Mary's family went to Disneyland. Her mom drove 75 miles an hour and her dad drove 60 miles an hour. If they drove for a total of 1710 miles, how many hours did each one of the drive?

Answer:

x  =  140  ft

w = 70 ft

A(max)  =  9800 ft²

Step-by-step explanation:

We have:

280 feet of fence to enclose three sides of a rectangular area

perimeter of the rectangle ( 3 sides ) is

p  =  L  =  x  +2w       w   = (L - x ) / 2       w   =  ( 280  -  x ) / 2

where:

x is the longer side

w is the width

A(x,w)  = x*w         ⇒   A(x)  =  x* ( 280 - x ) / 2  ⇒ A(x)  = (280x -x²)/2

Taking derivatives on bth sides of the equation

A´(x)  = ( 280 -2x)*2 /4          A´(x)  = 0      ( 280 -2x)  =  0

280 -2x  = 0     x = 280/2

x  =  140  ft

And   w  = ( 280 - x ) / 2  ⇒  w  =(  280  -140  )/ 2

w = 70 ft

A(max)  =  9800 ft²

Answer:

A. maximum value at 30

Step-by-step explanation:

−x² + 10x + 5

First, factor out the leading coefficient from the first two terms:

-1 (x² − 10x) + 5

Take half of the next coefficient, square it, then add and subtract the result.

(-10/2)² = 25

-1 (x² − 10x + 25 − 25) + 5

-1 (x² − 10x + 25) + 25 + 5

-1 (x² − 10x + 25) + 30

Factor the perfect square.

-1 (x − 5)² + 30

The equation is now in vertex form.  This is a downwards parabola with a vertex at (5, 30).  Since the parabola points down, the vertex is a maximum.

Answer:

y=525x+230

Step-by-step explanation:

525 is spent everyday. x is the number of days, so with each day $525 is spent.

$230 is a one time cost, regardless of how many days they stay on the trip.

The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of p value

hence option (c) is correct  

Test statistic is a way to check the authenticity of null hypothesis that is considered. Test statistic is extremely important to accept and reject the null hypothesis.

The data from the experiment is fed into the equation  and compares your result with the expected results of null hypothesis.

Test statistic is a number calculated from statistical test of a hypothesis.

It shows how closely our  data matches with the distribution expected under null hypothesis of the distribution.

Confidence interval

Confidence interval is the range of  plausible values of a random variable with a certain percentage of confidence level. Confidence level shows that how much certainty or uncertainty in test statistic considering the null hypothesis to be true. It is expressed in percentage. 98% , 95% and  90% Confidence intervals are a few examples.  

p- value is the probability of a happening of a particular event is  a random chance or some other event with similar probability or any rarer event considering null hypothesis to be true.

Alternate hypothesis

Alternate hypothesis is the opposite of Null hypothesis. Null hypothesis is the generally or by default accepted hypothesis which is tested by various statistical tests.

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Answer:

  m∠A = m∠D = 40°

Step-by-step explanation:

Angles A and D are corresponding angles in the congruent triangles, so have the same measure. You set one measure equal to the other:

  x + 20 = 2x

To solve this, subtract x from both sides:

  20 = x

Then both angle measures are 2x = 40°.

Answer:

From years 1988 to 1994

Step-by-step explanation:

The trick in this question is to start from last conditions.

Mr. Ruiz graduated in 1973. Started to teach 2 years after, which means, 1975.

He taught for 13 years, which means from 1975 to (1975 + 13)1988.

He became principle only after teaching for 13 years, which means he started to be principle for 1988. And he continued to be for 6 years which means, (1988 + 6) 1994.

Thus, years for which Mr. Ruiz was principle were From 1988 to 1994.

