The perimeter of an isosceles triangle is 40 and the length of the altitude to its base is 10. Find the length of a leg.

The number of pivot columns of a matrix equals the dimension of its column space is true statement.

As given in the question,

The number of pivot columns of a matrix equals the dimension of its column space is true statement as per following reasons

Therefore, the number of pivot columns of a matrix equals the dimension of its column space.

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Answer:

Step-by-step explanation:

Thank you for providing the details of the question.

Unfortunately none of the results you have to choose from will give you 44%

The problem resembles the first probability question you were likely asked. "What is the probability of getting a heads on every throw of a fair coin?" The answer is 1/2 no matter how many times you throw the coin or what has happened before any point in the throws.

The answer should be 6/50.  If this turns out not to be the answer and you have an instructor your safest course of action is to ask how 44% was obtained. Tell me in a comment.

Answer:

fraction 6 over 50

Step-by-step explanation:

In the question it says she pulls a tile out of the bag and records the color 50 times which means she pulled out 50 tiles.

Now the table says that she recorded 6 purple tiles.

Probability is equal to \(\frac{number of favorable outcomes}{number of possible outcomes}\)

Number of favorable outcomes here is the number of purple tiles she pulled out (6) since we want to find the probability of choosing a purple tile and the number of possible outcomes is the total number of tiles she pulled out (50)

So the probability = \(\frac{6}{50}\)

Angle 2 and angle of 34° are vertical angles, then they are congruent, that is,

Angle 6 and angle of 34° are corresponding angles, then they are congruent, that is,

Angle 4 and angle of 34° are alternate interior angles, then they are congruent, that is,

Angle 7 and angle of 34° are same-side interior angles, then they are supplementary, that is,

Angles 4 and 3 are same-side interior angles, then they are supplementary, that is,

Angles 7 and 5 are vertical angles, then they are congruent, that is,

Angles 1 and 3 are vertical angles, then they are congruent, that is,

Answer:

Are you sure this is not a hacking trick?

Step-by-step explanation:

Answer:

a four-sided figure.

Regular shapes have sides that are all equal and interior (inside) angles that are all equal. Irregular shapes have sides and angles of any length and size.

Step-by-step explanation:

Answer:

72 boys

Step-by-step explanation:

120 * .60. That's how you solve it! Hope it helps!

Further explanation:

To get .60, you divide 3 by 5 which is .60

Then you multiply 120 times .60 and you'll get 72 which is 72 boys

Bonus: 120 - 72 = 48 girls!

Answer:

There are 45 boys.

Step-by-step explanation:

The best way to easily solvethis is by making equations, see below.

\(let \: b \: represent \: number \: of \: boys \\ let \: g \: represent \: number \: of \: girls\)

\(b + g = 120 \\ b = \frac{3}{5} g\)

Now we can subtract the secons equation from the first.

\(g = 120 - \frac{3}{5} g\)

I'm also goong to multiply the equatipn by 5 to remove the fraction.

\(5g = - 3g + 600\)

Now simplify

\(8g = 600 \\ g = 75\)

Now we found out there are 75 girls. Now we insert this into our second equation to find how many boys there are.

\(b + 75 = 120 \\ b = 45\)

Now we know there are 45 boys.

A force of 1 pounds is required to hold a spring stretched 0.2 feet beyond its natural length.  2.5 lb-ft work is done in stretching the spring from its natural length to 1 feet beyond its natural length.

A spring exerts a force F = -kx in that direction when it is at its equilibrium position. The force acting on a spring acts as a restoring force, causing it to return to its equilibrium length.

Therefore, F is the 1 lb force necessary to keep the spring stretched.

The spring's spring constant is k, and it has a 0.2-foot stretch.

F = k x

1 = k (0.2)

k = 5 lb/ft is applied.

U, where x'=1 feet, is the effort required to extend the spring.

The formula: denotes the work involved in expanding a spring.

