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Aloiza [94]
3 years ago
9

3.

Mathematics
1 answer:
gayaneshka [121]3 years ago
5 0

Answer:

M(x,y) = (4.8,4.4)

Step-by-step explanation:

Given

P(x_1,y_1) = (6,2)

Q(x_2,y_2) = (3,8)

m:n = PM:MQ = 3 : 2

Required

Determine the coordinates of M

To solve this, we make use of the following partition formula:

M(x,y) = (\frac{nx_2+mx_1}{n+m},\frac{ny_2+my_1}{n+m})

Substitute values for m, n, x's and y's

M(x,y) = (\frac{2*3+3*6}{2+3},\frac{2*8+3*2}{2+3})

M(x,y) = (\frac{24}{5},\frac{22}{5})

M(x,y) = (4.8,4.4)

<em>Option D is correct</em>

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Which equation can be used to solve for x in the parallelogram below?
densk [106]

Answer:

B. (3x - 12)° = (2x + 8)°

Step-by-step explanation:

This equation can be used to solve x.

3x - 12 = 2x + 8

3x - 2x = 12 + 8

x = 20°

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

Verification:

3(20) - 12 = 2(20) + 8

60 - 12 = 40 + 8

48° = 48°

6 0
3 years ago
A city has a population of 280,000 people. suppose that each year the population grows by 4.5% . what will the population be aft
Anastasy [175]

Given that population of the city is 280000.

Rate of growth of the population = r = 4.5% = 0.045

We have to find population after 15 years so time

t = 15

We can use growth formula to find the required population which is given by :

A=P(1+r)^t

Where P= starting population = 280000

r= rate of growth = 0.45

t= time = 15

now plug these values into above formula.

A=280000(1+0.45)^{15}

A=280000(1.45)^{15}

A=280000(263.34194176)

A=73735743.6928

Hence population after 15 years will be approx 73735743.

8 0
3 years ago
On day two of a study on body temperatures, 106 temperatures were taken. Suppose that we only have the first 10 temperatures to
NemiM [27]

Answer:

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.2622

The margin of error is:

M = T*s = 2.2622*0.3 = 0.68

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF

The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF

The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF

4 0
3 years ago
1) Identify the slope of the given line
adell [148]

ok so here we go:

1) (-6,-2.5),(-4,-3)\ m= -0.25 or  -\frac{1}{4}

2 )y=-0.25x-4 so the answer is (0, -4) or -4

3) y=\frac{3}{2}x+1 m=\frac{3}{2}

4) y=[tex]\frac{3}{2}x+1[tex] so the answer is (0, 1) or 1

8 0
4 years ago
Read 2 more answers
Find the value of cos 28°​cos 62°​– sin 28°​sin 62°​
Romashka [77]
<h2>Answer:</h2>

cos 28°​cos 62°​– sin 28°​sin 62°​ = 0

<h2>Step-by-step explanation:</h2>

From one of the trigonometric identities stated as follows;

<em>cos(A+B) = cosAcosB - sinAsinB             -----------------(i)</em>

We can apply such identity to solve the given expression.

<em>Given:</em>

cos 28°​cos 62°​– sin 28°​sin 62°​

<em>Comparing the given expression with the right hand side of equation (i), we see that;</em>

A = 28°

B = 62°

<em>∴ Substitute these values into equation (i) to have;</em>

<em>⇒ cos(28°+62°) = cos28°cos62° - sin28°sin62°</em>

<em />

<em>Solve the left hand side.</em>

<em>⇒ cos(90°) = cos28°cos62° - sin28°sin62°</em>

⇒ 0 = <em>cos28°cos62° - sin28°sin62°     (since cos 90° = 0)</em>

<em />

<em>Therefore, </em>

<em>cos28°cos62° - sin28°sin62° = 0</em>

<em />

<em />

8 0
3 years ago
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