Marcus runs triathlons (races that involve running, biking, and swimming). To prepare for these triathlons, he follows a strategy of running twice as far as he swims and biking fours times as far as he runs. If he swims for 3 miles this week, what is the total distanch of his swimming, running and biking this week?

Yes, conditions of randomness and normality of the population met for this test.

The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.

So, yes, conditions of randomness and normality of the population met for this test.

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Answer:

x=-3

Step-by-step explanation:

Solution

Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290

The confidence interval formula is

Calculate the standard deviation of the data

The standard deviation is

237.67

Calculate the sample mean

The mean is 2262.91

Thus, the lower limit is

2122.455 ( 3 decimal places)

The Higher limit is 2403.363 ( 3 decimal places)

The transformation that relates the two functions:

f(x) = y = -√(-4x)

g(x) = y = √(-4x)

Is a reflection across the x-axis.

We define a reflection across the x-axis as a transformation that does a "vertical reflection" along the line y = 0 (which is the x-axis).

For a function f(x), a reflection across the x-axis generaste the new function g(x) that can be written as:

g(x) = -f(x).

In this case the original function is:

f(x) = y = -√(-4x)

And the transformed function is:

g(x) = y = √(-4x)

You can see that the only difference is the sign, such that we can write:

g(x) = -f(x) = -(-√(-4x)) = √(-4x)

So we conclude that the transformation is a reflection across the x-axis.

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The total cost for 6 movie tickets and 5 snacks is $97

The total cost for 6 movie tickets and x snacks is $(72 + 5x)

Given,

Miguel is going to see a movie with his 5 kids.

Number of people = 6

Cost for one ticket = $12

Cost of one snack = $5

Number of snacks = 5

We have to find the total cost spend by Miguel:

For tickets and 5 snacks:

For tickets and x snacks:

Now,

Total cost for tickets = 6 × 12 = $72

Cost for 5 snacks = 5 × 5 = $25

Therefore,

Total cost = 72 + 25 = $97

Next,

Cost for x snacks = 5x

Then,

Total cost = 72 + 5x

That is,

The total cost for 6 movie tickets and 5 snacks is $97

The total cost for 6 movie tickets and x snacks is $(72 + 5x)

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Answer:

Step-by-step explanation:

4 - 3 x = 6 - 5 xx

[tex]-3x+4=6-5xx^{2}[/tex]

x = 1

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

Answer:

x=1

Step-by-step explanation:

sense x's are on both sides you need to bring one of them over, add 3x to both sides to get 4=6-2x , then subtract 6 from each side to get -2=-2x , then to get x by itself divide both sides by -2 to get 1=x

The value of missing number is [tex]49[/tex].

The given equation is [tex]x^{2}+14x+c[/tex].

We have to find the missing value of [tex]c[/tex].

We can find the value of [tex]c[/tex] by perfect square trinomial.

A perfect square trinomial is a equation which we can get after the square  of binomial expression.

The equation [tex]ax^{2}+bx+c[/tex] said to be a perfect square if and only if it follows the condition [tex]b^{2}=4ac[/tex].

In the equation [tex]ax^{2}+bx+c[/tex], [tex]a,b[/tex] and [tex]c[/tex] are the real numbers.

Now we compare the given equation to [tex]ax^{2}+bx+c[/tex].

After comparing we get

[tex]a=1, b=14, c=c[/tex]

To find the value of [tex]c[/tex] we put the value of [tex]a,b,c[/tex] in expression [tex]b^{2}=4ac[/tex].

[tex](14)^{2}=4\times1\times c[/tex]

[tex]196=4\times c[/tex]

Divide by [tex]4[/tex] on both sides

[tex]\frac{196}{4}=\frac{4\times c}{4}[/tex]

[tex]c=\frac{196}{4} \\c=49[/tex]

Hence, the value of missing number is [tex]49[/tex].

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Answer:

2

Step-by-step explanation:

because average of 1 and 2 is 1.5 rounded is 2

The standard deviation of your revenues in a day is 14.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

Let x be the revenue from hats.

And let y be the revenue from sunglasses.

And z be the total revenue.

Then according to the question:

z = 10x + 5y

You know the expected number of hats sold in a day is 10 with standard deviation 1.

σₓ = 1

σy = 2

Taking squares of both of the equation.

σₓ² = 1² = 1

σy² = 2² = 4

To find the standard deviation of your revenues in a day:

V(z) = (10)²σₓ² + 5²σy²

V(z) = (100)(1) + (25)(4)

V(z) = 200

Standard deviation,

σz² = √(200)

σz² = 10√(2)

σz² = 14.14

σz² ≈ 14

Therefore, the required standard deviation is 14.

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By the concept of linear equation :

$1,500 was spent on flights,

$680 was spent on hotels,

$7,300 was spent on other purchases.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.

Given:

Flights: 4 points per dollar

Hotels: 2 points per dollar

Other: 1 point per dollar.

Total spent = $9,480

Points earned = 14,660

Let

x = money spent on flights

y = money spent on hotels

z = money spent on other purchases.

Because the money spent on flights was $140 more than twice the money spent on hotels, therefore

x = 2y + 140          (1)

Total charges were $9,480, therefore

x + y + z = 9480    (2)

Total points earned was 14,660. Therefore

4x + 2y + z = 14660   (3)

Subtract (2) from (3).

4x + 2y + z - (x + y + z)

= 14660 - 9480

3x + y = 5180             (4)

Substitute (1) into (4).

3(2y + 140) + y = 5180

7y + 420 = 5180

7y = 4760

y = 680

From (1), obtain

x = 2y + 140

= 2(680) + 140

= 1500

From (2), obtain

z = 9480 - (x + y)

= 9480 - (1500 + 680)

= 7300

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f(x) means the value of y

The graph has a part down the x-axis which means f(x) < 0

The graph has another part over the x-axis which means f(x) > 0

The value of x for the negative part is from - infinity to 3

Then f(x) < 0 at the interval (-00, 3)

The value of x for the positive part is from 3 to infinity

then f(x) > 0 at the interval (3, 00)

Then the answer is C

Answer:

x = 12

Step-by-step explanation:

Since they are opposite exterior angles, they are congruent, so you set them equal to each other

5x = 4x + 12

- 4x  - 4x

x = 12

For A and B to be parallel then the angle (4x+12)⁰ and the angle opposite to angle (5x)⁰ should be equal since the two are congruent to each other.

therefore

5x = opposite angle=(4x+12)

=> 5x=(4x+12)

=>5x-4x= 12

therefore

X =12⁰

Answer:

176 children and 105 adults.

Explanation:

Let's call x the number of children and y the number of adults.

If 281 people entered the park, we can write the following equation

x + y = 281

If they collected 684 dollars, we can write the following equation

1.5x + 4y = 684

because it cost $1.5 for children and $4 for adults.

Now, we have the following system of equations

x + y = 281

1.5x + 4y = 684

First, we need to solve the first equation for y, so

x + y = 281

x + y - x = 281 - x

y = 281 - x

Then, replace this expression on the second equation

1.5x + 4y = 684

1.5x + 4(281 - x) = 684

1.5x + 4(281) - 4(x) = 684

1.5x + 1124 - 4x = 684

-2.5x + 1124 = 684

Finally, we can solve the equation for x

-2.5x + 1124 - 1124 = 684 - 1124

-2.5x = -440

-2.5x/(-2.5) = -440/(-2.5)

x = 176

So, the value of y is equal to

y = 281 - x

y = 281 - 176

y = 105

Therefore, they admitted 176 children and 105 adults.

Answer:

x = 9

Step-by-step explanation:

x = 31.5 / 3.5

x = 9

Answer:

x = 9

Step-by-step explanation:

since 3.5 is being multiplied by x to get 31.5 to get rid of it and leave x by itself you have to divide both sides by 3.5

(3.5x)/(3.5)= (31.5)/(3.5)

x=9

Total time = 2 hours

Time playing video games = 50 minutes

We have to write an equation:

Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes

Time must be in the same unit ( minutes)

since 60 minutes =1 hour

2 hours = 2 (60) =120 minutes

Back with the equation:

120 x = 50

Solving for x

x = 50/120

x = 0.42

In percentage form:

0.42 x 100 = 42%

The length of the first piece is 3 inches, and the second and third pieces are each 9 inches

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Given that a 21-foot beam is to be cut into three pieces so that the second and third pieces are each 3 times the length of the first piece.

We have to determine the length of each piece.

Let x represents the length of the first piece

As per the given condition,

x + 3x + 3x = 21

7x = 21

x = 21 / 7

x = 3

Thus, the first piece is 3 inch

So 2nd piece is 3×3 = 9 inches ( 3 times to first piece )

And 3rd  piece is  3×3 = 9 inches (  3 times to first piece )

Therefore, the length of the first piece is 3 inches, and the second and third pieces are each 9 inches

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The percent of decrease in the billing rate is 2.37%.

It should be noted that a percentage decrease is calculated as

= Decrease in value / Initial value × 100

Let's assume the following:

Initial amount = $220

New amount = $214.79

Decrease in amount = $220 - $214.79 = $5.21

The percentage decrease will be:

= 5.21 / 220 × 100

= 2.37%

The question is incomplete and the values were assumptions.

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Answer:

=35/95

=(5 x7)/95

=5 x 7/5 x 19

=7/19

answer:

8.00 dollars

Step-by-step explanation:

4 x 1.50 = 6.00

38,00 - 6.00 = 32.00

32.00 divided by 4= 8.00

The height of the box is decreasing at a rate of 2/45 cm/sec.

The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.

Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,

A = a²

Differentiate the above equation with respect to t.

dA/dt = 2a(da/dt)

Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.

10 = 2(15)(da/dt)

da/dt = 1/3

The volume of the box can be written as,

V = (a)(a)(h) = a²h

Differentiate the above equation with respect to t.

0 = 2a(da/dt) + a² (dh/dt)

dh/dt = -2/a (da/dt)

Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.

dh/dt = -2/15 (1/3)

         = -2/45

Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.

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A. The weight of the copies and the quantity of papers are proportional.

B. There is no proportion between the number of books and their weight.

Given,

A. All versions of the document are 8.5 by 11 inches in size.

We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.

As a result, the weight of the copies and the quantity of papers are proportional.

B. Each book has a distinct weight, as we know.

Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.

Therefore, there is no proportion between the number of books and their weight.

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1) Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

2) Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

N(Pennies) = 6

N(Nickels) = 8

N(Dimes) = 4

N(quarters) = 7

N(total) = 6 + 8 + 4 + 7

N(total) = 25

1) The theoretical probability of selecting a dime = 4/25

The experimental probability of selecting a dime = 30/150 = 1/5

B is wrong because theoretical probability is 4/25, not 9/50

Wrong statement:

The theoretical probability of selecting a dime is

Correct statement:

The theoretical probability of selecting a dime is 4/25

2) The experimental probability of selecting a penny = 45/200 = 9/40

The theoretical probability of selecting a penny = 6/25

Difference between experimental and theoretical probability = 6/25 - 9/40

Difference between experimental and theoretical probability = 3/200

Wrong statement:

The difference between the experimental and theoretical probability is 1/10

Correct statement:

The difference between the experimental and theoretical probability is 3/200

Answer:

y = 3

Step-by-step explanation:

12.75y = 38.25

To find the value of y, divide each side by 12.75

12.75y/12.75 = 38.25/12.75

y = 3

1) Only 2

1) Examining the expressions we have

1. -5/8+3/5 =-1/40 Rational Expression

2. 1/2+ √2 Irrational Expression

3.(√5)×(√5)= 5 Rational Expression

4. 3×(√49) = 21 Rational Expression

2) Since √2 is an irrational number √2 = 1.4142.... non-periodic and infinite number, and number added to it will yield an irrational number.

3) So the answer is 1) Only 2

Answer:

[tex]5^{15}[/tex] × 120 = 30,517,578,125 × 120

Step-by-step explanation:

Answer: x=37/3

Step-by-step explanation:

8x-11+5x+2x+6=180 ==> three angles of a triangle add up to 180 degrees

8x+5x+2x-11+6=180

13x+2x-5=180

15x-5=180

15x=185

x=185/15

x=37/3

Using a system of equations, supposing that she spent $19.65, the amounts are as follows:

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of this problem.

For this problem, the variables are defined as follows:

She brought a total of 26 desserts, hence:

x + y = 26.

She spent a total of $19.65, hence, considering the price of each item:

0.65x + 0.9y = 19.65.

From the first equation, we have the following relation:

y = 26 - x.

Hence, replacing in the second, we can solve for x as follows:

0.65x + 0.9(26 - x) = 19.65

0.25x = 3.75

x = 3.75/0.25

x = 15 cookies.

Then the number of brownies is found as follows:

y = 26 - 15 = 11 brownies.

We suppose that she spent $19.65, and that the problems asks for the amounts of cookies and brownies purchased.

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Answer:

D

Step-by-step explanation:

Translation 4 units right and 1 unit up

Graph

Procedure

It will take 15 days for Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day.

To determine the number of days, we first represent the number of days to do a piece of work by each one of them in fractions as follows;

Fraction of work completed by Akash in 1 day = 1/20

Fraction of work completed by Sunil in 1 day = 1/30

Fraction of work completed by Rakesh in 1 day = 1/60

The total work done in 1 day can be given as;

Total work done by the three in one day = [(1/20) + (1/30) + (1/60)] = 1/10

Work done by Akash in two days = 2 × (1/20) = 2/20 = 1/10

The work done in three days (1 day of all three together + Work done by Akash in two days) = (1/10) + (1/10) = 1/5

Therefore; the total work done in 3 days = 1/5

At this rate, the total number of cycles required to finish the work =

(1) ÷ (1/5) = 5

Since each cycle has three days, the total number of days required to finish the work can be calculated as follows;

5 × 3 = 15 days

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