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Two of the known angles in a trianglemeasure 120 and 22 What is the measure of the third angle?

emmasim [6.3K]

Answer:

120+22+x=180

x=38

120+22+38=180

Step-by-step explanation:

Hope it helps

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8 0

3 years ago

The boy scouts are selling two types of popcorn as part of a fundraiser, butter and caramel. Butter popcorn sells for $5 per bag

Setler [38]

Answer:

Alec sold 26 bags of butter popcorn and 14 bags of caramel popcorn

Step-by-step explanation:

Let

x------> the number of bags of butter popcorn sold

y------> the number of bags of caramel popcorn sold

we know that

$x+y=40$ -----> equation A

$5x+6.5y=221$ -----> equation B

Solve the system of equations by graphing

see the attached figure

The solution is the point (26.14)

therefore

Alec sold 26 bags of butter popcorn and 14 bags of caramel popcorn

6 0

3 years ago

Read 2 more answers

PLEASE FAST 40 POINTS

Semenov [28]

Answer:

$\bold{\dfrac{11}{16}}$

Step-by-step explanation:

Given four tiles with numbers:

1, 4, 5 and 8

Tile chosen once and then replaced, after that another tile chosen:

All possibilities are:

{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)

(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)

(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Total number of possibilities = 16

When the sum is greater than 7, the possibilities are:

{(1, 8)

(4, 4) ,(4, 5) ,(4, 8)

(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Number of favorable cases = 11

Formula for probability of an event E is:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Hence, the required probability is:

$\Rightarrow \bold{\dfrac{11}{16}}$

4 0

3 years ago

Read 2 more answers

More Information From the Online Dating Survey A survey conducted in July 2015 asked a random sample of American adults whether

svet-max [94.6K]

Answer:

90% confidence interval for the proportion of all US adults ages 55 to 64 to use online dating is [0.095 , 0.148].

Step-by-step explanation:

We are given that a survey conducted in July 2015 asked a random sample of American adults whether they had ever used online dating.

The survey included 411 adults between the ages of 55 and 64, and 50 of them said that they had used online dating.

Firstly, the pivotal quantity for 90% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who said that they had used online dating = $\frac{50}{411}$ = 0.122

n = sample of adults between the ages of 55 and 64 = 411

p = population proportion of all US adults ages 55 to 64 to use online dating

Here for constructing 90% confidence interval we have used One-sample z proportion statistics.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.122-1.645 \times {\sqrt{\frac{0.122(1-0.122)}{411} } }$ , $0.122+1.645 \times {\sqrt{\frac{0.122(1-0.122)}{411} } }$ ]

= [0.095 , 0.148]

Therefore, 90% confidence interval for the proportion of all US adults ages 55 to 64 to use online dating is [0.095 , 0.148].

7 0

3 years ago

What is an equation of the line that passes through the points (-8, 2) and (-4, -3)?

Alexus [3.1K]

Answer:

y = -5/4x - 8

Step-by-step explanation:

Slope m = (y2-y1)/(x2-x1)

m = (-3 - 2)/(-4 - -8) = -5/4

Given (-8,2)

y = mx + b

2 = -5/4(-8) + b

2 = 10 + b

b = -8

y = -5/4x - 8

4 0

3 years ago