select the interval where h(x)<0
A. -3.5 B. -2 C. 2.5

The median is [tex]\(55\)[/tex], Q1 is approximately [tex]\(19.5\)[/tex], Q3 is [tex]\(79\)[/tex], and the interquartile range is [tex]\(59.5\).[/tex]

To find the median, first quartile (Q1), third quartile (Q3), and interquartile range (IQR) for the given set of numbers, you first need to arrange them in ascending order:

[tex]\[ 14, 25, 28, 38, 55, 66, 92, 94, 97 \][/tex]

Now, let's find each of the required values:

1. **Median (Q2)**: The median is the middle value of the dataset when arranged in ascending order. Since there are 9 numbers, the median will be the value at the [tex]\(\frac{9+1}{2} = 5\)[/tex]-th position, which is the 5th number in the sorted list: [tex]\(55\)[/tex].

2. **First Quartile (Q1)**: Q1 is the median of the lower half of the dataset. Since there are an odd number of data points in the lower half (4 points), Q1 will be the median of the first four numbers: [tex]\( \frac{14 + 25}{2} = 19.5 \).[/tex]

3. **Third Quartile (Q3)**: Q3 is the median of the upper half of the dataset. Similarly, since there are an odd number of data points in the upper half (also 4 points), Q3 will be the median of the last four numbers: [tex]\( \frac{66 + 92}{2} = 79 \).[/tex]

4. **Interquartile Range (IQR)**: IQR is the difference between Q3 and Q1. So, [tex]\( IQR = Q3 - Q1 = 79 - 19.5 = 59.5 \).[/tex]

So, the median is [tex]\(55\)[/tex], Q1 is approximately [tex]\(19.5\)[/tex], Q3 is [tex]\(79\)[/tex], and the interquartile range is [tex]\(59.5\).[/tex]

Answer:

67,500 residents

Step-by-step explanation:

The population density is defined as the average number of people living per square unit area.

-Given the density is 225res/sq mile and the area is 300 sq mile, the area's population is:

[tex]\rho=\frac{Population}{Area}\\\\Population=Area \times \rho\\\\=300 \ mi^2\times 225\ res/mi^2\\\\=67500\ residents[/tex]

Hence, there are 67,500 residents in Flint county.

To calculate the population of Flint County, the population density (225 residents/mile2) is multiplied by its area (300 mile2), resulting in a population of 67,500 residents.

To find the population of Flint County, we need to multiply the population density by the area of the county. The population density is given as 225 residents per square mile, and the area of Flint County is 300 square miles. By multiplying these two values together, we can determine the total population.

Population of Flint County = Population Density × Area = 225 residents/mile2 × 300 mile2

Population of Flint County = 225 × 300 = 67,500 residents

Therefore, the population of Flint County is 67,500 residents.

Answer: Yes and No

When the longest side is not longer than the sum of the two shorter

Step-by-step explanation:

Let first convert mile to kilometre

1 mile = 1.609km

AB = 0.5mile = 0.8045 km

BC = 1/3 miles = 0.53633 km

DE=0.205 kilometer

EF=0.01 kilometer

AC=1/4 mile = 0.40225

DF=0.02 kilometer

When the longest side is not longer than the sum of the two shorter sides , then a triangle can be made

Let's first consider AB, BC and AC Each set of line segments AB, BC and AC can form a triangle

Also DE, EF and DF

Each set of line segments DE, EF and DF can't form a triangle because the longest side is greater than the sum of the two shorter sides.

If you must solve this problem graphically, you have to draw the graph of the two functions and see where they meet.

Look at the attached image to see the two graphs.

You can see that they intersect twice, when x=1 and when x=3

Final answer:

The percentage increase in the perimeter of the rectangle is 6%.

Explanation:

To find the percentage increase in the perimeter of the rectangle, we need to calculate the new perimeter and compare it to the original perimeter.

The original length is 20 and the width is 30. The original perimeter is 2(20+30) = 100.

When the length is increased by 10%, it becomes 20 + 10% of 20 = 20 + 2 = 22. The width is increased by 5%, so it becomes 30 + 5% of 30 = 30 + 1.5 = 31.5.

The new perimeter is 2(22+31.5) = 106. The percentage increase in the perimeter is (106-100)/100 * 100 = 6%.

Answer:

Here we have the table for the 8 students that said yes.

a) Out of the 8 students, 5 purchased their favorite food more than four times a month.

