What are the 3 properties of a right triangle?

We have that for the Question "Ten less than half a number is 76. What is the number?" it can be said that the number is

x=172

From the question we are told

Ten less than half a number is 76. What is the number?

Generally the equation for the Statement  is mathematically given as

\(x/2-10=76\\\\Therefore\\\\x/2-10=76\\\\x/2=76+10\\\\x=2*(86)\\\\x=172\\\\\)

Therefore

The number is

x=172

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A boat takes 3.40 hours to travel 25.0 km down a river, then 4.60 hours to return, so the river is flowing at the speed of 0.95km/hrs.

Let x represent the boat's speed on still water.

Let y equal the current's speed.

The time is 3.40 hours, and the rate is x + y with the current.

The time is 4.60 hours, and the rate against the current is x - y.

rate x time = downstream

distance (x + y) * 3.40 = 25

Thus, upstream, 3.4x + 3.4y = 25. (x - y) * 4.60 = 25 so 4.6x - 4.6y = 25

Add 4.6 to both sides of the "downstream" equation and 3.4 to both sides of the "upstream" equation:

15.64x + 15.64y = 115

15.64x - 15.64y = 85

When the two equations are combined: 31.28x = 200, so x = 6.4

In other words, 15.64(6.4) + 15.64(y) = 115 and 100 + 15.64y = 115 are equivalent to 15.64x + 15.64y = 115.

120 is subtracted from both sides: 15.64y = 15, so y = 0.95

The speed of the boat in still water is 6.4 km per hour

The speed of the current is 0.95 km per hour.

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It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.

Cooking time in minutes = 5.17 pounds * 23 minutes/pound

Cooking time in minutes = 118.91 minutes

To convert minutes to hours, we divide the total minutes by 60:

Cooking time in hours = 118.91 minutes / 60

Cooking time in hours ≈ 1.98 hours

Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.

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Answer:

B (3,2)

Step-by-step explanation:

because it is the positive vertex it is asking

Answer:

B (3,2)

Step-by-step explanation:

The vertex of the the right quadratic is the only one on the positive quadrant and the coordinates are (3,2)

If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

5 x 2 ( 3 x + 2 )

Step-by-step explanation:

Answer:

Multiply by 3 on both sides of the equation.

2.78 × 3 = 8.34, so t = 8.34.

Substitute 8.34 for t to check the solution.

Step-by-step explanation:

To solve the equation  \(\frac{t}{3}\)= 2.78

we will use the steps below to solve this equation;

First, multiply by 3 on both-side of the equation. That is;

\(\frac{t}{3}\) ×  3= 2.78 × 3

On the left hand side of the equation 3 will cancel-out 3, leaving us with just t while 3 will be multiply by 2.77 on the right-hand side of the equation to give 8.34

t = 8.34

we can further substitute 8.34 for t to check the correctness of the solution

that is;

\(\frac{8.34}{3}\) =  2.78

Answer:

1,4,5

Answer:

Yes

Step-by-step explanation:

y-2=-5(x-2)

y=-3(x-2)

Answer:

4^20

Step-by-step explanation:

When you have an exponent raised to another exponent, you multiply the exponents.

The weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5. The correct option is A.

We know that the formula to calculate the weighted average is: weighted\ average=\frac{w_1x_1+w_2x_2+...+w_nx_n}{w_1+w_2+...+w_n} Where, $x_1,x_2,..x_n$ are the values, and $w_1,w_2,...,w_n$ are the weights. To find the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number, we substitute the values in the above formula as follows.

Weighted\ average=\frac{\frac{2}{3}\times 1+\frac{1}{3}\times 6}{\frac{2}{3}+\frac{1}{3}}\implies weighted\ average=\frac{\frac{2}{3}+2}{1}\implies weighted\ average=\frac{8}{3}\implies weighted\ average=2.67 approx 3.5 Therefore, the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5.

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Congruency is a term used to describe two objects with the same shape and size.

In this case, two triangles are congruent if they have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position.

For instance,

these triangles are congruent. They have the same sides but in different position.

Another example is

In this case the congruency is about angles. These 2 triangles have the same angles and the same sides but in different positions.

Another instance is

They are the same triangles but in different positions.

From the first question we can see that both triangles are congruent.

This imply that they are the same but in different position:

We can note that angle C is equal to angle T, therefore

In the same way, angle U is equal to angle B, then we have

We can find angle A by noticing that the interior angles of a triangle add up 180, that is

Since angle V is equal to angle A, also V=66

The equation of the line with slope m = 6/5 passing through the point (2, -1) is y = (6/5)x - 17/5.

To find the equation of a line with a given slope and a point on the line, we can use the point-slope form of a linear equation.

The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.

Given that the slope (m) is 6/5 and the point (2, -1) lies on the line, we can substitute these values into the point-slope form:

y - (-1) = (6/5)(x - 2).

Simplifying:

y + 1 = (6/5)(x - 2).

Next, we can distribute (6/5) to obtain:

y + 1 = (6/5)x - (6/5)(2).

Simplifying further:

y + 1 = (6/5)x - 12/5.

To isolate y, we subtract 1 from both sides:

y = (6/5)x - 12/5 - 1.

Combining the constants:

y = (6/5)x - 12/5 - 5/5.

Simplifying:

y = (6/5)x - 17/5.

Therefore, the equation of the line with slope m = 6/5 passing through the point (2, -1) is y = (6/5)x - 17/5.

The equation of the line is y = (6/5)x - 17/5.

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Answer:what

Step-by-step explanation:what does this mean

Rounded to three decimal places, the probability is approximately 0.457.

To find the probability that at least two bills must be selected to obtain a first $10 bill, we need to consider two scenarios.

Scenario 1: The first bill selected is a $10 bill. There are six $10 bills in the wallet, so the probability of selecting a $10 bill first is 6/15.

Scenario 2: The first bill selected is not a $10 bill. In this case, we need to calculate the probability of not selecting a $10 bill on the first draw, and then selecting a $10 bill on the second draw.

There are nine non-$10 bills in the wallet initially (3 $5 bills + 6 $1 bills), and there are a total of 14 bills left in the wallet after the first draw (15 bills - 1 non-$10 bill).

Therefore, the probability of not selecting a $10 bill on the first draw is 9/15, and the probability of selecting a $10 bill on the second draw is 6/14.

Multiplying these probabilities together, we get (9/15) * (6/14) = 54/210.

To obtain the final probability, we sum the probabilities from both scenarios: (6/15) + (54/210) = 16/35.

Rounded to three decimal places, the probability is approximately 0.457.

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The median is the best measure of center and equals 12. Therefore, option C is the correct answer.

Given that, a box plot uses a number line from 4 to 25 with tick marks every one unit.

The box extends from 10 to 15 on the number line.

Here, first quartile = 10 and the third quartile = 15

A line in the box is at 12.

Here, the median is 12.

The lines outside the box end at 5 and 24.

Here, the minimum value = 5 and the maximum value = 24

Therefore, option C is the correct answer.

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As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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The probability that the customer purchases calluge on the second purchase, given that they purchased it on the first purchase, is:

P(C2|C1) = p

The customer's behavior is independent from purchase to purchase, and the probability of purchasing calluge remains constant, then we can use the concept of conditional probability to calculate the probability that the customer purchases calluge on the second purchase, given that they purchased it on the first purchase.

Let P(C1) be the probability that the customer purchased calluge on the first purchase, and let P(C2|C1) be the conditional probability that the customer purchases calluge on the second purchase, given that they purchased it on the first purchase.

If we assume that the probability of purchasing calluge remains constant and is denoted by p, then we have:

P(C1) = p

Since the customer has already purchased calluge on the first purchase, the probability of purchasing it again on the second purchase depends on whether the customer is more likely to purchase it again or switch to another product.

