convert 4 5/7 to improper fraction

The amount invested in the 7% account (x) is $3000.

Word problems are the problems we encounter in our daily lives or places of work, and we can use mathematical approaches to solve and provide solutions to these problems.

The question given has to do with providing solutions to finance.

From the question, if we have an investment of $10,900 into two savings accounts.

Say, account x and account y;

Then; x + y = 10,900 --- (1)interest of x = 7%interest of y = 9%

From (1)y = 10900 - x0.07x + 0.09y = 9210.07x + 0.09(10900 - x) = 9210.07x + 981 - 0.09x = 921

Solving for x;

x = $3000

From x + y = 10,9003000 + y = 10900y = 10900 - 3000y = $7900

Therefore, we can conclude that the amount invested in the 7% account (x) is $3000.

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the distance from the center of the circle to a point on the circle is simply its radius, thus

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{(~~-4 - (-2)~~)^2 + (~~1 - 1~~)^2} \implies r=\sqrt{(-4 +2)^2 + (1 -1)^2} \\\\\\ r=\sqrt{( -2 )^2 + ( 0 )^2} \implies r=\sqrt{ 4 + 0 } \implies r=\sqrt{ 4 }\implies \stackrel{ radius }{r=2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~2^2\implies (x+2)^2 + (y-1)^2 = 4 \\\\\\ (x^2+4x+4) + (y^2 - 2y + 1) = 4\implies \boxed{x^2+4x +y^2 -2y + 1 = 0}[/tex]

Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  [tex]\boxed{y=\dfrac{-5}{2}x+1}[/tex]

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Sal needs to make at least 358 seven-letter words to break the record.

The total number of points Sal can earn by making w seven-letter words is given by:

100 + 50w

To break the record, Sal needs to earn 18,000 points or more, so we can write the inequality:

100 + 50w ≥ 18,000

Simplifying this inequality, we get:

50w ≥ 17,900

w ≥ 358

So Sal needs to make at least 358 seven-letter words to break the record.

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The percent increase in plant height is 11%.

To find the percent increase in plant height, we need to calculate the difference between the new height and the old height, divide it by the old height, and multiply the result by 100 to convert it to a percentage:

Percent Increase = (New Height - Old Height) / Old Height x 100%

Plugging in the values given in the problem, we get:

Percent Increase = (31 - 28) / 28 x 100% = 0.107 x 100% = 10.7%

Rounding to the nearest percent, we get that the percent increase in plant height is 11%.

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Step-by-step explanation:

Given that the range of the data is 25, we need to find the difference between the highest and lowest number in the dataset, excluding P. Let's first look at the known numbers:

828, 836, 836, 836, 840, 840, 853

The highest number currently in the dataset is 853, and the lowest number is 828.

To maintain a range of 25, we know that the highest number (H) minus the lowest number (L) must equal 25:

H - L = 25

We can now consider different scenarios for P:

1. If P is the lowest number (L), then:

H - P = 25

853 - P = 25

P = 853 - 25

P = 828

2. If P is the highest number (H), then:

P - L = 25

P - 828 = 25

P = 828 + 25

P = 853

In this case, the value of P can be either 828 or 853 in order to maintain a range of 25 within the dataset.

Answer:

The formula of the area of a triangle is A = (1/2) x b x h.

A = area

b = base width

h = height of the triangle

The formula for the perimeter of a triangle is p = a + b + c.

p = perimeter

a = side 1

b = side 2

c = side 3

The sum of the interior angles of a triangle will always equal 180 degrees.

Answer: I don't understand you question. Could you please rephrase your question?

Answer:

He can buy 12 notebooks Type A and 9 notebooks Type B.

Step-by-step explanation:

Type A = $1.50

Type B = $3.00

Spending money = $45

Note: He must have at least 6 of each item.

Type A

He can buy 12 notebooks

12 x $1.50 = $18

Type B

He can buy 9 notebooks

9 x $3.00 = $27

Answer:

a) $4,475.20

b) it would take approximately 0.846 years or approximately 10 months to pay off the loan.

Step-by-step explanation:

if we nevermind the deposit and repayment dates, since they are not relevant for this case, so we have only a loan for $800 to be repaid in 22 weeks, at 203.40 every other week, biweekly namely.

Now, we can also nevermind the biweekly part, 22 payments are 22 regardless if it's done daily or yearly or bimonthly or bidecade, 22 is just 22.

a)

22 payments at 203.4 is just (22)(203.4) = 4474.8.

b)

how long does that take?

well, hell the loaner doesn't give much choices, you pay it every other week 22 times, how many weeks is that? 22*2 = 44 weeks.

Since we know a year has 52 weeks, then 44 weeks is just 44/52 of a year, namely

[tex]\cfrac{44}{52}\implies \cfrac{11}{13} ~~ \approx ~~ \text{\LARGE 0.85}~years[/tex]

Yes, the results of this study provide convincing evidence that coffee drinkers generally prefer fresh-brewed coffee over instant coffee.

And, The sample of 50 coffee drinkers is large enough to provide a representative sample of the population of coffee drinkers in the small city.

Now, By having each participant taste two unmarked cups, one containing instant coffee and the other containing fresh-brewed coffee, the study provides a fair comparison between the two types of coffee.

And, The fact that 36 out of the 50 participants preferred fresh-brewed coffee suggests that a majority of coffee drinkers in this population do indeed prefer fresh-brewed coffee.

However, it is important to note that these results may not necessarily generalize to coffee drinkers in other populations or regions. This is significantly higher than the skeptic's claim that only 50% prefer fresh-brewed coffee, suggesting that there is a clear preference for fresh-brewed coffee among the sampled population.

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Answer:

$30 difference

Step-by-step explanation:

To find the difference between two numbers, you must subtract the larger number from the smaller number. So to find the difference between these two bills, you need to subtract 265 - 235 = 30.

The area of one of the triangular faces is 31.5 square cm

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

The square pyramid

The dimensions of the triangular faces are:

Base = 7 cm

Height = 9 cm

The area of the triangular faces is calculated as

Area = 1/2 * Base * Height

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

Area = 1/2 * 7 * 9

Evaluate

Area = 31.5

Hence. the area of one of the triangular faces is 31.5 square cm

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Hello!

[tex]\sf -5x - y = -11\\\\\boxed{\sf y = 11 - 5x}[/tex]

so:

[tex]\sf -8x - 4(11-5x) = 4\\\\-8x - 44 + 20x = 4\\\\12x - 44 = 4\\\\12x = 4 + 44\\\\12x = 48\\\\\\x = \dfrac{48}{12} \\\\\Large\boxed{\textbf{x = 4}}[/tex]

so:

[tex]\sf y = 11 - 5x\\\\y = 11 - 5*4\\\\y = 11 - 20\\\\\Large\boxed{ \textbf{y = -9}}[/tex]

Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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The number of hours that Joe needs to stay open would be = 6 hours when derived from the given graph. That is option A.

To determine the number of hours Joe needs to stay open, the marginal cost given should be traced for its interception with the appropriate value for hours on the X axis.

Marginal cost is defined as the expense you pay to produce another service or product unit beyond what you intended to produce.

When plotted against the open hours, the number of hours he should be open would be = 6 hours.

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Answer:

9 Apples

6 Muffins

21 Cookies

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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The required exponential function decays at half the rate of the quadratic function. Option A is correct.

From the graph, we can see that the quadratic function is decreasing faster than the exponential function over the interval -2 ≤ x ≤ 0. The decay rate of the quadratic function can be described as constant since it has a linear decrease. On the other hand, the decay rate of the exponential function is described by its rate parameter, which is the factor by which the function is decreasing at each unit of x.

To compare the decay rates of the functions, we can look at the slopes of their tangent lines at x = -1, which is the midpoint of the interval -2 ≤ x ≤ 0. The slope of the tangent line to the quadratic function at x = -1 is approximately -6, while the slope of the tangent line to the exponential function at x = -1 is approximately -3.

Since the slope of the tangent line to the exponential function is half of the slope of the tangent line to the quadratic function, we can conclude that the exponential function decays at half the rate of the quadratic function over the interval -2 ≤ x ≤ 0.

Therefore, the answer is, "The exponential function decays at half the rate of the quadratic function".

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Answer:

  A)  r = -2sin(θ)

  B)  r = 8

Step-by-step explanation:

You want the polar coordinate versions of these Cartesian equations:

The conversion between Cartesian coordinates and polar coordinates can be accomplished using the relations ...

