Evaluate the function.
f(x) = x² + 6x - 9
-
Find f(7)

Answer:

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.

By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.

So the probability of this happening is exactly 1 - it must be true

Considering the Graph and reading the distance blocks from the store to the bank we see a progression of 3blocks

This is further explained below.

Generally, There is a concept referred to as distance that may be used to quantify, either quantitatively or qualitatively, the distance that separates two items or sites.

When speaking about physics or using the phrase in everyday language, "distance" may either refer to a literal measurement or an estimate based on a number of other parameters.

Both meanings are appropriate when discussing or using the term.

The progression of existence and events that occur in what seems to be an unstoppable order beginning in the past, continuing through the present, and moving into the future is what we refer to as time.

Time may be broken down into three distinct parts: the past, the present, and the future.

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The distance between points A and B will be 19201.93 feet.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Mamadou notices an airplane arriving in a straight line and flying directly overhead on the radar. The plane stays at the same height of 7325 feet. Mamadou initially measures a 15-degree angle of inclination to the plane at point A. Later, he detects a 42-degree angle of elevation to the plane at point B.

The distance between points A and B will be given as,

D = 7325 / tan 15° - 7325 / tan 42°

D = 27337.27 - 8135.34

D = 19201.93 feet

The distance between points A and B will be 19201.93 feet.

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Answer:

19202 feet

Step-by-step explanation:

I got the same problem and got it right with that answer.

Answer:

32.5

Step-by-step explanation:

What is 25% of 130?

0.25 * 130 = 32.5

Answer: 1st option!

Step-by-step explanation:

Just did it on edg

The image of the function after it is vertically stretched is f'(x) = 4|x + 3|

The function is given as

f(x) = |x + 3|

The transformation is given as

Vertical stretch by a factor of 4

This implies that we stretch the function f(x) by a factor of 4

This transformation is represented mathematically as

(x, y) = (x, 4y)

So, we have

f'(x) = 4 * f(x)

So, we have the following equation

f'(x) = 4 * (|x + 3|)

Remove the bracket

So, we have

f'(x) = 4 * |x + 3|

Evaluate the products

So, we have

f'(x) = 4|x + 3|

Hence, the equation of f'(x) is f'(x) = 4|x + 3|

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The graph that is hardest to write the transformation using algebraic notation is the second top graph counting from left to right

A graph is a pictorial representation of data

A transformation is a movement that can be represented in a cartesian plane.

There several types of movement involved in transformation, some of them are:

The first top graph counting from the left is a translation to the left.

The first graph at the bottom counting from the left is a translation downwards

The next bottom graph is reflection along x axis and translation downwards

The most difficult which is the second at the top counting from left involves dilation.

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Answer:

3rd option

Step-by-step explanation:

the factors of 48 are

1 , 2, 3, 4, 6, 8, 12, 16 , 24 , 48

the factor pairs are

1 × 48 , 2 × 24 , 3 × 16 , 4 × 12 , 6 × 8

I will ask my question here

is p(x)

bye :)

Answer:

3.456e+12
or

3,456,000,000,000

Step-by-step explanation:

400 x 600 = 240,000

240,000 x 800 = 192,000,000

192,000,000 x 150 = 28,800,000,000

28,800,000,000 x 120 = 3,456,000,000,000

hope this helps you :D

Since we are measuring bank preference, we want to see the data in order of importance, then, the pareto chart is the most useful graph in this situation

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is significantly lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.05 and observe that p'.

Hypothesis test: A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters thanks to hypothesis testing.

Data are provided and noted.

X=6.8 display the sample mean

σ= 0.9 show the population's standard deviation.

n= 280 samples taken

μο=6.7 the value that we wish to test should be represented

α=0.1 signify the hypothesis test's level of significance.

The stat would be represented as z. (variable of interest)

p' indicate the test's p value (variable of interest)

Name the prevailing and competing hypothesis

The system of hypothesis must be tested to see if the true mean is below the criteria.

Null hypothesis:  μ ≥ 6.7

Alternative hypothesis: μ < 6.7

Applying a z test to compare the actual mean to the reference value is preferable if the sample size is greater than 30 and we are aware of the population variation. The statistic is given by:

z=(X-μο)/σ[tex]\sqrt{n}[/tex]  ......(1)

z-test: "enables the comparison of group means. One of the most widely used tests, it is used to determine whether the mean is (higher, lower, or not equal) to a given value ".