The proportion will be p = 5/8, and this can not be simplified anymore because 5 is a prime number and 5 is not a factor of 8.

b) The mean time will be equal to the amount of each of the 8 purchased their favourite food divided by the total sample (8)

This is:

m = (6 + 4 + 3 + 8 +6 + 9 + 4 + 7)/8 = 5.875

c) Out of a sample of 20, 8 buy lunch regularly, this is; p1 = 8/20

The amount of students that regularly buy food will be:

p1*1000 = (8/20)*1000 = 400

And of those 400, 5/8 buy their favourite lunch more than 4 times per month:

(5/8)*400 = 250

d: The mean number of times that a student regularly buys salad.

We have 3 students that regularly buy salad (so we only do the math with those 3)

The mean is (8 + 6 + 7)/3 = 7

So for the students that regularly buy salad, the mean of times that the buy salad in a month is 7 times.

Answer:

200 are on screen 1

125 are on screen 2

175 went to screen 3

Step-by-step explanation:

10% is 50 so 50 x 4 =200

25% of 500 is 12, divide 500 by 4

35% is 25% + 10% = 125 + 50 = 175

Answer: the first one

Step-by-step explanation:

Answer:

The first one graph

Step-by-step explanation:

I think

Answer:15

15 divided by 100 then multiplied by 20 equals 3

and 3+15 equals 18

Answer:

The sum of negative one - sixth and three times x minus 2 times y.

The required translation of the given expression is the sum of negative one-sixth and three times x minus 2 times y.  Option C is correct.

Given that,
To choose the translation that best fits the expression: − 1/6 + 3x − 2y

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression.
=− 1/6 + 3x − 2y
we can write such as,
-1/6 = negative one-sixth,
3x = three times x
2y = two times y
− 1/6 + 3x − 2y =  the sum of negative one-sixth and three times x minus 2 times y

Thus, the required translation of the given expression is the sum of negative one-sixth and three times x minus 2 times y.  Option C is correct.

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Answer:

How many repeating digits are in 0.ModifyingAbove 64 with bar?

2

What value is multiplied on both sides of the equals sign?

100

What fraction represents 0.ModifyingAbove 64 with bar?

64/99

Step-by-step explanation:

i got it right. :))

There are 2 repeating digits are in 0 when modifying above 64 with bar.

100 is multiplied on both sides of the equals sign.

64/99 represents 0.

Given that,

The question about converting 0. Modifying above 64 with the bar to a fraction.

We have to determine,

How many repeating digits are in 0? Modifying above 64 with bar?

What value is multiplied on both sides of the equals sign?

What fraction represents 0?

According to the question,

The question about converting 0. Modifying above 64 with the bar to a fraction.

Converting the 64 bar into a fraction,

[tex]\bar{64} = 0.64646464[/tex]

Therefore,

[tex]\rm 0. \bar{64}=\dfrac{3}{x}\\\\ 100 \times \dfrac{\bar{64}}{100}= \dfrac{3}{x}\times 100\\\\= \dfrac{64}{100} \times {\dfrac{1}{99}}=\dfrac{300}{x}\\\\ x = \dfrac{300 \times 9900}{64}\\\\x =\dfrac {2970000}{64}[/tex]

Hence, There are 2 repeating digits are in 0 when modifying above 64 with bar.

100 is multiplied on both sides of the equals sign.

64/99 represents 0.

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Answer:

3 42/48 + 6 12/48

Step-by-step explanation:

Final answer:

To find the equivalent expression, convert the mixed numbers to improper fractions, subtract the fractions, and then convert the result back to a mixed number.

Explanation:

The expression equivalent to 3 7/8 - 6 1/4 is:

Step 1: Convert the mixed numbers to improper fractions: 3 7/8 = 31/8 and 6 1/4 = 25/4.

Step 2: Subtract the fractions: 31/8 - 25/4 = 31/8 - 50/8 = -19/8.

Step 3: Convert the result back to a mixed number: -19/8 = -2 3/8.

Answer: x=8

Width=8 inches

Length=13 inches

Final answer:

The width of the rectangle is 8 inches and the length is 13 inches, as determined by solving the quadratic equation representing the area of the rectangle.

Explanation:

To solve for the dimensions of the rectangle, we need to find the value of x, which represents the width of the rectangle. The quadratic equation we have is x² + 5x - 104 = 0.

Factoring this equation, we are looking for two numbers that multiply to -104 and add to 5.

These numbers are 13 and -8, so the equation factors to (x + 13)(x - 8) = 0. Setting each factor equal to zero gives us two possible solutions for x: x = -13 or x = 8.

