He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?

Answer:

p=1

Step-by-step explanation:

2/5+p=4/5+3/5p

[tex]\frac{2}{5} +p= \frac{4}{5} +\frac{3}{5} p[/tex]

p or p/1 are same

LCD is 5, multiply 5 with each term. the equation becomes

[tex]\frac{2}{5} \cdot 5+p \cdot 5= \frac{4}{5} \cdot 5 +\frac{3}{5}p \cdot 5[/tex]

[tex]2+5p = 4 +3p[/tex]

Subtract 3p from both sides

[tex]2+2p = 4[/tex]

Subtract 2 on both sides

[tex]2p= 2[/tex]

Divide by 2 on both sides

p= 1

So the value of p =1  for the given equation

Answer:You would earn .05 x $500 or $25 over that time period.

Step-by-step explanation:

Answer:

6 truck containers can hold 144 cases

Step-by-step explanation:

A truck container holds 24 cases and we have to find number of cases would 6 truck container will hold.

We will solve this question by unitary method.

∵ One truck container holds cases = 24

∴ 6 truck containers will hold cases = 24×6 = 144

Therefore 144 cases is the answer.

After simplifying the original expression, the equivalent expressions to  [tex]21^x/7x[/tex] are C.  [tex]3^x[/tex] and F. [tex](21/7)^x.[/tex]

The original expression in the question is  [tex]21^x/7x[/tex]. To find equivalent expressions, we first simplify the original expression. The expression  [tex]21^x[/tex]is the same as [tex](7*3)^x,[/tex] which, by property of exponents, can be written as  [tex]7^x * 3^x.[/tex]Then, given the expression is divided by 7x, the x in the denominator cancels out with the x from [tex]7^x.[/tex] Hence, the simplified form will be  [tex]3^x.[/tex] Now, we compare it with the given options.

Option C is directly equal to the simplified form. While options A,D, E, and B are not equivalent to the original expression. Considering option F, 21/7 simplifies to 3 and so, [tex](21/7)^x[/tex] can be rewritten as  [tex]3^x[/tex] which is equal to the simplified form. Therefore, the equivalent expressions are C. [tex]3^x[/tex]and F.  [tex](21/7)^x.[/tex]

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The equivalent expressions to [tex]21^x/7x[/tex] are 3^x and [tex]7^x * 3^x/ 7^x[/tex], and[tex](21/7)^x,[/tex]which can all be simplified to result in 3^x.

The expressions equivalent to 21^x/7x are checked by determining if they simplify down to the same value as the original expression. Taking the original expression 21^x/7x, it's clear that 21 can be rewritten as 7*p, so 21^x/7x simplifies to [tex](7*3)^x/7x = 7^x*3^x/7x = 3^x[/tex] (because [tex]7^x/7^x = 1).[/tex]

From the given options, Option C: 3^x, and Option E: [tex]7^x * 3^x/ 7^x[/tex]satisfy this criterion, as they also simplify to 3^x. Option F: (21/7)^x also simplifies as explained earlier to 3^x. So, options C, E, and F are equivalent to the original expression.

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Answer:

Option D is correct.

Step-by-step explanation:

We are given,

Height of the candles, h  = 18 inches

Radius of the candles, r = 5 inches

Candles are in shape of cylinder.

We have to find correct representation of volume of candle.

Volume of cylinder = [tex]\pi r^2h[/tex]

Volume of candle = ]tex]\pi (5)^2\times18[/tex]

Therefore, Option D is correct.

Periodic data is useful for analyzing trends over time, helping to forecast future events, and measure frequencies of occurrences. It is applicable in various fields including business, environmental science, and health for planning strategies and understanding patterns.

Periodic data is useful when we are interested in analyzing and understanding trends over regular intervals of time. It helps us to observe patterns and forecast future occurrences based on historical information. For example, in business, we may look at quarterly sales figures to identify seasonal effects on sales and plan inventory accordingly. In environmental science, climate data recorded over decades can be critical for studying changes in weather patterns and predicting future climate events. In health, collecting epidemiological data periodically can enable public health officials to track the spread of diseases and the effectiveness of interventions.

Frequency, relative frequency, and cumulative relative frequency are measures that can describe how often certain events occur within periodic data. These measures help answer questions like 'How many students study five hours or more for an exam?' or 'What percent of families own two pets?' They are crucial for understanding the distribution of data and for making informed decisions based on that data.

Using the given principal of $4000, an annual interest of 5.1%, and a time period of 2 years, the amount in a continuously compounded account will be approximately $4483.48 using the formula A = P*e^(rt).

In this question, we are asked to find the amount in a continuously compounded account. The formula to calculate this is A = P*e^(rt), where A is the amount, P is the principal, r is the rate, t is the time, and e is the base of the natural logarithm, approximately equal to 2.71828.

In this case, P = $4000, r = 0.051 (5.1% expressed as a decimal), and t = 2.

Substituting these values into the formula, we get: A = 4000 * e^(0.051*2). Using a calculator, we can find this to be approximately $4483.48.

So, after 2 years with an annual interest rate of 5.1%, compounded continuously, the account will contain about $4483.48.

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The first step is to calculate the length of the diagonal of the square opening.

The length of a diagonal of square = [tex] \sqrt{2} [/tex] * side

Given side = 3 feet

Length of the square hole = [tex] \sqrt{2} [/tex] *3 = 4.24 feet

since the diagonal is 4.24 feet and the shorter side of the plywood piece is only 4 feet, we can slide it through the square hole diagonally

Answer is YES since the diagonal 4.24 feet is greater than the shorter side of the plywood piece *4 feet

The equation of the line through (-8,8) and (1,-10) is y = -2x - 8

Using the slope intercept form equation.

y = mx + b

where

m = slope

b = y-intercept

Therefore,

(-8,8) (1,-10)

m = -10  - 8 / 1 + 8 =  - 18  / 9 = -2

Therefore,

let's find b as follows:

(1, -10)

y = -2x + b

-10 = -2(1) + b

b = -10 + 2

b= -8

Therefore,

y = -2x - 8

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Final answer:

The typist earns $121.50 per week by multiplying the charge per page ($0.90) with the daily page average (45 pages) and the number of days worked per week (3 days).

Explanation:

The question asks us to calculate the weekly earnings of a typist who charges $0.90 per page and averages 45 pages per day, working 3 days a week. To find the total weekly earnings, we can multiply the number of pages typed per day by the charge per page, and then multiply that result by the number of days worked in a week.

Multiply the number of pages (45) by the charge per page ($0.90): 45 pages × $0.90 = $40.50 per day.

Multiply the daily earnings by the number of days worked in a week (3): $40.50 × 3 days = $121.50 per week.

Therefore, the typist earns $121.50 per week.

We have been given that a park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails.

We need to figure out the lurking variable that describes the given correlation.

Out of the given options, the most appropriate variable that describes that negative correlation between number of available campsites in the part and the amount of litter on the park's trails is number of visitors to the park.

The reason, why number of visitors to the park is the lurking variable for the given negative correlation, is that more the number of visitors, more the litter they produce and consequently, lesser the number of available campsites.

Final answer:

After computing the distances between the points L, M, and N using the distance formula and comparing them, it is clear that the sum of the lengths of any two sides is greater than the length of the third side, satisfying the conditions of a triangle.

Explanation:

To determine whether the given coordinates are the vertices of a triangle, we can check if the sum of the lengths of any two sides is greater than the length of the third side, which is a principle derived from the triangular inequality theorem. First, we calculate the distances between the points L(–24, –19), M(–22, 20), and N(–5, –7) using the distance formula: √((x2-x1)² + (y2-y1)²).

For LM: √((-22 + 24)² + (20 + 19)²) = √(4 + 1521) = √(1525)

For MN: √((-5 + 22)² + (-7 - 20)²) = √(289 + 729) = √(1018)

For LN: √((-5 + 24)² + (-7 + 19)²) = √(361 + 144) = √(505)

Now we compare the lengths:

LM + MN > LN

LM + LN > MN

LN + MN > LM

Since all three conditions are satisfied, the points L, M, and N form a triangle.