PLS HELP Write an equation in slope-intercept form for the line that satisfies the following condition.
slope 5 and passes through (2, 28)​

Answer: 17 Regular, 33 Valuable

Step-by-step explanation:

Given

Sal has 50 cards

He has 16 more valuable card than regular cards

Suppose he has x regular cards

So, valuable cards are x+16

Their sum must be 50

\(\Rightarrow x+x+16=50\\\Rightarrow 2x=50-16\\\Rightarrow 2x=34\\\Rightarrow x=17\)

Therefore, he has 17 regular cards and 33 valuable cards

Answer:

To solve the problem using unit rates, we can first find Lila's rate of phone calls per minute, which is given by:

rate = number of phone calls / time spent on the phone

Using the values given in the problem, we get:

rate = 24 phone calls / 72 minutes

rate = 1/3 phone calls per minute

This means that Lila routes 1/3 phone call per minute.

To find how many phone calls Lila needs to route to spend a total of 90 minutes on the phone, we can use the same rate and the formula:

number of phone calls = rate x time

Substituting the values, we get:

number of phone calls = (1/3 phone calls per minute) x (90 minutes)

number of phone calls = 30 phone calls

Therefore, Lila needs to route a total of 30 phone calls to spend a total of 90 minutes on the phone.

In this scenario, Florin and Guilder are two countries producing two goods, cheese (X) and grain (Y), using labor as the only input. Florin has 3 million workers, each capable of producing 2 blocks of X or 6 wagonloads of Y per year. Guilder has 9.6 million workers, each capable of producing 1 block of X or 4 wagonloads of Y per year. By analyzing their production possibilities frontiers (PPFs) and comparing their labor productivity, we can determine their absolute and comparative advantages, and predict the outcome of free trade.

a) The PPFs for Florin and Guilder can be plotted with X on the horizontal axis and Y on the vertical axis. Given that each country allocates one-third of its labor force to dairy production and two-thirds to wheat farming, we can identify the consumption points (A and A*) where the indifference curves representing their preferences intersect with their PPFs.

b) The PPF equation for Florin can be written as X = 2L/3 and Y = 6L/3, where L represents the labor force. For Guilder, the PPF equation is X = L/9.6 and Y = 4L/9.6.

c) Guilder has the absolute advantage in producing Y as its workers are more productive in Y compared to Florin. However, Florin has the comparative advantage in producing Y because the opportunity cost of producing Y in terms of X is lower for Florin than Guilder.

d) Under free trade, Guilder would export Y and Florin would export X. This is based on the principle of comparative advantage, where each country specializes in producing the good for which it has a lower opportunity cost.

e) When both countries fully specialize and trade, there can be a higher total production of both X and Y compared to the previous consumption points (A and A*). By focusing on producing the goods in which they have a comparative advantage and engaging in trade, both countries can benefit from increased efficiency and resource allocation.

f) To show the new Consumption Possibilities Frontier (CPF) relative to the Production Possibilities Frontier (PPF), we can plot the new CPF by using the given relative price of Y to X (0.3) and connecting the points where each country consumes along the CPF based on their respective comparative advantage and terms of trade.

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The number of revolution the wheel makes in 7 miles is 4706 revolutions

Since the wheel is a circle, its circumference is travelled in 1 revolution.

So, circumference C = πd where d = diameter of wheel = 30 in

So, C = πd

= π × 30 in

= 30π in

= 94.25 in

Now, we need to find the number of revolutions the wheel makes when the tractor travels D = 7 miles.

Since 1 mile = 63360 in,

Converting miles to inches, we have D = 7 miles

= 7 × 1 mile

= 7 × 63360 in

= 443520 in

So, the number of revolution the wheel makes in 7 miles is N = D/C

= 443520 in/94.25

= 4705.89

≅ 4706 to the nearest whole number

So, the number of revolution the wheel makes in 7 miles is 4706 revolutions

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Answer:

B

Step-by-step explanation:

The side EC is 6 units.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that Point B lies on line AC, as shown on the coordinate grid below.

AD = 2 units,

DB = 3 units, and

BE = 4 units

We need to find EC.

As we observe the triangle ADB is similar to BEC.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AD is corresponding side of BE and DB is corresponding side of EC.

As the sides are proportional

2/3=4/x

2x=12

x=6

Hence, the side EC is 6 units.

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We want to find the value of x, which is the hypotenuse of the triangle on the image.

We will see that the value of x is 5.77 units.

