2 fifths+3 fifths+=5fifths+1fifth=1 whole 1 fifth

1. In this context, the other variables that might be confounded with a mother's consumption of diet soda during pregnancy are the health of the mother during gestation period.

2. A sentences which can best describes a completely randomized design for this experiment on "Diet soda and pregnancy" is "adverse effect of intake of soda drinks on pregnancy".

Basically, completely randomized design is a type of experimental design in which the experimental units are assigned to the various treatments at random. When the experimental units are thought to be "uniform," that is, when there is no uncontrolled factor in the experiment, it is used.

It is a design where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment. For the CRD, any difference among experimental units receiving the same treatment is considered as experimental error.

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Answer:

1/8, 2/5 , 1/2, 3/4

Step-by-step explanation:

1/2= 0.5

1/8= 0.1

3/4= 0.8

2/5= 0.4

just arrange them in the order from smallest to largest......

Answer:

⅛ < ⅖ <  ½ < ¾

Step-by-step explanation:

First, rewrite the fractions so that they all have the same denominator.

The new denominator should be the lowest common multiple of the original denominators.

The L.C.M. of 2, 8, 4, and 5 is 40.

When multiplying the denominator to 40, make sure you multiply the numerator with the same value you use to multiply the denominator.

1/2 = 1x20 / 2 x 20 = 20/40

1/8 = 1x5 / 8x5 = 5/40

3/4 = 3x10 / 4x10 = 30/40

2/5 = 2x8 / 5x8 = 16/40

When all the denominators are the same, we can compare the numerator. The greater the numerator, the greater the fraction is.

Between 20, 5, 30, and 16, the smallest is 5, then 16, 20 and greatest is 30.

Since ascending order means listing them out from smallest to greatest, the order should be:

⅛ < ⅖ <  ½ < ¾

Answer:

The function f(t) = 0.0037(t + 14.979)^2 can be rewritten as f(t) = 0.0037(t^2 + 29.958t + 222.126). This is a quadratic function that has been stretched vertically by a factor of 0.0037 and shifted 14.979 units to the right and 222.126 units up.

To sketch the graph of this function, we can start with the graph of f(t) = t^2, which is a parabola that opens upwards. The transformation of this function stretches the parabola vertically by a factor of 0.0037, so its maximum and minimum values will be much smaller. The shift of 14.979 units to the right means that the vertex of the parabola will be located 14.979 units to the right of the vertex of the original parabola. The shift of 222.126 units up means that the minimum value of the function will be located 222.126 units above the minimum value of the original parabola.

On the interval 0 ≤ t ≤ 19, the graph of the function will be a parabola that stretches vertically by a factor of 0.0037 and is shifted 14.979 units to the right and 222.126 units up from the graph of f(t) = t^2.

To predict the mortgage debt in the year 2014, we can substitute t = 24 into the function f(t) = 0.0037(t + 14.979)^2. This gives us f(24) = 0.0037(24 + 14.979)^2 = 0.0037(39.979)^2 = 0.0037 * 1595.7441 = 5.90834 trillion dollars. This is the predicted mortgage debt in the year 2014.

Answer:

I don't see an attatchment :(     can u tell me the problem?

Step-by-step explanation:

Answer:

(0,0), (1,5), (2,10)

Step-by-step explanation:

Hi there,

In order to plot this linear graph, you should realize that this line will go through the origin (0,0) because there is no "b" from y = mx + b.

Since the slope is 5, we plot the points using the rise over run method. In this case, it will be rise 5, run 1. While you can plot many more points, there is space for only these three points: (0,0), (1,5), (2,10).

Hope this explanation helps. Cheers.

The shadow length is increasing at a rate of approximately 3.16m/s when Regina is 7m away from the point under the light.

A streetlight hangs 5 meters above the ground.

Regina, who is 1.5 meters tall, walks away from the point under the light at a rate of 2 meters per second.

The objective is to find the rate at which her shadow is lengthening when she is 7 meters away from the point under the light.

Let AB be the pole of the light and C be the shadow of Regina and CB be her shadow. We have,

AB = 5m and AC = 1.5m

Also, it is given that Regina is moving away from the point at a rate of 2m/s.

Now, it is required to find the rate at which CB is increasing, i.e., to find d(CB)/dt when Regina is 7m away from the pole.

