Harry got a pair of rain boots and a pair of tennis shoes. Kate got a pair of tennis shoes and sandals what fraction of the set of new shoes is the rain boots

Answer: height = 10 feet

Base = 24 feet

Step-by-step explanation:

Let h represent the height of the triangular flower bed.

Let b represent the base of the triangular flower bed

The formula for determining the area of a triangle is expressed as

Area = 1/2 × base × height

The area of a triangular flower bed in the park has an area of 120 square feet. This means that

1/2 × bh = 120

bh = 120 × 2

bh = 240- - - - - - - - - - - - - - - 1

The base is 4 feet longer than twice the height. This means that

b = 2h + 4

Substituting b = 2h + 4 into equation 1, it becomes

h(2h + 4) = 240

2h² + 4h = 240

2h² + 4h - 240 = 0

Dividing through by 2, it becomes

h² + 2h - 120 = 0

h² + 12h - 10h - 120 = 0

h(h + 12) - 10(h + 12) = 0

h - 10 = 0 or h + 12 = 0

h = 10 or h = - 12

Since the height cannot be negative, then h = 10

Substituting h = 10 into equation 1, it becomes

10b = 240

b = 240/10

y = 24

The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]

Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.

According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:

[tex]\[ b = 2h + 4 \][/tex]

The formula for the area [tex]\( A \)[/tex] of a triangle is given by

[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:

[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]

Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:

[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]

Now, solve for [tex]\( h \)[/tex]

[tex]\[ (2h + 4) \times h = 240 \][/tex]

[tex]\[ 2h^2 + 4h = 240 \][/tex]

[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]

Divide the entire equation by [tex]2[/tex] to simplify:

[tex]\[ h^2 + 2h - 120 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]

The solutions for [tex]\( h \)[/tex] are:

[tex]\[ h = \frac{20}{2} = 10 \][/tex]

[tex]\[ h = \frac{-24}{2} = -12 \][/tex]

So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]

Now, calculate the base [tex]\( b \)[/tex]

[tex]\[ b = 2h + 4 \][/tex]

[tex]\[ b = 2 \times 10 + 4 \][/tex]

[tex]\[ b = 20 + 4 \][/tex]

[tex]\[ b = 24 \][/tex]

The complete Question is

The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.

a. What is the base of the triangle ?

b. What is the height of the triangle ?

Answer:

12 fiction books.

Step-by-step explanation:

Let b represent number of non-fiction books.

We have been given that in the library at Lenape elementary school, there are 3/8 as many fiction books as there are nonfiction books. So number of fiction books would be [tex]\frac{3}{8}x[/tex].

We are also told that there are 44 books in school library. We can represent this information in an equation as:

[tex]x+\frac{3}{8}x=44[/tex]

Let us solve for x.

[tex]\frac{8x}{8}+\frac{3}{8}x=44[/tex]

[tex]\frac{8x+3x}{8}=44[/tex]

[tex]\frac{11x}{8}=44[/tex]

[tex]\frac{11x}{8}\cdot \frac{8}{11}=44\cdot\frac{8}{11}[/tex]

[tex]x=4\cdot 8[/tex]

[tex]x=32[/tex]

Therefore, there are 32 non fiction books in the library.

Number of fiction books would be [tex]\frac{3}{8}x\Rightarrow \frac{3}{8}*32=3*4=12[/tex]

Therefore, there are 12 fiction books in the library.

Answer:

The answer to your question is letter B

Step-by-step explanation:

Data

Vertex = (2, -4)

Process

From the image we know that it is a horizontal parabola that opens to the right so the equation must be

                         (y - k)² = 4p(x - h)

Let 4p be 1

- Substitution

                         (y + 4)² = (x - 2)

- Solve for  x

                        (y + 4)² = x - 2

- Result

                        x = (y + 4)² + 2            

The answer is letter B, because of the signs.              

Answer:

y = 2x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + ← is the partial equation of the parallel line

To find c substitute (- 1, 3) into the partial equation

3 = - 2 + c ⇒ c = 3 + 2 = 5

y = 2x + 5 ← equation of parallel line

Answer: Both Technicians are correct

Step-by-step explanation: Technician A talked about the functions of a MAF sensor which is to determine the fuel need of the engine based on the of air entering the engine.

Technician B talked about types of MAF sensor employed in vehicles and how they function

Step-by-step explanation:

[tex]height \: of \: {\parallel}^{gm} \\ \\ = \frac{area \: of \: {\parallel}^{gm} }{base} \\ \\ = \frac{211.41}{24.3} \\ \\ = 8.7 \: m[/tex]

Answer:

  you're not doing anything wrong

Step-by-step explanation:

In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.

__

Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.

As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.

__

This is a good one to discuss with your teacher.

Step-by-step explanation:

Here, given the line segment is AC.

Let us assume the coordinates of the point A = (p,q)

The point M (0,5.5) is the mid point of line segment AC.

By Mid-Point Formula:

The coordinates of the mid  point M of segment AC is given as:

[tex](0,5.5) = (\frac{p + (-3)}{2} ,\frac{q+ (6)}{2})\\\implies \frac{p + (-3)}{2} = 0 , \frac{q+ (6)}{2} = 5.5\\\implies p = 0 + 3 = 3, q = 5.5 (2) - 6 = 11-6 = 5\\\implies p = 3, q = 5[/tex]

So, the coordinates of the point A  is (3,5)

Answer:

Step-by-step explanation:

For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.

In the interval [-3, 3], the relative extrema are the turning points.

The relative minimum is at y = -9 on the y-axis.

The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.

Answer:

minimum: -9

maximum: -6

Step-by-step explanation:

Answer:

2nd option (B)

Step-by-step explanation:

(0,-6) works

(3,-7) works

(-3,-5) works

This means the answer is B

Answer: 28 fl oz

Step-by-step explanation:

84 fl oz. = 10.5 cups of water

10.5/3=3.5*8=28

why 3.5 times 8 is to get the exact amount of fluid ounces

Answer: he would need 14 fluid ounces of concentrated soap.

Step-by-step explanation:

The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.

1 cup = 8 fluid ounces

Converting 3 cups of water to fluid ounces, it becomes

3 cups = 3 × 8 = 24 fluid ounces

Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is

(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap

Answer:

21 years old.

Step-by-step explanation:

Given:

Waneta is 8 years old

Waneta is 4/7 as old as Elizabeth.

Chun is 1/2 as old as Elizabeth.

George is 3 time as old as Chun.

Question asked:

How many years old is George ?

Solution:

Let age of Elizabeth = [tex]x[/tex] years

Waneta is 4/7 as old as Elizabeth. ( given )

Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]

[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]

By cross multiplication:

[tex]4x=56[/tex]

By dividing both sides by 4

[tex]x=14\\[/tex]

Age of Elizabeth = [tex]x[/tex] = 14 years

Chun is 1/2 as old as Elizabeth. ( given )

Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]

                     = [tex]\frac{1}{2} \times14= 7\ years[/tex]

George is 3 time as old as Chun.  ( given )

Age of George = [tex]3\ times \ of \ Chun\\[/tex]

                         [tex]=3\times7=21\ years[/tex]

Therefore, George is 21 years old.

Answer:

The new break even point in units = 34400 units

Step-by-step explanation:

Fixed cost ( F ) = $ 645000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]

⇒ [tex]x_{BEP}[/tex] = 32250 units

Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]

⇒ [tex]x_{BEP}[/tex] = 34400 units

Therefore, The new break even point in units = 34400 units

Answer: the speed of the plane is 130 mph

Step-by-step explanation:

Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.

Time = Distance/speed

plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is

520/x

Also, the time it takes the car to drive 200 miles is

200/(x - 80)

Since the time is the same, it means that

520/x = 200/(x - 80)

Cross multiplying, it becomes

520(x - 80) = 200 × x

520x - 41600 = 200x

520x - 200x = 41600

320x = 41600

x = 41600/320

x = 130 mph

The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.

Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.

To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

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The final answer is 410.5 cubic centimeters.

1. Calculate the volume of a small scoop:

- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].

- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]

- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].

- Calculate:

[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.

2. Calculate the volume of a large scoop:

- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].

- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].

- Substitute the radius into the volume formula:

[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].

- Calculate:

[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.

3. Find the difference:

- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].

- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].

- Approximate [tex]\( \pi \)[/tex] to 3.14.

- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].

- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.

Answer:

it's Quadrant 1 because both of he cordnates

Step-by-step explanation:

Answer:

TRUE

Step-by-step explanation:

Answer:

0.3 liters

Step-by-step explanation:

Molly made 3600mL of tea for a party.

The tea was served equally in 12 cups.

We are to determine how many liters of tea Molly put in each cup.

Total Volume of Tea = 3600mL

Number of Cups=12

Volume Per Each Cup = 3600/12 = 300mL

Next, we convert our Volume Per Each Cup from mL to Liters

1000 Milliliter = 1 Liter  

300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters

Molly put 0.3 liters of tea in each cup.

