A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 60 child bikes and 6 adult bikes in a week? a No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 b No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 c Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 d Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answer:

Approximately 57 minutes.

Step-by-step explanation:

5 ÷ 45 = 1/9

1/9 · 8.5 = 17/18

An hour = 60 mins so

60 ÷ 18 = 10/3

10/3 · 17 = 56.6666667

also known as 56.67 minutes if rounded to hundreds, 56.7 minutes if rounded to the tenths, and 57 minutes if rounded to a whole number.

Answer:

Explanation:

30-45 = -15

percent of change = 100(-15/45) = -33.33%

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:

  g(x) = 3 + tan(πx/4)

Step-by-step explanation:

A tangent function has a period of π. In order to make it have a period of 4, it needs to be stretched horizontally by a factor of 4/π. A function is stretched horizontally by a factor of k by replacing x with x/k.

In order for the function to be shifted vertically up by 3 units, 3 must be added to the function value. That is, the transformed function becomes ...

  g(x) = tan(x/(4/π)) +3

  g(x) = tan(πx/4) +3

Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation:

The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).

The variables x and y are related to coordinates on the line in the linear equation y = mx + c.

The formula y = mx + c yields a result for y when we enter a value for x.

As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.

According to our question-

a line equation that is perpendicular to the line 2xy=5 and passes through the point (6, 4)

The slope of the given equation 2x-y=5 is first determined.

The line's equation is y=mx+b. where'm' represents the slope

Hence, The line that connects the coordinates (6, 4) and is perpendicular to the line 2xy=5 has the equation =y=1/2x-1.

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Answer:

1/2

Step-by-step explanation:

the circle has 8 pieces so that's how you get the denominator

you count how many A's there are and that is your numerator

so now 4/8 and reduce to get a half

Answer and Step-by-step explanation:

The answer is 2 (which is equal to x).

If you were to plug 2 in to the function, the result if 30.

\(x^{3}+ 6x^{2} -x\\\\\\\\(2)^3+6(2)^2 - 2 = 30 = f(2)\)

#teamtrees #PAW (Plant And Water)

Answer:

14.4 units²

Step-by-step explanation:

The ratio of Area of rectangle R to area of rectangle S = square of the length of rectangle R to square of lthe ength of rectangle S

Let the area of rectangle S be represented by x, therefore:

40 : x = 8² : 4.8²

40/x = 64/23.04

Cross multiply

x*64 = 40*23.04

64x = 921.6

x = 921.6/64

x = 14.4

Area of rectangle S = 14.4 units²

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)

Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

Answer:

Answer is A I believe

Step-by-step explanation:

The value of w from the given triangle VWX is 5 units. Therefore, option D is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle VWX, ∠X=51°, ∠W=16° and VW=x=14.

Here, sinX/x=sinW/w

sin51°/14=sin16°/w

0.7771/14=sin16°/w

0.7771/14=0.2756/w

0.0555=0.2756/w

w=0.2756/0.0555

w=4.965

w≈5

Therefore, option D is the correct answer.

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Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

Answer:

Child ticket: 12 dollars

Total price: 64 dollars

Step-by-step explanation(Child ticket price):

\(T = X(1 - P\%)\\T = 20(1 - 40\%)\\T = 20(1 - 0.4)\\T = 20(0.6)\\T = 12\)

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

Step-by-step explanation(Total price):

\(T(12) * 2 + (20.00 * 2) = \$64\)

Hope this helps.

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

Answer:

8(4 - n)

Step-by-step explanation:

Which expression correctly represents “eight times the difference of four and a number”? 8 (n minus 4) 8 (4 minus n) 8 (n) minus 4 8 (4) minus n

Do it one piece at a time.

“eight times the difference of four and a number”:     n

“eight times the difference of four and a number”:     4 - n

“eight times the difference of four and a number”:     8(4 - n)

Answer:

the answer is b

Step-by-step explanation:

We can say that approximately 4.29 inches of rain fell in 15 minutes.

We can apply a proportion to determine the amount of rain that fell in 15 minutes.

We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:

x inches in 15 minutes equals 12 inches in 42 minutes.

where x is how much rain fell in 15 minutes.

We can cross-multiply and simplify to find x's value:

42 minutes equals 12 inches times 15 minutes (x inches)

180 = 42x

x = 180 / 42

x = 4.2857...

We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.

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2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

To express 2 cos 35 sin 67 as a sum, we can use the trigonometric identity for the product of two sine or cosine functions.

Specifically, the identity states that 2 cos A sin B can be written as

sin(A + B) + sin(A - B).

Applying this identity, we have:

2 cos 35 sin 67 = sin(35 + 67) + sin(35 - 67)

Simplifying the expressions inside the sine functions:

sin(102) + sin(-32)

Since the sine function is an odd function,

sin(-x) = -sin(x),

so we can rewrite the equation as:

sin(102) - sin(32)

Therefore, 2 cos 35 sin 67 can be expressed as the sum of sin(102) and -sin(32).

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Equation representing person's systolic blood pressure

P= 0.005y² -0.03y +121

A. If Age is 43years systolic pressure is 128.96mm Hg.

B. If systolic pressure is 128.56 mm Hg then age is 42years.

As given,

Equation represent relation between systolic blood pressure 'P' mm Hg and age of the person 'y' years

P=0.005y² -0.03y +121 __(1)

A. For a person of age 43 years

Substitute y =43 in(1)

P = 0.005(43)² -0.03(43) +121

  = 9.245-1.29 +121

  =128.96 mm Hg

B. For a person's systolic pressure is 128.56 mm Hg

Substitute P = 128.56 in (1)

128.56=0.005y² -0.03y +121

⇒7.56= 0.005y² -0.03y

⇒y² -6y -1512=0

⇒y² -42y+36y-1512=0

⇒(y-42)(y+36)=0

⇒y=42 or -36

Age cannot be negative.

y=42years

Therefore, from a equation representing person's systolic blood pressure

P= 0.005y² -0.03y +121

A. If Age is 43years systolic pressure is 128.96mm Hg.

B. If systolic pressure is 128.56 mm Hg then age is 42years.

The complete question is:

A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation:      P= 0.005y² -0.03y +121 gives a person's blood pressure, P , at age y years. A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 43 years.

B.) If a person's systolic pressure is 128.56 mm Hg, what is their age (rounded to the nearest single year)?

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The statement which is true about the given system of equations as required is; The system of equations represents parallel lines.

As evident in the task content; The two equations given are;

y = 3x + 9 and y = 3x - 4

By comparison with the slope-intercept form equation of a line; y = mx + c;

The slope of both equations are equal while the y-intercepts are different.

Ultimately, the system of equations represents a pair of parallel lines.

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Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

\(\frac{dV}{dt}=15ft^3/min\)

We have to find the increasing rate of change of height of pile  when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r=\(\frac{d}{2}=\frac{h}{2}\)

Volume of pile=\(\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3\)

\(\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}\)

h=12 ft

Substitute the values

\(15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}\)

\(\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}\)

\(\frac{dh}{dt}=0.13ft/min\)

Answer:

Multiply 36 and 21 and put point(.) after two digits

Step-by-step explanation:

7.57

Answer:

$150 for each security camera

Step-by-step explanation:

If he wants to spend $450 or less for 3 security cameras, he will have to spend $150 for each security camera.

Answer:

the answer is $150

Step-by-step explanation:

If he wants to spend not less than $450, he has to buy one camera for $150

The equation for w(width of rectangle) is: W = (P - 2L)/2

The correct answer is an option (c)

We know that the formula for the perimeter of the rectangle is:

P = 2L + 2W

where P is the perimeter of the rectangle,

L is the length of the rectangle,

and W is the width of the rectangle.

We need to rearrange this equation for w.

Consider equation,

P = 2L + 2W

P - 2L = 2L + 2W - 2L      ......(subtract 2L from each side of equation)

P - 2L = 2W

(P - 2L)/2 = 2W/2             .....(divide each side by 2)

W = (P - 2L)/2

Therefore, the correct answer is  W equals the quantity P minus 2 times L all over 2

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The complete question is:

Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle. P = 2L + 2W.

a) W = 2P − 2L

b) W = P/ 2-2 times L

c) W equals the quantity P minus 2 times L all over 2

d) W = 2P + 2L

Answer:

c) W equals the quantity P minus 2 times L all over 2

Step-by-step explanation:i just took the test

Answer: a= \(\sqrt{2}\)\(\frac{d}{2}\) = \(\sqrt{2.}\)\(\frac{15}{2}\) = about 10.61 cm

Step-by-step explanation:

given that the diagonal of square is 15cm . We need to find out the length of the side . Now see the attached image. From image it is clear that im in triangle ABC ,

a² + a² = (15cm)² [Pythagoras theorem]

2a² = 225cm²

a² = 225cm²/2

a = √{225cm²}/√2

a = 15/√2cm = 15/1.414 cm

a = 10.6 cm [ required answer]

and we are done!

-Rishabh

The calculated area of the composite figure is 85 cm².

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

The composite figure (see attachment)

Where, we have

Rectangle:

Area = length × width.

Therefore, the area of the rectangle is 10 cm × 6 cm = 60 cm².

Triangle:

Area = (1/2) × base × height.

Therefore, the area of the triangle is (1/2) × 5 cm × 10 cm = 25 cm².

To find the total area of the composite figure, we add the areas of the rectangle and the triangle:

Total Area = Area of Rectangle + Area of Triangle

= 60 cm² + 25 cm²

= 85 cm².

Therefore, the area of the composite figure is 85 cm².

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