A roller coaster starts down the slope at 4 m/s. But 3 seconds later at the bottom of the slope it's speed is 22 m/s. What is the average acceleration?

Answer:

The dog ran 15 miles

Step-by-step explanation:

The combined speed of the 2 hunters is 7mph, therefore, they will met in 21/7 = 3 hours, becuse they are walking in opposite directions. In this 3 hours the dog kept running and thus it ran 3*5 = 15 miles. Note that the position of the dog is always between the position of both hunters, therefore when both hunters met each other, the dog will be alredy there.  

Answer:

  x = 4

Step-by-step explanation:

We assume your equation is intended to be ...

  2^(2x+7) = 2^15

Equating exponents gives ...

  2x +7 = 15

  2x = 8 . . . . . . subtract 7

  x = 4 . . . . . . . divide by 2

The value of x is 4.

The equation 2^2x+7 = 2^15 is solved by equating the exponents, simplifying the equation to find x, resulting in x = 4.

In the given question, you're dealing with an equation in the form of 22x+7 = 215. We can solve such problems by applying the rule that if ax = ay, then x = y.

Here the base for both the sides of equation is 2, thus 2z where x can be equated on both sides.

Comparing both sides of the equation, we get: 2x + 7 = 15.

To isolate x, we subtract 7 from both sides, therefore, x = (15 – 7) / 2 => x = 4.

So the solution to the equation 22x+7 = 215 is x = 4.

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Answer:

The number is 95.

Step-by-step explanation:

Solution,

Let the number be 'x'.

So, [tex]\frac{2}{5}[/tex] of 'x' = [tex]\frac{2}{5}x[/tex]

Now according to question, [tex]\frac{2}{5}x[/tex] is equal to 38.

So we can frame it as;

[tex]\frac{2}{5}x=38[/tex]

Now we solve it;

For solving it we will multiply both side by '5' using multiplication property and get;

[tex]\frac{2}{5}x\times5=38\times5\\\\2x=38\times5[/tex]

Now using division property, we will divide both side by '2' and get;

[tex]\frac{2x}{2}=\frac{38\times5}{2}\\\\x=19\times5=95[/tex]

Hence The number is 95.

Answer:

-8 ≤w ≤-2

Step-by-step explanation:

The inequality -8 ≤ w ≤ -2 combines the given conditions into a single expression stating that the variable 'w' can take any value between -8 and -2 inclusive.

In mathematics, when a single variable needs to satisfy multiple inequalities, we can write it in a combined form. Your conditions state that 'w' is less than or equal to -2, and 'w' is also greater than or equal to -8. This can be combined into a single inequality as follows: -8 ≤ w ≤ -2. This inequality indicates that the variable 'w' can take any value from -8 to -2, inclusive.

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Answer:

[tex]3\sqrt{29}[/tex] or approximately 16.16

Step-by-step explanation:

The diagonal (hypotenuse) mesures 19 inches.

The height of the computer monitor is 10 inches.

Use the Pythagorean theorem:

a and b are the triangle's legs

h is the hypotenuse

[tex]a^{2} + b^{2} = c^{2}\\ \\a^{2} + 10^{2} = 19^{2}\\ \\361 - 100 = a^{2}\\ \\a = \sqrt{261} \\\\a = 3\sqrt{29}[/tex]

It will take 4 seconds for the rock to hit the water.

To find out when the rock hits the water, we need to determine the time at which the height h becomes 0, because hitting the water means the height is 0.

Given the equation for the height h of the rock as a function of time t:

[tex]\[ h = -16t^2 + 52t + 48 \][/tex]

We set h to 0 and solve for t:

[tex]\[ 0 = -16t^2 + 52t + 48 \][/tex]

This is a quadratic equation. We can solve it using the quadratic formula:

[tex]\[ t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where a = -16, b = 52, and c = 48 .

