Darell and edmond are training for a marathon. darell runs 4 kilometers at a time while edmond prefers to run in blocks of 8 kilometers. at the end of a month, they realize that they have run same total number of kilometers. what is the smallest number of kilometers that each must have run?

The withdrawal of $170 can be represented as -$170.

Since withdrawal results in a deduction of the money from the total amount, Hence, it will be represented as a negative value.

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The probability of getting more than 52 girls in 100 births is 0.3446

This is further explained below.

Generally,  The ratio of females to boys per one hundred births is modeled here as:

[tex]\large X \sim Bin(n = 100, p = 0.5)[/tex]

Where

Bin shows binomial

n=sample size

p=sample proportion

The following is an approximation of this using the normal distribution:

[tex]\large X \sim N(\mu= np, \sigma^2 = np(1-p))\\\\\large X \sim N(\mu= 100*0.5 , \sigma^2 = 100*0.5*0.5)\\\\\large X \sim N(\mu= 50 , \sigma^2 = 25)\\\\\large X \sim N(\mu= 50 , \sigma = 5)[/tex]

In light of this, the formula for calculating the probability is as follows:

P(X > 52)

When we take into account the continuity correction factor, we obtain the following:

P(X > 52.5)

After transforming it into a regular variable according to the standards, the following is what we get:

P(Z > (52.5 - 50) / 5)

= P(Z > 0.5)

Taking this information from the usual normal tables, we get the following:

P(Z > 0.5) = 0.3085

in conclusion, the necessary probability in this scenario is 0.3085. It should be noted that we may do this without correcting the continuity, in which case:

P(X > 52)

[tex]= P(Z > (\frac{52 - 50}{ 5})[/tex]

= P(Z > 0.4)

= 0.3446

Hence, the necessary probability in this scenario is 0.3446.

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Answer:

answer c=3p in different ways.

Step-by-step explanation:

so the first one I think you put muliplys of 3..annd the second one you put a graph of 3

Answer:

6.9

Step-by-step explanation:

6 4/5 in decimal form is 6.8.
6.9 is higher than 6.8 but lower than 7.

Answer:4 and 3

Step-by-step explanation:

The solution of m for question 6 and the value of z for question 10 does not exist.

According to the question,

We have the following information,

6) 1/3 + 2m/3 = 2m/3-2/3

Now, moving the terms with the same variables in one side:

2m/3-2m/3+1/3 = -2/3

Now, when 2m/3 is subtracted from 2m/3 then we have no variable left.

So, the solution of this equation does not exist.

10) 2.5(2z+5) = 5(z+2.5)

Now, multiplying the numbers outside the bracket into bracket:

5z+12.5 = 5z+12.5

Moving the terms with the same variables on one side:

5z-5z+12.5 = 12.5

Now, when 5z is subtracted from5z then we have no variable left.

So, the solution of this equation does not exist.

Hence, the solutions of the equation 6 and equation 10 does not exist.

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In the given figure, RL, LG and RG are line segments, which are portions of a line q connecting two endpoints.

Therefore, RL, LG and RG a are another name of line q.

LQ is not another name of line q.

So, option B is correct.

Answer:

Yearly fee of $48 is better

Step-by-step explanation:

It is obvious. We know that a year have 12 months so if we compare between the $30 per months deal (which is $360 a year when we multiple it with 12) and the $48 a year deal, the difference is $312 which is a lott.

If Maria only want to use it for a month then its fine but if she want to use it more than 1 month, she definitely should choose the no 2 deal because if she even only rent it for 2 months using the no 1 deal ($30+$30=$60), the no 2 deal ($48) is far more better with a $12 difference.

Part A: Just like the top we know that its costs $34 per month and we need to know how much it would costs for 12 months/a year. So we just have to multiple it with 12=$408. Now which is better $495 or $408? Of course its $408 right? Maria could save $87 with renting the trombone than buying the trombone.

A reasonable domain and range of the function is as follows:

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

By critically observing the given sequence, we can reasonably and logically deduce that it follows the following function rule:

f(x) = -5(2)^{x - 1}

When x = 1, we have:

f(x) = -5(2)^{1 - 1}

f(x) = -5(2)^{0}

f(x) = -5

When x = 2, we have:

f(x) = -5(2)^{2 - 1}

f(x) = -5(2)^{1}

f(x) = -10

When x = 3, we have:

f(x) = -5(2)^{3 - 1}

f(x) = -5(2)^{2}

f(x) = -5(4)

f(x) = -20

When x = 4, we have:

f(x) = -5(2)^{4 - 1}

f(x) = -5(2)^{3}

f(x) = -5(8)

f(x) = -40

When x = 5, we have:

f(x) = -5(2)^{5 - 1}

f(x) = -5(2)^{4}

f(x) = -5(16)

f(x) = -80

Therefore, a reasonable domain and range of the function is given by:

Domain is equal to {1, 2, 3, 4, 5, ....}

Range is equal to {-5, -10, -20, -40, -80, ....}

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The measure of the interior angle x is 48°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

We know that sum of all the interior angles of a triangle is 180°.

