An olympian swam the 200-meter freestyle at a speed of 1.8 meters per second. An olympic runner ran the 200-meter dash in 21.3 seconds. How much faster was the runner’s speed than the swimmer’s speed to the nearest tenth of a meter per second?

Let [tex]x[/tex] be the amount of the 30% alloy and [tex]y[/tex] the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

[tex]x+y=100[/tex]

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

[tex]0.3x+0.6y=0.54(x+y)=54[/tex]

Now,

[tex]x+y=100\implies y=100-x[/tex]

[tex]\implies0.3x+0.6(100-x)=54[/tex]

[tex]\implies60-0.3x=54[/tex]

[tex]\implies0.3x=6[/tex]

[tex]\implies x=20[/tex]

[tex]\implies y=100-20=80[/tex]

Answer:

Step-by-step explanation:

Problem One

Blue =   5

Black  =2

Red    = 3

First of all there are 10 marbles, 2 of which are black.

That means that 8 others are not black

You can draw any one of the 8.

P(not black) = 8/10 = 4/5

Problem Two

There are 10 marbles in all

3 of them are red.

P(Red) = 3/10  

Answer:

See image

Step-by-step explanation:

Palto

B is the correct answer

The value of the integral ∫ ln(x)/x dx is  ln²(x)/2 + c

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

S lnx/x dx

Express properly

So, we have

∫ ln(x)/x dx

The above expression can be integrated using substitution method

Let u = ln(x)

So, we have

du/dx = 1/x

Make dx the subject

du = dx/x

So, we have

∫ u du

Apply the power rule to integrate

∫ u du = u²/2

Substitute u = ln(x)

When integrated, we have

∫ ln(x)/x dx = ln²(x)/2 + c

Where c is a constant

Hence, the value of the integral is ln²(x)/2 + c

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Answer:

6 ft^2 and 2ft^2

Step-by-step explanation:

Multiply the height and length of each hole to get the answers. Not sure if you wanted both or not.

Answer:

im on the same question but i think u just have to multiply length times width for all of them then u subtract. hope it helps

Step-by-step explanation:

Answer:

30°

Step-by-step explanation:

Given

BC=30°

Central abgle is equal to its arc

so <3=30°

Answer:

The answer is 30

Step-by-step explanation:

Answer:

C ≈ 87.96in

Step-by-step explanation:

Answer:

interest earned= 12.47

the future value of an annuity= 162.47

Step-by-step explanation:

Given Data:

Interest rate,r= 4%

time,t = 2 years

monthly payment, P= 150

n= 12 as monthly

At the end of 2 years, final investment A= ?

As per the interest formula for compounded interest

A= P(1+r/n)^nt

Putting the values in above equation

= 150(1+0.04/12)^24

 = 162.47

Interest earned = A-P

                          = 162.47-150

                           = 12.47 !

Answer:

7

Step-by-step explanation:

Given:

Simulation of randomly checking 25 vans, with over 100,000 miles=

                                                96408 03766 36932 41651 08410

Here  the digits 1, 2, and 3 represent a van with check engine light that turn on.

Approximately how many vans will have check engine lights come on?

From the above given data the digits 1, 2 and 3 that represented the particular model of van having check engine lights on are repeated 7 times in the simulation of randomly checking 25 vans, with over 100,000 miles

Hence 7 vans will have check engine lights come on!

In a simulation using the provided set of digits, we find that out of 25 vans, approximately 6 have check engine lights that turn on.

To solve this problem, we'd first identify all the digits that are either 1, 2, or 3 within the provided sequence of randomly generated digits. These digits, according to your problem, represent vans with check engine lights that turn on. The string you provided is 96408, 03766, 36932, 41651, and 08410.

Upon counting, the following digits in the string are 1, 2, or 3: '3', '2', '3', '1', '1', and '1'. This gives us a total of 6 occurrences.

Therefore, based on this simulation, if we were to randomly check 25 vans with over 100,000 miles, approximately 6 of them would have check engine lights that come on.

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Answer:

11.76%

Step-by-step explanation:

use % error formula:[tex]\frac{|approx-exact|}{exact}[/tex]

where approx is 60

and exact is 68

so

[tex]\frac{|60-68|}{68}[/tex]

[tex]\frac{|-8|}{68}[/tex] =0.1176

0.1176=11.76%

hope this helps!

Answer:

D) cylinder; radius = 6in.; height = 5 in.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

A solid figure is a three dimensional shape having length, width and height. Examples of three dimensional figures are prism, pyramid, cone, cylinder and so on.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

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Answer:

1.7

Step-by-step explanation:

( 5x + 2y = 7 ) 2

( - 2x + 6y = 9 ) 5

10x + 4y = 14

-10x + 30y = 45

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

34y = 59

y = 1.7

The y-coordinate of the solution to the system of equations 5x + 2y = 7 and -2x + 6y = 9 is 1.8 when rounded to the nearest tenth.

To solve the system of equations 5x + 2y = 7 and -2x + 6y = 9, we'll use the method of substitution or elimination. I will demonstrate the elimination method:

This is the y-coordinate of the solution for the given system of equations.

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Answer:

a segment cd only

Step-by-step explanation:

segment cd is the only line that passes through segment ab at a right angle

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

  y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

  x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

  x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

  substitute the three vertices of the feasible region in C and chose

  the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

The vertices of the feasible region are (0, 15), (10, 15), and (20, 5). The minimum value of the objective function C = 4x + 9y is 190 at the vertex (10, 15).

The feasible region is the area on a graph where all the constraints of a system of inequalities are satisfied. To find the vertices of the feasible region, we need to find the intersection points of the lines formed by the given constraints. By solving the system of equations, we find that the vertices of the feasible region are (0, 15), (10, 15), and (20, 5).

To find the minimum value of the objective function C = 4x + 9y, we substitute the x and y values of each vertex into the objective function and determine which vertex gives the smallest value. By evaluating the objective function at each vertex, we find that the minimum value is obtained at the vertex (10, 15) with a value of 4(10) + 9(15) = 190.

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For this case we have that by definition, the density is given by:

ρ =[tex]\frac {M} {V}[/tex]

Where:

M: It's the mass

V: It's the volume

The volume of a solid cone is given by:

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the data we have:

 [tex]V = \frac {1} {3} \pi * (4) ^ 2 * 21\\V = \frac {1} {3} \pi * 16 * 21\\V = 401.92 \ cm ^ 3[/tex]

On the other hand, we have that by definition, the density of the platini is given by:

[tex]21.45 \frac {g} {cm ^ 3}[/tex]

Substituting in the initial formula, we look for the mass:

[tex]M = 401.92 \ cm ^ 3 * 21.45 \frac {g} {cm ^ 3}\\M = 8621.184 \ g[/tex]

ANswer:

The mass of the platinum cone is 8621.2 grams.

To find the mass of a solid platinum cone with a height of 21 cm and a diameter of 8 cm, calculate the volume using the formula for a cone (⅓πr²h) and then multiply by platinum's density (21,450 kg/m³) to get approximately 30.342 kg.

Calculate the Mass of a Platinum Cone

To determine the mass of a solid cone made of platinum with a given height and diameter, we must first calculate its volume and then use the density of platinum to find its mass. The density of platinum is approximately 21,450 kg/m³. The volume of a cone is given by the formula ⅓πr²h, where r is the radius and h is the height. For our cone with a height (h) of 21 cm and a diameter of 8 cm, the radius (r) would be half of the diameter, so r = 4 cm = 0.04 m. Plugging the values into the formula, we get:

Volume (V) = ⅓π(0.04 m)²×21 cm = ⅓π(0.0016 m²)× 0.21 m = 0.0014136 m³.

To find the mass (m), we multiply the volume by the density of platinum (ρ):

Mass (m) = Density (ρ) × Volume (V) = 21,450 kg/m³ × 0.0014136 m³ = 30.342 kg.

Therefore, the mass of the solid platinum cone is approximately 30.342 kilograms.

[tex]

3x-4y=16 \\

5x+2y=44 \\ \\

3x-4y=16 \\

10x+4y=88 \\ \\

13x=104 \\

x=\boxed{104\div13=8}\\ \\

3\times8-4y=16 \\

24-4y=16 \\

-4y=-8 \\

y=\boxed{2}

[/tex]

Answer:

the answer is D (4,3)

Step-by-step explanation:

4y-7=2y-1

Subtract 2y from both sides

2y-7=-1

Add 7 to both sides

2y=6

Y=3

ANSWER

[tex](x + 5i)(x - 5i) = 0 [/tex]

EXPLANATION

The given function is

[tex] {x}^{2} + 25 = 0[/tex]

The zeros of this function are;

[tex]x = \pm5i[/tex]

Or

[tex]x = - 5i \: and \: x = 5i[/tex]

[tex]x + 5i = 0\: and \: x - 5i = 0[/tex]

Hence the factored form is:

[tex](x + 5i)(x - 5i) = 0 [/tex]

If the equation were:

[tex] {x}^{2} - 25 = 0[/tex]

Then the factored form is

[tex](x + 5)(x - 5) = 0 [/tex]

Answer:

7. C

8. D

Step-by-step explanation:

7. The interest rate is 8% or .08. You find that by solving I=Prt (interest=original amount*rate*time in years)

8. The discounted price would be $48 (80*(1-.40)) Then you multiply that 48 by .08 and add that amount to the $48.

Answer:

The correct options are 1 and 3.

Step-by-step explanation:

From the given box plot it is clear that

[tex]\text{Minimum values}=34[/tex]

[tex]Q_1=42[/tex]

Q₁ is 25% of a data.

[tex]Median=46[/tex]

Median is 50% of a data.

[tex]Q_3=70[/tex]

Q₃ is 75% of a data.

[tex]\text{Maximum values}=76[/tex]

34 is minimum value of the data and 46 is median it means 50% of the data values lies between 34 and 46. Therefore option 1 is correct.

42 is first quartile and and 70 is third quartile. it means 50% of the data values lies between 42 and 70. Therefore option 2 is incorrect.

The difference between Minimum value and first quartile, Maximum value and third quartile is less than 1.5×(IQR), therefore it is unlikely to have any outliers in the data.

Hence option 3 is correct.

The interquartile range of the data is

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=70-42=28[/tex]

The interquartile range is 28. Therefore option 4 is incorrect.

Range of the data is

[tex]Range=Maximum-Minimum[/tex]

[tex]Range=76-34=42[/tex]

The range is 42. Therefore option 5 is incorrect.

Answer:

A,C

Step-by-step explanation:

got it right on edge 2021

    have a wonderful day

4 + 4= 8/2= 4

the median number is 4

The answer is 24.

Hope this helps!

Answer: 3,658 miles

Step-by-step explanation:

118 x 31 = 3,658 miles

Multiply the daily value by the number of days to find the total.

Answer:

3,658

Step-by-step explanation:

So if Kellianna drives 118 Miles each day you would simply multiply the 118 x 31 (Days) = 3,658

40; base it off of the y-intercept [C]. What is the unit of measurement?

Answer:

The maxima is the point where it is the highest it can possibly get. I promise this isn't a scam but I have a picture that shows what I mean

Step-by-step explanation:

So this graph shows that (1.75, 89) is the maximum height

I hope this helps:)

Answer: OPTION C

Step-by-step explanation:

Given the quadratic equation [tex]x^2 - 7x + 10[/tex] and the value of the variable "x" [tex]x = -2[/tex], you need to substitute the given value of the variable. Then:

[tex]=(-2)^2 - 7(-2) + 10[/tex]

And finally, you need to evaluate.

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, you get the following result:

[tex]=4+14 + 10[/tex]

[tex]=28[/tex]

This matches with the option C.

Answer:

Two distinct real solutions.

Step-by-step explanation:

Given the equation in the form [tex]ax^2+bx+c=0[/tex], you need to find the Discriminant with this formula:

[tex]D=b^2-4ac[/tex]

For the equation [tex]-2x^2+5x-3=0[/tex] you can identify that:

[tex]a=-2\\b=5\\c=-3[/tex]

Then, substituting these values into the formula, you get that the Discriminant is:

[tex]D=5^2-4(-2)(-3)[/tex]

[tex]D=1[/tex]

 Since [tex]D>0[/tex], then [tex]-2x^2+5x-3=0[/tex] has two distinct real solutions.

A ratio is the part divided by the whole. Johnny took 3 pieces of pizza when the whole pizza had 8. Johnny has 3/8 (3 out of 8) pieces of pizza, or .375 parts. To find that number, literally divide your part from your whole to get the decimal form.

She bought 2 fancy shirts and 5 plain shirts.

2 x 28=$56, and 5x15=$75. 75 plus 56 is 131

Answer:

The value of the missing side is [tex]x=2\ units[/tex]

Step-by-step explanation:

In this problem i assume that the length side x is tangent to the circle

so

the length side x is perpendicular to the radius

Applying the Pythagoras Theorem in the right triangle

we have that

[tex](1.5+1)^{2}=1.5^{2}+x^{2}[/tex]

Solve for x

[tex](2.5)^{2}=1.5^{2}+x^{2}[/tex]

[tex]x^{2}=2.5^{2}-1.5^{2}[/tex]

[tex]x^{2}=4[/tex]

[tex]x=2\ units[/tex]

Answer:

x=2

Step-by-step explanation:

The area for one side is S^2 where S is the length of one side.

The area for one side = 1/2^2 = 1/4 square foot.

A cube has 6 sides. Total surface are = 1/4 x 6 = 1 1/2 square feet.

Volume of a cube is S^3

1/4^3 = 1/64 cubic foot.