A wire that is 76 feet long needs to be divided into lengths using the ratio 1 to 13. What is the longer length? Round your answer to two decimal places if necessary.

Answer:

converse of alternate exterior angle theorem

Step-by-step explanation:

um im not sure if i should explain the full proof but

Answer:

This question is incomplete, i will answer it as:

"The initial population of a town is ​A, and it grows with a doubling time of 10 years. What will the population be in X ​years?"

Ok, the growth of a population usually is an exponential growth, so we can write this as:

P(t) = A*exp(r*t)

Where A is the initial population.

r is the rate of growth, and t is our variable, in this case, number of years.

Now we know that when t = 10y, the population doubles, so we should have:

P(10y) = 2*A = A*exp(r*10y)

2 = exp(r*10)

ln(2) = r*10

ln(2)/10 = r = 0.069.

Then our equation is:

P(t) = A*exp(0.069*t)

Now, if we want to know the population in X years, we need to replace the variable t by X

P(t = X) = A*exp(0.069*X)

Answer:

36.1683

Step-by-step explanation:

45*80.374/100=

Answer:

x = 7

Step-by-step explanation:

7 = 7

It's given

Answer:

50*0.4*45=900cm²

Answer:

[tex](4,7)[/tex]

Step-by-step explanation:

Given

[tex]2x - 3 < y[/tex]

[tex](x,7)[/tex]

Required

Find one possible value of x

From the given parameters;

[tex](x,7)[/tex] is a possible solution of [tex]2x - 3 < y[/tex] where y= 7

Substitute 7 for y

[tex]2x - 3 < 7[/tex]

Add 3 to both sides

[tex]2x - 3 + 3 < 7 + 3[/tex]

[tex]2x < 10[/tex]

Divide both sides by 2

[tex]2x/2 < 10/2[/tex]

[tex]x < 5[/tex]

The result of the inequality implies that x is less than 5; So, the possible values of x is all real numbers less than 5;

Having said that;

[tex](4,7)[/tex] is one possible coordinate of [tex]2x - 3 < y[/tex]

Answer:

The  99%  confidence interval is

                     [tex]37.167< \= x < 44.833[/tex]

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 29[/tex]

  The  sample mean is  [tex]\= x =[/tex]$41

  The  sample standard deviation is  [tex]\sigma =[/tex]$8

   The  level of confidence is [tex]C =[/tex]99%

Given that the confidence level id  99% the level of confidence is evaluated as

        [tex]\alpha = 100 - 99[/tex]

        [tex]\alpha = 1[/tex]%

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

The reason we are obtaining values for  is because  is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while   is the area under the normal distribution curve for just one tail and we need the  value for one tail in order to calculate the confidence interval

Next we evaluate the margin of error which is mathematically represented as

          [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]

           [tex]MOE = 3.8328[/tex]

The 99% confidence level is constructed as follows

      [tex]\= x - MOE < \= x < \= x + MOE[/tex]

substituting values

    [tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]

     [tex]37.167< \= x < 44.833[/tex]

Answer:

a)  [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]

b)  [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]

Step-by-step explanation:

Part a:

every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:

[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]

Part b:

every 10 inches , 8 dominoes can be placed. then the rate can be written as:

[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]

Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:  Focus = (-2, 3)

Step-by-step explanation:

[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]

First let's find the vertex. We do that by finding the Axis-Of-Symmetry:

[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]

Then finding the maximum by inputting x = -2 into the given equation:

[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]

The vertex is: (-2, 4)

Now let's find p, which is the distance from the vertex to the focus:

[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]

The vertex is (-2, 4) and p = -1

The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Answer:

[tex]\boxed{Option \ 4}[/tex]

Step-by-step explanation:

∠YVZ = 180 - 52 - 43 - 38   (Angles on a straight line add up to 180 degrees so if we try to find an unknown angle on the straight line, we need too subtract all the other angles from 180 degrees)

=> ∠YUZ = 47 degrees

Step-by-step explanation: In the figure shown, <UVW is a straight angle.

This means it measures 180 degrees.

So to find <YVZ, we add up all the angles and subtract the sum

from 180 to get the answer to this problem.

43 + 52 + 38 gives us a sum of 133.

Now we take 180 - 133 yo get 47.

So m<YVZ is 47 degrees.

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2

Answer:

A. 3/5

Step-by-step explanation:

Simple math, 9/15. Divide both by 3.

3*3=9 and 3*5=15 so answer is 3/5!

Answer:

answer is A

Step-by-step explanation:

this is a probability question

divide the number of baskets made by the total number of attempts

9/15 = 3/5

Answer:

8.5cm

Step-by-step explanation:

convert 3.4metres to cm that is by multiplying by 100

3.4×100=340cm

1rep 40

?rep 340

that is 340/40

=8.5cm

Answer:

8.5 cm

Step-by-step explanation:

Scale = 1:40

Length of the room = 3.4 meters

3.4 meters =3.4 X 100 =340 cm

Since 1 unit on the diagram represents 40 units

The length of the diagram

[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]

The length of the room on the diagram is 8.5 cm.

Answer:

f(x)= 8(0.5)^x

Step-by-step explanation:

As you can see on the graph there are two specific points labeled:

(0,8) and (1,4)

The 8 would be the initial value and starting point of the "design"

A is always the initial value so replace that.

