The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm. If the area of the printed material on the poster is fixed at 864 cm2, find the dimensions of the poster with the smallest area.

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

The value of  annuity is  [tex]P_v = \$ 7929.9[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 250[/tex]

     The  interest rate  is   [tex]r = 5\% = 0.05[/tex]

     Frequency at which it occurs in a year is  n = 4 (quarterly )

      The number of years is  [tex]t = 10 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)

 substituting values

             [tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]

             [tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]

             [tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]

            [tex]P_v = \$ 7929.9[/tex]

Answer:

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Step-by-step explanation:

We formulate our hypotheses as

H0:p1=p2; Ha:p1≠p2, which is a two-tailed test.

Supposing the probability or proportion of the first survey is equal to the probability or proportion of the second survey. This will be the null hypothesis and the alternative hypotheses would be that these two proportions or probabilities are unequal.

This is a two tailed test.

Answer:

33333 x 166667 = 5555511111

I think that is the answer you wanted

Step-by-step explanation:

      166667

     x 33333

5555511111

Answer:

A) The slope of line MN is Two-thirds.

C) The slope of line RS is Negative three-halves.

E) Line RS is perpendicular to both line MN and line PQ.

Step-by-step explanation:

i did the work

Answer:

Question (2). Option (D)

Question (3). (a). 56

                     (b). 84

Step-by-step explanation:

Question (2).

Since, a% of b = [tex]\frac{a}{100}\times b[/tex]

42% of 350 = [tex]\frac{42}{100}\times 350[/tex]

Therefore, Option (d) is the correct option.

Question (3).

Total number of people who attended the music concert = 700

a). Percentage of people who arrived late in the concert = 8%

Therefore, number of people who attended the concert = 8% of 700

= [tex]\frac{8}{100}\times 700[/tex]

= 56

b). Percentage of people who bought the shirt = 12%

Number of people who bought the shirt = 12% of 700

= [tex]\frac{12}{100}\times 700[/tex]

= 84

Answer:

open side up: 2%

closed side up: 10%

landing on side: 88%

Step-by-step explanation:

Jake tossed it 50 times, so to figure out probability it is easier to make the fraction over 100 so multiply the open side up by 2 the closed side up by 2 and the landing side up by 2 and make it over 100 then divide them.

Answer:

(a) 27 degrees (nearest degree)

(b) 17.9 m  (to one decimal place)

Step-by-step explanation:

Wow, that's along ladder, perhaps for the firemen!

From diagram,

(a)

sin(x) = 9 / 20 = 0.45

x = arcsin(0.45) = 26.74 degrees

(b)

height of wall ladder reaches

h = 20*cos(x) = 20*cos(26.74) = 17.86 m

Answer:

3/8x - 9 4/5

Step-by-step explanation:

Well we need to simplify the following expression,

[tex]\frac{3}{4} (\frac{1}{2}x - 12) + \frac{4}{5}[/tex]

So we need to distribute 3/4 to (1/2x - 12)

3/8x - 9 + 4/5

3/8x - 9 4/5

Thus,

the answer is 3/8x - 9 4/5.

Hope this helps :)

Answer:

Step 1:

To find ordered pair solutions, you could create an x and y graph and fill out the x side. Then, plug in an x number to get your y number and graph the ordered pairs to see if they give you a straight line. I'm going to use these numbers: -1, 0, 1, and 2.

[tex]...x...|...y...[/tex]

[tex]\left[\begin{array}{ccc}-1&?\\0&?\\1&?\\2&?\end{array}\right][/tex]

Now, let's plug in -1 into the equation first to see what we get for y.

[tex]y=8(-1)+3\\y=-8+3\\y=-5\\(-1,-5)[/tex]

-5 is our y if x was -1.

We do the same for the other three numbers.

[tex]y=8(0)+3\\y=0+3\\y=3\\(0,3)[/tex]

[tex]y=8(1)+3\\y=8+3\\y=11\\(1,11)[/tex]

[tex]y=8(2)+3\\y=16+3\\y=19\\(2,19)[/tex]

Step 2:

With all that done, we can now fill out our table and graph the points.

