Item 18
Question 1
Of the students in your class, 12% are left-handed. What fraction of the students are left-handed? Are there more right-handed or left-handed students? Explain. Write your answers in simplest form.


of the students are left-handed.


of the students are right-handed.

A comparison of these two fractions is:

Answer:

[tex]y=-\frac{8}{3} x - 3[/tex]

Step-by-step explanation:

Slope-intercept form is y = mx + b.

You are given 8x + 3y = -9, so to convert this into slope-intercept form you would solve for y and rearrange the terms (if needed) to follow the format of mx + b.

Start by subtracting 8x from both sides of the equation.

3y = -9 - 8x

Divide both sides by 3 to isolate y.

y = -3 - 8/3x

Rearrange the terms so the "x" variable is first.

y = -8/3x - 3

Answer:

W = 10

L = 21

Step-by-step explanation:

Formula

P = 2*(L + W)

Givens

Solution

Answer

The width of the garden is 10 feet, and the length is 21 feet.

To find the dimensions of the rectangular garden, we can use the information provided in the question. Let's assume the width of the garden is 'x' feet. According to the question, the length is 1 foot more than twice the width, so the length would be '2x + 1' feet. Now, we can use the formula for the perimeter of a rectangle, which is 2(length + width), and set it equal to 62 feet:

2(2x + 1 + x) = 62

Simplifying the equation, we get:

6x + 2 = 62

Subtracting 2 from both sides:

6x = 60

Dividing both sides by 6:

x = 10

So, the width of the garden is 10 feet, and the length is 2x + 1 = 2(10) + 1 = 21 feet.

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Answer:

-1 < x < 0

AND

0 < x < 1

Step-by-step explanation:

graph is decreasing when x increases, y decreases

so the part of graph that is decreasing is between x = -1 n 1

ans is

-1 < x < 0

AND

0 < x < 1

Final answer:

The box fits four cubical blocks with a side of 2 cm, so its volume is four times the volume of one block, which is 32 cm³.

Explanation:

Each cubical block has a side of 2 cm, and since only four blocks fit in the box completely without any space left, we can understand that the box accommodates exactly four cubes. To find the volume of one cube, we calculate the volume of a cube which is given by side³. Since the side is 2 cm, the volume of one cube is 2 cm * 2 cm * 2 cm = 8 cm³. Therefore, the box that fits exactly four of these cubes would have a volume which is four times the volume of one cube, which is 4 * 8 cm³ = 32 cm³. Hence, the volume of the box is 32 cm³, which corresponds to option B.

Answer:

60

Step-by-step explanation:

The perimeter of the triangle is found by adding up the 3 sides

5+5+ unknown side = 15

10+unknown side = 15

Subtract 10 from each side

10-10 +unknown side = 15-10

unknown side = 5

All 3 sides are length 5

Since all 3 sides are the same, it is an equilateral triangle.

If it is an equilateral triangle, all 3 angles will be the same.

There are 3 angles and they add up to 180

x+x+x = 180

3x = 180

Divide by 3

3x/3 =180/3

x = 60

Final answer:

After 20 years, the amount in the account with an initial deposit of $7,000 at a 2% interest rate compounded monthly would be $10,408.98.

Explanation:

To find the amount in the account after 20 years with no withdrawals, we use the formula for compound interest:

[tex]A = P(1 + \(\frac{r}{n}\))^nt[/tex]

Where:

A = the future value of the investment/loan, including interest

P = the principal investment amount ($7,000)

r = the annual interest rate (decimal) (2%, or 0.02)

n = the number of times that interest is compounded per year (monthly, so 12)

t = the number of years the money is invested or borrowed for (20 years).

Plugging in the values, we get:

[tex]A = 7000(1 + \(\frac{0.02}{12}\))^(12*20)[/tex]

After calculating the values inside the parentheses and raising them to the power of 240 (12 times 20), we find:

A = 7000(1 + 0.00166667)^240

A = 7000(1.00166667)^240

A = 7000 * 1.48685385

A = $10,408.98

Therefore, after 20 years, the amount in the account would be $10,408.98 with no withdrawals, given a 2% interest rate compounded monthly.

Answer:

thousands

hope it helps

Step-by-step explanation

Answer:

84 people

Step-by-step explanation:

Since 30% of the people came from Germany then 84 people came from Germany.

On a flight from London with 280 passengers, 30% of the passengers, or 84 passengers, came from Germany.

To find out how many passengers came from Germany, we need to calculate 30% of the total number of passengers. Given that there were 280 passengers in total, we can find the number of passengers from Germany by multiplying 280 by 30/100:

Number of passengers from Germany = 280 × 30/100
= 84

Therefore, 84 passengers came from Germany on the flight from London.

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The ratio is 0.25:0.5

If he uses 1.5 cups of corn grits, the ratio is multiplied by 6.

So:

1.5 : 3.0

He will need 3 cups of water.

Method 1:

[tex]\begin{array}{ccc}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}\\\\1\dfrac{1}{2}=\dfrac{3}{2}\ \text{cup of corn}&-&x\ \text{cup of water}\end{array}\qquad\text{cross multiply}\\\\\\\dfrac{1}{4}\cdot x=\dfrac{3}{2}\cdot\dfrac{1}{2}\\\\\dfrac{1}{4}x=\dfrac{3}{4}\qquad\text{multiply both sides by 4}\\\\\boxed{x=3}[/tex]

Method 2:

[tex]\begin{matrix}\dfrac{1}{4}\ \text{cup of corn}&-&\dfrac{1}{2}\ \text{cup of water}&|\text{multiply both sides by 2}\\\\\dfrac{1}{2}\ \text{cup of corn}&-&1\ \text{cup of water}&|\text{multiply both sides by 2}\\\\1\ \text{cup of corn}&-&2\ \text{cup of water}&|\end{matrix}[/tex]

[tex]\begin{matrix}\left(\dfrac{1}{2}+1\right)\ \text{cups of corn}&-&(1+2)\ \text{cups of water}\\\\1\dfrac{1}{2}\ \text{cups of corn}&-&3\ \text{cups of water}\end{matrix}[/tex]

Answer:

this is to help im not sure To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is measurement of the surface of a shape.

Step-by-step explanation:

Answer:

Step-by-step explanation: 2(12+20)= 44ft hope this helps :) correct me if I am wrong pls

Answer:

-2

Step-by-step explanation:

5+(-1)+(-6)

We add from left to right

5+-1 = 5-1 = 4

4+ -6 = 4-6 =-2

Answer: I think the answer would be -2

Step-by-step explanation:

Answer:

4 scrunchies

Step-by-step explanation:

GIVEN :

Sara can spend up to $24.98.

She already spent $12.99

She wants scrunchies that are $3.00 each.

To Find : No. of scrunchies She can purchase.

Solution :

Since she can spend up to  $24.98.

She already spent $12.99

So, amount she can spend further = $24.98-$12.99 = $11.99

Now she wants to buy scrunchies

No. of scrunchies of $3.00 = 1

No. of scrunchies of $1.00 = 1/3

No. of scrunchies of  $11.99 :

= [tex]\frac{1}{3} *11.99[/tex]

⇒ [tex]3.99[/tex]

Thus no. of scrunchies of $11.99 =3.99≈4

Hence she can buy 4 scrunchies

The equivalent value of the fraction is A = 83 / 4 = 20.75

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the numerator of the fraction be p

where the value of p = 83

Let the denominator of the fraction be q

where q = 4

Now , the fraction is A = p/q

On simplifying the expression , we get

So , the left hand side of the equation is equated to the right hand side by the value of p/q

A = 83 / 4

A = 20.75

On further simplification , we get

A = 20.75

Therefore , the value of A = 20.75

Hence , the expression is A = 20.75

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Answer:

x = 1

y = 2

Step-by-step explanation:

y = 2x

-6x + 6y = 6

-6x + 6(2x) =6    Substitute the fist equation for the value of y

-6x + 12x = 6     Combine like terms

6x = 6     divide

x = 1

Then, substitute the value of x in the equation for y

y = 2x    y = 2(1)

              y = 2

So with using the substitution method, to be able to do so you must have one of the equations isolated with one of the variables. In this case, we see that the first equation has the y variable isolated. Now with this, we are going to substitute y in the second equation for 2x since y = 2x:

[tex]-6x+6(2x)=6[/tex]

From here, we can solve for x:

[tex]-6x+6(2x)=6\\-6x+12x=6\\6x=6\\x=1[/tex]

Since we have the x-value, substitute x for 1 into either equation to solve for y as such:

[tex]y=2*1\\y=2\\\\-6(1)+6y=6\\-6+6y=6\\6y=12\\y=2[/tex]

In short:

Answer:  The answer is given below.

Step-by-step explanation:  As shown in the attached figure, the prism-shaped roof has equilateral triangular bases, one of which is ΔABC. We need to  create an equation that models the height of one of the roof's triangular bases in terms of its sides. Let ii be AD.

SEe the figure attached herewith, ΔABC forms an equilateral triangle, in which AD is the height. So, D will be the mid-point of BC and ∠ADB = ∠ADC = 90°.

Now, in ΔADB, we have

[tex]AD^2=AB^2-BD^2\\\\\\\Rightarrow AD^2=AB^2-\left(\dfrac{1}{2}AB^2\right)^2\\\\\\\Rightarrow AD^2=\dfrac{3}{4}AB^2\\\\\\\Rightarrow AD=\dfrac{\sqrt 3}{2}AB.[/tex]

Thus, with the help of this model, we can find the height of any one of the roof's triangular bases.

Answer:

Copy and Paste Version

ADsqaured = ABsquared - BDsquared

ADsqaured = ABsquared - (1/2AB squared) 2

AD squared = 3/4AB squared

AD = square root 3/2 AB

​Now we can find the height of any of the bases

Step-by-step explanation:

Answer:

y=5

Step-by-step explanation:

1

Subtract 4 from both sides

8y=5y+19-4

2

8=5y+15

3

8-5y=15

4

3y=15

5

y=15/3

6

y=5

Translation of points involves shifting them along the coordinate plane. In this case, the points are translated 2 units left and 1 unit down. The translated points are Q'(-2, -2), D'(-4, 1), V'(0, 3), and J'(1, -1).

In mathematics, when we're asked to translate points by a certain amount, we are shifting them along the coordinate plane. Here, we are asked to translate points by 2 units left and 1 unit down. Here's how we do it:

So, the translated points are Q'(-2, -2), D'(-4, 1), V'(0, 3), and J'(1, -1).

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The correct free-body diagram representation of a body being pushed eastward by a force of four units and southward by a force of three units involves two force vectors: one pointing right with a length of 4 units, and the other pointing down with a length of 3 units.

The given problem encompasses the drawing of free-body diagrams and the application of vectors in Physics.

When a body is pushed eastward by a force of four units and southward by a force of three units, the correct way to represent this in a free-body diagram would be by drawing:

This corresponds to the option of two force vectors acting at a point, one pointing right with a length of 4 units and the other pointing down with a length of 3 units.

A(-2, 2), B(4, 2), C(-6, -1), D(0, -1)

AB = CD = 4 - (-2) = 4 + 2 = 6

BD = AC. Use the formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the points B and D:

[tex]d=\sqrt{(-1-2)62+(0-4)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

BD = AC = 5

The perimeter of parallelogram ABCD:

P = 2 · 6 + 2 · 5 = 12 + 10 = 22

Answer:

Feline Flavor is less expensive per pound.

Step-by-step explanation:

A unit price has  a 1 in the denominator

To find the unit price, we take the price  and divide by the amount.

Kitty Kibbles:  $24 for 16 lbs

$24/16 = $1.50 per lb

Feline Flavor:  $11.20  for 8 lbs

$11.20 / 8 = $1.40 per lb

Feline Flavor is less expensive per pound.

Answer:

x + 2y = 0

Step-by-step explanation:

Answer:

17.3

Step-by-step explanation:

tens  ones. tenths hundredths thousandths

1        7       .   2          5                    3

We are rounding to the nearest tenth

We are rounding the 2 so we look at the 5.  If it is 5 or above we round up.

Since it is, we will round the 2 to a 3

17.3

Answer:

Step-by-step explanation:-22

Answer:

False, it's a whole number.

Step-by-step explanation:

Answer:

y < 9

Step-by-step explanation:

y - 2 < 7

This is a one-step inequality. You have y - 2 on the left side. You want y alone on the left side. If you add 2 to the left side, you eliminate the -2. You must do the same operation to both sides of an inequality, so add 2 to both sides of the inequality to eliminate the -2 on the left side.

y - 2 + 2 < 7 + 2

y < 9

Answer: y < 9

Rounded to the nearest whole number, approximately 5 students must attend summer school for U.S. history.

Here, we have,

To determine the number of students who must attend summer school for U.S. history, we need to calculate the proportion of students who earned a grade less than or equal to 62.9.

First, we need to standardize the cutoff grade using the z-score formula:

z = (x - μ) / σ

Where:

x is the cutoff grade (62.9 in this case)

μ is the mean grade (79)

σ is the standard deviation (7)

Substituting the values into the formula:

z = (62.9 - 79) / 7

z ≈ -2.3

Next, we need to find the proportion of students with a z-score less than -2.3 using a standard normal distribution table or calculator. The corresponding proportion is approximately 0.0107.

To find the number of students who must attend summer school, we multiply this proportion by the total number of students:

Number of students attending summer school = 0.0107 * 440

Number of students attending summer school ≈ 4.7

Rounded to the nearest whole number, approximately 5 students must attend summer school for U.S. history.

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Final answer:

By calculating the Z-score for a grade of 62.9 and consulting a Z-table, approximately 4 students out of 440 at Thomas Paine high school must attend summer school for U.S. history.

Explanation:

To find out how many students at Thomas Paine high school must attend summer school for U.S. history based on their grades, we'll use the properties of the normal distribution. The distribution of grades is normally distributed with a mean of 79 and a standard deviation of 7. We are interested in the students scoring less than or equal to 62.9.

First, we need to calculate the Z-score for a grade of 62.9, which indicates how many standard deviations an element is from the mean. The Z-score is calculated as follows: (X - mean) / standard deviation, where X is the grade. For a grade of 62.9, Z = (62.9 - 79) / 7 = -2.3.

Next, we consult a Z-table to find the proportion of students scoring this Z-score or lower. A Z-score of -2.3 corresponds to approximately 1.01% of the distribution.

Finally, to find the number of students, we multiply this proportion by the total number of students taking U.S. history, which is 440. Therefore, roughly 0.0101 * 440 = 4.44, which when rounded to the nearest whole number, results in 4 students needing to attend summer school for U.S. history.

Answer:

1680 words

Step-by-step explanation:

560 / 20 = 28

28 x 60 = 1680

Answer:

1680 words.

Step-by-step explanation:

There are 60 minutes in an hour. So all you need to do it 560 + 560 + 560.

I say this because he types 560 word in 20 minutes..20+20+20 is 60 so that means you have to add 560, 3 times as well.

Hope this helped! :)

The coefficient of 10x and the last term 16 is what we'll focus on. Specifically just the numbers only (ignore the variable x for now).

Think of two numbers that both multiply to 16, and also add to 10. Those two numbers are 8 and 2 (in any order). You basically find this through trial and error.

8 + 2 = 10

8 * 2 = 16

So it factors to (x+8)(x+2). Since order of multiplication does not matter, this is the same as (x+2)(x+8)

Answer b for both on edg

Step-by-step explanation: