AB = 5 units and CD = 5 units, what is the length of your new segment, AD?

Answer:

[tex]|-8|<|-10| \Longleftrightarrow 8 < 10[/tex]

[tex]\text{Which property is shown by } 4+(5+6)=(4+5)+6?[/tex]

[tex]\text{It is the associative property of addition}[/tex]

You can group the addends in any combination and it won't change the result.

Answer:

The answer is 6

Step-by-step explanation:

2 x 5 = 10

10 - 4 = 6

Hope this helps!

Answer:

6

Step-by-step explanation:

2 x 5 = 10

10 - 4 = 6

I hope this helps!

Answer:

Step-by-step explanation:

[tex] \sf{3 - x = 5x + 21}[/tex]

Move 5x to left hand side and change it's sign

⇒[tex] \sf{ - x - 5x + 3 = 21}[/tex]

Move 3 to right hand side and change it's sign

⇒[tex] \sf{ - x - 5x = 21 - 3}[/tex]

Collect like terms

⇒[tex] \sf{ - 6x = 21 - 3}[/tex]

Subtract 3 from 21

⇒[tex] \sf{ - 6x = 18}[/tex]

Divide both sides of the equation by -6

⇒[tex] \sf{ \frac{ - 6x}{ - 6} = \frac{18}{-6}} [/tex]

Calculate

⇒[tex] \sf{x = -3}[/tex]

Hope I helped!

Best regards!!

Answer:

x = - 3

Step-by-step explanation:

3 - x = 5x + 21

- x + 3 = 5x + 21

(- x + 3) + (- 3 - 5x) = (5x + 21) + (- 3 - 5x)

(- x + 3) + (- 5x - 3) = (5x + 21) + (- 5x - 3)

- x + 3 - 5x - 3 = 5x + 21 - 5x - 3

- x - 5x + 3 - 3 = 5x - 5x + 21 - 3

- 6x = 18

x = - 18/6

x = - 3

Answer:

I believe the answer is A.

Step-by-step explanation:

If there are 13 daises per bouquet, that means one bouquet is all daises. The other bouquet has 30 flowers. 30-13 is 17 which means there are 17 other flowers rather than daises. 17 is greater than 13 by 4 which is not that  much. Therefore I think the answer is letter A.

Answer:

The correct answer is A.  The probability of randomly selecting a daisy from Bouquet S is less than the probability of randomly selecting a daisy from bouquet T.  

Step-by-step explanation:

We are told that Bouquet S contains 30 flowers and 13 of those flowers are daisies.   Therefore, the probability of selecting a daisy from Bouquet S can be modeled by:

13/30, which is greater than 1/3 but less than 1/2

We are also told that Bouquet T contains 13 flowers and 13 daises.  From this information, we can conclude that all of the flowers in Bouquet T are daises, or the probability can be modeled by:

13/13 = 1

Therefore, because the probability of selecting a daisy from Bouquet S is 13/30 and the probability of selecting a daisy from Bouquet T is 1, we can conclude that, as option A states, the probability of selecting a daisy from Bouquet S is less than the probability of selecting a daisy from Bouquet T.

Hope this helps!

Answer:

Decision rule : The  p-value  <  [tex]\alpha[/tex] so  the  null hypothesis is rejected

The test statistics is  [tex]t = -2.8[/tex]

The  manger will not be manager be satisfied that the company is not under-filling since the company is under-filling its cups

Step-by-step explanation:

From the question we are told that

    The  sample size is  n  =  16

     The  sample  mean is  [tex]\= x = 5.85[/tex]

     The  standard deviation  is  [tex]\sigma = 0.2[/tex]

      The  null hypothesis is  [tex]H_o : \mu \ge 6[/tex]

       The alternative  hypothesis is  [tex]H_a : \mu < 6[/tex]

       The  level of significance is  [tex]\alpha = 0.05[/tex]

Generally the test statistics is mathematically represented as

        [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]

=>    [tex]t = \frac{ 5.86 - 6 }{ \frac{ 0.2}{ \sqrt{ 16} } }[/tex]

=>   [tex]t = -2.8[/tex]

The  p-value is obtained from the z-table  the value is  

       [tex]p-value = P(Z < -2.8 ) = 0.0025551[/tex]

     [tex]p-value = 0.0025551[/tex]

 Given that the [tex]p-value < \alpha[/tex] we reject the null hypothesis

Hence there is sufficient evidence to support the concern of the quality control manager. and the manger will not be satisfied that since the test proof that the company is under-filling its cups

Answer:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

Step-by-step explanation:

Which ordered pairs are in the relation {(x, y) | x > y + 1} on the set {1, 2, 3, 4}

Assuming that:

R should be the set of real numbers such that:

R = { (x,y) | x > y + 1}  on the set {1, 2, 3, 4}

Then:

The ordered pairs for the relation can be computed as:

R = { ( 3 , 1 ) , (4 , 1) , (4 , 2) }

A)78°

135°+a° =180°

a°=45°

57°+x°+a°=180°

57°+x°+45°=180°

102°+x°=180°

x°=180°-102°

x°=78°

Answer:

False the conjugate of 2+5i is 2-5i .