Answer:

$7,661

Step-by-step explanation:

Closing balance = Opening balance + purchases - Issued items

Given

Office supplies account on January 1 = $6,791 - Opening balance

Purchases = $3,205

Supplies on hand on January 31 = $2,155 - Closing balance

Substituting into the formula above

2155 = 6791 + 3025 - Issued items

Issued items = 6791 + 3025 - 2155

                     = $7,661

The amount to be used for the appropriate adjusting entry is $7,661

Final answer:

The adjusting entry for the used office supplies for the month of January is $7,841, which is calculated by subtracting the supplies on hand at the month's end from the sum of the starting balance and purchases made during the month.

Explanation:

To calculate the adjusting entry for office supplies, you need to calculate the cost of supplies that were used during the month. Start with the balance of supplies on hand at the beginning of the month, add the purchases made during the month, and then subtract the balance of supplies on hand at the end of the month.

The calculation is as follows:

Starting balance on January 1: $6,791

Add purchases during January: $3,205

Subtract ending balance on January 31: $2,155

The adjusting entry for supplies used = (Starting balance + Purchases) - Ending balance
= ($6,791 + $3,205) - $2,155
= $9,996 - $2,155
= $7,841

Therefore, the adjusting entry to record the office supplies used would be for $7,841.

Answer:

The interest after 3 years is $360

Explanation:

Given the principal amount (P) = $3000

Rate of interest (R) = 0.04

Time period (T) is given as 3 years

The Simple Interest is calculated by the formula;

[tex]SI = Principal \times Rate of Interest \times Time[/tex]

Substituting the values in the above formula,

[tex]SI = 3000 \times 0.04 \times 3[/tex]

SI = $360

Therefore, the interest after 3 years is $360

Answer:

$360

Step-by-step explanation:

Answer: The rate in still water is 8m/s

The rate in current period is is 6 m/s

Step-by-step explanation:

In a canoe race, A team paddles downstream 480 m in 60 seconds. The same team makes the trip upstream and 80 seconds.

We observe that it took the team more time paddling upstream than paddling downstream even though it was the same distance.

Let us assume that on paddling downstream, they paddled in the same direction with the current. This means that they paddled on still water. On paddling upstream, they paddled in the opposite direction of the current.

Let the speed of the boat or teammates be

x m/s

Let the speed of the current be

y m/s

Distance = speed × time

Distance travelled on still water or downstream

= (x+y) × 60 = 60(x+y)

Distance travelled on upstream

= (x-y) × 80 = 80(x-y)

Since the distance is 480 miles for both upstream and downstream,

60(x+y) = 480

x + y = 480/60 = 8 - - - - - -1

80(x-y) = 480

x - y = 480/80 = 6 - - - - - -2

Adding equation 1 and 2,it becomes

2x = 14

x = 14/2 = 7 m/s

y = 8 - x = 8-7

y = 1 m/s

Rate in still water = x +y = 7+1 = 8m/s

Rate in current period = x - y = 7 - 1 = 6m/s

Answer: You would spend 160 hours in total of ten weeks.

Step-by-step explanation: Just add 12.5 + 3.5 which = 16. Then multiply 16 times 10 which is 160, and that is your answer.

95% confidence interval would be (58.96, 69.04).

Step-by-step explanation:

Since we have given that

Number of dogs' weight = 20

Mean = 64 ounces

Standard deviation = 11.5 ounces

We need to find the 95% confidence interval.

So, z = 1.96

so, interval would be

[tex]\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=64\pm 1.96\times \dfrac{11.5}{\sqrt{20}}\\\\=64\pm 5.04\\\\=(64-5.04,64+5.04)\\\\=(58.96,69.04)[/tex]

Hence, 95% confidence interval would be (58.96, 69.04).

Answer:

  f(0) = 1

Step-by-step explanation:

The ordered pair with first number 0 has second number 1. Each pair corresponds to (x, f(x)), so that pair has x=0 and f(0) = 1.

Answer:

[tex]f(0)=1[/tex]

Step-by-step explanation:

The given points are

[tex](-3,0), (-2,2),(0,1),(1,-2)[/tex]

Remember that each point has the form [tex](x,y)[/tex], where [tex]y=f(x)[/tex].

That means if we need to find [tex]f(0)[/tex], then we just need to look for the pair that belong to [tex]x=0[/tex].

If you observe, the pair we are looking for is [tex](0,1)[/tex], which relation is

[tex]f(0)=1[/tex].

Therefore, the answer is 1, that is, [tex]f(0)=1[/tex].

Answer:

In statistics, the chi-square test is used to prove a specific hypothesis, accepting or rejecting the null one. In order to find enough evidence to prove the hypothesis, we compare two group of frequencies, which belongs to two different groups (like a quasi-experimental design, with a control and experimental group). The researcher have set an expected frequency, based on the hypothesis, and then he/she will observe a frequency from the data recollected.

Therefore, by comparing this two frequencies (the expected with the observed), the researcher is able to demonstrate the hypothesis.

Answer: 85.333 or 256 over 3.

Answer: x = 2

Step-by-step explanation:

The diagram of the kite is shown in the attached photo.

The perimeter of the kite is the distance around the kite.

The kite has 2 pairs of equal sides.

This means that

Side ML = side MN and side NO =

side LO

If Side MN = 8x – 3 and side NO = 2x + 1, then The perimeter of the kite is ML + MN + NO + LO

The perimeter of kite LMNO is given as 36 feet.

Therefore

ML + MN + NO + LO = 36

8x – 3 + 2x + 1 +8x – 3 + 2x + 1 = 36

8x + 8x + 2x+ 2x -3 +1 - 3 + 1

20x -4 = 36

20x = 40

x = 40/20 = 2

Answer:

Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet

Step-by-step explanation:

Given:

Length of escalator = 30 feet

Distance between the floors = 12 feet

To find the distance from base of escalator to the point on the first floor directly below the top of the escalator  we will create the figure for the situation.

From the figure we see that a triangle ABC is formed.

We see that the Δ ABC is a right triangle.

Applying Pythagorean theorem for right triangle ABC to find the missing side.

[tex]AB^2=BC^2+AC^2[/tex]

AB = 30 feet

BC = 12 feet

Plugging in values in the theorem.

[tex]30^2=12^2+AC^2[/tex]

Solving for AC.

[tex]900=144+AC^2[/tex]

Subtracting both sides by 144.

[tex]900-144=144+AC^2-144[/tex]

[tex]756=AC^2[/tex]

Taking square root both sides.

[tex]\sqrt{756}=\sqrt{AC^2}[/tex]

[tex]27.5=AC[/tex]

∴ [tex]AC=27.5[/tex] feet.

∴ Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet

To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The distance is approximately 27 feet.

To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The length of the escalator represents the hypotenuse of a right triangle, and the distance between the floors represents one of the legs.

We can use the formula a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. Substituting the given values, we have 12^2 + b^2 = 30^2. Simplifying the equation, we get b^2 = 30^2 - 12^2. Calculating the value, we find that b^2 = 756, which means b is equal to the square root of 756. Rounding to the nearest foot, the distance from the base of the escalator to the point on the first floor directly below the top of the escalator is approximately 27 feet.

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Answer:

28.108 K.

Step-by-step explanation:

Given: Pressure (P)= 1.2atm

           Number of moles (n)=  2.6 moles

           Volume (V)= 5.00-L

Now finding the temperature (T).

Formula; T= [tex]\frac{P\times V}{n\times R}[/tex]

R is a constant factor which makes other factors work together.

There is a numerical value for R which we use is [tex]0.0821 \times \frac{L.atm}{mole.K}[/tex]

∴ Temperature (T)= [tex]\frac{1.2\times 5}{2.6\times 0.0821 \frac{L.atm}{mol.K} }[/tex]

⇒ Temperature (T)= [tex]\frac{6}{0.21346} = 28.1083\ K[/tex]

∴ Temperature is 28.108 K

Answer:

Let's x be the probability for 1, 3, 5 and 6.

The probability for 2 and 4 is going to be 3x.

The sum of the probabilities of all possible outcomes is always 1.

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

x + 3x + x + 3x + x + x = 1

10x = 1

x = 1/10

The probability of obtaining 1, 3, 5 or 6 is 1/10

The probability for 2 and 4 is 3/10

The probability of rolling a 2 or a 4 is [tex]$\frac{3}{14}$[/tex], and the probability of rolling any of the other numbers (1, 3, 5, or 6) is [tex]$\frac{1}{14}$.[/tex]

To solve this problem, we need to distribute the total probability of 1 (since the sum of all probabilities must equal 1) among the six outcomes of the die according to the given conditions.

 Let's denote the probability of rolling a 2 or a 4 as $p$. According to the problem, rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers. Therefore, the probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3}$.[/tex]

 Since there are two outcomes with probability $p$ (rolling a 2 and rolling a 4) and four outcomes with probability $\frac{p}{3}$ (rolling a 1, 3, 5, or 6), we can set up the following equation to represent the total probability:

[tex]\[ 2p + 4\left(\frac{p}{3}\right) = 1 \][/tex]

 Now, let's solve for $p$:

[tex]\[ 2p + \frac{4p}{3} = 1 \][/tex]

[tex]\[ \frac{6p + 4p}{3} = 1 \][/tex]

[tex]\[ \frac{10p}{3} = 1 \][/tex]

[tex]\[ 10p = 3 \][/tex]

[tex]\[ p = \frac{3}{10} \][/tex]

 So, the probability of rolling a 2 or a 4 is[tex]$p = \frac{3}{10}$.[/tex]

 The probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3} = \frac{3}{10} \times[/tex] [tex]\frac{1}{3} = \frac{1}{10}$.[/tex]

However, we must remember that the total probability must be distributed equally between rolling a 2 and rolling a 4. Since they are equally likely, each has a probability of half of $p$:

[tex]\[ p_{2} = p_{4} = \frac{p}{2} = \frac{3}{10} \times \frac{1}{2} = \frac{3}{20} \][/tex]

 Now, we can state the final probabilities for each outcome:

 - The probability of rolling a 1 is [tex]$\frac{1}{10}$.[/tex]

- The probability of rolling a 2 is [tex]$\frac{3}{20}$.[/tex]

- The probability of rolling a 3 is [tex]$\frac{1}{10}$.[/tex] - The probability of rolling a 4 is [tex]$\frac{3}{20}$.[/tex]

The probability of rolling a 5 is [tex]$\frac{1}{10}$.[/tex]

Answer:

The equation [tex]7\,\sqrt{x} =14[/tex] is a radical equation.

Step-by-step explanation:

If the equations given are (as I can read them from your typing):

a) [tex]x+\sqrt{5} =12[/tex]

b) [tex]x^2=16[/tex]

c) [tex]3+x\,\sqrt{7} =13[/tex]

d) [tex]7\,\sqrt{x} =14[/tex]

The only radical equation is the last one : [tex]7\,\sqrt{x} =14[/tex], because it is the only one where the unknown appears inside the root. The name "radical equations" is associated with the fact that the unknown is contained inside the root and therefore the process involved in solving for the unknown will need to include the elimination of the root via algebraic methods to free the unknown.

Notice that the options a) and c) have roots, but what appears inside them are numbers (5 and 7 respectively), and not an unknown like "x". Equation b) doesn't contain a root, and wouldn't classify as a radical equation.

A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.

Thus, by above definition, we will have the fourth option: [tex]7\sqrt{x} = 14[/tex] as a radical equation.

A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.

Since only in the fourth option we see there's root over x which is a variable here, thus the  fourth option: [tex]7\sqrt{x} = 14[/tex] is a radical equation.

Rest of the options, although containing roots, aren't having variables inside the root, thus they aren't classified as radical equations.

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Answer:

Oil: 24 ml; Onion: 56 g; Potatoes: 0.36 kg; Milk: 0.44 l

Step-by-step explanation:

First, we see how much of the soup recipe he wants make.

4 portions out of 20 portions = 4/20 = 1/5 = 0.2

He wants to make 0.2 of the amount of the recipe.

Now we multiply every amount by 0.2

Oil: 0.2 * 120 ml = 24 ml

Onion: 0.2 * 280 g = 56 g

Potatoes: 0.2 * 1.8 kg = 0.36 kg

Milk: 0.2 * 2.2 l = 0.44 l

Richard needs to use a scaling factor to reduce the amounts of each ingredient to make 4 portions of potato soup, resulting in 24 ml oil, 56 g onion, 360 g potatoes, and 0.44 liters of milk. Devon will require 37.5 liters of soup for a party of 100 guests.

To scale down the recipe from 20 portions to 4 portions of potato soup, Richard needs to multiply each ingredient by the scaling factor, which is 4/20 or 1/5. Here's how to calculate the amounts needed:

Therefore, for 4 portions, Richard needs 24 ml of oil, 56 g of onion, 360 g of potatoes, and 0.44 liters of milk.

Answer:

x = 36

Step-by-step explanation:

[tex] x - 12\sqrt{x} + 36 = 0 [/tex]

Subtract x and 36 from both sides.

[tex] -12\sqrt{x} = -x - 36 [/tex]

Divide both sides by -1.

[tex] 12\sqrt{x} = x + 36 [/tex]

Square both sides.

[tex] 144x = x^2 + 72x + 1296 [/tex]

Subtract 144x from both sides.

[tex] 0 = x^2 - 72x + 1296 [/tex]

Factor the right side.

[tex] 0 = (x - 36)^2 [/tex]

[tex] x - 36 = 0 [/tex]

[tex] x = 36 [/tex]

Since the solution of the equation involved squaring both sides, we musty check the answer for possible extraneous solutions.

Check x = 36:

[tex] x - 12\sqrt{x} + 36 = 0 [/tex]

[tex] 36 - 12\sqrt{36} + 36 = 0 [/tex]

[tex] 36 - 12\times 6 + 36 = 0 [/tex]

[tex] 36 - 72 + 36 = 0 [/tex]

[tex] 0 = 0 [/tex]

Since 0 = 0 is a true statement, the solution x = 36 is a valid solution.

The total weight of the smaller and the bigger cat Alberto has is 26 1/12 pounds.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Alberto has 2 cats.

The smaller cat weighs 10 3/4 pounds and the larger cat weighs 15 1/3 pounds.

Therefore, The weights of the cats together is the sum of their individual

weights which is,

= (10 3/4 + 15 1/3) pounds.

= (43/4 + 46/3) pounds.

= [(3×43 + 4×46)/12] pounds.

= (129 + 184)/12 pounds.

= 313/12 pounds.

= 26 1/12 pounds.

So, Together the cats weigh 26 1/12 pounds.

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Answer:

Step-by-step explanation:

For cost and revenue functions C(x) = 36400-83.2x and R(x) = 1248-8.32x², you want to know the selling price limits that will let the company make a profit.

Profit is the difference between revenue and cost.

  P(x) = R(x) -C(x)

  P(x) = 1248-8.32x² -(36400-83.2x) . . . . . . use the given functions

  P(x) = -8.32(x² -160x +4375) . . . . . . . . remove common factor

  P(x) = -8.32(x -35)(x -125) . . . . . . factor

The profit will be zero when the factors are zero, for x = 35 and x = 125.

We have to assume the demand function is found by dividing the revenue by the number of chairs sold.

  R(x) = x(price) = x(1248 -8.32x)

Then the price is ...

  price = 1248 -8.32x . . . . . . . . . . . where x is the number of chairs sold

When selling 125 chairs, the price is ...

  1248 -8.32(125) = 208 . . . . . dollars

When selling 35 chairs, the price is ...

  1248 -8.32(35) = 956.80 . . . . dollars

For the company to make a profit, the selling price can go no lower than $208 and no higher than $956.80.

__

Additional comment

These prices will result in 0 profit, as the number of chairs sold makes the revenue equal to the cost. If we require sales of 36 to 124 chairs, so profit is positive, then the price limits are $216.32 and $948.48. Profit will be maximized when 80 chairs are sold for $582.40 each.

Answer: the number of adult tickets is 210

The number if student tickets is 270

Step-by-step explanation:

Let x represent the number of adult tickets that were purchased.

Let y represent the number of student tickets that were purchased.

At the ritz, concert tickets for adults cost $6 and tickets for students cost $4. If the cost of total tickets purchased is $2340, then,

6x + 4y = 2340 - - - - - - - -1

Total number of tickets purchased is 480. This means that

x + y = 480

x = 480 - y

Substituting x = 480 - y into equation 1, it becomes

6(480 - y) + 4y = 2340

2880 - 6y + 4y = 2340

- 6y + 4y = 2340 - 2880

-2y = - 540

y = - 540/-2 = 270

x = 480 - 270

x = 210

Answer:

Step-by-step explanation:

Gabe went out for lunch with his best friend the bill costs $16.40

This amount was before tax and the tip that he wanted to give.

He paid a 9 percent tax on the bill. The amount of the 9 percent tax is 9/100 × 16.40 = 0.09 × 16.40 = $1.476

He left a 20 percent tip. This means that amount left as tip is 20/100 × 16.40 = 0.2×16.40 = $3.28

The amount that Gabe paid would be the sum of the bill, the tip and the amount paid on tax. It becomes

16.40 + 1.476 + 3.28 = $21.156

Answer:

9.5

Step-by-step explanation:

It keeps repeating the line goes all the way up then it keeps going to 9 then to 9.5 in the middle of 9 so it means its in between 10 so its 9.5 to 9 then 9.5 it repeats so mostly the answer is 9.5

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Answer:

6 minutes

Step-by-step explanation:

Machine A produces x boxes in 10 minutes

In one minute, the machine produces x/10 boxes

Machine B produces 2x boxes in 5 minutes

In one minute, the machine produces 2x/5 boxes

Therefore in one minutes, both boxes working together will produce

= 2x/5 + x/10

=5x/10

=x/2 boxes

To produce 3x boxes, the time required

= 3x/(x/2)

= 3 × 2

= 6

It take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes in 6 minutes

Answer:

Associative analysis

Step-by-step explanation:

Associative analysis is an approach that is used to analyses the peoples mental representation , focusing on meaning and similarities and differences across the culture.It determined that relationship that is hidden in the large data set.It determine the relationship in between two variable as well.

Answer:

(Solution: X=16 and Y=-10)

Explanation:

》Total money that will be spent on flour and corn meal altogether(T)

=$25

》Since it is not mentioned that whether corn and flour are bought in same quantity or not, we will assume them of different quantity.

i.e.,Suppose

》X pound of flour is bought

&

》Y pound of corn is bought.

So,

》Cost of flour(F)=$1.50X

》Cost of corn(C)=$2.50Y

So total cost will be sum of cost of flour and corn altogether,

Writing it in equation(linear),

F+C=T

Also,

Total pounds=6

ie,

The system of linear equations is x + y = 6 and 1.5x + 2.5y = 25.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Assume you purchase flour and corn dinner in mass to make flour tortillas and corn tortillas flour cost $1.50 per pound and corn feast cost $2.50 per pound would you like to spend veiling $25 on flour and corn feast yet you want somewhere around 6 pounds by and large

Let x be the number of pounds of flour and y be the number of pounds of corn meal. Then the system of linear equalities is given as,

x + y = 6

1.5x + 2.5y = 25

The system of linear equations is x + y = 6 and 1.5x + 2.5y = 25.

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