Since a width cannot be negative, the only sensible solution for this problem is x = 8 inches. Given that the length is 5 inches more than the width, the length will be 8 inches + 5 inches = 13 inches.

Dimensions of the rectangle:

Width = 8 inches

Length = 13 inches

Answer:

1.25 miles

Step-by-step explanation:

one day= 30 miles

one day=24 hours

so we can divide 30 to 24 to get miles travelling per hour.

1.25 miles

To solve for x when g(x) = 9 given the function g(x) = -x – 4, set the equations equal to each other. Rearrange the equation and solve for x, which gives x = -13

The question asked for the value of x when g(x) = 9 given the function g(x) = -x – 4. We can start by setting the two equations equal to each other. This gives us -x - 4 = 9. Next, we rearrange the equation to solve for x by adding 4 to each side, which gives us -x = 9 + 4 or -x = 13. To get x on its own, we divide each side by -1. This gives us x = -13. Therefore, when g(x) = 9, x is equal to -13.

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Answer:

The exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n

Step-by-step explanation:

The general formula for [tex](a+b)^n[/tex] is:

[tex]a^n + C_1a^{n-1}b + C_2a^{n-2}b^2 + ... + C_{n-1}a^2b^{n-2} + C_nab^{n-1} + b^n[/tex]

Therefore, the exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n

5)x= 67° and y= 32°

(x-15)°=52°(vertically opposite angles)

=>x= 52+15° = 67°

Similarly, 4y= 128°(vertically opposite angles)

=>y=128/4= 32°

6) x= 5° , y= 22°

12x+15=75°(vertically opposite angles)

12x=75-15°

12x=60°

x= 5°

6y-27°=105°

6y= 105+27°

6y= 132°

y= 22°

Answer:

You can either factor or use quadratic formula to find where h(x)=0

Step-by-step explanation:

Remember that the ball is on the ground when h(x)=0 since that is the height. There will be two zeros,  one is a negative number so would be before you kicked the ball, the other one will be when the ball comes back down.

Answer:

4 5/6 (the last option)

Step-by-step explanation:

to ensure and find out you can dive 5/6 then add 4 and you get 4.833333333333

Answer:

24 inches

Step-by-step explanation:

The area of the square is 36 in2. The area of square can be represented as side x side or side squared. So, the sides must be 6 inches in length since 6x6 is 36. If one side is 6, 4 sides are 24.

Answer:

-1

Step-by-step explanation:

The midline is the middle point

Subtract the midline from the maximum

5-2 = 3

Then we need to subtract this number from the midline to get to the minimum

2-3 = -1

The minimum is at -1

Answer:

-1

Step-by-step explanation:

Mean line is between min and max

2 = (5 + min)/2

4 = 5 + min

min = -1

Answer:

Yes

Step-by-step explanation:

If it could be a right triangle, then 12^2 + 35^2 would have to equal 37^2

12^2 = 144

35^2 = 1225

37^2 = 1369

1225 + 144 = 1369, which is 1369.

That means that it CAN form a right triangle

Answer:

yes

Step-by-step explanation:

Answer:

17.5  yds =r

Step-by-step explanation:

Circumference is given by

C = 2*pi*r

35pi = 2 *pi*r

Divide each side by 2pi

35pi/2pi = 2*pi*r/2pi

17.5 =r

Answer:

Final Answer -$50

Step-by-step explanation:

The account balance of Clare can be calculated using negative value. To solve the given problem we have to assume that her bank account has a negative value

Now Clare's account balance is $0.

Given:

Clare has $150 in her bank account.

She buys a bike for $200.

Determine the amount balance in Clare account.

Since the price of the bike is more than the account balance of Clare, we can assume that her bank account has a negative value, although since the bank account cannot go past 0, except for loans and debts, and it is not stated whether Clare has taken a loan.

Therefore we can state that the account balance of,

$0=$100 - $150= -$50

Thus, Now Clare's account balance is $0

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The instantaneous velocity of the baseball 3 seconds after it is hit is [tex]\( 24 \)[/tex] feet per second.

To find the instantaneous velocity of the baseball 1 second and 3 seconds after it is hit, we need to differentiate the height function [tex]\( s(t) \)[/tex] with respect to time [tex]\( t \)[/tex] to get the velocity function [tex]\( v(t) \).[/tex]

The height function is given by:

[tex]\[ s(t) = -16t^2 + 88t + 4 \][/tex]

1. Find the Velocity Function:

[tex]\[ v(t) = s'(t) \][/tex]

Differentiate [tex]\( s(t) \)[/tex] with respect to [tex]\( t \)[/tex]:

[tex]\[ v(t) = -32t + 88 \][/tex]

2. Evaluate the Instantaneous Velocity at [tex]\( t = 1 \)[/tex] second:

[tex]\[ v(1) = -32(1) + 88 = 56 \][/tex]

The instantaneous velocity of the baseball 1 second after it is hit is [tex]\( 56 \)[/tex] feet per second.