Plugging in these values:

[tex]\[ t = \frac{{-52 \pm \sqrt{{52^2 - 4(-16)(48)}}}}{{2(-16)}} \][/tex]

[tex]\[ t = \frac{{-52 \pm \sqrt{{2704 + 3072}}}}{{-32}} \][/tex]

[tex]\[ t = \frac{{-52 \pm \sqrt{{5776}}}}{{-32}} \][/tex]

[tex]\[ t = \frac{{-52 \pm 76}}{{-32}} \][/tex]

Now we have two possible values for t:

[tex]\[ t_1 = \frac{{-52 + 76}}{{-32}} \][/tex]

[tex]\[ t_2 = \frac{{-52 - 76}}{{-32}} \][/tex]

[tex]\[ t_1 = \frac{{24}}{{-32}} = -\frac{3}{4} \][/tex]

[tex]\[ t_2 = \frac{{-128}}{{-32}} = 4 \][/tex]

Since time cannot be negative, we discuss, and the only valid solution is t = 4.

Therefore, it will take 4 seconds for the rock to hit the water.

Step-by-step explanation:

Let l be the length of track.

Running speed = 4 m/s

Jogging speed = 2 m/s

Total time taken = 2 minutes 6 seconds. = 126 seconds

That is

            [tex]\frac{l}{4}+\frac{l}{2}=126\\\\0.75l=126\\\\l=168m[/tex]

Length of track is 168 meter

To find the length of the track, we need to calculate the time it took for the sprint and the jog back, and set up an equation using the formula for distance. Simplifying the equation will give us the length of the track. The length of the track is 168 meters.

To find the length of the track, we need to use the formula for distance: distance = rate × time. Let's call the length of the track 'd' meters. The sprinter ran to the end of the track at 4 meters per second, so the time it took for the sprint is d/4 seconds. The jog back to the starting point at 2 meters per second takes a time of d/2 seconds. And the total time given is 2 minutes 6 seconds, which can be converted to seconds as 126 seconds. So we can set up the equation: d/4 + d/2 = 126.

Simplifying the equation, we can multiply each term by 4 to get d + 2d = 504. Combining like terms gives us 3d = 504. Dividing both sides by 3, we find that the length of the track is d = 168 meters.

Therefore, the length of the track is 168 meters.

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The correct statement is,

⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

To find the correct statement about the expression.

Now, We have;

The expression is,

⇒ (2x - 5) (x² + 3x - 1)

Hence, We can simplify as;

⇒ (2x - 5) (x² + 3x - 1)

⇒ (2x³ + 6x² - 2x - 5x² - 15x + 5

⇒ 2x³ + x² - 17x + 5

Thus., The correct statement is,

⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.

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Answer: 455ways

Step-by-step explanation:

This can be done according to rule of combination because it talks about selection.

In order to select r object from a pool of n objects, it is represented as nCr = n!/(n-r)!r!

Therefore to select 3 students from a class of 15students, this will give us 15C3.

15C3 = 15!/(15-3)!3!

= 15!/12!3!

= 15×14×13×12!/12!×6

= 15×14×13/6

= 455ways

This selection can be done in 455ways

The question is an illustration of combination

There are 455 ways of selecting the students

The number of students is 15, and the students to select are 3.

So, the number of selections is:

[tex]*nC_r = \frac{n!}{(n -r)!r!}[/tex]

This gives

[tex]^nC_r = \frac{15!}{(15 -3)!3!}[/tex]

Evaluate

[tex]^nC_r = 455[/tex]

Hence, there are 455 ways of selecting the students

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ANSWER: Paz have $267.30

STEP BY STEP EXPLANATION

Let be Z for Zacarías and P for Pax

Z+P= 756.80

Z= 489.50

P=756.8 - Z

P=756.80 - 489.50

P= 267.30

Answer:

The answer is x^8

Step-by-step explanation:

x^4(x^4)

=x^4*x^4

=(x*x*x*x)*(x*x*x*x)

=x*x*x*x*x*x*x*x

=x8

Answer:

1 is concentric circles

2 is concentric circles, they have same center

3 is congruent circles, they have equal radii

4 is correct

5 is correct

Step-by-step explanation:

Congruent circles are circles of the same size while concentric circles are circles that have same center but different radii. Diameter is the line passing through the center of a circle joining two points on the circumference while radius is the joining the center of the circle to any point on the circumference.

Answer:

Step-by-step explanation:

The higher standard deviation of any data represents diversified data or data having more scattered value . Average value may be same for two samples of data having different standard deviation . So option one is incorrect. 3 rd option is also incorrect.

The scores of the second test were more widespread  than the first , because its standard deviation is more for second test. option 2 is in- correct .

none is correct.

None of the supplied statements are true. The standard deviation is a measure of dispersion from an average, showing the spread of test scores, not average scores or proximity of scores. Therefore, a higher standard deviation means scores were more dispersed, not closer together.

The correct statement is None of the above are true. The standard deviation is a measure of dispersion from an average. It reflects the variability or spread in a set of data. It does not provide information about the actual scores, their averages, or whether one test's scores were generally higher or lower than another's.

In this case, a standard deviation of 3.8 for the first test and 4.8 for the second test indicates that the test scores were more spread out around the mean on the second test compared to the first. It does not point to an increase in the average test grade. Furthermore, a higher standard deviation does not mean that the test scores were closer together; actually, it's the opposite – a higher standard deviation indicates that scores were more widely dispersed.

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[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]

Solution:

Given that, we have to perform the indicated operation

[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})][/tex]

We can use BODMAS rule to perform the operation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

So, in the given expression, we have to solve for brackets first

Solve the innermost bracket

[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}][/tex]

Now solve the bracket again

[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}] = \frac{5}{8}-[\frac{4+2}{8}] = \frac{5}{8}-[\frac{6}{8}][/tex]

Now remove the parenthesis

[tex]\rightarrow \frac{5}{8} - \frac{6}{8}[/tex]

Now perform subtraction operation

[tex]\rightarrow \frac{5}{8} - \frac{6}{8} = \frac{5-6}{8} = \frac{-1}{8}[/tex]

Thus we got,

[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]

Thus the indicated operation is performed

Answer:

x^2−18x+81

x^2+2x+1

Step-by-step explanation:

we know that

A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself

so

[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]

Verify each case

case a) x^2−10x−25

we know that

[tex](x-5)^2=x^2-10x+25[/tex]

therefore

Is not a perfect square trinomial

case b) x^2−18x+81

we know that

[tex](x-9)^2=x^2-18x+81[/tex]

therefore

Is a perfect square trinomial

case c) x^2+2x+1

we know that

[tex](x+1)^2=x^2+2x+1[/tex]

therefore

Is a perfect square trinomial

case d) x^2+7x+49

we know that

[tex](x+3.5)^2=x^2+7x+12.25[/tex]

therefore

Is not a perfect square trinomial

Answer:

The required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.

Step-by-step explanation:

Consider the provided information.

The Volume square base pyramid is: [tex]V=\dfrac{a^2h}{3}[/tex]

Where a is the edge length and h is the height of the pyramid.

It is given that length of the side  is s units and height of the pyramid is h unit.

Substitute the respective values in the formula above

The Volume square base pyramid is:

[tex]V=\dfrac{s^2h}{3}[/tex]

Hence the required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.

Answer:

The answer to your question is    the second option     [tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

Expression

                       [tex][\frac{(x^{2}y^{3})^{-2}}{(x^{6}y^{3}z)^{2}}]^{3}[/tex]

Process

1.- Divide the fraction in numerator and denominator

a) Numerator  

 [(x²y³)⁻²]³ = (x⁻⁴y⁻⁶)³ = x⁻¹²y⁻¹⁸

b) Denominator

 [(x⁶y³z)²]²= (x¹²y⁶z²)³ = x³⁶y¹⁸z⁶

2.- Simplify like terms

a) x⁻¹²x⁻³⁶ = x⁻⁴⁸

b) y⁻¹⁸y⁻¹⁸= y⁻³⁶

c) z⁻⁶

3.- Write the fraction

        [tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

First, Second, and fourth answers :)

Step-by-step explanation:

Answer:

76.8

Step-by-step explanation:

Answer:

The answer is letter A, Ed, Derek, Mike, Tom

Explanation:

The question is asking for the order from the 1st to the 4th (first to last). All you have to do is to follow the instruction or draw an illustration (if you can).

If Derek is 10 yards ahead of Mike, this means that Derek's position is ahead of Mike.

If Mike is 5 yards ahead of Tom, then this means that Mike's position is ahead of Tom.

If Ed is 20 yards ahead of Derek, then this means that Ed's position is ahead of Derek.

