Calculate the product below and give your answer in scientific notation.
(1.3 x 10-^2) x (0.05) = ?

Step-by-step explanation:

Adding 10 to both sides of the original equation gets us q = 6(r + 1) + 10. Since q is equal to h(r), we get h(r) = 6(r + 1) + 10 = 6r + 16.

The sum of all two-digit numbers that have exactly three factors is 126.

To find the sum of all two-digit numbers that have exactly three factors, we need to determine which numbers satisfy this condition.

A number has exactly three factors if it is a perfect square. In other words, the number must be the square of a prime number.

The prime numbers less than 10 that have two-digit squares are 4, 5, 6, and 7. So we need to find the sum of their squares: 4^2 + 5^2 + 6^2 + 7^2 = 16 + 25 + 36 + 49 = 126.

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Answer:

Step-by-step explanation:

C

Answer: 3 teaspoons.

Step-by-step explanation: Notice that 5 cups is half of the original 10 cups, so the half of the original 6 teaspoons will be 3 teaspoons.

True. In 2016, the percentage of the ageing population (55 years or older) in state prisons surpassed the percentage of people aged 18-24 for the first time.

This trend reflects the overall growth of the ageing population within the United States and is a result of various factors such as longer life expectancy, harsher sentencing laws, and an increase in older individuals being convicted of crimes.
As the ageing population in state prisons continues to grow, it poses several challenges for the correctional system. These challenges include providing appropriate healthcare and accommodations for older inmates and addressing the specific needs of this population, such as mobility assistance and specialized medical care.
In conclusion, the shift in the age demographics of state prisons has significant implications for the management and administration of correctional facilities. It is crucial to address the unique needs of the ageing population within these institutions and adapt policies and practices accordingly to ensure the well-being and fair treatment of all inmates, regardless of their age.

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Answer:

1) The volume of the frustum is 27·(√3)·h

2) The surface area the frustum is 24·h + 54·√3

Step-by-step explanation:

1) A frustum of the regular triangular prism is a portion of the triangular prism

The length of the edge of the triangle prism = 12

The area of the triangular face, A = (√3/4)·a²

∴ A = (√3/4)·12² = 36·√3

When

The volume of the triangular prism, V = A·h = (36·√3)·h

By triangle proportionality theorem, the cross sectional area of the top half of the triangular prism =  (√3/4)·6² = 9·(√3)

The volume of the top half, V₂ = 9·(√3)·h

The volume of the frustum = V - V₂ = (36·√3)·h - 9·(√3)·h = 27·(√3)·h

The volume of the frustum = 27·(√3)·h

2) The surface area of the triangular side of the frustum is given as follows;

A = 36·√3- 9·(√3) = 27·(√3)

The surface area the frustum, \(F_A\) = 2×27·(√3) + 2 ×6 ×h + 12×h = 24·h + 54·√3

The surface area the frustum = 24·h + 54·√3

The ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and

3x + 2y ≤ 6.

To find an ordered pair that is a solution to the system of inequalities:

Start with the first inequality:

x + y > 2.

Choose a value for x and y that satisfies this inequality. For example, let's choose

x = 1 and

y = 2.

Substituting these values into the inequality:

1 + 2 > 2, which is true.

Now, let's move to the second inequality:

3x + 2y ≤ 6.

Substitute the same values, x = 1 and

y = 2, into this inequality:

3(1) + 2(2) ≤ 6.

Simplifying, we have:

3 + 4 ≤ 6, which is true.

Therefore, the ordered pair (1, 2) is a solution to the given system of inequalities.

Hence the ordered pair (1, 2) is a solution to the system of inequalities

x + y > 2 and 3x + 2y ≤ 6.

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If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.



To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).

Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.

Number of individuals in each group = dftotal / number of treatment conditions

Number of individuals in each group = 32 / 3

Number of individuals in each group ≈ 10.67

Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.

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The graphs of the three functions on the graph can be compared in a few different ways.

The square root and quadratic function share a y-intercept of 0, since the quadratic function is y = x2 and the square root function is y = √x. The square root and absolute value function share an x-intercept of 0, since the equation for the absolute value function is y = |x|.The range of the square root and quadratic function are different, since the maximum of the quadratic function is at (0, 0), while the maximum of the square root function is at (1, 1). The range of the square root and absolute value function are also different, since the maximum of the absolute value function is at (0, 0), while the maximum of the square root function is at (1, 1).Finally, the quadratic function and the absolute value function have a minimum, which is at (0, 0). On the other hand, the square root function has a maximum, which is at (1, 1).

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Answer: Its A and D

Step-by-step explanation:

Arthur and George are travelling in the same direction, but George was already 12 kilometers ahead of Arthur.

This is because George's speed is slower than Arthur's. Arthur's speed is 4 km/h, and George's speed is 3 km/h. Therefore, Arthur is able to catch up with George.Arthur would have to cover the distance George had already covered, plus the 12 kilometers between them.

The distance Arthur has to cover to catch up with George is given by:

Distance = 12 km + distance George covered Arthur's speed = 4 km/hGeorge's speed = 3 km/hTime taken to catch up is given by:Time = Distance / Speed = (12 km + distance George covered) / (4 km/h - 3 km/h) = (12 km + distance George covered) / 1 km/h

We can simplify the expression by equating distance George covered to the time George spent travelling at his speed.Distance George covered = 3 km/h x time = 3t kmDistance = 12 km + 3t km Time = Distance / Speed = (12 km + 3t km) / (4 km/h - 3 km/h) = (12 km + 3t km) / 1 km/hSimplifying, 12 km + 3t km = 4t kmSo, t = 12 km.To summarise, Arthur took 12 hours to catch up with George.

It took Arthur 12 hours to catch up with George.  Conclusion:Arthur took 12 hours to catch up with George who was already 12 kilometers ahead.

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Answer:

Step-by-step explanation:

2. 9a +4c=43

a+c=7

The total tickets for adults and children = 7 (a+c =7)       7 people in all

price for adult = $9  (9a)   Price per child =$4 (4c)

total price =$ 43

  9a +7c = 43

The equivalent Fractions with the LCD

LCD = 48 so its D. 16

Rewriting input as fractions if necessary:

2/3, 1/16, 1/8

For the denominators (3, 16, 8) the least common multiple (LCM) is 48.

LCM(3, 16, 8)

Therefore, the least common denominator (LCD) is 48.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

2/3 = 2/3 × 16/16 = 32/48

1/16 = 1/16 × 3/3 = 3/48

1/8 = 1/8 × 6/6 = 6/48

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What number is missing in the fractions to have a LCD of 48? 2/3, 1/?, 1/8 A.2 B.6 C.12 D.16

Hello!

In the given figure we can see that it is a right angled triangle .

Where,

Base is 9

We have to find the value of x i.e Hypotenuse

Here we are given base and we need to find the Hypotenuse.

Also we have been given the value of theta = 45°

Using trigonometric ratio :

cos \(\theta = \dfrac{ B}{H} \)

As per the question we have hypotenuse = x

Plugging the required values,

\( \cos 45 \degree = \dfrac{9}{x} \)

\( \dfrac{1}{ \sqrt{2} } = \dfrac{9}{x} \: \: \: \: \bigg(\because \cos 45\degree = \dfrac{1}{\sqrt2} \bigg)\)

further solving by cross multiplication

\(x = 9 \sqrt{2} \)

Hence, The value of x is 9√2

Answer : Option 1

Hope it helps! :)

when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.

What is External validity?

The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.

An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.

Question

When you are interrogating the external validity of a sample, which is the most important question to ask?

a. how many people are in the sample?

b. how was the sample collected?

c. how were the participants measured?

d. how many people are in the population?

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Answer:

9) y>0 or y<−14 10) Each artwork sold for $34.4

Step-by-step explanation:

#9 is fairly easy, just plug in a calc and pull out ans.

#10 so he needs to make $300 + $44 in total to recover everything as he wants $300 more in profit. set up the equation:

$300 (Profit) + $44 (Initial) = 10 ( # of paintings) x (how much to be sold for

Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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30 percent of the 90-gallon is 27 gallons and the average person consumes this much of water as well.

The amount of water used overall must be multiplied by the proportion utilized outside to determine how much water is used outside:

27 gallons from 0.3 x 90 gallons.

Hence, each day the average person consumes around 27 gallons of water outside.

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Answer:

(x - 4)² - 9 = 0

Step-by-step explanation:

x² - 8x + 7 = 0

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² - 8x

x² + 2(- 4)x + 16 - 16 + 7 = 0

(x - 4)² - 9 = 0

Your sister is using the "shadow and similar triangles" method to approximate the height of the rock wall. By setting up a proportion between the vertical and horizontal distances, she can find the height of the wall. Her approximation in this case is 66 inches.

Your sister is using a method called "shadow and similar triangles" to approximate the height of the rock wall. This method involves using the ratios of corresponding sides of similar triangles to find unknown measurements.

Let's break down the problem step by step:

Convert the measurements to a consistent unit:

The horizontal distance from your sister to the rock wall is 13 feet 5 inches. Convert this to inches: 13 feet × 12 inches/foot + 5 inches = 157 inches.

The vertical distance from the ground to her eyes is 5 feet 6 inches. Convert this to inches: 5 feet × 12 inches/foot + 6 inches = 66 inches.

Set up the proportion using the similar triangles:

Let h represent the height of the rock wall.

We can set up the proportion: (height of the wall)/(vertical distance) = (horizontal distance)/(distance to the wall)

h/66 = 157/157

h/66 = 1

Solve for the height of the rock wall:

Cross-multiply the proportion: h = 66 × 1

h = 66 inches

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The ceiling for this problem is given as follows:

450 m.

The three trigonometric ratios are defined as follows:

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

tan(71.5º) = x/150

x = 150 x tangent of 71.5 degrees

x = 448.3 m.

Adding 1.7 m, the ceiling is obtained as follows:

448.3 + 1.7 = 450 m.

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Answer:

x = 3

y = -4

Step-by-step explanation:

multiply the second equation by 2 to get:  -14x - 4y = -26

                                                       now add  5x + 4y = -1

-9x = -27

x = 3

solve for 'y':

5(3) + 4y = -1

15 + 4y = -1

4y = -16

y = -4

Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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Answer:

She will run 3 1/3 miles in 2 days

Step-by-step explanation:

1 2/3 + 1 2/3 = 2 4/3

= 3 1/3

Answer:

10/3 and mixed fraction is 3 1/3

Step-by-step explanation:

The values of function being changed according to the recursive formulae  a) f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96, b)  f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576, c) f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

Let's find the values of f(1), f(2), f(3), f(4), and f(5) for each of the given recursive definitions:

(a) f(n+1) = -2f(n)

Using this recursive formula, we can calculate the values as follows:

f(1) = -2f(0) = -2(3) = -6

f(2) = -2f(1) = -2(-6) = 12

f(3) = -2f(2) = -2(12) = -24

f(4) = -2f(3) = -2(-24) = 48

f(5) = -2f(4) = -2(48) = -96

Therefore, f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96.

(b) f(n+1) = 3f(n) + 7

Using this recursive formula, we can calculate the values as follows:

f(1) = 3f(0) + 7 = 3(3) + 7 = 9 + 7 = 16

f(2) = 3f(1) + 7 = 3(16) + 7 = 48 + 7 = 55

f(3) = 3f(2) + 7 = 3(55) + 7 = 165 + 7 = 172

f(4) = 3f(3) + 7 = 3(172) + 7 = 516 + 7 = 523

f(5) = 3f(4) + 7 = 3(523) + 7 = 1569 + 7 = 1576

Therefore, f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576.

(c) f(n+1) = f(n)² – 2f(n) – 2

Using this recursive formula, we can calculate the values as follows:

f(1) = f(0)²  - 2f(0) - 2 = 3²  - 2(3) - 2 = 9 - 6 - 2 = 1

f(2) = f(1)²  - 2f(1) - 2 = 1²  - 2(1) - 2 = 1 - 2 - 2 = -3

f(3) = f(2)²  - 2f(2) - 2 = (-3)²  - 2(-3) - 2 = 9 + 6 - 2 = 13

f(4) = f(3)²  - 2f(3) - 2 = 13²  - 2(13) - 2 = 169 - 26 - 2 = 141

f(5) = f(4)²  - 2f(4) - 2 = 141²  - 2(141) - 2 = 19881 - 282 - 2 = 19597

Therefore, f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

Therefore, The values of function being changed according to thr recursive formulae a) f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96, b)  f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576, c) f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

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Answer:-1

Step-by-step explanation: Just solve for x

Answer:

RT=FE, since this is using SAS (side-angle-side)

The measure of the mid - segment is 53 .

Given :

the measures of the bases of a trapezoid are 35 and 71.

What is trapezoid ?

A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .

Mid segment :

A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Measure of mid segment = sum of two bases / 2

= 35 + 71 / 2

= 106 / 2

= 53

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The average daily balance after 20 days is; $1750

The initial balance after grace period is; $25,000

Afterwards, A payment of $5,000 each is made on the 10th and 20th day.

Hence, the total balance after 20 days is;

The average daily balance is therefore the quotient of $35,000 and 20 days

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If the sum of two vectors, vector-a plus vector-b, is zero then the components of the two vectors; vector-a and vector-b, must be equal and opposite.

The vector is a physical quantity that has both magnitude and direction. The sum of two vectors refers to the process of adding two vectors. When two vectors are added together, a new vector is formed, and the process is known as vector addition.

The vector addition is done geometrically by placing the initial point of the second vector on the terminal point of the first vector, and the terminal point of the second vector is the final point of the resultant vector. If the sum of two vectors, vector-a plus vector-b, is zero, then it means that the two vectors are equal and opposite.

Therefore, the components of the two vectors; vector-a and vector-b, must be equal and opposite.

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