From the figure, we can observe that:  AB/BC = AC/CB

By differentiating w.r.t time t on both sides, we have:

d(AB)/dt / BC + AB / d(BC)/dt = - d(AC)/dt / CB - AC / d(CB)/dt

Now, we substitute the given values into the above equation, we get:

d(AB)/dt = 0, AB = 5m

BC = 7m

AC = 1.5m

d(AC)/dt = -2m/s

Substituting these values, we get;

0/7 + 5 / d(BC)/dt = -(-2) / CB - 1.5 / d(CB)/dt

On solving, we get;

d(CB)/dt = 60 / 19 ≈ 3.16m/s

Therefore, the shadow length is increasing at a rate of approximately 3.16m/s when Regina is 7m away from the point under the light.

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the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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Answer:

Step-by-step explanation:

Given the height of the rocket modelled by the equation;

y=-16x^2+152x+83

The rocket reaches its maximum height when the velocity of the rocket is zero.

Since velocity is the change in displacement with respect to time;

velocity v = dy/dx

dy/dx = -32x + 152

at dy/dx = 0

-32x + 152 = 0

-32x = -152

x = -152/-32

x = 4.75s

To get maximum height reached by the ball, we will substitute x = 4.75 into the modeled function as shown;

y(4.75) = -16(4.75)^2+152(4.75)+83

y(4.75) = -361+722+83

y(4.75) = 444m

Hence the maximum height reached by the ball is 444m

To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.

The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.

Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.

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The point that lies on the circle is represented by the equation (x−3)² + (y+4)² = 6² is (-3,-4).

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h, k) coordinate. Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The sole point that lies on the circle when a circle is graphed with the equation on the graph and all the specified points are graphed is (-3,-4).

Consequently, the equation (x-3)² + (y+4)² = 6² represents the point on the circle (-3,-4).

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Answer:

a) 2a + 3c = $44.50

     a + 2c + $25.50

b) $19

Step-by-step explanation:

Simultaneous equations. A = adult. C = children

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Now solve this using the method of elimination:

2a + 3c = $44.50 (EQUATION 1)

a + 2c = $25.50 (EQUATION 2)

Multiply equation 2 by 2 so that both equations have the same a coefficient.

2a + 4c = $51 (NEW EQUATION 2)

Now subtract equation 1 from equation 2:

2a - 2a + 4c - 3c = $51 - $44.50 (2a cancels out)

c = $6.50

Now substitute c into one of the equation, in this case, I'm using original equation 2.

a + 2($6.50) = $25.50

a + $13 = $25.50

a = $12.50

Total cost of one adult and child = $6.50 + $12.50

                                                       = $19

Answer:

option d

Step-by-step explanation:

hope this helps

Answer: 50% is the answer

Answer: 50%!

Step-by-step explanation:

The set of equations that corresponds to the specified function are

y = 5 - x and 5 - x = 9x².

What is linear equation in two variables?

If an equation is expressed as ax + by + c=0, where a, b, and c are all real integers and a and b, the coefficients of x and y, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

The given equation is :

\(y=9x^{2}\) equation 1.

\(x+y=5\) equation 2.

From equation 2.

\(x+y=5\\y=5-x\)

substituting into 1 equation.

\(5-x=9x^{2}\)

The system of equations that is equivalent to the provided function is shown by the resulting equation, which is y = 5 - x and \(5-x=9x^{2}\)

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Answer: True

Step-by-step explanation:

The most relevant answer to this question is researcher conducting a qualitative study knows that saturation of information has occurred when data collected confirms theoretical models.

In qualitative research, data saturation refers to when the collection of new data no longer leads to additional ideas or themes.

In other words, saturation occurs when data has been thoroughly explored and little or no new information or new patterns emerge.

so, the researcher can be sure that he or she has collected enough data to answer the research question, and collecting more data is unlikely for new insights.

Therefore, Using the data provided, we can calculate:  

x = (38.1 + 38.4 + 38.3 + 38.2 + 38.2 + 37.9 + 38.7 + 38.6 + 38.0 + 38.2) / 10 = 38.25

In a t distribution table or calculator, find the t value with 9 (n-1) degrees of freedom and 95% confidence intervals. This is approximately 2.262.

Substituting these values ​​into the formula gives:

therefore, the most relevant answer to this is data collected confirms theoretical models.

This means that the researcher has collected enough data to confirm or disprove their original theoretical models, and collecting more data is unlikely to change those models. 

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Let x be the cost of the bench. According to the question, the garden table costs $92 more than the bench.

Therefore, the cost of the garden table would be x + $92.

We know that the combined cost of the garden table and bench is $992.

That means we can write the following equation:x + (x + $92) = $992

Simplifying the above expression we get,2x + $92 = $992

Subtracting $92 from both sides of the equation:

2x = $900

Dividing both sides by 2:x = $450

Therefore, the cost of the bench is $450.

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Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.

What is derivative?

The derivative provides information about the slope or steepness of a curve at various points and can be used to find critical points, determine the concavity of a function, and solve optimization problems. The derivative is denoted using various notations, such as f'(x), dy/dx, or df/dx, depending on the context and notation conventions.

To find the slope of the tangent line to the polar curve r = 5 + 2θ at the point specified by θ = π/3, we need to determine the derivative of the polar curve with respect to θ and evaluate it at θ = π/3.

The polar curve r = 5 + 2θ can be expressed in Cartesian coordinates as x = (5 + 2θ) * cos(θ) and y = (5 + 2θ) * sin(θ).

Now, let's find the derivative of y with respect to x using the chain rule:

dy/dx = (dy/dθ) / (dx/dθ)

To find dy/dθ and dx/dθ, we differentiate the expressions for y and x with respect to θ:

dy/dθ = d/dθ [(5 + 2θ) * sin(θ)] = (2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)

dx/dθ = d/dθ [(5 + 2θ) * cos(θ)] = (2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)

Now, we can calculate the derivative of y with respect to x:

dy/dx = [(2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)] / [(2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)]

To find the slope of the tangent line at θ = π/3, substitute θ = π/3 into the expression for dy/dx:

dy/dx = [(2 + 2(π/3)) * sin(π/3) + (5 + 2(π/3)) * cos(π/3)] / [(2 + 2(π/3)) * cos(π/3) - (5 + 2(π/3)) * sin(π/3)]

Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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The number 1.368 is approximately 2 more than its cube.

To find a real number that is exactly 2 more than its cube, we can set up the equation:

x = x^3 + 2

Rearranging the equation, we have:

x^3 - x + 2 = 0

To find the solution to this equation, we can use numerical methods such as Newton's method or trial and error. Applying trial and error, we can find one such value accurate to three decimal places:

x ≈ 1.368

If we substitute this value into the equation x = x^3 + 2, we get:

1.368 ≈ (1.368)^3 + 2

1.368 ≈ 2.001

The number 1.368 is approximately 2 more than its cube.

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The final answer is `f(2) - f(a)` knots.

Given data: t is measured in hours and f'(t) is measured in knots;

1 knot = 1 nautical mile/hour

The integral `integrate d from a to 2 f^ * (t)` can be solved using the integration by substitution method.

So let, `u = f(t)`.

Therefore, `du/dt = f'(t)`.

Differentiating both sides with respect to t, we get `du = f'(t) dt`.

Hence, `integrate d from a to 2 f^ * (t)` becomes `integrate du/dt * dt from a to 2 f(t)`.

Substituting u and du, we get `integrate du from f(a) to f(2)`.

Integrating with respect to u, we get `u` from `f(a)` to `f(2)`.

Substituting back u = f(t), we get the final integral as follows:

`f(2) - f(a)` knots which is equal to the distance covered in nautical miles from `t=a` to `t=2`.

Therefore, the final answer is `f(2) - f(a)` knots.

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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11)

The formula for calculating slope is expressed as

slope = (y2 - y1)/(x2 - x1)

From the information given,

x1 = 5, y1 = - 2

x2 = 6, y2= - 5

Slope = (- 5 - - 2)/(6 - 5) = (- 5 + 2)/1

Slope = - 3

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

y - y1 = m(x - x1)

where

m = slope = - 3

The equation of the line is

y - - 2 = - 3(x - 5)

y + 2 = - 3(x - 5)

When x = 0,

y + 2 = - 3(0 - 5) = - 3 * - 5 = 15

y = 15 - 2

y = 13

When x = 1,

y + 2 = - 3(1 - 5) = - 3 * - 4 = 12

y = 12 - 2

y = 10

Thus, two other points are

(0, 13)

(1, 10)

The radius of the cylinder is approximately 10.61 yards.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The volume of a cylinder is given by the formula:

V = πr²h

where V is the volume, r is the radius, h is the height, and π is approximately 3.14.

We are given that the volume of the cylinder is 6,458.98 cubic yards and the height is 17 yards.

r² = V / (πh)

r² = 6,458.98 / (3.14 × 17)

r² = 112.58

r = √112.58

r = 10.61

Therefore, the radius of the cylinder is approximately 10.61 yards.

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Answer:

r = -1

Step-by-step explanation:

This is the answer because:

1) You can take the root of both sides and solve

2) You can also isolate the variable and solve for it

1. r9 + 1 = 0, divide 9 and 0 first. 9 x 0 = 0

2. r + 1 = 0, subtract 0 and 1. 0 - 1 = -1

Hope this helps!

The average daily snowfall estimate for Wyoming's greatest 7-day snowfall is significantly different from the average daily snowfall estimate for South Dakota's greatest 7-day snowfall.

Wyoming and South Dakota are both known for their cold winters and heavy snowfall. However, the average daily snowfall estimate for Wyoming's greatest 7-day snowfall is likely to differ from that of South Dakota. Several factors contribute to this difference.

Firstly, Wyoming is home to the Rocky Mountains, which are known for their high elevation and heavy snowfall. This region experiences more frequent and intense winter storms, leading to higher snowfall amounts. South Dakota, on the other hand, has a relatively flatter terrain compared to Wyoming, resulting in less snow accumulation.

Secondly, geographical location plays a role. Wyoming is located further west and is influenced by Pacific weather systems, which can bring moisture-laden storms and heavy snowfall. South Dakota, being more inland and farther away from major moisture sources, may receive less precipitation overall.

Lastly, climate patterns can vary between the two states. Factors such as proximity to large bodies of water, prevailing wind patterns, and local topography can influence snowfall amounts. These variations can lead to differences in the average daily snowfall estimate for the greatest 7-day snowfall in Wyoming compared to South Dakota.

In conclusion, while both Wyoming and South Dakota experience significant snowfall, the average daily snowfall estimate for Wyoming's greatest 7-day snowfall is expected to be different from that of South Dakota. Factors such as elevation, geographical location, and climate patterns contribute to these differences in snowfall amounts between the two states.

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Answer:

-5x-2=11

+2

-5x=9

÷-5

x=1.8

Step-by-step explanation:

Answer:

x = -2.6

or x=-2 and 3/5

Step-by-step explanation:

Simplifying

11 = -5x + -2

Reorder the terms:

11 = -2 + -5x

Solving

11 = -2 + -5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5x' to each side of the equation.

11 + 5x = -2 + -5x + 5x

Combine like terms: -5x + 5x = 0

11 + 5x = -2 + 0

11 + 5x = -2

Add '-11' to each side of the equation.

11 + -11 + 5x = -2 + -11

Combine like terms: 11 + -11 = 0

0 + 5x = -2 + -11

5x = -2 + -11

Combine like terms: -2 + -11 = -13

5x = -13

Divide each side by '5'.

x = -2.6

Simplifying

x = -2.6

Answer:

14y-13y² is the answer. sorry for dirty handwriting

Answer:

The answer is 8.

Step-by-step explanation:

If you multiply each of the measurments by 1.5 they equal the measurments on the larger trapazoid. I can't see the full question but im assuming It's asking for the measurment (2x-16). So 12 divided by 1.5 equals 8. And to get eight you replace x with 4. Hope I helped. :)

\(\\ \sf\longmapsto \dfrac{2x-16}{12}=\dfrac{12}{18}\)

\(\\ \sf\longmapsto \dfrac{x-8}{6}=\dfrac{2}{3}\)

\(\\ \sf\longmapsto 3(x-8)=12\)

\(\\ \sf\longmapsto 3x-24=12\)

\(\\ \sf\longmapsto 3x=36\)

\(\\ \sf\longmapsto x=12\)

Answer:

37162.09

Step-by-step explanation:

Answer:

75 students

Step-by-step explanation:

divide by .4