Step-by-step explanation:

Hope it will help you :)

Answer:

[tex]\Huge \boxed{-2-m}[/tex]

Step-by-step explanation:

2 + m

Rewrite with variable first.

m + 2

m + 2

Can’t be simplified further.

m - (-2)

Distribute negative sign.

m + 2

-2-m

Rewrite with variable first.

-m - 2

The last expression is not equivalent to m+2.

Answer:

Hey there!

We have cosine 61=y/500

cosine 61(500)=242.4 ft.

Let me know if this helps :)

Answer:

$9261

$1261

Step-by-step explanation:

Principal: $8000

Interest rate: 5% PA compounded annually

Time: 3 years

Answer:

C. Why? No repeating x values.

Answer:

ratio of hours lisa works to hours lisa sleeps= 3:8

Step-by-step explanation:

lisa goes to school for 7 hours per day lisa works 3 hours per day

Lisa sleeps 8 hours per day.

For the ratio of hours lisa works to hours lisa sleeps

ratio of hours lisa works to hours lisa sleeps= hours Lisa works/hours Lisa sleeps

ratio of hours lisa works to hours lisa sleeps= 3/8

ratio of hours lisa works to hours lisa sleeps= 3:8

Answer:

AM= Half of AB

or, 3x+3=(8x-6)/2

or, 6x+6=8x-6

or, 2x=12

Therefore,x=6

so,AM=3*6+3=21

So the units is 21

Answer:

[tex]\Huge \boxed{21}[/tex]

Step-by-step explanation:

AM = 3x + 3

AB = 8x - 6

Point M is the midpoint of AB.

So, AM = AB/2

3x + 3 = (8x - 6)/2

Multiplying both sides by 2.

2(3x + 3) = 8x - 6

Expanding brackets.

6x + 6 = 8x - 6

Subtracting 6x from both sides.

6 = 2x - 6

Adding 6 to both sides.

12 = 2x

Dividing both sides by 2.

6 = x

Let x = 6 for the length of AM.

3(6) + 3

18 + 3

21

Answer:

The equations needed to solve this problem are:

y = 12 + 6x

y = 12x

The number of posters completed by each Avenger will be 24.

Step-by-step explanation:

The information provided are:

Ms. Ironperson has completed 12 posters and will complete 6 more per day.

Mr. Thoro has not started yet but can make 12 per day.

The variable x denotes the number of days and y denotes the number of posters.

So, after x day the number of poster completed by Ms. Ironperson will be:

y = 12 + 6x

And after x day the number of poster completed by Mr. Thoro will be:

y = 12x

Thus, the equations needed to solve this problem are:

y = 12 + 6x

y = 12x

Compute the value of x as follows:

12x = 12 + 6x

6x = 12

x = 2

The number of posters completed by each Avenger is:

y = 12x = 12 × 2 = 24

Thus, the number of posters completed by each Avenger will be 24.

[tex](0,-4)[/tex] fits the linear equation perfectly.

Hope this helps.

Answer:

the y-intercept is the point (0, -4) on the plane

Step-by-step explanation:

In order to find the y-intercept, write the equation in "slope intercept form"  solving for "y":

[tex]2\,y=x-8\\y=\frac{x-8}{2} \\y=\frac{x}{2} -\frac{8}{2} \\y=\frac{x}{2} -4[/tex]

Recall now that the y-intercept is the value at which the line crosses the y-axis (when x = 0), therefore:

[tex]y=\frac{x}{2} -4\\y=\frac{0}{2} -4\\y=-4[/tex]

So the y-intercept is the point (0, -4) on the plane.

Answer:

Option B

Option E

Step-by-step explanation:

By the use of following postulates we can prove the two right triangles to be congruent.

1). HA - [Equal hypotenuse and an cute angles]

2). LL - [Two legs should be equal]

3). LA - [One leg and one angle must be equal]

4). ASA - [Two angles and the side containing these angles should be equal]

In the given right triangles,

1). OJ ≅ IL

2). ∠O ≅ ∠I

3). ∠J ≅ ∠L

Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.

Options A and E will be the answer.

Answer:

asa, ha, aas

Step-by-step explanation:

Answer:

a. The probability of a value between 75.0 and 90.0 is 0.40173

b. The probability of a value of 75.0 or less is 0.35942

c. The probability of a value between 55.0 and 70.0 is 0.19712

Step-by-step explanation:

To solve for this we make use of the z score formula.

z = (x-μ)/σ,

where

x = raw score

μ = the population mean

σ = the population standard deviation.

a. Compute the probability of a value between 75.0 and 90.0.

When x = 75

μ =80.0 and σ = 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

z = -0.36 to 2 decimal places

Using the z score table to find the probability

P(x = 75) = P(z = -0.36)

= 0.35942

For x = 90

z = 90 - 80/14

z = 0.71429

z = 0.71 to 2 decimal place

Using the z score table to find the probability

P(x = 90) = P(z = 0.71)

= 0.76115

The probability of a value between 75.0 and 90.0 is:

75 < x < 90

= P( x = 90) - P(x = 75)

= 0.76115 - 0.35942

= 0.40173

Therefore, probability of a value between 75.0 and 90.0 is 0.40173

b. Compute the probability of a value of 75.0 or less.

For x = 75

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 75 - 80/ 14

z = -0.35714

z = -0.36 approximately to 2 decimal places.

P-value from Z-Table:

P(x ≤ 75) = 0.35942

c. Compute the probability of a value between 55.0 and 70.0.

For x = 55

From the question, we know that

mean of 80.0 and a standard deviation of 14.0.

z = (x - μ)/σ

z = 55 - 80/ 14

z = -1.78571

z = -1.79 approximately to 2 decimal places

Using the z score table to find the probability

P(x = 55) = P(z = -1.79)

= 0.036727

For x = 70

z = 70 - 80/14

z = -0.71429

z = - 0.71 approximately to 2 decimal place.

Using the z score table to find the probability

P(x = 70) = P(z = -0.71)

= 0.23885

The probability of a value between 55.0 and 70.0 is:

55 < x < 70

= P( x = 70) - P(x = 55)

= P( z = -0.71) - P(z = -1.79)

= 0.23885 - 0.03673

= 0.19712

Answer:

alpha = 2

beta = -6

Step-by-step explanation:

let everything inside the ln be 'a'

use the chain rule to to differentiate ln a with respect to a

since the differentiation of lnx is 1/x , the differentiation of lna will be 1/a

after the differentiation, you will get: [tex]\frac{1}{a}[/tex] X [tex]\frac{d[(x+1)^{2}X (2x-1)^{2} ] }{dx}[/tex]

you need to use the product rule to differentiate the second part, then multiply 1/a by both the equations being added

replace a with its actual value

you will get [tex]\frac{2}{x + 1}[/tex] and [tex]\frac{-6}{2x -1}[/tex]

by comparing it to the given equation, we get α = 2  and  β = -6

Answer:

[tex] x = \sqrt{30} [/tex]

Step-by-step explanation:

BD is the altitude of the right ∆ which divides the hypotenuse to create two line segments, CD, and AD.

According to the right triangle altitude theorem,

[tex] BD = \sqrt{CD*AD} [/tex]

CD = 3, AD = 7, therefore,

[tex] BD = \sqrt{3*7} [/tex]

[tex] BD = \sqrt{21} [/tex]

Find x using Pythagorean theorem

[tex] x^2 = BD^2 + CD^2 [/tex]

[tex] x^2 = (\sqrt{21})^2 + 3^2 [/tex]

[tex] x^2 = 21 + 9 [/tex]

[tex] x^2 = 30 [/tex]

[tex] x = \sqrt{30} [/tex]

Answer:

According to the picture you have AD AND BC

Step-by-step explanation:

Step-by-step explanation:

(A) Let a triangle be formed with height of pole h, length of base b and angle of elevation 58°. (Due to lack of a figure).

Tan 58° = h / b = 1.6

(B) Let another triangle be formed with height of pole h, length of base (b + 90) and angle of elevation 36°. (Due to lack of a figure).

Tan 36° = h / (b + 90) = 0.72

(C) Simplifying the two equations :

1.6b = 0.72b + 64.8

b = 64.8 / 0.88 = 73.6 m

h (height of pole) = 1.6 * 73.6 = 117.76 m

==========================================

Explanation:

The equation should be h(t) = -16t^2 + (initial height). If you subtract off the initial height, then you'll have a negative starting height, which is not correct. Try plugging t = 0 into h(t) = -16t^2 - (initial height) and you'll see what I mean.

The initial height is 5184. We want to find the t value when h(t) = 0. So we want to find the time value when the height is 0.

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

h(t) = -16t^2 + (initial height)

h(t) = -16t^2 + 5184

0 = -16t^2 + 5184

16t^2 = 5184

t^2 = 5184/16

t^2 = 324

t = sqrt(324)

t = 18

It takes 18 seconds for the rope to hit the ground.

Answer:

x = -4

Step-by-step explanation:

This vertical line is x = -4.  That's all we need here.

Answer:

Step-by-step explanation:

First of all we need to convert 14.0 acres to m²

1.00 acre = 4046.86 m²

14.0 acres = 14 × 4046.86 = 56656.04 m²

Area of a circle = πr²

where

r is the radius

To find the radius substitute the value for the area into the above formula and solve for the radius

That's

[tex]56656.04 = \pi {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{56656.04}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{56656.04}{\pi} } [/tex]

r = 134.29139

r = 134.29 m to 2 decimal places

Hope this helps you

Answer:

we have no way of knowing

Step-by-step explanation:

it could be a jedi mind trick.

Answer:

Ok, the EZ plan can be written as:

C1(x) = $0.15*x

where x is the number of minutes used in the whole Month.

The 40 to Go Plan can be written as:

C2(x) = $0.05*x + $40.

So we have two linear relationships.

The Ez plan has a larger slope, but has no y-intercept.

So we now can find the number of minutes needed to have the exact monthly cost in each plan:

C1(x) = C2(x)

$0.15*x = $0.05*x + $40

($0.15 - $0.05)*x = $40

$0.10*x = $40

x = $40/$0.10 = 400.

So if in one month, you use exactly 400 minutes, you will pay exactly the same wich each plan.

Now, if you speak less than 400 minutes, is better to use the EZ Pay Plan, because it has o y-intercept, and is more efficient for lower values of x.

If you will use more than 400 minutes per month, then the 40 to Go Plan is better, because the slope is smaller.

Answer:

$32.58

Step-by-step explanation:

The area needed to be painted = 9 feet × 16 feet = 144 ft². The cost of painting a 53 ft² room is a quart of paint which costs $11.99, therefore the quart needed to paint 144 ft² area is:

[tex]Number\ of \ quart=\frac{144\ ft^2}{53\ ft^2} =2.717\ quart\\[/tex]

Since one quart cost $11.99, therefore the cost of 2.717 quart is:

Cost = 2.717 × $11.99 = $32.58

It would cost $32.58 to paint a 9 feet by 16 feet

Answer:

1. Yes, there is sufficient evidence to support the claim that student cars are older than faculty cars.

2. The 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].

Step-by-step explanation:

We are given that randomly selected 110 student cars to have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars to have ages with a mean of 5.3 years and a standard deviation of 3.7 years.

Let [tex]\mu_1[/tex] = mean age of student cars.

[tex]\mu_2[/tex]   = mean age of faculty cars.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \leq \mu_2[/tex]      {means that the student cars are younger than or equal to faculty cars}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex]      {means that the student cars are older than faculty cars}

(1) The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;

                             T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)} {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~   [tex]t_n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years

[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years

[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years

[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years

[tex]n_1[/tex] = sample of student cars = 110

[tex]n_2[/tex] = sample of faculty cars = 75

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(110-1)\times 3.6^{2}+(75-1)\times 3.7^{2} }{110+75-2} }[/tex]  = 3.641

So, the test statistics =  [tex]\frac{(8-5.3)-(0)} {3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} } }[/tex]  ~ [tex]t_1_8_3[/tex]

                                     =  4.952    

The value of t-test statistics is 4.952.

Since the value of our test statistics is more than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we support the claim that student cars are older than faculty cars.

(2) The 98% confidence interval for the difference between the two population means ([tex]\mu_1-\mu_2[/tex]) is given by;

98% C.I. for ([tex]\mu_1-\mu_2[/tex]) = [tex](\bar X_1-\bar X_2) \pm (t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} })[/tex]

                                 = [tex](8-5.3) \pm (2.326 \times 3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} })[/tex]

                                 = [tex][2.7 \pm 1.268][/tex]

                                 = [1.432, 3.968]

Here, the critical value of t at a 1% level of significance is 2.326.

Hence, the 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].

Answer: 49+64i

Step-by-step explanation:

Concept to know:

i=√-1

i²=-1

i³=-i

[tex]i^{4}[/tex]=1

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

 (-5+8i)(3-8i)

=-15+40i+24i-64i²

=-15+64i-64i²

=-15+64i+64  (remember, i²=-1)

=49+64i

Hope this helps!! :)

Please let me know if you have any question or need further explanation