Alan is conducting a survey to find out the type of art preferred by students at the town’s high school. Identify the population of his survey and describe a possible sample of the population.

Step-by-step explanation:

|h-3|<5

This implies that

h-3<5 or h-3<-5

h<5+3 or h<-5+3

h<8 or h<-2

Hence the solution set is {h:h<-2 or h<8 }

Therefore the number line in the picture shows the solution set for |h-3|<5

The inequality |h-3|<5 means that h is a numerical value between -2 and 8. A number line representing this solution set would be marked between these two values.

The inequality |h-3|<5 represents all numbers that are less than 5 units from 3 on the number line. It leads to two simple inequalities. When we remove the absolute value we get -5 < h-3 < 5, which simplifies to -2 < h < 8. So the number line that shows the solution set will have a line drawn between -2 and 8, indicating all the numbers between these two values satisfy the inequality.

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Answer:

3800 square centimeters

Step-by-step explanation:

We need to find the surface of the rectangular prism shown.

The surface area is the area of all the surfaces (including the bottom and top).

There are 6 surfaces, top and bottom is squares and 4 sides are rectangles.

The area of square is side * side, and

The area of rectangle is length * width

Top Area = 10 * 10 = 100

Bottom Area = 10 * 10 = 100

Area of 1 side = 90 * 10 = 900

Hence, area of 4 of these same sides is:  900 * 4 = 3600

Total Surface Area = 3600 + 100 + 100 = 3800

Total Carpet Needed = 3800 square centimeters

Answer:

3800

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

This graph is linear

Answer:

You're not giving enough details about the figure

The rate at which the vehicle can travel is 6 miles per gallon

Solution:

Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water

To find: Rate at which the vehicle can travel, in miles per gallon of water

distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]

gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]

Miles per gallon is given as:

[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]

Substituting the given value we get,

[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]

So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon

Answer:

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

Step-by-step explanation:

we have

[tex]f(x)=2x^{2}+3x-5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

The coordinates of the vertex is the point (h,k)

step 1

Find the vertex of the quadratic function

Factor the leading coefficient 2

[tex]f(x)=2(x^{2}+\frac{3}{2}x)-5[/tex]

Complete the square

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}[/tex]

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}[/tex]

Rewrite as perfect squares

[tex]f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}[/tex]

The vertex is the point (-\frac{3}{4},-\frac{49}{8})

step 2

Find the x-intercepts (values of x when the value of f(x) is equal to zero)

For f(x)=0

[tex]2(x+\frac{3}{4})^{2}-\frac{49}{8}=0[/tex]

[tex]2(x+\frac{3}{4})^{2}=\frac{49}{8}[/tex]

[tex](x+\frac{3}{4})^{2}=\frac{49}{16}[/tex]

take the square root both sides

[tex]x+\frac{3}{4}=\pm\frac{7}{4}[/tex]

[tex]x=-\frac{3}{4}\pm\frac{7}{4}[/tex]

[tex]x_1=-\frac{3}{4}+\frac{7}{4}=1[/tex]

[tex]x_2=-\frac{3}{4}-\frac{7}{4}=-2.5[/tex]

therefore

The function f(x) is negative in the interval (-2.5,1)

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

see the attached figure to better understand the problem

Option B

-0.249851765 is a irrational number

Solution:

Given number is -0.249851765

We have to classify the number

Let us first understand about irrational, real, whole, integer and rational numbers

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043

Every integer can be expressed as a decimal, but most numbers that can be expressed as a decimal are not integers. If all the digits after the decimal point are zeroes, the number is an integer. If there are any non-zero digits after the decimal point, the number is not an integer.

Thus -0.249851765 has non zero digits after decimal point. So it is not a integer

Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."

But the given number -0.249851765 is negative number. So it is not a whole number

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc. Natural numbers are also called "counting numbers" because they are used for counting.

A decimal is a natural number if it is non-negative and the only digits after its decimal points are zero

So the given number -0.249851765 is a negative number and so it is not a natural number

A rational number is a number that can be expressed as a fraction (ratio) in the form [tex]\frac{p}{q}[/tex] where p and q are integers and q is not zero.

The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another.

When a rational number fraction is divided to form a decimal value,  it becomes a terminating or repeating decimal.