The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Given, An exterior angle that measures 64° and two opposite interior angle measuring 16° and x°.

∴ x° + 16° = 64°.

x = (64 - 16)°.

x = 48°.

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From the graph, the athlete spent 2 hours biking (from hour 1 to hour 3)

And, the athlete spent 3 hours running (from hour 3 to hour 6)

Then, the athlete spent equal amounts of time biking and running is false

The transformation of the functions from f(x) to g(x) is translate 7 units right and 2 units up

The equations of the functions are given as

f(x) = 3x + 9

g(x) = 3x - 10

Let the translations from f(x) to g(x) be h and k

So, we have

g(x) = f(x + h) + k

This gives

f(x + h) = 3(x + h) + 9 + k

Open the brackets

f(x + h) = 3x + 3h + 9 + k

Substitute f(x + h) = 3x + 3h + 9 + k in g(x) = f(x + h) + k

g(x) = 3x + 3h + 9 + k

This means that

3x + 3h + 9 + k = 3x - 10

Evaluate the like terms

3h + 9 + k = - 10

This gives

3h + k = - 19

Express -19 as -21 + 2

3h + k = -21 + 2

Express 21 as 3 * 7

3h + k = -3 * 7 + 2

By comparison, we have

h = -7 and k = 2

This means that the transformation is 7 units right and 2 units up

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Answer:

Step-by-step explanation:

I believe the equation would be 3(f-5)=60.

The answer to that equation would be:

3(f-5)-60

3f-5=60           Open parentheses

3f=60+5            Take 5 to the other side

3f=65                 Add 60 and 5

f=65/3               Divide the sum of 60 and 5 with 3

f=21.6 Answer

Answer:

Given that,

Karen Gaines invested $14,000 in a money market account with an interest rate of 1.75% compounded semiannually.

Six years later, Karen withdrew the full amount to put toward the down payment on a new house.

To find the amount withdraw.

we know that, formula for finding amount of compound interest as,

where P is the principal, nis the number of years, r is the rate of interest per annum.

Given that, interest rate of 1.75% compounded semiannually, therefore number of years is 6x2=12 years.

Substitute the values we get,

Karen withdraws $17,240.15 from the account.

Using the graph, where the vertical axis represents ounces of food and horizontal axis represents the days bag was bought,

a. It took 24 days for the cat food to be 16 ounces

b. The weight of the bag before it was opened is 56 ounces,.

The graph represents the number of ounces of cat food that were left in the bag and the days it was bought.

The vertical axis represents the ounces of cat food bought while the horizontal axis represents the days since the bag was bought.

Therefore, according to the graph, the days the bag takes to contain 16ounces of cat food can be calculated as follows:

According to the y-axis, the ounces of cat food reduces as the days goes by.

If you trace 16 ounces of cat food to the horizontal side, it shows it took 24 days for the cat food to be 16 ounces.

The amount the bag weigh before it was open should be on zero's days.

Therefore, the amount of bag is 56 ounces before it was opened.

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Answer: b = -5

Step-by-step explanation:

-10 = 5/7 (-7) +b

-10 = -5 + b

-5 = b

The final stock price will be equal to $87.57.

Percentage may be defined as a form of expressing a number as a fraction of hundred. To find the percentage of a number we divide the number by the total amount and then multiply the answer with hundred. We have the initial value of stock price as $83.60, and the stock price changed by 4.75%. Now, if we find 4.75% 0f $83.60 we get

(4.75/100) × $83.60 = $3.97 which is the change occurring in price. We add this amount in the initial amount and we get $83.60 + $3.97 = $87.57. If we look at the initial and final amount of stock, we see that Luis benefitted from the stock as he gained an amount of $3.97.

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Answer:

A

Step-by-step explanation:

the slope of the line is a measure of the rate of change.

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (2, 5) ← 2 points on the line

m = [tex]\frac{5-(-3)}{2-(-2)}[/tex] = [tex]\frac{5+3}{2+2}[/tex] = [tex]\frac{8}{4}[/tex] = 2

the rate of change of y with respect to x is 2

Answer:

A) 2

Step-by-step explanation:

Rise over run,

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}}[/tex]

-2 will be [tex]x_{1}[/tex] and -3 will be [tex]y_{1}[/tex]

2 will be [tex]x_{2}[/tex] and 5 will be [tex]y_{2}[/tex]

It doesn't matter which order you place the points, for [tex]x_{1}[/tex], or [tex]x_{2}[/tex] but  [tex]x_{1}[/tex] and and [tex]y_{1}[/tex] must be one point while [tex]x_{2}[/tex] and [tex]y_{2}[/tex] must be one point.

Then, we replace the values to find:

[tex]\frac{5-(-3)}{2-(-2)}[/tex]

We then simplify this expression to [tex]\frac{8}{4} = 2[/tex]

Therefore, our slope for this function is 2

Answer:

(x, y) to (-y,-x)

Step-by-step explanation:

You have to find the reflection which is the opposite so the opposite of x is -x the opposite of y is -y!

X is the number of lillipops

y is the cost

the first point on the graph is 1 unit away from origin through x axis and 0.75 unit unit away from origin through y axis

so, x = 1 , y =0.75

The second coordinate is 2 unit away from origin through x axis and 1.5 unit away from origin through y axis

Answer: 0.75

Step-by-step explanation:

Answer:

True

False

False

False

Step-by-step explanation:

1) a rhombus is a quadrilateral that has four equal sides.  The angles do not have to be 90°, but if they are 90°, it would be a square.

2) Rhombus has all four sides equal  A rectangle does not have to have all four side lengths equal.

3) A quadrilateral means that it is a four sides figure.  A rectangle is a 4 sided figure will parallel sides and opposite sides of equal length.

4) Parallelograms mean that the opposite sides have to be equal.  A rectangle is a parallelogram, but it does not have to be a square.

Answer:

Yes, it is possible

Step-by-step explanation:

Take a function y= f(x). When it is reflected across the x-axis the x-coordinates do not change but the y coordinates become the negative of the pre-image

In other words reflection f'(x) of f(x) over the x-axis is y = -f(x)

If we reflect f'(x) over the x-axis then the resultant reflection is

f''(x) = -f'(x) = -(-f(x)) = f(x)

So we get the original image after two consecutive reflections along the x-axis

The number of seasoning batches required by the teacher is 4.

Given, there are 26 students in a class.

The teacher is adding 1 batch of hawaiian popcorn seasoning to 13 cups of popcorn.

Each student gets 2 cups of popcorn.

If 26 students are getting 2 cups of popcorn, then the total cups required by the students will be :

26×2

= 52 cups.

Now, one batch of seasoning is consumed by 13 cups.

how many batches of seasoning will be required for 52 cups = ?

⇒ 13 cups + 13 cups + 13 cups + 13 cups = 52 cups

Hence 4 batches of seasoning is required for 26 students to get two cups each popcorn with seasoning.

Therefore 4 batches of seasoning the teacher used.

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Answer:...

Step-by-step explanation:

Answer:

x = 7 km

Step-by-step explanation:

Perimeter of a polygon is  P = sum of the sides of a polygon

In this figure we are given all the sides except one designated as x and the perimeter

We can add up all the sides and solve for x

Sum of sides = 4 + 3 + 12 + 9 + x

Perimeter = 35

=> 4 + 3 + 12 + 9 + x = 35

=> 28 + x = 35

=> x = 35 - 38 = 7

The probability that you have a peanut allergy given a positive test result is 50%.

To find the probability that you have a peanut allergy given a positive test result, we can use Bayes' theorem.

Let's define the following events:

A: You have a peanut allergy.

B: The test result is positive.

We are given the following probabilities:

P(A) = 1/5 = 0.2 (1 in 5 individuals is allergic to peanuts).

P(B|A) = 0.4 (if you have a peanut allergy, the test will give a positive result 40% of the time).

P(B|not A) = 0.1 (if you don't have a peanut allergy, the test will give a positive result 10% of the time).

We want to find P(A|B), which is the probability that you have a peanut allergy given a positive test result.

Bayes' theorem states:

P(A|B) = (P(B|A) × P(A)) / P(B)

Now, let's calculate P(B):

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

P(not A) is the probability of not having a peanut allergy, which is equal to 1 - P(A):

P(not A) = 1 - P(A) = 1 - 0.2 = 0.8

Now, we can calculate P(B):

P(B) = (0.4 × 0.2) + (0.1 × 0.8) = 0.08 + 0.08

= 0.16

Now, let's calculate P(A|B) using Bayes' theorem:

P(A|B) = (P(B|A) × P(A)) / P(B)

P(A|B) = (0.4 × 0.2) / 0.16

P(A|B) = 0.08 / 0.16

P(A|B) = 0.5

Therefore, the probability that you have a peanut allergy given a positive test result is 50%.

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Answer:

He is expected to pay $2.73

Explanation:

We can solve this, by adding 0.39 7 times:

Thus, 7 pound of bananas cost $2.73

The statement that best describes the depth of the fish based on the given equation is: C. From the starting position of 3 meters below sea level, the fish is descending 7 meters per second.

A negative slope implies a negative constant rate of a linear equation. In slope-intercept form, the linear equation is expressed as y = mx + b, where the constant rate is represented as "m", while the starting value is represented as "b".

In the given scenario, the equation y = -7x - 3 models the depth, y, the fish swims below the sea level at x number of seconds.

This implies that:

The starting value (b) = -3, represents the starting position of the fish, which is 3 meters below the sea level.

-7 is the constant rate of the linear equation, which is the rate at which the fish is descending below the  sea level, which is: 7 meters per second. The best statement is therefore: C.

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