All categories

2 years ago

A teacher reviews 4-1/2 papers per hour, how many papers will that teacher review in 6-1/3 hours

Mathematics

1 answer:

MrRa [10]2 years ago

5 0

Answer:

$28\frac{1}{2}\ papers$

Step-by-step explanation:

step 1

Convert mixed numbers to an improper fractions

$4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}$

$6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}$

step 2

we know that

A teacher reviews 9/2 papers per hour

using proportion

Find how many papers will the teacher review in 19/3 hours

Let

x-----> the number of papers

$(9/2)/1=x/(19/3)$

$x=(19/3)(9/2)$

$x=28.5\ papers$

Convert to mixed numbers

$28.5=28\frac{1}{2}\ papers$

You might be interested in

Alice studies the relationship between climate and heart disease around the world. H(t)H(t)H, left parenthesis, t, right parenth

ddd [48]

Answer:

The domain of the function H(t), is [-5, 30].

The range of the function H(t), is [(10% + average), (average - 20%)]

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

For this question, the function is H(t), with the temperature, t, serving as the independent variables and H(t) the evidently dependent variable.

The domain of a function refers to all the possible independent variable values that will give corresponding real dependent variable values.

For this question, Alice's model has the probability for the occurrence of heart disease (in percents relative to the global average) at an area, H(t) varying with the temperature of that area in degree Celsius.

At a temperature of -5°C (the lowest temperature in the model), the probability is 10% above the average.

Then, the probability decreases with increase in temperature, taking a value 20% lower than the average when the temperature is at its highest of 30°C in the model.

So, temperature ranges from -5°C to 30°C and the probability for the occurrence of heart disease ranges from 10% above the average to 20% below the average.

The domain of the function H(t), from the definition given above would therefore be [-5, 30]

And the range of the function H(t), is [(10% + average), (average - 20%)]

Hope this Helps!!!

7 0

2 years ago

Read 2 more answers

Find the markup and the cost of the following item. Round answers to the nearest cent.

scoray [572]

Answer:

1st question: M=22.62 while C=75.38

2nd question: M=.22 while C=1.97

Step-by-step explanation:

If a mirror costing x dollars is marked up 30%, then we have to find x such that 30%x+x is 98 dollars.

We are solving:

.3x+x=98

Combine like terms:

1.3x=98

Divide both sides by 1.3:

x=75.38

M=98-75.38=22.62

C=75.38

So M=22.62 while C=75.38.

If ream of paper cost x and is marked up 11%, then we have to find x such that 11%x+x is 2.19.

We are solving:

.11x+x=2.19

1.11x=2.19

x=1 97

M=2.19-1.97=.22

So M=.22 while C=1.97

8 0

2 years ago

Suppose that – in any given time period – a certain stock is equally likely to go up 1 unit or down 1 unit, and that the outcome

Scorpion4ik [409]

Answer:

Step-by-step explanation:

From the given information:

Let X represent the amount of the stock that goes up in the first period; &

Let Y denote the cumulative amount that goes up in the first three periods.

Then,

$X= X_1 + X_2 \\ \\ \\EX= EX_1 +EX_2\\ \\\\Now ; EX = 0 \\ \\ EX = \dfrac{1}{2}\times 1 + \dfrac{1}{2}\times -1 \\ \\ EX = \dfrac{1}{2}-\dfrac{1}{2} \\ \\ EX = 0$

$Cov(x,y) = Var(X_1) +Var(X_2) \\ \\ =\dfrac{1}{2}(1+1) + \dfrac{1}{2}(1+1) \\ \\ = \dfrac{1}{2}(2)+ \dfrac{1}{2}(2) \\ \\ = 1+1 \\ \\ =2$

$Var (X) = Var (X_1+X_2)\\ \\ = 2 \ Var(X_1) \\ \\ = 2 \times (1) \\ \\ = 2$

$Var (Y) = Var (X_1 +X_2+X_3) \\ \\ = 3 \times Var(X_1) = \\ \\ = 3 \times 1\\ \\ = 3$

∴

$Corr(x,y) = \dfrac{2}{\sqrt{6}} \\ \\ = \dfrac{2}{\sqrt{2\times 3}} \\ \\= \sqrt{\dfrac{2}{3}}$

3 0

1 year ago

The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. I

Lostsunrise [7]

Answer:

The option which is:

On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).

Step-by-step explanation:

At first we should know the rules of translation

1) {f(x) + a} is f(x) shifted up (a) units

2) {f(x) – a} is f(x) shifted down (a) units

3) {f(x + a)} is f(x) shifted left (a) units.

4) {f(x – a)} is f(x) shifted right (a) units.

Given:

f(x) = x²

g(x) = (x-5)² + 1

By comparing [ the translation from f(x) to g(x) ] with the rules of translation

We can deduce that g(x) is the image of f(x) by translation 5 units right and 1 unit up ( rules 1 and 4)

See the attached figure which represent the graph of f(x) and g(x)

As shown g(x) goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10)

3 0

2 years ago

Read 2 more answers

Which of the following could be the equation for a parabola that opens to the left with vertex (-17,2)?

Sholpan [36]

A sideways opening parabola is in the form $x= y^{2}$ , so we know from the process of elimination that it will either be b or c. Next we have to realize that if the parabola opens to the left it is a negative parabola, just like if a parabola opens upside down it is a negative parabola. So the one that has the negative out front is b.

3 0

2 years ago

Read 2 more answers