Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= -7x+3
y = -x-3

Answer:

Answer:-

a) The circumference of the circle  C = 21.98 m

b) The circumference of the circle  C = 37.68 ft

c)  The circumference of the circle  C = 40.82 km

d) The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

e) The circumference of the circle = 21.98 inches

  Step-by-step explanation:

a)  In First diagram

Given radius of the circle 'r' = 7.1 m

  The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (7.1)

                                                            C = 21.98 m

The circumference of the circle  C = 21.98 m

b) In second diagram

Given diameter of the circle 'd' = 12 ft

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×12

The circumference of the circle  C = 37.68 ft

c)

Given diameter of the circle 'd' = 13 km

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×13

 The circumference of the circle  C = 40.82 km

7) The circumference of the circle  C = 2πr

    Given The circumference of a circle is 34.54 cm

          Now       2πr = 34.54

                   2(3.14) r = 34.54

                           [tex]r = \frac{34.54}{3.14} = 11[/tex]

   The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

8) Given radius of the circle 'r' = 3.5 inches

   The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (3.5)

                                                            C = 21.98

  The circumference of the circle = 21.98 inches

Answer:

all real x

Step-by-step explanation:

-3(x-1) > -3x - 2​

Distribute

-3x +3> -3x -2

Add 3x to each side

-3x +3 +3x > -3x+3x - 2​

3 > -2

This is always true so the inequality is true for all x

Answer:

B

Step-by-step explanation:

Answer: $7

Step-by-step explanation:

35/ 5 = 7

Answer:

$7

Step-by-step explanation:

Bc/ 35/5=7

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

[tex]f_k=\frac{\mu^ke^-^\mu}{k!}[/tex]

a) Evaluating at k=3

[tex]f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240[/tex]

b)Evaluating at k=0,1,2:

[tex]f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498[/tex]

[tex]f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494[/tex]

[tex]f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240[/tex]

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

Answer:

0.00420 is the answer

Step-by-step explanation:

The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

The rounding number of 0.004198223 to 3 significant figures is 0.0042

Here,

The number is 0.004198223.

We have to find,  0.004198223 to 3 significant figures.

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

Here,

The number is 0.004198223.

To find 3 significant figures,

We round a number to three significant figures in the same way that we would round to three decimal places.

Then, We count from the first non-zero digit for three digits. We then round the last digit.

Here, the digit is 9 then it will be round.

We get, the number is;

0.0042

We fill in any remaining places to the right of the decimal point with zeros.

So, The rounding number of 0.004198223 to 3 significant figures is 0.00420

Learn more about the rounding number visit:

https://brainly.com/question/4896544

#SPJ2

Answer:

48x>+2

Step-by-step explanation:

Answer:

The maximum life expectancy for humans is approximately 87 years.

Step-by-step explanation:

We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.

NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.

The linear function for Life expectancy from birth can be calculated as:

[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]

The linear function for Life expectancy from age 65 can be calculated as:

[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]

Then, the time t where both functions intersect is:

[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]

The time t=136.36 corresponds to the year 1900+136.36=2036.36.

Now, we can calculate with any of both functions the maximum life expectancy:

[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]

The maximum life expectancy for humans is approximately 87 years.

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

[tex]\frac{12}{15} \div \frac{25}{16}[/tex]

[tex]\frac{12}{15} \times \frac{16}{25}[/tex]

[tex]\frac{12 \times 16}{15 \times 25}[/tex]

[tex]\frac{192}{375}[/tex]

[tex]\frac{64}{125}=0.512[/tex]

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]

Changing the division sign into multiplication and inverting the term after the sign.

=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]

=> [tex]\frac{12*16}{15*25}[/tex]

=> [tex]\frac{192}{375}[/tex]

=> [tex]\frac{64}{125}[/tex]

This is the required form.

Answer:

B.

Step-by-step explanation:

B.

- 9 ≤ - 3x - 6 ≤ 6

1 part.

- 9  +6 ≤ - 3x - 6 +6

- 3/(- 3) ≤ - 3x/(- 3)

1 ≥ x

2d part

- 3x - 6 +6≤ 6 + 6

- 3x ≤ 12

- 3x/(-3) ≥ 12/(-3)

x ≥ - 4

x ≥ - 4 and x≤ 1

Answer:

middle is 2.5 ft

right is 4375 ft

left is 1875 ft

Step-by-step explanation:

FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

Learn more about the area;

https://brainly.com/question/1658516

#SPJ2

Answer:

When x = 1 and z = 4,   [tex]y=\frac{80}{9}[/tex]

Step-by-step explanation:

The variation described in the problem can be written using a constant of proportionality "b" as:

[tex]y=b\,\,x\,\,z^2[/tex]

The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":

[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]

Knowing this constant, we can find the value of y when x=1 and z=4 as:

[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]

Answer:

Weekly Mean Number of 50-kg bags =10.8 bags

Step-by-step explanation:

In Week 1, Kim uses 7  50kg bags of flour

In Week 2, Kim uses 14  50kg bags of flour

In Week 3, Kim uses 8 X 50kg bags of flour

In Week 4, Kim uses 13 X 50kg bags of flour

In Week 5, Kim will make 2400 loaves.

Each of these loaves will need 250g of flour.

Total Mass of flour that will be used =2400 X 250=600,000 grams

[tex]600,000$ grams=600,000 \div 1000$ kg =600kg\\Number of 50-kg bags =600 \div$ 50 =12 bags[/tex]

In Week 5, Kim will use 12 bags.

Therefore:

Weekly Mean number of 50kg bags of flour used in these 5 weeks.

[tex]=\dfrac{7+14+8+13+12}{5}\\\\ =\dfrac{54}{5}\\\\=10.8 \\ \approx 11$ bags[/tex]

Answer:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Step-by-step explanation:

Information given

[tex]\bar X=25.5[/tex] represent the sample mean

[tex]s=1[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =26[/tex] represent the value to verify

[tex]\alpha=0.06[/tex] represent the significance level  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to est

We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25.5[/tex]  

Alternative hypothesis:[tex]\mu < 25.5[/tex]  

The statistic for this case is given by;

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Answer:

Option (4)

Step-by-step explanation:

From the figure attached,

Quadrilateral ABCD has been translated to form an image A'B'C'D' by shifting 'a' units right and 'b' units up.

Let the rule for translation is,

(x, y) → (x + a, y + b)

Coordinates of point A is (-4, 4) and the coordinates of the image A' are (-2, 5).

So, (-4, 4) → [(-4 + 2), (4 + 1)]

Therefore, the translation can be represented by [tex]T_{2, 1}(x, y)[/tex] (shifted 2 units right and 1 unit up).

Option (4) will be the answer.

Answer:

T2,1(x,y)

Step-by-step explanation:

Answer:

B:

Step-by-step explanation:

Measure of ARC AFB is 180°

Why?

This is because AB is a diameter.

Answer:

Step-by-step explanation:

Area of rectangle = l × b

= 23 × 6

= 138 feet

hope this helps

plz mark it as brainliest!!!!!!!

Answer:

  2082.12 was the total invested

Step-by-step explanation:

Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...

  112%(x -580) +114%(x) = 2358.60

  2.26x -649.60 = 2358.60

  2.26x = 3008.20 . . . add 649.60

  x = 1331.06 . . . . . . divide by 2.26

  x -580 = 751.06

The total invested was 1331.06 +751.06 = 2082.12 cedis.

__

Check

The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.

The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.

The accumulated total amount was 841.19 +1517.41 = 2358.60.

Hi

X-17 = -5

X = -5+17

X = 12

Answer:

Step-by-step explanation:

I'm pretty sure that you have to add 17 on both sides to keep the final number, not negative.  

So like:

x-17=-5

+17   +17

x-0=12            

and because 0 is nothing really, x=12

Answer:

The real number 'a' = 32

The real number 'b' = 0

Step-by-step explanation:

Product of a number of a number and its conjugate = a + bi

The number is = -4 + 4i

Conjugate of this number is = -4 - 4i

Product of the number and it's conjugate

= (-4 + 4i)(-4 - 4i)

= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]

= 16 + 16i - 16i - 16i²

= 16 - 16(-1)

= 16 + 16

= 32

a + bi = 32 + (0)i

By comparing both the sides,

a = 32

b = 0

Answer:

r = 1.499619733762 m  There is no such thing a quarter radius!

C = 9.4223886775301 m

A = 7.065 m^2

Step-by-step explanation:

Calculate r and C | Given A

Given the area of a circle calculate the radius and circumference

r = √(A / π)

C = 2πr

Agenda:

r = radius

C = circumference

A = area

π = pi = 3.1415926535898

√ = square root

Answer:

dA/dt = 12 - 2A/(100 + t)

Step-by-step explanation:

The differential equation of this problem is;

dA/dt = R_in - R_out

Where;

R_in is the rate at which salt enters

R_out is the rate at which salt exits

R_in = (concentration of salt in inflow) × (input rate of brine)

We are given;

Concentration of salt in inflow = 4 lb/gal

Input rate of brine = 3 gal/min

Thus;

R_in = 4 × 3 = 12 lb/min

Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min

So, after t minutes, there will be (100 + t) gallons in the tank

Therefore;

R_out = (concentration of salt in outflow) × (output rate of brine)

R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min

R_out = 2A(t)/(100 + t) lb/min

So, we substitute the values of R_in and R_out into the Differential equation to get;

dA/dt = 12 - 2A(t)/(100 + t)

Since we are to use A foe A(t), thus the Differential equation is now;

dA/dt = 12 - 2A/(100 + t)

Answer: the answer is A 5 units

The length of L'L in the dilated figure is 5 units.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure.

Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.

Given that ML' = 2.5 units, hence:

L'L = (2.5 * 3) - 2.5 = 5 units

The length of L'L in the dilated figure is 5 units.

Find out more on transformation at: https://brainly.com/question/1620969

Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

[tex]4+2(1+3x)[/tex]

Distribute:

[tex]=4+(2)(1)+(2)(3x)[/tex]

[tex]= 4+2+6x[/tex]

Combine Like Terms:

[tex]=4+2+6x[/tex]

[tex]=(6x)+(4+2)[/tex]

[tex]=6x+6[/tex]

The Final Answer is : [tex]6x+6[/tex]

The expression that is equivalent to 4+2(1+3x) is 6x+6.

Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.

Given, 4+2(1+3x)

Firstly distribute 2(1+3x) to get 2+6x then,

4+2(1+3x)

=4+2+6x

=6x+6

Thus, 4+2(1+3x)=6x+6

For more simplification visit- https://brainly.com/question/953809?referrer=searchResults

#SPJ2

Answer:

E(X ¯)=210,000.

Step-by-step explanation:

A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:

[tex]\mu_s=\mu=210,000\\\\\sigma_s=\sigma/\sqrt{n}=35,000/\sqrt{49}=35,000/7=5,000[/tex]

If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.

Answer:

750ft²

Step-by-step explanation:

Area of rectangle = L*B

Before we find the area of the given rectangle, we need to convert the dimensions using the given scale.

Thus, dimensions of the given rectangle using the scale factor of 4in:5ft would be:

==> Length = 60in = (60*5)/4 = 75ft

Breadth or Width = 8in = (8*5)/4 = 10ft

Therefore, area of rectangle = L * B

= 75ft * 10ft

= 750 ft²

Area of rectangle = 750ft²

Answer:

c

Step-by-step explanation:

Answer:

1/x = 1/2÷4/5

1/x=1/2 x 5/4

1/x=5/8

5x=8

x=1.6