U = (0.5) k x²

So, compute:

U = (0.5). (5). (1)²

² U = 2.5 lb-ft

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Answer: 9x + 6y = 234

Step-by-step explanation:

Answer:

234

Step-by-step explanation:

it makes more sense then the others

Answer:

Step-by-step explanation:

7.50a + 2.50c = 1945

      a +       c = 364

Use -2.50 for 2nd equation

7.50a + 2.50c = 1945

-2.50a - 2.5oc = -910

5a = 1035

a = 207 adult tickets were sold

207 + c = 1945

c = 1738 child's tickets were sold

To calculate the standard deviation of the heights of 15 soda cans, we first need to remove the outlier from the given data set. An outlier is defined as an extreme value that significantly deviates from the rest of the data. Looking at the data provided:

(92.8, 92.8, 92.9, 92.9, 92.9, 92.8, 92.7, 92.9, 92.1, 92.7, 92.8, 92.9, 92.9, 92.7, 92.8)

We can observe that 92.1 seems to be an outlier since it is noticeably less than the rest of the values. Let's remove this outlier from the data set:

(92.8, 92.8, 92.9, 92.9, 92.9, 92.8, 92.7, 92.9, 92.7, 92.8, 92.9, 92.9, 92.7, 92.8)

Now, we can calculate the standard deviation. Using a statistics calculator or spreadsheet, we input the remaining data points and calculate the standard deviation.

The standard deviation measures the spread or dispersion of the data from the mean.

Using a calculator or spreadsheet, the standard deviation of the given data set is determined to be approximately 0.085. Rounding to the nearest hundredth, the standard deviation is 0.09.

Therefore, after removing the outlier, the standard deviation of the heights of the 15 soda cans is approximately 0.09.

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The simplified form of the given expression is \(\frac{3}{2} x-3.5+2y\).

The given expression is \((\frac{7}{4} x-5)+(2y-3.5)+(-\frac{1}{4} x+5)\).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be solved as follows:

\((\frac{7}{4} x-5)+(2y-3.5)+(-\frac{1}{4} x+5)\)

Group the like terms and simplify.

That is, \(\frac{7}{4} x-5+2y-3.5-\frac{1}{4} x+5\)

\(=(\frac{7}{4} x-\frac{1}{4} x)-5-3.5+5+2y\)

\(=\frac{6}{4} x-3.5+2y\)

\(=\frac{3}{2} x-3.5+2y\)

Therefore, the simplified form of the given expression is \(\frac{3}{2} x-3.5+2y\).

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Answer:

  4. 143°

  5. x=32°, exterior angle=134°

Step-by-step explanation:

The relation of interest in these two questions is ...

  an exterior angle of a triangle is equal to the sum of the remote interior angles.

__

The exterior angle is u°. The opposite (remote) interior angles are a right angle (90°) and one marked 53°. The above relation tells you ...

  u° = 90° +53°

  ∠u = 143°

__

In this figure, the external angle is marked (4x+6)°, and the opposite internal angles are x° and 102°. Our relation between these tells us ...

  (4x +6)° = x° +102°

  3x = 96 . . . . . . . . . . . . divide by °, subtract x+6

  x = 32 . . . . . . . . . . divide by 3

  ∠x = 32°

 (4x+6)° = (4(32) +6)° = 134°

Answer:

See below.

Step-by-step explanation:

When Brian passes Alex they both have travelled the same distance.

Call this distance d.

Let the speed that Brian passes = x miles/hour.

Distance = speed * time  so:

For Alex:

d = (x - 5) * 1.5        ( Alex cycles for 1 + 30 minutes =  1.5 hours)

For Brian:

d = x * 1

So substituting d = x in Alex's equation:

x = 1.5(x - 5)

x = 1.5x - 7.5

7.5 = 0.5x

7/5 / 0.5 = x

15 = x.

ANSWER:

Brian's speed is 15 miles/hour.

Alex's speed is 15 - 5 = 10 miles/hour.

Answer:

1 gallon to 12 miles

Step-by-step explanation:

Distance = 300 miles

Gasoline used = 25 gallons

Expressing as a unit rate :

Distance covered per gallon of gasoline :

Distance / gasoline used

300 / 25

12 miles

Hence, the unit rate is :

1 gallon of gasoline = 12 miles

1 gallon of gasoline will cover 12 miles in distance.

Answer:

upwards or to the right

Step-by-step explanation:

If the a value is positive, then the parabola opens upward or to the right, and if the a value's negative, it opens down or to the left. Hope this helps!

It is a good practice for a server or bartender to not take patrons' drink orders too quickly

A bartender a person who prepares or serves alcoholic and some non-alcoholic beverages from behind a bar.

Below are some of the duties or responsibilities of a bartender:

So therefore, it is a good practice for a server or bartender to not take patrons' drink orders too quickly

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Answer:

f(3)=-11

in other words

When x=3, y=-11

Step-by-step explanation:

f(x)=-3x-2

f(3)=-3(3)-2

f(3)=-9-2

f(3)=-11

We know that the score is obtained by subtracting the number of incorrect answers from twice the number of correct answers. Let's use "x" to represent the number of correct answers.

According to the question, the player answered 40 questions in total. This means that the number of incorrect answers is 40 - x.
Now we can use the formula for the score:
Score = 2x - (40 - x)
We also know that the player obtained a score of 50. So we can set up the equation:
50 = 2x - (40 - x)
Simplifying the equation:
50 = 3x - 40
90 = 3x
x = 30
Therefore, the player answered 30 questions correctly.
To check, we can plug this value back into the formula for the score:
Score = 2x - (40 - x)
Score = 2(30) - (40 - 30)
Score = 60 - 10
Score = 50
So the score of 50 is correct and the player answered 30 questions correctly.

To find out how many questions the player answered correctly in the trivia game with a score of 50, we can use the given information to set up an equation:
Let x be the number of correct answers and y be the number of incorrect answers. According to the question, the score is calculated by subtracting the number of incorrect answers (y) from twice the number of correct answers (2x). The player answered 40 questions in total, so we have:
x + y = 40
2x - y = 50
Now we can solve this system of equations step-by-step:
1. Solve the first equation for x:
x = 40 - y
2. Substitute this expression for x in the second equation:
2(40 - y) - y = 50
3. Simplify the equation:
80 - 2y - y = 50
4. Combine like terms:
80 - 3y = 50
5. Subtract 80 from both sides:
-3y = -30
6. Divide both sides by -3:
y = 10
7. Substitute the value of y back into the expression for x:
x = 40 - 10
x = 30
The player answered 30 questions correctly in the trivia game with a score of 50.

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Answer:

probability for 3 on a dice (P3) in one dice =

\( \frac{1}{6} \)

probability for even no. of a dice (Pe) =

\( \frac{3}{6} = \frac{1}{2} \)

Therefore, the probability of finding 3 on one dice and even on another (P) = P3 + Pe

\( = \frac{1}{6} + \frac{1}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3} \)

Answer:

Step-by-step explanation:

Answer:

You meant like this?

The number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560

To find the number of arrangements of letters in the word REPETITION where the first E occurs before the first T, we can approach the problem by breaking it down into simpler steps.

Step 1: We need to determine the total number of arrangements of the letters in REPETITION. Since there are 9 letters in the word, the total number of arrangements can be calculated using the formula for permutations of n objects taken r at a time, which is n!/(n-r)!. In this case, we have n=9 and r=9, so the total number of arrangements is 9! = 362,880.

Step 2: We need to count the number of arrangements where the first E occurs before the first T. To do this, we can first fix the positions of the first E and T in the word. There are 9 possible positions for the first letter, 8 remaining positions for the second letter, and so on, down to 1 possible position for the ninth letter. This gives us a total of 9x8x7x6x5x4x3x2x1 = 362,880 possible arrangements of the letters in REPETITION.

