What will be the ages of Rona and Diana in 12 years if rona is 5 years younger than Diana today. The sum of their ages is 89?

Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

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The average rate of change of the function over the interval is -6

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

The answer is 86  −  2 i

Step-by-step explanation:

The value of the equation is A = 86 - 2i

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p = ( 7 + 5i )

Let the second number be q = ( 8 - 6i )

Now , A = p x q

Substituting the values in the equation , we get

A = ( 7 + 5i ) ( 8 - 6i )

On simplifying the equation , we get

A = 7 ( 8 ) + 5i ( 8 ) - 7 ( 6i ) - 5i ( 6i )

A = 56 + 40i - 42i - 30i²

The value of i² = -1

So , A =  56 - 2i + 30

A = 86 - 2i

Therefore , the value of A is 86 - 2i

Hence , the equation is A = 86 - 2i

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The measure of side SQ from the given similar triangles is 40.9 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle NOP is similar to triangle QRS.

Since the triangles are similar,

NP/SQ = NQ/QR

10/SQ = 13/53.2

13SQ=532

SQ=532/13

SQ=40.9 units

Therefore, the measure of side SQ is 40.9 units.

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When given the base of and height of a triangle, you can use this formula:

\(area = \frac{1}{2} bh\)

Plug in the known values:

\(area = \frac{1}{2} (18)(6)\)

Solve:

\(area = \frac{1}{2} \times 108\)

\(area = 54\)

Add units:

\(area = 54cm^{2} \)

Answer:

1 4/5 pounds

Step-by-step explanation:

15-6= 9

9-4=5

3/5+4/5=7/5 or 1 2/5

5-1=4

4-2/5=3 3/5

half of 3 is 1.5 or 1 5/10

3/5=6/10 half of 6/10 is 3/10

3/10+5/10= 8/10

simplify 1 8/10= 1 4/5

The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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The mean of the sampling distribution is 606060 and the standard deviation is 871.78.

As long as the sample size is sufficient (usually, n 30), the central limit theorem implies that if we repeatedly take random samples from a population, the sampling distribution of the sample means will resemble a normal distribution, regardless of the form of the population distribution. This indicates that given the sample mean and standard deviation, we may utilise the normal distribution to draw conclusions about the population mean. Because it enables us to estimate population parameters even when we don't know the population distribution, the central limit theorem is significant.

Given that,

n = 757575

p = 80% = 0.8

q = 1 - 0.8 = 0.2

The mean of the binomial distribution is given as:

Mean: μ = np = (757575)(0.8) = 606060

The standard deviation of the binomial distribution is given as:

σ = √(npq) = √((757575)(0.8)(0.2)) = 871.78

Hence, the mean of the sampling distribution is 606060 and the standard deviation is 871.78.

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Answer:

Step-by-step explanation:

the answer is 16.8

Explanation: well for starters you have to do what's in the parenthesis, so 4 times 1.4 is equal to 5.6. so now we add up the equation and get 28, so now we are left with 28-5.6-5.6 which equals 16.8

hoped this helped;)

Answer:

She subtracted the lengths of the diagonal lines instead of adding them.

Step-by-step explanation:

a. The table represents a proportional relationship

b. The constant of proportionality is 5/6

Proportional relationship are relationship between variable where their ratios are equivalent. The variables in our case are total weight(pounds) and number of books.

Therefore, let's check if the table represent a proportional relationship.

let

total weight = x

number of book = y

k = constant of proportionality

y = kx

10 = k12

k = 10 / 12 = 5 / 6

y = kx

15 = 18k

k = 15 / 18

k = 5 / 6

y = kx

25 = 30k

k = 25 / 30

k = 5 / 6

y = kx

50 = k60

k = 50/60 = 5 / 6

The constant of proportionality is the same. Therefore, the table represents a proportional relationship

The constant of proportionality(k) is 5/6.

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Answer:

14

Step-by-step explanation:

Answer:

A, x=14

Step-by-step explanation:

We know that <HJL is a right triangle, therefore 90 degrees.

