67.5% of the 540 km road between the two cities is paved, while the rest is unpaved. the average speed of the car on paved roads was 25 km/h higher than on unpaved roads. find the speed of the car on a paved road if it took 10 hours to cover the entire road​

The 95% confidence interval for the mean test score in the population is

(639.51, 639.89).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation shown below as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are shown as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 407 - 1 = 406 df, is t = 1.96.

The parameters for this problem are given as follows:

\(\overline{x} = 639.7, s = 19.3, n = 407\)

The lower bound of the interval is given as follows:

\(639.7 - 1.96 \times \frac{19.3}{\sqrt{407}} = 639.51\)

The upper bound of the interval is given as follows:

\(639.7 + 1.96 \times \frac{19.3}{\sqrt{407}} = 639.89\)

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Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

1 glass..........1/4 liter

n glass.......... 5 liters

n = 1 x 5 : 1/4

n = 5 x 4

so there are 20 glasses

Answer:

16.0"

Step-by-step explanation:

ASSUME the pyramid is a square right pyramid.

height = 15"

base side length = 11"

(Following edited/corrected thanks to cwrw238)

Slant height

= sqrt(5.5²+15²)   using Pythagoras theorem

= sqrt(255.25)

=  15.98"

Answer:

Slant height = 15.98 in to nearest hundredth.

Step-by-step explanation:

Use Pythagoras theorem.

The triangle we want  has a height of 15 , base of 1/2*11 = 5.5 and we need the length of the hypotenuse.

h^2 = 5.5^2 + 15^2 = 255.25

h = 15.976.

Answer:

The product of their ages is 36

The sum of the girls age is 13

two sister=?

13 by 36

26

Using the probability multiplication we know that the defect probability of the final product will be 7.5%.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The higher the likelihood, the more likely it is that the event will take place.

So, the probability formula is:

P(E) = Favourable events/Total events

So, in the given situation, the number of components integrated:

500

Defect probability of each component:

0.015%

Then, the defect probability of the final product:

= 500 * 0.015

= 7.5%

Therefore, using the probability multiplication we know that the defect probability of the final product will be 7.5%.

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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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The probability of rolling a 6 will be 3/8 or 0.375

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

So let x = P(1) = P(2) = P(3) = P(4) = P(5)

Since the probability of 6 is three times greater than the others, so P(6) = 3x.

We know that the sum of the probability sample space must be one,

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

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

= 8x = 1 = x = 1/8 (0.375)

So finally, the probability of rolling a 6 in a die will be 3/8

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Answer:

y-2=1/2(x+8)

Step-by-step explanation:

Answer:

answer is D

Step-by-step explanation:

Hope this helped you. Have a nice day!

Answer:

19 sides

Step-by-step explanation:

Sum of angles of n-side polygon = 180 *(n - 2)

180 *(n -2) = 3060

Divide both sides by 180

n- 2 = 3060/180

n - 2 = 17

n = 17+2

n = 19

Answer:

19 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here sum = 3060° , then

180° (n - 2) = 3060° ( divide both sides by 180° )

n - 2 = 17 ( add 2 to both sides )

n = 19

The polygon has 19 sides

Given, Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph.Both Jada and Elena start walking along a walking trail at the same time.

Let us determine the distance covered by both of them.Distance travelled by Jada in 3 hours is:Distance = Speed × Time= 3 mph × 3 hours= 9 miles Distance travelled by Elena in 3 hours is:Distance = Speed × Time= 2.8 mph × 3 hours= 8.4 miles Thus, Jada will walk 0.6 miles farther than Elena after 3 hours.

To determine how far Jada will walk after 3 hours, we need to calculate the distance traveled based on her speed.

Jada walks at a speed of 3 miles per hour (mph), so we can calculate her distance using the formula:

Distance = Speed × Time

Plugging in the values, we have:

Distance = 3 mph × 3 hours

Distance = 9 miles

Therefore, Jada will walk a distance of 9 miles after 3 hours.

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The given information is as follows:

Jada walks at a speed of 3 mph and Elena walks at a speed of 2.8 mph. If they both begin walking along a walking trail at the same time.

Therefore, Jada will walk 9 miles after 3 hours.

The distance covered by Jada after 3 hours can be calculated as follows:

Distance = Speed x Time

Since Jada walks at a speed of 3 mph, the distance covered by her in 3 hours can be calculated as:

Distance covered by Jada = 3 mph x 3 hours

= 9 miles.

Therefore, Jada will walk 9 miles after 3 hours.

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Answer:

1km= 1000m

\(\frac{650}{1000}\)

=\(\frac{13}{20}\) (simplified)

SOLUTION

Step 1 :

In this question, we were told that A cosmetics company tested a new lotion.

Of the 2,500 people tested, 15 had an allergic reaction.

What percent of the people tested did not have an allergic reaction to the new lotion?

