Paper and Pencil Construction: Construct a Line Perpendicular to a Given Line through a Point on the Line

Answer:

6/5, or 1.2

Step-by-step explanation:

The right answer is 6/5

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer:

2x(2x - 1)(x + 3)

Step-by-step explanation:

4x^3 + 10x^2 - 6x =

Factor out the common factor 2x.

= 2x(2x^2 + 5x - 3)

Factor the trinominal.

= 2x(2x - 1)(x + 3)

Answer:

[tex]=2x\left(2x-1\right)\left(x+3\right)[/tex]

Step-by-step explanation:

[tex]4x^3+10x^2-6x\\\mathrm{Factor\:out\:common\:term\:}2x:\quad 2x\left(2x^2+5x-3\right)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=4x^2x+10xx-6x\\\mathrm{Rewrite\:}6\mathrm{\:as\:}2\cdot \:3\\\mathrm{Rewrite\:}10\mathrm{\:as\:}2\cdot \:5\\\mathrm{Rewrite\:}4\mathrm{\:as\:}2\cdot \:2\\=2\cdot \:2x^2x+2\cdot \:5xx-2\cdot \:3x\\\mathrm{Factor\:out\:common\:term\:}2x\\=2x\left(2x^2+5x-3\right)\\\mathrm{Factor}\:2x^2+5x-3:\quad \left(2x-1\right)\left(x+3\right)[/tex]

[tex]2x^2+5x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(2x^2-x\right)+\left(6x-3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-x\mathrm{:\quad }x\left(2x-1\right)\\2x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=2xx-x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(2x-1\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}6x-3\mathrm{:\quad }3\left(2x-1\right)\\6x-3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3\cdot \:2x-3[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}3\\=3\left(2x-1\right)\\=x\left(2x-1\right)+3\left(2x-1\right)\\\mathrm{Factor\:out\:common\:term\:}2x-1\\=\left(2x-1\right)\left(x+3\right)\\=2x\left(2x-1\right)\left(x+3\right)[/tex]

Answer:

Option B.

Step-by-step explanation:

Let the radius of the snare drum = r

and radius of the model = R

Ratio of the dimensions of the snare drum and the model = 1 : 4

So, [tex]\frac{r}{R}=\frac{1}{4}[/tex]

Now as per question, dimensions of the snare drum is multiplied by a scale factor of [tex]\frac{1}{2}[/tex]

Radius of the snare drum = [tex]\frac{r}{2}[/tex]

Ratio of the radius of the snare drum and cylindrical model ,

[tex]\frac{\frac{r}{2}}{R} =\frac{1}{4}[/tex]

[tex]\frac{r}{2R}=\frac{1}{4}[/tex]

[tex]\frac{r}{R}=\frac{1}{2}[/tex]

Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2

Option B is the answer.

Answer:

25 miles per gallon

Step-by-step explanation:

We want to find miles per gallon so take the miles and divide by the gallons

500 miles / 20 gallons

25 miles per gallon

Answer:

[tex]= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ [/tex]

Step-by-step explanation:

You have to find miles per gallon.

So to solve that you have to divide miles by gallon.

[tex] \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Step-by-step explanation:

Abby’s Expression:

Double m, giving 2m. She then takes 20% of the result, which we can write 0.2(2m). Finally she subtracts this from 2m, giving 2m−(0.2)2m

2m − (0.2)2m

Renato’s Expression:

Divide m by 5, giving m ÷ 5 = m/5, and then multiplies the result by 8, giving:

8(m/5)

Answer:

6m = b

Step-by-step explanation:

The area of triangle when angle and sides are given = 1/2* sin angle*ab

Area = 1/2 * sin 30 * 4*b

Area = 6m²

6 = 1/2 * sin 30 * 4*b

(6*2)/(sin 30 * 4)= b

12/(0.5*4) = b

12/2 = b

6m = b

Answer:

[tex]2mn[/tex]

Step-by-step explanation:

[tex]6m^3n,\:8mn^2[/tex]

Find the GCD of [tex]6,\:8[/tex]:

[tex]6[/tex]

[tex]=2\cdot \:3[/tex]

[tex]8[/tex]

[tex]=2\cdot \:4[/tex]

[tex]=2\cdot \:2\cdot \:2[/tex]

So the prime factor common to 6, 8 is:

[tex]2[/tex]

So the factor common to [tex]6m^3n,\:8mn^2[/tex]:

[tex]=2mn[/tex]

Step-by-step explanation:

3 + 15 + 75 + 375 + 1,875

This is a geometric series.  The first term is 3, the common ratio is 5, and the number of terms is 5.

∑₁⁵ 3 (5)ⁿ⁻¹

∑₀⁴ 3 (5)ⁿ

3 + 12 + 48 + 192 + 768

This is a geometric series.  The first term is 3, the common ratio is 4, and the number of terms is 5.

∑₁⁵ 3 (4)ⁿ⁻¹

∑₀⁴ 3 (4)ⁿ

4 + 32 + 256 + 2048 + 16,384

This is a geometric series.  The first term is 4, the common ratio is 8, and the number of terms is 5.

∑₁⁵ 4 (8)ⁿ⁻¹

∑₀⁴ 4 (8)ⁿ

2 + 6 + 18 + 54 + 162

This is a geometric series.  The first term is 2, the common ratio is 3, and the number of terms is 5.

∑₁⁵ 2 (3)ⁿ⁻¹

∑₀⁴ 2 (3)ⁿ

Answer:

9x^3-21x^2+19x-6

Step-by-step explanation:

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6

9x^3-21x^2+19x-6

First you have to distribute the first equation into the second since the two are being multiplied:

(3x^2-5x+3)(3x-2)

9x^3-6x^2-15^2+10x+9x-6

(simplify)

9x^3-21x^2+19x-6 is the answer to the question

Answer:

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

Given a negative square root √(-x);

From our knowledge of complex numbers, we know that

i^2 = -1 and vise versa

To simplify

√(-x) = √((x)(-1)) = √((x)(i^2))

√(-x) = √(i^2) × √x = i√x

For example;

Simplify √-9

√-9 = √(-1×9) = √-1 × √9

√-9 = √(i^2) × √9 = i × 3

√-9 = 3i

Step-by-step explanation:

The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.

If A × A = B

Then √B = A.

Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.

2 × 2 = -2 × -2 = 4

3 × 3 = -3 × - 3 = 9

And so on.

So, the square root of 4 = 2 or -2

The square root of 9 = 3 or -3

But if one of the numbers is positive while the other is negative, then the result is negative.

2 × -2 = -4

3 × -3 = -9

Clearly, √(-4) ≠ 2 ≠ -2

√(-9) ≠ 3 ≠ -3

It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.

Let i² = -1, then we have that

√(-1) = i.

This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.

-A = -1 × A

So, √(-A) = √(-1 × A)

= √(-1) × √A

= i × √A

= i√A

Example, to simplify √(-16)

√(-16) = √(-1 × 16)

= √(-1) × √16

= i × ±4

= ±4i

Answer:

I think it changed from 36x to 48x

Depending on how you look at it, it could have changed from 3x to 4x or 36x to 48x.

If they said it was 18 feet instead of 18 inches, it would be 3x or 4x, but they had it as inches.

18 inches = 1.5 feet

72/1.5 = 48

54/1.5 = 36

So originally, it would have been a scale of 1 in : 36in , but it changed to 1 in : 48 in  

Sorry if this was confusing.

Answer:

One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale. Otherwise known as D

I got 100% on my quiz.

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

The congruent triangles are:

Triangle MNO and Triangle NMO

The above means that:

Sides MN and NO or MN and MO are equal

So, the triangles are isosceles triangles

However, it is possible that sides NO and MO are congruent

Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.

