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olganol [36]
3 years ago
8

The difference of two numbers is 5. If the sum of four times the first number and the second number is 50, find the numbers. Put

in an ordered pair.
Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

11,6

Step-by-step explanation:

Idk if this is correct

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In a party, there are 10 pairs arriving, each consisting of a boy and a girl. Then, there is a dance, where each boy dances with
tekilochka [14]

Answer:

Expected no. of squads = 184755

Step-by-step explanation:

In a party, there are 10 pairs arriving, each consisting of a boy and a girl.

So that means there are 10 boys and 10 girls.

A squad is defined as a collection of boy-girl pairs and one single pair is also a squad on its own.

We are asked to find out the the expected number of squads.

For 10 pairs of boys and girls:

Number of squads = ₁₀C₁₀ × ₁₀C₁₀ = 1 × 1 = 1

For 9 pairs of boys and girls:

Number of squads = ₁₀C₉ × ₁₀C₉ = 10 × 10 = 100

For 8 pairs of boys and girls:

Number of squads = ₁₀C₈ × ₁₀C₈ = 45 × 45 = 2025

For 7 pairs of boys and girls:

Number of squads = ₁₀C₇ × ₁₀C₇ = 120 × 120 = 14400

For 6 pairs of boys and girls:

Number of squads = ₁₀C₆ × ₁₀C₆ = 210 × 210 = 44100

For 5 pairs of boys and girls:

Number of squads = ₁₀C₅ × ₁₀C₅ = 252 × 252 = 63504

For 4 pairs of boys and girls:

Number of squads = ₁₀C₄ × ₁₀C₄ = 210 × 210 = 44100

For 3 pairs of boys and girls:

Number of squads = ₁₀C₃ × ₁₀C₃ = 120 × 120 = 14400

For 2 pairs of boys and girls:

Number of squads = ₁₀C₂ × ₁₀C₂ = 45 × 45 = 2025

For 1 pairs of boys and girls:

Number of squads = ₁₀C₁ × ₁₀C₁ = 10 × 10 = 100

The expected number of squads is

Expected no. of squads = 1 + 100 + 2025 + 14400 + 44100 + 63504 + 44100 + 14400 + 2025 + 100

Expected no. of squads = 184755

7 0
2 years ago
Can anybody help me with this
ivolga24 [154]

A = (4, 5)   B = (-2, 1)

<u>Midpoint of A and B</u>

C=(X_M, Y_M) = \bigg(\dfrac{X_A+X_B}{2}, \dfrac{Y_A+Y_B}{2}\bigg)\\\\. \qquad \qquad \qquad =\bigg(\dfrac{4-2}{2},\dfrac{5+1}{2}\bigg)\\\\. \qquad \qquad \qquad =\bigg(\dfrac{2}{2},\dfrac{6}{2}\bigg)\\\\. \qquad \qquad \qquad =(1, 3)


<u>Distance from A to B</u>

d_{AB}=\sqrt{(X_B-X_A)^2+(Y_B-Y_A)^2}\\\\.\qquad =\sqrt{(-2-4)^2+(1-5)^2}\\\\.\qquad =\sqrt{(-6)^2+(-4)^2}\\\\.\qquad =\sqrt{36+16}\\\\.\qquad =\sqrt{52}\\\\.\qquad =7.2


<u>Equation of line through AB</u>

m_{AB}=\dfrac{Y_B-Y_A}{X_B-X_A}\\\\.\qquad =\dfrac{1-5}{-2-4}\\\\.\qquad =\dfrac{-4}{-6}\\\\.\qquad =\dfrac{2}{3}

Y-Y_A=m_{AB}(X-X_A)\\\\Y-5=\dfrac{2}{3}(X-4)\\\\Y-5=\dfrac{2}{3}X-\dfrac{8}{3}\\\\Y=\dfrac{2}{3}X+\dfrac{7}{3}


<u>Line parallel to AB (same slope as AB) through point (3, -5)</u>

Y-Y_A=m_{AB}(X-X_A)\\\\Y+5=\dfrac{2}{3}(X-3)\\\\Y+5=\dfrac{2}{3}X-2\\\\Y=\dfrac{2}{3}X-7


AB is <u>perpendicular</u> to A'B' so slopes are <u>opposite reciprocals</u>

A' = (3, 0)

B' = (-1, 6)

C = (1, 3)

C' = (7, 3)

D = (5, 3)

D' = (5, 1)



3 0
2 years ago
In a previous​ year, 58​% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different tod
Gemiola [76]

Answer:

z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744  

Since is a bilateral test the p value would be given by:  

p_v =2*P(z  

And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58

Step-by-step explanation:

Information given

n=600 represent the random sample selcted

X=339 represent the number of females aged 15 and older that living alone

\hat p=\frac{339}{600}=0.565 estimated proportion of females aged 15 and older that living alone

p_o=0.58 is the value that we want to check

\alpha=0.01 represent the significance level

z would represent the statistic

p_ represent the p value

Sytem of hypothesis

We want to check if the true proportion females aged 15 and older that living alone is significantly different from 0.58.:  

Null hypothesis:p=0.58  

Alternative hypothesis:p \neq 0.58  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info given we got:

z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744  

Since is a bilateral test the p value would be given by:  

p_v =2*P(z  

And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58

5 0
3 years ago
Use the figure shown.
mr Goodwill [35]

Answer:

Step-by-step explanation:

5 0
2 years ago
1. The temperature was -8°F and rose by 2°F. What is the new temperature? Expression:​
aev [14]
New temperature: -6°
-8 +2= -6
3 0
2 years ago
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