in square units, what is the largest possible area a rectangle inscribed in the triangle shown here can have?

Answer:

Y = 4x

Step-by-step explanation:

In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.

Answer:

Let's represent the amount invested at 10% as x and the amount invested at 6% as y. Then we can set up a system of two equations to represent the given information:

x + y = 20,000 (since the total amount invested is 20,000)

0.10x + 0.06y = 1,470 (since the interest earned is 1,470 and the interest rate at which x is invested is 10% and the interest rate at which y is invested is 6%)

We can use the first equation to solve for one of the variables in terms of the other:

x = 20,000 - y

Now we can substitute this expression for x into the second equation and solve for y:

0.10(20,000 - y) + 0.06y = 1,470

2,000 - 0.10y + 0.06y = 1,470

-0.04y = -530

y = 13,250

So $13,250 was invested at 6%. We can find the amount invested at 10% by plugging in this value of y into the first equation:

x + 13,250 = 20,000

x = 6,750

So $6,750 was invested at 10%.

Answer:

20÷100×4.75=0.95

4.75-0.95=$3.8

Answer:

i got 4.55$

Step-by-step explanation:

i just converted the percentage (20%) and then subtracted that number (0.2) from the original price (4.75$)

The probability of drawing an ace and a queen from a pack of cards without replacement is 1/78. This can be explained as follows:

In a standard pack of 52 cards, there are 4 aces and 4 queens. When two cards are drawn without replacement, the probability of drawing an ace and then a queen is 4/52 x 3/51 = 12/2652. This can be simplified to 1/78.

Without replacement means that the card that is drawn is not replaced in the deck before the next card is drawn. In this case, when the first card is an ace, there are only 3 queens left in the deck so the probability of the second card being a queen is 3/51.

To put it another way, the chances of drawing an ace and a queen when the cards are drawn without replacement can be thought of as a ratio of the favorable outcomes to the total number of possible outcomes. There is only one favorable outcome (ace-queen) out of a total of 78 possible outcomes (4 aces and 4 queens combined with the remaining 44 cards). Thus, the probability of drawing an ace and a queen is 1/78.

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The probability that the taxi at fault was blue given an eyewitness said it was is approximately 0.436.

To find the probability that the taxi at fault was blue given an eyewitness said it was, we can use Bayes' theorem. Bayes' theorem is expressed as: P(A|B) = (P(B|A) * P(A)) / P(B)

Where:
- P(A|B) is the probability of A given B (the probability the taxi is blue given the eyewitness said it was blue)
- P(B|A) is the probability of B given A (the probability the eyewitness said the taxi was blue given it was actually blue)
- P(A) is the probability of A (the probability the taxi is blue)
- P(B) is the probability of B (the probability the eyewitness said the taxi was blue)

First, let's define our events:
- A: The taxi is blue (Blue Cab), with a probability of 12% (0.12)
- B: The eyewitness said the taxi was blue

Now, we need to find P(B|A) and P(B).

1. P(B|A) = 0.85 (the probability the eyewitness correctly identifies the blue taxi)
2. P(B) can be found using the law of total probability: P(B) = P(B|A) * P(A) + P(B|A') * P(A')
  - A': The taxi is not blue (Green Cab), with a probability of 88% (0.88)
  - P(B|A') = 1 - 0.85 = 0.15 (the probability the eyewitness incorrectly identifies the green taxi as blue)

So, P(B) = 0.85 * 0.12 + 0.15 * 0.88 = 0.102 + 0.132 = 0.234

Now, we can apply Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.85 * 0.12) / 0.234
P(A|B) ≈ 0.4359

Rounded to three decimal places, the probability that the taxi at fault was blue given an eyewitness said it was is approximately 0.436 or 436/1000 as a reduced fraction.

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Answer:

a. The triangular prism has 5 faces, 9 vertices, and 12 edges.

b. To find the volume of the packaging, we need to multiply the area of the base (an equilateral triangle) by the height of the prism.

The area of an equilateral triangle with side length 3.6 cm is given by:

$A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4}(3.6\text{ cm})^2 \approx 5.270\text{ cm}^2$

So, the volume of the Toblerone packaging is:

$V = Ah = (5.270\text{ cm}^2)(21\text{ cm}) \approx 110.59\text{ cm}^3$

Therefore, the volume of the Toblerone packaging is approximately 110.59 cubic centimeters.

Answer:

Step-by-step explanation:

Standard: 2x^3 - 7x^2 -x-2

Quotient: 2x^3- 7x^2 -x-2

remainder: 0

The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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answer - y = -5x + 1

To maintain an average of 79, Aldo must obtain a score of 82 in his upcoming exam.

To get the solution, let's calculate the total of the first five scores.

Total of the first five scores = 77 + 88 + 77 + 87 + 63 = 392

Now we know that there are a total of six scores, so to get the mean, we will divide the total by six.

Mean = Total/Number of ScoresTherefore, 79 = 392 + x/6

We need to find the value of x that will satisfy the above equation.