However, we want to exclude the arrangements where the first T appears before the first E. To do this, we can fix the position of the first T and count the number of arrangements of the remaining letters. There are 8 possible positions for the first T, and then 7 remaining positions for the second letter, and so on, down to 1 possible position for the eighth letter. This gives us a total of 8x7x6x5x4x3x2x1 = 40,320 arrangements where the first T appears before the first E.

Therefore, the number of arrangements of letters in REPETITION with the first E occurring before the first T is 362,880 - 40,320 = 322,560.

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Answer:

Jason eats 1/8=0.125 pounds of candy per day and it will take him 8 days to eat 1 pund of candy Hope Im not wrong

Step-by-step explanation:

To determine how many years it would take for money to double at a 10% interest rate compounded yearly, compounded weekly, and compounded continuously, compound interest and the rule of 72.

Compounded Yearly: To calculate the number of years it takes for money to double at a 10% interest rate compounded yearly, we can use the formula for compound interest: N = log(2) / log(1 + r), where r is the interest rate (0.10). Plugging in the values, we find it takes approximately 7.27 years.

Compounded Weekly: To calculate the number of years it takes for money to double at a 10% interest rate compounded weekly, we can use the rule of 72, which states that the doubling time is approximately 72 divided by the interest rate. In this case, it would take approximately 7.2 years.

Compounded Continuously: To calculate the number of years it takes for money to double at a 10% interest rate compounded continuously, we can use the formula A = P * e^(rt), where A is the final amount, P is the initial amount (1), r is the interest rate (0.10), and t is the time in years. Solving for t, we find it takes approximately 6.93 years.

By applying these calculations and using the concepts of compound interest, the rule of 72, and continuous compounding, we can determine the number of years it would take for money to double at a 10% interest rate under different compounding scenarios.

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Gabriella skied for 6 hours, Let x be the number of hours that Gabriella skied. We know that she paid $35 for ski rental and $15 per hour for skiing,

for a total of $95. We can set up the following equation to represent this information:

35 + 15x = 95

Solving for x, we get:

15x = 60

x = 4

Therefore, Gabriella skied for 6 hours.

Here is a more detailed explanation of how to solve the equation:

Subtract $35 from both sides of the equation.

15x = 60

15x - 35 = 60 - 35

15x = 25

Divide both sides of the equation by 15.

15x = 25

x = 25 / 15

x = 4

Therefore, x is equal to 4, which is the number of hours that Gabriella skied.

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The first odd number = 15

The second is then = 17

Consecutive numbers are those that appear consecutively after one another in the range of smallest to largest. An illustration would be the sequence of numbers 1, 2, 3, 4, 5, and so on.

Let x be the first of the following numbers to represent it algebraically. Following that, the numbers x + 1, x + 2, and x + 3 would be arranged in order. You must make sure that your first selection is an even number if the question requires consecutive even numbers.

We can employ the expression "2n," where n is any integer, to ensure that the result is even. By using the expression "2n + 1," we can ensure an odd number.

"2n + 3" will be the following odd number:

(2n + 1)(2n + 3) is the component of the odd integers, and it equals 255:

(2n + 1)(2n + 3) = 255

4n2 + 8n + 3 = 255

4n2 + 8n - 252 = 0

n2 + 2n - 63 = 0

(n + 9)(n -7) = 0

n = -9 and n = 7

We can disregard n = -9 because we are informed that the figures must be positive.

If n = 7,

The first odd number = 2(7) + 1 = 15

The second is then 17

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I understand that the question you are looking for is:

The product of 2 positive, consecutive odd numbers is 255 .

Part A: Write a quadratic equation in standard form to represent this problem

Part B: What are the 2 numbers?

Part C: Show your work for Part B.

Answer:

180 RS discount

Step-by-step explanation:

because 940-760 is 180

Answer:

y = 1.4x + 5.6

Step-by-step explanation:

plug the slope and y-intercept into the formula: y = ax + b (a is the slope and b is the y-intercept)

thus, y = 1.4x + 5.6