Write the number in standard form
-2.7 x 10-²

Answer:

F'(-3) = 18

Step-by-step explanation:

Let g(x) = u and apply the chain rule

\(F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}\)

\(\frac{du}{dx}=g'(x)\)

\(\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)\)

We now have all of the necessary definite values to solve the expression for x= -3:

\(F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18\)

Finally, we have that F'(-3)= 18.

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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I think I already answered it to you from the same question you asked earlier.

But anyways, the answer is in the image below and the steps are also in one of the images too.

Hope this helps! :)

Answer:

15/4 × 7/5

= 105/20

= 5 5/20

= simplified 5 1/4

Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that \(n = 34\)

We have that \(\mu = 0.937, \sigma = 0.009\)

By the Central Limit Theorem, \(s = \frac{0.009}{\sqrt{34}} = 0.0015\)

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(-2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = -2.575*0.0015\)

\(X = 0.933\)

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

\(Z = \frac{X - \mu}{s}\)

\(2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = 2.575*0.0015\)

\(X = 0.941\)

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Answer:

a) (-1,0) and (3,0)

b) x=1

c) (1, -4)

Step-by-step explanation:

As you can see in the graph below, the x intercepts of this graph are at (-1,0) and (3,0), the axis of symmetry is x=1, and the vertex is at (1,-4). Hope this helps!

One of the Possible values of length and width of the prism are 15 cm and 0.5 cm

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given here: The volume of the prism is 2¹/₂=2.5 cm³

And the height is 1/3 cm

let the length and breadth of the prism is x and y respectively.

We know the volume of the prism as

1/3 × x×y=2.5

x×y=7.5

Thus possible values of length and breadth are the factors of 7.5

out of which one of the pair whose length is 15 cm and width 0.5 cm

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Answer:

35 dollars (0.08)

Step-by-step explanation:

35 + 8%, taxes are most likely in cents

Answer:

35 dollars (0.08)

Step-by-step explanation:

A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket?

A.35 dollars (0.08)

B.35 dollars (8)

C.35 dollars (0.08) + 35 dollars

D.35 dollars (8) + 35 dollars

because i just took the test and i got 94.3 and this question is right.

Hopefully this helps.

Answer:

\( \tt \: true\)

Step-by-step explanation:

\(The \: ordered \: pair \: (1, \: 0) \: is \: a \: solution \: to \: the \: inequality \: y.\)

Answer:x= 16.5

Step-by-step explanation:as both the triangles are similar, then

AB/ PQ=AC/ PR

16/24=18/(2x-6)

x= 16.5

Answer:

the answer is 45

Step-by-step explanation:

the answer is 384

Step-by-step explanation:

a1 = 2, a2 = 3, a3 = 4,

an = ?

n = 44

d = a2 - a1 = 3 - 2 = 1

d = a3 - a2 = 4 - 3 = 1

Here, the common difference is the same everywhere

So,

\( a_{n} = a + (n - 1) \times d\)

\(a_{44} = 2 + (44 - 1) \times 1\)

\(a_{44} = 2 + 43\)

\(a_{44} = 45\)

Answer:

You woke up at 7:00 AM

You finished your shower at 7:30 AM

You finished your meal at 7:40 AM

You finished your videogames at 8:00 AM

8:00 AM - 7:40 AM = :20

So, you played video games for 20 Minutes! That sure must be a quick game...

Hopefully this helped!

Answer:

Vertical and horizontal lines are perpendicular. Two lines are parallel lines if they are coplanar and do not intersect.

Step-by-step explanation:

Lines that are not coplanar and do not intersect are called skew lines. Two planes that do not intersect are called parallel planes. hope this helps you :)

Work Shown:

x^2 - 9 = 0

x^2 - 3^2 = 0

(x-3)(x+3) = 0 ..... difference of squares rule

x-3=0 or x+3=0

x = 3 or x = -3

Answer:

-3/4

Step-by-step explanation:

Have a nice day

Answer:

\(x=19\)

Step-by-step explanation:

1) Use this rule: \((x^a)^b=x^a^b\) .

\((x-3)^{\frac{1*1}{2*2} } =\sqrt{x-15}\)

2) Simplify 1 * 1 to 1.

\(\sqrt[2*2]{x-3} =\sqrt{x-15}\)

3) Simplify 2 * 2 to 4.

\(\sqrt[4]{x-3} =\sqrt{x-15}\)

4) Square both sides.

\(\sqrt{x-3} =x-15\)

5) Square both sides.

\(x-3=x^2-30x+225\)

6) Move all terms to one side.

\(x-3-x^2+30x-225=0\)

7)  Simplify \(x-3-x^2+30x-225\) to \(31x-228-x^2\).

\(31x-228-x^2=0\)

8) Multiply both sides by -1.

\(x^2-31x+228=0\)

9) Factor \(x^2-31x+228\).

1)  Ask: Which two numbers add up to -31 and multiply to 228?

\(-19\) and \(-12\)

2) Rewrite the expression using the above.

\((x-19)(x-12)\)

10) Solve for \(x\).

1) Ask when will \((x-19)(x-12)\) equal zero?

When \(x-19 =0\) or \(x-12=0\)

2) Solve each of the 2 equations above.

\(x=19,12\)

11)  Check solution.

When \(x=12\) 2, the original equation \(\sqrt{\sqrt{x-3}}=\sqrt{x-15}\) does not hold true. We will drop \(x=12\) from the solution set.

12) Therefore,

\(x=19\)

Check the Answer:

\(\sqrt{\sqrt{x-3}}=\sqrt{x-15}\)

1) Let \(x=19\).