Calculate the statistic

We can replace in formula (1) the info given like this:

z=(6.8-6.7)/0.9[tex]\sqrt{280}[/tex]

P-value

Since is a one sided test the p value would be:

p'=p(z<0.0066)

We can infer that we have sufficient evidence to reject the null hypothesis and that the true mean is considerably lower than 6.7 at 10% of significance if we compare the p value and the significance level given =0.1 and observe that p'.

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The most appropriate choice for exponent will be given by-

Fourth option is correct

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2\times 2\times 2 \times 2[/tex], here, 2 is multiplied by itself 4 times.

If  [tex]a^m = a\times a\times a \times.....\times a[/tex] (m times), a is the base and m is the index.

The laws of index are

[tex]a^m \times a^n = a^{m + n}\\\\\frac{a^m}{a^n} = a^{m-n}\\\\a^0 = 1\\\\(a^m)^n = a^{mn}\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\a^mb^m = (ab)^m[/tex]

Here,

For first option

[tex]\frac{4^{11}}{4^{14}}\\\frac{1}{4^{14 - 11}}\\\frac{1}{4^3}\\\frac{1}{64} < 1[/tex]

For second option

[tex](5^4)^2 \times 5^{-11}\\5^8 \times 5^{-11}\\5^{8-11}\\5^{-3}\\(\frac{1}{5})^3\\\frac{1}{125} < 1[/tex]

For the third option,

[tex](2^3)^{-2}\\2^{-6}\\(\frac{1}{2})^6\\\frac{1}{64} < 1[/tex]

For the fourth option
[tex]\frac{(3^5)^2}{3^4}[/tex]

[tex]\frac{3^{10}}{3^4}\\3^{10 - 4}\\3^6\\ 729 > 1[/tex]

Fourth option does not have an expression greater than 1

Fourth option is correct.

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For the length to be sides of a triangle, the sum of any two sides triangle must be greater than third side.

Condition is true.

Condition is true.

Condition is true.

The triangle inequality satisfied for the triangle. So length belongs to a side of triangle.

Answer: yes

Answer: [tex]x=15[/tex]

Step-by-step explanation:

By the consecutive interior angles theorem,

[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]

Answer:

P(x) = x (x²- 2x + 5)

Step-by-step explanation:

First factor x out:

P(x) = x (x²- 2x + 5)

Then, try to simplify (x²- 2x + 5):

However, there is no way to further simplify.

So, the answer should be x (x²- 2x + 5).

Answer: [tex]\frac{21}{2}+\frac{\sqrt{41}}{2}, \frac{21}{2}-\frac{\sqrt{41}}{2}[/tex]

Step-by-step explanation:

Let the two numbers be x and y.

[tex]x+y=21 \implies y=21-x\\\\xy=100\\\\\therefore x(21-x)=100\\\\21x-x^2 =100\\\\x^2 -21x+100=0\\\\x=\frac{21 \pm \sqrt{21^2 -400}}{2}=\frac{21}{2} \pm \frac{\sqrt{41}}{2}[/tex]

Answer:

See the picture below

Step-by-step explanation:

Answer:

Inline range: 2 ≤ n < 8

Interval range: [ - 2, 8 )

Loop: n = - 2; n < 8;

Step-by-step explanation:

The filled circle means inclusive while outlined circle means exclusive.

Answer:

-2 ≤ x > 8

Step-by-step explanation:

x = a possible number based on the diagram

the black-filled-in dot on the line above the number line indicated that it can either be '≤' or '≥'

the empty-not-filled-in dot means that it can be either '<' or '>'

the '≤' means x can be equal or greater to -2

and the '>' means that x must be less than 8

hope this helps!

Answer:

The equation is an example of the associative property of addition.

Step-by-step explanation:

Associative property of addition: changing the grouping of addends does not change the sum.

For example: A+(B+C) = (A+B)+C.

The mean and standard deviation are given as 6 and 0.48 respectively.

According to the question The Population Mean number of strikes per square kilometer (μ) = 6 and the Population standard deviation of strikes per square kilometer (σ) = 2.4. The Sample size is equal to (n) = 16. We know that the sample mean number of strikes per square kilometer (m) = mean Number of strikes per square kilometer in the population. From this observation it is clear that the mean will be equal to

μ = m = 6

So, the Sample mean = 5

Now, the Standard deviation = standard error = σ/√n. Now we get

Standard Error = 2.4 / √25

Standard Error = 2.4 / 5

Standard Error = 0.48

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Answer:

-3

Step-by-step explanation:

We know that,

( + ) × ( + ) = ( + )

( - ) × ( - ) = ( + )

( + ) × ( - ) = ( - )

Accordingly, let us solve the given fraction.

