Write these fractions in their simplest forms:
a)
2
10
b)
9
24

Answer:

Hi! Maria is 15 years old, Selena - 17 and Sofía - 12

Answer:

6/5

Step-by-step explanation:

We can use the slope formula to find the slope

Slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\), where the x and y values are derived from know points

The points chosen can vary as there are many given but the ones I chose were (6,9) and (11,15)

Now that we chose two points we want to define the variable ( the variables are x2, x1, y2 and y1 )

Define Variables

x1 = x value of first point which would be 6

x2 = x value of second point which would be 11

y1 = y value of first point which would be 9

y2 = y value of second point which would be 15

Now that we have defined our variables the next step is to plug in the variables into the slope formula

slope formula: \(m = \frac{y_2-y_1}{x_2-x_1}\)

y2 = 15, y1 = 9, x2 = 11 and x1 = 6

* plug in values *

\(m=\frac{15-9}{11-6}\)

subtract top numbers

\(m=\frac{6}{11-6}\)

subtract bottom numbers

\(m = \frac{6}{5}\)

there is no simplification needed meaning that the slope in simplest form is 6/5

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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The alternative hypothesis is stated as Ha: μ1 - μ2 ≠ 0, for the given sample mean 7.24 minutes and standard deviation of 1.88 minutes.

Based on the given information, the auditor wants to determine whether the population mean call duration is different for the call center in Auburn compared to the call center in Lewiston. The auditor uses recordings from randomly sampled calls for this analysis.

The sample mean of the 125 randomly selected calls to the Auburn call center is 7.24 minutes, with a sample standard deviation of 1.88 minutes. The sample mean of the 125 randomly selected calls to the Lewiston call center is 7.93 minutes, with a sample standard deviation of 2.13 minutes.

To test the hypothesis, the auditor assumes that the population standard deviations of the two groups are equal. The alternative hypothesis is stated as Ha: μ1 - μ2 ≠ 0.

Please note that the significance level (α) is not mentioned in the question.

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To be able to determine how many times we have to travel around the circumference of the Earth to equal the distance from the Earth to the Moon, simply divide the distance from the Moon to the Earth by the circumference of the earth.

This means we have to travel around the circumference of Earth 9.06 times to equal the distance from the Earth to the Moon.

Answer:

16.8 pounds

Step-by-step explanation:

Given the following :

Body fat percentage = 12.1%

Weight = 139 pounds

How may pounds of the person's weight is made up of fat:

That is 12.1% of the person's entire body weight

Pound of person's weight composed of fat:

12.1% of 139

(12.1 / 100) × 139

0.121 × 139

= 16.819 pounds.

= 16.8 pounds

Answer:

No, it is not possible.

Step-by-step explanation:

The Triangle Sum Theorem states that all the interior angles of a triangle will always add up to 180°, but 150 + 20 + 20 = 190.

Answer:

False

Step-by-step explanation:

For example, if I have -12- (-10) it equals-2, but if you have -12 + 13= 1

Answer:

False

Step-by-step explanation:

I Think

Answer: The ratio would be 73.6

Answer:

okay so IM not 100 percent sure but I think its 64 = 92

Answer:

slope is -1/12

Step-by-step explanation:

slope =y2 - y1 / x2-x1

The approximate values of y₁, y₂, y₃, and y₄ using Euler's method with a step size of 0.5 are:

y₁ ≈ -2.5

y₂ ≈ -2.21875

y₃ ≈ 2.828125

y₄ ≈ -3.36767578125

We have,

To use Euler's method with a step size of 0.5 to approximate the values of y₁, y₂, y₃, and y₄ of the given initial-value problem, we'll use the following iteration formula:

yᵢ₊₁ = yᵢ + h f(xᵢ, yᵢ)

where yᵢ is the approximate value of y at the i-th step, xᵢ is the value of x at the i-th step (in this case, xᵢ = i * h), h is the step size (0.5 in this case), and f(x, y) is the derivative function.

Given the initial condition y(0) = -2, we start with y₀ = -2 and calculate the subsequent values of y using the iteration formula.

Let's calculate the values of y₁, y₂, y₃, and y₄ using Euler's method:

Step 1:

x₀ = 0

y₀ = -2

y₁ = y₀ + h f(x₀, y₀)

= -2 + 0.5 f(0, -2)

To find f(0, -2), we substitute x = 0 and y = -2 into the derivative function y' = -1 - 5x²y:

f(0, -2) = -1 - 5 (0)² (-2)

= -1 + 0

= -1

y₁ = -2 + 0.5 (-1)

= -2 - 0.5

= -2.5

Therefore, y₁ = -2.5.

Step 2:

x₁ = 0.5

y₁ = -2.5

y₂ = y₁ + h f(x₁, y₁)

= -2.5 + 0.5 f(0.5, -2.5)

To find f(0.5, -2.5), we substitute x = 0.5 and y = -2.5 into the derivative function y' = -1 - 5x²y:

f(0.5, -2.5) = -1 - 5 (0.5)² (-2.5)

= -1 - 5 * 0.25 * (-2.5)

= -1 - 5 * 0.25 * (-2.5)

= -1 - 5 * (-0.3125)

= -1 + 1.5625

= 0.5625

y₂ = -2.5 + 0.5 * (0.5625)

= -2.5 + 0.28125

= -2.21875

Therefore, y₂ = -2.21875.

Step 3:

x₂ = 1.0

y₂ = -2.21875

y₃ = y₂ + h * f(x₂, y₂)

= -2.21875 + 0.5 * f(1.0, -2.21875)

To find f(1.0, -2.21875), we substitute x = 1.0 and y = -2.21875 into the derivative function y' = -1 - 5x^2y:

f(1.0, -2.21875) = -1 - 5 * (1.0)² * (-2.21875)

= -1 - 5 * 1.0 * (-2.21875)

= -1 - 5 * (-2.21875)

= -1 + 11.09375

= 10.09375

y₃ = -2.21875 + 0.5 * (10.09375)

= -2.21875 + 5.046875

= 2.828125

Therefore, y₃ = 2.828125.

Step 4:

x₃ = 1.5

y₃ = 2.828125

y₄ = y₃ + h * f(x₃, y₃)

= 2.828125 + 0.5 * f(1.5, 2.828125)

To find f(1.5, 2.828125), we substitute x = 1.5 and y = 2.828125 into the derivative function y' = -1 - 5x^2y:

f(1.5, 2.828125) = -1 - 5 * (1.5)² * (2.828125)

= -1 - 5 * 2.25 * 2.828125

= -1 - 11.3916015625

= -12.3916015625

y₄ = 2.828125 + 0.5 * (-12.3916015625)

= 2.828125 - 6.19580078125

= -3.36767578125

Therefore, y₄ = -3.36767578125.

Thus,

The approximate values of y₁, y₂, y₃, and y₄ using Euler's method with a step size of 0.5 are:

y₁ ≈ -2.5

y₂ ≈ -2.21875

y₃ ≈ 2.828125

y₄ ≈ -3.36767578125

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Given that a circle with radius 20 has a corresponding angle of 305°.

To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.

Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`

Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192

Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.

The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`

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Answer:

b. 98

Step-by-step explanation:

brainliest pls

Answer:

d

Step-by-step explanation:

srry im doing a thing

where i have to do 30 Q to get $300

Answer:

The mass of 3.5 moles of Ca (Sodium)  is 140 g to two significant figures.

The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .

We need to Know about Hypothesis testing and independent t test to answer this-

Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.

An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.

We can find the difference caffeine content following these steps -

1)H0=Null hypothesis=tea and coffee has same caffeine level

HA=tea and coffee has different caffeine level

2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.

The t value obtained should be then performed under hypothesis testing.

3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.

Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.

Hence null hypothesis will be rejected.

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answer:

53

explanation

Line segment AB is the same length as line segment CD.

A line segment is defined as the part of a line that is divided in parts using two or more end points for easy observation.

From the given diagram, the line segment AB is the same as the line segment CD because the line segment CD was shifted a bit from the point of origin of line segment AB.

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The next term would be 3 then 1 in the sequence 243, 81, 27, 9,... by the term of sequence and series through mathematical sequencing.

A grouping of numbers in a kind of a specific order is known as a sequence. On the other hand, a series can also be described as the accumulation of a kind of a sequence’s constituent parts.

Basically, the sequence proceeds with a dividing term of 3. The sequence will go on with the square root of the previous number. Basically, from backward, the sequence is an exponential multiple of 3.

Mathematical sequence and series formulas pertain to several kinds of sequences and series. A series is the accumulation of elements in a sequence, which is a group of arranged elements that follow a pattern.

The formulas for the nth term and the sum are typically included in the sequence and series formulas.

A series is made up of all the elements in a sequence, while a sequence is a certain arrangement of elements in a specific order.

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Answer:

Step-by-step explanation:

-38 = 2x - 10 becomes -28 = 2x, NOT -48 = 2x.

We need to decide whether the given equations are always or never true for values of x .The given equations are ,

solve out for x,

\(\longrightarrow x -x =12+1\\ \)

\(\longrightarrow 0 =13\\ \)

This can never be true. Hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow x -x =\dfrac{3}{4}+\dfrac{3}{4}\\ \)

\(\longrightarrow 0=\dfrac{3}{2}\)

This can never be true. hence the equation is never true for any values of x.

solve out for x,

\(\longrightarrow 4x +12=8x+12-4x\\\)

\(\longrightarrow 4x -8x +4x =12-12\\\)

\(\longrightarrow 0=0\)

hence this equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x -x -x =8+8\\ \)

\(\longrightarrow 0=0 \)

hence the equation is true for all values of x.

solve out for x,

\(\longrightarrow 2x +10+3x =5x-25\\ \)

\(\longrightarrow 5x -5x =-25-10\\\)

\(\longrightarrow 0 =-35\)

This can never be true. hence the equation is never true for any values of x.

and we are done!

The distance on map exists 32 cm and actual area exists 37.5 km².

Given: Scale of the map exists at 1:250000.

(a) Distance between two cities = 80 km

= 80000 m

= 8000000 cm

Distance on map = 8000000 \(*\) 1/ 250000

= 32 cm

(b) Area of map = 6 cm²

Actual area = \(6(250000)^2\) cm²

\(= 6 * 625 * 10^8\) cm²

\(= 3750 * 10^8/ 10^{10}\)

= 37.5 km²

Therefore, the distance on map exists 32 cm and actual area exists 37.5 km².

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Answer:

The correct answer is 1/2×8×3.

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Given the following function:

f(x) = 3x - 3

Let's determine the value at f(-3),

This means that we will be replacing all x variables of f(x) by -3.

We get,

f(x) = 3x - 3

f(-3) = 3(-3) - 3

= -9 - 3

f(-3) = -12

Therefore, f(-3) = -12

Answer:

37.5

Step-by-step explanation:

Answer:

6 is 16% of the number 37.5

Step-by-step explanation:

We have, 16% × x = 6

or, 16/100 × x = 6

Multiplying both sides by 100 and dividing both sides by 16,

we have x = 6 × 100/16

x = 37.5

Answer:

A

Step-by-step explanation:

i stands for square root of negative 1. If you multiple i and square root of 23 you will end up with the original

Answer:

y= -5/3 + 5

Step-by-step explanation:

5x-3y=15 first move the 5x to the right side of the equation which becomes 3y= -5x +15 and then divide the whole equation by 3 because u want y to be on its own so then the answer is y= -5/3 + 5

The number of toffee cookies Sarah baked is:

4x = 4(17) = 68

If 2/7 of the cookies are chocolate cookies then the number of chocolate cookies Sarah baked is:

2/7 x 420 = 120

If 35% of the cookies are raisin cookies then the number of raisin cookies Sarah baked is:

35/100 x 420 = 147

Let the number of toffee cookies be 4x and the number of plain cookies be 5x x is a constant.

The total number of cookies is the sum of the number of chocolate raisin toffee and plain cookies:

Total number of cookies = Number of chocolate cookies + Number of raisin cookies + Number of toffee cookies + Number of plain cookies

Substituting the values we know:

420 = 120 + 147 + 4x + 5x

Simplifying and solving for x:

420 = 267 + 9x

9x = 153

x = 17

The number of toffee cookies Sarah baked is:

4x = 4(17) = 68

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(y2-y1)/(x2-x1)

19-10=9

6-3=3

9/3=3

slope: 3

y-int: 1

y=3x+1

The postulate that can be used to prove that triangles ABC and DEF are similar triangles is A. AA Similarity Postulate.

According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell. As just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.

We have, triangles ABC and DEF with:

two pairs of congruent angles - ∠B ≅ ∠E and ∠C ≅ ∠F.

Therefore, the postulate that has been used to prove that the triangles ABC and DEF are similar triangles is AA Similarity Postulate.

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The complete question is:

Which theorem or postulate proves that â–³ABC and â–³DEF are similar?Select from the drop-down menu to correctly complete the statement. The two triangles are similar by the ________. A. AA Similarity Postulate B. SSS Similarity Theorem C. SAS Similarity Theorem