<HJK + < KJL = <HJL

<HJK + 50 = 90

<HJK = 40

We replace HJK with 3x-2

3x-2 =40

3x=42

x= 14, A

I hope this helped! :)

Answer:

-$0.15

Step-by-step explanation:

We have been given win = $10, and loss = $-1

This deck of cards has 4 aces out of a total of 52 cards.

Then the probability can be explained as the number of favorable outcome/number of what is the possible outcome.

P(win) = number of favorable outcome/number of possible outcome

= 4/52

= 1/13

P(loss) = number of favorable outcome/number of possible outcome

= 48/52

= 12/13

Then we have

$10x1/13 + (-1)x12/13

= 10/13-12/13

= -2/13 dollars

= -$0.15

Using the principle of discrete probability, the expected value, which a measure of the mean amount after many plays is - 2/13

Calculating the required probabilities :

P(winning) = P(drawing an Ace) = 4/52 = 1/13

Hence, P(losing) = 1 - 1/13 = 12/13

X :____ 10 _____ - 1

P(X) : _ 1/13_____ 12/13

The expected value :

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence, the measure of the mean amount is -2/13.

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Answer:

10x + 2

Step-by-step explanation:

lim f(x + h) - f(x) / h = f'(x) = (5x² + 2x)' = 10x + 2

h→0

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

The equation of a line can be describe as follows:

y = mx + b

where

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Answer:

- \(\frac{1}{6}\) and 1 \(\frac{1}{6}\)

Step-by-step explanation:

we require to calculate

\(\frac{1}{2}\) - \(\frac{2}{3}\)

= \(\frac{3}{6}\) - \(\frac{4}{6}\)

= - \(\frac{1}{6}\)

and

\(\frac{1}{2}\) + \(\frac{2}{3}\)

= \(\frac{3}{6}\) + \(\frac{4}{6}\)

= \(\frac{7}{6}\)

= 1 \(\frac{1}{6}\)

y<2 is the solution to the inequality

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

According to the question

2y+3<7

subtracting 3 from both sides

we get,

2y<4

dividing both sides with 2

we get,

y<2

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Answer:

1320 ways

Step-by-step explanation:

To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!

12! is the same as 12x11x10x9x8... etc

But in this problem, we are only looking for the top 3.

We can set up a formula

\(\frac{n!}{(n-r)!}\)

N is the number of options that are available and r represents the amount we are choosing

In this case, we have 12 teams so n=12

We are looking for the top 3 so r=3

\(\frac{12!}{(12-3)!}\)

\(\frac{12!}{9!}\)

We expand the equation and cancel out

\(\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}\)

Notice how both sides can cancel out every number 9 and below

That leaves us with 12x11x10

1320 ways

The possible ways for the gold, silver, and bronze medals to be awarded is 1320

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.

We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,

Using the concept of permutation, to find the number of ways

ⁿPₓ = n!/(n-x)!

= 12! / (12-3)!

= 12! / 9!

= 1320

Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320

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Answer:

You want to solve the equation

x2=2x3 ,

which is equivalent to

x2(1−2x)=0 .

The product of two factors is zero if and only if one of the factors is zero. Thus, this implies that either  x2=0  or that  1−2x=0 .

In the former case we have  x=0 , which isn’t a positive number. In the latter case you have  x=1/2 , which is the solution that we want.

Step-by-step explanation:

Answer:

width = 18 cm

Step-by-step explanation:

perimeter of rectangle = 2(length + width)

then:

90 = 2(27+w)

90/2 = 27+w

w = width

45 = 27+w

45 - 27 = w

18 = w

Check:

90 = 2(27+18)

90 =2*45                                       =

Answer:

280in

Step-by-step explanation:

Answer:

280 in. ^3

Step-by-step explanation:

40 x 7

Answer:

1,200

Step-by-step explanation:

If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

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complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

Answer:

Here is the desmos graph

Step-by-step explanation:

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Surface Area of a cuboid = 2(lb+bh+hl)

= 2[(9×6)+(6×8)+(8×9)] = 348 in²

hence, option B is right ...

Hope u got what u were looking for :D

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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