If we assume that the customer's behavior is independent from purchase to purchase, then the probability of purchasing calluge on the second purchase is also p.

If we assume that the probability of purchasing calluge remains constant and the customer's behavior is independent from purchase to purchase, then the probability that the customer purchases calluge on the second purchase, given that they purchased it on the first purchase, is equal to the probability that they purchased calluge on the first purchase, which is denoted by p.

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We cannot determine the probability that a customer who initially purchased Calluge will purchase Calluge on the second purchase without additional information.

The probability that a customer who initially purchased Calluge will purchase Calluge on the second purchase can be calculated using the concept of conditional probability. Let P(A) represent the probability of an event A occurring and P(B|A) represent the probability of an event B occurring given that event A has occurred.

Let us assume that P(C) represents the probability of a customer purchasing Calluge on the second purchase, given that they have already purchased Calluge on the first purchase. This can be written as P(C|C).

We can use Bayes' theorem to calculate P(C|C). Bayes' theorem states that:

P(C|C) = P(C and C)/P(C)

Here, P(C and C) represents the probability of a customer purchasing Calluge on both the first and second purchases, and P(C) represents the probability of a customer purchasing Calluge on the first purchase.

Since we are given that a customer initially purchased Calluge, we can assume that P(C) = 1 (i.e., the probability of purchasing Calluge on the first purchase is 1).

Now, we need to find the probability of a customer purchasing Calluge on both the first and second purchases, which can be written as P(C and C) or P(C)^2. However, we do not have any information about the probability of a customer purchasing Calluge on both the first and second purchases.

Therefore, we cannot determine the probability that a customer who initially purchased Calluge will purchase Calluge on the second purchase without additional information.

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Answer:

A) $425.92

Step-by-step explanation:

The new price percentage with relation to the previous can be determined by dividing \(p = \frac{484}{550}\). Once we calculate p, we can multiply it by 484, which is equivalent to applying the same discount, thus \(\frac{484}{550}484=425.92\)

1. Derivation of  β^​ols​ and Var(β^​ols​) is represented as :  Σ(xi)(yi - α) = βΣ(xi^(2)).

2.The Gauss-Markov theorem states that under the CLRM assumptions, the OLS estimator is unbiased, has the minimum variance among all linear unbiased estimators, and is consistent.

Let's see in detail:

Deriving β^(ols):

To estimate β^(ols), we need to minimize the sum of squared residuals. The objective function is given by:

S(β) = Σ(yi - α - βxi)^(2)

To minimize S(β), we take the partial derivative with respect to β and set it equal to zero:

∂S(β)/∂β = -2Σ(xi)(yi - α - βxi) = 0

Expanding and rearranging the equation, we get:

Σ(xi)(yi - α - βxi) = 0

Σ(xi)(yi - α) - βΣ(xi^(2)) = 0

Σ(xi)(yi - α) = βΣ(xi^(2))

Gauss-Markov theorem:

The Gauss-Markov theorem states that under the assumptions of the classical linear regression model (CLRM), the Ordinary Least Squares (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) among all linear unbiased estimators.

Proof of Gauss-Markov theorem:

To prove the Gauss-Markov theorem, we need to show that the OLS estimator is unbiased, has the minimum variance among all linear unbiased estimators, and is consistent.

(i) Unbiasedness:

The OLS estimator β^(ols)is unbiased if E(β^(ols)) = β, where β is the true population parameter. Since OLS estimators are linear, we have:

E(β^(ols)) = E(Σ(xi)(yi - α) / Σ(xi^(2)))

= Σ(xi)E(yi - α) / Σ(xi^(2))

= Σ(xi)(E(yi) - E(α)) / Σ(xi^(2))

= Σ(xi)(E(yi) - α) / Σ(xi^(2))

Since E(yi) = α + βxi, we can substitute this into the equation:

E(β^(ols)) = Σ(xi)(α + βxi - α) / Σ(xi^(2))

= Σ(xi)(βxi) / Σ(xi^(2))

= βΣ(xi^(2)) / Σ(xi^(2))

= β

Therefore, the OLS estimator is unbiased.

