If triangle ABC, m B = 90°, cos(9 = 17, and AB = 16 units.
Based on this information, m Note that the angle measures are rounded to the nearest degree.
units.

Answer:

P = 57°

Step-by-step explanation:

Given the following :

PQ = 17

QR = 15

PR = 14

Using the cosine formula since the length of the three sides are given:

a2 = b2 + c2 – 2bccos(A)

To find P:

QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)

15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)

225 = 289 + 196 - 476 cosP

476*CosP = 485 - 225

476*CosP = 260

CosP = 260/476

CosP = 0.5462184

P = Cos^-1(0.5462184)

P = 56.892029

P = 57°

Answer:

57 degrees

Step-by-step explanation:

just took the test on edg2020

A Gallup poll asked 1200 randomly chosen adults what they think the ideal number of children for a family is. Of this sample, 53% stated that they thought 2 children is the ideal number. Construct and interpret a 95% confidence interval for the proportion of all US adults that think 2 children is the ideal number.

Answer:

at 95% Confidence interval level: 0.501776   < p < 0.558224

Step-by-step explanation:

sample size n = 1200

population proportion [tex]\hat p[/tex]= 53% - 0.53

At 95% confidence interval level;

level of significance ∝ = 1 - 0.95

level of significance ∝ = 0.05

The critical value for [tex]z_{\alpha/2} = z _{0.05/2}[/tex]

the critical value [tex]z _{0.025}= 1.96[/tex] from the standard normal z tables

The standard error S.E for the population proportion can be computed as follows:

[tex]S,E = \sqrt{\dfrac{\hat p \times (1-\hat p)}{n}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (1-0.53)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.53 \times (0.47)}{1200}}[/tex]

[tex]S,E = \sqrt{\dfrac{0.2491}{1200}}[/tex]

[tex]S,E = 0.0144[/tex]

Margin of Error E= [tex]z_{\alpha/2} \times S.E[/tex]

Margin of Error E= 1.96 × 0.0144

Margin of Error E= 0.028224

Given that the confidence interval for the proportion  is  95%

The lower and the upper limit for this study is as follows:

Lower limit: [tex]\hat p - E[/tex]

Lower limit: 0.53 - 0.028224

Lower limit: 0.501776

Upper limit: [tex]\hat p + E[/tex]

Upper limit: 0.53 + 0.028224

Upper limit: 0.558224

Therefore at 95% Confidence interval level: 0.501776   < p < 0.558224

Answer:

111/20 = 5.55

Step-by-step explanation:

He used a total of 1  3/4 and  3  4/5 salt.

Convert both these mixed numbers into fractions.

=> 7/4 + 19/5

Take the LCM of the denominators

=> 35/20 + 76/20

Add the numerators

=> 111/20 = 5.55

He used a total of 111/20 or 5.55 kgs of salt.

Answer:

B

Step-by-step explanation:

The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)

So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 =  16√3

sine and cosecant.

you can see the graph or on unit circle, as the for these ratios, (which depend on y coordinate) 1st and 2nd quadrant have positive y coordinate

Answer:

I believe the answer is A. 130

Answer:

A 130

Step-by-step explanation:

Answer:

y = x + 15

Step-by-step explanation:

My friend swims x minutes.

I swim 15 minutes more than my friends, so I swim x + 15 minutes.

I swim y minutes, so y equals x + 15

Answer: y = x + 15

Answer:

1. 1 point

2. The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution = -16/17

Step-by-step explanation:

Given that the equation is of the form;

y = -2³×x and y = 9·x - 2, we have;

y = -8·x and y = 9·x - 2

1. Given that the two lines are straight lines, the number of points of intersection is one.

2. The x-coordinate of the solution

To find a solution to the system of equations, we equate both expression of the functions and solve for the independent variable x as follows;

-8·x = 9·x - 2

-8·x - 9·x=  - 2

-17·x = -2

x = 2/17

The x-coordinate of the solution = 2/17

3. The y-coordinate of the solution

y = 9·x - 2 = 9×2/17 - 2 = -16/17

y = -16/17

The y-coordinate of the solution = -16/17.

Answer:

Z - score = 2.83

Step-by-step explanation:

Given the following :

Number of samples (N) = 60

Sample mean (x) = 41.9mg

Population mean (μ) = 40mg

Population standard deviation (sd) = 5.2

Using the relation :

Z = (x - μ) / (sd / √N)

Z = (41.9 - 40) / (5.2 / √60)

Z = 1.9 / (5.2 / 7.7459666)

Z = 1.9 / 0.6713171

Z = 2.8302570

Therefore, the z-score = 2.83

Answer:

3.625 gpm

Step-by-step explanation:

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312

           [tex]\sigma[/tex] = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

                      P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           [tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]                

                            [tex]\sigma=\frac{-\$5312}{-1.645}[/tex]  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)

 P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

                    P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           [tex]\frac{x-\$6312}{3229.18}=1.88[/tex]                

                         [tex]{x-\$6312}=1.88\times 3229.18[/tex]  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Answer:

a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

   (ii) [tex]k=2[/tex]

Step-by-step explanation:

It is given that,

[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

a)

We need to find the value of a+b+c.

[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]

[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]

b)

(i) We need to find the value of a+2c.

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]

[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]

(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.

[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]

[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]

On comparing both sides, we get

[tex]k=2[/tex]

Answer:

Step-by-step explanation:

[tex]Volume = 392.5\\r = 5\\h =?\\\\V= \frac{1}{3} \pi r^2 h\\\\392.5 = \frac{1}{3} \times 3.14 \times 5^2 \times h\\\\392.5 = \frac{78.5h}{3} \\\\392.5 = 26.16h\\\\\frac{392.5}{26.16} =\frac{26.16h}{26.16} \\\\h = 15.00[/tex]

Answer:

h=15 in

Step-by-step explanation:

V=πr²(h/3)

h=3v/πr²

h=[3(392.5)]/[3.14(5)²]

h= 15 in

Answer:

No. he need 64 more

Step-by-step explanation:

Answer:

[tex]\Large \boxed{-10x-50}[/tex]

Step-by-step explanation:

[tex]-10(x+5)[/tex]

Distribute -10 to the terms in the brackets.

[tex]-10(x)-10(5)[/tex]

[tex]-10x-50[/tex]

Answer: -10x - 50

Step-by-step explanation:

Distribute -10 to both terms.

-10 * x = -10x

-10 * 5 = -50

The equation now looks like this:

-10x - 50

You have nothing to simplify, so you're finished.

Hope this helps!

Answer:

First. 115°

Second. 65°

Third. 65°

Fourth. 7

Fifth. 425.25

First

angle DAB = angle ADC (since this is an isosceles trapezoid)

Second

In a trapezoid adjacent angle are supplmentary (that is their sum is 180°)

180-115 is 65°

Third

(Same reason as second)

Fourth

The side 3x+4 is same as the opposite side

So 3x + 4 = 25

on solving you get x = 7 in

Fifth

[tex]area \: = \frac{1}{2} \times length \: of \: the \: perpendicular \: (b1 + b2)[/tex]

area = 1/2 × 13.5 (20+43)

area = 1/2 × 13.5 × 63

Thus area is 425.25

Answer:

Step-by-step explanation:

1)As ABCD is isosceles trapezium,

∠ADC= ∠DAB

∠ADC = 115°

2) AD //BC

∠ADC + ∠DCB = 180°   {co interior angles}

115 + ∠DCB = 180

 ∠DCB = 180 - 115

 ∠DCB = 65°

3) As ABCD is isosceles trapezium,

∠CBA = ∠DCB

∠CBA = 65°

4) As ABCD is isosceles trapezium, non parallel sides are congruent.

AB = DC

3x + 4 = 25 in

3x = 25 - 4

3x = 21

x = 21/3

x = 7 in

5) height = 13.5 in

a= 43 in

b= 20 in

Area of trapezium = [tex]\frac{(a+b)*h}{2}\\[/tex]

                   [tex]= \frac{(43 +20)*13.5}{2}\\\\=\frac{63*13.5}{2}\\\\\\= 425.25 in^{2}[/tex]

Answer:

30 crayons

Step-by-step explanation:

Let x be the number of crayons he started with

gave out 14 crayons

x-14

Got 12 back

x-14+12

Gave out 11 after lunch

x-14+12 -11

This equals 17

x-14+12 -11 =17

Combine like terms

x-13 = 17

Add 13 to each side

x -13+13 =17+13

x = 30

Answer: 30

Step-by-step explanation:

For this problem work backwards. Start from 17 and add 14. You should get 31. Then subtract 12, which equals 19. Finally add 11 to 19, which equals 30. Basically you are doing the inverse operation to get your answer. Hope this helps!

Answer:

Step-by-step explanation:

[tex]x^{2} -x-x<[/tex] 0

[tex]x^{2} -2x[/tex] < 0

x^2-2x+1<1

(x-1）^2<1

-1<x-1<1

0<x<2

[tex](x-1)^{2}[/tex][tex](x-1)^{2}[/tex]

Answer:

x=-12

Step-by-step explanation:

8x=-104

8x÷8=-104÷8

x=-104÷8

x=-13

Step-by-step explanation:

8x:-104

8÷8x:-104÷8

x:13

Answer:

convert into a whole number 6

Answer:

Area= 108ft²

Step-by-step explanation:

To find the area of a rectangle, you must do the following formula:

Area= Length × Width

A represents Area

L represents Length

W represents Width

Because the length (length is always longer than width) is 12 ft and the width (width is always shorter than length) is 9 ft. Your equation should be:

A= L × W

= 12ft × 9ft

= 108 ft²

Remember: The answer to a question asking for the area of a shape that is 2D, is always squared (let x represents the answer: x²). And the question asking the area of a shape that is 3D always cubed (let x represents the answer: x³). Always write the unit of measurement (let x represent the answer and cm as the example of unit of measurement: x cm²)

I hope this helps! I'm sorry if it's too complicated.

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

1000ml

Step-by-step explanation:

4 days she drank ½ of the bottle

so she drank ⅛ l of juice everyday

so

1000ml is the answer

Answer:

:

"(100 + 3) (100 + 7)

Now, by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 3 , b = 7

= (100)² + (3+7)*100 + (3*7)

= 10000 + 1000 + 21

= 11021

.

(110 - 7) (110 - 3)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-7) , b = (-3)

= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}

= 12100 + (-10)*110 + 21

= 21200 - 1100 + 21

= 11021

.

➖➖➖➖➖➖➖➖➖➖

.

(90 + 5) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 5 , b = 6

= (90)² + (5+6)*90 + (5*6)

= 8100 + 990 + 30

= 9120

.

(100 - 5) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-5) , b = (-4)

= (100)² + { (-5) + (-4) }*100 + 20

= 10000 + (-9)*100 + 20

= 10000 - 9000 + 20

= 10020 - 900

= 9120

.

➖➖➖➖➖➖➖➖➖➖

.

(100 + 4) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 4 , b = (-4)

= (100)² + { 4 + (-4) }*100 + 4*(-4)

= 10000 + (4 - 4)*100 - 16

= 10000 + 0*100 - 16

= 10000 - 16

= 9984

.

(90 + 14) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 14 , b = 6

= (90)² + (14 + 6)*90 + (14*6)

= 8100 + 20*90 + 84

= 8100 + 1800 + 84

= 9984"

This answer was in another question

This answer was given by BloomingBud

Step-by-step explanation:

Answer:

1) 9120 2) 11021

Step-by-step explanation:

95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120

103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

Answer:

m=48

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

m = 48

▹ Step-by-Step Explanation

Rewrite:

m/8 = 6

Use the inverse operation:

8 * 6 = 48

m = 48

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

2 in

Step-by-step explanation:

18/3=6 , 6 is the scale factor

12/6=2

Answer:

width= 2

Step-by-step explanation:

18 inches is the original height and we are now reducing that to 3 inches.

In order to do that, we have to divide 18 by 3 which equals 6.

Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which  equals 2.

Your final answers should be: width= 2

Hey There!!~

Your best answer choice is B). x > 1.

Good Luck!!

Answer:

no real numbers

Step-by-step explanation:

x^2 − 10 x + 25

Factor

What 2 numbers multiply to 25 and add to -10

-5*-5 = 25

-5+-5 = -10

( x-5) (x-5)

This touches the graph at x =5

The parabola is positive so there are no values where the graph is negative

Answer:

No real solutions

Step-by-step explanation:

Part 1: Factoring the quadratic

The equation is in quadratic form - ax² + bx + c = 0.

Therefore, we can use a factoring technique to solve for x. I will use the quadratic formula - [tex]x=\frac{-b \pm \sqrt{b^{2}-4ac} }{2a}[/tex].

[tex]x=\frac{-(-10)\pm \sqrt{(-10)^{2}-4(1)(25)} }{2(1)}\\\\x=\frac{10\pm\sqrt{100-4(25)} }{2}\\\\x=\frac{10\pm\sqrt{100-100}}{2}\\\\x=\frac{10\pm\sqrt{0}}{2}\\\\x=\frac{10\pm0}{2}\\\\x=\frac{10}{2}\\\\\boxed{x=5}[/tex]

Part 2: Using discriminant to determine roots

Because the discriminant (square root portion of formula) was equivalent to zero, this is the only solution that proves the equation correctly. Therefore, there is no possible negative value that can be substituted for x  without altering the final value that the equation is equal to.

Answer:

D

Step-by-step explanation: