Find the length of the toothpick nearest millimeter

After 5 minutes, the two balloons' height will be 40 + 10 + 5 = 90 ft.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

Mohammed's altitude will be after a certain amount of time.

40 +10m

Dana's elevation will be...

165 -15m

When..., the elevations will be the same.

40 +10m = 165 -15m

25m = 125

add 15m-40

M = 5 is divided by 25 using the formula:

After five minutes, the two balloons' height will be 40 + 10 + five feet, or 90 feet.

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Answer:

There are several ways to look at this

Consider the interior angles of a triangle:

33 + A = 90

52 + B = 90

85 + A + B = 180       interior  angles of a triangle must sum to 180

So 180 - 85 = 95     which completes the triangle and would be EKD

Or 33 counterclockwise + X clockwise + 52 counter clockwise = 0

X must be 85 and is exterior to EKD and again

EKD = 180 - 85 = 95

If you consider the geometry and the corresponding angles you should be able to get a satisfactory answer

One can draw the line ED and consider the angles involved

The quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.

When we divide a number, the result we ultimately get is the quotient. Division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). For instance, three groups of 15 balls each need to be equally divided. Therefore, the division formula is 15 3 = 5 when we divide the balls into three equal groups. Here, the quotient is 5, so. This implies that there will be 5 balls in each group.

The given expression is:

21x^3 - 42x^2 + 3x

Divide the equation by 3x:

21x^3 - 42x^2 + 3x / 3x

Divide each term with 3x.

Using the rule of exponents we have a^n/ a^m = a^(n-m):

7x^2 - 14x + 3

Hence the quotient when 21x^3-42x² + 3x is divided by 3x is 7x^2 - 14x + 3.

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The Medicine Concentration drops 70 % each hour .

What is a graph ?

graph can be defined as a visual indicator in which we can represent the data.

Given,

A certain medicine is injected, its concentration in the bloodstream changes exponentially over time as shown in graph

Concentration of medicine when it was injected

=> at t = 0

Hence 100  mg/l  was concentration when medicine was injected

Nt  = No [tex]e^{-kt}[/tex]

N₀  - initial Quantity = 100 mg/l

at  t = 1  Concentration is 70 mg/l

=>  70 = 100   [tex]e^{-kt}[/tex]

=> k =  0.3567

Decay Constant = 0.3567

T = Half life period

50 = 100  [tex]e^{-kt}[/tex]

=> -0.693 = -kT

=>  1.943 hr

Hence , Medicine Concentration drops 70 % each hour .

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After simplification, the value of expression is,

⇒ 15 + y - 9a + ax - 9u + ux

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (15 + y) - (a + u) (3² - x)

Now, Simplify the expression as;

⇒ (15 + y) - (a + u) (3² - x)

⇒ (15 + y) - (a + u) (9 - x)

⇒ (15 + y) - (9a - ax + 9u - ux)

⇒ 15 + y - 9a + ax - 9u + ux

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The quantity of units that the company needs to sell in order for the net income to equal $0 would be = 8.

The net income of the company in thousands of dollars is represented with the function;

f(x) = 9x2 – 54x – 144,

It can be simplified as follows:

f(x) = 9(x² - 6x - 16)

Then:

f(x) = 9[(x + 2)(x - 8)]

It has a net income equals to 0 when:

f(x) = 0, hence:

x + 2 = 0 -> x = -2.

x - 8 = 0 -> x = 8.

The positive value and not a negative shows that there are amount of products sold which should be = 8.

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The difference would be $61.60 in favor of the daily compounded scenario.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To calculate the difference between the two scenarios you have provided:

$1,000 compounded daily at 5% for 8 years would earn $1,472.11

$1,000 compounded semiannually at 5% for 8 years would earn $1,410.51

Hence, the difference would be $61.60 in favor of the daily compounded scenario.

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the radial form is, 6 times the eight root of x to the fifth power.

Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.

here, given that,

6x^5/8

now,

the radial form is,

6 times the eight root of x to the fifth power.

