In the first round of math contest, each students had to answer 2 questions. Miriam averaged 76 seconds per question. Jake and Rafael averaged 84 seconds per question, and Sam averaged 80 seconds per question. At the end of the first round, what was the total time for all 4 students?
a) 324 seconds
b) 400 seconds
c) 480 seconds
d) 568 seconds
e) 648 seconds

The volume of the cylindrical Pringles chip can is 1508 cm³

From the question, we are to determine the volume of cylindrical can

The volume of a cylinder is given by the formula

V = πr²h

Where V is the volume of the cylinder

r is the radius

and h is the height

From the given information,

Diameter = 8 cm

But,

Radius = Diameter / 2

Therefore,  

r = 8 / 2 = 4cm

h = 30 cm

Thus,

Volume of the cylindrical can = π× 4² × 30

Volume of the cylindrical can = π× 16 × 30

Volume of the cylindrical can = 480π cm³

Volume of the cylindrical can = 1507.96447 cm³

Volume of the cylindrical can ≈ 1508 cm³

Hence,

The volume is 1508 cm³

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The cost of 190 bon-bons is $154.8

According to the question ,

The shape of chocolate bon-bons is Sphere

Radius of sphere = 1.7cm

Density = 1.32g/cm³

[tex]Volume \ of\ sphere = \frac{4}{3}\pi r^{3}\\[/tex]

[tex]Volume of chocolate bon-bons = \frac{4}{3}\pi (1.7)^{3}[/tex]

[tex]= \frac{4}{3}\pi (4.913)\\= 20.5795cm^{3}[/tex]

Weight of bon-bons = volume × density

weight = 20.5795 × 1.32

= 27.1649g

Given , the cost of chocolate = $0.03

then cost of bon-bons = 0.03 × 27.1649

= $0.81494

We have to find cost of 190 bon-bons.

Cost of 190 bon-bons = 190 × 0.81494

= $ 154.8

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Marlee is in short of -768.95 inches of wire for making jewelry.

Given that, Marlee is making jewelry for a class craft show. She began with 115 inches of wire.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The numerical expression for the given situation is
115-25.75+3014-(3812+60.2)

= 89.25+3014-3872.2

= 3103.25-3872.2

= -768.95 inches

Therefore, Marlee is in short of -768.95 inches of wire for making jewelry.

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P(-4,-1) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Let A(-5,-4), B(3,-4), C(-1,6) be the vertices of the given △ABC.

Let P(x,y) be the circumcentre of △ABC. Then,

PA = PB = PC

Also, PA² = PB² = PC²

PA² = PB²

(x-(-5))² + (y-(-4))² = (x-3)² + (y-(-4))²

(x+5)² + (y+4)² = (x-3)² + (y+4)²

x²+10x+25 + y²+8y+16 = x²-6x+9 + y²+8y+16

10x-6x = 9-25

4x = -16

x = -16/4 = -4

Also, PB² = PC²

(x-3)² + (y+4)² = (x+1)² + (y-6)²

x²-6x+9 + y²+8y+16 = x²+2x+1 + y²-12y+36

-6x-2x+8y+12y = 37-9-16

-8y+20y = 12

-2x+5y = 3 .......(1)

put x= -4 into (1):

-2(-4)+5y = 3

8+5y = 3

5y = 3-8

5y = -5

y = -1

Therefore, the coordinates of circumcentre of △ABC are P(-4,-1)

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Answer:

y = x - 3

Step-by-step explanation:

y - y1 = m( x - x1 )

y - (-2) = 1 (x - 1)

y + 2 = x - 1

y = x - 3

The correct order is -3/10, -0.2, 2.02, 4.22, 4 1/8 .

Firstly we will convert the fractions into decimal units i.e

-3/10 = -0.3

41/8 = 5.125

We know that the higher the number in negative number line lower will the value of it so the -0.3 < -0.2

Now we can easily arrange these numbers according to the number line i.e;

Negatives will be first to come on number line and the correct order will be as follow :

-0.3 , -0.2,  2.02, 4.22, 4 1/8

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Answer:

a = 3, b = 12

Step-by-step explanation:

x^2-6x-3=(x-a)^2-b

Lets expand the right side:

(x-a)^2-b = (x-a)(x-a)-b

(x-a)(x-a)-b = x^2 -2ax + a^2 - b

The left side is equal to the right, as per the original equation:

x^2-6x-3 = x^2 -2ax + (a^2 - b)

Compare each term:

1)  x^2 = x^2 OK

2) -6x = -2ax;  a = 3 so that -6x = -2(3)x

3)  -3 = (a^2-b);  a^2 = (b-3)

    a = [tex]\sqrt{b-3}[/tex]

   a is 3, from above

    3 =  [tex]\sqrt{b-3}[/tex]