Answer:

13 units

Step-by-step explanation:

Im doin this in class to so i got you

the equation would be d=(8-(-5))2-(-3-(-2))2

Next solve in the parenthesis 13 power of 2 +-1 power of 2

Then do the powers 169+1

d=170

Then you square 170 which is 13.03840481

That simplifies to 13

yayyyy

Answer:

  4. 16

  5. $88

  6. $687.50

Step-by-step explanation:

4. Let n represent the number.

An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...

  0.9n -6.3

We want that result to be 4.5, so we have the equation ...

  0.9n -6.3 = 4.5

Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...

  n -7 = 9

Adding 7 gives ...

  n = 16

The number is 16.

_____

5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.

The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.

__

It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...

  (A -18)/5 +18 = 32

and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.

  (A -18)/5 = 14

  A -18 = 70

  A = 88 . . . . . . . . the amount the friends split unevenly

_____

6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...

  P -50 -(0.20P) = 500

  0.80P = 550 . . . . . add 50, collect terms

  P = 687.50 . . . . . . . divide by the coefficient of P

The original price was $687.50.

To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]

Given that after three years its value is $425, we can set up the equation:

[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]

Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]

So, the initial value of the computer was $3400.

Answer:

HL theorem.

Step-by-step explanation:

This states that if the hypotenuse (H) and  one leg (L) of one  right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Answer:

ASA Postulate

Step-by-step explanation:

[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\

QT || SR\\\\

\angle QTS \cong \angle SRQ... (each\: 90°)\\\\

TS \cong QR.... (given) \\\\

\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\

\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]

RHS Postulate can also be applied to prove both the triangles as congruent.

Answer:

200 rooms are available to sell.

Step-by-step explanation:

Given,

Total number of rooms for Monday night = 500,

Occupancy percentage for Monday night = 60%,

Thus, the remaining rooms available for Monday Night

= (100-60)% of total rooms

= 40% of 500

[tex]=\frac{40\times 500}{100}[/tex]

[tex]=\frac{20000}{100}[/tex]

= 200

Therefore, there are 200 rooms available to sell for Monday night.

Answer: B) 1 and -3

Step-by-step explanation:

On a Quadrant Plane:

Q1: (+,+)

Q2: (-,+)

Q3: (-,-)

Q4: (+,-)

Answer:

B

Step-by-step explanation:

because the 4th quadrant is positive and negative which option B is the only one that has that option in the same order . HOPE THIS HELPED!

Answer:

6.93

Step-by-step explanation:

f(x) = 15 / (1 + 4e^(-0.2x))

f(x) = 15 (1 + 4e^(-0.2x))^-1

Taking first derivative:

f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))

f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)

f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2

f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2

Taking second derivative:

f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

Set to 0 and solve:

0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

0 = 0.1e^(0.1x) − 0.4e^(-0.1x)

0.1e^(0.1x) = 0.4e^(-0.1x)

e^(0.1x) = 4e^(-0.1x)

e^(0.2x) = 4

0.2x = ln 4

x = 5 ln 4

x ≈ 6.93

Graph: desmos.com/calculator/zwf4afzmav

The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

Given is the function f(x) as follows -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

The given logistic function is -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.

Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

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Answer:

w(2,-3)

Step-by-step explanation:

the initial coordinates of point w are  w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)

the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)

Answer:

A chord

Step-by-step explanation:

By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)

For the cylinder whose surface area is  527.52 square meter, the total steel cost per square meter is $33.

The following information given in the question:

Height of the cylinder = 8 m

Diameter of the cylinder = 12 m

And the total cost of the steel = $17,408.16

We have to find the steel cost per square meter.

We know the radius is half of the diameter.

So, the radius (r) of the cylinder = 12/2 = 6 m

[tex]\text{Cost per square meter} = \dfrac{\text{total cost}}{\text{total surface area}}[/tex]

Surface area of the cylinder is calculated by the following formula:

Total surface area= 2πr(r+h)

=2×(3.14)×6(6+8)

=527.52 square meter

That means the steel cost for the 527.52 square meter is $17,408.16 (given in the question)

So, Cost per square meter = [tex]\dfrac{17,408.16}{527.52 }[/tex]

The steel cost of per square meter = $33

Hence, the steel cost of per square meter will be $33.

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Yes it can be, it will be a fraction

Answer:

[image]

Step-by-step explanation:

follow the steps provided in the picture

Answer:

there are n flute players so that means that you have a n amount of flute players.

Step-by-step explanation:

You would need n flute players to play ou would have n trumpet players