You are building an arc entrance over a roadway. The road under
the arc is 20 feet wide with a 6-foot sidewalk on both sides of
the road. Write an equation to accomplish this task.

Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

Answer:

8

Step-by-step explanation:

you first do operation in the brackets and then multiply and then divide:

2*2*2*2*2 / 4 = 8

Answer:

8

Step-by-step explanation:

\(\angle RPS = 3x + 12,\ \angle QPR = 7x + 88\ =>\ \angle QPS = 3x + 12 + 7x + 88 = 180\)

\(3x + 12 + 7x + 88 = 180\)

\(10x + 100 = 180\)

\(10x = 80\)

\(x = 8\)

Answer: 27 x 1/3

Step-by-step explanation: 27/1 x 1/3 = 9 orchards per store

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

John manages 27 apple orchards in North Georgia. He wants to split the orchards into thirds so that he can open 3 local stores.

Then the number of orchards in each store will be

⇒ 27 / 3

Then the expression can be written as,

⇒ 27 x (1/3)

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

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The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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The type of model that would be the most appropriate would be the exponential model: An exponential model is appropriate because the relationship between days and the natural log of views is linear, and the residual plot does not show a clear pattern.

This is the term that is used to refer to the process that is known to show a growth that is double its rate of growth. That is, it is used to show that there is the existence of a speed up in the rate at which the data is growing and it would follow a particular patter. This can be shown as:  y = ab^x.

This is the term that is used to show the graphical representation that is done by showing the existing relationship that exists between two variables in a graph. That would be the x variable and the y variable.

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The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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The value of x in the given triangle is 12, Option C is correct.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

here, we have,

from the given figure, we get,

The given triangle is a right angled triangle.

We need to find the value of x.

We know that cosx is adjacent side by hypotenuse.

Cos 37 = Adjacent side/ Hypotenuse

The value of cos37 degrees is 0.7654

0.7654 = x/15

15×0.7654=x

11.5 =x

12=x

Hence, The value of x in the given triangle is 12, Option C is correct.

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Answer: 14,605 pieces.

Step-by-step explanation:

In the second quarter, the company produced 795 pieces more than in the first quarter.

So, the total pieces produced in the second quarter can be calculated as:

6905 + 795 = 7700

The total pieces produced in the first semester (two quarters) can be calculated as:

6905 + 7700 = 14,605

Therefore, the company produced 14,605 pieces in the first semester.

The number of pieces the company produced in the first semester was 14,605 pieces.

The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.

In the first quarter, the company produced 6,905 pieces, as indicated in the question.

Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:

6,905 + 795 = 7,700 pieces.

To know the company's total production in the first semester, just add the productions of the two quarters:

6,905 + 7,700 = 14,605 pieces

Answer:

\(xy = 4 \)

Step-by-step explanation:

Taking the first equation , we have ,

\(\implies x + (xy)^{\frac{1}{2}} + y = 14 \\\\\implies x + \sqrt{xy}+ y = 14 \\\\\implies x + y = 14 -\sqrt{xy}\\\\\implies (x+y)^2 = (14-\sqrt{xy})^2 \\\\\implies x^2+y^2+2xy = 196 + xy -28\sqrt{xy} \\\\\implies x^2+y^2+xy = 196 - 28\sqrt{xy}\)

Now according to second equation,

\(\\\\\implies 84 = x^2+xy+y^2 \)

Plug on this value ,

\(\implies 84 = 196 -28\sqrt{xy}\\\\\implies -112 = -28\sqrt{xy}\\\\\implies \sqrt{xy}=\dfrac{112}{28}\\\\\implies \boxed{\boxed{ xy = 16 }}\)

On substituting this value in terms of one variable of the equation you can get the values of x and y .

Answer:

4/7 of 28 robots is 16.

Step-by-step explanation:

This is because 4/7 is equal to 16/28 when you simplify it. multiply 7 by four and you get 28 as your denominator and 16 as your numerator.

Answer:

Step-by-step explanation:

Radius of semicircle = 2 ft

Area of semicircle = 0.5πr² = 0.5π2² = 6.28 sq ft

Area of rectangle = 10 × 4 = 40 sq ft

Total area = 46.28 sq ft

Answer:

46.28

Step-by-step explanation:

A decrease of 50%

1) Considering the first number to be 30 we can write out

30 ------100%

15 ------- x

2) Cross multiplying it, we have:

1500=30x

x=50

Since 15 is 50% then we can subtract 50% from 100% and the answer is

A decrease of 50%

Answer:

x < 0

Step-by-step explanation:

|120+x| , if x < −120

1. Set |120+x| = 0

2. x < 0

Answer:

|120+x| x<-120 so, -121

|120+(-121)|

l-1l

=1

Answer:

The stock price beyond which 0.05 of the distribution fall is $12.44.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of $8.52 with a standard deviation of $2.38

This means that \(\mu = 8.52, \sigma = 2.38\)

The stock price beyond which 0.05 of the distribution fall is

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 8.52}{2.38}\)

\(X - 8.52 = 1.645*2.38\)

\(X = 12.44\)

The stock price beyond which 0.05 of the distribution fall is $12.44.

Solution :

Here the subintervals of equal length will be :

\([6:00, 6:30], [6:30, 7:00], [7:00, 7:30], [7:30, 8:00], [8:00, 8:30], [8:30, 9:00]\)

So thee mid points are

\(x_1 = 6:15, \ x_2=6:45, \ x_3=7:15, \ x_4=7:45, \ x_5, 8:15, \ x_6 = 8:45\)

The length of each sub-interval is = \(\frac{9-6}{6} = \frac{3}{6} = 0.5\)

So, total amount of rainfall will be :

\($=0.5 \sum^6_{i=1} f(x_i)$\)

\($=0.5\left( f(x_1)+f(x_2)+....+ f(x_6)\right)$\)

= 0.5 (2.8 + 3.5 + 4.2 + 5.6 + 3.3 + 0.4)

= 0.5 (19.8)

= 9.9

The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.

Given that,

The rate of rainfall (mm per hour) over time.

Rate of rainfall;

6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00

Time  

2.0  2.8   3.0   3.5    3.8    4.2   4.8   5.6   4.0   3.3   1.8  0.4   1.2  

We have to determine,

0.4 9:00 am 1.2.

The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is?

According to the question,

Rate of rainfall;

6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00

Time  

2.0  2.8   3.0   3.5    3.8    4.2   4.8   5.6   4.0   3.3   1.8  0.4   1.2  

Here, the midpoints sum with 6 equal subintervals are,

\(\rm x_1 = 6;15, \ x _2 = 6;45, \ x_3 = 7;15, \ x_4 = 7;45, x_5 = 8;15 , \ x_6 = 8;45\)

Then, the length of each subinterval is,

\(= \dfrac{9-6}{6}\\\\= \dfrac{3}{6}\\\\= \dfrac{1}{2}\)

The total amount of rainfall that falls between 6;00 to 9;00 am using the midpoint subinterval is,

\(\rm = \dfrac{1}{2} \sum^{6}_{i=0} f(x_i)\\\\= \dfrac{1}{2} \sum^{6}_{i=0} f(x_1)+ f(x_2) + f(x_3) + f(x_4) +f(x_5)+f(x_6)\\\\= \dfrac{1}{2} (2.8+ 3.5+4.2+ 5.6+3.3+0.4}\\\\= \dfrac{1}{2} \times 19.8\\\\= 9.9\)

Hence, The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.

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Answer:

8*(6+4)=(8*6)+(8*4)

Step-by-step explanation:

Actually the distributive property of multiplication over Addition means --

a*(b+c)=(a*b)+(a*c)

Answer:

11

Step-by-step explanation:

f(16) = 7 + 16/4

= 7 + 4

= 11

Answer:

1. Undefined

2. Negative

3. Zero

4. Positive

Step-by-step explanation:

1. Undefined, the line moves in both directions vertically. It's impossible to tell what the slope is.

2. Negative, the line is decreasing at a constant rate, the slope is negative.

3. Zero, the line doesn't increase or decrease, therefore the slope is 0. (No changes)

4. Positive, the line is increasing at a large rate, the slope is positive.

Answer:

Step-by-step explanation:

Slope intercept form of a line is

y=mx+b, where m=slope and b=y intercept

m=(y2-y1)/(x2-x1) I chose points (0,3) and (4,4) from graph so

m=(4-3)/(4-0)=1/4 so now the line is

y=x/4+b, using point (4,4) we can solve for b

4=4/4+b

4=1+b

b=3 so the line is

y=x/4+3 or more neatly

y=(x+12)/4

Answer:

A.

(i) 9.3 ft

(ii) 16.5 ft

(iii) 153.45 ft^2

B.

(i) 25.5 ft

(ii) 42 ft

(iii) 1070 ft^2

Answer:

8

6

7

4

5

these are all the answers

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

12:32

Step-by-step explanation:

8x4 is 32 so 3x4 is 12 :) hope it works and 12+32 is 44

Answer:

12 boys I hope this helps

Answer:

64

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

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

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

We want to get the equation on the graphed line.

The equation of the line is: y = 8*x - 9

Then the line is something like:

y = 8*x + b

To find the value of b, we can use one of the two points we got above.

The point (0, -9) means that when x = 0, y is equal to -9, then we can write:

-9 = 8*0 + b

-9 = b

Finally, the equation of the line is:

y = 8*x - 9

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P = 1 / n (Celia is first and Felicity is last in line) (n - 1)

P (in the line, Celia and Felicity are next to one another) = 2/n

A class consists of n kids.

These n kids line up for recess.

Out of n kids, there are two kids named Celia and Felicity.

(b) There are n positions and n! ways for n youngsters to stand in a line.

Consequently, n is the entire number of possible situations!

Felicity is standing in the last position while Celia is in the first (fixed position)

The remaining (n - 2) children can stand in the remaining 8 (n - 2) positions! ways

As a result, Celia is first in line and Felicity is last in line for the number of favorable situations, which is (n - 2)!

P (Celia is first in line and Felicity is last in line) = [(n - 2)! / n!]

P = (n - 2)! / [n(n - 1)(n - 2)!]

P = 1 / n(n - 1)

The likelihood that Celia and Felicity are on the same row as one another.

Consider Celia and Felicity as a single student, then multiply by the number of pupils (n - 1)

One can arrange (n - 1) pupils in (n - 1) positions! ways

However, there are two methods to organize Celia and Felicity among themselves.

There are therefore 2 good reasons to put Celia and Felicity adjacent to each other (n - 1)!

P(Celia and Felicity in the line are next to one another) = 2! * (n - 1)! / n!

P = 2 * (n - 1)! / n (n - 1)

P = 2/n

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