How many ordered pairs (x, y) of positive integers satisfy the inequality 4x + 5y < 20?

The area of the shaded region is 294.5 m².

The area of the entire circle is calculated as follows;

A = πr²

where;

A = π ( 11.1² )

A = 387.1 m²

The area of the sector is calculated as follows;

A = ( θ/360 ) πr²

A = ( 130/360 ) x π ( 11.1² )

A = 139.8 m²

The area of the triangle is calculated as follows;

A = ¹/₂ ( sinθ )r²

A = ¹/₂ ( sin 130 ) (11.1²)

A = 47.2 m²

Area of the unshaded region is calculated as;

A' = 139.8 m²  -  47.2 m²

A' = 92.6 m²

The area of the shaded region is calculated as follow;

A'' = 387.1 m² - 92.6 m²

A'' = 294.5 m²

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Answer:

x = 10i - 10i

Step-by-step explanation:

3x^2 + 300 = 0

3(x^2 + 300) = 0

x^2 + 100 = 0

x^2 = -100

x = -100 (sqr root)

x = 10i - 10i

Hope this is more of the answer you where looking for.

Answer:

10

Step-by-step explanation:

it just is

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Step-by-step explanation:

so, it is

sqrt(y + 3) = sqrt(y) + sqrt(3)

first we square both sides :

y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =

= y + 3 + 2×sqrt(3y) =

= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)

0 = sqrt(12y)

we square again :

0² = 12y

0/12 = 0 = y

Answer:

35

Step-by-step explanation:

Edit :: The angle for <2 is given, so the other corresponding angles have to be equal

Answer:

0

Step-by-step explanation:

Answer:

  (b)  ∠EGF ≅ ∠BDC

Step-by-step explanation:

Angles D and G are both marked with double arcs, indicating they are congruent:

  ∠EGF ≅ ∠BDC

__

Other choices:

BD is the short segment between the marked angles. It has no "decoration." EF is the longer segment with a single hash mark decoration. These are not corresponding parts, so are not congruent. There is no right angle in these triangles, so the Pythagorean theorem is not applicable.

__

CD is the longest side, with no decoration. EF is the middle-length side with a single hash mark decoration. These are not corresponding sides.

Answer:

I don't know I'm sorry soo just try to work it out if u don't know how than ask someone you know okay, ur welcome.

The sampling distribution has a mean value of 171.3 feet; two standard deviations from the mean are 295.3 feet in a positive direction and 47.3 feet in a negative direction.

To calculate these values, the formula for standard deviation is used, which is:

Standard Deviation = (X-mean)/standard error

Therefore, to calculate two standard deviations from the mean in the positive direction, we use:

295.3 ft = (X-171.3)/48

To calculate two standard deviations from the mean in the negative direction, we use:

47.3 ft = (X-171.3)/48

Therefore, the mean of the sampling distribution is 171.3 ft, and two standard deviations from the mean in the positive direction is 295.3 ft, and two standard deviations in the negative direction is 47.3 ft.

Complete Question:

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 171.3 ft and standard deviation 48 ft.

You intend to measure a random sample of n =28 trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes of the mean, and two standard deviations from the mean in the positive and negative direction. Be accurate to two decimal places.

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Answer:

Step-by-step explanation:

speed = 240 miles/(6 hours) = 40 miles/hour

360 miles × 1 hour/(40 miles) = 9 hours

Answer:

4%

Step-by-step explanation:

20% more ➞ 100% +20%= 120%

20% less ➞ 100% -20%= 80%

\(J= 120\% Y ---(1)\\ B= 80\% J ---(2)\)

Subst. (1) into (2):

\(B = \frac{80}{100} ( \frac{120}{100}Y) \\ B = \frac{4}{5} ( \frac{6}{5} Y) \\ B = \frac{24}{25}Y \\ B = 0.96Y \\ B = 96\%Y\)

Difference

= 96% -100%

= -4%

Thus, Bob had 4% less money than Yao.

Parallel lines are lines which are equidistant to each other long every point on both lines.

We know that,

A line is said to be perpendicular if it crosses another line at exactly 90°. Hence, as depicted in the image attached, TZ is perpendicular to RS.

here, we have,

given that,

Topic 16-1 number 13.Draw and label parallel lines XY and RS.Then draw and label TS so it is perpendicular to both XY and RS.Draw point Z on TS.

It is important to note that perpendicular lines always bisect one another and that the slopes of lines that are perpendicular are negative of each other and reciprocals.

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Answer:

1/12

3/10

22/9

357/4

91/8

2/7

12/5

7/4

124

49

hope this will help you

Answer:

i dont understand the question please be more precise

Step-by-step explanation:

So,

We're going to evaluate each expression as follows:

Let's begin with a:

Now, b:

And, finally, c:

Notice that if the parentheses change, the results wouldn't be the same.

