Convert the decimal expansion of each of these integers to a binary expansion.
a) 321
b) 1023
c) 100632

Answer:

(-6, 1)

Step-by-step explanation:

Since DE to DF is 5:8, we need to add 5/8 of the difference in x- and y-coordinates to the coordinates of point D to find point E.

Difference in x from D to F:

-9 - (-1) = -8

5/8 * (-8) = -5

Difference in y from D to F:

-5 - 11 = -16

5/8 * (-16) = -10

x: -1 - 5 = -6

y: 11 - 10 = 1

Answer: (-6, 1)

The coordinates are (-6, 1).

When a point divides a line segment externally or internally in some ratio, we use the section formula to find the coordinates of that point. It is a handy tool used to find the coordinates of the point dividing the line segment in some ratio. This section formula can also be used to find the midpoint of a line segment and for the derivation of the midpoint formula as well.

Given:

D(-1,11) and F(-9,-5)

DE : DF is 5:8

So,

DE: EF= 5 : 3

Using section formula

x= 3*(-1) + 5*(-9)/5+3

x= -3 -45 /8

x= -48/8

x= -6

and,

y= 3*11 + 5*(-5) / 8

y= 33-25/8

y= 8/8

y=1

Hence, the coordinates are (-6, 1).

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Answer:

m<FEH = 15

Step-by-step explanation:

We can find angle G

The three angles of a triangle add to 180

90 + 75+ G = 180

165 + G = 180

G = 180-165

G = 15

Since the triangles are similar, <E = <G

<E = 15

So m<FEH = 15

Answer:

m>FMH

Step-by-step explanation:

Answer:

Part A: The student forgot to distribute the subtraction across the entire polynomial.

Part B: 8[tex]x^{2}[/tex]-6[tex]x^{2}[/tex]-7x+x-2-3 = 2[tex]x^{2}[/tex]-6x-5

Part C: The terms are 2[tex]x^{2}[/tex], -6x, and -5. The coefficient of [tex]x^{2}[/tex] is 2. The coefficient of x is -6.  

Step-by-step explanation:

Part A: When subtracting polynomials you have to make sure the subtraction is distributed to every term in the second polynomial.

Part B: Distributing the subtraction across the entire term we see that we need to subtract 6[tex]x^{2}[/tex], add x, and subtract 3. Then we just do the math and we get the answer.

Part C: Since they're asking for the simplified polynomial, they want the answer to the subtraction problem.  The terms are separated by + and - signs and the coefficients  are the numbers being multiplied against variables.

Answer:

311 days

Step-by-step explanation:

I(t) = 1.5 cos(2π/365 t) + 4.3

5.2 = 1.5 cos(2π/365 t) + 4.3

0.9 = 1.5 cos(2π/365 t)

0.6 = cos(2π/365 t)

2π/365 t = cos⁻¹(0.6)

2π/365 t = 0.927, 5.356

t ≈ 54, 311

Answer:

First time is 54

Second time is 311

Step-by-step explanation:

You plug in the numbers to get the answer.

cos⁻¹(0.6) = 2π/365t

0.927, 5.356 = 2π/365t

t = 54 or 311

Answer: 80

Step-by-step explanation:

A) The first domino is 3, the second is 4. Hence 34.

B) The first domino is 5, the second is 1. Hence 51.

C) The first domino is 6, the second is 11. Hence 71.

D) The first domino is 7, the second is 10. Hence 80.

Answer:

d ≈ 7.280 units

Step-by-step explanation:

(-5, 1) & (2, -1)

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(2 + 5)² + (-1 - 1)²]

d = √[(7²) + (-2²)

d = √(49 + 4)

d ≈ 7.280

Answer:

Step-by-step explanation:

hello, you know that

[tex]\sqrt[5]{x^5}=x[/tex]

so, I can write

[tex]\sqrt[5]{2^5}=\sqrt[5]{32}=2\\\\\sqrt[5]{3^5}=\sqrt[5]{243}=3\\\\\sqrt[5]{4^5}=\sqrt[5]{1024}=4\\\\\sqrt[5]{5^5}=\sqrt[5]{3125}=5[/tex]

So, the winners are 32, 243, 1024, 3125 !!

You know that [tex]i^2=-1[/tex], right?

[tex]\sqrt{-9}=\sqrt{(3i)^2}=3i[/tex]

So, the answer is 3i

Thank you

Answer:

The answer is Zero ( 0 ).

