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The information required for ΔTUX to be congruent with ΔDEO by Hl is the corresponding legs of the right triangle. i.e. option a. TX ≅ DO

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.

Congruent triangles are triangles that have the same size and shape.

Therefore, ΔTUX is congruent to ΔDEO.

Triangle can be congruent base of HL(hypotenuse and leg).

Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.

Therefore, the additional information needed to prove ΔTUX ≅ ΔDEO by HL is TX ≅ DO.

TX and DO are the corresponding legs which are suppose to be equal.

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Answer:

croissants: 10        pain au chocolat: 12

Step-by-step explanation:

85c + 95p = 2000

c + p = 22

85c + 95p = 2000    

                               -

85c + 85p = 1870

         10p = 120

           p = 12

c + p = 22

c + 12 = 22

c = 10

Answer:

Step-by-step explanation: Let C be the number of croissants and P be the number of pain au chocolat that Didier buys. We know that C + P = 22 and 0.85C + 0.95P = 20.

We can solve this system of equations using substitution. First, we solve the first equation for P: P = 22 - C. Then, we substitute this expression for P into the second equation: 0.85C + 0.95(22 - C) = 20. Expanding the expression inside the parentheses and combining like terms, we get: 0.85C + 21.1 - 0.95C = 20.

Then, we can solve for C by moving all the terms to one side of the equation: -0.1C = -1.1. Dividing both sides by -0.1, we get: C = 11.

Substituting this value for C back into the equation P = 22 - C, we get: P = 22 - 11 = 11.

Therefore, Didier buys 11 croissants and 11 pain au chocolat.

Answer:

The answer is 15 workers are needed to complete the work in 16 days.

Step-by-step explanation:
To this incomplete sentence. ill try to answer it

Answer:

Step-by-step explanation:

You want values of p, q, r and s such that (2x + 3) (px^3 +qx^2 +rx +s) ≡ 2x^4 +13x^3 +7x^2 +18.

Multiplying out the left side of the equation, we have ...

  2px^4 +(3p+2q)x^3 +(2r +3q)x^2 +(2s +3r)x +3s

When we match coefficients between the two polynomials, this gives rise to 5 equations in the four unknown values:

The first and last equations tell us ...

  p = 2/2 = 1

  s = 18/3 = 6

Using these values in the 2nd and 4th equations makes them be ...

  3 +2q = 13   ⇒   q = 10/2 = 5

  12 +3r = 0   ⇒   r = -12/3 = -4

The values of p, q, r, s are ...

__

Check

We can use the 3rd equation to check these results:

  2r +3q = 7

  2(-4) +3(5) = 7

  -8 +15 = 7 . . . . . . . true

Answer:

a) The cost of buying x bottles of water is represented by the equation v = 0.50x, where v is the cost in dollars and x is the number of bottles of water. The gradient of this equation, which is 0.50, represents the cost per bottle of water.

b) The total cost of buying one bottle of water per day for a year (365 days) is 365 * 0.50 = $182.50.

c) If a refillable water bottle costs $40, then a person would have to drink 40 / 0.50 = 80 bottles of water in order for the refillable water bottle to be more cost effective.

d) Some factors that might influence someone's decision to carry their own water bottle or to buy bottled water include convenience, availability of clean drinking water, personal preference, and environmental impact.

Answer: Using the triangle theorem, the angle (64 + x)° and 110° are alternate angles, therefore the angle marked, x is 46°

Step-by-step explanation: Alternate angles are equals :

(64 + x)° = 110°

We can solve for x thus ;

x + 64 = 110

x + 64 - 64 = 110 - 64

x = 46°

Hence, the value of x in the triangle is 46°

Answer:

[D] $ 24,250

Step-by-step explanation:

$24,250 dollar will I have after three years.

By using the concept of simple interest, it can be calculated that

Brionny has invested £8400.

What is simple interest?

Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time

For the first year-

Principal = £P

Rate = 2%

Time = 1 year

Interest = [tex]\frac{P \times 2 \times 1}{100}[/tex] =  £[tex]\frac{P}{50}[/tex]

Amount = £[tex](P + \frac{P}{50})[/tex]

             = £[tex](\frac{50P + P}{50})[/tex]

             = £[tex]\frac{51P}{50}[/tex]

For the Second year:

Principal =  £[tex]\frac{51P}{50}[/tex]

Rate = 1%

Time = 1 year

Interest = [tex]\frac{51P \times 1 \times 1}{50 \times 100}[/tex] =  £[tex]\frac{51P}{5000}[/tex]

Amount = £[tex](\frac{51P}{50} + \frac{51P}{5000})[/tex]

             = £[tex](\frac{5100P + 51P}{5000})[/tex]

             = £[tex]\frac{5151P}{5000}[/tex]

By the problem,

[tex]\frac{5151P}{5000} = 8653.68\\P = \frac{8653.68 \times 5000}{5100}\\[/tex]

P =  £8400

Brionny has invested £8400.

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Viktor is in the 60th percentile, which is 85, while the percentile for 71 is 26.666.

Percentile is defined as the value below which a given percentage falls under. Ben, for instance, is the fourth tallest child in a group of 20, and eighty percent of the kids are shorter than you. As a result, Ben is in the 80th percentile.

We have the data

Sort the data as follows: 58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

employing the percentile formula,

Percentile is calculated as follows: 71 Percentile

(4 / 15)*100 Percentile

26.666 Percentile = (Number of Values Below "x" / Total Number of Values) 100

Consequently, 71's percentile is equal to 26.666.

Identifying the rank

Thus, the ranking is 0.6.

To find the rank for viktor

Find the percentile using the formula,

Percentile = Rank × Total number of the data set

Percentile = 0.6 × 15

Percentile = 9

Now, counting 9 values from left to right we reach 85, and we can say that all the values below 85 will come under the 60th percentile. In other words, 60% of the values are below 85.

The 60th percentile is 85

Thus viktor is in 60th percentile is 85

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Answer:

[tex]\frac{5}{7}[/tex] x + 2

Step-by-step explanation:

([tex]\frac{2}{7}[/tex] x - 6) + ([tex]\frac{3}{7}[/tex] x + 8) ← remove parenthesis

= [tex]\frac{2}{7}[/tex] x - 6 + [tex]\frac{3}{7}[/tex] x + 8 ← collect like terms

= ( [tex]\frac{2}{7}[/tex] x + [tex]\frac{3}{7}[/tex] x ) + ( - 6 + 8 )

= [tex]\frac{2+3}{7}[/tex] x + 2

= [tex]\frac{5}{7}[/tex] x + 2

Answer:

(-1/10)

Step-by-step explanation:

I'll assume 1/4xy is (1/4)xy and not 1/(4xy).

(1/4)xy

(1/4)(-2/3)(3/5)

Multiple the numerators and denominators separately:

Numerator + 1*(-2)*3 = -6

Deniominator 4*3*5 = 60

Put them back together:  (-6/60)  This reduces to (-1/10)

The minimum number would you need to survey sample Size N = 752.

A population proportion is the percentage of a population that falls into a specific category. Population proportions are estimated using confidence intervals.

Given,

A margin of error of 0.03

Z = 1.645 at a 90% confidence level

We use P=0.5 because there is no prior information about the population proportion.

To find the minimum number of subjects n= (Z*/M.E.)2 x P (1-P)

Solving by entering the given values into a formula: -

n = (1.645/0.03)2 × 0.5(1-0.5)

n = 3006.70 X 0.25

n= 751.67

Sample Size N = 752

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Answer: D

Step-by-step explanation:

The exact answer is 2.571281591, which is between:

D) 2 and 3

The domain and range of the function shown on the graph are (a) Domain is x ≥ 0, and range is y ≥ 0

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we can see that the line is a straight line

This means that the graph is a linear function

However, the function only covers the positive axes

This means that

Domain is x ≥ 0, and range is y ≥ 0

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answer is a. this is the long method but there is a short method — angles on a "z" since there are 2 parallel lines and a straight line across

Answer:

A. 47

Step-by-step explanation:

they are two parallel lines where by a transversal has passed throw them ; but first of all you have to look at the corresponding angles followed by alternative angles and so on;as angles on a str

The number 58 represents the Degree of freedom in the equation: t(58)=2.001, p<.05.

Option (c) is the correct choice.

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample.

A straightforward statistical method may be used to calculate degrees of freedom. It reads as follows: df = N-1 and indicates that degrees of freedom are equal to the number of values in a data collection minus 1. N is the number of values in the data collection, in this case (sample size).

The degrees of freedom, or the number of free data points available in a t-test to compare two groups, are shown in the above t-test by the number 58.

(A T-test is employed in statistics to compare the means of two groups. The t-value, p-value, and degrees of freedom are the values needed for a t test.)

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The complete question may be:

What does the number 58 represent in the following: t(58)=2.001, p<.05?

(a) Test statistic

(b) T-value

(c) Degrees of freedom

(d) Significance level

Between $80,000 and $85,000, there is an outlier. Means are not immune to outliers, but medians are.

How do you define medians?

The middle number in a sorted series of numbers is referred to as the median in mathematics. Ordering the numerals reveals the center one. In descending sequence, the numbers are listed. The middle number, when the numbers are arranged, is referred to as the data set's median.

Why is median significant?

A useful way to determine where a dataset is in the middle is to use the median. You may gain a sense of a dataset's distribution by comparing both median and mean. The dataset is almost uniformly scattered from the mean if both mean and median are equal.

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The probability that detector B goes off is 0.75

In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.

Here, the probability that detector A will not go off is 0.35

And the probability that A will go off and B will not go off is 0.25

We need to find the probability that B goes off

The probability that detector A will go off would be,

1 - P( detector A will not go off )

= 1 - 0.35

= 0.65

And the probability that both A and B will go off would be,

= P(A will go off) - P( A will go off and B will not go)

= 0.65 - 0.25

= 0.40

Now we find the required probability.

P(B goes off) = P(both A and B will go off) + P(detector A will not go off)

                     = 0.40 + 0.35

                     = 0.75

Therefore, the required probability is 0.75

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The tax paid by Kerry is $2.89

As per the given data in question:

Kerry bought a bag of dog food for $37. 99.

Total cost = $37. 99

Rate of sales tax is 7.6 %

A sales tax is a consumption tax paid to a government on the sale of certain goods and services.

Sales tax: = Sales tax percent / 100.

[tex]=\frac{7.6}{100}[/tex]

= $0.076

Tax paid by Kerry = Total cost × Sales tax

= 37. 99 × 0.076

= $2.89

Therefore the tax paid by Kerry is $2.89

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Answer:

children = $6 ; adults = $13

Step-by-step explanation:

6c + 8a = 140

12c + 9a = 189

3c + 4a = 70

4c + 3a = 63

3c = 70 - 4a

c = 70/3 - 4/3 a

4(70/3 - 4/3 a) + 3a = 63

280/3 - 16/3 a + 3a = 63

(-16a + 9a)/3 = 63 - 280/3

-7/3 a = (189 -280)/3

-7/3 a = -91/3

a = - 91/3 · -3/7

a = 91/7

a = $13

c = 70/3 - 4/3 · 13

c = 70/3 - 52/3

c = (70-52)/3

c = 18/3

c = $6

Predicted amount of time to travel 30 kilometers is 7 hours and 40 minutes. If A train travels from City A to City B.

The pace at which an object's position changes in any direction is referred to as speed. The distance travelled in relation to the time it took to travel that distance is how speed is defined.

Given,

Average speed

Speed = Distance/Time

Speed = 9/3

Speed = 3 km/h

When distance is 12 and time is 4

Speed = 12/4

Speed = 3 km/h

When distance is 18 and time is 9

Speed = 18/9

Speed = 2 km/h

Average speed = 3 + 3 + 2/3

Average speed = 8/3

Average speed = 2.6

Predicted amount of time to travel 30 kilometers

Time = Distance/Speed

Time - 30/2.7

Time = 7.4

Time = 7 hours and 40 minutes

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Answer:

d: 7, 38/6, -1.2, -3 1/4, -19/2.

Step-by-step explanation:

First, divide the fractions to get decimals, this is an easier approach to compare all the numbers.

-19/2 = -9.5

-3 1/4 = 4 x -3 = -12 + 1 = -3.25

38/6= 6.3333 (terminal 3)

The greatest numbers for this list is 6.33, -3.25, and -9.5. The rest of the numbers include -1.2 and 7.

With the entire order, we observe which lists are descending, starting with a positive or a negative number.

1. order can be: 7, 6.33, -1.2, -3.25, and -9.5 or 7, 38/6, -1.2, -3 1/4, -19/2.

2. order commonly confused can be: -9.5, -3.25, -1.2, 6.33, and 7 or -19/2, -3 1/4, -1.2, 38/6, 7.

The only order showing this is d: 7, 38/6, -1.2, -3 1/4, -19/2.

The reason why its not the second order starting with -19/2 is because descending typically refers to a positive number going down to a negative number. However, both orders can be right. For the sake of this problem, the best option is d.

Answer: 56%

Step-by-step explanation:

Pot A

75% = 0.75

12 times 0.75 = 9 seeds sprouted

Pot B

50% = 0.5

20 times 0.5 = 10 seeds sprouted

Pot C

50% = 0.5

18 times 0.5 = 9 seeds sprouted

Add total; we get 28 seed sprouted

Then we take 28 divided by 50, times 100% = 56%

So, 56% of the seeds from the packet sprouted!

Answer:

2x-3>1

Step-by-step explanation:

lets say x is the interger

so twice an interger would be 2*x or 2x

and three less than 2x would be 2x-3

and 2x-3 is greater than 1

so 2x-3>1

The value of I in the obtained inequality is the number of levels that can be played for free.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

Set up time + time taken in complete levels ≤ 60

For I number of levels,

5(¹/₆) + 7(¹/₃)I ≤ 60

By comparing the given inequality,

I = number of levels that are played for free.

Hence "The number of levels that can be played for free is the value of I in the resulting inequality".

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Answer:

2

Step-by-step explanation:

First distribute the first x into the first parenthesis:  x (2x - 4) = (2x + 1) (x - 2)

x times 2x is [tex]2x^{2}[/tex] and x times -4 is -4x

This changes the equation to: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)

Now multiply the other parentheses: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)

Do this by using the Foil method (I attached a picture of the method if you don't know it)

First: (2x + 1) (x - 2)

Do 2x times x which = [tex]2x^{2}[/tex]

Then 2x times -2 which = -4x

Then 1 times x which = x

Lastly, 1 times -2 which = -2

The order you do this is the order that the foil method says.

Now the equation is:

[tex]2x^{2}[/tex]-4x =[tex]2x^{2}[/tex]-4x+x-2 (I just added all the numbers we just got)
Next cancel out the equal terms. To combine like terms you'd usually move the right [tex]2x^{2}[/tex]  over to the left one and subtract it. But since they are the same number, subtracting it would leave you with 0. So you can just get rid of both.

You can also do this with both -4x

This leaves you with:

0=x-2

Now you move the variable to the left

you also make it negative since it is going to the other side of the =

this leaves: -x=-2

You can't have a negative x so now you have to change the signs for both. Make them both positive.

Now you have x=2

so your answer is 2

Answer:

A(1,2), B(-1,7) C(-4,8)

Step-by-step explanation:

I think that is the answer.

risk involved with the investment. Higher potential returns often come with a higher level of risk, as the investor is taking on the possibility of losing some or all of their investment in exchange for the chance to earn a higher return. It's important for investors to carefully consider the level of risk they are comfortable with and to do their due diligence before making any investment decisions. This may include researching the company or investment, reviewing financial statements, and consulting with financial professionals. Investors should also consider the potential tax implications of any investment, as well as how it fits into their overall financial plan.

It would take about 18 days for a pair of chickens to lay three dozen of eggs.

The unitary method is a method for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. Finding the value of just one unit is the key to answering such questions.

Given that 1.5 chickens can lay 1.5 eggs in a day.

The number of eggs 1 chicken can lay in a day = (1.5/1.5) eggs = 1 egg.

Then, two chickens can lay about 2 eggs in a day.

The number of days it takes for two chickens to lay 3 dozen (3×12=36) eggs is given by

[tex]\frac{\text{total number of eggs}}{\text{number of chicken}}=\frac{36}{2}=18\;\text{days}[/tex]

The answer is 18 days.

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