The diagonal and the longer side of a rectangle make an angle of 43.2°. If the longer
side is 12.6cm. Find the length of the shorter Side.​

Answer:

120 degrees

Step-by-step explanation:

plugged into calculator

cos inverse of -1/2

Please mark Brainliest if you feel like it:)

Answer:

[tex]p \± ME[/tex] [tex]\to[/tex] [tex]71.2\% \± 7.9\%[/tex]

Step-by-step explanation:

Given

[tex](63.3\%,79.1\%)[/tex]

Required

Express in form of: [tex]p \± ME[/tex]

First, calculate the midpiont (p)

[tex]p = \frac{63.3\% + 79.1\%}{2}[/tex]

[tex]p = \frac{142.4\%}{2}[/tex]

[tex]p = 71.2\%[/tex]

The margin of error (ME) is:

[tex]ME =79.1\% - 71.2\%[/tex]

[tex]ME =7.9\%[/tex]

So, we have:

[tex]p \± ME[/tex] [tex]\to[/tex] [tex]71.2\% \± 7.9\%[/tex]

Answer:

121.50

Step-by-step explanation:

Let x be the earnings

2x+10 = 253

Subtract 10 from each side

2x+10-10 = 253-10

2x = 243

Divide by 2

2x/2 = 243/2

x = 121.50

Answer:

[tex]s = - \frac{1}{4} [/tex]

Step-by-step explanation:

For m to be equal to n,

[tex]2s = \frac{2s- 1}{3} [/tex]

Multiply both sides by 3:

[tex]6s = 2s - 1[/tex]

Minus 2s on both sides:

[tex]4s = - 1[/tex]

Divide by 4 on both sides:

[tex]s = - \frac{1}{4} [/tex]

Answer:

c > 5.28

Step-by-step explanation:

From the quadratic formula when the quantity under the square root sign, known as the determinant, is positive there will be two real solutions

b² - 4ac > 0

(-13)² - 4(8)c > 0

169 - 32c > 0

-32c > -169

c > 5.28125

Rounded

c > 5.28

Answer:

Approximately 92

Step-by-step explanation:

Using technology, the linear regression model obtained by fitting the data points is:

Y = 0.0914X1 - 0.3741

Where x = test score ; y = average sleep

Slope = 0.0914 ; intercept = - 0.3741

The test score of a student that sleeps 8 hours

y = 8

8 = 0.0914X1 - 0.3741

8 + 0.3741 = 0.0914X1

X = 8.3741 / 0.0914

X = 91.62

Answer:

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

Answer:

Step-by-step explanation:

W=[tex]\sqrt{x-a/a}[/tex]

squaring both sides

W^2=([tex]\sqrt{x-a/a}[/tex] )^2

W^2=x-a/a

wa=x-a

a=x-a/w

[tex] \boxed{\boxed{\huge{ \mathrm{  \underline{ Answer} \:  \:  ✓ }}}}[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer: 77

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

The ratio is 5:2 , simplify an you'll get 1:2/5

Answer:

2912

Step-by-step explanation:

the answer is 2912 toys.....

Answer:

4 cm

Step-by-step explanation:

The Area of a parallelogram is given by :

Area = base * height

Area = 120 cm² ; height = 30

Area = base * height

120 = base * 30

Base = 120 / 30

Base of parallelogram = 4 cm

Answer:

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Given the following data;

Present value, P = $300

Interest rate, r = 8%

Number of times, n = 1/4

Note: Future value = 2 * P = 2*300 = $600

Compound interest is generally calculated based on the interest rate on a loan, principal and the accumulated interest gained from previous periods. This interest is compounded for a certain number of times such as daily, weekly, quarterly or annually.

To find how long she would have to invest her money in order to double it, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{n})^{nt}[/tex]

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

n is the number of times the interest is compounded in a year.

t is the number of years for the compound interest.

Answer:

1 3/7

Step-by-step explanation:

5 / 7 ÷ ½

Copy dot flip

5/7 * 2/1

10 /7

Changing from an improper fraction

7/7 + 3/7

1 3/7

Answer:

(9,11)

(15,17)

(18,20)

Step-by-step explanation:

9-6=3

11-8=3

18-6=12

20-8=12

15-6=9

17-8=9

3*1=3

3*4=12

3*3=9

Answer:

735 mm³

Step-by-step explanation:

49 x 15 = 735

Answer:

735mm

Step-by-step explanation:

Answer:

5x² - 10

Step-by-step explanation:

Step 1:

( [tex]3x^{2}[/tex] + 4x - 8 ) - ( [tex]-2x^{2}[/tex] + 4x + 2 )   Equation

Step 2:

3x² + 4x - 8 + 2x² - 4x - 2    Open Parenthises

Answer:

5x² - 10          Simplify

Hope This Helps :)

Answer:

5x² + 10

Step-by-step explanation:

Given Equation :-

( 3x² + 4x - 8 ) - ( -2x² + 4x + 2)

Solution :-

Step 1:- Remove unnecessary parantheses.

Step 2 :- arranging like terms.

Step 3 :- Calculate like terms.

Answer:

15, 8, 66%, 40

Step-by-step explanation:

Hi! ok so in ogive charts its really about finding the corresponding data points and sometimes it's a lot of estimation so these answers may not be exact but they'll be close.

In the image, you'll see a bunch of lines, basically what youre doing is finding the corresponding frequency of the dollars or vice versa.

question a)

50 dollars or less, so the area of 50 dollars and below that.

from the chart we can see that this lines up to around 15 people.

question b)

now this one is a little bit more challenging, but you can use the same process as you did for the first question. so we can see who spent 100 dollars or less. this value is around 42 (just from looking at the graph)

we know if you didn't spend 100 dollars or less, you must have spent more than that.

so take 50-42=8

around 8 people spent 100 dollars or more.

question c)

basically the same question as the first but more calculations are involved. from the graph we can see around 33 people spent 80 dollars or less. but the question is asking the percentage. so what percent of 50 (people) is 33.

33/50 = 0.66

around 66%

question d)

80th percentile means less than or equal to 80% of the frequencies/the data. so we first need to find what value that is in terms of frequency.

50 times 0.8 = 40

40 people

now just plot that on the graph (sorry i did it wrong in the image)

Answer:

13/16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.

We'll find the equation of the line and solve the system to find the center.

Midpoint of the chord:

Equation of the line through chord (-1,2) and (2,3):

Perpendicular bisector is:

And the given line is:

Solve the system:

Find y:

The center is (-1, 7)

Find the radius, the distance from center to one of points on circle

The equation of circle is:

Hope This Helps!!!

Hope This Helps!!!Have A GREAT DAY!!!

Total number of plants,

= 13 + 2 = 15

Number of plants in a row = 3

Hence, Total Number of rows,

Therefore, he will have five rows.

Answer:

The equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is [tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex].

Step-by-step explanation:

A sphere is described by its radius and center, the radius of the largest sphere contained in the first octant are determined by the least distance of the center with respect to an orthogonal axis, that is:

Distance regarding x-axis:

[tex]d_{x} = 10 - 0[/tex]

[tex]d_{x} = 10[/tex]

Distance regarding y-axis:

[tex]d_{y} = 8 - 0[/tex]

[tex]d_{y} = 8[/tex]

Distance regarding z-axis:

[tex]d_{z} = 7 - 0[/tex]

[tex]d_{z} = 7[/tex]

Hence, the radius of the sphere must have a measure of 7. The equation of the sphere is represented by the following geometric locus:

[tex](x-h)^{2} + (y-k)^{2} + (z - j)^{2} = r^{2}[/tex] (1)

Where:

[tex]h, k, j[/tex] - Coordinates of the center.

[tex]r[/tex] - Radius of the sphere.

If we know that [tex](h,k,j) = (10, 8, 7)[/tex] and [tex]r = 7[/tex], then the equation of the largest sphere with center (10, 8, 7) that is contained completely in the first octant is:

[tex](x-10)^{2} + (y - 8)^{2} + (z - 7)^{2} = 49[/tex]

Answer:

hope it helps you see the attachment for further information

sorry but my phone couldn't captured r=2

Answer:

9 days before only 8 mg is still emitting radiation.

Step-by-step explanation:

The exponential model is:

[tex]y(t) = a(0.5)^{\frac{t}{28}}[/tex]

In which a is y(0), that is, the initial quantity.

10 mg is ingested by a patient

This means that [tex]a = 10[/tex], and thus:

[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]

How many days before only 8 mg is still emitting radiation?

This is t for which y(t) = 8. So

[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]

[tex]8 = 10(0.5)^{\frac{t}{28}}[/tex]

[tex](0.5)^{\frac{t}{28}} = \frac{8}{10}[/tex]

[tex](0.5)^{\frac{t}{28}} = 0.8[/tex]

[tex]\log{(0.5)^{\frac{t}{28}}} = \log{0.8}[/tex]

[tex](\frac{t}{28})\log{0.5} = \log{0.8}[/tex]

[tex]\frac{t}{28} = \frac{\log{0.8}}{\log{0.5}}[/tex]

[tex]t = 28\frac{\log{0.8}}{\log{0.5}}[/tex]

[tex]t = 9[/tex]

9 days before only 8 mg is still emitting radiation.

Answer:

[tex]\text{a) }1,080^{\circ}, \\\text{b) }360^{\circ}, \\\text{c) }135^{\circ}, \\\text{d) }45^{\circ}[/tex]

Step-by-step explanation:

a) The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, substitute in [tex]n=8[/tex]:

[tex](6-2)180=\boxed{1,080^{\circ}}[/tex]

b) The sum of the exterior angles for any polygon is equal to [tex]360^{\circ}[/tex].

c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be [tex]\frac{1080}{8}=\boxed{135^{\circ}}[/tex]

d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is [tex]360^{\circ}[/tex], thus we have [tex]\frac{360}{8}=\boxed{45^{\circ}}[/tex]