Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow procedure that utilized water containing the nutrient, they planted six tomato plants and recorded the heights of each plant 14 days after germination. Those heights, measured in millimeters, were as follows: 53.1, 60.2, 60.6, 62.1, 64.4, 68.6. Given a margin of error of 5.4 mm, construct a 95% confidence interval for the population mean height.

Answer:

probability that the page opened will start with S

Step-by-step explanation:

14/90

0.15556

Answer:

3 swimmers

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Tally question

There are 6 marks for A out of 30 total

6/30 = 1/5

Sample space question

{run 50  run 100 run 150, swim 50 swim 100 swim 150}

We have to list all the possible choices that the spinners can land

run         50

swim      100

               150

There are 2*3 = 6 choices

Tomas Game

1/36

The normal die has 1,2,3,4,5,6

P(5) = Number of 5's / total number of numbers = 1/6

Then roll another 5

P(5) = Number of 5's / total number of numbers = 1/6

P(5,5) = 1/6*1/6 = 1/36

Joe game

1/4

1,2,3,4,5,6  triangle, square

P(0dd) = {1,3,5}/ 6 numbers = 3/6 = 1/2

P (square) = square/ total  = 1/2

Coin

1/2

HT HH TH TT

We want one heads and one tails

2 of the four

2/4 = 1/2

P (odd,square) = P(odd) * P(square) = 1/2*1/2 = 1/4

Answer:

1) ⅕

2) sample space: D

3) 1/36

4) P(odd & square) = ¼

5) ½

Step-by-step explanation:

1) P(A) = 6/30 = 1/5

2) sample space is the collection of all possible outcomes

{activity & distance}

3) P(5 & 5) = 1/6 × 1/6

1/36

4) odd: 1,3,5

P(odd) = 3/6 = 1/2

P(square) = 1/2

1/2 × 1/2 = 1/4

5) P(H & T) = 1/2 × 1/2 = 1/4

2 × 1/4 = 1/2

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m = [tex]\frac{1}{3}[/tex]      So substitute/plug it into the equation

y = mx + b

[tex]y=\frac{1}{3} x+b[/tex]   To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself

[tex]0=\frac{1}{3} (-6)+b[/tex]

0 = -2 + b         Add 2 on both sides to get "b" by itself

0 + 2 = -2 + 2 + b

2 = b

[tex]y=\frac{1}{3} x+2[/tex]       Your answer is the 4th option

The equation in slope-intercept form is y = 1/3x  + 2

The equation of the line in point slope form is expressed as:

where:

Substitute:

y - 0 = 1/3(x+6)

Write in slope-intercept form

y = 1/3(x+6)

3y = x + 6

y = 1/3x + 6/3

y = 1/3x + 2

Hence the equation in slope-intercept form is y = 1/3x  + 2

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Answer:

x=5 feet

Step-by-step explanation:

At floor level y=0

If the expression is:

[tex]0=1/3(x-5)(x+5)\\0=1/3(x^2-25)\\0=1/3x^2-25/3\\25/3=1/3x^2\\25=x^2\\x=5[/tex]

But, with the negative sign, the answer is x= 5i (where i is imaginary)

Final answer:

The width of the arch at floor level is found by determining the points where the parabola intersects the x-axis, which are at x = 5 and x = -5. The width is the distance between these points, which is 10 feet.

Explanation:

To find the width of the arch at floor level, we need to determine the distance between the two points where the parabola represented by the equation y = -1/3(x-5)(x+5) intersects the x-axis. The x-axis represents the floor, and the points of intersection occur where y is equal to 0.

Setting the equation to 0 gives:

0 = -1/3(x-5)(x+5)

By solving for x, we get x = 5 and x = -5, which are the points where the parabola intersects the x-axis. The distance between -5 and 5 on the x-axis is 10 feet, so the width of the arch at floor level is 10 feet.

Answer:

119°

Step-by-step explanation:

In circle with center B, JH is diameter.

[tex]m\angle GHI = 360° - (90° + 151°)\\

m\angle GHI = 360° - 241°\\

m\angle GHI = 119°\\

\because\overset{\frown}{GHI} =m\angle GHI\\

\huge \red{ \boxed{\therefore \overset{\frown}{GHI} =119°}}\\ [/tex]

Answer:

1/22 gallons per mile

Step-by-step explanation:

We want to find gallons per mile, so we take the gallons and divide by the mile

10gallon/ 220 mile

1/22 gallons per mile

Answer:

1/22 gallons per mile

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

One side is half of the other (5/2.5=2)

So 14/2=7

Answer:

( x + 3)² + ( y + 7)² = 361

Step-by-step explanation:

The equation of a circle written in standard form is ( x – h)² + ( y - k)² = r². The center is (h, k) and the radius is r.

With the given information of center (-3, -7) and radius 19, we get

[ x – (-3)]² + [ y - (-3)]² = (19)²

( x + 3)² + ( y + 7)² = 361

Answer: No!

Step-by-step explanation:

Answer: No

Step-by-step explanation: If you take 944544 and divide it by 5, you will end up with 188908.8

Answer:

simplify question is 3a^2 +6a+9ab

Step-by-step explanation:

Answer:

16.56‬

Step-by-step explanation:

The area of the square is 2 × 2

The area of the circle is-

A=πr²

A=3.14 × 2²

A=3.14 × 4

A=12.56

You don't need to divide it by half because there are two half circles so it would be a whole circle

12.56 + 4 = 16.56

Sorry if it is wrong

Answer:

Area of square =side( square)

(2) square

4

diameter= 2

radius=2/2

= 1

Area of circle=πrsquare

22/7×1×1

3.14

Area of figure= Area of square+area of circle

4+3.14

7.14

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                             25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                             [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

                  c² = 64 - 25

                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

The center of the ellipse is (0,0), the vertices are (5.657, 0) and (-5.657, 0), and the foci are (3.317, 0) and (-3.317, 0).

The given equation of the ellipse is 25x^2 + 64y^2 = 1600.

To find the center of the ellipse, we can rewrite the equation in standard form: x^2/32 + y^2/25 = 1. The center is (0,0) since the x and y terms are squared and have the same coefficients.

To find the vertices of the ellipse, we can calculate the distance from the center to the major axis. The length of the major axis is 2*a, where a is the square root of the denominator of the x term. In this case, a = sqrt(32) ≈ 5.657. So the vertices are (5.657, 0) and (-5.657, 0).

To find the foci of the ellipse, we can calculate the distance from the center to the foci. The length of the foci is 2*c, where c is the square root of the difference between the squares of a and b (sqrt(32-25) ≈ 3.317). So the foci are (3.317, 0) and (-3.317, 0).

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Answer:

The answer to your question is     y = -2x - 13

Step-by-step explanation:

Data

Original line    y = 1/2x - 7

Point = (-10, 7)

New line = ?

Process

1.- Find the slope of the original line

    The slope is the coefficient of the x

                     y = 1/2x - 7

    slope = 1/2

2.- Find the slope of the new line

The new line is perpendicular to the original line

    slope = -2

3.- Find the equation of the new line

          y - y1 = m(x - x1)

          y - 7 = -2(x + 10)

-Simplification

          y - 7 = -2x - 20

          y = -2x - 20 + 7

          y = -2x - 13

Answer: The equation is y = -2x - 13.

We compare the given line with y = mx + b.

So slope = m = [tex]\frac{1}{2}[/tex].

We know that the slope of the perpendicular line is negative reciprocal.

It means the slope of the required line will be -2.

Given point = (-10, 7).

So, using the point slope formula the equation of the line is:

[tex]y-7=-2(x+10)\\y-7=-2x-20\\y=-2x-13[/tex]

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Answer:

The volume of the paper weight is 942.8 cubic cm.

Step-by-step explanation:

We are given the following in the question:

Dimensions of paperweight :

Radius, r = 10 cm

Height,h = 9 cm

Volume of paper weight = Volume of cone

[tex]V= \dfrac{1}{3}\pi r^2 h[/tex]

where r is the radius and h is the height of the cone.

Putting values, we get,

[tex]V = \dfrac{1}{3}\times \dfrac{22}{7}\times (10)^2\times 9\\\\V = 942.8\text{ cubic cm}[/tex]

Thus, the volume of the paper weight is 942.8 cubic cm.

The volume is 942.5 [tex]cm^{3}[/tex].

To calculate the volume of a cone, you can use the formula:

V = (1/3)πr²h

where:

1. For Marta's paperweight with a radius of 10 centimeters and a height of 9 centimeters, you substitute the values into the formula as follows:

V = (1/3)π(10 cm)²(9 cm)

2. First, calculate the base area:

(10 cm)² = 100 cm²

3. Then, multiply by the height:

100 cm² × 9 cm = 900 cm³

4. Finally, multiply by (1/3)π:

V = (1/3)π × 900 cm³ ≈ 942.5 cm³

Therefore, the volume of the cone is approximately 942.5 [tex]cm^{3}[/tex], rounded to the nearest tenth.

Answer:

The answer to your question is below

Step-by-step explanation:

Process

To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.

a)    25² = 20² + 7²

      625 = 400 + 49

     625 ≠ 449              It is not a right triangle

b)   26² = 24² + 10²

      676 = 576 + 100

      676 = 676               it is a right triangle

c)   13² = 8² + (√10)²

     169 = 64 + 10

      169 ≠ 74                 it is not a right triangle

d)   52² = 48² + 20²

      2704 = 2304 + 400

      2704 = 2704               it is a right triangle

Answer:

4 dollars and 20 cents

Step-by-step explanation:

5.00-.80=4.20

Answer:

$4.20

Step-by-step explanation:

What you bought will be subtracted from how much you paid with.

amount paid - amount bought

We paid for the cookie with $5, and bought something for 80 cents.

$5 is equal to 5.00, and 80 cents is equal to 0.8

5.00-0.8=4.2

So, you would get $4.20 back in change

Answer:

y = (-1/8)x^2

Step-by-step explanation:

Start with y = x^2.  When the original parabola has been reflected across the x-axis, the pertinent equation becomes y = -x^2.

Now if this is scaled vertically by a factor of 1/8, we get:

y = (-1/8)x^2

Answer:

D

Step-by-step explanation:

sqrt(7) = about 2.6

and that divided by 2 is

0.8  which means D is the Answer

Answer:

Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.

Step-by-step explanation:

To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.

The volume of the cone is:

V_cone = (1/3)*pi*r^2*h

Where V_cone is the volume, r is the radius and h is the height. So:

V_cone = (1/3)*pi*2^2*6 = 25.1327 in3

The volume of a sphere is:

V_sphere = (4/3)*pi*r^3

Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:

V_sphere = (4/3)*pi*2^3 = 33.5103 in3

The volume of the sphere is higher, so the cone will overflow.

The volume of the melted ice cream scoop[tex](\( 33.51032 \, \text{cubic inches} \))[/tex] is greater than the volume of the cone [tex](\( 25.13272 \, \text{cubic inches} \))[/tex] the cone will overflow if the entire scoop of ice cream melts into it.

Step 1: Volume of the Cone

The formula for the volume of a cone is:

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi r^2 h\][/tex]

where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.

Given:

[tex]\[r = 2 \, \text{inches}, \quad h = 6 \, \text{inches}\][/tex]

Substitute these values into the formula:

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (2)^2 (6)\][/tex]

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (4) (6)\][/tex]

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (24)\][/tex]

[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]

Step 2: Volume of the Ice Cream Scoop

The formula for the volume of a sphere is:

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi r^3\][/tex]

where [tex]\( r \)[/tex] is the radius of the sphere.

Given that the diameter of the sphere is [tex]4\ inches[/tex], the radius [tex]\( r \)[/tex] is:

[tex]\[r = \frac{4}{2} = 2 \, \text{inches}\][/tex]

Substitute this value into the formula:

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (2)^3\][/tex]

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (8)\][/tex]

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]

Step 3: Compare the Volumes

The volume of the cone:

[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]

The volume of the ice cream scoop:

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]

Let's convert them to decimal form for easier comparison:

[tex]\[V_{\text{cone}} = 8 \pi = 8 \times 3.14159 = 25.13272 \, \text{cubic inches}\][/tex]

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi = \frac{32}{3} \times 3.14159 = 33.51032 \, \text{cubic inches}\][/tex]

Answer:

25%(1/4)

Step-by-step explanation:

The probability of getting tails on the first flip and heads on the second flip of a coin is 25%, as each flip is an independent event.

The question pertains to the probability of an event occurring in two successive trials - flipping a coin twice. Firstly, we need to recognize that each flip is an independent event. An independent event is one in which the outcome of the first event does not affect the outcome of the second. When you flip a coin, the probability of getting tails is 1/2 or 50%, and the probability of getting heads is also 1/2 or 50%. Since these are independent events, we multiply the probabilities to get the result.

When you multiply 1/2 (probability of getting tails on the first flip) by 1/2 (probability of getting heads on the second flip), your result is 1/4 or 25%.

So, the probability of getting tails on the first flip and heads on the second flip is 25%.

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Answer:

61 67     71 73 79

There you go:)

Answer:

53, 59, 61, 67, 71.

Step-by-step explanation:

It goes on....

53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109

, 113, 127, 131, 137, 139

I hope this helps :)

Answer:

3/13

Step-by-step explanation:

There are 52 card in a deck of cards

12 of them are face cards   3 cards *4 suits =12

P (face card) = 12/52 = 3/13

Answer:1/3 decimal form: 0.333 repeating percent: 3.33%

Answer:

18.00 dollars

Step-by-step explanation:

message me if you need help. Or this was not the answer you were looking for.

The value of Pascale's savings account at the end of the fifth year, with a 7.5% interest rate compounded annually and an additional $500 deposited each year, is approximately $3,122.00.

To calculate the value of Pascale's account at the end of the fifth year, we must use the compound interest formula which is A = P (1 + r)^t, where:

However, since Pascale deposits an additional $500 at the beginning of each year, the calculation is more complex than a single application of the formula. Our calculation should reflect the compound interest earned on each individual $500 deposit, not just the initial deposit.

Let's calculate the value at the end of year 5 step by step, adding $500 at the beginning of each year:

Therefore, the value of the account at the end of the fifth year is approximately $3,122.00.

Answer:

Universal set ( U ) = Set of prime numbers

Step-by-step explanation:

Solution:-

- All even numbers are numbers that are divisible by 2 or have at-least an LCM of 2 associated with that number.

- All prime numbers are divisible by 1 and the number itself. Which 2 which is divisible by 1 and itself is a prime number and an even number.

- Considering only positive integers.

- Carrie is looking for a set of even numbers within the set of prime number.

- As stated above, the only integer, 2, is common to both prime number set and even number set.

- Hence, universal set ( U ) should be prime numbers.

- Universal set ( U ) = Set of prime numbers.

Answer:

c. prime numbers

Step-by-step explanation:

edg 2020

Answer:

24.

Step-by-step explanation:

The is the number of permutations of 3 digits from 4

= 4P3

= 4! / (4- 3)!

= 4 *3 *2 *1 / 1!

= 24/1

= 24.

S=wl

0.24=wl

it can be w=0,6 and l=0,4 or w=0,4 and l=0,6

Answer:

Since you provided no graphs, I just graphed y=(x+3)(x+3). I hope this helps.

Final answer:

The graph defined by the function y = (x+3)(x+3) is a parabola opening upwards with its vertex at (-3, 0), represented by a U-shaped curve on the coordinate plane.

Explanation:

The function given by y = (x+3)(x+3) represents a quadratic equation, which can be expanded to y = x^2 + 6x + 9. This is a parabola that opens upwards because the coefficient of the x^2 term is positive. The graph of this function will have its vertex at the point (-3, 0), which is obtained by setting the inside of the parentheses to zero. To visualize this function, you would plot a series of points by choosing different values for x, calculate the corresponding y values, and then plot these points on a coordinate plane. Connecting these points will reveal the U-shaped curve typical for a quadratic function.

Answer:

The correct option is;

A. The mean speed and the range of the speeds of the motorists decreased

Step-by-step explanation:

Here we have the speeds given as

                  Before Sign Installation

Speed                                                   Frequency

20                                                             1

24                                                             1

25                                                             4

30                                                             2

35                                                             2

38                                                             1

40                                                             1

∑ 212                                                        12

Mean = 17.67

Median (25 + 30)/2 = 27.5

Range  = 40 - 20 = 20

                     After  Sign Installation

Speed                                                   Frequency

20                                                             1

22                                                             1

25                                                             4

28                                                             1

30                                                             3

35                                                             2

∑ 160                                                        12

Mean = 160/12 = 13.33

Median = (25+28)/2 = 26.5

Range  = 35 - 20 = 15.

Therefore, the mean speed and the range of the speeds of the motorists decreased