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2 years ago

If 10a+10b=35, what is the average (arithmetic mean) of a and b?

Mathematics

1 answer:

worty [1.4K]2 years ago

6 0

Answer:

1.75

Step-by-step explanation:

If a and b are two numbers, then their arithmetic mean is

$\dfrac{a+b}{2}$

Given:

$10a+10b=35$

Divide this equation by 10:

$a+b=3.5$

Now, divide it by 2:

$\dfrac{a+b}{2}=\dfrac{3.5}{2}\\ \\\dfrac{a+b}{2}=1.75$

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A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certai

bonufazy [111]

Answer:

C. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.

Step-by-step explanation:

From the given information;

A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate.

A random sample is usually an outcome of any experiment that cannot be predicted before the result.

SO;

One plan is to select 400 voters, another plan is to select 1,600 voters

If the study were conducted repeatedly (selecting different samples of people each time);

Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion. This is because a sample proportion deals with random experiments that cannot be predicted in advance and they are quite known to be centered about the population proportion.

5 0

2 years ago

Emma earns $6 each time she mows the lawn and $8 per hour for babysitting. She is saving up to buy a new pair of jeans that cost

dangina [55]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x------> the number of times Emma mows the lawn

y------> the number of hours Emma babysits

we know that

$6x+8y\geq 48$ ------> inequality that represent the situation

The solution is the shade area above the solid line between the values of x and y positive

The equation of the solid line is equal to $6x+8y=48$

The slope of the line is negative $m=-\frac{3}{4}$

The y-intercept of the line is the point $(0,6)$ (value of y when the value of x is equal to zero)

The x-intercept of the line is the point $(8,0)$ (value of x when the value of y is equal to zero)

The graph in the attached figure

6 0

2 years ago

Read 2 more answers

In ΔDEF, d = 92 cm, e = 42 cm and ∠F=141°. Find the length of f, to the nearest centimeter.

tresset_1 [31]

Answer:

f=127 cm

Step-by-step explanation:

Law of Cosine:

x squared=92 squared+42 squared-2(92)(42)(cos 141)

x squared =8464+1764-7728(cos 141)

x=127 cm

5 0

1 year ago

Find the GCF of 44j5k4 and 121j2k6.

BartSMP [9]

Answer:

D. $11j^2k^4$

Step-by-step explanation:

We are asked to find the GCF of $44j^5k^4\text{ and }121j^2k^6$ .

Since we know that GCF of two numbers is the greatest number that is a factor of both of them.

First of all we will GCF of 44 and 121.

Factors of 44 are: 1, 2, 4, 11, 22, 44.

Factors of 121 are: 1, 11, 11, 121.

We can see that greatest common factor of 44 and 121 is 11.

Now let us find GCF of $j^5\text{ and }j^2$ .

Factors of $j^5$ are: $j*j*j*j*j$

Factors of $j^2$ are: $j*j$

We can see that greatest common factor of $j^5\text{ and }j^2$ is $j*j=j^2$ .

Now let us find GCF of $k^4\text{ and }k^6$ .

Factors of $k^4$ are: $k*k*k*k$

Factors of $k^6$ are: $k*k*k*k*k*k$

We can see that greatest common factor of $k^4\text{ and }k^6$ is $k*k*k*k=k^4$ .

Upon combining our all GCFs we will get,

$11j^2k^4$

Therefore, GCF of $44j^5k^4\text{ and }121j^2k^6$ is $11j^2k^4$ and option D is the correct choice.

3 0

2 years ago

Read 2 more answers

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt. Long-sleeved shirts are $10

charle [14.2K]

Answer:

Maximum number of long sleeved shirt that can be purchase is, 8

and

Minimum number of long sleeved shirt that can be purchased is, 0

Step-by-step explanation:

let y represents the number of short sleeves and x represents the number of long sleeves.

As per the given condition:

Members of a school club are buying matching shirts. They know at least 25 members will get a shirt.

we have;

$x+y\geq 25$ or

$y\geq 25 -x$ ....[1]

Since, long sleeves shirt are $ 10 each and short sleeves shirt are $ 5 each.

then;

Total cost of long sleeves is 10x and

the total cost of short sleeves is 5y

Also; the club can spend no more than $ 165

then;

$10x+5y\leq 165$

$5y\leq 165 -10x$ or

$y\leq 33-2x$ ......[2]

Solving the inequality equation with the graph :

Plot equation [1] and [2]; we get the maximum at point (8 , 17)

so, x= 8.

If we take minimum value of x =0 then y is between 25 and 33.

so, the solution area is between the lines to the left of where the lines intersect.

Therefore, the maximum number of long sleeved shirts can be purchased is 8 and the minimum number of long sleeved shirt can be purchased is 0

6 0

2 years ago

Read 2 more answers