[tex]....x...|...y....[/tex]

[tex]\left[\begin{array}{ccc}-1&-5\\0&3\\1&11\\2&19\end{array}\right][/tex]

If you graph these points on graph paper / a graphing website, you will see that these points go in a straight line. If you are given an ordered pair already (for example: (3,5)), then all you have to do is plug in the x into the equation (3) and see if the outcome is true (5).

[tex]5=8(3)+3\\5=24+3\\5\neq 27[/tex]

Since they don't equal each other, then (3,5) is false.

Here is the graph for the table above. I hope I helped you!

Lets go over the solutions.

Let's start with (1, 11). After substituting x = 1 and y = 11, it results in the equation 11 = 11, which is a true statement. Hence, this is one solution.

Now, let's look at (-1 -5). After substituting x = -1 and y = -5, it results in the equation -5 = -5, which is also a true statement. So, this being said, (-1, -5) would also be a solution.

Hence, our two solutions are:

Both [tex](1, 11)[/tex] and [tex](-1, -5)[/tex].

Hope this helps!

Answer:  see below

Step-by-step explanation:

In order to partition line segment AB so that AP and PB have a ratio of 3 : 1

1) Find the x- and y-lengths of the segment AB.

2) Divide the x- and y-lengths by (3 + 1) to find the length of one section.  

3) Add 3 times those lengths to point A to find point P ...or...

   Subtract 1 times those lengths from point B to find point P.

For example: Consider A = (0, 0) and B = (4, 8)

1) The length from A to B is

   x = 4-0 = 4

   y = 8-0 = 8

2) Divide those by (3 + 1):

   x = 4/4 = 1

   y = 8/4 = 2

3) Add 3 times those values to A to find point P:

   x = 0 + 3(1) = 3

   y = 0+3(2) = 6  

   --> P = (3, 6)

Note: We could have also subtracted 1 from the x-value of B and 2 from the y-value of B to find that point P = (4-1, 8-2) = (3, 6)

Now we know that the distance from point A to point P is 3 times the distance from point P to point B.

Answer: $951,064.06 would be your answer.

Step-by-step explanation: Hope that helped!

Answer:

First, a absolute value function is something like:

y = f(x) = IxI

remember how this work:

if x ≥ 0, IxI = x

if x ≤ 0, IxI = -x

Notice that I0I = 0.

And the range of this function is all the possible values of y.

For example for the parent function IxI, the range will be all the positive reals and the zero.

First, if A is the value of the vertex of the absolute function, then we know that A is the maximum or the minimum value of the function.

Now, if the arms of the graph open up, then we know that A is the minimum of the function, and the range will be:

y ≥ A

Or all the real values equal to or larger than A.

if the arms of the graph open downwards, then A is the maximum of the function, and we have that the range is:

y ≤ A

Or "All the real values equal to or smaller than A"

Answer:

9 years = 12 grams

Step-by-step explanation:

0 years = 96 grams

After 3 years , the amount left is 1/2 of what you started with

3 years = 1/2 *96 = 48 grams

After 3 years , the amount left is 1/2

6 years = 1/2 (48) = 24 grams

After 3 years , the amount left is 1/2

9 years = 1/2 ( 24) = 12 grams

Answer:

90/x=70/100 that's my answer

[tex]90 \x = 70 \100[/tex]

Answer:

90/x = 70/100

Step-by-step explanation:

Is means equals and of means multiply

90 = 70% *x

Changing to decimal form

90 = .70x

Changing to fraction form

90 = 70/100 *x

Divide each side by x

90/x = 70/100

Answer:

[tex]m^3+m^2[/tex]

Step-by-step explanation:

=> [tex]2m^2-m^2(7-m)+6m^2[/tex]

Collecting like terms and expanding the brackets

=> [tex]2m^2+6m^2-7m^2+m^3[/tex]

=> [tex]8m^2-7m^2+m^3[/tex]

=> [tex]m^2+m^3[/tex]

=> [tex]m^3+m^2[/tex]

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

Answer:

a.  0.6588

b. 0.3978

c. 0. 279

Step-by-step explanation:

In the given question the success and failure are given the number of outcomes is fixed so binomial distribution can be applied.