Answer:

Reflect of X-axis -> diolate by a factor of 2

Remember to say thanks and mark brainliest

The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2

What is Reflection and Dilation?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be ΔABC

Now , the coordinates of the triangle ABC is given as

A = A ( -4 , 2 )

B = B ( -2 , 4 )

C = C ( 0 , 2 )

And , the triangle be ΔDEF

Now , the coordinates of triangle DEF is given as

D = D ( -8 , -4 )

E = E ( -4 , -8 )

F = F ( 0 , -4 )

Now , on reflecting the triangle ABC along the x-axis , we get

The reflected triangle be A'B'C' will be the reflection of point (x, y) across the x-axis is (x, -y)

So ,

A' = A' ( -4 , -2 )

B' = B' ( -2 , -4 )

C' = C' ( 0 , -2 )

Now , on dilating the triangle A'B'C' with a scale factor of 2 , we get

D = 2 x A'

D = D ( -8 , -4 )

E = 2 x B'

E = E ( -4 , -8 )

F = 2 x C'

F = F ( 0 , -4 )

Therefore , the coordinates of the triangle DEF is

D = D ( -8 , -4 )

E = E ( -4 , -8 )

F = F ( 0 , -4 )

So , the triangle ABC is transformed into triangle DEF by a reflection across x-axis and a dilation by a scale factor of 2.

Hence , The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2

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Answer:

Hey there!

Length: [tex]l\\[/tex]

Width: [tex]1/3l-1[/tex]

Expression to find the area: [tex]l(1/3l-1)[/tex], or [tex]1/3l^2-l[/tex].

Expression to find the perimeter: [tex]2l+2(1/3l-1)[/tex], or [tex]8/3l-1[/tex].

Perimeter divided by area: [tex]\frac{\frac{8}{3}l-1 }{1/3l^2-l}[/tex]

Let me know if this helps :)

Answer:

x = 8.3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 44 = 6/x

x cos 44 / 6

x = 6/ cos 44

x=8.340981546

x = 8.3

Answer:

Decimal

Step-by-step explanation:

When using decimals the bigger number is greater.

Example) .3 > .2

If there are more 0's in front of the number in a decimal it is smaller.

Example) .003 > .0003

The reason why it is harder to visualize that a fraction is greater is because there are two numbers to look at. You basically have to take an extra step and divide.

Answer:

n = 12

Step-by-step explanation:

27 = 15 + n

27 - 15 = n

12 = n

Answer:

n= 12

Step-by-step explanation:

27=15+n

15+n=27

n=27-15

n=12

Answer:

a) State the random variable

Random variable : x

which refers to a randomly selected student from the college that is left-handed.

b) state population parameter

population parameter : P

which is the percentage of all students from the college that are left handed

c) state the hypotheses

The hypothesis are;

Null hypothesis                H₀ : p = 0.11

Alternative hypothesis    H₁ : p > 0.11

d) State the Type I error in the context of this problem.

Type - I Error: Rejecting that the % of all the students from the college that are left-handed is 11% when actually the % is really 11%

(Reject H₀ when H₀ is true)

e) State the Type 11 error in the context of this problem

Type-II Error: Failing to Reject that the % of all the students from the college that are left-handed is 11% when the % is really higher than that

(Fail to reject H₀ when H₀ is false)

Answer:

Any equation shown in the explanation

Step-by-step explanation:

Hello!

Combining like terms means combining terms with the same variables.

So combing all x's, all y's, all numbers, etc.

2/3x - 9 - 2x + 2 = 1

combine the x's

-1 1/3 x - 9 + 2 = 1

combine normal numbers

-1 1/3 x - 7 = 1

Add 7 to both sides

-1 1/3x = 8

Make mixed number into improper fraction

-4/3x = 8

Multiply both sides by 3

-4x = 24

Divide both sides by -4

x = -6

The answer would be any of the equation I showed above

Hope this helps!

Hello, please consider the following.

[tex]\displaystyle 1+2+3+...+12=\sum_{k=1}^{k=12} {k}=\dfrac{12*13}{2}=6*13=78[/tex]

For the second we will need to put on the same denominator.

[tex]\displaystyle \dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{14}=\sum_{k=1}^{k=7} {\dfrac{1}{2k}}\\\\=\dfrac{1}{2}\dfrac{420+210+140+105+84+70+60}{5*7*3*2*2}\\\\=\dfrac{1}{2}\dfrac{1089}{420}\\\\=\dfrac{1089}{840}=1.296429...[/tex]

Thank you.

Answer:

Step-by-step explanation:

f(x) = 2x + 2

g(x) = x² - 1

To find (f - g)(x) subtract g(x) from f(x)

That's

(f - g)(x) = 2x + 2 - [ x² - 1]

(f - g)(x) = 2x + 2 - x² + 1

Group like terms

That's

(f - g)(x) = - x² + 2x + 2 + 1

We have the final answer as

Hope this helps you

Answer:

-x2+2x+3

Step-by-step explanation:

(2x+2)- (x2-1)

2x+2-x2+1

-x2+2x+3

Hi there! :)

Answer:

[tex]\huge\boxed{y = -1/4, 1/2.}[/tex]

Given the equation:

8y² - 2y - 1 = 0

Find two numbers that multiply into -1 and sum up to -2. Remember, the 8 as the leading coefficient must be taken into account.

After guessing and checking, we get:

(4y + 1) (2y - 1) = 0

Use the Zero-Product Property to solve for y:

4y + 1 =

4y = -1

y = -1/4

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

2y - 1 = 0

2y = 1

y = 1/2

Therefore, solutions to this equation are:

y = -1/4, 1/2.

Answer:

d) 205

Step-by-step explanation:

Step(i):-

x             :   100      150      200      250      300

p(X=x)    :   0.10     0.20    0.30     0.30      0.10

Step(ii):-

Let 'X' be the discrete random variable

Expected value of the random variable

   E(X) = ∑ x P(X=x)

           =  100 X 0.10 + 150 X 0.20 + 200 X 0.30 +250 X 0.30 + 300 X 0.10

          =   205

Final answer:-

The expected value     E(X) = 205

Answer:

[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]

[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]

[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]

Step-by-step explanation:

The Law of Sines states that:

[tex]\frac{a}{\sin A} = \frac{b}{\sin B}=\frac{c}{\sin C}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Angles opposite to respective sides, dimensionless.

Given that [tex]a = 71[/tex], [tex]b = 104[/tex], [tex]\angle A = 21^{\circ}[/tex], the sine of angle B is:

[tex]\sin B = \frac{b}{a}\cdot \sin A[/tex]

[tex]\sin B = \frac{104}{71}\cdot \sin 21^{\circ}[/tex]

[tex]\sin B = 0.525[/tex]

Sine is positive between 0º and 180º, so there are two possible solutions:

[tex]\angle B_{1} \approx 31.668^{\circ}[/tex]

[tex]\angle B_{2} \approx 148.332^{\circ}[/tex]

The remaining angle is obtained from the principle that sum of internal triangles equals to 180 degrees: ([tex]\angle A = 21^{\circ}[/tex], [tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex])

[tex]\angle C_{1} = 180^{\circ}-\angle A - \angle B_{1}[/tex]

[tex]\angle C_{1} = 180^{\circ}-21^{\circ}-31.668^{\circ}[/tex]

[tex]\angle C_{1} \approx 127.332^{\circ}[/tex]

[tex]\angle C_{2} = 180^{\circ}-\angle A - \angle B_{2}[/tex]

[tex]\angle C_{2} = 180^{\circ}-21^{\circ}-148.332^{\circ}[/tex]

[tex]\angle C_{2} \approx 10.668^{\circ}[/tex]

Lastly, the remaining side of the triangle is found by means of the Law of Sine: ([tex]a = 71[/tex], [tex]\angle A = 21^{\circ}[/tex], [tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex])

[tex]c_{1} = a\cdot \left(\frac{\sin C_{1}}{\sin A} \right)[/tex]

[tex]c_{1} = 71\cdot \left(\frac{\sin 127.332^{\circ}}{\sin 21^{\circ}} \right)[/tex]

[tex]c_{1} \approx 157.532[/tex]

[tex]c_{2} = a\cdot \left(\frac{\sin C_{2}}{\sin A} \right)[/tex]

[tex]c_{2}= 71\cdot \left(\frac{\sin 10.668^{\circ}}{\sin 21^{\circ}} \right)[/tex]

[tex]c_{2}\approx 36.676[/tex]

The answer are presented below:

[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]

[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]

[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]

Answer: 8008

Step-by-step explanation:

Total entrees = 16

Number of entrees to choose = 6

Since order does not matter , so we combinations .

Number of combinations to choose r things out of n = [tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]

Then, total ways to choose 6 entrees = [tex]C(16,6)=\dfrac{16!}{6!10!}[/tex]

[tex]=\dfrac{16\times15\times14\times13\times12\times11\times10!}{(720)10!}\\\\= 8008[/tex]

Hence, the required number of ways= 8008

Answer:

Step-by-step explanation:

Two groups were tested to compare their speed at working math problems.

Aim/Objective of experiment:

To test their speed (each group and then compare) at working math problems

Control Group:

The group of students computing math problems without a calculator

Experimental Group:

The group of students computing math problems with a calculator

Statistical Hypothesis:

Null hypothesis: Both the control and the experimental group worked math problems at the same pace or speed

Alternative hypothesis: The experimental group worked math problems with a greater speed than the control group

This hypothesis is derived from the thought or knowledge that calculators help solve math problems faster. Your hope would be to refute the null hypothesis and accept the alternative hypothesis; after testing.

Answer;

=-6p-10

Step-by-step explanation:

Lesson: It's about the using properties to simplify expression.

First, you apply by the rule.

-12-6p+2

Then, subtract by the numbers.

-12-6=-6

-6p-12+2← (group like terms)

And finally, add or subtract by the numbers.

-12+2 =-10

12-2=10

Answer:  -6p-10

Hope this helps!

Answer:

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Step-by-step explanation:

Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs ([tex]n[/tex]) after a certain amount of years (t) is given by the following formula:

[tex]n = n_{o} + \frac{\Delta n}{\Delta t}\cdot t[/tex]

Where:

[tex]n_{o}[/tex] - Initial amount of jobs in pipe fitting industry, measured in thousands.

[tex]\frac{\Delta n}{\Delta t}[/tex] - Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)

If [tex]n_{o} = 546.5[/tex], [tex]t = 2025-2015 = 10\,years[/tex] and [tex]\frac{\Delta n}{\Delta t} = -3\,\frac{1}{years}[/tex], then:

[tex]n = 546.5+\left(-3\,\frac{1}{year}\right)\cdot (10\,years)[/tex]

[tex]n = 516.5[/tex]

The percent change in jobs from pipe fitting industry is calculated as follows:

[tex]\%n = \left(1-\frac{n}{n_{o}}\right)\times 100\,\%[/tex]

[tex]\% n = \left(1-\frac{516.5}{546.5}\right)\times 100\,\%[/tex]

[tex]\%n = 5.5\,\%[/tex]

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Answer:

60km/hr

Step-by-step explanation:

considering it travels for 6 hours

360 divided by 6= 60km/hr

Step-by-step explanation:

(A) 1 L = 0.00629 barrel

12 L = 0.0755 barrel

(B) 1 ounce = 0.0296 L

65 ounces = 1.922 L

(C) 1 min = 0.000694 day

75 min = 0.05 day

Answer:

  all real numbers

Step-by-step explanation:

The domain of any polynomial function is "all real numbers." There is no value of x for which y is undefined.

Step-by-step explanation:

Some of the property of log are as follows :

1. [tex]\text{log a}-\text{log b}=\text{log} \dfrac{\text{a}}{\text{b}}[/tex]

2. [tex]\text{log a}+\text{log b}=\text{log}(a{\cdot} b)[/tex]

3. [tex]\text{log}a^n=n\ \text{log} a[/tex]

Now coming to question,

(a) [tex]\text{log 5}-\text{log 8}=\text{log} \dfrac{\text{5}}{\text{8}}[/tex] (using property 1)

(b) [tex]\text{log 1}+\text{log 3}=\text{log}(1{\cdot} 3)=\text{log} 3[/tex] (using property 2)

(c) [tex]\text{log} 4=\text{log} 2^2=2\ \text{log} 2[/tex] (using property 3)

Hence, this is the required solution.

Answer:

π

Step-by-step explanation:

Any other irrational number, actually, so √2 would also do the trick.

Answer:

Pi, since pi is irrational

Step-by-step explanation:

Any irrational number, such as √2

Answer:

Graph the parent function f(x)=ln and translate all points 4 to the left and 5 up

Step-by-step explanation: