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6 days ago

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Of 162 students honored at an academic awards banquet, 48 won awards for mathematics and 78 won awards for English. There are 14

students who won awards for both mathematics and English. A newspaper chooses a student at random for an interview. What is the probability that the student interviewed won an award for English or mathematics?

1 answer:

tester [3.9K]6 days ago

3 0

Answer: 56/81

Step-by-step explanation:

refer to the attached document

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Find three solutions for the linear equation 4x −3y = 1, and plot the solutions as points on a coordinate plane.

lawyer [4039]

Answer:

(1, 1), (2, 2.333) and (3, 3.666).

Step-by-step explanation:

To solve this equation, we can select various values for x and then compute the corresponding y values.

<pFor instance, when x = 1, we find:

4*1 - 3y = 1

3y = 3

y = 1

When x = 2, we discover:

4*2 - 3y = 1

3y = 7

y = 2.333

Then for x = 3, we have:

4*3 - 3y = 1

3y = 11

y = 3.666

Therefore, the coordinates we will plot are (1, 1), (2, 2.333), and (3, 3.666).

Refer to the attached image for the plot.

4 0

3 days ago

Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes

Zina [3917]

Let x represent the number of caps

cost per cap = $6

cost for x caps = 6x

shipping charge = $25

overall budget = $1000

We can set up the following inequality:

Because the total amount cannot exceed 1000, we have

25 + 6x ≤ 1000

6x ≤ 975

x ≤ 162.5

rounding,

x ≤ 163

This means she can purchase a maximum of 163 caps.

5 0

10 days ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

Svet_ta [4341]

We are given the triangle

△ABC, with m∠A=60° and m∠C=45°, and AB=8.

To start, we will calculate all angles and sides.

Finding angle B:

The total of all angles in a triangle equals 180.

m∠A + m∠B + m∠C = 180.

Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

Calculating BC:

Using the law of sines,

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

We can substitute in the values.

$\frac{8}{sin(45)}=\frac{BC}{sin(60)}$

$BC=\frac{8}{sin(45)} \times sin(60)$

$BC=9.798$

Finding AC:

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

Now we'll input the values.

$\frac{8}{sin(45)}=\frac{AC}{sin(75)}$

$AC=\frac{8}{sin(45)} \times sin(75)$

$AC=10.928$

Calculating Perimeter:

$p=AB+BC+AC$

We substitute values here as well.

$p=10.928+8+9.798$

$p=28.726$

Calculating Area:

Using the area formula,

$A=\frac{1}{2}AB \times AC \times sin(A)$

we can then insert values.

$A=\frac{1}{2}8 \times 10.928 \times sin(60)$

$A=37.85570$ ...............Answer

6 0

12 days ago

Read 2 more answers

10 times as many as blank hundreds or 60 hundreds is blank thousands

Svet_ta [4341]

The result of multiplying 10 by 6 hundreds equals 60 hundreds, which can also be expressed as 6 thousands.

Explanation

This can be simplified as follows:

10 times a given quantity of _____ hundreds results in 60 hundreds
60 hundreds convert to _____ thousands

We will divide this into two segments:

$\boxed{ \ 10 \times (N \times 100) = 60 \times 100 \ }$ ... Equation-1

$\boxed{ \ 60 \times 100) = M \times 1,000 \ }$ ... Equation-2

This straightforward multiplication relates to the place value system. We need to perform calculations to find the values of N and M.

Initially, let's focus on Equation-1.

We will move the variable M to one side of the equation in order to isolate it and solve for its value.

$\boxed{ \ 10 \times (N \times 100) = 60 \times 100 \ }$

$\boxed{ \ 1,000 \times N = 6,000 \ }$

Both parts will be divided by 1,000, essentially being multiplied by $\frac{1}{1,000}$ .

$\boxed{ \ \frac{1}{1,000} \times 1,000 \times N = \frac{1}{1,000} \times 6,000 \ }$

Thus, we conclude with $\boxed{\boxed{ \ N = 6 \ }}$

Next, we process Equation-2 to derive M's value.

$\boxed{ \ 60 \times 100) = M \times 1,000 \ }$

$\boxed{ \ 6,000 = M \times 1,000 \ }$

Rearranging this equation to place M on the left side appears as follows:

$\boxed{ \ M \times 1,000 = 6,000 \ }$

Again, both sides undergo division by 1,000, which translates to multiplication by $\frac{1}{1,000}.$ .

$\boxed{ \ \frac{1}{1,000} \times M \times 1,000 = \frac{1}{1,000} \times 6,000 \ }$

This results in $\boxed{\boxed{ \ M = 6 \ }}$

- - - - - - -

Alternative approach for the second step:

60 hundreds equals to __ thousands

$\boxed{ \ 6 \times 10 \ hundreds = \ M \ thousands} \ }$

$\boxed{ \ 6 \times thousands = \ M \ thousands} \ }$

$\boxed{\boxed{ \ M = 6 \ }}$

Additional resources

A more detailed version of this topic
2 thousands 7 tens divided by 10 equals what?
100 is equivalent to 1/10 of which number?

Keywords: 10 times as many as, blank, hundreds, 60 hundreds, or, thousands, isolate, operations, multiply, divide, fraction, both sides, equal, the opposite, both sides are multiplied by, divided by, rearrange

4 0

11 days ago

Read 2 more answers

Angie baked 100 cookies and 20 brownies. She wants to split them into equal groups for the big sale. Each group must have the

zzz [4035]

Avoid repeating the question as it can be perplexing.

Given 100 cookies and 20 brownies,
What is the highest number you can divide them equally by?

To find the greatest common factor,
Factor them:
100 = 2*2*5*5
20 = 2*2*5
Thus, the greatest common factor, which is shared between them, is 2*2*5 or 20.

Calculating further, 100/20=5
20/20=1

This means there are 20 groups, each containing 5 cookies and 1 brownie.

20 groups

7 0

2 days ago