-7 - ( - 4 )

-7 + 4

-3

In this problem the function that models the hight is:

So when the water hits the grownd h=0 so we replace that and solve for t so:

To solve this expression we can use the cuadratic equation:

and we operate so:

Now we solve bout of the equation so:

So the answer that have sense is the secon one so the water hits the ground after 1.27 seconds

A) To find the length AC, we must use the trigonometric ratio

adjacent = 5cm

hypothenuse = AC

B) To find the length AB, we will use the value of AC just obtained to get it

since triangle ABC is a right-angled triangle, we will use Pythagoras theorem

so that

|AC|^2 = |AB|^2 +|BC|^2

AC = 5.8332cm

BC = 4cm

|AB|^2 = |AC|^2 - |BC|^2

C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.

Perimeter = AD +CD + BC + AB

We do not have CD and we must find CD

Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm

D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.

Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter

Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter

Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter

Step-by-step explanation:

I assume, based on what I see, that the solid line is just cos(x), right ?

and we need to find the equation that draws the dotted line, correct ?

the notation is strange, as it seems we need to find a multiplication factor for x in the cos function.

but there is no multiplication factor that moves the cosine wave by pi to the left or to the right (so that the max. happens, where originally the minimum happens, and vice versa).

so, we need to add (or subtract) pi in the cosine function.

the rest is clear :

the normal distance between min. and max. of the cosine function is 2 (between +1 and -1). the target is 4. so we need to multiply by 2.

and since the values of that function have to be between -4 and 0 (instead of -2 and +2), we have to subtract overall 2.

giving us the function :

y = 2×cos(pi + x) + -2

We were told that Ben earned 625.5 points out of 700 on an essay. Expressing his score in the essay in terms of percentage, it becomes

625.5/700 x 100 = 89.29%

Also, he scored 65 out of 70 on an assignment. Expressing his score in the assignment in terms of percentage, it becomes

65/70 x 100 = 92.86%

We would find the average between the two percentages

Average = sum of percentages/number of percentages

Average = (89.29 + 92.86)/2

Average = 91.075

Average is approximately 91%

Since in order to earn an A in the class, he needed to average a 91 on these two

assignments and he got an average of 91%, then we can conclude that he got an A

the data are normally distributed with a mean of 74.674.6 hours and a standard deviation of 9.19.1 hours. So  10.2% of gadgets were powered by batteries for fewer than 63 hours.

Given that,

Data have a mean of 74.6 hours and a standard deviation of 9.1 hours, and they are regularly distributed.

The standard deviation is defined as ?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

[tex]p(X\leq 63) = p(Z\leq 63-74.6/9.1)[/tex]

From standard deviation,

         [tex]p(X\leq 63) = p(Z\leq -1.279)= 0.1061[/tex]

a certain percentage of gadgets have battery life of less than 63 hours.

X= 63 hours

Percentage of devices ran on the batteries for fewer than 63 hours = 10.2%

Therefore, 10.2% of electronic devices had battery life of less than 63 hours

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We will have that the expression has the solution of:

Therefore the solution is D. -5.

When we elevate to the power of 3 -5 will be equal to -125.

Dividing 7 and 2 over 3 ÷ negative 3 and 1 over 5 will give a quotient of  negative 2 and 19 over 48

information gotten from the question include

Divide 7 and 2 over 3 ÷ negative 3 and 1 over 5.

Division is a basic mathematical operator that performs the function of sharing

division of fraction is done as follows

7 and 2 over 3

= 7 2/3

= 23/3

negative 3 and 1 over 5.

= -3 1/5

= -16/5

= 23/3 ÷ -16/5

= 23/3 * -5/16

= -115/48

= -2 19/48

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The equation of  line that passes through the points (-6,-5) and (-4,-4) is  x - 2y = 4 .

The equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .

y-y₁ = m(x-x₁)

In the question ,

it is given that

the required line passes through the points (-6,-5) and (-4,-4) ,

So , the slope(m) is = (-4 -(-5)/(-4 -(-6))

= (-4+5)/(-4+6)

= 1/2

the equation of the line passing through (-4,-4) and slope as 1/2  is

(y -(-4)) = (1/2)(x -(-4))

y + 4 = (x+4)/2

2y + 8 = x + 4

x - 2y = 8-4

x - 2y = 4

Therefore , The equation of  line that passes through the points (-6,-5) and (-4,-4) is  x - 2y = 4 .

The given question is incomplete , the complete question is

Complete the equation of  line that passes through the points (-6,-5) and (-4,-4) .

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