On the figure we can see a right triangle, we want to find the value of x, which is the hypotenuse of this triangle.

To do so, we can use the trigonometric relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Where θ is an internal angle of the triangle, and the adjacent cathetus is the cathetus that forms the angle.

Here we can use θ = 30°, and the adjacent cathetus is the one that has a measure of 5 units,  then the value of x is given by the equation:

cos(30°) = 5/x

Solving that for x we will get:

x = 5/cos(30°) = 5.77

The hypotenuse measures 5.77 units.

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Part A

we have the equation

(x-13)^2+(y-4)^2=16

Rewrite as

(x-13)^2+(y-4)^2=4^2

so

The center of the circle is the point (13,4)

The radius of the circle is 4 units

using a graphing tool

Part B

Remember that

If an ordered pair lies on the circle, then the ordered pair must satisfy the equation of the circle

so

Verify each ordered pair

Hunter (11,4)

For x=11 and y=4

substitute in the equation of the circle

Is not true

so

Hunter is not in the spotlight

Joe (8,5)

x=8 and y=5

Is not true

so

Joe is not in the spotlight

Mason (15,5)

x=15 and y=5

Is not true

Mason is not in the spotlight

Answer:4¹⁵/110

Step-by-step explanation:

Take x to be the number

X=4.13636363

Since the repeating numbers are 2 you multiply the number by 100

100x =413.636363

When we minus 413.6363 and 4.136363 we will get a decimal

We multiply the value for x by 1000 we get 4136.3636

And when we minus 4136.3636 by the values of 1x and 100x we will still get a decimal

We multiply the value of x by 10000 we will get 41363.6363 when we divide it by the values of 1x we will get a decimal but when we divide it by the value of 100x we will not get a decimal

Then we minus them

10000×-100×=9900x

41363.6363-413.6363=40950

9900x=40950

Divide both sides by 9900

9900x÷9900=40950÷9900

X=4¹⁵/110

Answer:

4x^5y^5z^7

Step-by-step explanation:

4x^5y^5z^7

Answer:

\((2xyz^2)^5\)

This equation shows us that the whole thing in the parenthesis need to be multiplied by 5 times.

The result:

\(=32x^5y^5z^{10}\)    

(\(\left(a^b\right)^c=a^{bc}\) this is how I got the exponent 10 for z)

The factor of the \(18x^{2} -21x-15\) will be 3(3x-5)(2x+1).

Given quadratic equation is \(18x^{2} -21x-15\)

By taking 3 common from whole of the equation it becomes.

\(3(6x^{2} -7x-5)\)

now by factorization equation will be.

\(3(6x^{2} -10x+3x-5)\)

3[(2x(3x-5)+1(3x-5)]

Taking (3x-5) common from whole equation it will become

3(3x-5)(2x+1).

Hence the factor of the \(18x^{2} -21x-15\) will be 3(3x-5)(2x+1).

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a school has 2500 pupils. when 52 boys and 1/9 of the girls are absent, the number of the boys present is equal to the number of girls. how many pupils does the school have ?

Let the number of boys be x

Data :

Total pupils = 2500

Absent no. of boys and girls = 52 and 1/9

Now,

Remaining no of pupils = 2500 - 52 ➝ 2448

Hence, the no. of girls absent = 1/9 of 2448 ➝ 272

Therefore,

Total no. of pupils absent = 52 + 272 ➝ 324

No. of pupils present = 2500 - 324 ➝ 2176

Henceforth, 2176 pupils are present

Let V be a vector space, and T:V→V a linear transformation then the value of T(v⃗ 1) = -v⃗ 1, T(v⃗ 2) = v⃗ 2 and T(4v⃗ 1 − 4v⃗ 2) = -4v⃗ 1 - 4v⃗ 2.

We can use the given information to find the value of T for various vectors in V and T:V→V a linear transformation such that T(5v⃗ 1+3v⃗ 2)=−5v⃗ 1+5v⃗ 2 and T(3v⃗ 1+2v⃗ 2)=−5v⃗ 1+2v⃗ 2.

