if a certain positive two-digit number has tens' digit w and units' digit x , what is the value of w x ?

The rate of change of length of his shadow when he is 30ft away from the lamp post is  3 ft/sec .

In the question ,

it is given that ,

the length of the man is = 6 ft ,

le the distance of the man from the base of the lamp post at time "t" is = x

let the length of the shadow at time "t" = y ,

given that dx/dt = 6 ft/sec .

From the figure given ,

In triangle ABC and triangle ADE ,

AB/BC = AD/DE

that is , y/6 = (x+y)/18

after simplification ,

we get ,

2y = x .

differentiating both with respect to "t" ,

we get

2 * dy/dt = dx/dt

Substituting dx/dt = 6  ,

we get ,

dy/dt = 3 ft/sec .

Therefore , the rate of change of the length of the shadow is 3 ft/sec .

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The mean is 65 inches and the standard

standarddeviation is three (3) inches for the women have heights less than 62 inches. about 97.5% of the women have heights less than 71 inches.

In a set of girls, the distribution of heights is more or less normal. Women who're shorter than sixty two inches in top make up 16% of the population.

The empirical rule, much less than µ - o of 16% of the records is accurate.

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56 is 80% of what number?

Formula - [tex]\dfrac{Number\times100}{Percent}[/tex]

______________________

[tex]\dfrac{56\times100}{80} =\dfrac{5600}{80}=\fbox{70}[/tex]

The words that fills the blank space on the method used to find the length of the diagonal AG, using Pythagorean Theorem are as follows;

Blank 1; The Pythagorean Theorem

Blank 2; Square root of 73

Blank 3; A leg

Blank 4; The hypotenuse

Blank 5; 9.4 cm

Pythagoras Theorem indicates that the square of the longest side of a right triangle is equivalent to the sum of the square of the other two sides.

The diagonals from point A to point G in the cuboid can be found using Pythagoras Theorem as follows;

The diagonal of the base rectangle, ABCD, is found as follows;

AC = √(8² + 3²) = √(73)

Using the side CG as the leg of the right triangle ΔACG, with AG being the hypotenuse, we get;

CG = 4 indicated in the diagram in the question

(AG)² = (AC)² + (CG)²

(AG)² = 73 + 4² = 89

AG = √(89) ≈ 9.4

The completed statement is therefore;

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a) The expressions are given as follows:

b) The total cost for each present is of:

Hence the present that they can buy with the least amount of money is:

Jewelry.

The costs are found applying the proportions in this problem.

As a function of d, the functions are found multiplying the decimal equivalents of each discount by the cost expression.

The decimal equivalents of each discount are given as follows:

Then the actual costs are calculated replacing the instances of d in each item with the numeric value d = 79.

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At the end, the distance to the car will be 17 miles, and the distance that they walked is 13 miles.

We want to find the total distance at which the hikers are at the end.

Notice that each little square represents one mile. And the line ends at two little squares above the marking of 15 miles, then the distance to the car at the end is:

15mi + 2 mi = 17 miles.

We also could want to find the distance they walked on the given graph. To find that, we need to take the difference between the final distance and the initial distance.

The final distance is 17 miles, we already know this, and the initial distance is the y-intercept, which in this case is 4 miles.

Then the distance that they walked is:

D = 17mi - 4mi = 13mi

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Therefore the answer to following is probabilities of following problems are  (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6 .

To investigate unpredictability, mathematicians utilize probability. It discusses the possibility (the likelihood) of an event happening. For instance, if you flip a fair coin four times, you might not get two heads and two tails each time.

Here,

(A) The event cannot happen if the probability is zero.

(b) The event is guaranteed to occur if the probability is 1.

(c) An event is very unlikely to happen if the probability is less than 0.01.

(d) The occurrence is more likely to happen if the probability is 0.6. (because the probability is greater than 0.6).

(a) 0

(b) 1

(c) 0.01

(d) 0.6

Therefore the answer to following is probabilities of following problems are  (a) 0 ,(b) 1 ,(c) 0.01 and (d) 0.6

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The slope of the line passing through the two points [tex](-4,5)[/tex] and [tex](2,3)[/tex] is [tex]\frac{-1}{3}[/tex]

The formula for finding the slope when two points are given

[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{3-5}{2-(-4)} \\y=\frac{-2}{6} \\y=\frac{-1}{3}[/tex]

The slope of the line is [tex]\frac{-1}{3}[/tex]

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If the measure of angle JKL is 132°  and the measure of angle LKM is 48° . then the pair of angle JKL and angle LKM called a Linear Pair .

In the question ,

it is given that ,

the measure of angle JKL is = 132°    and

the measure of angle LKM is = 48°  ,

we know that when the sum of two angles is 180° , then the pair is called as Linear Pair .

According to the question ,

angle JKL + angle LKM = 180°

132° + 48° = 180°

180° = 180°

So , the given pair of angles forms a Linear Pair .

Therefore , the angle JKL and angle LKM forms a Linear pair .

The given question is incomplete , the complete question is

If the measure of angle JKL is 132°  and the measure of angle LKM is 48° . What is the pair of angle JKL and angle LKM called ?

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Answer:

180 degrees in a triangle

Values are paired in the form:

(X1, Y1),.. (Xn, Yn)

(3.25, 3.2)

"Information available from the question"

In the question:

College administrators noticed that students who had higher high school GPAs tend to have higher college GPAs.

The data in the table show various high school GPAs and college GPAs for a sample of students. A 2-column table with 16 rows.

Column 1 is labeled high school g p a with entries.

3. 25, 3. 5, 3. 5, 3. 25, 2. 5, 4, 4, 3. 5, 3. 25, 3. 5, 3. 5, 4, 3, 3. 5, 2. 25, 2. 5

Column 2 is labeled college g p a with entries 3. 2, 3. 0, 2. 9, 3. 0, 3. 0, 3. 0, 3. 1, 3. 1, 3. 1, 3. 0, 3. 0, 3. 1, 3. 0, 3. 1, 2. 9, 2. 8

Now, According to the question:

Column 1 High School G P A:

3.25, 3.5, 3.5, 3.25, 2.5, 4, 4, 3.5, 3.25, 3.5, 3.5, 4, 3, 3.5, 2.25, 2.5

Column 2 College G P A :

3.2, 3.0, 2.9, 3.0, 3.0, 3.0, 3.1, 3.1, 3.1, 3.0, 3.0, 3.1, 3.0, 3.1, 2.9, 2.8.

To prepare a scatter plot ; with x - axis plotted against y - axis ;

Each point on the x - axis is paired with a corresponding point on the y - axis ;

With high school GPA on the x axis and College GPA on y :

Values are paired in the form:

(X1, Y1),.. (Xn, Yn)

(3.25, 3.2)

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The solution is, the simplified value is 2107/5 = 421.4.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

24 3/5 +4^3x(8 1/5 -2)

we have to

Simplify the Equation

With Converting 24 3/5 to a improper fraction

Calculate the Power of 4^3

Then convert 8 1/5 to a improper fraction

Subtract 41/5 and 2 to get 31/5

Then Multiple the product,

64 • 31/5 to get 1984/5

After add the fractions up

123/5 + 1984/5

=2107/5

=421.4

Hence, The solution is, the simplified value is 2107/5 = 421.4.

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The number of bottles of soda is  4 and the number of bottles of juice purchased is  8.

We know that linear system of equation in two variables is required to solve the problem. Let suppose number of bottles of soda purchased by Jacob is x and number of bottles of juice purchased by Jacob is y

Since, it is given that Jacob bought 25 bottles in total, it means

=>x + y=12-----(eq1)

Also, it is given that total amount of sugar is 240grams.Now,amount of sugar present in soda bottle is 25x and amount of sugar present in juice bottles is 12y

Therefore,25x + 12y=240-----(eq2)

On solving eq1 and eq2,we get

=>x+y=12

and 25x+10y=240

Using elimination technique to solve, make x terms coefficient equal.

Multiplying eq1 by 25,we get

=>25x + 25y=25×12

=>25x +25y=300------(eq3)

Using eq3 and eq4,we get

=>25x+25y=300

and 25x+10y=240

Cancelling x terms, we get

=>15y=60

=>y=(60/15) grams

=>y=4 bottles

Now, putting value of y in eq1 ,we get

=>4+y=12

=>y=12-4

=>y=8bottles.

Hence, required value of number of bottles of soda is 4 and number of bottles of juice is 8.

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Answer:

final amount = $16512.36

Step-by-step explanation:

The question asks us to find the value of Gavin's deposit of $12,000 after 16 years, given that the interest rate of 2% is compounded quarterly.

To do this, we have to use the following formula for compound interest:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],

where:

A → amount at the end

P → principal (original) amount

r → interest rate (in decimal)

n → number of times per year that the interest is compounded

t → time (in years).

From the question, we know that the initial amount deposited is $12,000. Therefore, P = 12000. We also know that the interest rate is 2%, but the formula requires the rate to be in decimal, so r = 0.02. The time for which the money is deposited is 16 years, and therefore, t = 16. We are told that the interest is compounded quarterly, that is, every 3 months. This means that the interest is compounded 4 times yearly, so n = 4.

From the above information and formula, we can calculate the final amount:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

⇒ [tex]A = 12000(1 + \frac{0.02}{4})^{4 \times 16}[/tex]

⇒ A = $16512.36

Therefore, the final amount after 16 years is $16512.36.

Tt takes 1.5 min of time  to travel a distance of 1 km by bus

Since here we need to find the time, which basically depends on the speed of the bus, as we know the formula we refer to for calculating the time is distance/speed, here we are provided with the distance which is  1km also equal to 1000m. Now considering a normal condition where the speed of  the bus is h 40km per hour, therefore

=>Distance = Speed × Time

=?1km = 40 Km/hr × Time

Time = 1/40 hr = 0.025 hr ,Which is almost 1.5 min

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f and g are inverses of each other and g is a reflection of y = x thus options (B) and (C) are correct.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given functions,

f(x) = [tex]2^{x}[/tex] and g(x) = [tex]log_{2} x[/tex]

It is known that the exponential function and logarithm function are inverse of each other for the same base as shown below.

It is also clear that g(x) is the reflection of x = y.

Hence "g is a reflection of y = x and f and g are inverses of one another.".

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Answer:

Do you have a picture of the graph?

Step-by-step explanation:

If so can you pls insert :)

The summary of the ruler placement postulate is: A direct relationship exists between the set of points on the line and the collection of real numbers, where each point is matched to a single real number and   The magnitude of the gap between two points is equal to the absolute value of the subtraction of the two associated values.

The ruler placement postulate states that if two points are given, it is possible to measure the distance between them by taking the point of reference as zero. This means that any point can be chosen as an origin, and the distance between the two points can be calculated by measuring the number of units between them. This postulate also applies to curves, and the distance between two points on a curve can be measured by taking a point of reference as zero and measuring the number of units between them. This postulate is essential in the measurement of distances between points and curves in geometry.

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The choice of the probability distribution for a random variable can be guided by Historical Data

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

In probability theory and statistics, a probability distribution is a mathematical function that calculates the likelihood of a range of potential experiment results. It is a mathematical explanation of a random phenomenon in terms of its sample space and event probability.

The choice of the probability distribution for a random variable can be guided by Historical Data

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The total amount the mechanic will need in retirement savings to meet their retirement income goal is 870,000. The correct option is C.

In mathematics, an expression is a combination of numbers, symbols, and operations (such as addition, subtraction, multiplication, and division) that represents a quantity or a value.

Expressions can be very simple, such as a single number or variable, or they can be more complex, such as a combination of multiple terms with different operators.

The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x 43,500 = $34,800 per year

The mechanic plans to draw 4% the first year from their retirement savings, which means the total retirement savings needed are:

34,800 / 0.04 = $870,000

Therefore, the answer is C) 870,000.

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The population increase between the 2nd and the 7th years as 440.

What is Total Change from a Rate of Change?

Total increase = ∫ab rate dt

= ∫₁³ 200+10t dt

= 200t +5t² |₁³

= [200(3) + 5(3)²] - [ 200(1) + 5(1)²]

= 600 + 45 - 200 -5

= 440

Hence, the population increase between the 2nd and the 7th years as 440.

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The value of x in the regular polygon is 120 degrees.

The regular polygon is a triangle. A regular polygon has all it interior angles equal to each other. Therefore, the triangle above is an equilateral triangle.

An equilateral triangle has all its sides equal to each other and the angles are also congruent.  Each angle of an equilateral triangle is 60 degrees.

Exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore,

60 + 60 = x

Hence,

x = 120 degrees.

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Answer: 12

You're Welcome :D

Answer:

4 / 1 /3 = 4/3

Step-by-step explanation:

There is 46% probability of experiencing neither of the side effects.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

While taking drug, chances of experiencing nausea (n)= 24 %,

Chances of experiencing decreased sexual drive (d) = 46 %.

Also, there are 60% chances of experiencing both side effects.

Use vain diagram to solve this type of questions,

Total chances of experiencing side effects = 8 + 30 + 16 = 54

The chances of experiencing neither of the side effects = 100 - 54 = 46

So there is 46% probability of experiencing neither of the side effects.

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The forward rate for the third year 3.06%

The forward rate is the interest rate applied to future financial transactions. The forward rate is calculated from the spot rate, adjusted for maintenance costs to determine future interest rates that equalize the strategy to extend short-term investments and the total return on long-term investments.

This term can also refer to interest rates charged on future financial obligations, such as interest rates on loan payments.

(n1 – n2) reservation rate calculation number. A few years later n2 no. The number of years of Forward rate = [(1 + S1)n1 / (1 + S2)n2]1/(n1-n2) – 1.

According the question:

S3 = [(1 + S₁) × (1 + F(1,2))²]¹/³ ⁻¹

= [(1 + 2.658%) × (1 + 2.340%)²]¹/³ ⁻¹

= [1.02658 × 11.1556]¹/³ ⁻¹

= (12.18)¹/³ ⁻¹

= 3.06

Therefore, calculation of spot rate for three years will be, 3.06%

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Answer:

6.3

Step-by-step explanation:

We can use the four theorems - SSS, SAS, ASA, AAS - to prove that two triangles are congruent.

To prove that the given triangles are congruent there are some rules, one of which it must satisfy to show that the two are congruent. The four theorems are stated and explained below-

SSS rule: If the 3 sides of both of the given triangles are equal, then the triangles are congruent.

SAS rule: If the 2 sides and one of the three angles of both of the given triangles are equal, then the triangles are congruent.

ASA rule: If 2 of the total three angles and a side (in the middle of the angles)of both of the given triangles are equal, then the triangles are congruent.

AAS rule: If 2 angles and a side(adjacent to the angles) of the given two triangles are equal, then the triangles are congruent.

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Answer: 537 stuffed animals

Step-by-step explanation:

Take 939 - 402 = 537

So she gave away 537 stuffed animals

The total amount Andrea paid for her computer is $1611.425.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100

In this situation, Andrea ordered a computer on the Internet and the computer cost $1,499 plus 7 1/2% sales tax.

The amount that will be paid will be:

= Cost of computer + Tax

= $1499 + (7.5% × $1499)

= $1499 + $112.425

= $1611.425

The amount is $1611.425.

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