Point A is graphed on the coordinate plane. What ordered pair represents point A?

Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.

Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:

X ~ N (12, 3²)

Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:

P (X ≤ K) = 0.15

When we transform this into a typical normal variable, we get:

P [Z ≤ (K - 12) / 3] = 0.15

From the common normal tables, we can deduce:

P (Z ≤ -1.036) = 0.15

Comparing the two equations above, we obtain:

(K - 12) / 3 = -1.036

K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892

As a result, 8.892 ounces of gold are needed.

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Answer:

20

Step-by-step explanation:

do parenthesis first

1/5(3+2+ 5)² =

1/5(10)² =

then exponent

1/5(10)² =

1/5(100) =

20

Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.

The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.

Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:

n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.

Suppose an initial number of insects is x and after 15 hours it becomes 2x.

2x = x[tex]e^{15r}[/tex]

[tex]e^{15r}[/tex] = 2

Take the log of both sides of the equation

ln [tex]e^{15r}[/tex]= ln 2

15r = ln 2

r = 0.693147/15

Now, population after 1-hour = x [tex]e^{r}[/tex]

= 1.047

≈ 1.05

Hence the population of insects after 1 hour will be about 1.05 times.

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Based on the image attached, the relationship are:

a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.

b). AE and BF - Both segments are said to be parallel

c). EF and ED - Both are skew

d). Plane ABC and plane ABF - Both of the planes do  intersect at point AB

e). Plane AED and plane BFC - Both of the given planes are known to be parallel

if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.

If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.

Therefore,

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Answer:I think $1064

Step-by-step explanation:

First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.

Answer:

y = 2.60 (to 3sf)

Step-by-step explanation:

Since x is directly proportional to y², then x = ky², where k is a constant.

When x = 4, y = 3,

 4 = k(3)²

 4 = 9k

9k = 4

∴[tex]k =\frac{4}{9}[/tex]

∴ When x = 3,

[tex]\frac{4}{9}y^{2} = 3[/tex]

∴y = 2.60 (to 3sf)

The missing angle is as follows:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.

Therefore, the triangle ABC is congruent to EDF.

Hence,

∠A = ∠D

∠B = E

∠C = ∠F

Therefore,

m∠C = x

m∠F = 2x - 30

Hence,

m∠C = m∠F

x = 2x - 30

x - 2x = -30

-x = -30

x = 30

m∠C = 30 degrees

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Answer:

Answer is: 8 2/3 but improper is 26/3

The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.

In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.

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Value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

What do you mean by algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are 3 main types of algebraic expressions which include:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression which is having only one term is known as a monomial.

Given expression:

a + 4/a = 4

We need to simplify the above expression and will find the value of a.

[tex]a+\frac{4}{a}=4[/tex]

⇒ [tex]\frac{a^2+4}{a}=4[/tex]

⇒ [tex]a^{2}+4=4a[/tex]

⇒ [tex]a^2-4a+4=0[/tex]

⇒ [tex]a^2-2a-2a+4=0[/tex]

⇒ a(a-2) -2(a-2) = 0

⇒ (a-2)(a-2) = 0

⇒ a = 2

Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]

[tex]2^5-\frac{1}{2^5}[/tex]

= 32 - 1/32

= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]

Therefore, value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

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Answer:

5 - [tex]\frac{40}{5}[/tex] = 5 - 8 = -3

Step-by-step explanation:

The first mistake made by the student is in Step A where the problem was not copied down correctly.

The final price of the comic book after it is marked up is $5.79.

Since we have given that

Cost of a comic book including tax = $ 3.99

According to the question, it is given that it is marked up 45%,

=3.99 × (100+45)÷100

=3.99 × 145/100

=399 × 1.45

=5.79

Hence, the final price of the comic book after it is marked up is $5.79.

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Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.

How to solve this problem?
Stacey and Andrew in the mentioned problem will meet in a time frame only when the both have travelled equal distances in respect to another.

Given, speed at which Andrew was travelling = 12 mi/h
Speed at which Stacey was travelling = 16 mi/h
Let the time taken by Stacey be = t hours
Therefore, the time taken by Andrew = (t + 0.5) hours
When Stacey overtakes Andrew, they must have covered the same distance, therefore:
16t = 12×(t + 0.5) ⇒ 16t = 12t + 6 ⇒ 4t = 6 ⇒ t = 6/4 ⇒ t = 3/2 ⇒ t = 1.5
Therefore, Stacey meets Andrew 1.5 hours after she starts travelling at 11:30 AM and Andrew meets Stacey 2 hours after he starts travelling at 11:30 AM.

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Answer:

5/12

6/15

10/18

Step-by-step explanation:

Answer:

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

The measure of the angle ACB is 87°.

Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.

An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.

When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.

In triangle ADE and triangle ACB, the triangles are similar.

So,

∠AED/ ∠ABC = ∠DAE/∠CAB

∠AED = ∠ABC

11x-2 = 6x + 13

11x - 6x = 13 + 2

5x = 15

x = 15/5

x = 3

So, the measure of angle ABC is

∠ ABC = 6(3)+13

∠ ABC = 18+13

∠ ABC  = 31°

Now, consider triangle ABC, the sum of all angles = 180°

So, 62° + 31° + ∠ACB = 180°

∠ACB + 93° = 180°

∠ACB =  180° - 93°

∠ACB = 87°

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The slope is m = 5.

What is slope?

The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.

We have to find the slope of the points given.

First to find the change between each y - value.

16 - 11 = 5

21 - 16 = 5

26 - 21 = 5

31 - 26 = 5

So the change between each y - value is 5.

Now, to find the slope of the points.

Since,

Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]

Hence, the slope of the given points is 5.

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Answer:

The answer is 5

Step-by-step explanation:

Though there is also a bottom number, just put a 1 in the bottom number

Answer:

x=145 at 8 minutes

im not sure what tt means but please read my note at the end.

Step-by-step explanation:

if the initial temp is 65 and it increases at a rate of 10 per min the use

65+10(x)

let x be the number of minutes

65+10(8)

65 +80= 145

after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65

The simplified answer is 8i-15.

What do you mean by iota?

Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.

According to the given question,

We have: [tex](4i+1)^{2}[/tex]

Now, we will solving this by formula,

[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]

Putting the values in it,

[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]

Therefore, the required answer is 8i-15.

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The correct number in the function f (3) will be;

⇒ f (3) = 2

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The graph is shown in figure.

Now,

Clearly, By the image of the graph;

At x = 3,

The function is defined as;

⇒ f (3) = 2

Thus, The correct number in the function f (3) will be;

⇒ f (3) = 2

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The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.

What is inequality?

In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.

According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].

Now, combine the two expressions as follows:

9<2x

[tex]2x\le45[/tex]

[tex]9 < 2x\le45[/tex]

Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].

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Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.

In the given question,

The given principal amount = Rs 3000

The given time = 5 years

Interest amount = 525

Now finding the rate of interest.

As we know that the formula of simple interest.

I = P*R*T/100

525 = 3000*R*5/100

Multiply by 100 on both side we get

52500 = 15000*R

Divide by 15000 on both side

R = 52500/15000

R = 3.5

In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.​

To find the interest put the value in I = P*R*T/100

As given P=2200, R=3.5%, T=6 years

I = P*R*T/100

I = 2200*3.5*6/100

I = 462

Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.

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The coordinate of image of P is (-6,-4)

What in math is a coordinate?

a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)

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Answer:

6x^2+17x+12

Step-by-step explanation:

(3x+4) * (2x+3)

3x * 2x = 6x^2

3x * 3 = 9x

+4 * 2x = +8x

+4 * +3 = +12

6x^2+ 9x+8x +12

Simplify:
6x^2+17x+12

a) The Probability density function of given uniform distribution example is

F(x) = 1/3.5 for 8.5 < x< 12

Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where

x ---> minimum value and y---> maximum value

Probability density function is a probability function which defines the density of continuous random variable lying between specified range

values. It is denoted by f( a<X<b)

Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.

We have following informations,

weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.

Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.

this implies a = 8.5 , b = 12

F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12

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#Complete Qestion :

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?

Answer:

119days

Step-by-step explanation:

1 week= 7 days

take week as w

so 1w=7 or w=7

now 17 weeks=??

17w=??

w=7 so input in above statement:

17(7)=119days

Answer: 119 days

Step-by-step explanation:

       We can set up a dimensional analysis problem to solve.

               [tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]

       The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.

               [tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]

The following are the equations which matches the given word problems:

a. Skate rental charges an additional $3 :

y = x+3

b. Jeff is 3 years less than Tony's age:

y=x-3

c. Marie buys balloons for a party that are $3.00 each:

y = 3x

Given, we have the word problems:

a. Skate rental charges an additional $3 :

here, based on the fixed charge, additional charge is taken as $3.

let the total charge be represented as y and

x represent the fixed charge,

hence the equation we get is:

y = x+3

b. Jeff is 3 years less than Tony's age.

let y represent the age of Jeff

and x represent the age of Tony.

hence we frame the equation as:

y = x - 3

c. Marie buys balloons for a party that are $3.00 each:

let the cost of the balloon be represented as y

and x represent the number of balloons Marie wants to buy for $3 each.

hence the equation we frame is:

y = 3x

Hence we get the required equations.

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The skydiver falls a distance of 36 feet after 1.5 seconds.

Now, we have:

To calculate distance:

Therefore, the skydiver falls a distance of 36 feet after 1.5 seconds.

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