9 = b-3

b = 12

Answer:

[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Given variables:

Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:

[tex]\implies x^2+h^2=a^2[/tex]

[tex]\implies x^2+h^2=8.9^2[/tex]

[tex]\implies x^2+h^2=79.21[/tex]

[tex]\implies x^2=79.21-h^2[/tex]

Differentiate with respect to h:

[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]

Given:

[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]

Therefore:

[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]

Calculate x when h = 2:

[tex]\implies x^2=79.21-2^2[/tex]

[tex]\implies x^2=79.21-4[/tex]

[tex]\implies x^2=75.21[/tex]

[tex]\implies x=\sqrt{75.21}[/tex]

Substitute the values of h and x into the equation for dx/dt:

[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]

Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)

The probability that at least one of the shirts you draw will be pink 46/51.

What is probability?

The likelihood of an event happening is determined by probability. There are many instances in real life where we may need to make predictions about how something will turn out combination . The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence. By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. The likelihood of an event occurring might range from 0 to 1.

Here the number of pink shirts=8

Number of green shirts=6

Number of red shirts=4

Here if you draw 2 shirts random then,

P(neither the shirt is blue) = [tex]\frac{6}{18} *\frac{5}{17}[/tex] = [tex]\frac{5}{51}[/tex]

Now the at least one of the shirt is pink then,

=> P( at least one shirt is pink)= 1-[tex]\frac{5}{51}[/tex] = [tex]\frac{51-5}{51}[/tex] = [tex]\frac{46}{51}[/tex]

Hence the probability that at least one of the shirts you draw will be pink 46/51.

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If Otis made [tex]1\frac{3}{5}[/tex]  cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal

Total quantity of oatmeal that Otis made = [tex]1\frac{3}{5}[/tex]  cups of oatmeal

Convert mixed fraction to simple fraction

[tex]1\frac{3}{5}[/tex]  cups = 8/5 cups

The quantity of oatmeal in each bowls =  2/3  cup of oatmeal

Then the number of bowls of oatmeal that he made = Total quantity of oatmeal that Otis made ÷ The quantity of oatmeal in each bowls

Substitute the values in the equation

The number of bowls of oatmeal that he made = 8/5 ÷ 2/3

= 8/5 × 3/2

= 12/5 bowls

Hence, if Otis made [tex]1\frac{3}{5}[/tex]  cups of oatmeal and he put 2/3 cup of oatmeal into each bowl, then he made 12/5 bowls of oatmeal

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They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.

Given that,

The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.

I=interstate

L=local

using d=rt the first rows gives you d=55t

the second row gives you 560-d=45(t-2)

Since the two distances add up to 560.  Add the two distance expression and set their sum equal to the given total

560=55t+45(t-2) which equals

560=55t+45t-90

650=55t+45t

650=100t

6.5=t

Hence on local roadways, they traveled at various average speeds for 6.5 hours.

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Answer:

Step-by-step explanation:

Answer x = 4 or x = -4.

Explanation: you can make what is called a 3-4-5 triangle. The base in this case is 3(from -2 to -5 there is 3 units), the hypotenuse is 5(length given in the question) therefore the height (also known as the y coordinate) is 4 or -4 if you flip the triangle.

Answer:

Step-by-step explanation:

When x varies inversely as the square root of y, and x=1 when y=4, you want to find ...

The given relation can be written using a constant of proportionality as ...

  x = k/√y  . . . . x varies as the inverse of the square root of y

The value of k can be found from the given values for x and y:

  1 = k/√4 = k/2

  2 = k . . . . . . . . . multiply by 2

The relationship between x and y can be written as ...

  x = 2/√y

Solving for y, it can also be written as ...

  y = 4/x²

The value of x is ...

  x = 2/√9

  x = 2/3

The value of y is ...

  y = 4/12² = 4/144

  y = 1/36

The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.

It follows from the task content that the direct variation of equation of the two points given be determined.

On this note, since the relation is said to be a direct variation.

It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;

10/-5 = 4/-2 = k = -2.

Therefore, the required direct variation equation is written as;

y = -2x.

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The equations for the functions are f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the two given points for f, we can find the slope:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (-3 - (-9))

m = -4 / 6

m = -2/3

Let's use the point (-9, -2):

y - (-2) = (-2/3)(x - (-9))

y + 2 = (-2/3)(x + 9)

Multiplying both sides by 3 to get rid of the fraction:

3y + 6 = -2x - 18

3y = -2x - 24

y = (-2/3)x - 8

So the equation for f is:

f(x) = (-2/3)x - 8

To find the equation for g, we can use the fact that the y-intercept is 6 greater than the y-intercept of f. So if the y-intercept of f is b, then the y-intercept of g is b + 6.

f(x) = (-2/3)x - 8

0 = (-2/3)x - 8

2/3 x = -8

x = -12

The x-intercept of both f and g is -12.

Now we can use the y-intercept and x-intercept to write the equation for g. The slope of g is the same as the slope of f, which is -2/3.

y - (b + 6) = (-2/3)(x - (-12))

y - b - 6 = (-2/3)(x + 12)

Multiplying both sides by 3 to get rid of the fraction:

3y - 3b - 18 = -2x - 24

3y = -2x + 3b - 6

y = (-2/3)x + (3/3)b - 2

y = (-2/3)x + b - 2

So the equation for g is:

g(x) = (-2/3)x + b - 2

We know that the x-intercept of g is -12, so we can plug that in and solve for b:

0 = (-2/3)(-12) + b - 2

0 = 8 + b - 2

b = -6

So the y-intercept of g is -6 + 6 = 0.

Therefore, the equation for g is:

g(x) = (-2/3)x - 2

Hence , the equations for f and g are: f(x) = (-2/3)x - 8 and g(x) = (-2/3)x - 2

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Answer:zh  0 89 1 87.6

Step-by-step explanation: 0 89 1 87.6

Step-by-step explanation:

s = 17b

when b  =2:

s = 17b

s = 17(2)

s = 34

when b = 4

s = 17b

s = 17(4)

s = 68

Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10

Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.

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Answer:

1/2

Step-by-step explanation:

if you take the (2,2) and make it (6,10), you add 4 to the x and 8 to the y. putting this as rise over run (x/y) it comes out to four eighths (4/8). reducing that comes out to one half (4/8).

The measure of angle 11x+1 is 100°.

According to the question,

We have the following information:

We have a figure where two parallel lines are divided by a line. We know that the vertically opposite angles are equal. And when two parallel lines are cut by another line then the alternate interior opposite angles are equal.

Now, we have 10x+10 as the alternate opposite interior angle to 11x+1.

So, we have the following expression:

10x+10 = 11x+1

11x-10x = 10-1

x = 9

Putting the value of x in 11x+1:

11*9+1

99+1

100°

Hence, the measure of angle 11x+1 is 100°.

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Answer: 2

Step-by-step explanation:

This is because it is a scaled copy which means that the smaller has to multiply either by a whole or a fraction and the bigger can be divided by a whole or a fraction in order to be the smaller triangle if that makes sense. so 5*2=10, 12*2=24 thus if you were to divide 10/2=5, 24/2=12.

Answer:

The answer is 2:1

Step-by-step explanation:

This is because it is a 2/1 ratio

Answer:

Step-by-step explanation:

Dibuja una diagrama de cinta dividido en 3 y pinta 2 de los espacios

De nada :>

1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.

2. 9(x + 3) = 9x + 12 ; This is true for no values of x.

3. 4(2x + 3) = 12 + 8x ; True for any values of x.

Given,

The equations;

1. 3x + 9 = -4.5x + 20

2. 9(x + 3) = 9x + 12

3. 4(2x + 3) = 12 + 8x

We have to find whether each equation is true for all, one or no values of x.

Here,

1. 3x + 9 = -4.5x + 20

Solve for x;

3x + 4.5x = 20 - 9

7.5x = 11

x = 11/7.5

x = 1.47

Then,

This is true for one value of x.

2. 9(x + 3) = 9x + 12

Solve using distributive property;

9x + 27 = 9x + 12

9x - 9x = 12 - 27

0 = -15

This is true for no values of x.

3. 4(2x + 3) = 12 + 8x

Use distributive property and solve;

8x + 12 = 12 + 8x

8x - 8x = 12 - 12

0 = 0

True for any values of x.

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In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.

A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value. Statistical significance is commonly defined as a p-value of 0.05 or less. The sample data, test type, and sampling distribution of the test statistic under the null hypothesis are used to determine the p-value (lower-tailed test, upper-tailed test, or two-sided test).

Given,

Cook-it rice cooker has a mean time before failure of 38 months with a standard deviation of 4 months, and the failure times are normally distributed.

The 7th percentile, or X when Z has a p-value of 0.08, or X when Z = 0.4720, should serve as the warranty period.

Z = X - Mean/ standard deviation

0.472 = x - 38/4

0.472 (4) - x - 38

1.888 = x - 38

x = 39.88

x = 40

In 40 months, so that the manufacturer will not have more than 7% of the rice cookers returned.

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