Find the slope of a line parallel to the line that crosses ( 3 , − 2 ) and the y -intercept is ( 0 , − 3 ) . I finally figured out how to write my equations in slope intercept form and NOW this pops up, can someone please explain it to me

Step-by-step explanation:

the probability of 1 tested insect is killed is 60% or 0.6.

the probability that it is not killed is then 1-0.6 = 0.4.

when we test 7 insects and exactly 4 survive is the event that

3 insects are killed, 4 insects survive.

the probability for one such case is

0.6×0.6×0.6 × 0.4×0.4×0.4×0.4

how many such cases do we have ?

as many as ways we can select 4 insects out of the given 7.

these are 7 over 4 combinations :

7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35

so, the probability that exactly 4 out of 7 tested insects survive is

35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935

The derivatives of the functions are listed below:

(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]    

(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]

(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²    

(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]

(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶

(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]

(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]

(h) f'(x) = cot x + cos (㏑ x) · (1 / x)

In this question we must obtain the first derivatives of each expression by applying differentiation rules:

(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]

(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]

(c) f(x) = (sin x - cos x) / (x² - 1)

(d) f(x) = 5ˣ · ㏒₅ x

(e) f(x) = (x⁻⁵ + √3)⁻⁹

(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]

(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]

(h) f(x) = ㏑ (sin x) + sin (㏑ x)

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Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

Answer:

I believe its 20.8, but I may be wrong

Step-by-step explanation:

so hmmm on average on the last 7 test, you get 82, so hmmm we could say that on each of the 7 tests you got 82, so you got 82, 7 times.

now, let's say in the 8th test, you get a grade of "g", now, if we were to get an average of all 8 tests, that means the average will simply be (82*7) + "g", and we know that's 84, so

[tex]\cfrac{(\stackrel{\textit{sum of all first seven tests}}{82+82+82+82+82+82+82})~~ + ~~g}{8}~~ = ~~84\implies \cfrac{(82\cdot 7)~~ + ~~g}{8}~~ = ~~84 \\\\\\ \cfrac{574+g}{8}=84\implies 574+g=672\implies g=672-574\implies g=98[/tex]

You must score 98 on the eighth test to raise your average to 84.

Average = Sum of all scores / Number of scores

The average score is given as 82, so the sum of the first 7 test scores would be 82 multiplied by 7.

The average to 84, we need to find the sum of all 8 test scores. Let's represent the score we need on the eighth test as "x."

Average = Sum of all scores / Number of scores

Using this equation, we can write:

84 = (Sum of the first 7 test scores + x) / 8

Multiply both sides of the equation by 8:

8 * 84 = Sum of the first 7 test scores + x

672 = Sum of the first 7 test scores + x

Subtract:

672 - Sum of the first 7 test scores = x

Substitute the sum of the first 7 test scores (82 * 7) into the equation:

x = 672 - (82 * 7)

x = 672 - 574

x = 98

Therefore, you must score 98 on the eighth test to raise your average to 84.

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Answer:

[tex]g(x)=-7x+6[/tex]

Step-by-step explanation:

Translations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:

[tex]f(x)=-7x+7[/tex]

Translation of 2 units left:

[tex]\implies f(x+2)=-7(x+2)+7[/tex]

Translation of 13 units up:

[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]

Simplifying:

[tex]\implies g(x)=-7(x+2)+7+13[/tex]

[tex]\implies g(x)=-7x-14+7+13[/tex]

[tex]\implies g(x)=-7x+6[/tex]

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Based on the residual plot given, the statement that describes if the model is good is B. The regression line is a good model because the residuals are randomly distributed.

For a model to be considered ideal or good, the residuals from the model should be randomly distributed in an equal manner around the regression line.

The residual plot shows that the residuals are randomly distributed which means that the regression line is a good model.

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Answer:

I think that I am right.  One train is traveling at 75 mph and the other train is traveling at 91 mph

Step-by-step explanation:

Answer:

Length = 52 ft

Width = 40 ft

Step-by-step explanation:

Given information:

Scale

[tex]\implies \sf 3 \: in : 8 \: ft[/tex]

[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]

To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:

[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]

[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]

Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.

Scale is 3in:8ft

So

Length

Width

Answer:

The value of C will be -1.

Step-by-step explanation:

Greetings !

[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]

The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]

Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]

In order to factorize the given expression, take out the common terms and then simplify further.

[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.

A number can have either positive or negative factors.

A number has a finite number of factors.

A number's factor will never be more than or equal to the provided number.

Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.

Finding a number's factors involves using the division and multiplication operations.

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The chance or probability of landing on a number divisible by 2 is 1/2.

The likelihood of an event occurring is defined by probability. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

According to the question,

Total number of outcomes = 6

Favorable number of outcomes = 3

Thus, the required Probability = 3/6 =1/2

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There are 151200 distinct ways to arrange the letters of the word CONNECTION

The word is given as:

CONNECTION

In the above word, we have the following parameters:

Total number of characters, n = 10

The repeated letters are:

C's = 2

O's = 2

N's = 3

The number of arrangements of the letters is then calculated as:

Arrangements = n!/(C! * O! * N!)

Substitute the known values in the above equation

Arrangements =  10!/(2! * 2! * 3!)

Evaluate the expression

Arrangements =  151200

Hence, there are 151200 distinct ways to arrange the letters of the word CONNECTION

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Answer: C

Step-by-step explanation:

The zeros of a graph are where the graph intersects the x-axis.

Answer:

  1.6 times   or   60% more than

Step-by-step explanation:

The question seems to be asking about the growth factor in the given exponential function.

A generic exponential function will have the form ...

  quantity = (initial value) × (growth factor)^(number of intervals)

Comparing this form to the given formula ...

  f(x) = 58 × 1.6^x

we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.

Each year the expected number of birds is 1.6 times the number the year before.

__

Additional comment

A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.

  growth factor = 1 + growth rate

  1.6 = 1 + 0.60 = 1 + 60%

The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.

Answer: 1.6

Step-by-step explanation:

Once you detect that there is a delay or disability, then you should continue to be the reliable partner in child care to the family so this is True.

The observation and screening process can lead to a child care partner discovering a delay or disability.

When this happens, you should report to your supervisor to check if the child is eligible for federal and state programs related to their condition. Whatever the case, you should remain accessible to the family as their partner in child care.

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Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.

According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:

It is given by the square root of the sum of the standard errors of each sample squared, hence:

s = sqrt(1.1² + 1.63²) = 1.97.

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Thee diagonal of the rectangle is 13.86 cm long.

We are given that;

Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;

W = 2L - 9

Area formula for a rectangle is;

A = Length * Width

We are given area of rectangle = 96 cm²

Thus;

L(2L - 9) = 96

2L² - 9L = 96

2L² - 9L - 96 = 0

Using online quadratic equation calculator gives;

L = 9.53 cm

Thus;

W = 2(9.53) - 9

W = 19.06 - 9

W = 10.06 cm

The diagonal of the triangle will be gotten from Pythagoras theorem;

D = √(9.53² + 10.06²)

D = √192.0245

D = 13.86 cm

Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.

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Answer:

37.5

Step-by-step explanation:

So whenever you want to find "x" percent of a number, you just do: [tex]\frac{x}{100} * n = \text{x\% of n}[/tex]. You're essentially converting the percentage to it's decimal value by dividing by 100.

Given this information, we're solving for x, instead of x% of n. In this case n = 56,000, and x% of 56,000 is 21,000

[tex]\frac{x}{100} * 56000 = 2100[/tex]

Divide both sides by 56,000

[tex]\frac{x}{100} = \frac{21,000}{56,000}[/tex]

Multiply both sides by 100

[tex]x = 100(\frac{21,000}{56,000})[/tex]

Simplify:

[tex]x = 37.5\%[/tex]

This can be generally thought of as:

[tex]x=100(\frac{part}{whole})[/tex]

where part = partial amount, or how much is after finding what x% is of the whole amount, but in this case we know what it is, we just don't know what the "x" percent is.

Answer:

Step-by-step explanation: -3/2 divided by 9/6

= -3/2 multiply (to divide fractions we multiply by their recipical) 6/9
Then, simplify
= -3/3 = 1
Answer: -1

Hope this helps lol

The simplified result is -1. The correct option is b.

Given that:

Expression, -3/2 ÷ 9/6

To solve the given expression, follow as:

Rewrite the division as multiplication by the reciprocal of the second fraction.

-3/2 ÷ 9/6 = -3/2 × (6/9)

Now, simplify the fractions:

-3/2 × (6/9) = -3/2 × (2/3)

-3/2 × (6/9) = - (3 × 2)/(2 × 3)

-3/2 × (6/9) = -6/6

Finally, the simplified expression is -6/6. However, further simplify it by dividing the numerator and denominator by their greatest common divisor, which is 6:

-6/6 = -1

So, the simplified result is -1. The correct option is b.

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Complete question:

Simplify Negative 3 over 2 divided by 9 over 6.

a. −4

b. −1

c. 4

d. 1

Answer:

1 13/30

Step-by-step explanation:

10/12 + 6/10 =

= 5/6 + 3/5

= 25/30 + 18/30

= 43/30

= 30/30 + 13/30

= 1 13/30

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Equation:}[/tex]

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\huge\textsf{Solving:}[/tex]

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]

[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]

[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]

[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]

[tex]\mathsf{= \dfrac{43}{30}}[/tex]

[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: 45%

Step-by-step explanation:

Given:

Find:

The number of groups which contains 9 is 9 and the total number of groups are 20.

So,

P = 9 / 20 = 0.45 = 45%

Therefore, the experimental probability is 45%

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]

( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )

[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]

[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]

[tex]\qquad❖ \: \sf \:6x = 168[/tex]

[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]

[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]

( x = 28° )

[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]

Answer:

Second one from the left

Answer:

b

Step-by-step explanation:

edg 22'

Answer:

33 units²

Refer to the attached page

I've shown the complete calculation over there.

Answer: 33

Step-by-step explanation:

one easy way to do it is by finding the area of the 4 triangles.

because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.

3 plus 3 plus 13.5 plus 13.5

to get 33

Answer:

11% more people voted for Candidate B than Candidate A

Step-by-step explanation:

15+6=21

9+23=32

32-21=11

The detail  Description on how to create a number line with the above  points is given below:

Note that we were given the following: points 4, 1, 25, and opposite of 2. The step to take  to First draw on Number Line.

Since Numbers with a negative sign are known to be less than zero ( Right of zero is shown by ‘+’ sign and to the left of zero is shown by ‘–’ sign while the + sign numbers can be depicted as simply numbers)

Then:

Therefore, The detail  Description on how to create a number line with the above points given above is correct:

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Using the probability concept, considering complementary probabilities, there is a 0.12 = 12% probability that the integer is of 20 or more.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

If two events are complementary, the sum of their probabilities is of 1. In this problem, we have that an integer being less than 20 is complementary to an integer being 20 or more.

We have that:

These events are complementary, hence:

0.88 + x = 1

x = 1 - 0.88

x = 0.12

There is a 0.12 = 12% probability that the integer is of 20 or more.

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