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2 years ago

What is the area of the triangle in the diagram?

Mathematics

2 answers:

dsp732 years ago

5 0

Answer:

The answer is the 2nd one

Step-by-step explanation:

mariarad [96]2 years ago

5 0

Answer:

(B)

Step-by-step explanation:

Given: A triangle whose coordinates are (0,0), $(x_{1},y_{1})$ and $(x_{2},y_{1})$ .

To find: The area of the triangle.

Solution: We know that Area of triangle= $\frac{1}{2}{\times}base{\times}height$ .

Now, Base= $\sqrt{(x_{2}-x_{1})^{2}+(y_{1}-y_{1})^{2}}$

Base= $(x_{2}-x_{1})$

And height= $\sqrt{(0-0)^2+(y_{1}-0)^2}$

Height= $y_{1}$

Therefore, area of triangle= $\frac{1}{2}{\times}(x_{2}-x_{1})}{\times}y_{1}$

Area of triangle= $\frac{1}{2}y_{1}(x_{2}-x_{1})}$

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The number of bacteria in a petri dish on the first day was 113 cells. If the number of bacteria increase at a rate of 82% per d

Tresset [83]

Answer:

4107 cells

Step-by-step explanation:

From the question, we have the following values:

Day 1 : 113 cells

Number of cells increases by day by 82%

Hence,

Day 2

113 × 82% = 92.66cells

Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells

Day 3

205.66 × 82% = 168.6412 cells

Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells

Day 4

374.3012 × 82% = 306.926984 cells

Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells

Day 5

681.228184 × 82% = 558.60711088 cells

Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells

Day 6

1239.8352949 × 82% = 1016.6649418 cells

Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells

Day 7

2256.5002367 × 82% = 1850.3301941 cells

Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells

Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells

3 0

2 years ago

Preston is making cookies. He has fraction 4 over 5 cup of flour in a bag. He then used two fraction 1 over 10 cup scoops of flo

Art [367]

I'm pretty sure the answer will be 6/10

Hope this helps, best of luck, terribly sorry if I'm wrong if I am my apologies

~Animaljamissofab ♥

5 0

2 years ago

Read 2 more answers

Alliance Cannery has two assembly lines. One produces 24 cans of fruit per minute; the other produces 64 cans of vegetables per

sergey [27]

Let
x----------------------- > number of cans of fruit-----------------> 24 per minute
y----------------------- > number of cans of vegetables-------> 64 per minute
z----------------------- > number of cans of food per minute
t----------------------- > time in minutes

z=(x+y)*t
z=(24+64)*t--------------- > 88t
z=88t---------------------------------- > this is the equation required
we know that z=384
then
384=88t------------- > t=4.36 minutes

5 0

2 years ago

Read 2 more answers

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

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 samples 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

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

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

2 years ago

Find the values of x and y that satisfy the equation. 4x+2i=8+yi x= and y=

stiks02 [169]

Answer:

The values of x and y that satisfy the equation are 2 and 2, respectively.

Step-by-step explanation:

Two complex numbers are identical if and only each pair of respective coefficients are identical on both sides. Then, we need to observe the following conditions:

Real component

$4\cdot x = 8$ (1)

Imaginary component

$2 = y$ (2)

The solution of this system of equations is $x = 2$ and $y = 2$ .

The values of x and y that satisfy the equation are 2 and 2, respectively.

5 0

2 years ago