So -0.249851765 is not a rational number

An irrational number is real number that cannot be expressed as a ratio of two integers.

When an irrational number is expressed in decimal form, it goes on forever without repeating

So the given number -0.249851765 is irrational number

We can conclude that:

-0.249851765 is a irrational number, So Option B is correct

Answer:

7000

Step-by-step explanation:

because 6532 is closer to 7000 then 6000.

Answer:

Step-by-step explanation:

x = 60

ΔMAD ≅ Δ SUN

So corresponding parts of congruent triangle are congruent.

∠MDA = ∠NSU

Answer:

x = 90

Step-by-step explanation:

Remember you have to post complete questions in order to get good and exact answers. So here I'll assume a diagram shown below. From the statement. we know that:

△MAD ≅ △SUN

This implies that triangle MAD is congruent to triangle SUN meaning that corresponding sides and angles measure the same. In other words:

∠M = ∠S

∠A = ∠U

∠D = ∠N

And:

MA = SU

AD = UN

MD = SN

So, from the figure:

∠S = ∠M = 30°

As the sum of internal angles of every triangle measures 180°, then:

∠S + ∠U + ∠N  = 180°

And:

∠U = x°

So:

30° + x° + 60°  = 180°

x° = |80° - 30° - 60°

x° =  90°

So:

x = 90

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Brainliest?, also let me know if i am wrong, Good Luck.

Answer:

the boat travel one way = 2 x 14.16 = 28.32 miles

Step-by-step explanation:

the return trip only takes 1.7 miles (?) ... is it 1.7 hours (?)

the boat travels 2.5 miles (per hour ?) faster downstream

I calculate it on the assumption of my guess stated above ...

X: represent the boat speed / hour

distance one way = 2X

and Distance also = 1.7 * (x + 2.5 ) on return

2x = 1.7 x + 1.7 * 2.5 = 1.7x + 4.25

0.3 x = 4.25

x = 14.16

the boat travel one way = 2 x 14.16 = 28.32 miles

Answer:

see the prime factors

Step-by-step explanation:

24= 6*4=3*2*2*2

=2*3*4

Answer:

No

Step-by-step explanation:

First off, the number 4 is not a prime number and the prime factorization of a number has to consist of all prime numbers. 2*3*4 does result in 24 but 4 is not prime because a prime number is a whole number with exactly two factors, itself and 1. 4 has more than two factors; the factors of 4 are 1, 2, and 4 so 4 isn't prime.

2*2*2*3 is the prime factorization of 24 because when you break down 24 into prime numbers, the results are 2*2*2*3.

24=2*12(here, we broke the number 24 into two factors 2 and 12. it doesn't matter which factors you break the number into because you still get the same result.)

2*12=2*2*6(we broke the number 12 into 2*6 because 12 isn't prime. we have to break each number into prime numbers.)

2*2*6=2*2*2*3(finally, we broke down 6 because it is the only number left that is not prime. 2*3=6 and 2 and 3 are prime so we break down 6 into 2*3)

Now you have the prime factorization of 24!

24=2*2*2*3

Answer:

Therefore values of a and b are

[tex]a=3\ and\ b = 2[/tex]

Step-by-step explanation:

Rewrite [tex]x^{2}-6x+7=0[/tex] in the form

[tex](x-a)^{2}=b[/tex]

where a and b are integers,

To Find:

a = ?

b = ?

Solution:

[tex]x^{2}-6x+7=0[/tex] ..............Given

Which can be written as

[tex]x^{2}-6x=-7[/tex]

[tex](\frac{1}{2} coefficient\ of\ x)^{2}=(\frac{1}{2}\times -6)^{2}=9[/tex]

Adding half coefficient of X square on both the side we get

[tex]x^{2}-6x+9=-7+9=2[/tex] ...................( 1 )

By identity we have (A - B)² =A² - 2AB + B²

Therefore,

[tex]x^{2}-6x+9=x^{2}-2\times 3\times x+3^{2}=(x-3)^{2}[/tex]

Substituting in equation 1 we get

[tex](x-3)^{2}=2[/tex]

Which is in the form of

[tex](x-a)^{2}=b[/tex]

On comparing we get

a = 3 and b = 2

Therefore values of a and b are

[tex]a=3\ and\ b = 2[/tex]

