The sequence 15, 21, 27, 33, 39, ...., 75 has 11 terms. Evaluate the related series.
a.) 0420
b.) 495
c.) 0210
d.) 480

Answer:

6 cans

Step-by-step explanation:

I used Improper Fractions to solve this question.

3/4 is enough to paint 1/8

Therefore we can multiply 3 by 8 to calculate how much paint is required for the whole wall.

3 * 8 = 24

24/4 = 6

Answer:

10feet

Step-by-step explanation:

We solve this question, using Pythagoras Theorem to solve for the other side.

Pythagoras Theorem states that

c² = a² + b²

c = √(a² + b²)

In the question, a = 6 feet

b = 8 feet

c = length of the rope

c = √6² + 8²

c = √36 + 64

c = √100

c = 10 feet

The length of the rope is 10 feet

Answer:

15 units

Step-by-step explanation:

Distance from the x-axis is measured vertically, so you would look at the second number of the coordinates, the y value. Point Z is 15 units below the x-axis.

Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.

What is the axis?

An axis in mathematics is defined as a line that is used to make or mark measurements.

Here given that,

[tex]Z= (16,-15)[/tex]  which is on the x-axis.

So,

The shortest distance between the coordinate [tex](16,-15)[/tex] and [tex](16,15)[/tex].

Now, applying the distance formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here,

[tex](x_1,y_1)=(16,0)\\(x_2,y_2)=(16,-15)[/tex]

Substituting these values in the formula

[tex]d=\sqrt{(16-16)^2+(-15-0)^2}\\\\d=\sqrt{(0)^2+(-15)^2}\\\\d=\sqrt{0+225}\\\\d=15[/tex]

Hence, the distance from [tex]Z= (16,-15)[/tex] to the x-axis is [tex]15[/tex] units.

To know more about the axis

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Answer:

462 ways

Step-by-step explanation:

Answer: [tex](x+10)^2+119=0[/tex]

Step-by-step explanation:

For a quadratic equation, the vertex form is given by : [tex]y=a(x-h)^2+k[/tex], where (h, k) is the vertex.

The given quadratic equation: [tex]x^2 + 20x + 28 = 9[/tex]

Subtract 9 from both sides

[tex]=x^2+20x+19=0[/tex]

compare this to [tex]x^2+bx=c[/tex], and add [tex](\frac{b}{2})^2[/tex] both sides

b= 20

[tex]x^2+20+100+19=-100[/tex]   [(b/2)²=20/2=10]

[tex]\Rightarrow\ x^2+2(x)(10)+10^2+119=0[/tex]

[tex]\Rightarrow\ (x+10)^2+119=0\ \ \ [\because\ (a+b)^2=a^2+b^2+2ab][/tex]

So, the vertex form : [tex](x+10)^2+119=0[/tex]

Answer:

[tex]\boxed{V = 1436.8 cm^3}[/tex]

Step-by-step explanation:

Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]

Where r = 7 cm

Volume of Sphere = [tex]\frac{4}{3} (3.14)(7)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(343)[/tex]

V = 4310/3

V = 1436.8 cm³

Answer:

Solution,

Radius= 7 cm

Volume of sphere:

[tex] \frac{4}{3} \pi \: {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {7}^{3} \\ = \frac{4}{3} \times 3.14 \times 343 \\ = 1436.8 \: {cm}^{3} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The tree grows 33cm per year.

Step-by-step explanation:

The table to represent a linear function with a rate of change of +5

So, m = 13 + 5 = 18

a = 18

The slope-intercept pattern of the linear function equation. As a result, it is written as f(x) = mx + b, where m denotes the slope and b the line's y-intercept.

The graph in the table shows a linear function.

The linear function's general equation is written as y = ax+b, where a is the slope and b is a constant.

Finding the linear function's equation by using the first and third points from the table

at x = 3  ⇒ y = 13   and   at x = 5 ⇒ y = 23

13 = 3a+b → (1)

23 = 5a+b → (2)

solve (1) and (2) to find a and b

So,  a = 5  and b = -2

∴ y = 5x - 2

After that by substitution with x = 4 int the equation of y

∴ y = 5*4-2 = 18

m= 18

Thus, option C is correct.

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Answer:

4.(3)

Step-by-step explanation:

3x+3 = 12

Subtract 3 to both sides.

3x = 9

Divide the left side by 3, then divide the right side by 3

x = 3

Answer:

Hi! your answer should be D. 3

Step-by-step explanation:

1. 3x+3=12

-3 -3

2. 3x=9

÷3 ÷3

3. x= 3

[So, your answer should be D. x=3]

Hope this helps!

Answer:

xx

Step-by-step explanation:

Answer:

120 km squared.

Step-by-step explanation:

The shape shown has 5 sides: three rectangles and 2 triangles.

If you examine each triangle closely, they are 3-4-5 triangles. The area of one triangle is 3 * 4 * 1/2 = 12 * 1/2 = 12 / 2 = 6. Since there are two triangles, the total area of the triangles is 6 * 2 = 12 km squared.

The three rectangles have the same length, but their widths differ. They all have a side length of 9 km, but the largest rectangle has a width of 5 km, the medium has a width of 4 km, and the smallest has a width of 3 km.

So, the rectangles' areas added up will be (9 * 5) + (9 * 4) + (9 * 3) = 45 + 36 + 27 = 108 km squared.

And so, the total surface area is 12 km squared + 108 km squared, or 120 km squared.

Hope this helps!

Answer:

13.896 kg

Step-by-step explanation:

You can find the mass of the bar by first finding the volume.

V = BH

where B = area of the base (the trapezium), and

H = height (distance trapezium between bases)

The area of a trapezium is

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases of the trapezium (the parallel sides), and

h = the altitude of the trapezium (distance between the bases of the trapezium)

V = (b1 + b2)h/2 * H

V = (12 cm + 6 cm)(5 cm)/2 * 16 cm

V = 720 cm^3

The volume of the bar is 720 cm^3.

Now we use the density and the volume to find the mass.

density = mass/volume

mass = density * volume

mass = 19.3 g/cm^3 * 720 cm^3

mass = 13,896 g

Now we convert grams into kilograms.

1 kg = 1000 g

mass = 13,896 g * (1 kg)/(1000 g)

mass = 13.896 kg

Answer: 1.3896 kg

Answer:

65 units

Step-by-step explanation:

Let the length of the perpendicular dropped from the right angle to the hypotenuse be h units.

Now by geometric mean property:

[tex]h = \sqrt{144 \times 25} \\ h = 12 \times 5 \\ h = 60 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^{2} = {h}^{2} + {25}^{2} \\ {x}^{2} = {60}^{2} + {25}^{2} \\ {x}^{2} = 3600 + 625 \\ {x}^{2} = 4225 \\ x = \sqrt{4225} \\ \huge \red{ \boxed{x = 65\: units }}[/tex]

Answer:

x=2   (−∞,∞)

Step-by-step explanation:

The roots (zeros) are the  x  values where the graph intersects the x-axis. To find the roots (zeros), replace  y  with  0  and solve for  x

Hope this helps (sorry if it's confusing)

Answer:

x = 1.71282

Step-by-step explanation:

2x^3+3x^2-4x-12

2 x³ + 3 x² - 4x - 12 = 0

x = 1.71282

see attachment.

Answer: idk jus needed the points so im answering

Answer:

Y=sqrt x

Step-by-step explanation:

I literally just know how to look

Answer:

EH = 3.31

Step-by-step explanation:

We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.

Where,

EK = Base = 3

KH = perpendicular altitude

EH = Hypotenuse

m<K = 90

m<E = 25

We know that

cosθ = Base/ Hypotenuse

cos 25 = 3/ EH

EH = 3/cos25

EH = 3.31

Perpendicular alitutude can also be calculated by using the formula for tanθ.

Answer:

<3, 7>

AND

[tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex]

Step-by-step explanation:

I did the plato

The vectors that represent the reflection of the vector across the x-axis are; <3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if we're seeing it in a mirror.

If we study it more, you will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

The vectors that represent the reflection of the vector across the x-axis are;

<3, 7> and [tex]\left[\begin{array}{ccc}3\\7\end{array}\right][/tex].

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Answer:

Right now it would be

[tex]-40[/tex]

Since desend means down add -20 to -40

[tex]-40+(-20)=-60[/tex]

         or

[tex]-40-20=-60[/tex]

Then is goes up 35, which is positive

[tex]-60+35=-25[/tex]

Therefore, the answer is -25

Hope this helps

Answer by

Fishylikeswater

Answer:

A. -25M

Step-by-step explanation:

The submarine starts at -40M underwater which then it descends ( goes down ) another -20M which added means it is now -60M underwater. It then rises 35M so you would then add -60M + 35M = -25M

Hope this helps :)

Answer:

77

Step-by-step explanation:

2+3+5+7+11+13+17+19=77

Answer:

[tex]1\frac{5}{7}[/tex]

Step-by-step explanation:

[tex]4\frac{3}{7} -2\frac{5}{7}[/tex]

Step 1. Simplify left side 4*7+3 , Right Side 2*7+5

[tex]=\frac{31}{7} -\frac{19}{7} = \frac{12}{7}[/tex]

Step 2. Re-write 12/7 as mixed number

[tex]\frac{12}{7} = 1\frac{5}{7}[/tex]

Answer:

A 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].

Step-by-step explanation:

We are given below the ages (in years) of randomly selected race car drivers;

Ages: 32, 40, 27, 36, 29, 28.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                           P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean age = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{32+40+27+36+29+28}{6}[/tex] = 32 years

           s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex]  = 5.1 years

           n = sample of car drivers = 6

           [tex]\mu[/tex] = population mean age of all race car drivers

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.571 < [tex]t_5[/tex] < 2.571) = 0.95  {As the critical value of t at 5 degrees of

                                                freedom are -2.571 & 2.571 with P = 2.5%}  

P(-2.571 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.571) = 0.95

P( [tex]-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                                  = [ [tex]32-2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] , [tex]32+2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] ]

                                                  = [26.65, 37.35]

Therefore, a 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].

Answer:

Using SohCahToa we know it will be opposite over adjacent, opposite being the side across from theta and adjacent being the side next to theta, Using Toa we know it will be opposite over adjacent so the answer will be 6/2sqrt5

If they wants you to simplify more than you cant have a sqrt on the bottom so to fix this you will multiply the top and bottom by sqrt5 leaving you with 6sqrt5/ 2*5 or 6sqrt5/15

hope this helped

Answer:

C. 3^5/5

Step-by-step explanation:

To find the common difference, subtract all the numbers in order.

56 - 49 = 7

49 - 42 = 7

42 - 35 = 7

Therefore, common difference is 7.

Best of Luck!

Answer:

The answer is -7

(got this answer right on the lesson)

Step-by-step explanation:

Answer: 0.20

Step-by-step explanation:

As per given :

P(student enrolled in a math class ) = 65% = 0.65

P( student enrolled in a science class) = 43%= 0.43

P( student enrolled in both ) = 13% = 0.13

Formula of conditional probability :

[tex]P(A|B)=\dfrac{P(A\text{ and }B)}{P(B)}[/tex]

Using the above formula,

The probability that the student is enrolled in a science class given that he is enrolled in maths class :

[tex]P(\text{science}|\text{math})=\dfrac{P(\text{science and maths})}{P(\text{math})}\\\\=\dfrac{0.13}{0.65}\\\\=\dfrac{13}{65}\\\\=\dfrac{1}{5}=0.20[/tex]

Hence, the probability that the student is also enrolled in a science class =  0.20 .

Answer:

Step-by-step explanation:

In this sense "area" refers to a geographical area in which people may or may not live; any "population" refers to the group of people living in a specific area.  We might discuss the "population" of the "Los Angeles area," which refers to people living within the geographic boundaries of the City of Los Angeles.

"Urban" characterizes a given area where the land is thickly settled with human residents (as opposed to open, commercial or rural land).  Most of the area within the boundaries of "Los Angeles" are "urban."

"Density" refers to "population density," defined as the number of people per square mile (or other measure of area); as an example we might refer to the population density of the City of Los Angeles, and that reasure might be in the area of "246,000 residents per square mile."

Answer:

Search the words up on google and it will explain better then me

Step-by-step explanation:

Answer:

Bob's home will worth $296,779.25 after 12 years.

Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]

Step-by-step explanation:

Current value of Bob's house =[tex]FV = $175,000( 1 + 4.5/100)^12\\FV = $175,000( (100+ 4.5)/100)^12\\FV = $175,000( (104.5)/100)^12\\FV = $296,779.25[/tex]

market is improving at 4.5% annually.

This, means that the value of house gets appreciated by 4.5% each year from its previous year value.

This is a problem of compound interest formula

[tex]FV = PV(1+r/100)^n[/tex]

where PV is the present value of any thing

FV is the future value

r is the annual rate of interest

t is the time in number of year for which rate is applicable.

_____________________________________

Given

PV = $175,000.

r = 4.5%

t = 12 years

Value after 12 year will be given by

[tex]FV = $175,000( 1 + 4.5/100)^(12)\\FV = $175,000( (100+ 4.5)/100)^(12)\\FV = $175,000( (104.5)/100)^(12)\\FV = $296,779.25[/tex]

Thus, Bob's home will worth $296,779.25 after 12 years.

Equation used is [tex]FV = $175,000( 1 + 4.5/100)^(12)\\[/tex]

Answer:

The answer is 3 mark as brainliest

Step-by-step explanation:

3 *3-4*4+2*5

9-16+10

9-6=

3

Answer:

Hey there!

3a-4b+2c

3(3)-4(4)+2(5)

9-16+10

3

Your answer would be 3.

Hope this helps :)