Hence, the radical form is, 6 times the eight root of x to the fifth power.

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The probability that the student really knew the correct answer is 0.9375, or 93.75%.

(i) If the probability that the student knows the answer to the question is 0.75 and the probability that the student guesses is 0.25, the probability that the question is answered correctly is:

P(correct) = P(knowing the answer) * P(guessing correctly given knowing the answer) + P(guessing) * P(guessing correctly given guessing)

In this case, the probability of guessing correctly given knowing the answer is 1, since the student knows the correct answer. And the probability of guessing correctly given guessing is 0.25.

Therefore, P(correct) = 0.75 * 1 + 0.25 * 0.25 = 0.75 + 0.0625 = 0.8125

(ii) If it is answered correctly, what is the probability that the student really knew the correct answer?

This is called conditional probability and is represented as P(knowing the answer | correct). To calculate it we use Bayes' theorem,

P(knowing the answer | correct) = P(correct | knowing the answer) * P(knowing the answer) / P(correct)

In this case, P(correct | knowing the answer) = 1, P(knowing the answer) = 0.75 and P(correct) = 0.8125

Therefore, P(knowing the answer | correct) = 1 * 0.75 / 0.8125 = 0.9375

So the probability that the student really knew the correct answer is 0.9375, or 93.75%.

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According to the given statement If each can sold in accounted for as to its cost Last in first out.

The average is determined by adding together all of the numbers as well as dividing the total by the total number of figures provided. It represents the midpoint of the supplied data set. The numerical number that may display a lot of facts is the average value. We constantly encounter the average computation in our daily lives.

The four sorts of average that we recognize are mean, mode, median, and range. Although the others are our most popular "measures of central tendency," range is actually a measure of spread or dispersion.

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The profit per foot of the satin ribbon that the craft store buys and sells is $0.80.

The profit generated by the craft store per foot is determined by reducing the transactions to their unit cost and price.

The profit per unit becomes the difference between the unit selling price and the unit cost.

In other words, the profit per unit is the unit rate (per-unit profit) or ratio obtained as a difference between two unit parameters.

The cost of buying 150 feet of satin ribbon = $13.50

The unit cost per foot = $0.09 ($13.50/150)

The sales price for 5 feet = $0.80

The unit selling price per foot = $0.16 ($0.80/5)

The profit per unit = $0.80 ($0.16 - $0.80)

Profit percentage = 100% ($0.80/$0.80 x 100)

Thus, we can conclude that the craft store generates a 100% profit or $0.80 per foot.

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The sum of the three integers is 57.

The term integer in math is known as the collection of whole numbers and negative numbers.

Here we have given that the product of three different positive integers is equal to 7³.

Here let us consider that x,y,z be three positive number.

Then based on the given is written as

=> xyz = 7³

When we expand the equation, then we get,

=> xyz = 343

Here we have expand the equation as,

=> xyz = 1 × 7 × 49

Then the equation written as

=> x + y + z = (1 + 7 + 49)

Then the sum equation is calculated as

=> x + y + z = 57

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Answer:

To find the percent markup, we can use the following formula:

Markup = (selling price - cost price) / cost price * 100

We know that the department store buys 100 shirts at a cost of $1,200 and sells them at a selling price of $20 each.

Markup = ($20 - $12) / $12 * 100

Markup = $8 / $12 * 100

Markup = 2/3 * 100

Markup = 67%

So the percent markup is 67%.

From the given line equation, the closet point to the origin is (-6/5, 3/5).

Here we have given that the point on the line y=2x+3 that is closest to the origin.

As we all know that the closest point from origin will be the perpendicular distance from origin to the line.

Here we need to find an equation of the perpendicular from (0,0) on y = 2x + 3.

As we all know that the standard form of the equation is in slope-intercept form is written as,

=> y = mx + c

While we comparing this with the given equation, then we get the value of the Slope that is m = 2 and the Slope of the perpendicular is calculated as,

=> - (1/m) = -1/2

Now, we have to write the equation of the perpendicular is found by using the formula,

=> (y - y1) = m (x - x1)

Apply the value on the equation, then we get,

=> y - 0 = (-1/2) (x - 0)

=> y = (-1/2)x

therefore, the resulting perpendicular equation is written as,

=> 2y + x = 0 ----------------(2)

When we solving (1) and (2), then we get,

=> 5y = 3

Therefore, y = 3/5

And the value of x is calculated as

=> x + 2(3/5) = 0

=> x = -6/5

So the point on the line is (-6/5, 3/5).

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The requried, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

Null Hypothesis (H0): The mean height of five-year-old children in the city is not greater than 42.5 inches.

Alternative Hypothesis (Ha): The mean height of five-year-old children in the city is greater than 42.5 inches.

We will conduct a one-sample t-test since we have the sample mean and standard deviation.

Let's calculate the t-statistic and find the corresponding p-value.

The formula for the t-statistic is:

[tex]t=\dfrac{x-\mu}{s/\sqrt n}[/tex]

Where:

x  is the sample mean (44.1 inches),

μ is the population mean under the null hypothesis (42.5 inches),

s is the sample standard deviation (3.5 inches),

n is the sample size (40).

Let's calculate the t-statistic:

[tex]t=\dfrac{44.1-42.5}{3.5/\sqrt n}\\t=2.89[/tex]

Now, we need to locate the p-value associated with this t-statistic. The p-value is the probability of observing a t-statistic as extreme as the one calculated (or even more extreme) under the assumption that the null hypothesis is true.

The p-value can be looked up using a t-distribution table or calculated with statistical software. In this matter, since the t-statistic is quite large, the p-value will be very small.

Suppose the p-value is less than the significance level (α) chosen for the test (commonly 0.05). In that case, we reject the null hypothesis in favor of the alternative hypothesis. This means there is convincing evidence that the mean height of five-year-old children in this city is greater than 42.5 inches.

Conversely, if the p-value is greater than the chosen significance level, we fail to reject the null hypothesis, meaning we don't have enough evidence to conclude that the mean height is greater than 42.5 inches.

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The equation of the normal line of the curve f(x) = x³ - 14x² + 64x - 93 at point (3,0) is y = (-1/7) x +3/7

The slope of a tangent line of a curve at a given point is equal to its derivative at that point.

The normal line is a line which perpendicular to tangent line. Two lines are perpendicular to each other if the product of their slopes is equal to -1.

The equation of the curve is:

   f(x) = x³ - 14x² + 64x - 93

Take the derivative:

f '(x) = 3x² - 28x + 64

Therefore, the slope of the tangent line at point (3,0) is:

f '(3) = 3(3)² - 28(3) + 64 = 7

Hence, the slope of the normal line is:

m = -1/7

The equation of the normal line:

(y - 0) = (-1/7) (x - 3)

y = (-1/7) x +3/7

Your question is incomplete. Most likely, it was:

For each problem, find the equation of the line normal to the function at the given point. If the normal line is a vertical line, indicate so. Otherwise, your answer should be in slope-intercept form.

   f(x) = x³ - 14x² + 64x - 93 at (3,0)

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The equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

What is point slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

One of the formulas used to determine a line's equation is the point slope formula. According to the point slope formula, y - y1 = m (x - x1) is the equation for a line with slope "m" and the points (x, y1) on it.

We have to find the equation of line that passes through the points (6, 5) and (0, -7).

First to find the slope of the line,

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{-7-5}{0-6}= \frac{-12}{-6} = 2[/tex]

Now, consider the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 2, (x_1, y_1) = (0, -7)[/tex]

⇒

[tex]y-(-7)=2(x-0)\\y+7=2x\\y=2x-7[/tex]

Hence, the equation of line that passes through the points (6, 5) and

(0, -7) is y = 2x - 7.

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Answer:

H(x) = (x - 5) * (1 - 0.25) = x - 5 - 0.25x = 0.75x - 5

Answer:

The function H(x) that represents how much you would pay if you use the mall coupon followed by applying the discount from the store would be:

H(x) = (x - 5) * 0.75

Step-by-step explanation:

First, we apply the mall coupon by subtracting $5 from the original cost of the jeans represented by x. This gives us the function f(x) = x - 5.

Next, we apply the store discount of 25% by multiplying the result of f(x) by 0.75. This is because 25% expressed as a decimal is 0.25, and to apply a discount, we multiply by the decimal form of the percentage (1 - decimal form).

So, the final function H(x) represents the cost of the jeans after both the mall coupon and store discount have been applied, and is equal to (x - 5) * 0.75.

The spinner above is used in a game. the theoretical probability of the given event with one spin is 1/2.

Given that a circular spinner with equal sectors for the numbers 1 through 8 is present.

Therefore, the likelihood of receiving any number from 1 to 8 is equal.

=1/8

Probability that the number is between 2 and 7 is known as the required probability.

The numbers 3,4,5, and 6 fall between 2 and 7.

So, favorable events equal 4,

Events totaling 8 P(a number between 2 and 7)=4/8 =1/2

The result is 1/2.

Theoretically, there is a 0.50 percent chance that the event, which is the number landing in a range between 2 and 7, will occur after one spin.

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Answer:

A. Even

Step-by-step explanation:

Even Function

A function is "even" when:

[tex]f(x) = f(-x) \;for\; all\; x\\\\[/tex]

Stated in other terms, the function graph is symmetric about the vertical(y-axis). The right part of the function graph about the y-axis is a reflection of the left part of the function graph  about the y-axis

Looking at the function graph, we see it is indeed symmetric about the y-axis

Hence an even function

For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].

Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.

The function f(x) = -2(x + 4)+2 is minimum point and g(x) = 2(x - 2)-2 is maximum point.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = -2(x + 4)+2 and g(x) = 2(x - 2)-2

As, the equation are in the form

y = a (x-h) + k

For 1st function: f(x) = -(x + 4)²+2

f(x) = -2(x+4) + 2

So, the vertex is (4, 2) and a = -2 < 0 which is minimum point.

Now,  g(x) = 2(x - 2)-2

So, the vertex is (-2, -2) and a = 2 > 0 which is maximum point.

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The Z-score is (b) -1.64.

Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

To find the z-score corresponding to an observation of 4.7, we can use the formula:

z = (x - mu) / sigma

where x is the observation, mu is the mean, and sigma is the standard deviation.

Given that X-N(5.7, 0.61) we can substitute

z = (4.7 - 5.7) / 0.61 = -1.64

So the answer is (b) -1.64.

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Answer:

a. y = 2x - 6

To find the slope of the equation, we need to find the coefficient of x which is 2. So the slope of this equation is m=2

To find the y-intercept, we can substitute x = 0 into the equation:

y = 2(0) - 6

y = -6

So the y-intercept of this equation is b = -6

b. y = 1/2 * x + 12

To find the slope of the equation, we need to find the coefficient of x which is 1/2. So the slope of this equation is m=1/2

To find the y-intercept, we can substitute x = 0 into the equation:

y = 1/2(0) + 12

y = 12

So the y-intercept of this equation is b = 12

Therefore, the slope-intercept form of the equation is y = 2x - 6 and y = 1/2x + 12 respectively.

2.

D

Answer:

4

Step-by-step explanation:

Answer:

A triangle is a right angle triangle if and only if the Pythagorean theorem holds true for the sides of the triangle. The Pythagorean theorem states that in a right angle triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can call the side opposite the right angle the hypotenuse, and the other two sides the legs. According to the information given, the hypotenuse is AC, and the legs are AB and BC.

So, we can use the Pythagorean theorem to check if this triangle is a right angle triangle:

AC^2 = AB^2 + BC^2

26^2 = 10^2 + 25^2

676 = 100 + 625

676 = 725

This equation does not hold true, so the triangle is not a right angle triangle.

Answer:

C(220^2 + 420*2.5) = 800C + 200C = 1000C

Step-by-step explanation:

Let the length of the square base be L cm, and then the height of the container will be H cm. The volume of the container is given by the formula V = L^2 * H = 2000 cm3.

The cost of the top and bottom is 2C, where C is the cost per square centimeter for the sides. The cost for the top and bottom is 2 * L^2 * C. The cost for the sides is 4LH * C.

So the total cost is C(2L^2 + 4LH).

We can use the volume equation to find the height in terms of the length (H = 2000/L^2) and substitute it back into the cost equation.

C(2L^2 + 4L(2000/L^2)) = C(2L^2 + 8000/L)

To minimize the cost, we need to minimize the function 2L^2 + 8000/L, so we need to find the value of L that minimizes it.

Take the derivative of the function and make it equal to 0, then solve for L.

d/dL(2L^2 + 8000/L) = 4L - 8000/L^2 = 0

4L = 8000/L^2

L^3 = 2000

L = (2000)^(1/3) = 20

Therefore, the square base of the container should have a length of 20 cm, and the height of the container will be 2000/L^2 = 2000/20^2 = 2.5 cm.

The lowest cost would be C(220^2 + 420*2.5) = 800C + 200C = 1000C

The right answer involves doing both studies with the identical data set, drawing conclusions regarding means, and using a two-sided significance test.

An algorithm which it sets two ratios to the same value is called a fraction. You might, for instance, write its ratio as follows: 1: 3 in the case of 1 male & Three girls (for every one boy there are 3 girls) There are 3 out of 4 females and 1 out of 4 guys. 0,25 are men (by dividing 1 by 4)

A ratio that connects a part to yet another is a percentage. For instance, there are 100 students in the class containing 20 men or 80 women. The percentage of males is 20/100, or 20%. 80 out of 100, or 80%, are women.

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Thus, the solution of equation problem is  they need to be rewarded a minimal of 26 more times than usual to be able to enjoy a party.

A formula requires the equals sign (=). Because there is a scalar value on either part of an equation, you should think of it as either a left variable but a right side. As a set of scales, think of an equation. For it to be resolved, each side should be equally balanced, even though you can use various amounts on each side. In an algebraic equation, an unknown will be always present. Symbols like x, y, etc z are used to represent this.

Given:

Mrs. Morton places three marbles in a marble jar to give as a reward to her pupils for good conduct.

if the container holds 24 marbles. The essential equation is 24 + 3r 100 when r stands for how many extra awards there are for the class.

We'll get the bare minimum of marbles the jar can contain, which is 24 if we can figure it out.

Take 24 away from each side to find the answer to the puzzle.

=> 3r ≥100 -24

=> 76≤3r

=>76/3 ≤ r

=> r ≥ 25.33

=> r≈ 26

So they need to be rewarded at least an additional 26 times before they may enjoy a party.

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The correct option is option b) subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It doesn't use facts or formal computations; instead, it merely includes the subject's ideas and prior experience.

A subjective likelihood varies from person to person and is not based on previous facts or market data. In other words, it is not founded on reality but rather is the result of an individual's opinion.

In the majority of probability theories, quantifiable data is evaluated to ascertain the likelihood of an event occurring. However, subjective probability lacks a formal calculation, is influenced by human ideas, and is not based on quantitative data.

Therefore, The correct option is option b) subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots.

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If store c sells 122,420 products, then store b sells 6121 products.

Let x = number of products store a sells

If store a sells one fifth as many as store c, then we can write this expression as:

x = 1/5(122,420)

Evaluating, we have:

x = 24,484

If store a sells four times as many products as store b, then we can write the expression for the number of products store b sells as:

x = 4(number of products store b sells)

Plug in the value of x, we have:

24,484 = 4(number of products store b sells)

number of products store b sells = 6121

Therefore, store b sells 6121 products.

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