In the following exercises, multiply the binomials. Use any method.
247. (p + 12)(p − 5)

Answer:

b) The two triangles are similar by SAS

Step-by-step explanation:

From the diagram below, we can tell that

SAS similarity (Side-Angle-Side similarity) is a criterion used to determine whether two triangles are similar.

It states that if two sides of one triangle are proportional to two sides of another triangle, and the included angles between these sides are congruent, then the two triangles are similar.

In other words, if in two triangles, the ratio of the lengths of corresponding sides is equal, and the included angles between these sides are congruent, then the two triangles are considered similar.

The corresponding angles are congruent and the sides are in proportion

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Answer:1981

Step-by-step explanation:

Answer:

3x-10=x+40

X=25

Angels are 65

Ans:c

The sample size which will produce sample proportion of 0.3 and 95% confidence interval is 36.

Given sample proportion of 0.3, confidence level 95%.

A confidence interval of proportions is given by:

π±z[tex]\sqrt{}[/tex]π(1-π)/n

In which :

π is the sample proportion,

z is the critical value

n is the sample size.

Margin of error=z[tex]\sqrt{}[/tex]π(1-π)/n

z value for confidence level of 95% is 1.96

Margin of error=1.96[tex]\sqrt{0.3*0.7/n}[/tex]

The widest interval has the highest margin of error, since the margin of error and since the margin of error is inversely proportional to the sample size , a lower sample size generates a higher margin of error.

Hence sample size which is correct is 36.

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Question is incomplete as it also includes options like:

a)46

b)68

c)56

d)36.  

Answer:

55

Step-by-step explanation:

[tex] \frac{n(n + 1)}{2} \\ n = 10 \\ substitutig \\ \frac{10(10 + 1)}{2} \\ \\ \frac{10(11)}{2} \\ \\ \frac{110}{2} = 55 [/tex]

Answer:

24p^2q^2 - 42pq + 15

Step-by-step explanation:

Answer:

Hence the expression [tex]$$(6pq-3)(4pq-5)=24p^2q^2-42pq+15$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{matrix}{} & {} & {} & {} & 6pq & - & 3 \\ \times & {} & {} & {} & 4pq & - & 5 \\ \end{matrix}$$[/tex]

_________________

[tex]$$\begin{matrix}{} & {} & {} & - & 30pq & + & 15 \\ {} & {} & 24{{p}^2}{{q}^2} & - & 12pq & {} & {} \\ \end{matrix}$$[/tex]

___________________

[tex]$$\begin{matrix}{} & {} & 24{{p}^2}{{q}^2} & - & 42pq & + & 15 \\ \end{matrix}$$[/tex]

Answer:

it means y intercept

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

mean = 140+20=160

160/2

= 80

Answer: 160

Step-by-step explanation:

Just took it

Answer:

3 < QS < 13.

I just did it on edge

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The length of QS can lie between 3 < QS < 13.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

Here, we have,

As per the given law of triangle inequality, the sum of the two sides of the triangle is greater than the third side.

x + 8 > 5

x > -3

x + 5 > 8

x > 3

8 + 5 > x

13 > x

Hence, In triangle QRS the length of QS can lie between 3 < QS < 13.

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Answer:

9cm

Step-by-step explanation:

The CIRCUMFERENCE OF A CIRCLE is the distance round the circle.

It has the formular 2πr.

were r = radius

C = 2πr

72 = 2 × 3.142 × r

72 = 6.284r

dividing bothsides by 6.284

r = 72/ 6.284

r = 11.457

AB is an arc.

Lenght of an arc

[tex] \frac{ \alpha }{360} \times 2\pi \: r \\ \\ \frac{45}{360} \times 2 \times 3.142 \times 11.457 \\ \\ \frac{45}{360} \times 71.995 \\ \\ = 8.999 \\ \\ = 9cm[/tex]

Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:

[tex]\mu = 15 \times \frac{45}{120} = 5.625[/tex]

The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004[/tex]

[tex]P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02[/tex]

[tex]P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057[/tex]

[tex]P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107[/tex]

[tex]P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150[/tex]

[tex]P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169[/tex]

Then:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507[/tex]

0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

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Answer:

the widths of the wire :)

Step-by-step explanation:

The number of possible passwords is 26^4 * 10^4.

We will make 4 picks from each category (letters and numbers).

We can duplicate them (i.e., pick each character more than once.)

so, for your 4 picks from the letters, you'll have

26 * 26 * 26 * 26 = 26^4 possible selections.

For each of these, you'll have 4 picks from the digits. Similar reasoning, this works out to

10^4 combinations of digits.

This means you'll have 26^4 * 10^4

Possible combinations of 4 letters and 4 digits, and, for each of these, you now need to work out how many unique ways to arrange them.

We will have 8 possible choices for the 1st character, 7 for the second, 6 for the third, etc. This works out to 8!

different orderings for each of your

26^4 * 10^4

The number of possible passwords is 26^4 * 10^4.

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Answer:

0.3 gallon

Step-by-step explanation:

To do this problem, we must divide the amount of cement by the number of feet to see how much cement he used for each foot.

15/50 = 0.3 gallon

Answer:

0.3 gallons per foot

Step-by-step explanation:

We know that he used 15 gallons of cement for 50 feet.

We want to find the amount per foot or the amount per each 1 foot.

So we have to divide the 15 gallons by the 50 feet.

15 / 50 = 0.3 gallons per foot.

Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]

So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]

Answer:

x > 9

Step-by-step explanation:

Hello!

First let's solve the inequality for x.

Flip the sign if you are dividing by a negative number.

Now let's graph it on a number line. If it is a greater or less than symbol, we use an open circle. If it is a greater than or equal to or a less than or equal to, we use a closed circle.

Plot the point of 9 with an open circle, and shade in a line towards the right (all values greater than 9).

Answer:

[tex]\boxed{Circuit_{\Delta ABC} = 15~cm }[/tex]

Step-by-step explanation:

The ABC triangle is an equilateral triangle.

[tex]\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

The drawing in the attachment.

I am entering meaningfully:

a - side length of an equilateral triangle

[tex]a=\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

[tex]P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}[/tex]  -   equilateral triangle area formula

[tex]P_{\Delta} =\dfrac{25 \sqrt{3} }{4}~~\land~~P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}~~\Rightarrow~~\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}\\\\\\\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}~~\mid~~\div ~~\dfrac{\sqrt{3} }{4} \\\\\\\dfrac{a^{2} \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } =\dfrac{25 \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } \\\\a^{2} =25~~\\\\a^{2} =5^{2} ~~\land~~a > 0~~\Rightarrow~~\boxed{a=5~cm}\\\\\\[/tex]

[tex]Circuit_{\Delta ABC} =a+a+a\\\\Circuit_{\Delta ABC} =3a~~\land~~a=5~cm\\\\\boxed{Circuit_{\Delta ABC} =3\cdot 5 = 15~cm }[/tex]

There is no solution for the equation | 3x+7|-5.

When asked to explain why there is no solution to |3x+7|-5 Jack said, "It is not a solution because the 5 is negative." Jack is on the right track but his reasoning is incomplete

equation are format of a link which process over mathematical operators like addition, subtraction etc.

| 3x+7|-5 has no solution because the data is incomplete. Without know there limits or equal to zero, less than zero or greater than zero this system of equation cannot be defined. That is why there is no solution for | 3x+7|-5.

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1+3-2+0=2

-3-2+1+2=-2

Answer:

d.-½ ,represent change of y with respect to x

Step-by-step explanation:

The values of y with respect to x are :-

Thus, -½ in the value of the change in y with respect to x.

Answer:

The correct answer would be B) 2

Answer:

C 1/2

Step-by-step explanation:

Since the angels of these triangles are same,they are totally similar.

The ratios of their sides are

10/20=1/2

8/16=1/2

6/12=1/2

So, The scale factor is 1/2.

Considering the problem described, we have that:

a) The normal distribution can be used, as both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

b) There is a 0.0132 = 1.32% probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are:

n = 2000, p = 0.92.

Hence:

Since both [tex]np \geq 10, n(1 - p) \geq 10[/tex], a normal approximation can be used. The mean and the standard deviation of the approximation are given as follows:

The probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less, using continuity correction, is P(X < 175.5), which is the p-value of Z when X = 175.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{175.5 - 184}{3.8367}[/tex]

Z = -2.22.

Z = -2.22 has a p-value of 0.0132.

0.0132 = 1.32% probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less.

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The average speed of Ken is 70 m/min. Using the relation between the speed and distance, the required speed for Ken is calculated.

The relationship between speed S and distance D with a period T is formed as

S = D/T

Units: m/sec (basic unit)

Given that,

Jaylen and Ken started jogging from the same place in opposite directions along a straight path.

This means, that the sum of distances traveled by both of them in opposite directions = 13.6 km (since it is given that at the end of their jogging, they are 13.6 km apart)

Consider,

The distance traveled by Jaylen = x km

Then the distance traveled by Ken = x - 2.4 km (since Jaylen jogged 2.4 km more than Ken)

Step 1: Finding the distance traveled by them:

x + x - 2.4 = 13.6

⇒ 2x = 13.6 + 2.4

⇒ 2x = 16

⇒ x = 8 km

So, the distance travelled by Jaylen = 8 km and by Ken = 8 - 2.4 = 5.6 km

Step 2: Finding the average speed traveled by Ken:

Since it is given that,

Jaylen's speed was 30 m/min faster than Ken's speed.

So,

For 30 m, the time = 1 min

then for 2.4 km i.e., 2400 m, the time = 80 min.

Therefore,

the average speed of Ken S = D/t

⇒ S = 5600 m / 80 min

∴ S = 70 m/min.

So, the average speed of Jaylen will be 70 m/min + 30 m/min = 100 m/min.

Thus, the average speed of Ken is 70 m/min.

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A circle and a triangle can intersect in a point.

This refers to the fact that two lines are able to meet at a given point. The point where they meet is the point of intersection.

A circle is known to be able to intersect with a triangle in three different ways and at one point.

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Parallel lines are lines in a plane that are always the same distance apart.

☆...hope this helps...☆

_♡_mashi_♡_

Lines with the same slope that never touch each other.

Parallel lines share the same slope (direction). Attached is an example of two lines parallel to each other, [tex]y=2x-1[/tex] in red and [tex]y=2x+1[/tex] in green. They both have a slope of [tex]2[/tex], which is what makes them parallel.

The estimated probability that at least one of the next four fish Roxanne catches will be a perch is 34%

Probability is the likeliness of an event to happen. It has a range of 0 to 1, where 0 indicates uncertainty and 1 indicates certainty.

It is given that

0, 1, and 2 represent trout , 3 and 4 represent bass , 5 represent perch , 6, 7, 8, and 9 represent other fish

From the data it can be observed that

Total number of single digits numbers = 80

No. of Perch , "5 " = 8

Probability of getting a perch in next fish = 8/80 = 0.1

Probability that at least one of the next four fish Roxanne catches will be a perch = 1- P(no perch)

P ( no perch) = 1 - 0.1 = 0.9

for 4 fishes

= 1 - 0.9⁴

= 0.3439

= 34.39%

≈ 34%

Therefore the estimated probability that at least one of the next four fish

Roxanne catches will be a perch is 34%.

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The value of x would make the triangles similar by the SSS similarity theorem would be 30 . Option C

The SSS similarity theorem of triangles holds that if the three sides of two triangles are proportional, then the triangles are similar.

If the two triangles are to be similar, we have that:

45/x = 75/50

Cross multiply

x = (45 × 50)/75

x = 2250/75

x = 30

Therefore, the value of x would be 30 . Option C

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Step-by-step explanation:

[tex] = \frac{ \frac{10}{3} }{ \frac{2}{3} } [/tex]

[tex] = \frac{10}{3} \div \frac{2}{3} [/tex]

[tex] = \frac{10}{3} \times \frac{3}{2} [/tex]

[tex] = \frac{9 + 1}{3} \times \frac{3}{2} [/tex]

[tex] = 3 \frac{1}{3} \times \frac{3}{2} [/tex]

[tex] = 3 \frac{1}{3} .( \frac{3}{2} )[/tex]

The answer is B.

The graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

The inequalities given in the task content can be solved as follows;

For –2x + 4 ≤ 8

-2x ≤ 8 -4

x >= -2

For –2x + 4 > –6

–2x > –6 -4

x < 5

Hence, the graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

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Answer: θ≈48,81°.

Step-by-step explanation:

[tex]sin\theta=\frac{8}{\sqrt{113}}\\sin\theta } =\frac{8*\sqrt{113} }{\sqrt{113}*\sqrt{113} } \\sin\theta=\frac{8*\sqrt{113} }{113} \\sin\theta\approx0,75258\\\theta\approx48,81^0.[/tex]

Good luck an' have a nice day!

Mickey, Making errors could be that he must be found out that cost of one carton is $0.50, by dividing 12 cartons with total cost and by this  e figured it out the cost of 7 carton is just $3.5.

In this question is  arithmetic, what we have in, the question is 12 cartons of eggs cost $22.20. we need to find out the cost of seven cartons.

In mathematics it deals with numbers of operations according to the statements.

Here, the cost of one carton is given by;
  =  22.20/12  = $1.85

now the cost of seven cartons,

   = 1.85 x 7 = 12.95 ≅ $ 13

Thus, Mickey made the mistake in his calculation and didn't get the right cost for seven cartons which is $13.

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