Here success=  p = 12 % or 12/100 = 0.12

failure = q= 1-p = 1-0.12 = 0.88

n= 10

Using binomial probability distribution

a. Probability that the number of selected adults saying they were too young is 0 or 1 is calculated as:

P (x=0,1) = 0.12 ⁰(0.88)¹⁰10 C0  + 0.12 (0.88)⁹ 10 C1=  1* 0.279 * 1  + 0.12 ( 0.3165) 10 =  0. 279 + 0.3978=  0.6588

b. Probability that exactly one of the selected adults says that he or she was too young to get tattoos is calculated as

P (x=1) =  0.12 (0.88)⁹ 10 C1=  0.12 ( 0.3165) 10 =  0.3978

c. Probability that none of the selected adults say that they were too young to get tattoos is

P (x=0) = 0.12 ⁰(0.88)¹⁰10 C0  =  1* 0.279 * 1   =  0. 279

Answer:

Step-by-step explanation:

Hello,

We can write three equations thanks to Pythagoras

   [tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]

So it comes

[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]

Hope this helps

Answer:

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

Step-by-step explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values

[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 21 ( take the square root of both sides )

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

Answer: Sample mean [tex](\overline{x})[/tex]

Step-by-step explanation:

Given: A study was conducted to determine the average birth weight (in ounces) of babies born in hospitals in a five county area of a given state.

i.e. The parameter of the study is [tex]\mu[/tex] . (Population mean).

A Simple Random Sample of Recent birth records at the local hospitals were selected and the confidence interval was calculated to be (117.89 ounces, 124.91), at a 95% level of confidence.

Since a measure of sample is a statistic , and this case statistic is sample mean denoted by [tex]\overline{x}[/tex].

Hence, the statistic is appropriate for this confidences interval : [tex]\overline{x}[/tex]

Answer: Receipts appear to climb faster than outlays in 2001, 2002, 2003 and 2004

Step-by-step explanation: So if you see the graph you can see that receipts started to climb faster by the middle of 2001 so in conclusion  Receipts appear to climb faster than outlays in 2001, 2002, 2003 and 2004 hope that help you

When government revenues exceed government outlays in a particular year, this is called a d) budget surplus.

A budget surplus occurs when a government's income from taxes and other sources of revenue exceed its expenses and spending on public programs, services, and infrastructure. A budget surplus is a positive indicator for the government's financial health as it indicates that the government is able to manage its finances well, generate more revenue than it spends, and potentially pay off any debts.

Here, we have,

In contrast, a budget deficit occurs when government spending exceeds its revenue, resulting in increased debt and a potentially negative impact on the government's credit rating.

Budget surpluses can be used to invest in public projects or programs, reduce debt, or returned to taxpayers in the form of tax cuts.

However, it is important to note that budget surpluses can also be a result of reduced spending on public programs, which can have a negative impact on social services and infrastructure.

Therefore, the correct answer is d) budget surplus.

Learn more about budget surplus here:

brainly.com/question/30453443

#SPJ2

coomplete question:

When government revenues exceed government outlays in a particular​ year, this is called

A.

the national debt.

B.

a budget deficit.

C.

fiscal policy.

D.

a budget surplus.

Answer:

a. (0.656, 1.064)

Step-by-step explanation:

The sample of cereal is :

n = 32, Standard deviation = 0.81

The confidence interval is 95%

degrees of freedom = df = 31 (n - 1)

[tex]\alpha[/tex] = 95%

1 - 0.95 = 0.05

1 - [tex]\frac{ \alpha }{2}[/tex]

1 - 0.025 = 0.975

Using chi square distribution we get,

0.656, 1.064

Answer:

Volume: 366.6

Surface Area: 314.2

Explanation (look at below)

Step-by-step explanation:

Volume:

The radius of this sphere is 5 (half of 10). The equation will be [tex]\frac{4}{3} \pi[/tex]5^3

When you calculate that, it will become: 366.6<-- rounded to the nearest tenth.

Surface Area:

4[tex]\pi[/tex]5^2

=100Π

=314.2<-- rounded to the nearest tenth.

314.2 is the nearest tenth digit no.

Answer:

B.

Step-by-step explanation:

The function above the x-axis looks like a parabola, so it must have an x^2 term. It also has an open circle, so it must have a > symbol.

The function below the x-axis has a closed circle, so it must have a <= symbol. It is also a 3rd degree polynomial.

Answer: B.

Step-by-step explanation:

Check that attachment

Hope it helps :)

Hey! :)

________ ☆ ☆_________________________________________

Answer:

There are six trigonometric ratios, which will be under “Explanation”

Step-by-step explanation:

Trigonometric ratios are a measurements of a right triangle.

Here are the all the six trigonometric ratios.

1. cotangent (cot)

2. cosecant (csc)

3. cosine (cos)

4. secant (sec)

5. sine (sin)

6. tangent (tan)

Hope this helps! :)

_________ ☆ ☆________________________________________

By, BrainlyMember ^-^

Good luck!

Answer:

Step-by-step explanation:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}[/tex]

Domain:

[tex]x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3[/tex]

solution:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}[/tex]

use (a - b)(a + b) = a² - b²

[tex]\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}[/tex]

multiply both sides by (x - 3) ≠ 0

[tex]\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}[/tex]

cancel (x - 3)

[tex]\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3[/tex]

subtract [tex]\frac{4(x-3)}{x}[/tex] from both sides

[tex]\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}[/tex]

cross multiply

[tex](4)(x)=(x+3)(-x+12)[/tex]

use FOIL

[tex]4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36[/tex]

subtract 4x from both sides

[tex]0=-x^2+12x-3x+36-4x[/tex]

combine like terms

[tex]0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36[/tex]

change the signs

[tex]x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0[/tex]

The product is 0 if one of the factors is 0. Therefore:

[tex]x-9=0\ \vee\ x+4=0[/tex]

[tex]x-9=0[/tex]            add 9 to both sides

[tex]x=9\in D[/tex]

[tex]x+4=0[/tex]          subtract 4 from both sides

[tex]x=-4\in D[/tex]

Answer:

1). f(x) = x² if ∞ < x < 2

2). f(x) = 5 if 2 ≤ x < 4

Step-by-step explanation:

The graph attached shows the function in two pieces.

1). Parabola

2). A straight line parallel to the x-axis.

Standard equation of a parabola is,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the given parabola is (0, 0).

Equation of the parabola will be,

y = a(x - 0)² + 0

Therefore, the function will be,

f(x) = ax²

Given parabola is passing through (-1, 1) also,

1 = a(-1)²

a = 1

Therefore, parabolic function will be represented by,

f(x) = x² if ∞ < x < 2

2). Straight line parallel to the x-axis,

y = 5  if 2 ≤ x < 4

Function representing the straight line will be,

f(x) = 5 if 2 ≤ x < 4

Answer:

Please mark me as Brainliest :)

Step-by-step explanation:

Answer:

A.y = −8x + 80B

Step-by-step explanation:

first you have to find the slope :

P1(2,64). P2(6,32)

slope=Y2-Y1/X2-X1

slope=64-32/2-6

slope= -8

y= -8x + b. now solve for "b" by using one of the coordinates given above.

y= -8x + b. I will use coordinate p(2,64)

64= -8(2) + b

64 + 16 = b

80= b

you can use any of the coordinates i.e either P1(2,64)or P2(6,32) it doesn't affect the value of "b".

line of equation is :

.y = −8x + 80B

Answer: y= -8x+80

Step-by-step explanation:

Answer:

-5/48

Step-by-step explanation:

(8 · 2⁷ˣ)⁴ = (1/16)⁵ˣ · 128

Take log of both sides.

log (8 · 2⁷ˣ)⁴ = log ((1/16)⁵ˣ · 128)

Use log exponent/product rules.

4 log (8 · 2⁷ˣ) = log (1/16)⁵ˣ + log 128

Use log exponent/product rules.

4 (log 8 + log (2⁷ˣ)) = 5x log (1/16) + log 128

Use log exponent rule.

4 (log 8 + 7x log 2) = 5x log (1/16) + log 128

Distribute.

4 log 8 + 28x log 2 = 5x log (1/16) + log 128

Write as powers of 2.

4 log 2³ + 28x log 2 = 5x log (2⁻⁴) + log 2⁷

Use log exponent rule.

12 log 2 + 28x log 2 = -20x log 2 + 7 log 2

Combine like terms.

5 log 2 + 48x log 2 = 0

Divide by log 2.

5 + 48x = 0

Solve for x.

x = -5/48