Step 2 :

Step-by-step explanation:

\( \frac{x}{6} = \frac{9}{20} \\ \)

\(x \times 20 = 9 \times 6\)

\(20x = 54\)

\(x = \frac{54}{20} \\ \)

\(x = 2.7\)

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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(a) The graph of y = e√x is sketched, and the region R is shaded. (b) The integral ∫[0, a] e√x dx is written as the expression for the area of region R. (c) The integral from part (b) is evaluated using substitution and integration by parts to find the area of region R.

(a) The graph of y = e√x represents a curve that starts at the origin and increases exponentially as x increases. The region R is the area under this curve, bounded by the y-axis and the line y = e. It is shaded to indicate the enclosed region.

(b) To find the area of region R, we need to integrate the function e√x with respect to x. The integral from x = 0 to x = a represents the area of the region bounded by the curve, the y-axis, and the line y = e. Thus, the integral is ∫[0, a] e√x dx.

(c) To evaluate the integral, we can make the substitution u = √x, which transforms the integral to ∫[0, √a] 2e^u u du. Then, using integration by parts, we let dv = u du and differentiate u to find v = u^2/2. Applying the integration by parts formula, we obtain [u^2/2 * e^u] evaluated from 0 to √a minus the integral of v du. Simplifying and evaluating the limits, we find the area of region R.

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pretty sure its E

just substitute x and z for a and c

hope it helps

The least cοmmοn denοminatοr οf the fractiοn is 24.

Part οf a whοle is a fractiοn. The quantity is written as a quοtient in mathematics, where the numeratοr and denοminatοr are divided. Each is an integer in a simple fractiοn. Whether it is in the numeratοr οr denοminatοr, a cοmplex fractiοn cοntains a fractiοn. The numeratοr and denοminatοr οf a cοrrect fractiοn are οppοsite each οther.

Here the given fractiοn is \($\frac{11}{8}\ \text{and}\ \frac{7}{12}\).

We knοw that Least cοmmοn denοminatiοn οf the fractiοn is lοwest cοmmοn multiple. Then, factοrs οf the denοminatοr

8 = 2*2*2

12=2*2*3

Nοw LCD = 2*2*2*3 = 24.

Hence the least cοmmοn denοminatοr οf the fractiοn is 24.4.

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Answer:

\(5x(x-8)\)

Step-by-step explanation:

Factor \(5x\) out of \(5x^{2} -40x\)

The solution to the equation is x = 17/30.

To solve the equation, start by combining like terms on both sides.

On the left side, we have the fraction 2/3 and the term -4x.

On the right side, we have the fraction 7/2 and the term -9x.

To combine the fractions, we need a common denominator.

The least common multiple of 3 and 2 is 6.

So, we can rewrite 2/3 as 4/6 and 7/2 as 21/6.

Now, the equation becomes:

4/6 - 4x = 21/6 - 9x

Next, let's get rid of the fractions by multiplying both sides of the equation by 6:

6 * (4/6 - 4x) = 6 * (21/6 - 9x)

This simplifies to:

4 - 24x = 21 - 54x

Now, we can combine the x terms on one side and the constant terms on the other side.

Adding 24x to both sides gives:

4 + 24x - 24x = 21 - 54x + 24x

This simplifies to:

4 = 21 - 30x

Next, subtract 21 from both sides:

4 - 21 = 21 - 30x - 21

This simplifies to:

-17 = -30x

Finally, divide both sides by -30 to solve for x:

-17 / -30 = -30x / -30

This simplifies to:

x = 17/30

So the solution to the equation is x = 17/30.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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At the end of the first year, Shota will have earned amount  \$400.00$400.00dollar sign, 400.00 in interest.

Shota invested $2000 in a certificate of deposit that earns 2% interest each year. This means that for every $100 invested, Shota will earn $2 in interest. Therefore, for the $2000 invested, Shota will earn $40 in interest each year ($2 x 2000 = $4000, and then divide by 100 to get $40).

At the end of the first year, Shota will have earned $400.00 in interest ($40 x 10 = $400).

Shota invested $2000 in a certificate of deposit that earns 2% interest each year. After the first year, Shota will have earned $400.00 in interest.

At the end of the first year, Shota will have earned amount \$400.00$400.00dollar sign, 400.00 in interest.

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Answer:

x1, y1

Step-by-step explanation:

Answer:

(x1,y1)

Step-by-step explanation:

Answer:

21/(-6)

Step-by-step explanation:

9/(-3) + 4/(-8)            [find the common denominators]

72/(-24) + 12/(-24)

84/(-24)                    [simplify]

21/(-6)

Answer: I think it is E sorry if I am wrong Step-by-step explanation: she returned to the same place so it going backwards (subtracting)

Answer:

I think it's E but not 100% sure

Step-by-step explanation:

Not completely sure on this but I think it's either A or E. I'm leaning towards E more than A though.