3. Evaluate the Instantaneous Velocity at [tex]\( t = 3 \)[/tex] seconds:

[tex]\[ v(3) = -32(3) + 88 = 24 \][/tex]

The answer is [tex]\( 24 \)[/tex] feet per second.

So, after differentiating the height function to get the velocity function, we substituted the given values of time [tex](\( t = 1 \)[/tex] and [tex]\( t = 3 \))[/tex] into the velocity function to find the corresponding instantaneous velocities.

The instantaneous velocity provides information about the speed and direction of the baseball at a specific moment in time. In this case, 1 second after being hit, the baseball is moving upward with an instantaneous velocity of [tex]\( 56 \)[/tex] feet per second, and 3 seconds after being hit, it is still moving upward but with a reduced instantaneous velocity of[tex]\( 24 \)[/tex] feet per second.

The complete question is given here :

A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 88 feet per second. The function [tex]s(t) = -16t^2 + 88t + 4[/tex] describes the ball's height above the ground, s(t), in feet, t seconds after it was hit. What is the instantaneous velocity of the ball 1 second after it is hit? 3 seconds after it is hit?

Step-by-step explanation:

L = 20t

Step-by-step explanation:

The length increases by 20 millimeters per minute

Answer: L=20t

Step-by-step explanation:

Answer:

The thickness of the pile is [tex]2\frac{1}{4} in.[/tex] or 2.25 inches thick

Step-by-step explanation:

Here we have from the line plot, the four thinnest books given by;

Two books of 1/2 inch thickness and two books 5/8 inch thickness

Therefore when the two 1/2 inch thick books are piled on top of the to 5/8 inch thick books we have the total thickness of the pile given as follows;

[tex]2\times \frac{1}{2} in. + 2\times \frac{5}{8} in.= \frac{9}{4} in. = 2\frac{1}{4} in.[/tex]

The thickness of the pile =[tex]2\frac{1}{4} in.[/tex]

Answer:

4 3/4

Step-by-step explanation:

I did the test

Final answer:

To convert the tree's circumference from inches to centimeters, multiply 17 inches by the conversion factor of 2.54 cm per inch, resulting in 43.18 cm, which is not an exact match to the provided options but the closest option is 42.5 cm.

Explanation:

To convert James' measurement of the tree's circumference from inches to centimeters, we use the conversion factor that 1 inch equals 2.54 centimeters. Therefore, if the tree's circumference is 17 inches, we multiply 17 by 2.54 to get the circumference in centimeters.

The calculation is as follows:

Multiply the circumference in inches (17 inches) by the conversion factor (2.54 cm per inch).

The result is 17 inches × 2.54 cm/inch = 43.18 cm.

Therefore, the tree's circumference in centimeters is 43.18 cm, which rounds down to 43 cm when measuring to the nearest whole number, none of the options exactly match but option A is the closest. So, we must choose the closest option, which is A. 42.5 cm.

Answer:

The student answer is wrong. The correct length of the hypotenuse is 12

Step-by-step explanation:

The question is incomplete without diagram. Find the diagram attached below.

The longest side of the right angled triangle is the hypotenuse.

The side facing the angle 30° is the opposite side of the triangle.

To find the hypotenuse, we will use the SOH CAH TOA method in trigonometry identity.

According to SOH:

Sin30° = Opposite/Hypoenuse

Sin30° = 6/Hypotenuse

Hypotenuse = 6/sin30°

Hypotenuse = 6/0.5

Hypotenuse = 6×2

Hypotenuse = 12

The student answer is wrong. The correct length of the hypotenuse is 12

Answer:

The surface area is 294 ft^2 (please give branliest)

Step-by-step explanation:

area of one side 49

multiply by 6 sides

The surface area of the cube is equal to 294 square inches.

How to calculate the surface area of the cube

In this problem we find the representation of a cube, whose surface area, that is, the sum of the areas of all faces of the cube, must be computed in accordance with this formula:

A = 6 · l²

Where:

If we know that l = 7 in, then the surface area of the cube is equal to:

A = 6 · (7 in)²

A = 6 · 49 in²

A = 294 in²

The cube has a surface area of 294 square inches.