A reservoir contained 200 gallons of water. Jake drained the reservoir at a constant rate of 25 gallons per hour.
Which equation represents this situation if x is the number of hours the reservoir was draining and y is the number of gallons of water in the
reservoir?

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

Learn more about parallelogram at: https://brainly.com/question/10744696

#SPJ1

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

know more about multiply here;

https://brainly.com/question/30875464

#SPJ11

Answer: The answer is c

Step-by-step explanation:

cause common sense

Answer:

700

Step-by-step explanation:

Answer:

$712

Step-by-step explanation:

A x (1 + 4,8%)¹³ = 1310

=> A = 1310 : (1 + 4,8%)¹³ = 712,1551532

The total price of 2 bags of apples and 3 bags of oranges can be calculated by adding 2 times the price of a bag of apples to 3 times the price of a bag of oranges.

To determine the total price of 2 bags of apples and 3 bags of oranges, you need to know the price per bag of apples and the price per bag of oranges. Let's assume the price per bag of apples is $A and the price per bag of oranges is $O.

The total price of 2 bags of apples would be 2 * A, and the total price of 3 bags of oranges would be 3 * O. To find the overall total price, you can simply add these two amounts together:

Total price = (2 * A) + (3 * O)

To know more about total price,

https://brainly.com/question/26976946

#SPJ11

The correct expression for e (spring extension) is \(e=l_{1}+2Lcos\)θ.

To determine the correct expression for e, we need to understand the variables involved and their relationships.

Let's analyze the given expressions one by one:

\(e-2Lcos\)θ\(-l_{1}\):

This expression does not accurately represent the spring extension because the subtraction of \(l_{1}\) is incorrect. The correct relationship is that the spring extension is equal to \(2Lcos\)θ.

\(e-2Lsin0-L_{o}\):

This expression introduces variables \(O\) and \(L_{0}\) that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

\(e-l_{1} -2Lcos\)θ

This expression has the correct terms, but the subtraction of \(l_{1}\) is incorrect. The correct relationship is that the spring extension is equal to \(l_{1}\) plus the term \(2Lcos\)θ,  not minus.

\(e-h-2Lsin0\)

that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

Similar to expression 2, this expression introduces variables \(h\) and \(O\) that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

Among the four given expressions, the correct expression for e (spring extension) is \(e=l_{1}+2Lcos\)θ. This expression accurately represents the relationship between the spring extension \(e\), the arm length \(L\), and the angle θ.

To know more about spring visit

https://brainly.com/question/1968517

#SPJ11

Therefore, the integral is given by\(7 [(t^3 + 3t)/3 - 2(t + 1/t)] + 14t^-1 - 7t^-3 + C\) of the given equation.

We have to evaluate the integral using the given function. The given function is: \(7 tan^2(x) tan^4(x) dx\) Integral is given as:integral \(7 tan^2(x) tan^4(x) dx\)

Step 1:We can rewrite \(tan^4(x) as tan^2(x) × tan^2(x).\)Therefore, the given integral becomes integral \(7 tan^2(x) × tan^2(x) × tan^2(x) dx\)

Step 2:We can rewrite the term \(tan^2(x) as sec^2(x) - 1\).Therefore, the given integral becomes integral 7 (sec^2(x) - 1) × (sec^2(x) - 1) × tan^2(x) dx

Step 3:Let’s assume t = tan(x).Hence, \(dt/dx = sec^2(x)dx and dx = dt/sec^2(x)\) After substitution, the given integral becomes\(∫7 (t^2 + 1 - 1/t^2) (t^2 + 1 - 1/t^2) dt/t^2\)

Step 4:Simplifying the expression, we get\(7 ∫(t^2 + 1)^2/t^2 dt - 7 ∫dt/t^2 - 7 ∫1/t^4 dtOn solving the above integral, we get7 ∫(t^4 + 2t^2 + 1)/t^2 dt - 7 ∫dt/t^2 + 7 ∫t^-4 dt\)

Step 5:Solving the integral\(7 ∫(t^4 + 2t^2 + 1)/t^2 dt = 7 ∫(t^2 + 2 + 1/t^2) dt= 7 ∫(t^2 + 1/t^2) dt + 14∫ dt Using the formula, a^2 + 2ab + b^2 = (a + b)^2 and substituting t + 1/t = u, we can write the above integral as∫(t^2 + 1/t^2) dt = ∫(t + 1/t)^2 - 2 dt= ∫u^2 - 2 du= u^3/3 - 2u + C= (t^3 + 3t)/3 - 2(t + 1/t) + C\)

After substitution, we get

\(7 [(t^3 + 3t)/3 - 2(t + 1/t)] + 14t^-1 - 7t^-3 + CTherefore, the integral is given by7 [(t^3 + 3t)/3 - 2(t + 1/t)] + 14t^-1 - 7t^-3 + C.\)

To know more about integral Visit:

https://brainly.com/question/31059545

#SPJ11

The commission of the agent is 196000

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

Commission percentage = 7%

Earnings = 2.8 million

Using the above as a guide, we have the following:

Commission = 7% * Earnings

Substitute the known values in the above equation, so, we have the following representation

Commission = 7% * 2.8 million

Evaluate

Commission = 196000

Hence, the commission is $196000

Read more about commission at

https://brainly.com/question/26283663

#SPJ1

The distance from.Amelia to the top of the tower is; 100ft

According to the question;

The angle subtended by Amelia's position and the top of the tower is; ,30°

Hence, from Trigonometric identities;

Hence, x = 50/sin30°

Read more on Trigonometric identities;

https://brainly.com/question/24496175

The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

Visit here to learn more about probability:

brainly.com/question/13604758

#SPJ11

Answer: 7 - 3/v

Our expression is rewritten in mathematical form is  

Step-by-Step Explanation:

Since we have given that

7 minus the quotient of 3 and v

As we know that

The quotient of 3 and v is rewritten as

7 minus from it:

So, our expression is rewritten in mathematical form is

Step-by-step explanation: 7-3/v

Answer:

75 meters

Step-by-step explanation:

30/50 = 45/x

x = 75

Answer:

x= 75m

Step-by-step explanation:

If we call the angle in the bottom left θ, then the sinθ=(opposite side)/(hypotenuse).

For the smaller triangle:

sinθ=30/50

And for the bigger triangle:

sinθ=45/x

So:

30/50=sinθ=45/x

30/50=45/x

x=(45•50)/30=2250/30=75

So x= 75 meters

The average Honda beat the Dodge but couldn't pass the Smart Car, and the Mini couldn't pass the Audi, so the Audi won the race.

The Honda was able to defeat the Dodge but was unable to pass the Smart Car, so it was the Audi that arrived first in the race.

The Mini was then forced to settle for defeating the Smart Car after failing to pass the Audi. The Audi was the only vehicle that was able to stave off the competition and maintain its lead all the way to the finish line, making it the eventual race winner. Following the Audi in that order, the Honda, Dodge, Smart Car, and Mini were all overrun by the vehicle in front of them before the Mini was able to surpass the Smart Car and finish in fourth place.

Learn more about average here

https://brainly.com/question/24057012

#SPJ4

Answer:

Step-by-step explanation:

f(x)=ln(7−9x⁴+x⁵)

ln rule:

\(\frac{d}{dx}lnx = \frac{1}{x}\)

What is inside the parenthesis is like your x, that polynomial will go on bottom but then you also need to multiply by the derivative of what is inside the parenthesis

f'(x) = \(\frac{-36x^{4}+5x^{4} }{7-9x^{4} +x^{5} }\)

Answer:

125

Step-by-step explanation:

Measure of d will be,

⇒ d = 125°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Here, r and s are two parallel lines

And, q is the Transversal

Here, Uppercase left angle is 125 degrees

And, The bottom right angle is d degrees

We know that the sum of supplementary angles is 180°

Hence, By the figure, we get;

125 + x = 180

x = 180 - 125

x = 55°

Also we know that

Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure.

So, Measure of d will also be,

d = 125°

Or,

d = 180 - 55

   = 125°

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ6

Answer:

Step-by-step explanation:

C(x) = 15            0 ≤ x ≤ 2

C(x) = 5x + 10    2 < x ≤ 6

C(x) = 50           x > 6

Step-by-step explanation:

Let's define

x: Gigabytes Used

C(x): Monthly Cost in dollars

The graph has three parts. In the first part, the cost has a constant value of 15. The closed circles indicate that endpoints (at 0 and 2) are included in this segment.

In the second part, a line (which pass through (2, 20) and (6,40)) is shown. Its parameters are:

slope = (40 - 20)/(6-2) = 5

y-intercept: 20 = 5*2 + b <=> b = 20 - 5*2 =  10

Therefore, the equation of the line is: y = 5x + 10

The open circle at the beginning of the line indicates that it is not present in the segment. The closed circle at the end of the line indicates that it is present in the segment.

In the third part, the cost has a constant value of 50. The open circle indicates that the endpoint (6,50) is not included in this segment.

Hello there, and welcome to Brainly!

In this case, x is to be made the subject of the equation, setting x by itself.

Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract n from both sides of the equation:

m (-n) = n (-n) + (x/p)

m - n = x/p

Next, fully isolate the x by multiplying p to all terms on both sides of the equation:

(p) * (m - n) = (x/p) * (p)

p * (m - n) = x

Next, simplify. Distribute p to all terms within the parenthesis:

p(m - n) = x

pm - pn = x

x = pm - pn is your answer.

~

a. The decision rule for the 0.050 significance level is to reject the null hypothesis H0: ρ ≤ 0 in favor of the alternative hypothesis H1: ρ > 0 if the test statistic is greater than the critical value.

b. The value of the test statistic can be calculated using the sample correlation coefficient r and the sample size n.

c. Based on the test statistic and the significance level, we can determine if we can conclude that the correlation in the population is greater than zero.

a. The decision rule for a significance level of 0.050 states that we will reject the null hypothesis H0: ρ ≤ 0 in favor of the alternative hypothesis H1: ρ > 0 if the test statistic is greater than the critical value. The critical value is determined based on the significance level and the sample size.

b. To compute the test statistic, we use the sample correlation coefficient r, which is given as 0.77. The test statistic is calculated using the formula:

t = \((r * \sqrt{(n - 2)} ) / \sqrt{(1 - r^2)}\),

where n is the sample size. In this case, since the sample size is 16, we can calculate the test statistic using the given correlation coefficient.

c. To determine if we can conclude that the correlation in the population is greater than zero, we compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence of a positive correlation in the population. If the test statistic is not greater than the critical value, we fail to reject the null hypothesis and do not have sufficient evidence to conclude a positive correlation.

To learn more about null hypothesis, refer:-

https://brainly.com/question/28920252

#SPJ11

Answer:

answer is 1

I hope it's helps you

Answer:

the answer is 1

Step-by-step explanation:

Hopes this helps...

Answer:

Let's solve your equation step-by-step.

4x−(8−x)−2=9x−20+x−5

Step 1: Simplify both sides of the equation.

4x−(8−x)−2=9x−20+x−5

4x+−8+x+−2=9x+−20+x+−5

(4x+x)+(−8+−2)=(9x+x)+(−20+−5)(Combine Like Terms)

5x+−10=10x+−25

5x−10=10x−25

Step 2: Subtract 10x from both sides.

5x−10−10x=10x−25−10x

−5x−10=−25

Step 3: Add 10 to both sides.

−5x−10+10=−25+10

−5x=−15

Step 4: Divide both sides by -5.

Answer:

x=3

    hope this helps (>'-'<)

Answer:

0.4545...

Step-by-step explanation:

To convert a fraction to a decimal take the numerator (5) and divide it by the denominator (11):

5 ÷ 11 = 0.454545... the 45 keeps repeating because it's a repeating decimal

Answer: 10 km/ hr

Step-by-step explanation:

In the graph below, Diego's speed at various points during his 10 kilometer race is shown on the y axis while the distance is shown on the x axis.

Looking at the 1km mark on the x axis, Diego's speed on the y-axis is at 10km/ hr and this was the speed he started the race with. After the kilometer mark however, his speed changed and went on to increase to 11km/ hr by the second kilometer mark.

The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

Let the number of number of red pencils be 'x'.

Total blue pencils = 5.

Ratio = blue pencils/red pencils

5/x = 1/2

x = 5 x 2

x = 10

Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.

To know more about the ratio of the number, here

https://brainly.com/question/2914376

#SPJ4

Answer:

50percent

Step-by-step explanation:

30 is half 60

Answer:

m>2 is the correct answer

Answer:

m > 2

Step-by-step explanation:

The arrow is pointing to the right, so m must be larger than 2. When the 'alligator mouth' is pointing to m, that means m is a higher number. It is the > symbol instead of ≥ because the circle is NOT filled in, so therefore NOT equal to or more than.

The answer is number 2 , or

m > 2

Answer:

the correct answer is the last graph

Step-by-step explanation:

Sum is 2600 (for first question) , Sum is 2250 (for second question) , Sum is 1525 (for third question) , Sum is 16250 (for fourth question) , Sum is 385 (for fifth question) .

Here n= 25

1. Sequence: 200, 192, 184, 176

The comon diference (d) is = -8.

first term (a1) is 200.

The 25th term (\(a_2_5\)) = a1 +d (n -1)

\(a_2_5\) = 200+  (-8) (25 -1) = 200 -192 =8

sum =  (n/2)(\(a_1\)+\(a_2_5\))

= (25/2) × (200 +8)

=25 × 104 =2600

2. Sequence is :  6+13+20 +27 +..

difference = (d) =7.

25th term  (\(a_2_5\))= a1 +d (n -1)

(\(a_2_5\)) = 6 + 7(25-1)

=6+ 7×24

=174

Sum is =(n/2) (\(a_1\)+\(a_2_5\))

= 25/2 ×180

=2250

3. Sequence is : 13+17+21+25

difference = (d) = 4

25th term  (\(a_2_5\))= a1 +d (n -1)

(\(a_2_5\)) = 13+4 (25-1)

= 13+ 4 (24)

= 109

Sum is =(n/2) (\(a_1\)+\(a_2_5\))

=25/2 × (13 +109)

=25/2 ×122

=1525

4. Sequence is :50, 100, 150, 200..

difference = (d)= 50

25th term  (\(a_2_5\))= a1 +d (n -1)

=50+ 50 (25-1)

=50 +50×24

=1250

Sum is =(n/2) (\(a_1\)+\(a_2_5\))

=25/2 × (50+1250)

=25/2 × 1300

=16250

5. Sequence is= 1, 2.2, 3.4, 4.6, 5.8, ...

difference = (d)= 1.2

25th term  (\(a_2_5\))= a1 +d (n -1)

=1+1.2 (25-1)

=1+1.2 (24)

=29.8

Sum is =(n/2) (\(a_1\)+\(a_2_5\))

=25/2 × (1+29.8)

=25/2 × 30.8

= 385

Leran more about the mean here

https://brainly.com/question/12373434

#SPJ1

Answer:

Y=3x because that slope is 3 and if you times it by 4 you get 12

Step-by-step explanation:

The probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).

Given information:

five program systems are prepared so that they work independently of each other. Each system has a 0.3 chance of detecting an error.

Find the probability that at least one program system will detect an error. Use 4 decimal places.The probability of a system detecting an error is 0.3.

The probability of a system not detecting an error is 1 - 0.3 = 0.7.

Probability that none of the five systems detects an error is, P(error not detected in any of the five systems) = P(not detected in 1st) x P(not detected in 2nd) x ... x P(not detected in 5th) = 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 0.16807.

The probability that at least one system detects an error is, P(at least one system detects an error) = 1 - P(error not detected in any of the five systems) = 1 - 0.16807 = 0.8319 (approx).

Therefore, the probability that at least one program system will detect an error is 0.8319 (approx) or 0.832 (approx).

Hence, the correct option is 0.832.

Learn more about probability at

https://brainly.com/question/31112325

#SPJ11