Substituting for x and y, we have ...

  (r·cos(θ))² +(r·sin(θ))² = -2r·sin(θ)

Dividing by r and using the Pythagorean identity, we have ...

  r = -2·sin(θ)

Substituting for x and y, we have ...

  (r·cos(θ))² +(r·sin(θ))² = 64

Using the Pythagorean identity sin(θ)² +cos(θ)² = 1, this becomes ...

  r² = 64

Taking the square root, we have ...

  r = 8 . . . . . . the equation of a circle of radius 8.

__

Additional comment

You know the Cartesian equation for a circle is ...

  (x -h)² +(y -k)² = r² . . . . . . . circle of radius r centered at (h, k)

The equation of (A) can be rearranged to x² +(y +1)² = 1, by adding 2y and completing the square. This is a circle of radius 1 centered at (0, -1), as shown in the graph.

The Cartesian equation of (B) is clearly a circle centered at the origin with radius 8, as shown in the graph.

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Answer:

Step-by-step explanation:

You want the values of A, B, C in A·log(x) +B·log(y) +C·log(z) = log(x^8y^19/z^17).

It is helpful to remember that ...

  log(ab) = log(a) +log(b)

  log(a/b) = log(a) -log(b)

  log(a^b) = b·log(a)

  [tex]\log{\left(\dfrac{x^8y^{19}}{z^{17}}\right)}=\log(x^8)+\log(y^{19})-\log(z^{17})\\\\=8\log(x)+19\log(y)-17\log{z}[/tex]

  A = 8, B = 19, C = -17

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There are seven(7) rectangles altogether.

How many rectangles are here altogether?

A rectangle is a form of quadrilateral having opposing sides parallel and four right angles.

Rectangle ABCD

Rectangle ADEF

Rectangle FECB

Rectangle AGFO

Rectangle FOBH

Rectangle OEHC

Rectangle GDOE

In conclusion, there are 7 rectangles in the diagram.

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Answer:

Max=3693.71

Direction=z

Step-by-step explanation:

The maximum rate of change of f(x, y, z) = e^(3x) * sin(y + 2z) at (3, -1, 1) is given by the magnitude of the gradient vector at that point.

The gradient of f(x, y, z) is given by the partial derivatives with respect to x, y, and z:

∇f(x, y, z) = <3e^(3x) * sin(y + 2z), e^(3x) * cos(y + 2z), 2e^(3x) cos(y + 2z)>

Evaluating this at (3, -1, 1), we get:

∇f(3, -1, 1) = <3e^9 * sin(1), e^9 * cos(1), 2e^9 cos(1)>

The magnitude of this gradient vector is:

|∇f(3, -1, 1)| = sqrt( (3e^9*sin(1))^2 + (e^9*cos(1))^2 + (2e^9*cos(1))^2 )

|∇f(3, -1, 1)| = sqrt( 13e^18*cos^2(1) + 9e^18 * sin^2(1) )

|∇f(3, -1, 1)| = sqrt( 22e^18 - 4e^18 * sin^2(1) )

|∇f(3, -1, 1)| ≈ 3693.71

Therefore, the maximum rate of change of f(x,y,z) at (3,-1,1) is approximately 3693.71.

To find the direction in which this maximum rate of change occurs, we need to look at the direction of the gradient vector:

∇f(3, -1, 1) = <3e^9 * sin(1), e^9 * cos(1), 2e^9 cos(1)>

The direction of the gradient vector is the unit vector in the same direction, which is:

u = <3e^9 * sin(1)/|∇f(3, -1, 1)|, e^9 * cos(1)/|∇f(3, -1, 1)|, 2e^9 cos(1)/|∇f(3, -1, 1)|>

u ≈ <0.000810088, 0.000274316, 0.999999>

Therefore, the maximum rate of change of f(x,y,z) occurs in the direction of the vector u≈<0.000810088, 0.000274316, 0.999999>, which points in the z-direction.

Answer:

Step-by-step explanation:

The price with coupon B is $25.20 less than the price with coupon A.

To determine which coupon gives the lower price, let's calculate the prices with each coupon.