Answer 2: a = 3 and b = 2

Answer:

f(3)=11

Step-by-step explanation:

given f(x)=4x-1.............(1)

put x=3

f(3)=[tex]4\times3[/tex]-1

f(3)=12-1

f(3)=11 answer

Answer:

The answer is 6 ratio because when you divide these two number then the anwer is 6

Answer:

ratio of food costs to take away home 1:6

Step-by-step explanation:

$1500: $250

150:25

30:5

6:1

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Solution:

Given that area of mirror is 225 square inches

[tex]width = 13\frac{3}{4} \text{ inches }[/tex]

Converting the above mixed fraction we get,

[tex]width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }[/tex]

Let us find the length of mirror

The area of mirror is given as:

area of mirror = length x width

Substituting the given values,

[tex]225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36[/tex]

Thus length of mirror is 16.36 inches

Will the mirror fit in a space that is 15 inches by 16 inches?

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Because length of mirror is 16.36 inches whereas the given space is 15 inches long

16.36 > 15 so the length of mirror will not fit inside the space

Also width of mirror is [tex]\frac{55}{4} = 13.75[/tex] inches which is less than the given space whose width is 16 inches

13.75 < 16 so the width of mirror will not fit inside the space

Answer: 54678 years

Step-by-step explanation:

This can be solved by the following equation:

[tex]N_{t}=N_{o}e^{-\lambda t}[/tex] (1)

Where:

[tex]N_{t}=54\%=0.54[/tex] is the quantity of atoms of carbon-14 left after time [tex]t[/tex]

[tex]N_{o}=1[/tex] is the initial quantity of atoms of C-14 in the mammal hide

[tex]\lambda[/tex] is the rate constant for carbon-14 radioactive decay

[tex]t[/tex] is the time elapsed

On the other hand, [tex]\lambda[/tex] has a relation with the half life [tex]h[/tex] of the C-14, which is [tex]5730 years[/tex]:

[tex]\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}[/tex] (2)

Substituting (2) in (1):

[tex]0.54=1e^{-(0.000121 years^{-1}) t}[/tex] (3)

Applying natural logarithm on both sides of the equation:

[tex]ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})[/tex] (4)

[tex]-0.616=-(0.000121 years^{-1}) t[/tex] (5)

Isolating [tex]t[/tex]:

[tex]t=\frac{-0.616}{-0.000121 years^{-1}}[/tex] (6)

[tex]t=54677.68 years \approx 54678 years[/tex] (7)  This is the age of the mammal hide

The age of the mammal hide to the nearest year is approximately 11,239 years.

To find the age of the mammal hide with 37% of its original amount of C-14 remaining, we can use the decay formula for a substance undergoing exponential decay, which is described by the equation N(t) = N0(1/2)t/T, where N(t) is the remaining amount of substance, N0 is the original amount of substance, t is the time that has elapsed, and T is the half-life of the substance.

In this case, the half-life of C-14 is 5,730 years. Since we know the remaining amount of C-14 is 37% of the original amount, we can set up the equation 0.37 = (1/2)t/5730. To solve for t, we take the natural logarithm of both sides:

ln(0.37) = ln((1/2)t/5730)

ln(0.37) = (t/5730) * ln(1/2)

t = (ln(0.37)/ln(1/2)) * 5730

When we compute the value for t, we get the age of the mammal hide. By performing this calculation, we find that t is approximately 11,239 years. This is the estimated age of the mammal hide to the nearest year.

155-45=110

3850÷110=385 bicycles

Answer:

35

Step-by-step explanation:

3850/(155-45)

3850/110

35

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Answer:

5.   m < 1 = 72 degrees.

6.    m < 1 = 80 degrees.

Step-by-step explanation:

5. < 1 = 72 degrees.

If we draw a line through the point of < 1,  We see that  We have have 2 angles  of 40 and 32 ( alternate angles).

6.  By the same reasoning m < 1 = 60 + 20

= 80 degrees.

Answer:

All real numbers are solution for the inequality.

Step-by-step explanation:

Given expression:

[tex]2(-6n-5)<-3(4n+2)[/tex]

Solving the inequality.

Using the distribution.

[tex](2(-6n))+(-2(-5)<(-3(4n))+(-3(2))[/tex]

[tex]-12n-10<-12n-6[/tex]

Adding [tex]12n[/tex] to both sides.

[tex]-12n+12n-10<-12n+12n-6[/tex]

We have,

[tex]-10<-6[/tex]

The above statement is always true and thus the inequality has all real number solutions.

The number line graph for the inequality can be shown.

Answer:

y+1=5(x+2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=5(x-(-2))

y+1=5(x+2)

The answer is 25.12 exactly

To find the height of the baby giraffe given the average height of it and a giraffe is 6m, and it is 2/3 the giraffe's height, first solve for the giraffe's height to find it is 7.2m. Then, calculate 2/3 of this to get the baby giraffe's height, which is 4.8m.

The question asks to determine the height of a baby giraffe given the average height of a giraffe and a baby giraffe together is 6m, and the baby giraffe's height is 2/3 that of the giraffe's height. Let X be the height of the giraffe. Then, the baby giraffe's height would be 2/3 X. Given the average of these two heights is 6m, the equation to find the height of the baby giraffe is:

(X + (2/3)X) / 2 = 6

By solving this equation:

Hence, the height of the baby giraffe is 4.8m.

Answer:

Carrie read at a rate of 21 2/3 pages per hour

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time Ms. Graves gave her class to read = 18 minutes

Number of pages Carrie read in 18 minutes = 6 1/2 pages

2. At what rate, in pages per hour, did Carrie read?

Rate = Number of pages/Time given

For getting the exact rate per hour, we should use the Rule of Three Simple, this way:

Number of pages in 60 minutes * 18 = 6 1/2 * 60

Number of pages in 60 minutes = (6.5 * 60)/18

Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3

Carrie read at a rate of 21 2/3 pages per hour

Answer:

Angular cut

Step-by-step explanation:

If you cut it horizontally, the cross-section would be a square.

If you cut it vertically, it would be  result as a triangle.

If you cut angular, it would result as a trapezoid.

Answer: Horizontal cut

Step-by-step explanation:

Answer:

8 ounces of vinegar

36 ounces of dressing

Step-by-step explanation:

Marco makes his famous salad Jackson by mixing 5 1/4 ounces of olive oil with 1 1/2 ounces of vinegar.

Olive oil                 Vinegar

5 1/4                           1 1/2

28                                x

Write a proportion:

[tex]\dfrac{5\frac{1}{4}}{28}=\dfrac{1\frac{1}{2}}{x}\\ \\5\dfrac{1}{4}\cdot x=28\cdot 1\dfrac{1}{2}\ [\text{Cross multiply}]\\ \\\dfrac{21}{4}x=28\cdot \dfrac{3}{2}\\ \\\dfrac{21 x}{4}=42\\ \\x=42\div \dfrac{21}{4}\\ \\x=42\cdot \dfrac{4}{21}\\ \\x=2\cdot 4\\ \\x=8\ ounces[/tex]

Marco will make

[tex]28+8=36[/tex] ounces of dressing

Answer:

23*0.15=$3.45

Step-by-step explanation:

23*0.15=$3.45

Answer:

The wingspan of 26 atlas moths are 286 inches.

Step-by-step explanation:

Given:

An Atlas moth has a wingspan of 11 inches.

Now, to find the wingspan of 26 atlas moths.

So, we use unitary method:

As given an atlas wingspan has 11 inches.

Then for wingspan of 26 atlas we multiply it by 11 inches:

⇒  [tex]26\times 11\ inches[/tex]

[tex]=286\ inches.[/tex]

Therefore, the wingspan of 26 atlas moths are 286 inches.

Final answer:

To find the total wingspan of 26 Atlas moths, multiply the wingspan of one moth, 11 inches, by 26, resulting in a total of 286 inches.

Explanation:

The question involves simple multiplication to determine the total wingspan of 26 Atlas moths. If one Atlas moth has a wingspan of 11 inches, then the wingspan of 26 Atlas moths can be found by multiplying 11 inches by 26.

Step-by-step calculation:

Determine the wingspan of one Atlas moth, which is already given as 11 inches.

Multiply the wingspan of one moth by the total number of moths: 11 inches * 26 = 286 inches.

Therefore, the total wingspan of 26 Atlas moths is 286 inches.

Answer:

If today is Saturday, the probability that tomorrow is Sunday.

Step-by-step explanation: