2.5ft

Then the measures of the door are:

L = 6ft + 0.6...ft = 6.6...ft

W = 2.5ft

The area will be:

A = L*W = 6.6...ft*2.5ft = 15 ft^2

Then the surface area that you should report to the hardware store is 15 ft^2.

Trigonometry is the application of certain functions to determine the value of a quantity. The tree stands 10.77 meters tall.

Some trigonometric functions can be used to solve the given problem. Let s represent the distance from the tip of the tree's shadow to where Aria stands, so that;

s = 27.75 - 23.5

= 4.25 m

s = 4.25 m

Also, let the angle formed by the line connecting the tree's tip and the shadow's tip be, so that;

Tan θ = opposite / adjacent

Here given,

Opposite side = 1.65

Adjacent side = 4.25

          = 1.65 / 4.25

          = 0.3882

θ = Tan⁻¹ 0.3882

  = 21.216

θ = 21.216°

We get θ = 21.216°

The tree's height, h, can be calculated as follows:

Tan 21.216° = h/27.75

h = Tan 21.216° x 27.75

  = 0.3882 x 27.75

h = 10.77m

As a result, the tree's height is 10.77m.

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The class width used for the frequency distribution is 6.

The class midpoint for the class 23-29 is 26.

The class midpoint for the class 30-36 is 33.

The class midpoint for the class 37-43 is 40.

To find the class width of the frequency distribution, we need to determine the range of each age class. The range is the difference between the upper and lower boundaries of each class. Looking at the table, we can see that the class boundaries are as follows:

23-29

30-36

37-43

For the class 23-29, the lower boundary is 23 and the upper boundary is 29. To find the class width, we subtract the lower boundary from the upper boundary:

Class width = 29 - 23 = 6

So, the class width for the frequency distribution is 6.

To find the class midpoint for each class, we take the average of the lower and upper boundaries of each class.

For the class 23-29:

Class midpoint = (23 + 29) / 2 = 52 / 2 = 26

For the class 30-36:

Class midpoint = (30 + 36) / 2 = 66 / 2 = 33

For the class 37-43:

Class midpoint = (37 + 43) / 2 = 80 / 2 = 40

So, the class midpoint for the class 23-29 is 26, for the class 30-36 is 33, and for the class 37-43 is 40.

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Answer:

Longer Leg = 5

Shorter Leg = 144

Hypotenuse = 169

Step-by-step explanation:

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.

First, we need to find the derivative of the function f(x) = x + 10x.

The derivative is given by:

f'(x) = 1 + 10

Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:

y - 6 = (1 + 10)(x - a)

y = (1 + 10)(x - a) + 6

Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).

Let's assume that the value of "a" is 1.

So, f(a) = f(1) = 1 + 10(1) = 11

And the equation of the tangent line is:

y = (1 + 10)(x - 1) + 6 = 11x - 4

Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:

T(1.07) = 11 * 1.07 - 4 = 10.77

Finally, we compare this value with the actual value of f(1.07), which is:

f(1.07) = 1.07 + 10 * 1.07 = 11.77

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Answer:

\(y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}\)

Step-by-step explanation:

\(y''-y=5e^{-4x}+2x,\: y(0)=y'(0)=0\\\\\mathcal{L}\{y''\}-\mathcal{L}\{y\}=\mathcal{L}\{5e^{-4x}\}+\mathcal{L}\{2x\}\\\\s^2Y(s)-sy(0)-y'(0)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\s^2Y(s)-Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\(s^2-1)Y(s)=\frac{5}{s+4}+\frac{2}{s^2}\\ \\Y(s)=\frac{5}{(s+4)(s^2-1)}+\frac{2}{s^2(s^2-1)}\\ \\Y(s)=\frac{5s^2+2(s+4)}{s^2(s+4)(s^2-1)}\\ \\Y(s)=\frac{5s^2+2s+8}{s^2(s-1)(s+1)(s+4)}\)

Perform the partial fraction decomposition

\(\frac{5 s^{2} + 2 s + 8}{s^{2} \left(s - 1\right) \left(s + 1\right) \left(s + 4\right)}=\frac{A}{s}+\frac{B}{s^{2}}+\frac{C}{s + 1}+\frac{D}{s - 1}+\frac{E}{s + 4}\\\\5 s^{2} + 2 s + 8=s^{2} \left(s - 1\right) \left(s + 1\right) E + s^{2} \left(s - 1\right) \left(s + 4\right) C + s^{2} \left(s + 1\right) \left(s + 4\right) D + s \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) A + \left(s - 1\right) \left(s + 1\right) \left(s + 4\right) B\)

\(5 s^{2} + 2 s + 8=s^{4} A + s^{4} C + s^{4} D + s^{4} E + 4 s^{3} A + s^{3} B + 3 s^{3} C + 5 s^{3} D - s^{2} A + 4 s^{2} B - 4 s^{2} C + 4 s^{2} D - s^{2} E - 4 s A - s B - 4 B\\\\5 s^{2} + 2 s + 8=s^{4} \left(A + C + D + E\right) + s^{3} \left(4 A + B + 3 C + 5 D\right) + s^{2} \left(- A + 4 B - 4 C + 4 D - E\right) + s \left(- 4 A - B\right) - 4 B\)

Solve for each constant

\(\begin{cases} A + C + D + E = 0\\4 A + B + 3 C + 5 D = 0\\- A + 4 B - 4 C + 4 D - E = 5\\- 4 A - B = 2\\- 4 B = 8 \end{cases}\)

\(-4B=8\\B=-2\)

\(-4A-B=2\\-4A-(-2)=2\\-4A+2=2\\-4A=0\\A=0\)

\(A+C+D+E=0\\C+D+E=0\\E=-C-D\)

\(-A+4B-4C+4D-E=5\\4(-2)-4C+4D-(-C-D)=5\\-8-4C+4D+C+D=5\\-3C+5D=13\\5D=13+3C\)

\(4A+B+3C+5D=0\\4(0)+(-2)+3C+13+3C=0\\-2+6C+13=0\\11+6C=0\\6C=-11\\C=-\frac{11}{6}\)

\(5D=13+3C\\5D=13+3(-\frac{11}{6})\\5D=13-\frac{33}{6}\\5D=\frac{15}{2}\\D=\frac{15}{10}\\D=\frac{3}{2}\)

\(E=-C-D\\E=-(-\frac{11}{6})-(\frac{3}{2})\\E=\frac{11}{6}-\frac{3}{2}\\E=\frac{2}{6}\\E=\frac{1}{3}\)

Take the inverse transform and solve for the IVP

\(Y(s)=\frac{0}{s}+\frac{-2}{s^2}+\frac{-\frac{11}{6}}{s+1}+\frac{\frac{3}{2}}{s-1}+\frac{\frac{1}{3}}{s+4}\\ \\y(x)=-2x-\frac{11}{6}e^{-x}+\frac{3}{2}e^x+\frac{1}{3}e^{-4x}\)

The central angle of Bathing = 108 degrees.

In the given pie chart,

Since we know,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The whole circle is 360 degrees

which represents 100%.

It is given that,

Bathing = 30%

So have need to find 30% of 360 degrees.

Therefore,

Bathing = (30/100)x360

            =  (30/10) x 36

            = 3x36

            = 108

Hence,

The central angle = 108 degrees.

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The complete question is:

To the nearest degree, what is the measure of the central angle for bathing?

Answer:

In 5 years the account will be $ 21,549.68.

Step-by-step explanation:

Given that Meg invested $ 16,000 in a savings account, if the annual interest rate is 6%, to determine how much will be in the account in 5 years for quarterly compounding, the following calculation must be performed:

16,000 x (1 + 0.06 / 4) ^ 5x4 = X

16,000 x 1,015 ^ 20 = X

16,000 x 1.34685500 = X

21,549.68 = X

Therefore, in 5 years the account will be $ 21,549.68.

Answer:

Step-by-step explanation:

A+?
P=$16,000
r=0.06
t=5

A=P(1+r/n)∧ nt

A=16,000(1+0.06/12)∧12⋅5

A=$21,581.60

The dimensions of the room are approximately 5.87 meters by 7.63 meters.

Let's assume the width of the room is "x" meters.

According to the problem, the length of the room is 1.3 times the width, so the length would be 1.3x meters.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 27 meters.

Perimeter = 2(length + width)

Substituting the values we know:

27 = 2(1.3x + x)

Simplifying:

27 = 2(2.3x)

27 = 4.6x

Dividing both sides by 4.6:

x = 27 / 4.6

x ≈ 5.87

The width of the room is approximately 5.87 meters.

To find the length, we can multiply the width by 1.3:

Length = 1.3 * 5.87 ≈ 7.63

The length of the room is approximately 7.63 meters.

Therefore, the dimensions of the room are approximately 5.87 meters by 7.63 meters.

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Answer:

There is obviously only 1 10x10 square. If we start with a 9x9 square in the top left corner, we can move it down 1, across 1 and back up 1, so there are 4 possible 9x9 squares.

For 8x8 we can move down 1, then 2 and we can move across 1 or 2 so that's 9 possible 8x8 squares.

For 7x7 we can go down 3 and across 3, so that's 4x4=16 possible squares.

The pattern is now clear the total number if squares is 1+4+9+16+…+100.

There's a formula for this, which I had to look up, but any the sum of the first n squared is 1/6n(n+1)(2n+1)1/6n(n+1)(2n+1), so the total number of squares is 10x11x21/6=5x11x7=385.

Answer:

Step-by-step explanation:

Answer:  -1≥ x > 7    or x>7  and x ≤ -1

Step-by-step explanation:

-6x + 14 < -28      

           -14  -14

-6x < -42

  x> 7        

AND

3x + 28 ≤ 25

      -28   -28

3x ≤ -3

x ≤ -1

x>7 and x≤ -1    

Answer

x>7 and x<-1

Step-by-step explanation:

1a.) -6x+14<-28

2a.) subtract 14 from 14 and -28 (what you do to one you do to other)

3a.) you are left with -6x<-42

4a.) divide by -6 eache side of "<"

5a.) you HAVE to flip the sign when you divide by a negative

6a.) x>7

1b.) 3x+28<25

2b.) subtract 28 from 28 and 25 (what you do to one you do to other)

3b.) 3x<-3

4b.) divide both sides by 3

5b.) x<-1

Answer:

73°

Step-by-step explanation:

This equation uses two supplementary angles. Supplementary angles are two angles that add up to 180 degrees.

The triangle has two angles implied, 30 degrees and (180-137) degrees.

(180 - 137) = 43 degrees

Now that we have two angles inside the triangle, we subtract them from 180 to find the last angle.

180 - 43 - 30 = 107

The angle with a measure of 107 degrees and angle 3 are supplementary

180 - 107 = 73 degrees

Answer:73.4° Fahrenheit.

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the given information:

Mean \(\mu\) = 3.2

Standard deviation \(\sigma\) = 1.9

sample size  n  = 38

Mean of sampling distribution \(\mu _{\bar x} = \mu = 3.2\)

Standard deviation of the sample mean is:

\(\sigma _{\bar x} = \dfrac{\sigma}{\sqrt{n}} \\ \\ = \dfrac{1.9}{\sqrt{38}} \\ \\ = 0.3082\)

a)

To find P(x < 3.4)

\(= P\Big( \dfrac{(\bar x - \mu_{\bar x} ) }{\sigma_{\bar x}} < \dfrac{3.4 - 3.2}{0.3082}\ \Big)\)

\(= P\Big( Z< \dfrac{0.2}{0.3082}\ \Big) \\ \\= P\Big( Z< 0.65 \ \Big)\)

Using the standard normal table

\(P(z < 0.65) = 0.7422\)

The Bell curved shape is attached in the diagram below.

b)

To find P(3 < x < 3.6)

\(= P\Big( \dfrac{3.0-3.2}{0.3082} < \dfrac{(\bar x - \mu_{\bar x} ) }{\sigma_{\bar x}} < \dfrac{3.6 - 3.2}{0.3082}\ \Big)\)

\(= P\Big( \dfrac{-0.2}{0.3082} < \dfrac{(\bar x - \mu_{\bar x} ) }{\sigma_{\bar x}} < \dfrac{0.4}{0.3082}\ \Big)\)

\(= P (-0.65 < Z < 1.30)\)

\(= P(Z < 1.30) - P(Z < -0.65)\)

Using the standard normal table

= 0.9032 -0.2578

=0.6454