\(\sqrt{\sqrt{19-3}}=\sqrt{19-15}\)

2) Simplify 19 - 3 to 16.

\(\sqrt{\sqrt{16}}=\sqrt{19-15}\)

3) Since 4 * 4 is 16 6, the square root of 16 is 4.

\(\sqrt{4}=\sqrt{19-15}\)

4) Since 2 * 2 = 4, the square root of 4 is 2.

\(2=\sqrt{19-15}\)

5)  Simplify  19 - 15  to  4.

\(2=\sqrt{4}\)

6) Since 2 * 2 = 4, the square root of 4 is 2.

\(2 = 2\)

Answer:

Correct option is B)

252=

2×2

​

×

3×3

​

×7

The prime factor 7 does not appear in pairs. To make 252 a perfect square we need one more 7.

Hence, the smallest number  by which 252 must be multiplied so that

the product is a perfect square is 7.

And, 252×7=

2×2

​

×

3×3

​

×

7×7

​

252×7

​

=

2×2

​

×

3×3

​

×

7×7

​

​

=2×3×7=42

Step-by-step explanation:

To find the smallest whole number by which 2268 should be multiplied to get a perfect square, we need to factorize 2268 into its prime factors. Then, we can determine which prime factors are needed to make the number a perfect square.

The prime factorization of 2268 is:

2268 = 2^2 * 3^2 * 7 * 9

To make it a perfect square, we need to include the missing factors. In this case, we are missing a factor of 2 and a factor of 3. Therefore, we need to multiply 2268 by 2 * 3 = 6.

2268 * 6 = 13608

Now, we have a perfect square number, 13608.

To find the square root of 13608, we can take the square root of each of its prime factors:

√(2^2 * 3^2 * 7 * 9)

= √2^2 * √3^2 * √7 * √9

= 2 * 3 * √7 * 3

= 6 * √7

So, the square root of the square number 13608 is 6√7.

Answer:

a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:

P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2

Step-by-step explanation:

b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:

P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)

P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875

c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:

P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

520

Step-by-step explanation:

I used big brain

-

Answer:

No.

Step-by-step explanation:

No.

An obtuse angle has a measure between 90° and 180°.

A reflex angle has a greater measure than that.

The number of hamburgers sold on Saturday is 108

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Given that:

1. The combined total of hamburgers and cheeseburgers is 432.

2. The number of cheeseburgers sold was three times the number of hamburgers sold

Let h and c represent hamburgers and cheeseburgers respectively

1st sentence can be written as:

h + c = 432   .... (1)

2nd sentence can be written as:

c = 3h   .... (2)

Substitute (2) into (1):

h + 3h = 432

4h = 432

h = 432/4 = 108

Therefore, 108 hamburgers were sold on Saturday

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Answer:

50 degrees

Step-by-step explanation:

A whole line is 180 degrees.Subtract the known angle from 180 to find the missing angle,which is 50 degrees.

Answer:

a) P(F) = 0.15

b) P(F/B) =  0.13

c) 5% customers order neither food not beverage.

Further explanation is in the explanation section

Step-by-step explanation:

Solution:

Data given:

B = The customer orders a beverage

F = The customer orders food.

F + B = The customers order food and a beverage.

Percentage share:

F = 3%

B = 92%

F + B = 12%

a)

So, the Probability of B, the customer orders a beverage will be:

P(B) = 92% = 0.92

Probability of (F+B), the customers orders food and beverage will be:

P(F ∩ B) = 12% = 0.12

And we know that, 3% customers order food alone so,

P(F) - P(F ∩ B) = 3% = 0.03

So,

P(F) = (P(F) - P(F ∩ B)) + P(F ∩ B)

P(F) = 0.03 + 0.12

P(F) = 0.15

It means that 15% customer order food only.

b) Probability that the customer orders food given that they order a beverage.

P(F/B) =  (Probability that the customer orders food given that they order a beverage.)

P(F/B) = P(F∩B)/P(B)

P(F/B) = 0.12/0.92 = 0.13

P(F/B) =  0.13

Symbolic form of the required probability is = P(F/B)

c) If 180 customers are randomly selected, how many of them can we expect to order neither food nor a beverage?

Probability of ordering food and beverage will be:

P(F U B)

So,

Probability of ordering neither food nor beverage will be = 1 - P(F U B)

And,

P(F U B) = P(F) + P(B) - P(F ∩B)

P(FUB) = 0.15 + 0.92 - 0.12

P(FUB) = 0.95

Probability of ordering neither food nor beverage will be = 1 - P(F U B)

Probability of ordering neither food nor beverage will be = 1 - 0.95

Probability of ordering neither food nor beverage will be = 0.05

Hence, 5% customers order neither food not beverage.

So, we have selected 180 random people so, 5% of 180 =

number of people order neither food  nor beverage = 5/100 x 180

number of people order neither food  nor beverage = 9 people

It means we can expect out of 180 people, 9 people will not order food or beverage.

The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Answer:

-6 ≤ x ≤ 7

Step-by-step explanation:

"Inclusive" here means that the endpoints -6 and 7 are part of the solution set.  This set includes all numbers between -6 and 7:

[-6, 7] or -6 ≤ x ≤ 7

Answer:

take 1/4 to the other side since 1/2 and 1/4 are like terms then solve for X getting 16/5 as the answer

Have a wonderful time

Answer:

3/4 or 15/20

Step-by-step explanation:

this is because, you know there is 3 girls named the same thing and two boys named the same thing so if you know there are 20 people in the class, you do 3g + 2b = 5/20

So the fraction is either 15/20 or 3/4 for reduced fraction.