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9514 1404 393

Answer:

  ∠4 = 45°

Step-by-step explanation:

Angles 1, 2, and 4 are all congruent.

  ∠4 = ∠2

  x +30 = 2x +15

  15 = x . . . . . . . . . . . . . subtract x+15

  x + 30 = 45 = ∠4

Answer:

Step-by-step explanation:

As all edges of a cube are expanding at a rate of 2 centimeters per second.

i.e ds/dt = 2 cm/s

The formula of volume of cube: V = s³

Differentiating the volume:

dv/dt = 3s²

Write ds/dt following derivative of volume

dv/dt = 3s² ds/dt

plug in the value: ds/dt = 2 cm/s

dv/dt = (3s²) (2)

dv/dt = 6s²

Given the edge is 2cm.

so plug in the value: s=2

dv/dt = 6s²

          = 6(2)²=6(4)=24 cm³/per second

SIMILARLY,

When the edge is 14cm

dv/dt = 6s²

plug in the value: s=14

dv/dt = 6s²

         = 6(14)²=6(196)=1176 cm³/per second

Thus,

The volume will be:

(a) 24 cm³

(b) 1176 cm³

Given:

Expanding rate,

Let,

(a)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]= 3\times 2^2\times 2[/tex]

        [tex]= 3\times 4\times 2[/tex]

        [tex]= 24 \ cm^3[/tex]

(b)

When,

then,

→ [tex]\frac{dx}{dt} = 2 \ cm/sec[/tex]

Let,

→ [tex]V = x^3[/tex]

→ [tex]\frac{dV}{dt} = 3x^2 \frac{dx}{dt}[/tex]

        [tex]=3\times 14^2\times 2[/tex]

        [tex]= 1176 \ cm^3[/tex]

Thus the above answer is correct.

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Answer: D) No; If x is 5, the expression on the left simplifies to 8, making the inequality false.

In other words, if x = 5, then x+3 becomes 5+3 which ultimately becomes 8, but this is not greater than 8 on the right side.

Your steps could look like this

x+3 > 8

5+3 > 8 ... replace x with 5

8 > 8 ... this is a false inequality

Step-by-step explanation:

a) For a 95% confidence interval we use the formula

First we need to establish the sample proportion

The sample size is

n = 200

and the critical value of z for a 95% confidence interval is

z* = 1.960

This gives us

This gives us an upper confidence limit of

.525 + .069 = .594 or 59.4%

and a lower confidence limit of

.525 - .069 = .456 or 45.6%

b) At this point her supporters wonder what her chances of winning are. 45.6% is below 50%, so she might lose. To find her chances of losing, consider the bell shaped curve

top

Her probability of winning is the area to the right of 50%. We need to turn the 50% into a z score

= -.708

We look up a z-score of -.71 in Table A and get an area of .2389. This is the probability that she will lose. the probability that she will win is

.7611

c) The candidate's supporters would like to be more sure that she will win. They decide to increase the sample size until the 95% confidence interval is only plus or minus 3%. They want to know how large of a sample they will need to get that kind of accuracy. We use the formula for the margin of error.

top

To solve for n, first square both sides to get rid of the radical.

Multiply both sides by n and divide both sides by m2.

For a 95% confidence interval z* = 1.96. We put in our other numbers

= 1064.4433

so they would have to survey 1065 people in order to get a 95% confidence interval that would only stretch up and down 3%.

top

Answer:

85+25x=y

Step-by-step explanation:

if you plug in the number of months for x, and multiply that number by 25, you will get the total amount.

Answer:

ya we have to tell its initial value after 11 years it too simple

Answer:

The value after 11 years would be: 2880 us dollars

Step-by-step explanation:

Given the function

[tex]v\left(t\right)=32,000\left(0.80\right)^t[/tex]

The initial value is basically the first output value when the input value = 0.

Here,

The initial value can be obtained by putting t=0 in the function

[tex]v\left(0\right)=32,\:000\left(0.80\right)^0[/tex]

[tex]\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0[/tex]

[tex]0.8^0=1[/tex]

Thus,

[tex]v\left(0\right)=32000\cdot \:\:1[/tex]

        [tex]=32000[/tex]

Thus, initial value  = v(0) = 32000

Value after 11 years can be obtained by putting t=11 in the function

[tex]v\left(11\right)=32,\:000\left(0.80\right)^{11}[/tex]

as

[tex]0.8^{11}=0.09[/tex]

so the expression becomes

[tex]v(11)=32000\cdot \:\:0.09[/tex]

         [tex]=2880[/tex] us dollars

Thus, the value after 11 years would be: 2880 us dollars

Answer:

The 3rd term is 11

Step-by-step explanation:

The given parameters for the Arithmetic Progression, AP, are;

The ratio of the 7th term to the 10th term = (a + 6·d)/(a + 9·d) = -1

The 16th term = -15 = a + 15·d

The 3rd term= a + 2·d

From the 7th to the 10th term ratio, we have;

a + 6·d = -a - 9·d

2·a = -15·d

-2·a = 15·d...(1)

From the 16th term of the AP, we have;

-15 = a + 15·d =  a + -2·a = -a

a = 15

From equation (1), -2·a = 15·d, we have;

-2·a = -2 × 15 = 15·d

15·d = -2 × 15

d = -2 × 15/15 = -2

d = -2

The 3rd term = a + 2·d = 15 + 2 × -2 = 11

∴ The 3rd term = 11

Answer:

C

Step-by-step explanation:

I inserted 5 for a and c is the correct answer

The Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

The graph of the function y=f(x/a) represents a Horizontal Stretch by a factor of a of the graph y=f(x)    , where a>0 and a≠1 .

To find the horizontal stretch we divide the input by a ,

In the given question

f(x)=3x-9 , is horizontally stretch by a factor of 6.

So we divide the inputs by 6 .

On dividing the inputs by 6 , we get

f(x/6)=3(x*1/6)-9        (...as 3/6=1/2)

Let g(x) represents the horizontal stretch of f(x) by factor 6 , So

g(x)=x/2-9

Therefore , the Horizontal stretch of the function f(x)=3x-9 by a factor of 6 is g(x)=x/2-9 .

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Answer:

C.) 120 or Option C is incorrect.

The answer is B.) 110

Step-by-step explanation:

See screenshot below

Hope this helps!

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Two standards $6$-sided dice are rolled. The probability that the sum rolled is a perfect square 7/36.

Likelihood is the part of math concerning mathematical portrayals of how likely an occasion is to happen, or how likely it is that a suggestion is valid. Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a recommendation is valid. Likelihood and measurements, the parts of science worried about the regulations administering arbitrary occasions, including the assortment, investigation, understanding, and show of mathematical information. While calculation and variable based math were concentrated on by old Greek mathematicians over long time back, the ideas of likelihood just arose in the seventeenth and eighteenth 100 years.

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The number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

The given parameters are:

Bacteria cell = 3 x 10^-6 m

Amoeba cell = 4.5 x 10^-4 m

The number of times (n) is calculated as

n = Amoeba cell/Bacteria cell

This gives

n = (3 x 10^-6 m)/(4.5 x 10^-4 m)

This gives

n = 0.7 * 10^-2

Rewrite as

n = 7 * 10^-1

Hence, the number of times the bacterial cell is smaller than the amoeba cell is 7 * 10^-1

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Answer: B. ZX is parallel to CA

Step-by-step explanation:

B is the correct answer because ZX and CA form parallel lines which shows they are parallel to each other.

Answer: either 14

Step-by-step explanation:

Answer: The reason why the narrator throw the umbrella down the sewer after the car accident is that the umbrella symbolized the rejection of her mother The narrator feel ashamed about her working mother who cannot afford her the standard of living like she's seen in her friends. in the end, she feel ashamed of this and the umbrella remind her of her shameful thought about her mother

Step-by-step explanation:

Answer:

At first, she was upset. She had seen how Eugenie Roberts’s mother acted to her child and how she had treated them, with kindness and utmost interest. She was jealous because her mother had been working all of the time. After her mother came to pick them up, she told her mother she wanted her to quit her job, she didn't want her to work, she wanted to feel like every kid and have her mother there with her to let her know she loved her. And then she had gotten into an accident, in her anger, her mother tilted her head back and closed her eyes, waiting for the yelling people to approach her car. But she thought her mother was dead, she screamed at her mother to open her eyes, before her mother told her to be quiet because people were already going to yell at her and she couldn't take any more yelling. She threw her umbrella in the sewer. Deciding to never be that angry with her mother, for working again.

I hope this helps! :)

Answer:

0- -3 1/4+1 3/4

Step-by-step explanation:

i belive this is the answer, but im not 100% sure sry if im wrong

Answer:

h'(t)= -12

Step-by-step explanation:

h'(t)=d/dt (-6t x 2 + 24 + 6)

h'(t)=d/dt (-12t + 24 + 6)

h'(t)=d/dt (-12t + 30)

h'(t)=d/dt (-12t) + d/dt (30)

h'(t)= -12+0

a) After 2 seconds the rock will be 30 feet above the surface.

b) After 3.83, 0.17 seconds the rock will be 10 feet above the surface.

a) Given that the height = h(t) =30

Plug it in the equation and find t.

[tex]30=-6t^2+24t+6\\6t^2-24t+24=0\\6(t^2-4t+4)=0\\6(t-2)^2=0\\t=2[/tex]

b) Given that the height = h(t) =10

Plug it in the equation and find t.

[tex]10=-6t^2+24t+6\\6t^2-24t+4=0\\2(3t^2-12t+2)=0\\3t^2-12t+2=0[/tex]

Then use the quadratic formula.

[tex]t=\frac{12 \pm \sqrt{(-12)^2-4(3)(2)} }{2(3)}\\ t=\frac{12 \pm \sqrt{120} }{6}\\\\t=3.83, 0.17[/tex]

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Answer:

94

Step-by-step explanation:

Answer:

T<5,-2>

Step-by-step explanation:

It goes to the the right 5 and down 2 but it is put in a proper format

Answer:

17/30

Step-by-step explanation:

Answer:

it has to be whole numbers

Step-by-step explanation:

because all of them are whole number no matter if there negative or positive

Answer:

1: yes

2:no

3:yes

Step-by-step explanation:

that's what i know

Answer:

The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

Step-by-step explanation:

We need to write the point-slope form of the equation of the line passing through the point (6,-5) and perpendicular to the line [tex]y=-\frac{1}{3}x+4[/tex]

The general form of point-slope is; [tex]y-y_1=m(x-x_1)[/tex]

where m is slope and [tex](x_1,y_1)[/tex] is the point

We need to calculate slope.

We are given equation of line [tex]y=-\frac{1}{3}x+4[/tex] that is perpendicular to the required line.

The equation is given in slope-intercept form [tex]y=mx+b[/tex] where m is slope.

Comparing both equations we get m= -1/3

But we know that when lines are perpendicular their slopes are opposite reciprocal of each other i.e [tex]m=-\frac{1}{m}[/tex]

So, slope of required line is m = 3 (opposite reciprocal of -1/3)

Now, the equation in point-slope form having slope m=3 and point (6,-5) is

[tex]y-y_1=m(x-x_1)\\y-(-5)=3(x-6)\\y+5=3(x-6)[/tex]

So, The equation in point-slope is [tex]\mathbf{y+5=3(x-6)}[/tex]

The altitude of the airplane after it descends is 13,409 feet.

The meaning of ALTITUDE is the vertical elevation of an object above a surface (such as sea level or land) of a planet or natural satellite.

Now it is given that,

Initial Altitude of airplane = 14,382 feet

Then plane ascends = 9,372 feet

So, Altitude of airplane = 14,382 feet + 9,372 feet = 23,754 feet

Again airplane descends = 10,345 feet

So, Altitude of airplane = 23,754 feet - 10,345 feet

⇒ Altitude of airplane = 13,409 feet

Thus, the altitude of the airplane after it descends is 13,409 feet.

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Answer:

The line should look like: y=5x+4

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is your slope and b is your y-intercept.

Therefore, if we plug in the given values, our equation should look like the following:

y=5x+4

Answer:

y=5x+4

y=mx+b

Answer:

one spool of thread costs $1.89

Step-by-step explanation:

$8.99x3=$26.97

$32.64-$26.97=$5.76

$5.76 divided by 3=$1.89