Read more about congruent triangles at:

https://brainly.com/question/1675117

Answer:

[tex] |T- 98.6| \geq 3[/tex]

And in order to solve this we have two possibilities:

Solution 1

[tex] T -98.6 \leq -3[/tex]

And solving for T we got:

[tex] T \leq 98.6- 3[/tex]

[tex] T\leq 95.6[/tex]

Solution 2

And the other options would be:

[tex] T -98.6 \geq 3[/tex]

[tex] T \geq 101.6[/tex]

Step-by-step explanation:

For this case we can define the variable os interest T as the real temperature and we know that if we are 3 F more than the value of 98.6 we will be unhealthy so we can set up the following equation:

[tex] |T- 98.6| \geq 3[/tex]

And in order to solve this we have two possibilities:

Solution 1

[tex] T -98.6 \leq -3[/tex]

And solving for T we got:

[tex] T \leq 98.6- 3[/tex]

[tex] T\leq 95.6[/tex]

Solution 2

And the other options would be:

[tex] T -98.6 \geq 3[/tex]

[tex] T \geq 101.6[/tex]

Answer:

  14 ft

Step-by-step explanation:

After the sides are folded up, the depth of the box is 2 ft, so the area of the square bottom is ...

  (200 ft^2)/(2 ft) = 100 ft^2

The edge dimension of the bottom is then ...

  √(100 ft^2) = 10 ft

Each side adds 2+2=4 ft to the bottom dimension in each direction, so the original square piece of metal was 14 ft square.

Answer:

565.71 yd²

Step-by-step explanation:

Surface area = [tex]2 \pi r (r+h)[/tex]

Area = 2 × 22/7 × 6 (6 + 9)

Area = 22 × 12/7 × 15

Area = 565.71 yd²

Answer:

565.71 yd²

Step-by-step explanation:

Surface area =

Area = 2 × 22/7 × 6 (6 + 9)

Area = 22 × 12/7 × 15

Area = 565.71 yd²

Answer:

a) [tex] \mu_m -\mu_a [/tex]

[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning

[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon

[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning

[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon

[tex]n_{m}=49[/tex] sample size for the morning

[tex]n_{a}=54[/tex] sample size for the afternoon

b) Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]

Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]

c) [tex] t_{\alpha}= 1.66[/tex]

d) [tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]  

The p value would be:

[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]

e) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance

Step-by-step explanation:

Part a

[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning

[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon

[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning

[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon

[tex]n_{m}=49[/tex] sample size for the morning

[tex]n_{a}=54[/tex] sample size for the afternoon

t would represent the statistic

[tex]\alpha=0.05[/tex] significance level

The parameter of interest is:

[tex] \mu_m -\mu_a [/tex]

Part b

We want to verify if the people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]

Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]

The statistic is given by:

[tex]t=\frac{\bar X_{m}-\bar X_{a}}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{a}}{n_{a}}}}[/tex] (1)

Part c

Based on the significance level[tex]\alpha=0.05[/tex] and the degrees of freedom given by:

[tex] df = 49+54-2= 101[/tex]

We can find the critical value in the t distribution iwth 101 degrees of freedom who accumuate 0.05 of the area in the right and we got:

[tex] t_{\alpha}= 1.66[/tex]

Part d

[tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]  

The p value would be:

[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]

Part e

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance

Answer:

(-21a^5×b)/(2+4b)

Step by step explanation:

The question isn't complete and clear as we were not told what to determine from the expression.

Looking at the question, we can tell we are to simplify the expression.

[(-7a² × 9a³x³) :(-3ax³)] : [( 10a) -(-20a b) : (-5a²b)]

First we would work with expressions in each parenthesis (bracket).

Then we would work on the answer we derive after opening the parenthesis.

See attachment for detail

Answer:

So the answer is the first one

Answer:

Below.

Step-by-step explanation:

Yes - those are 2 semicircles so their combined area = πr^2

= 3^2π

= 9π.

Yes.. You can count it as full circle.

Answer:

3.9 squre inch

Step-by-step explanation:

Two semicircles are inscribed in a square of side 6 in. Both the semicircles if combined together will form a full circle.

Area of the yellow region would be half of the areas of the difference between area of square and area of two semicircles each with radius 3 inches.

Therefore,

Area of yellow region

[tex] = \frac{1}{2} (area \: of \: square - 2 \times area \: of \: semicircle) \\ \\ = \frac{1}{2} ( {6}^{2} - 2 \times \frac{1}{2} \pi {r}^{2} ) \\ \\ = \frac{1}{2} ( {6}^{2} - 3.14 \times {3}^{2} ) \\ \\ = \frac{1}{2} ( 36 - 3.14 \times 9 ) \\ \\ = \frac{1}{2} ( 36 - 28.26 ) \\ \\ = \frac{1}{2} \times 7.74 \\ \\ = 3.87 \: {in}^{2} \\ \\ = 3.9 \: {in}^{2}[/tex]

Answer:

Step-by-step explanation:

The sum of 7 and 10 is 17. So 123 / 17 = 7.235 (roughly)

7.235 x 10 (for Adriana's aunt's age) equals 72.35

And to double check: We can find adriana's age by doing. 7.235 x 7 = 50.645. If we add 50.645 and 72.35 we get 122.995 which is roughly 123 and the reason why it is not 123 on the dot is because 123 / 17 is roughly 7.235 the full expanded one is: 7.23529411765

You may try checking with the full number without estimating but i am sure of my answer

Answer:

Cost of tools: $100

Cost for each chair: $25

Step-by-step explanation:

You can see that before 1 chair, the cost is at 100. This means that the cost of the tools is $100. Another way to determine this is to see that at 1 chair, the cost is $125. At 2, it's $150, and at 3 it's $175, etc. This tells you that the cost to produce each chair is $25, but it also tells you that the tools cost 100 dollars, since the total cost at 1 chair is $125, and each chair only costs $25.

Hope this helps!

Answer:

100,25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)

At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.

1) Using the records obtained for both groups, she  intends to conduct an independent t-test to analyze her claim.

X₁: BES results of a youth offender treated with the new treatment.

X₂: BES results of a youth offender treated with the standard treatment.

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α:0.05

test statistic

[tex]t_{H_0}= -0.32[/tex]

p-value: 0.7517

The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of  the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.

I hope this helps

(Box plot in attachment)

Answer:

Below.

Step-by-step explanation:

sin ((x))-(y)) / cos (x) sin (y)

    sin x cos y - cos x sin y

=  ----------------------------------

           cos x sin y

     sin x cos y

=    ----------------   -   1

     cos x sin y

But tan x = sin x / cos x  and cot y = cos y / sin y

So the above =  tan x cot y - 1.

Answer:

The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Step-by-step explanation:

We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.

Let X = Chipotle meals having calories

So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])

Now, the 68-95-99.7 rule states that;

So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;

                               [tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]

                                        =  -2

Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.

SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.

Answer:

1899

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 3234

Standard deviation = 871

Percentage of newborns who weighed between 1492 grams and 4976 grams:

1492 = 3234 - 2*871

So 1492 is two standard deviations below the mean.

4976 = 3234 + 2*871

So 4976 is two standard deviations above the mean.

By the Empirical Rule, 95% of newborns weighed between 1492 grams and 4976 grams.

Out of 1999:

0.95*1999 = 1899

So the answer is 1899

Answer:

fifty nine hundredths

Answer:

5.75 ft ≈ 6 ft

2.47 ft ≈ 2 ft

perimeter of the rectangular counter top  = 16 ft

Step-by-step explanation:

The counter top he is installing is a rectangular piece of quartz that is 5.75 ft long and 2.47 ft wide. The length and the width can be rounded off to the nearest whole number as follows.

length = 5.75 ft to the nearest whole number will be 6 ft

width = 2.47 ft to the nearest whole number will be 2 ft

The logic in rounding off the number to the nearest whole number is that the value on the left hand side of the decimal is rounded off to an integer. If the number at the right hand side of the number is greater or equal to 5 we borrow 1 and add to the left hand side number of the decimal number.

Therefore,

Perimeter of the rectangle = 2l + 2w

perimeter of the rectangle = 2 × 6 + 2 × 2

perimeter of the rectangle = 12 + 4

perimeter of the rectangle = 16 ft

Explanation:

The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.

320 + 25 + c = 430

         345 + c = 430

345 - 345 + c = 430 - 345

c = 85

The cost of the coat was $85.

Answer:

$85 for the coat

Step-by-step explanation:

1 dress = $80

4 dress =$80×4

=$320

sweater=$25

coat=?

4 dresses plus the sweater cost :

$320+$25=$345

The cost of all the item $430

cost of the coat :

$430-$345=$85

Answer:

1,664 fluid ounces = 13 gallons

Step-by-step explanation: