(25 points)

Which inequality is represented by this number line?

Answer:

5\(\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{50}\)

\(\sqrt{25} = 5^{2}\)•\(2\)

\(\sqrt{5^{2} }\)×\(\sqrt{2}\)

since 5 is squared the square root cancels out

so 5\(\sqrt{2}\)

The volume of the other solid (Solid B) is 3456 cubic feet.

Solid A has edges of 4 feet, and its volume is given as 16 cubic feet. Solid B has edges of 24 feet.

Since the solids are similar, they have the same shape, and their corresponding lengths are proportional. To find the ratio of their corresponding lengths, we can divide the length of an edge of Solid B by the length of an edge of Solid A:

Ratio = (length of edge of Solid B) / (length of edge of Solid A)

Ratio = 24 feet / 4 feet

Ratio = 6

Now that we have the ratio of their corresponding lengths, we can find the ratio of their volumes. The ratio of the volumes of similar solids is the cube of the ratio of their corresponding lengths:

Volume ratio = (length ratio)³

Volume ratio = 6³

Volume ratio = 216

Now we can use the volume ratio to find the volume of Solid B:

Volume of Solid B = (Volume of Solid A) × (Volume ratio)

Volume of Solid B = 16 ft³ × 216

Volume of Solid B = 3456 ft³

So, the volume of the other solid (Solid B) is 3456 cubic feet.

Read more on volume here:https://brainly.com/question/1972490

#SPJ1

Answer:

3

Step-by-step explanation:

The slope is rise/run and for this case, it is 3/1 which equals 3!!!

Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

To know more about Inverse, visit

brainly.com/question/3831584

#SPj11

The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

to know more about vectors refer to the link https://brainly.com/question/19754999?referrer=searchResults.

#SPJ4

Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?

Answer:

dawdaw

Step-by-step explanation:

dawda

We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

Learn more about exponents here:

https://brainly.com/question/13669161

#SPJ1

The least value that should be given to * so that the number 92*389 is divisible by 11 is 7.

To determine the least value that should be given to * so that the number 92*389 is divisible by 11, we can use the divisibility rule for 11.

The divisibility rule for 11 states that a number is divisible by 11 if the difference between the sum of its digits at even positions and the sum of its digits at odd positions is either 0 or a multiple of 11.

In the number 92*389, the sum of the digits at even positions (counting from the right) is 2 + 9 + 8 = 19, and the sum of the digits at odd positions is 3 + * + 9 = 12 + *.

For the number to be divisible by 11, the difference between the sums should be 0 or a multiple of 11. Therefore, we need to find the least value of * that makes the difference a multiple of 11.

19 - (12 + *) should be a multiple of 11.

To make the difference a multiple of 11, we need to find the smallest value of * that satisfies the equation:

19 - (12 + *) ≡ 0 (mod 11)

Simplifying the equation:

19 - 12 - * ≡ 0 (mod 11)

7 - * ≡ 0 (mod 11)

-* ≡ -7 (mod 11)

≡ 7 (mod 11)

To know more about least value refer to-

https://brainly.com/question/28769760

#SPJ11

Answer:

Height after 5 seconds is 215 ft

Step-by-step explanation:

Given that:

The initial velocity of object which is projected upwards is 123 ft/sec.

Height of the object, h after time t in seconds,  is given as:

\(h=-16t^2+123t\)

Here, t will always be positive, so \(123t\) and \(16t^2\) will also be positive.

But coefficient of \(16t^2\) is negative, that means something is subtracted from the positive term \(123t\).

To find:

Height of object after 5 seconds.

Solution:

Given that \(t=5\) seconds.

Let us put the value in the given relation of \(h\) and \(t\):

\(h=-16\times 5^2+123 \times 5\\\Rightarrow h=-400+615\\\Rightarrow \bold{h = 215\ ft}\)

So, height after 5 seconds is 215 ft.

Using three equal subintervals and a right riemann sum, left riemann sum, and a midpoint sum is -6.4, 3.8, -1.0.

1) Integral with left end points:

         A-left = -3.4*2 + (-0.6)*2 + 0.8*2 = -6.4

2) Integral with right end points:

        A-right = -0.6*2 + 0.8*2 + 1.7*2 = 3.8

3) Integral with midpoints:

         A-mid = -2.2*2 + 0.2*2 + 1.5*2 = -1.0

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

Learn more about Reimann sum:

https://brainly.com/question/4144102

#SPJ4

Answer:

Product is rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

the product is rational

American Vietnam War protests intensified when the United States and South Vietnamese forces invaded Cambodia in 1970.

In April 1970, President Richard Nixon authorized the expansion of the Vietnam War into neighboring Cambodia with the aim of disrupting North Vietnamese supply routes and bases. This decision sparked a wave of protests across the United States as it represented an escalation of the war and a widening of the conflict beyond the borders of Vietnam. The invasion of Cambodia led to a significant increase in anti-war demonstrations and rallies, with many people expressing their opposition to the expansion of the war effort.

This sparked outrage among anti-war activists who saw it as an escalation of the conflict and an unjustifiable expansion of the war. The protests led to widespread demonstrations, strikes, and student unrest across the country, ultimately contributing to a shift in public opinion against the war.

To know more about Vietnam War:

https://brainly.com/question/182779

#SPJ11

A compound shape is a shape that is made up of other simple shapes. In this article, we will be working out the area of an L shape (made up of two rectangles). To find the area of a compound shape, follow these simple steps:

Step 1: Work out the missing lengths around the edge of the compound shape.

Step 2: Divide your L shape into two rectangles. This can be done in 2 different ways (both methods will give the same answer).

Step 3: Work out the area of each rectangle. Do this by multiplying the base of the rectangle by the height of the rectangle.

Step 4: Add the areas of the rectangles together to give the total area of the L shape.

Complete question: How do you find the area of an L angle?

To know more about L angle visit: brainly.com/question/18913751

#SPJ4

The combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.

To solve this problem, we'll calculate the value of each investment separately and then combine them.

First, let's calculate the value of your great uncle's investment in treasury bills. The nominal rate of 1.95% compounded every 73 days can be converted to an effective rate per year using the formula:

Effective rate = (1 + (nominal rate / m)) ^ m - 1

Where "m" is the number of compounding periods per year. In this case, there are approximately 365 days in a year, so the number of compounding periods is:

m = 365 / 73 = 5

Effective rate = (1 + (0.0195 / 5)) ^ 5 - 1 = 0.0200

Now, let's calculate the value of the treasury bills investment after 2 years (from January 1st, 2017, to January 1st, 2019):

Value of treasury bills = $20,000 * (1 + 0.0200)^(2 * 365/73) = $20,000 * (1.0200)^(10) ≈ $20,825.40

Next, let's calculate the value of your mother's investment, which is compounding continuously at a rate of 4% per year:

Value of mother's investment = $10,000 * e^(0.04 * 2) ≈ $10,816.65

Finally, let's calculate the combined value of these two accounts:

Combined value = Value of treasury bills + Value of mother's investment

= $20,825.40 + $10,816.65 ≈ $31,642.05

Therefore, the combined value of the two accounts on January 1st, 2019, is approximately $31,642.05.

To learn more about “treasury bills” refer to the https://brainly.com/question/13095860

#SPJ11

Answer:

\(\frac{ - 5}{54} + \frac{5 \times 6}{9 \times 6} = \frac{ - 5 + 30}{54} = \frac{25}{54} \)

\( \frac{15}{4} \div \frac{3}{8} = \frac{15}{4} \times \frac{8}{3} = 10\)

\(10 \times \frac{25}{54} = \frac{250}{54} = 4 \times \frac{17}{27} \)

b )

\(4 \times \frac{17}{27} = \frac{125}{27} =\)

cube root =

\( \frac{5}{3} \)

c ) square root

\( \frac{125}{27} = \frac{ \sqrt{25 \times 5} }{ \sqrt{3 \times 9} } = \frac{5 \sqrt{5} }{3 \sqrt{3} } \)

Answer:

The equation is p = (8/3) t + 24

In 2020, we will have about 48 horses.

Step-by-step explanation:

In 3 years  the family increased by 32 - 24 = 8.

So the  constant of proportionality = 8/3.

The required equation is p = (8/3)tx + 24

where p = the population and t is the number of years after 2011.

So in 2020 we can predict that in 2020 the number of horses

=  (8/3) * 9 + 24

= 72/3 + 24

= 24 + 24

= 48.

Answer:

see below

Step-by-step explanation:

Angle B is 100 degrees because vertical angles are equal

<B and angle X are same side interior angles and since AD and EH are parallel lines same side interior angles are complementary

B + X = 180

100 +x = 180

x = 180-100

x = 80

Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

\(\frac{15}{9}\) = x , that is

x = \(\frac{5}{3}\)

y = \(\frac{5}{3}\) x ← equation of variation

when y = 30 , then

30 = \(\frac{5}{3}\) x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

Step-by-step explanation:

Note that the first 2 points have the same y-coordinate (5) which means that the line joining them is horizontal so its length is -1  - (-4) = 3 units.

The line joining the last 2 points is also horizontal  and its length is

4 - (-4) = 8 units.

If we draw the polygon on the coordinate plane we see that the polygon is a trapezoid so its area

= 1/2 h (a + b) where a and b are the above 2 lines and h is the distance between these lines.

h = 5 - (-3) = 8

so the area = 1/2 * 8(3 + 8)

                   = 44 unit^2.

Answer:

-4x² +8x +2

Step-by-step explanation:

Answer: -4x^2+8x+2

Step-by-step explanation: Because, -4 x to the second power is added to 8x and again to 2. Which is above as an expression as the answer.

Raina can run any number of laps (n) less than 8 to ensure her total running time is less than 48 minutes.

To find the possible numbers of laps Raina will run today, we can set up an inequality based on the given information.

Let's assume Raina will run n laps today, and each lap takes 6 minutes. Therefore, the total time she will take to run n laps is 6n minutes.

The problem states that Raina will run less than 48 minutes today. Therefore, we can write the inequality as:

6n < 48.

To solve this inequality for n, we need to isolate n on one side of the inequality.

Dividing both sides of the inequality by 6, we get:

n < 48/6

Simplifying the right side, we have:

n < 8

Therefore, the inequality solved for n is:

n < 8

This means that the possible numbers of laps Raina will run today are any positive integer value less than 8.

Since the number of laps cannot be negative or zero, the feasible values for n are 1, 2, 3, 4, 5, 6, and 7.

For similar question on inequality.

https://brainly.com/question/30681777  

#SPJ8

A 24-hour collection provides a more comprehensive and reliable assessment of certain values.

A 24-hour collection is a better indicator of some values than a random specimen because it provides a more comprehensive and representative sample of the specific substance or parameter being measured.

It captures variations in levels throughout the day and allows for the detection of fluctuations that may not be captured by a single random specimen.

A 24-hour collection involves collecting samples over a full day, typically for substances such as urine or hormones. This method provides a more accurate representation of the average levels of the substance being measured. It takes into account the diurnal rhythm or cyclical variations that may occur throughout the day.

For example, hormone levels often fluctuate throughout the day, with different peaks and troughs at specific times.

By collecting samples at regular intervals over a 24-hour period, a more accurate picture of the average hormone levels can be obtained, allowing for a better assessment of hormonal imbalances or abnormalities.

In contrast, a random specimen may only capture a snapshot of the substance's level at a specific moment, which may not be representative of the overall pattern.

Fluctuations in levels throughout the day can be missed, leading to potential inaccuracies or misinterpretation of the data.

Therefore, a 24-hour collection provides a more comprehensive and reliable assessment of certain values by capturing variations and trends over time, making it a better indicator than a single random specimen.

Learn more about hormones here:

https://brainly.com/question/30367679

#SPJ11

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

For more references on division, click;

https://brainly.com/question/21416852

#SPJ1

Answer:

C

Step-by-step explanation:

a) The slope of tangent is 12.

b) The equation of the tangent is given by : y = 12x - 7.

a)The given parabola is y = 6x².

Differentiating with respect to x, we have;

dy/dx = 12x.

The slope of the tangent at point (1, 5) is

dy/dx = 12x = 12(1) = 12.

So, the slope of the tangent is 12.

b)We have the slope of the tangent as 12 and the point (1, 5).

The equation of the tangent is given by

y - y₁ = m(x - x₁).

Substituting y₁ = 5, x₁ = 1, and m = 12, we have;

y - 5 = 12(x - 1).

Expanding the equation, we get;

y = 12x - 7.

f(a)To find f(a), we are given f(x) = 4x² - 3x + 2.

Substituting x = a, we get;

f(a) = 4a² - 3a + 2.

Substituting a = -10, we get;

f(-10) = 4(-10)² - 3(-10) + 2

= 40

2.Estimate the average rate of cell phone growth

(i) from 1998 to 2002:

The change in the number of phone subscribers is 233 - 109 = 124 million.

The change in the number of years is 2002 - 1998 = 4 years.

So, the average rate of cell phone growth from 1998 to 2002 is;

124/4 = 31 million phones/year.

(ii) from 2000 to 2002:

The change in the number of phone subscribers is 233 - 141 = 92 million.

The change in the number of years is 2002 - 2000 = 2 years.

So, the average rate of cell phone growth from 2000 to 2002 is;

92/2 = 46 million phones/year.

(iii) from 1998 to 2000:

The change in the number of phone subscribers is 141 - 109 = 32 million.

The change in the number of years is 2000 - 1998 = 2 years.So, the average rate of cell phone growth from 1998 to 2000 is;

32/2 = 16 million phones/year.

(b) Estimate the instantaneous rate of growth in 2000:

We are given the change in the number of phone subscribers from 1998 to 2000 as 32 million and from 2000 to 2002 as 92 million.

The change in the number of years is 2 years.

Therefore, the average rate of cell phone growth in 2000 is;

(32 + 92)/2 = 62 million phones/year.

Know more about the slope of tangent

https://brainly.com/question/16930692

#SPJ11

Answer:

GCF of 3 and 6 is 3.

LCM of 3 and 6 is 6.

Step-by-step explanation:

Step-by-step explanation:

5 +0.24 = 5 + 24 = 12 = 6

100 50 25

= 5 6

25