Coupon A: 30% off of a $36 jacket:

Discounted price = $36 - 30% of $36

Discounted price = $36 - (0.30 × $36)

Discounted price = $36 - $10.80

Discounted price = $25.20

Coupon B: $14 rebate on a $36 jacket:

Discounted price = $36 - $14

Discounted price = $22

Comparing the prices, we can see that Coupon B gives the lower price of $22.

The price with coupon B is $25.20 less than the price with coupon A.

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The exact value of cos(-10π/3) is 1/2.

To find the exact value of the expression cos(-10π/3), we can use the properties of the cosine function and the unit circle.

First, let's determine the equivalent angle within one revolution of the unit circle for -10π/3.

-10π/3 is equivalent to -3π + (2π/3).

Now, recall that the cosine function has a period of 2π. So, an angle that differs by any multiple of 2π will have the same cosine value.

We can rewrite -3π + (2π/3) as -π/3, which is an angle within one revolution.

The cosine function evaluated at -π/3 is cos(-π/3).

Now, looking at the unit circle, we can determine the cosine value for -π/3. At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2.

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The first derivative of [tex]f(x) = (7x + 3)(4 - 3x)[/tex] with respect to x is [tex]-42x + 19[/tex].

To find the first derivative of the function [tex]f(x) = (7x + 3)(4 - 3x)[/tex], we can apply the product rule of differentiation.

According to the product rule, if we have two functions, u(x) and v(x), the derivative of their product is given by:

[tex](fg)'(x) = f'(x)g(x) + f(x)g'(x)[/tex]

In our case, let's designate u(x) = 7x + 3 and v(x) = 4 - 3x. We can now compute the derivatives of u(x) and v(x):

u'(x) = 7 (the derivative of 7x is 7)

v'(x) = -3 (the derivative of -3x is -3)

Now, we can apply the product rule:

[tex]f'(x) = (7x + 3)(-3) + (7)(4 - 3x)[/tex]

        [tex]= -21x - 9 + 28 - 21x[/tex]

        [tex]= -42x + 19[/tex]

Therefore, the first derivative of [tex]f(x) = (7x + 3)(4 - 3x)[/tex] with respect to x is [tex]-42x + 19[/tex].

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The radius and height of the cylindrical portion is 1.93 ft and 7.72 ft.

The total volume of the figure is the sum of the volume of the two hemisphere and a cylinder is calculated as follows;

V = ²/₃πr³  + πr²h  +  ²/₃πr³

V = ⁴/₃πr³ + πr²h

when the height of the cylinder is given as 4r, and radius r.

V = ⁴/₃πr³ + πr²(4r)

V = ⁴/₃πr³ + 4πr³

When the total volume of the tank is 120 ft³, the radius and height of the cylinder is calculated as follows;

120 = ⁴/₃πr³ + 4πr³

3(120) = 4πr³ + 12πr³

360 = 16πr³

r³ = 360/16π

r³ = 7.162

r = ∛ (7.162)

r = 1.93 ft

The height of the cylinder is calculated as follows;

h = 4r

h = 4 x 1.93 ft

h = 7.72 ft

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Answer:

y=2x-5

Step-by-step explanation:

Answer:

y = -3x + 7

Step-by-step explanation:

Parallel lines have equal slopes, so we already know that the slope of the other line is -3.

Now we can plug in (2,1) into point-slope:

                             [tex]\begin{gathered}\bf{y-1=-3(x-2)}\\\bf{y-1=-3x+6}\\\bf{y=-3x+6+1}\\\bf{y=-3x+7}\end{gathered}[/tex]

Therefore, the equation is y = -3x + 7

Info related to the question

Answer:

[tex]2z + 38[/tex]

Step-by-step explanation:

[tex]1. \: 4 + 2z + 34 \\ 2. \: 2z + (4 + 34) \\ 3. \: 2z + 38[/tex]

The area of the posters is given as [tex]250cm*^2 and 285cm^2[/tex]

A poster is a large sheet that is placed either in a public space to promote something or on a wall as decoration

The area of a rectangle is given as l*w or l*b

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

where b = w

Area is 10*25

Therefore the area of the poster is given as [tex]250cm^2[/tex]

And the second poster is given as lbArea = 15*19 =[tex]285cm^2[/tex]

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