For 5v⃗ 1 + 3v⃗ 2, we have:

T(5v⃗ 1+3v⃗ 2) = −5v⃗ 1+5v⃗ 2

5T(v⃗ 1) + 3T(v⃗ 2) = -5v⃗ 1 + 5v⃗ 2

Similarly, for 3v⃗ 1 + 2v⃗ 2, we have

T(3v⃗ 1+2v⃗ 2) = −5v⃗ 1+2v⃗ 2

3T(v⃗ 1) + 2T(v⃗ 2) = -5v⃗ 1 + 2v⃗ 2

Solving these equations for T(v⃗ 1) and T(v⃗ 2), we get

T(v⃗ 1) = -v⃗ 1

T(v⃗ 2) = v⃗ 2

Now, we can use these values to find T(4v⃗ 1 − 4v⃗ 2)

T(4v⃗ 1 − 4v⃗ 2) = 4T(v⃗ 1) - 4T(v⃗ 2)

= 4(-v⃗ 1) - 4(v⃗ 2)

= -4v⃗ 1 - 4v⃗ 2

Therefore, T(4v⃗ 1 − 4v⃗ 2) = -4v⃗ 1 - 4v⃗ 2.

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Answer: $49.056

Step-by-step explanation:

Salim bought 32 feet of window trim at a hardware store and the trim cost $1.75 per foot. The total cost will then be:

= 32 × $1.75

= $56

She used a 20% coupon to purchase the window trim. The amount she will pay will be:

= $56 - (20% × $56)

= $56 - (0.2 × $56)

= $56 - $11.2

= $44.8

A sales tax of 9.5% was then applied to the total purchase. The amount Salim will end up paying will be:

= $44.8 + (9.5% × $44.8)

= $44.8 + (0.095 × $44.8)

= $44.8 + $4.256

= $49.056

Answer:10

Step-by-step explanation:Use the Pythagorean theorem a^2 + b^2 = c^2, a is 8 and b is 6 so now you have 8^2 + 6^2 = C^2 this simplifies to 64 + 36 = c^2 those 2 numbers add up to 100 so C^2 is 100 then to get C you take the square root of 100 which is 10

The missing side 10.

Option C is the correct answer.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Applying the Pythagorean theorem.

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = √100

c = 10

Thus,

The missing side is 10.

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Answer:

i think the answer is 738

The total possible number of outcomes for the season record is 3¹⁸, or 387,420,489. This is because there are three possible outcomes for each of the 18 games: win, loss, or tie.

To find the total number of outcomes, you can use the fundamental counting principle, which states that the total number of outcomes is equal to the product of the number of outcomes for each event. For example, if you flip a coin twice, there are two possible outcomes for each flip: heads or tails. Using the fundamental counting principle, you can find the total number of outcomes by multiplying the number of outcomes for each event:2 x 2 = 4So there are four possible outcomes for flipping a coin twice: heads-heads, heads-tails, tails-heads, or tails-tails. Using the same logic, you can find the total number of outcomes for the soccer team's season record by multiplying the number of outcomes for each game:3 x 3 x 3 x ... (18 times)= 3¹⁸= 387,420,489So there are 387,420,489 possible outcomes for the soccer team's season record.

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Answer:

your answer would be b

Step-by-step explanation:

if you divide each side by 5 you get

15/5:5/5

3:1

hope this helps! have a nice day!

Answer:

4a + 4b = 10

6a + 6b = 12

Step-by-step explanation:

Putting the equation in a system of linear equation :

We donate, apples and oranges using any preffered letter or alphabet

Let :

Apples = a ; oranges = b

4 apples and 4 oranges equals $10

4a + 4b = 10

6 Apples and 6 oranges equals $12

6a + 6b = 12

Hence, the system of linear equation :

4a + 4b = 10

6a + 6b = 12

Answer:

No Solution

Step-by-step explanation:

It would require different amounts of dollars to fulfill eah equation.

Answer:

To the nearest whole percent is 26%

Step-by-step explanation:

First half of the year = 54 students

Second half of the year = 68 members

find the percent of increase in club membership to the nearest whole percent ?

% increase in club membership = (new member - old member) / old member × 100

= (68 - 54) / 54 × 100

= 14 / 54 × 100

= 0.259 × 100

= 25.9 %

To the nearest whole percent is 26%

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

99.8% confidence interval with a margin of error of 0.02, using the estimated proportion of 0.31 from the previous poll.

To find the sample size needed to construct a confidence interval for a proportion with a specified margin of error, we use the following formula:

n = (z^2 * p * q) / E^2

where:

n is the sample size

z is the z-score corresponding to the desired level of confidence (99.8% in this case)

p is the estimated proportion from the previous poll (0.31 in this case)

q = 1 - p

E is the desired margin of error (0.02 in this case)

First, we need to find the value of z for a 99.8% confidence level. Using a standard normal distribution table, we can find that the z-score for a 99.8% confidence level is approximately 2.967.

