what is the 25th term of the arithmetic sequence of -84, -77, -70, ...

Answer:

In that day 1300 children and 700 adults were admitted.

Step-by-step explanation:

Since the people who enter the park are either adults or children, the sum of these two types of people must be equal to the total amount that entered the park. So we have:

children + adults = 2000

The total amount collected must be the sum of the people that entered the park multiplied by the ticket fee for each type. We have:

1.5*children + 4*adults = 4750

We now have two equations and two variables so we can solve the system.

children + adults = 2000                                             equation 1

1.5*children + 4*adults = 4750                                     equation 2

We can multiply the equation 1 by -1.5 and sum it with the equation 2 to solve for adults, we have:

-1.5*children - 1.5*adults = -3500

1.5*children + 4*adults = 4750

2.5*adults = 1750

adults = 1750/2.5 = 700

To solve for children we apply the found value for adults on the equation 1.

children + 700 = 2000

children = 2000 - 700 = 1300

In that day 1300 children and 700 adults were admitted.

Answer:

700 adults and 1300 children

Step-by-step explanation:

Let 'C' represent number of children

'A' represent number of adults

->If  2,000 people entered the park, the equation will be

C+A=2000

C=2000-A ->eq(1)

->$1.50 for children and $4.00 for adults.

$1.50C+$4.00A=$4,750

Substituting for C from above.

$1.50(2000-A)+$4.00A= $4,750

$3000-$1.50A+$4.00A=$4,750

$2.50A = $4,750 - $3000

$2.50A=$1750

A= 700

and for children:

eq(1)=>

C=2000-700

C= 1300

Thus, 700 adults and 1300 children were admitted.

Answer:

communicating results

Step-by-step explanation:

hope this helps

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]

-------------------------------------------------------------------------------

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )

n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator

n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

-----------------------------------------------------------------------------------

Answer:

m= -7

Step-by-step explanation:

using the slope formula, plug in the variables and solve

m=rise/run

m=y2-y1 / x2-x1

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Answer:

[tex]slope=-7[/tex]

Step-by-step explanation:

Use the slope formula for when you have two points:

[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:

(-4,6) (-3,-1)

[tex]\frac{-1-6}{-3-(-4)}[/tex]

Simplify

[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]

Simplify

[tex]\frac{-7}{1}=-7[/tex]

Done.

Answer:

Step-by-step explanation:

Given

Volume of Cylinder (V)= 480 cm

height (h) = 30 cm

radius (r) = ?

WE KNOW THAT WE HAVE FORMULA

Volume (V) = [tex]\pi r^{2} h[/tex]

           480 = 3.14 * r^2 *30

            480 = 94.2 r^2

             480/94.2 = r^2

               r^2 = 5.1

                 r =[tex]\sqrt{5.1}[/tex]

Therefore r = 2.3 cm

Answer:

1 μ = M μ ≠ M 2

2 μ > M μ < M 1

3 μ < M μ > M 1

If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not

reject H0 : pf = pm. T

Answer:

The balance after 7 years would be $2,548.79

Step-by-step explanation:

We are given the following in the question:

P = $1800

r = 5% = 0.05

t = 7 years

The compound interest is given by:

[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]

where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.

When compounded quarterly, n = 4

Putting values, we get,

[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]

Thus, the balance after 7 years would be $2,548.79

The front wheel of the bicycle makes approximately 18 complete revolutions.

To find the number of complete revolutions the front wheel makes, we need to know the circumference of the wheel. Let's assume the diameter of the wheel is 0.7 meters. The circumference of the wheel can be calculated using the formula C = πd, where C is the circumference and d is the diameter. Substituting the given values, C = 3.14 * 0.7 = 2.198 meters.

Since the bicycle travels 40 meters, we can divide the distance traveled by the circumference of the wheel to find the number of complete revolutions. 40 / 2.198 = 18.19.

So, the front wheel of the bicycle makes approximately 18 complete revolutions.

https://brainly.com/question/30725021

#SPJ12

Final answer:

To find the total daily water usage of the family, divide the amount of water they use for cleaning, 68.9 gallons, by the percentage of their total usage that goes to cleaning, which is 26.5%. The result is that the family uses about 260 gallons of water every day.

Explanation:

To calculate how many gallons of water the family uses every day, we need to establish the total daily water usage based on the percentage used for cleaning.

Since we know that 26.5% of their total water usage is allocated for cleaning, and they use 68.9 gallons for this purpose, we can find the total daily usage with a simple division:

Total daily water usage = Water used for cleaning / Percentage used for cleaning Total daily water usage = 68.9 gallons / 0.265 Total daily water usage = 260 gallons (rounded to the nearest whole number)

Thus, the family uses approximately 260 gallons of water per day for all their needs, including cooking, cleaning, and drinking.

Final answer:

To find out how many gallons a family uses every day, set up a proportion to find the total amount of water used for cleaning and solve for x. The family uses approximately 259.62 gallons of water every day.

Explanation:

To find out how many gallons a family uses every day, we need to determine the total amount of water used for cleaning. The question states that 26.5% of the water used each day is for cleaning, and the family uses 68.9 gallons for cleaning. We can set up a proportion to find the total amount of water used:

26.5% / 100% = 68.9 / x

Now we can solve for x by cross multiplying:

26.5x = 68.9 * 100

Dividing both sides of the equation by 26.5, we find that x is approximately 259.62.

Therefore, the family uses approximately 259.62 gallons of water every day.

Answer:

4

Step-by-step explanation:

As you only need the answer (•‿•)

Answer:

5 shirts

Step-by-step explanation:

First, subtract the shipping from her money. 45 - 2.50 = 42.50. Now divide this by the price of each shirt. 42.50 ÷ 8.50 = 5. The shipping fee only applies once because it is for the entire order.

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given:

Skylar has 1/2 of her sub left from lunch she wants to cut it into thirds

Question asked:

Find the length of each piece ?

Solution:

Sub left from lunch = [tex]\frac{1}{2}[/tex]

As she want to cut into third, we will divide [tex]\frac{1}{2}[/tex] into [tex]\frac{1}{3}[/tex]

[tex]=\frac{1}{2}\div\frac{1}{3}\\ \\ =\frac{1}{2}\times\frac{3}{1} \\ \\ =\frac{3}{2}[/tex]

Thus, length of each piece will be [tex]\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

the answers for "in e^3" is 3

                          "in e^2y" is 2y

                          "e^in 1" is 1

                          "e^in 5x" is 5x

Answer: 3, 2y, 1, 5x.

We have to simplify the given expressions.

We use the formula: [tex]ln(e^a)=a[/tex].

So, [tex]ln(e^3)=3[/tex], here a = 3.

[tex]lne^{2y}=2y[/tex], here a = 2y.

We will use that: ln(1) = 0 and [tex]e^{ln(b)}=b[/tex]

[tex]e^{ln(1)}=e^0=1[/tex]

[tex]e^{ln(5x)}=5x[/tex], here b = 5x.

Learn more: https://brainly.com/question/13769924

Answer:

45.9ft/s

Step-by-step explanation:

Simply plug your given value into the function

[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]

Answer:

a) [tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

Part a

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

Part b

For this case we can use an estimator for p as [tex]\hat p=0.5[/tex]

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Answer:

[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]

Complete Question:

Justify the rationale behind Ms Calcutta's decision to use the circumcenter

Answer:

Check below for the answer and explanations.

Step-by-step explanation:

Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.

Answer:

Number of seconds to reach maximum height = 3 seconds

Maximum height = 144 ft

Step-by-step explanation:

We are given that;

s(t) = -16t² + 96t

Now, s(t) is a function whose graph is an upside-down parabola, so the maximum s value occurs at the vertex.

Thus, the applicable formula for coordinate of vertex is t = -b/(2a) where a is the coefficient -16 and b is 96

Thus,t = -96/(2 x - 16)

t = 96/32

t = 3

Thus maximum height will be at 3 seconds.

Thus;

Max height = s(3) = -16(3)² + 96(3)

Max height = -144 + 288 = 144 ft

The object will reach its maximum height of 144 feet in 3 seconds.

Given information:

An object is projected upward from ground level with an initial velocity of 96 ft per​ sec.

The height in feet after t seconds is given by [tex]s(t)=-16t^2+96t[/tex].

Now, it is required to find the time at which the object will reach its maximum height.

The object will reach maximum height when velocity of the object becomes zero.

So, the velocity of the object can be written as,

[tex]s(t)=-16t^2+96t\\v(t)=\dfrac{d(s(t))}{dt}=-32t+96[/tex]

So, the time at maximum height can be calculated as,

[tex]v(t)=-32t+96=0\\t=3[/tex]

So, after 3 seconds the object will reach its maximum height.

Now, the maximum height of the object will be,

[tex]s(t)=-16t^2+96t\\s(3)=-16\times 3^2+96\times 3\\s(3)=144\rm \; ft[/tex]

Therefore, the object will reach its maximum height of 144 feet in 3 seconds.

For more details, refer to the link:

https://brainly.com/question/11535666

Answer:

Add 8x to both sides of the inequality

Step-by-step explanation:

took the quiz

Final answer:

The shortest side of the new similar triangle, where the longest side is 9 inches, is found to be 4.8 inches. This is determined by using the scale factor 3/5, obtained from the original triangle with sides 15 inches, 8 inches, and 10 inches.

Explanation:

The student asks for the length of the shortest side of a new triangle similar to the one given, with the length of the longest side being 9 inches. To find this, we need to use the concept of similar triangles. Similar triangles have proportional corresponding sides.

The original triangle has sides of lengths 15 inches (longest side), 8 inches (shortest side), and 10 inches. Given that the longest side of the new triangle is 9 inches, we can find the scale factor by dividing the new longest side by the original longest side: 9 inches / 15 inches = 3/5.

Now, we use this scale factor to find the length of the shortest side in the new triangle: 8 inches (original shortest side) x 3/5 (scale factor) = 4.8 inches.

Therefore, the length of the shortest side of the new triangle is 4.8 inches.

Learn more about Similar Triangles here:

https://brainly.com/question/34830045

#SPJ11

Answer:

Step-by-step explanation:

hello :

Ax + 3x = bx + 5

Ax + 3x-bx = bx-bx + 5

x(A+3-b) =5

x= 5/(A+3-b)

Answer:

The answer is 5, 10, 15, 20 or any positive multiples of 5

Step-by-step explanation:

Since the ratio of green grapes to the total number of grapes is 9:14 and there are only purple and green grapes on the shelf. It implies the total number of purple grapes to overall grapes is 5:14.

Since this ratio is already at it's lowest form, it implies the possible number of purple grapes are 5, 10, 15, 20 or any positive multiple of 5.

Answer:

The x-intercepts would be where the line hits the x-axis, so the x-intercepts would be:

-3, 2, and 5.

Step-by-step explanation:

Answer:

q4 is -3,2,5

and for q3 is the start point

Answer:

The answer to your question is the letter a

Step-by-step explanation:

 |    1    4    -1   |      |  2    -1   |

 |    3   2    2   |      |  0     3  |         Product  = 2 x 3   and 3 x 2  = 2 x 2

                              | 5     2  |          It is possible to do this product,

                                                      the result will be a 2 x 2 matrix

Process

1.- Multiply first row by first column and second row by second column.

2.- Multiply the second row by the first column and second row by the second column.

  = (1 x 2) + (4 x 0) + (-1 x 5) = 2 + 0 - 5 = -3

  = (1 x -1) + (4 x 3) + (-1 x 2) = -1 + 12 - 2 = 9

  = (3 x 2) + (2 x 0) + (2 x 5) = 6 + 0 + 10 = 16

  = (3 x -1) + (2 x 3) + (2 x 2) = -3 + 6 + 4 = 7

Result

             |  3   9  |

             | 16   7  |    

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------------------

Answer: The population is 1,625.

So the equation is:

p = 35t + 1,450.

t = the number of years since 2015.

2020 - 2015 = 5.

So now we are in 2020, which is 5 years ahead from 2015.

So: t = 5.

Now we need to rewrite the equation, then evaluate.

35(5) + 1,450 =

175 + 1,450 =

Answer:

2 grams is bigger than 2.300 mg.

Step-by-step explanation:

1 milligram is equal to 0.001 gram.

1 gram is equal to 1000 milligrams.

If this helped you, Brainliest is appreciated.

Answer:

2 grams is bigger

Step-by-step explanation:

Two grams is bigger than 2.3 milligram . This is because 1 gram is equivalent to 1000 milligrams. To work that out you would multiply 2 by 1000, which is 2000

1 gram=1000 milligram

1) Multiply 2 by 1000.

[tex]1000*2=2000 mg[/tex]

However if it was a misplaced decimal and it was meant to be 2300 milligrams, then 2300 milligrams would be bigger.

Answer:

C

Step-by-step explanation:

You distribute the 11 with the numbers in the parenthesis

By interpreting the stem-and-leaf plot, it is found that no zoos have exactly 17 sloths.

In the stem-and-leaf plot, we locate the stem which corresponds to the number '1', and then we check the corresponding leaves. In this case, the appropriate stem is '1' and the leaves under this stem correspond to the tens place of the number of sloths. So, now we check the leaf '7' under stem '1'. Seeing the 7 in the ones place next to the stem of 1, we find that there is no such instance in the plot. Therefore, we can conclude that no zoos have exactly 17 sloths.

https://brainly.com/question/31866107

#SPJ3

Stem-and-leaf plots represent numerical data in statistics. The analysis of the provided stem-and-leaf plot reveals that 2 zoos have exactly 17 sloths.

Stem-and-leaf plots are used in statistics to represent numerical data. Each observation is divided into a stem (leading digit(s)) and a leaf (final significant digit). In the given plot, if a zoo has exactly 17 sloths, then the stem is 1 and the leaf is 7. By looking at the plot, it can be observed that there are 2 zoos with exactly 17 sloths.

here is the full question- A zookeeper created the following stem-and-leaf plot showing the number of sloths at each major zoo in the country:

0 3

1 6 7 7

2 0 4

3 0 1 1 2 4 7 9 9

4 1 2 3 5 7

Key: 4|1=41 sloths How many zoos have exactly 17 sloths? x=frac =frac (-)²(-)² 2005.

Answer:

CI=[ 7.1302,7.2698]

we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Step-by-step explanation:

-Given that the sample size, n=1546  the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]

-The 95% confidence interval can be calculated using the formula:

[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]

The confidence intervals is therefore 7.1302,7.2698]

Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Answer:

20 gallons per 180 miles

Step-by-step explanation: