One number is 24 more than the other. What are the numbers if their sum is 84

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Rule:

If cos(A) = sin(B), then A+B = 90

This can be proven through the use of drawing a right triangle with acute angles A and B. Let's say C is the 90 degree angle.

Then note how cos(A) = adjacent/hypotenuse = AC/AB while sin(B) = opposite/hypotenuse = AC/AB. We see that both evaluate to AC/AB. So this confirms cos(A) = sin(B) is true.

The condition that A+B = 90 is from from the fact that any pair of acute angles of a right triangle are complementary angles.

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Using that rule, we can say

cos(77) = sin(theta)

leads to

77+theta = 90

and that solves to

theta = 90-77 = 13

Answer:

D: 4 2/3

Step-by-step explanation:

First convert these mixed numbers into improper fractions:

8/3 x 7/4 =

(8x7)/(3x4)= 56/12.

Now simplify 56/12, which would be 14/3. Now convert this into a mixed number: 4 2/3.

What is 2 2/3 x 1 3/4                                                              estimate: 2 ₓ 4 Or 8

             5 / 2 ₓ 15/ 4 = 75/8

                               =9 3/8                                                 Convert to mixed                                  

                                                                                        number, divide 75 by 8.

Answer:

1/3

Step-by-step explanation:

There are 9 total outcomes, and 3 are favorable, or are two of the same color in a row. 3/9 simplifies to 1/3. Hope this helps!

Answer:

Brothers Sorry I don't

Step-by-step explanation:

Please give thanks to all my answers and please mark as brilliant and please follow me

Answer:

67.5,

Step-by-step explanation:

22.5x3 =67.5,   P=2(l+w)=2·(22.5+67.5)=180

the answer is will be +50a+125

Answer:

54.5

Step-by-step explanation:

[tex]x \degree = \frac{1}{2} (160 \degree - 51 \degree) \\ \\ x \degree = \frac{1}{2} \times 109 \degree \\ \\ x \degree = 54.5 \\ \\ x = 54.5 [/tex]

Answer: what does this say

Step-by-step explanation:

Answer:

Proved

Step-by-step explanation:

Given

[tex]a_n = 2n[/tex]

Required

Prove that [tex]S_n = n(n+1)[/tex]

The given sequence is an arithmetic sequence.

The Sn of this sequence is:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

Calculate a1

[tex]a_n =2n[/tex]

[tex]a_1 =2*1[/tex]

[tex]a_1 =2[/tex]

So, we have:

[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]

[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]

Factor out 2

[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]

[tex]S_n = n(1 + n)[/tex]

[tex]S_n = n(n + 1)[/tex] --- Proved

Answer:

93°

Step-by-step explanation:

In triangle ABC

one angle = 68°

Another angle = 19°

Let the third angle be X Then

x + 68° + 19° = 180° { being sum of angles of triangle }

x = 180° - 87°

x = 93°

The measure of the third Angle is 93°

Hope it will help :)

Answer:

3

Step-by-step explanation:

Adding 2x and x gets you 3x-5y+3. Counting each term gives you three seperate terms, meaning your answer is 3.

Answer:

answer is 3

Step-by-step explanation:

adding 2x and x gets you 3x-5y+3

Answer:

x = 7 times the square root of 3      

y = 14

Step-by-step explanation:

Answer: it’s 13.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

The null and alternative hypothesis:

[tex]H_o \text{: Quality of management and reputation of company are independent}[/tex]

[tex]H_a \text{: Quality of management is not independent of the reputation of company }[/tex]

The observed values:

                      Excellent     Good    Fair    Total

Excellent           40               25        8        73

Good                 35               35        10       80

Fair                     25              10         12       47

Total                 100             70          30      200

The expected values  = (Row total/column total)/grand total)

                      Excellent     Good        Fair    

Excellent           36.5          25.55      10.95  

Good                  40             28             12

Fair                    23.5         16.45         7.05

O                E                    (O - E)²/E

40              36.5                0.3356

35              40                   0.6250

25              23.5                0.0957

25              25.55              0.0118

35              28                    1.7500

10               16.45                2.5290

8                 10.95               0.7947

10                12                    0.3333

12                 7.05                3.4755

                                            9.951

[tex]X^2 = \sum \dfrac{(O-E)^2}{E} \\ \\ \mathbf{X^2 = 9.951}[/tex]

Degree of freedom [tex]df = (r-1)(c-1)[/tex]

[tex]df = (3 - 1 ) (3 - 1)[/tex]

[tex]df = (2)(2)[/tex]

[tex]df = 4[/tex]

Using Excel formula =CHIDIST(x²,d.f)

The P-value = 0.0413

Answer:

$480

Step-by-step explanation:

10 times 12 is 120

So 120 ft in yards is 40 yards

40 times 12 is 480

Answer:

0

Step-by-step explanation:

what happened that 0 ok live bistro 2.52 and 10 1 which is the quality of the line or 3 x + 100 s y if x = 25

I KNOW ITS SAS....................

you need to use SAS

Step-by-step explanation:

so first you write PQ=QR

PQS=SQR

PS=SR

Answer:1 and 1/2

Step-by-step explanation:

Answer:60,400,696.72

Step-by-step explanation:

it just is...

The most appropriate graph is the (d) line graphs

From the question, we understand that:

Clusters and gaps are easily identified in line graphs, more than the other graphs.

This is also known as the dot plot

Hence, the most appropriate graph is the (d) line graphs

Read more about graphs at:

https://brainly.com/question/24309209

#SPJ1

Answer:

It should be the first quadrant

Hope that helps!

Answer:

Step-by-step explanation:

Answer:d) 40 students

for the second one, it would be 26.

Step-by-step explanation:

My answer: i need a graph

Answer:

X can either be 7, or -10. You can prove this by plugging in the numbers yourself :)

Step-by-step explanation:

Please mark as brainliest

Solution :

It is given that :

P (positive | Has disease) = 0.7

P (positive | No disease) = 0.08

P (has disease) = 0.18

P (No disease) = 1 - 0.18

                        = 0.82

Now if test administered to the individual is positive, the probability that the person actually have the disease is

P (Has disease | positive)  [tex]$=\frac{P(\text{positive}| \text{has positive}) \times P(\text{Has disease})}{P(\text{positive})}$[/tex]  ......(1)

The P(positive) is,

[tex]$P(\text{positive}) = P(\text{positive} \cap \text{Has disease})+P(\text{positive} \cap \text{No disease})$[/tex]

                = P(positive | has disease) x P(Has disease) + P(positive | no disease) x P(No disease)

                 = 0.7 (0.19) + 0.04 (0.81)

                = 0.1654

Now substituting the values in the equation (1), we get

P (Has disease | positive)  [tex]$=\frac{P(\text{positive}| \text{has positive}) \times P(\text{Has disease})}{P(\text{positive})}$[/tex]  

                                           [tex]$=\frac{0.7(0.19)}{0.1654}$[/tex]

                                          = 0.8041  

Step-by-step explanation:

substitute the value in the value of x and u will get the result.

Answer:

[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ;  

where k is the proportionality  constant

Step-by-step explanation:

Let

The number of people who are infected with the flu = x(t)

Total number of students = 1000

So,

Total number of student who do not expose with the flue = 1000 - x(t)

As given,

We have to find the differential equation such that

The rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students show have not been exposed to it.

⇒[tex]\frac{dx}{dt}[/tex] ∝ x(t) . [ 1000 - x(t) ]

⇒[tex]\frac{dx}{dt}[/tex] = k.x.[1000 - x] ; where k is the proportionality  constant

Answer:

Q-22 (a) area of each face (square) = sxs

= 10 x 10

= 100 inches²

Total surface area = 6a²

= 6 x 10 x 10

= 600 inches²