Now we will solve for x.79 = 392 + x/6

(Multiply both sides by 6) 6 * 79 = 6 * 392 + x6 * 79 = 2352 + xx = 6 * 79 - 392x = 474 - 392x = 82

Therefore, Aldo needs to score 82 on his next test to achieve an average of 79.


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the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.

The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:

F'(x) = 3x/|x|

Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.

Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:

g'(x) = -1 + 8

Simplifying the expression, we get:

g'(x) = 7

Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.

To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.

Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

     <=====o------------------------>

         x<0                    x>0

In this interval, both functions are increasing as x becomes more negative.

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z = 110°

mEB = 90°

mCE = 74°
I’m not sure about x or y but I think these are right.

If a research company claims that more than 55% of americans regularly watch public access television, the test statistic for the population proportion is 1.61.

To calculate the test statistic for the population proportion, we first need to set up the null and alternative hypotheses. Let p be the true proportion of Americans who regularly watch public access television.

H0: p ≤ 0.55 (null hypothesis)

Ha: p > 0.55 (alternative hypothesis)

We use a one-tailed test with α = 0.05 level of significance.

Next, we calculate the sample proportion:

p' = 255/425 = 0.60

Then, we calculate the standard error of the proportion:

SE = √(p'(1-p')/n) = √(0.60*0.40/425) ≈ 0.031

Finally, we calculate the test statistic:

z = (p' - p0)/SE = (0.60 - 0.55)/0.031 ≈ 1.61

where p0 is the value of the proportion under the null hypothesis.

The test statistic is approximately 1.61. To determine whether this value provides evidence to reject the null hypothesis, we compare it to the critical value of the z-distribution at α = 0.05 level of significance.

For a one-tailed test with a significance level of 0.05, the critical value is 1.645. Since our test statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the claim that more than 55% of Americans regularly watch public access television.

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The number of square units enclosed by the polygon is 18.

First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.

So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.

So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17

Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.

Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.

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Answer:

-10

Step-by-step explanation:

I added a photo of my solution

Answer:

Answer is -10

Step-by-step explanation:

Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

Scaling up, David has 220 coins in his collection with 5% of 11 of the coins kept in his box.

A scale up represents an increase or growth.

Scale factors are ratios comparing two quantities or values.

Proportionately, if 5% represent 11 coins, 100% will be 220 coins.

The number of coins David keeps in his box = 11

The percentage of the coins kept in the box = 5%

Thus, proportionately, 11 = 5%; therefore, 100% = 220 (11 ÷ 5%).

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We can say with 95% confidence interval that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

To calculate the confidence interval, we use the formula:

CI = x-bar ± z* (σ/√n)

where x-bar is the sample mean (50,000 miles), z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence level), σ is the standard deviation (5,000 miles), and n is the sample size (100).

Plugging in the values, we get:

CI = 50,000 ± 1.96*(5,000/√100)

Simplifying the expression, we get:

CI = 50,000 ± 980.

Therefore, we can say with 95% confidence that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

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Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.

What is red light in Photosynthesis?

Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.

Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.

In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.

As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.

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the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = [tex]e^(-kt)\\[/tex] * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = [tex]e^(0 * k)[/tex] * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = [tex]e^(-8k)[/tex] * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The quadratic equation in standard form is 4x² + x + 19 = 0.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). The two most well-known groups of equations in algebra are the linear equations and the polynomial equations. The phrase "equation in one variable" refers to an equation with just one variable. The following are a few crucial equation types: Linear equations, Quadratic equations, Cubic equation, and Quartic equations.

The standard form of the quadratic equation is:

ax² + bx + c = 0

The given equation is:

-4x² - 19 = x

Add 4x² on both sides of the equation:

-19 = 4x² + x

Add 19 on both sides of the equation:

4x² + x + 19 = 0

Hence, the quadratic equation in standard form is 4x² + x + 19 = 0.

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The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

The lowest common multiple 3 and 4 is 12.

Step-by-step explanation:

The total multiples of both 3 and 4 between 1 - 100 are 100/12 = 8 4/12 i.e. 8.

To get an output of 5 from a function, the second point must be at a distance of 5 units above the x-axis.

The function represents the relationship between the inputs and the outputs. The function's domain is the set of all possible input values, while the range is the set of all possible output values. The function's graph is the set of all ordered pairs (x, y), where x is the input and y is the output.To get an output of 5 from the function, the second point must be at a distance of 5 units above the x-axis. This implies that the y-value of the second point is 5. The x-value of the second point is arbitrary, and it can be any value. The point (0,5) is an example of a point that is 5 units above the x-axis.

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Answer:

Step-by-step explanation:

28x14x4x6x2+18816

Answer: D = 3c-5

Step-by-step explanation:

The first shape shows the input, C, the second one multiplies it by 3, next, it subtracts C by 5, leaving you with D equaling C times three, minus five.
You can simplify this equation into this:

D=3C (multiplied by 3)

Then subtract by 5
D=3C-5