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2 years ago

Three copies of a triangle were rotated and positioned as shown.

Mathematics

1 answer:

lara31 [8.8K]2 years ago

4 0

The question aks us to determine which statement is always true about the angles in the figure. If angle A and B form a right angle, then C must be also a right angle, which is not correct. Also if A and C form a right angle, then angle B must be a right angle. So answers A and C are false. Also thet we know that the sum of the interior angles of the triangle is 180 degrees. A + B + C = 180 deg. ( or a straight angle ). Answer: B. Angle A, angle B, and angle C, form a straight angle.

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If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x?A. -2B

podryga [215]

Answer:

B) -3/2

Step-by-step explanation:

If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.

Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since -1 is an integer and -1<0. Then x/2>-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.

Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that -1<-3/4≤0 as required.

3 0

2 years ago

The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probab

kolezko [41]

Answer:

(a) 0.6579

(b) 0.2961

(d) 240

Step-by-step explanation:

The random variable X can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable X thus follows a Poisson distribution with parameter, λ = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.

The mean of the approximated distribution of X is:

μ = λ = 250

The standard deviation of the approximated distribution of X is:

σ = √λ = √250 = 15.8114

Thus, $X\sim N(250, 250)$

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

$P(235$

$=P(-0.95$

Thus, the value of P (235 < X < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

$P(48$

$=P(-0.28$

Thus, the value of $P(48$ .

(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

$P(48$

$=P(-0.40$

Thus, the value of $P(48$ .

(d)

Let the sample size be n.

$P(48$

$0.95=P(-z$

The value of z for this probability is,

z = 1.96

Compute the value of n as follows:

$z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241$

Thus, the sample selected must be of size 240.

5 0

2 years ago

16. Write the inequality that is shown on the graph.

TiliK225 [7]

Answer: 5<x<9

Step-by-step explanation:

Graph is from 5 to 9, not including 5 and 9. Let's say x is all the values from 5 to 9, not including 5 and 9.

So, answer is 5<x<9

3 0

11 months ago

The graph below shows the solution to which system of inequalities?

nlexa [21]

Answer:

Option D.

Step-by-step explanation:

Consider option D. $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

Take point (0,0)

On putting this point in inequation $y\leq \frac{3x}{4}+10$ , we get

$0\leq 10$ which is true . So, solution is region towards the origin i,e region below the line $y= \frac{3x}{4}+10$ including the line itself .

On putting (0,0) in inequation $y\leq \frac{-x}{2}-3$ , we get $0\leq -3$ which is false , so solution is region away from the origin i.e region below line $y= \frac{-x}{2}-3$ including the line itself .

So, common solution to both the inequations is the shaded part in the given figure .

In other words, we can say that the graph shown in the given figure represents system of equations: $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

5 0

2 years ago

A farmer grows corn, tomatoes, and sunflowers on a 320-acre farm. This year, the farmer wants to plant twice as many acres of to

svet-max [94.6K]

Set it up with variables; tomatoes=t, sunflowers=s, corn=c

320=t+s+c

This year;
t=2s
c=t+40

so, replace 2s for t; c=2s+40

now we can put those factors in for 320=t+c+s

320= 2s+2s+40+s
(SIMPLIFY)---> 320=5s+40----> 5s+280----> s=56

now incorporate the s value into the other equations.

c=2s+40----> c=56(2)=40 ----> c=152
t=2s -----> t=2(56) ----> t=112

TOMATOES= 112 acres
CORN= 152 acres
SUNFLOWERS= 56 acres

To check your work: 320=t+s+c ----> 320=112+156+56

5 0

2 years ago

Read 2 more answers