HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4

Answer:

False

Step-by-step explanation:

A regular sided polygon means all the sides have the same length and all angles the same size.  This polygon has 2 sides the same length, not 3 sides the same length, so it cannot be regular.

Hi there! :)

Answer:

Length = 4 cm

Width = 9 cm

Step-by-step explanation:

Here's the information we know:

- Perimeter = 26 cm

- Width = x (I just replaced the width by "x" because it's what we are looking for)

- Length = x - 5

Now before we can do anything, you need to know what the formula for the perimeter of a rectangular is: P = (2 × Length) + (2 × Width)

Replace all the information you know in the formula and solve the equation by isolating "x":

P = (2 × Length) + (2 × Width)

26 = ( 2 × (x - 5)) + (2 × x)

Multiply "2" and "x" together → 2 × x = 2x

26 = ( 2(x - 5)) + 2x

Distribute the "2" to the entire parentheses → 2 × x = 2x & 2 × -5 = -10

26 = 2x - 10 + 2x

Add similar terms together → 2x + 2x = 4x

26 = 4x - 10

Add 10 to each side of the equation → 26 + 10 = 36

36 = 4x

Divide each side of the equation by 4 → 36 ÷ 4 = 9

9 = x ⇒ Measure of the width

Since the lenght is 5 centimeter less than the measure of the width, in order to find the measure of the length you'll need to subtract "5" from the measure of the width, which is "9":

9 - 5 = Length rectangle

9 - 5 = 4 ⇒ Length rectangle

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

+8

Step-by-step explanation:

They gained 8 yards so it is +8.

Answer: + 8

Step-by-step explanation: A gain is considered a good thing. It is represented with a positive integer. Here, the gain is represented by +8, or simply 8.

Answer:

8/pi

Step-by-step explanation:

To find the rate of change from 0 to pi/2  we need the values at 0 and pi/2

f(0) = -4

f(pi/2) = 0

rate of change = change in f(x)/ change in x

                        = (f(x2) -f(x1))/( x2-x1)

                        = (0--4) / (pi/2 - 0)

                         = (0+4) / (pi/2)

                        = 4 / (pi/2)

                          = 8/pi

Answer:

38 grams

Step-by-step explanation:

7.6*5=38

Answer:

8, 9

Step-by-step explanation:

1/2x + 2(x + 1) = 22

1/2x + 2x + 2 = 22

1/2x + 2x = 20

5/2x = 20

5x = 40

x = 8

8, 9

4 + 18 = 22

Answer:

8 and 9

Step-by-step explanation:

hope this helps!

Answer:

2 sqrt(3) = n

k = 4 sqrt(3)

Step-by-step explanation:

We know that cos 30 = adjacent/ hypotenuse

cos 30 = 6 /k

Multiply each side by k

k cos 30 = 6k * k

k cos 30 = 6

Divide each side by cos 30

k cos 30/ cos 30 = 6/ cos 30

k = 6 / cos 30

k = 6/ (sqrt(3)/2)

k =12 / sqrt(3)

We cannot leave the sqrt in the denominator

k = 12 / sqrt(3) * sqrt(3)/sqrt(3)

k = 12 sqrt(3)/3

k = 4 sqrt(3)

We know tan 30 = opposite/adjacent

                tan 30 = n/6

Multiply each side by 6

                  6 tan 30 = n

                  6 * (sqrt(3)/3) = n

                   6/3 * sqrt(3) = n

                    2 sqrt(3) = n

The correct option is d. The values are 2 sqrt(3) = n, k = 4 sqrt(3)

 We know that cos 30 = adjacent/ hypotenuse

Multiply each side by k

k cos 30 = 6k * k

k cos 30 = 6

Divide each side by cos 30

k cos 30/ cos 30 = 6/ cos 30

k = 6 / cos 30

k = 6/ (sqrt(3)/2)

k =12 / sqrt(3)

We cannot leave the sqrt in the denominator

k = 12 / sqrt(3) * sqrt(3)/sqrt(3)

k = 12 sqrt(3)/3

k = 4 sqrt(3)

We know tan 30 = opposite/adjacent

tan 30 = n/6

Multiply each side by 6

6 tan 30 = n

6 * (sqrt(3)/3) = n

6/3 * sqrt(3) = n

2 sqrt(3) = n

Through hypothesis testing, we cannot reject the null hypothesis at the 1% level of significance. Thus, there is no strong evidence to suggest that the mean nicotine content is greater than what is advertised.

The subject here is statistics, specifically hypothesis testing. For this problem, we are asked to test the null hypothesis H0: m = 1.5 against the alternative hypothesis Ha: m > 1.5 at 1% level of significance.

Using the given data, we calculate the test statistic (z) using the formula: z = (x - µ) / (s/√n), where x is the sample mean, µ is the population mean, s is the standard deviation, and n is the sample size. Substituting the given values, we get z = (1.52 - 1.5) / (0.1/√400) = 2.

The z-score at 0.01 level of significance is -2.33 on the left and 2.33 on the right. As our test statistic (2) falls within this range, we fail to reject the null hypothesis (H0: m = 1.5). This suggests that there's no strong evidence to support that the mean nicotine content is greater than advertised.

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Answer:

The price of one cookie is $1.25 and the price of one cake is $15.

Step-by-step explanation:

Let $x be the price of one cookie and $y be the price of one cake.

1. On Monday, Sean bought 3 cookies and 5 cakes, then he spent $(3x+5y) and this is $78.75. Thus,

[tex]3x+5y=78.75.[/tex]

2. On Tuesday, Sean bought 8 cookies and 2 cakes, then he spent $(8x+2y) and this is $40. Thus,

[tex]8x+2y=40.[/tex]

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}3x+5y=78.75\\8x+2y=40\end{array}\right.[/tex]

Multiply the first equation by 2 and the second equation by 5 and subtract them:

[tex]2(3x+5y)-5(8x+2y)=2\cdot 78.75-5\cdot 40,\\ \\6x+10y-40x-10y=157.5-200,\\ \\-34x=-42.5,\\ \\x=\$1.25.[/tex]

Then

[tex]8\cdot 1.25+2y=40,\\ \\2y=40-10,\\ \\y=\$15.[/tex]

Question

G.O. Is going on a hike in the mountains on a hot summer day. He has 4/5 gallon of water that he spilt into 4 bottles. What fraction of a gallon is in each bottle?:

Answer:

Answer:

Jo's drink is bigger than the tropical punch, both have more orange juice than pineapple.

Step-by-step explanation:

Tropical punch is 2 cups of pineapple juice and 3 cups of orange juice

We express those numbers is fraction ,  to get the denominator we add the 2 parts, 2 cups + 3 cups= 5

Then,  

pineapple juice=2/5

orange juice=3/5

Drink is 3 cups of pineapple juice with 4 cups of orange juice

Denominator is 3  + 4 = 7

pineapple juice=3/7

orange juice=4/7

Jo's drink is bigger than the tropical punch, both have more orange juice than pineapple.

Answer:

B. 1/7

Step-by-step explanation:

The triangles are similar, so the ratios of corresponding sides are the same.

... UV/XY = 3/21 = 1/7 . . . . . matches B

_____

When we talk about the ratio "A to B", we usually mean A:B or A/B. There's the possibility that the question could be interpreted to mean, "what factor do I multiply by to get from A to B?" In that case, the result here would be 7, because XY is 7 times the length of UV.

The only triangle with the usual triangle centers coincident is an equilateral triangle.

The centroid is the meet of the medians, which are the segments from a vertex to the midpoint of its opposite side. The centroid is the balance point of the triangle.  It always divides the medians into a 2:1 ratio, the long piece connected to the vertex.

The circumcenter is the center of the circumcircle, which is the circle through the vertices.  That's only going to be the centroid when that 2 part of the 2:1 ratio is the same for each median.  That's only going to happen when the sides are the same length so the centroid makes congruent triangles.

The incenter is the center of the inscribed circle, which is the meet of the angle bisectors of each vertex.  Again it wont be the centroid unless the sides are equal.

The orthocenter is the meet of the altitudes and it's the same story.

An equilateral triangle is the only type of triangle where its circumcenter, incenter, centroid, and orthocenter coincide at the same point. This unique property emphasizes the symmetry of the equilateral triangle.

The type of triangle where its circumcenter, incenter, centroid, and orthocenter are all at the same point is an equilateral triangle. In an equilateral triangle, all sides are equal in length, and all angles are equal to 60 degrees.

An equilateral triangle has the unique property that its circumcenter (intersection of perpendicular bisectors of sides), its incenter (intersection of angle bisectors), its centroid (intersection of medians), and its orthocenter (intersection of altitudes) all coincide at the same point, which is the geometric center and also the triangle's center of mass.

This property is exclusive to equilateral triangles and emphasizes their symmetry. This also applies in three-dimensional forms such as in an icosahedron where each face is an equilateral triangle, demonstrating further the symmetrical properties of these shapes.

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Answer:

3%

Step-by-step explanation:

In order to find out the percent in commissions a car salesman received, you need to divide $1953 by $65100.  The result is .03, which translates to 3%.

Hope that helps!

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

Read two points from graph

y-intercept: (0, -3) → b= -3

x-intercept: (-2, 0).

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{0-(-3)}{-2-0}=\dfrac{3}{-2}=-\dfrac{3}{2}[/tex]

Therefore we have the equation of a line in slope-intercept form:

[tex]y=-\dfrac{3}{2}x-3[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]

[tex]y=-\dfrac{3}{2}x-3[/tex]     multiply both sides by 2

[tex]2y=-3x-6[/tex]      add 3x to both sides

[tex]3x+2y=-6[/tex]

Answer:

y=mx+b

Step-by-step explanation:

Look at the picture.

[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]

We have the right triangle x, y and r. From the Pythagorean theorem we have:

[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]

We have the point

[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]

Substitute:

[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]

[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]

Final answer:

The cosecant of the angle can be determined as the reciprocal of the sine value of the angle, which is √3/√5.

Explanation:

Calculating the cosecant of the angle:

To find the cosecant of the angle, we need to use the definition of cosecant which is the reciprocal of the sine function. Since the point (-2/3, √5/3) lies on the unit circle, the y-coordinate (√5/3) can be used as the sine value of the angle.

Therefore, the cosecant of the angle is the reciprocal of the sine value, which is 1/(√5/3) = √3/√5.

[tex]0.001y^{12}=(0.1)^3y^{4\cdot3}=(0.1)^3(y^4)^3=(0.1y^4)^3\\\\0.008b^6=(0.2)^3b^{2\cdot3}=(0.2)^3(b^2)^3=(0.2b^2)^3\\\\-\dfrac{2}{27}a^{15}=\left(-\dfrac{2}{3}\right)^3a^{5\cdot3}=\left(-\dfrac{2}{3}\right)^3(a^5)^3=\left(-\dfrac{2}{3}a^5\right)^3\\\\\text{Used:}\\\\(a^n)^m=a^{n\cdot m}\\\\(ab)^n=a^nb^n[/tex]

The expressions 0.001y^12, 0.008b^6 and -8/27a^15 can be written as the cubes of the monomials 0.1y^4, 0.2b^2 and -2/3a^5 respectively.

The expressions provided can be written as a cube of a monomial. A monomial is a single term, and the cube of a monomial is a term raised to the third power. First, let's begin by expressing the coefficients as cubes:

Then, for the variables, divide the exponent by 3:

Combining the cubed coefficient and the cubed variable, we have:

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A recursive rule for a geometric sequence:

[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]

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

[tex]a_1=2;\ a_n=\dfrac{4}{9}a_{n-1}\to r=\dfrac{4}{9}[/tex]

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

The exciplit rule:

[tex]a_n=a_1r^{n-1}[/tex]

Substitute:

[tex]a_n=2\left(\dfrac{4}{9}\right)^{n-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\left(\dfrac{4}{9}\right)^{-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\dfrac{9}{4}\\\\\boxed{a_n=\dfrac{9}{2}\cdot\left(\dfrac{4}{9}\right)^n}[/tex]

Answer: Choice C

The first inequality is [tex]124+121+x \ge 400[/tex]

The second inequality is [tex]x \ge 155[/tex]

Replace x with whatever letter your teacher is using

=========================================================

Let x be the number of cans collected on week 3

Add this to the previous totals (for weeks 1 and 2) to get 124 + 121 + x. I'm going to leave this as is and not simplify. This is so the answer matches up. This total must be greater than or equal to 400, meaning 124+121+x can be 400 or larger.

124+121+x >= 400

245+x >= 400 .... combine like terms

x >= 400-245 .... subtract 245 from both sides

x >= 155

So you need to collect at least 155 cans for the third week so that you'll have at least 400 cans total.

Final answer:

To model the situation with an equation, use the quantities of CDs and books as variables c and b, and their prices to create the equation 10c + 6b = 32, which represents spending exactly $32.

Explanation:

To create an equation modeling the situation where you want to spend exactly $32 on CDs and books, we need to use the given prices for each item. Let c represent the number of CDs you buy at $10 each, and let b represent the number of books you buy at $6 each.

The total amount spent will be the sum of the amount spent on CDs and the amount spent on books. Using the price of each item, we can write the following equation:

10c + 6b = 32

This equation can now be written in standard form, which is Ax + By = C, where A, B, and C are integers, and A is non-negative. Therefore, our equation in standard form is:

10c + 6b = 32

Answer:

D. y-intercept = 5

Step-by-step explanation:

I majored in Mathematics

Answer:

Jessica reads 15 newspaper articles

Step-by-step explanation:

Jim reads 3

Jessica read 5 times MORE than Jim

5 x 3= 15

So Jessica reads 15 articles

Answer:

No the two expressions are not equivalent.

Step-by-step explanation:

the given two expressions t=5 and t=9 are not equivalent because t being a variable cant take two numbers at a same time.however if they are placed in given two expressions of 't' such that that they give equal value when the first expression gives a value 'a' at t=5 while the other expression gives a value 'a' at t=9 then those two expressions will be equal.

Answer:

your answer is D.)

Step-by-step explanation:

The third quartile value for the given data 20,21,24,25,28,29,35,37,42 is 36.

The median is the middle value of a data which is arranged in either ascending/descending order.

The lower/first quartile is the median of the bottom half of the data.

The higher/third quartile is the median of the upper half of the data.

Arranging the given sequence in ascending order:

20,21,24,25,28,29,35,37,42

Calculating the median of this sequence:

Median(odd no. of terms) = ((n+1)/2)th term

Median(9 terms) = ((9+1)/2)th term

Median = 5th term

Median = 28

Now, the upper half of the data is:

29,35,37,42

Median(even no. of terms) = Median of the two middle terms

Median = ((35+37)/2)

Median = 36

Hence the third quartile of the given data is 36

Learn more about quartiles here:

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Answer:

a. x-3/x+2

Step-by-step explanation:

Answer: A

Step-by-step explanation:

 [tex]\dfrac{x^{2}+x-6}{x^{2}-4}*\dfrac{x^{2}-9}{x^{2}+6x+9}[/tex]

[tex]=\dfrac{(x+3)(x-2)}{(x+2)(x-2)}*\dfrac{(x-3)(x+3)}{(x+3)(x+3)}[/tex]

[tex]=\dfrac{(x+3)}{(x+2)}*\dfrac{(x-3)}{(x+3)}[/tex]

[tex]=\dfrac{(x+3)(x-3)}{(x+3)(x+2)}[/tex]

[tex]=\dfrac{(x-3)}{(x+2)}[/tex]

Answer:

its -11

Step-by-step explanation:

Answer:

The first option [tex]x^4-21x^2-100=0[/tex].

Step-by-step explanation:

To have exactly 2 real and two non real solutions, the degree of the polynomial must be a degree 4. Degree is the highest exponent value in the polynomial and is also the number of solutions to the polynomial. This polynomial ha 2 real+2 non real= 4 solutions and must be [tex]x^4[/tex]. This eliminates the bottom two solutions.

In order to have two real and two non real solutions, the polynomial must factor. If it factors all the way like

[tex]x^4-100x^2=0\\x^2(x^2-100)=0\\x^2(x-10)(x+10)=0\\\\x^2=0\\x-10=0\\x+10=0[/tex]

This means x=0, 10, -10 are real solutions to the polynomial. It has no non real solutions. This eliminates this answer choice.

Only answer choice 1 meets the requirement.

Answer:

A. x^4 - 21x^2 - 100 = 0