If Derek is ahead of Mike, Mike being ahead of Tom and Ed being ahead of Derek, then you'll be able to tell the positions now.

This means that the 1st runner is Ed, while the second runner is Derek. The third runner is Mike, while the fourth runner is Tom.

Thus, this explains the answer.

The correct order of runners from 1st to 4th based on their positions relative to each other is Ed, Derek, Mike, Tom. This placement was determined by analyzing the distances between each runner as provided.

To solve this problem, let's visually represent the position of each runner in relation to each other based on the information provided. We start by listing the distances given in the question: Ed is 20 yards ahead of Derek, Derek is 10 yards ahead of Mike, and Mike is 5 yards ahead of Tom. This information allows us to order the runners from first to last.

Therefore, the correct order from 1st to 4th is Ed, Derek, Mike, Tom, which corresponds to option A. Ed,Derek,Mike,Tom.

Answer:

The solution for the given equation is 0 and 2.

Step-by-step explanation:

Given equation:

[tex]2-9|-8b+8|=-70[/tex]

To solve for [tex]b[/tex].

Solution:

In order to solve the given equation, we will first isolate the absolute value expression:

Step 1: Isolating the absolute value expression

[tex]2-9|-8b+8|=-70[/tex]

Subtracting both sides by 2.

[tex]2-2-9|-8b+8|=-70-2[/tex]

[tex]-9|-8b+8|=-72[/tex]

Dividing both sides by -9.

[tex]\frac{-9|-8b+8|}{-9}=\frac{-72}{-9}[/tex]

[tex]|-8b+8|=8[/tex]

Step 2: Set the value of the absolute value expression to positive and negative.

[tex]-8b+8=8[/tex]              and       [tex]-8b+8=-8[/tex]

Step 3: Solve for the unknown.

Solving for [tex]b[/tex].

Subtracting both sides by 8.

[tex]-8b+8-8=8-8[/tex]       and       [tex]-8b+8-8=-8-8[/tex]

[tex]-8b=0[/tex]                  and       [tex]-8b=-16[/tex]

Dividing both sides by -8.

[tex]\frac{-8b}{-8}=\frac{0}{-8}[/tex]          and       [tex]\frac{-8b}{-8}=\frac{-16}{-8}[/tex]

[tex]b=0[/tex]       and       [tex]b=2[/tex]     (Answer)

Thus, the solution for the given equation is 0 and 2.

Answer:

B

Step-by-step explanation:

For Plan A ---> you pay $50 per month flat

For Plan B,

average usage = 6 GB

cost per GB = $5 per GB

average cost per month = $5 per GB x 6 GB = $30

comparing the cost per month between the 2, we can clearly see that for plan B, $30 a month is the least expensive option

Plan B would be the least expensive option for someone who uses about 6 GB of data per month, costing $30, compared to Plan A's flat rate of $50 per month. It is important to also consider other costs and usage patterns when selecting a phone data plan.

When finding the least expensive phone data plan between a flat rate plan and a pay-per-gigabyte plan, you need to calculate the total costs based on the average data usage. In this case, Plan A offers unlimited data for a flat rate of $50 per month, while Plan B charges $5 per gigabyte of data used, with no monthly base cost.

For an average use of 6 GB of data per month:

Plan A would cost $50 every month, regardless of how much data you use.

Plan B would be 6 GB x $5/GB = $30 per month.

Comparing the two plans, Plan B is the least expensive option for someone who uses about 6 GB of data each month, as it would cost $30 as opposed to the $50 charged by Plan A.

However, it's important to consider your personal usage patterns and other potential costs, such as monthly charges for other services, occasional charges for peripherals or repairs, and any relevant annual costs or major costs when choosing a plan that fits your budget effectively.

Answer:

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Step-by-step explanation:

Given:

The combined height of 1 oak tree and 1 pine tree = 21 meters

Height of 4 oak trees = 24 meters more than 1 pine tree

To find the height of 1 pine tree and height of one oak tree.

Solution:

Let the height of one oak tree be = [tex]x[/tex] meters.

Let height of one pine tree = [tex]y[/tex] meters.

Combined height can be given as :

[tex]x+y=21[/tex]-------------[1]

Height of 4 oak trees = 24 meters more than 1 pine tree

The above statement can be given as :

[tex]4x=24+y[/tex]------------[2]

Rearranging equation [2] by subtracting both sides by [tex]y[/tex].

[tex]4x-y=24+y-y[/tex]

[tex]4x-y=24[/tex]-------------[2]

Adding rearranged equation [2] to [1].

[tex]x+y=21[/tex]

[tex]4x-y=24[/tex]

+--------------------

[tex]5x\ = 45[/tex]

Dividing both sides by 5.

[tex]\frac{5x}{5}=\frac{45}{5}[/tex]

∴ [tex]x=9[/tex]

Plugging in  [tex]x=9[/tex] in equation [1]

[tex]9+y=21[/tex]

Subtracting both sides by 9.

[tex]9-9+y=21-9\\\therefore y=12[/tex]

Height of an oak tree= 9 meters

Height of a pine tree = 12 meters

Answer:

  8 groups

Step-by-step explanation:

The number of possible groups can be found from ...

  (10.5 cups)/(1.2 cups/group) = 8.75 groups

Ms. Paulino has enough candy to give the exact amount required to 8 groups.

_____

She will have (3/4)×(1 1/5) = 9/10 of a cup of candy left over.

Answer:

C

Step-by-step explanation:

Final answer:

Traveling by car would cost a total of $356, while traveling by plane would total $535. These costs include expenses for gas, food, and lodging when traveling by car, and the airfare and cab fare when traveling by plane. Therefore, Option c is the correct answer.

Explanation:

To find the total cost for each mode of transportation for Daniel and Elizabeth, one must calculate the expenses for both the car trip and the plane trip.

Cost by Car:

Gas: $60

Food: $25 per day for 4 days for 2 people = $200 ($25 x 4 days x 2 people)

Lodging: $48 per night for 2 nights = $96 ($48 x 2 nights)

Total Car Cost: $60 (gas) + $200 (food) + $96 (lodging) = $356

Cost by Plane:

Round-trip airfare for two: $260 per person x 2 = $520

Round-trip cab fare: $15

Total Plane Cost: $520 (airfare) + $15 (cab) = $535

Comparing both options, traveling by car would cost $356, and by plane, it would cost $535. Therefore, Option C is the correct answer.

Step-by-step explanation:

Height of shadow of basketball hoop = 109 inches

Height of person = 5 foot 8 inches = 68 inches

Height of shadow of person = 62 inches

[tex]\frac{\texttt{Height of person}}{\texttt{Height shadow of person}}=\frac{68}{62}=\frac{34}{31}[/tex]

[tex]\frac{\texttt{Height of basketball hoop}}{\texttt{Height of shadow of basketball hoop}}=\frac{34}{31}\\\\\frac{\texttt{Height of basketball hoop}}{109}=\frac{34}{31}\\\\\texttt{Height of basketball hoop}=119.55inches=120inches[/tex]

Height of the basketball hoop = 120 inches

Answer:

67

Step-by-step explanation:

48=6

35=8.5

67

Answer:

A.)$68

B.)$32

Step-by-step explanation:

For 8.5 hours of babysitting, Tiva will earn $ 68

If Tiva babysits for  4 hours, she will earn $32.

Answer:20 incorrect questions

Step-by-step explanation: using the ratio formula

Add up the correct n incorrect

4+9= 13 is the total ratio

Incorrect answer ratio is 4

So to know the number of incorrect answer is

4/13* number of questions on the test

4/13* 65= 20 incorrect answer

Answer:

V≈950.3

Step-by-step explanation:

d = 12.2mm

r = 1/2 d = 6.1

V = 4/3 Pi r^3

V = 1.33 (3.14) (6.1)^3

V = 950.3

Answer:

Step-by-step explanation:

Total staff is 32

Security guards = 5/8 of 32

= 5/8 × 32

= 5 × 4

= 20 security guards

There were total 20 security guards.

Fractions are used to represent smaller pieces of a whole.

Given that, There are a total of 32 staff members working in the aquarium, 5/8 of the staff are security guards.

Total staff is 32

Security guards = 5/8 of 32

= 5/8 × 32

= 5 × 4

= 20

Hence, there were 20 security guards.

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