All categories

3 years ago

E e e e e e e e e ) ∘

Mathematics

2 answers:

ad-work [718]3 years ago

8 0

The answer is a because 180=119+m
-119 -119

61=m

timofeeve [1]3 years ago

5 0

Answer:

⏩ 61°

Step-by-step explanation:

m + 119° = 180°( Being linear pair)

m = 180° - 119°

m = 61°

Hope it will help :)❤

You might be interested in

62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r

dedylja [7]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

62% of owned dogs in the United States are spayed or neutered.

This means that $p = 0.62$

48 owned dogs are randomly selected

This means that $n = 48$

Mean and standard deviation, for the approximation:

$\mu = E(x) = np = 48*0.62 = 29.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36$

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180$

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, $P(X \leq 33 + 0.5) = P(X \leq 33.5)$ , which is the pvalue of Z when X = 33.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33.5 - 29.76}{3.36}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is $P(X \geq 31 - 0.5) = P(X \geq 30.5)$ , which is 1 subtracted by the pvalue of Z when X = 30.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, $P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5)$ , which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

X = 23.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{23.5 - 29.76}{3.36}$

$Z = -1.86$

$Z = -1.86$ has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

8 0

3 years ago

You are reducing a map of dimensions 2 ft by 3 ft to fit on a piece of paper 8 in. by 10 in. what are the dimensions of the larg

stepan [7]

Answer:

The dimensions of the largest possible map that can fit on the page are 10 inches by $6\frac{2}{3}$ inches.

Step-by-step explanation:

You are reducing a map of dimensions 2 ft by 3 ft

Lets change them to inches.

1 foot = 12 inches

So, 2 feet = $2\times12=24$ inches

3 feet = $3\times12=36$ inches

So, dimensions are : 24 inches x 36 inches

$\frac{24}{36}=\frac{2}{3}$

Since 10 inch will be the longer side, we can find the shorter side by :

$\frac{x}{10}=\frac{2}{3}$

$3x=20$

$x=\frac{20}{3}$

or $x=6\frac{2}{3}$ inches

So, the dimensions of the largest possible map that can fit on the page are 10 inches by $6\frac{2}{3}$ inches.

5 0

3 years ago

Identify the number in the hundredths place in the numeral: 364.158.

Marrrta [24]

The number in the hundredths place is the 6. Tens, Hundredths, Thousands..etc..
But, on the right side of the decimal, 5 is in the hundredths.

5 0

4 years ago

Can somebody help me with this I don’t get it?

Inessa [10]

Answer:

the time means how long it takes to get to that distance below it

Step-by-step explanation:

4 0

3 years ago

I'm having a bit of a problem with this piecewise function I will upload a photo

kipiarov [429]

Given the piecewise function:

$f(x)=\begin{cases}-0.5x-4,x\le-2 \\ 5,-24\end{cases}$

So, for the given function, we will graph it as follows:

1) graph the line (-0.5x-4) as x less than or equal to -2

To graph the line, we need two points

We will substitute with two values less than -2 and calculate the corresponding values of f(x)

When x = -4, f(x) = -0.5 * -4 - 4 = -2

When x = -6, f(x) = -0.5 * -6 - 4 = -1

So, the line will pass through the points ( -4, -2) and ( -6, -1)

The line will start from the point ( -2, -3)

The dot at x = -2 will be closed.

2) Graph the line (y = 5) as x between -2 and 4

The line will be horizontal at this interval

the dot at x = -2 will be open

The dot at x = 4 will be closed

3) Graph the line ( -x + 5 ) as x greater than 4

As in (1), substitute with 2 values of x greater than 4

When x = 5, f(x) = -5 + 5 = 0

When x = 6, f(x) = -6 + 5 = -1

So, the line will pass through the points ( 5, 0 ) and ( 6, -1 )

The graph of the function will be as shown in the following picture:

8 0

1 year ago