Hi

let's call X the initial deposit.

the interest rate is 5.2 %

so each year X increase by 1.052.

so we have : X *1.052^7 =2300

X = 2300/1.052^7

X = 1612,94

please note that the deposit was rounded to the next cent. as the result would be 1612,937...

Answer:

1686.22

Step-by-step explanation:

1686.22

 2300=P(1+(0.052x7))  

2300=P1.364  

P=2300/1.364  

=1686.217...  

=1686.22..

=1686 for the nearest dollar

The extra amount that Robby is to pay in interest to purchase the television is calculated as: $98

To calculate the extra amount paid in interest, you need to determine the total cost of the loan, including the interest, and subtract the original amount borrowed.

Here's the formula to calculate the extra amount paid in interest:

Extra Amount Paid in Interest = Total Cost of Loan - Original Amount Borrowed

Where, Total Cost of Loan = Original Amount Borrowed + Interest

To calculate the interest, you can use the following formula:

Interest = Original Amount Borrowed x Interest Rate x Time

The interest on the cash advance is calculated as follows:

$350 x 28% = $98

So, the total amount Robby will pay for the television after interest is:

$350 + $98 = $448

Therefore, the extra amount Robby will pay in interest to purchase the television is:

$448 - $350 = $98

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Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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11) (Level 2):

I believe if you just multiply the shaded area (10x6), then maybe subtract the non-shaded area (20cm and 10 cm). After doing this process, I believe you will get: 200-60 = 140! (But then again I could be wrong, I’ll admit it I’m not a pro but at least I gave effort!)

Fraction: 14/10

Decimal: 1.4

Percent: 140%

12) (Level 3):

I have absolutely no idea about this question and I don’t want to guess! Sorry!

Answer:

C

Step-by-step

c

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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The monthly payment of $310 compounded monthly at 8% and 3% will have a principal of $15,288.71 and $17,252.23 respectively

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

In order to solve this question, we can use the formula of monthly payment we can use a simple formula for that

\(A = p \frac{r(1+r)^n}{(1+r)^n-1}\)

In the first scenario, we can find the monthly payment at 8%

Substituting the values into the equation and solve

The principal at 8% is $152888.71 and the principal at 3% is at $17252.23

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Answer:

Step-by-step explanation:

given:

line f:  y+3 = \(\frac{1}{6}\)(x-2)

line g:   P1=(x1,y1) = ( -6,1)    and parallel to  f  ( same slope)

use point-slope, again  

y-y2 = m(x-x1)

y-1=\(\frac{1}{6}\)(x-(-6))

y-1 =\(\frac{1}{6}\)(x+6)

y-1 = \(\frac{1}{6}\)x +1

y = \(\frac{1}{6}\)x + 1 +1

y = \(\frac{1}{6}\)x + 2   ( in slope intercept form  y= mx+b)

3/2 part of the garden is planted by both the sisters.

A division is a process of splitting a specific amount into equal parts.

Given,

Jane's family divided up their garden so that 2/3 of garden will have vegetables.

Jane and her sister will plant2/3 of the vegetable portion of the garden

2/3 is the vegetable portion

In this vegetable portion 2/3 part is of the vegetable portion of the garden

3/2/2/3

3/2×3/2

6/4

3/2

Hence, 3/2 part of the garden is planted by both the sisters.

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$3299.62

total money he will have : $13,123.62

Answer:

Interest = $3,299.64 (nearest cent)

Step-by-step explanation:

Compound interest formula:  \(\sf I=P(1+\frac{r}{n})^{nt}-P\)

where:

Given:

Substituting given values into the formula and solving for I:

\(\sf \implies I=9824(1+\frac{0.0362}{365})^{365 \times8}-9824\)

\(\sf \implies I=13123.62461-9824\)

\(\sf \implies I=3299.62 \ (nearest \ hundredth)\)

Answer:

C

Step-by-step explanation:

1 foot = 12 inches                          Find 1/4 foot in inches

1/4 a foot = 1/4 * 12 = 3 inches

6 1/4 feet = (6 + 1/4) * 12

=72 + 3

75 inches

Answer:

72; Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The height of the rectangular prism is 21 cm.

A rectangle is a quadrilateral with four right angles (90 degree angles) and two pairs of opposite sides that are equal in length. It is a special case of a parallelogram where all angles are right angles.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. We are given that the volume is 1,680 cm^3, but we don't have enough information to determine the height directly without knowing the other dimensions.

If we are given the dimensions of the rectangular prism or any relationship between them, we can use algebraic methods to solve for the height. For example, if we are given that the length is twice the width and the height is three times the width, we can write:

l = 2w

h = 3w

Substituting these expressions into the volume formula, we get:

\(V = lwh\\\\1680 = (2w)(w)(3w)\\\\1680 = 6w^3\)

\(w^3 = 280\)

\(w = 7 cm\)

Now that we know the width is 7 cm, we can use one of the expressions for the height to find its value:

h = 3w = 3(7) = 21 cm

Therefore, the height of the rectangular prism is 21 cm.

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Complete question: