Solve for x.

− x/2<−1

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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Hello!

0.85b-0.2b

0.65b

0.65b=0.65b

So these expressions are equivalent.

Hope it helps!

~Just a determined gal

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\(MysteriousNature\)

The field width of a 460-mm camera lens at a distance of 890 feet with the viewing angle of the lens at π/18 is approximately 155.33 feet

How to find the approximate field width of a 460-mm camera lens

Given data

length of chord = L = r * √( 2 - 2cos θ)

distance = 890 feet

viewing angle of the lens = π / 18

Field width

field width = viewing angle in radians * distance

field width = π/18 * 890 feet

field width = 155.33 feet ( to the nearest hundredth )

The term field width refers to the the distance that the viewing angle of the lens of a camera covers. The field width is proportional to the viewing angle and the distance in the sense that increasing viewing angle leads to increasing of the field width. This is similar to the distance when the distance increases the field with also increases.

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Answer: False

Step-by-step explanation: this is false because Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. ... So, any terminating decimal is a rational number.

Answer:

7 19/24

Step-by-step explanation:

Add. That is your answer.

The true statement about the result is that D. The survey suffers from voluntary response bias and may not estimate true support for the extended hours

From the information, in order to measure support for extended hours, the citizen visits neighborhood homes and asks adults the research question.

This illustrates bias as the citizen wants to propose to the city council extending the hours at the local public library on some weekdays.

Therefore, the true support may not be illustrated. In conclusion, the correct option is D.

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Answer:

---------------------

Given sequence:

This is a AP since the difference is common:

The previous term is going to be 7 less than the subsequent term:

The midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

To find the point with the position vector 1/3(a+b+c), we can use the fact that the position vector of a point that divides a line segment in a given ratio can be found by taking the weighted average of the position vectors of the endpoints.

Given that D, E, and F are the midpoints of line segments BC, AC, and AB, respectively, we know that:

D = (B + C) / 2

E = (A + C) / 2

F = (A + B) / 2

To find the point with the position vector 1/3(a+b+c), we can substitute a = 3F - 2D - E into the equation:

1/3(a + b + c) = 1/3((3F - 2D - E) + b + c)

Expanding the equation further:

1/3(a + b + c) = 1/3(3F - 2D - E + b + c)

= (F - (2/3)D - (1/3)E) + (1/3)(b + c)

Therefore, the point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

Substituting the midpoints:

P = (A + B) / 2 - (2/3)((B + C) / 2) - (1/3)((A + C) / 2) + (1/3)(b + c)

= (A + B - 2B - 2C - A - C + b + c) / 2 + (1/3)(b + c)

= (b + c - B - C) / 2 + (1/3)(b + c)

Therefore, the midpoint of three points with the position vector 1/3(a + b + c) is given by:

P = (b + c - B - C) / 2 + (1/3)(b + c)

The point with the position vector 1/3(a + b + c) is given by:

P = F - (2/3)D - (1/3)E + (1/3)(b + c)

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Answer: -1364

Step-by-step explanation:

This is a geometric series with first term 4 and a common ratio of -2.

Using the sum of a geometric series formula, we get this sum to be equal to:

\(\frac{4(1-(-2)^{10}}{1-(-2)}=\boxed{-1364}\)

Answer:

Let x be the number we are looking for.

We know that 12 is at most a number decreased by 7, which can be written as:

x - 7 >= 12

To solve for x, we add 7 to both sides of the inequality:

x - 7 + 7 >= 12 + 7

Simplifying, we get:

x >= 19

Therefore, the solution to the inequality is x >= 19.

The answer is:

Work/explanation:

Let w be the number. Now, let's write an inequality to solve for w.

Let's focus on the part that says "at most a number". At most means that the number can't be greater than something, it can only be less than. So the symbol for "at most" is ≤, which also means "less than".

Now, decreased by 7 means we subtract 7 from w.

With all this information, we are ready to write the inequality.

The inequality is:

\(\sf{12\leqslant w-7}\)

Now, let's solve it for w.

_________________________

Add 7 on each side

\(\sf{12+7\leqslant w}\)

\(\sf{19\leqslant w}\)

The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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Answer:

$1.19

Step-by-step explanation:

8.33 / 7 = 1.19 each

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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Answer:

93%

Step-by-step explanation:

From the question given above, the following data were obtained:

Total number of student = 300

Number of student that can not drive = 21

Percentage of student that can drive =.?

Next, we shall determine the number of student that can drive. This can be obtained as follow:

Total number of student = 300

Number of student that can not drive = 21

Number of student that can drive =?

Number of student that can drive = (Total number of student) – (Number of student that can not drive)

Number of student that can drive = 300 – 21

Number of student that can drive = 279

Finally, we shall determine the percentage of student that can drive as illustrated below:

Total number of student = 300

Number of student that can drive = 279

Percentage of student that can drive =?

Percentage of student that can drive =

279/300 × 100

= 93%

Thus, 93% of the student can drive.

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Step-by-step explanation:

the second option.

a transition of 7 units right shifts it completely to the right side of the y axis.

a transition then of 5 units down shifts it completely into the second quadrant (positive x, negative y). it is now completely below the x axis and right of the y axis.

and now a reflection across the y axis keeps it below the x axis but shifts it completely to the left of the y axis. and it is therefore more in the third quadrant (negative x, negative y).

Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

The domain would be given by D = {X ≥ 2} X = [2, Z]. Since the variable Z is the number of children in the school. And the 6 children should not survey the same person, it would be Z / 6 for each interviewer.

Step-by-step explanation:

- If the group of children surveys more than 2 classmates, it means that the number with which the survey begins is 12 students.

And since the maximum number of students in the school is given by the variable of Z, then Z is the number with which the domain closes.

The rank would be given by the set of [2, Z]

Z / 6 being the maximum number of children surveyed by 1 interviewer.

The Domain of given function is, \(x\geq 2\)

The Domain of function is defined as, all input values for which function is defined.

 The total number of completed survey is given by a function,

                        \(s(x)=6x\)

Since, If the group of children surveys more than 2 classmates, it means that the number with which the survey begins is 12 students.

It means value of x is always greater and equal to 2.

                        So that,   \(x\geq 2\)

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Answer:

C. 7°F

Step-by-step explanation:

Answer:

1114 sodas

Step-by-step explanation:

If you simplify 8:4, you will get 2:1. Given that information, since there are twice as many diet sodas as regular sodas, all you have to do is divide 776 by 2. You should get 338. All you have to do now is add 776 and 338 to get 1114.

Step-by-step explanation:

NOT rolling a four means out of six posssible rols you can roll a 1.2.3.5 or 6

 or      5 / 6

Answer:

27/16

Step-by-step explanation:

Divide 3/8 by 2/9 by multiplyinh 3/8 by the reciprocal of 2/9

3/8* (9/2)

Multiply 3/8 times 9/2 by multiplying the numerator time the other numerator and denomator times the other denominator

3 * 9 = 27

8 * 2 = 16

Do multiplication in the fraction

27 /16

Examining the word problem we can say that, Molly used 160 beads to make the necklace.

Let's assume the number of beads used to make the bracelet is x.

We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,

x + 5x = 192

6x = 192

solve for x

x = 192 / 6

x = 32

Molly used 32 beads to make the bracelet.

number of beads used to make the necklace

Number of beads used for the necklace = 5 * 32

Number of beads used for the necklace = 160

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Answer:

(C) 1466

Step-by-step explanation:

The hour hand makes one revolution each 12 hours. So it makes 2 revolutions a day.

The minute hand makes one revolution each hour. So it makes 24 revoulutions a day.

The second hand makes one revolution each minute. So it makes 24*60 = 1440 revolutions a day.

In total:

2 + 24 + 1440 = 1466

The correct answer is C.

\( \bf \underline{Given :-}\)

\( \\ \\ \)

\( \bf \underline{ To \: find:-}\)

\( \\ \\ \)

\( \bf \underline{Solution:-}\)

Strongly recommend to keep up with Digram , as name of sides are based according to Digram.

As we know soccer feild is rectangle , therefore ∠A = ∠B = ∠C = ∠D = 90°

Now as we have to just find value of diagonal AD therefore just focus on triangle ACD.

we know ∠C = 90° , triangle ACD. is a right angled triangle.

\( \\ \\ \)

\( \bigstar \boxed{ \rm Hypotenuse^2 = Base^2 + Perpendicular^2}\)

Here :-

Hypotenuse = AD

Base = CD

Perpendicular = AC

\( \\ \)

Therefore :-

\( \\ \)

\( \dashrightarrow\sf AD^2 =CD^2 + AC^2 \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =(130)^2 + (80)^2 \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =130 \times 130 + (80)^2 \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =16900+ (80)^2 \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =16900+80 \times 80 \\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =16900+6400\\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD^2 =23300\\ \)

\( \\ \\ \)

\( \dashrightarrow\sf AD= \sqrt{23300} \\ \)

\( \\ \\ \)

\( \dashrightarrow\bf AD =152.643 \: yds\\ \)

\( \\ \\ \)

The value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.

The given integral is;

y = ∫18x sin (9x² + 8) dx

Put u = 9x² + 8

Then, on differentiation

18x dx = du

substitute the values:

y = ∫ sin (u) du.

y = -cos u

Put u = 9x² + 8

y = -cos (9x² + 8) + c

c is the constant of integration.

Thus, the value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.

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Answer:

$43

Step-by-step explanation:

Multiply 1.75 and 8 which equals 14

2.00 times 13 is 26

.25 times 12 is 3

Add 'em all up and you get $43(before dividing them up in thirds)

If you divide them by 3 each third is 14.33 repeating.

Answer:

\(5(4x + 3) = 20x + 15\)

\(20x + 3\)

5(4x + 3) is not equal to 20x + 3. The 5 is distributed to the 4x and 3 resulting in 20x + 15 and not 20x + 3.

Answer:

The most appropriate way to state the conclusion is:

d. There is not enough evidence to say that men have a longer mean nose length than women.

Step-by-step explanation:

We have the result of a hypothesis test.

The claim was that men have a longer mean nose length than women.

That means that the alternative hypothesis states that men's mean nose length is higher than the women's mean nose length.

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0\)

The P-value of the test is 0.225, which for any usual significance level is large enough to fail to reject the null hypothesis. Then, there is no enough evidence to support the claim that men have a longer mean nose length than women.

a. Men have a longer mean nose length than women.

FALSE. There is no enough evidence to support the claim.

b. The probability is 0.225 that men and women have the same mean nose length.

FALSE. That is not the meaning of the P-value.

c. The mean nose lengths of the populations of men and women are identical.

FALSE. We can not claim that the null hypothesis is true, even when we havo no enough evidence to reject it.

d. There is not enough evidence to say that men have a longer mean nose length than women.

TRUE. This is the the most appropriate way to state the conclusion.