Then proceed to divide 4 by 8 to figure out the percentage change its 0.5

leave x as it is

An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

Learn more about Outlier:

https://brainly.com/question/26958242

#SPJ2

Answer:

792

Step-by-step explanation:

The first three composite numbers are 4,  6 ,8

so 4^3+6^3+8^3=64+216+512=792

Triangle DAC is congruent to triangle BCA by SAS congruence theorem.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, AD = BC and AD || BC.

AD = BC (Given)

AD || BC (Given)

AC = AC (Reflexive property)

∠DAC=∠BCA (Interior alternate angles)

By SAS congruence theorem, ΔDAC≅ΔBCA

By CPCT, AB=CD

Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

#SPJ5

Answer:

C-(7)

Step-by-step explanation:

Given figure is a trapezoid and 21 - x is the mid segment.

Therefore by mid-segment formula of a trapezoid, we have:

21 - x = 1/2(17 + 11)

21 - x = 1/2 * 28

21 - x = 14

21 - 14 = x

7 = x

x = 7

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

4.647 to the nearest thousandth.

Step-by-step explanation:

The formula for the length of an arc between  x = a and x = b is

  a

    ∫  √( 1 + (f'(x))^2) dx

  b

Here f(x) = √x so

we have  ∫  (√( 1 + (1/2 x^-1/2))^2 )   between x = 0 and x = 4.

=   ∫ ( √( 1 + 1/(4x)) dx   between  x = 0 and x = 4.

This is not easy to integrate  but some software I have gives me the following

length =  √17 + 1/8 log(33 + 1/8 √17)

= 4.647.

Answer:

We can think that the line of the kite is the hypotenuse of a triangle rectangle, and the altitude is one of the cathetus of the triangle.

And we know that it makes an angle of 65° with the horizontal (i guess this is measured between the hypotenuse and the horizontal adjacent to the kite.

This angle is complementary to the top angle of our triangle rectangle, such that A + 65° = 90°

A = 90° - 65° = 25°

Then the altitude of the kite is the adjacent cathetus to this angle.

We can use the relation:

sin(A) = Adjacent cathetus/hypotenuse.

Sin(25°) = X/350ft

Sin(25°)*350ft = X = 147.9m

The kite is flying at an altitude of approximately 317.20 feet.

The situation will form a right angle triangle.

The hypotenuse of the triangle is the will be the line of the kite which is 350 ft long.

The line makes an angle of 65° with the horizontal  direction. The horizontal direction is the adjacent of the triangle formed.

Using trigonometric ratio, the altitude of the kite can be found below.

The altitude of the kite is the height/ opposite side of the triangle.

Therefore,

sin 65° = opposite / hypotenuse

sin 65° = opposite / 350

cross multiply

opposite = 350  × sin 65

altitude of the kite = 350 × 0.90630778703

altitude of the kite = 317.207725463

altitude of the kite ≈ 317.20 ft

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Answer:

1.

a. 20 m²: barn door is 5m x 4m

b. 468 m²:surface area of barn

i. left and right barn walls: 2(15 x 7) = 210

ii. back wall: 7 x 8 = 56

iii. front wall: (7 x 8) - 20* = 36

*20 for the barn door

iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16

*I split the triangle into 2 smaller triangles

v. sides of roof: 2(5 x 15) = 150

2.

a. 15 m²: silo door is 3m x 5m

b.  244.18 m²: surface area of silo

i. SA(silo)=2πrh+2πr²

ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²

iii. SA(silo) = 259.18

iv. SA(silo - door) = 259.18 - 15

v. SA(silo - door) = 244.18

3.

a. 712.18 m²: total surface area painted red

i. add both surface areas: 468 + 244.18 = 712.18 m²

hope this helps :)

Answer:

(11π/9 )ft/s

Step by step Explanation

Let us denote the height as h ft

But we were told that The diameter of the base of the cone is approximately three times the altitude, then

Let us denote the diameter = 3h ft, and the radius is 3h/2

The volume of the cone is

V = (1/3)π r^2 h

Then if we substitute the values we have

= (1/3)π (9h^2/4)(h) = (3/4)π h^3

dV/dt = (9/4)π h^2 dh/dt

We were given as 22feet and rate of 8 cubic feet per minute

h = 22

dV/dt = 8

8= (9/4)π (22) dh/dt

= 11π/9ft/s

Therefore, the rate is the height of the pile changing when the pile is 22 feet is

11π/9ft/s

Answer:

3.924×10∧-9

Step-by-step explanation:

Royal flush contains five cards and it's probability is 0.3924%≈0.003924

Straight contain five cards and it's probability is 0.0001%≈0.000001

The probability including straight and royal flushes will be 0.003924×0.000001≈3.924×10∧-9

Answer:

(a) $7/ticket

(b) 3 cats/dog

(c) 10 ft/sec

(d) 16 cups/gal

Step-by-step explanation:

(a) $35 for 5 tickets

$35/(5 tickets) = $7/ticket

(b) 21 cats and 7 dogs

21 cats/(7 dogs) = 3 cats/dog

(c) 40 ft in 4 seconds

40 ft/(4 sec) = 10 ft/sec

(d) 48 cups for 3 gallons

48 cups/(3 gal) = 16 cups/gal

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

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

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer:

D (The last choice)

Step-by-step explanation:

We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.