(ii) Minimum variance:

The OLS estimator has the minimum variance among all linear unbiased estimators. This can be shown using the property that the OLS estimator is the Best Linear Unbiased Estimator (BLUE) in the CLRM.

(iii) Consistency:

Under the CLRM assumptions, the OLS estimator β^(ols) is consistent, meaning that as the sample size increases, the estimator converges to the true population parameter β.

Overall, the Gauss-Markov theorem states that under the CLRM assumptions, the OLS estimator is unbiased, has the minimum variance among all linear unbiased estimators, and is consistent.

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Answer:

15+11t

Step-by-step explanation:

A product is the result of a multiplication expression.

Answer:64

Step-by-step explanation:

Answer:

64 is the answer :)

Step-by-step explanation:

i hope its correct

Answer:

5.6 ft

Step-by-step explanation:

Answer:

\(\sf c = -4\)  and  \(\sf b = -6\)

Explanation:

using the formula: \(\sf x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\)

Here the a = 1

using the equation:

\(3 \pm\sqrt{13}= \frac{ -b \pm \sqrt{b^2 - 4(1)c}}{2(1)}\)

\(6 \pm2\sqrt{13}= -b \pm \sqrt{b^2 - 4(1)c}}\)

matching the coefficients: b = - 6

find c:

\(6 \pm2\sqrt{13}= -(-6) \pm \sqrt{(-6)^2 - 4(1)c}}\)

\(6 \pm2\sqrt{13}= 6 \pm \sqrt{36 - 4c}}\)

\(\sf 6 \pm\sqrt{52}= 6 \pm \sqrt{36 - 4c}}\)

\(\sf 36-4c = 52\)

\(\sf -4c = 52-36\)

\(\sf -4x = 16\)

\(\sf c = -4\)

The expected number of adults who prefer coffee is 150.

We must determine the anticipated number of adults who prefer coffee in order to test for independence between age and drink preferences.

First, let's look at the totals of the rows and columns to figure out the expected values for each category. The formula is available to us:

Anticipated esteem = (Line absolute * Section complete)/Stupendous aggregate

The stupendous complete for this situation is 1000.

Number of adults expected to prefer coffee:

= (Adults total minus Coffee total) / Grand total = (600 minus 250) / 1000 = 150; consequently, 150 adults are anticipated to prefer coffee.

In this way, the right response is (a) 150.

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Answer:

the slope-intercept is minus 4

Step-by-step explanation:

y = mx + b

y = -4x+ -5

im pretty sure this is right bc im in highschool rn and i just did this last year so if i forgot than  -_-

The value of the expression tan(-5π/6) can be determined using trigonometric properties and  identities.

First, let's consider the unit circle. The angle -5π/6 is measured in the clockwise direction from the positive x-axis. In this position, the reference angle is π/6, which is the positive angle formed with the x-axis.

The tangent function (tan) is defined as the ratio of the sine (sin) of an angle to the cosine (cos) of the angle. Using the reference angle π/6, we can determine the value of tan(π/6) as the ratio of sin(π/6) to cos(π/6). sin(π/6) equals 1/2, and cos(π/6) equals √3/2. Therefore, tan(π/6) is (1/2) divided by (√3/2), which simplifies to 1/√3 or √3/3. Since tan is an odd function, tan(-5π/6) is equal to the negative of tan(5π/6). Therefore, tan(-5π/6) has the same value as -√3/3.

In conclusion, the value of tan(-5π/6) is -√3/3, which means that the tangent of the angle -5π/6 is negative and equal to the ratio of -√3 to 3.

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