Substituting the given values into the formula, we have:

n = (2.967^2 * 0.31 * 0.69) / 0.02^2

n = 1202.19

Rounding up to the nearest whole number, we need a sample size of n = 1203 to construct a 99.8% confidence interval with a margin of error of 0.02, using the estimated proportion of 0.31 from the previous poll.

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For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis C. is rejected

A one-tailed hypothesis test refers to a statistical test in which the alternative hypothesis is either greater than or less than the null hypothesis, but not both. Since the problem states that it is a one-tailed hypothesis test (upper tail), the alternative hypothesis, H1, will be a greater than or > sign. Hypothesis testing is the method of determining whether or not an assertion about a population parameter is consistent with sample data. A hypothesis test is conducted to assist in deciding between two competing hypotheses. One hypothesis is the null hypothesis (H0), which is a statement of the population parameter that is being tested.

In a hypothesis test, the null hypothesis is rejected if the test statistic falls in the rejection region. The test statistic, which measures the distance between a sample estimate and the null hypothesis, is used to assess whether or not the null hypothesis should be rejected. Reject the null hypothesis if the p-value is less than or equal to α. Since the p-value of 0.034 is less than the level of significance, α, of 0.05, the null hypothesis will be rejected, according to the question above. Therefore, option C is correct.

The Question was Incomplete, Find the full content below :

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. could be rejected or not rejected depending on the sample size.

b. could be rejected or not rejected depending on the sample mean.

c. is rejected.

d. is not rejected.

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To solve the differential equation dy/dx = cos^2(x) with the curve passing through the point (0, 0), we can integrate both sides of the equation.  The solution to the differential equation is y = (1/2)x + (1/4)sin(2x).

The given differential equation is dy/dx = cos^2(x). To solve this equation, we integrate both sides with respect to x.

∫ dy = ∫ cos^2(x) dx.

The integral of cos^2(x) can be rewritten using the identity cos^2(x) = (1 + cos(2x))/2:

∫ dy = ∫ (1 + cos(2x))/2 dx.

Integrating each term separately:

y = (1/2)x + (1/2) ∫ cos(2x) dx.

The integral of cos(2x) is sin(2x)/2:

y = (1/2)x + (1/4)sin(2x) + C.

We can determine the value of the constant C using the initial condition that the curve passes through the point (0, 0). Substituting x = 0 and y = 0 into the equation:

0 = (1/2)(0) + (1/4)sin(2(0)) + C,

0 = 0 + 0 + C,

C = 0.

Therefore, the solution to the differential equation dy/dx = cos^2(x) with the curve passing through the point (0, 0) is y = (1/2)x + (1/4)sin(2x).

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Answer:

The constant of variation 'k' is NOT constant.

Therefore, we conclude that Taylor did not charge a constant rate. The rates are not equal because his rate changed.

Step-by-step explanation:

Given the table

Number of Lawns         1           2            3              4

Amount Earned ($)      16         32          54            72

We know that when y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality.

In our case, the 'Amount earned ($) ' is represented by 'y', and the 'Number of Lawns' is represented by 'x'.

Let us check the constant of proportionality using the equation

k = y/x

k = 16/1 = 16

k = 32/2 = 16

k = 54/3 = 18

k = 72/4 = 18

It is clear that that the constant of variation 'k' is NOT constant.

Therefore, we conclude that Taylor did not charge a constant rate. The rates are not equal because his rate changed.

The rate at which the level in the coffee pot is rising, when the coffee in the pot is 10 cm, is approximately 20 cm/min. To find the rate at which the level in the coffee pot is rising, we can consider the volume of coffee that is draining from the filter into the pot.

The rate at which the coffee drains from the filter is given as 100 cc/min. Since the filter and pot have the same diameter, the area of the base of the filter and pot is the same.

The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. The volume of coffee draining per minute can be calculated using the height of the cone, which is 15 cm. Substituting the values, we have V = (1/3)π(7.5²)(15) cc/min.

When the coffee in the pot is 10 cm, the volume of coffee in the pot is given by V =π(7.5²)(10) cc. Now, we can differentiate the volume with respect to time to find the rate at which the level is rising.

dV/dt = π(7.5²)(dh/dt)

100 cc/min = π(7.5²)(dh/dt)

Simplifying the equation, we can find that dh/dt is approximately 20 cm/min. Therefore, the rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm is approximately 20 cm/min.

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Answer:

i think 840 i searched it up

Step-by-step explanation: