Solve the following quadratic equation for all values of xx in simplest form. 16+2x²=30​

Answer:

x=  -16/19

Step-by-step explanation:

x−14x+4+12=6x+32

−13x+16=6x+32

16=6x+32+13x

16=19x+32

16−32=19x

−16=19x

-16/19=x

a. The scatter plot of the data shows the incidence of diagnosed cases of celiac disease since 1950.

b. A linear regression model would best fit this data.

c. The equation for the curve of best fit is y = 0.603x + 8.821, where y represents the number of diagnosed cases of celiac disease (per 1000) and x represents the years since 1950.

d. Using the regression model, approximately 10.835 cases of celiac disease may be diagnosed in 2020.

a. To create a scatter plot of the data, we plot the number of diagnosed cases of celiac disease (y-axis) against the years since 1950 (x-axis). Each data point represents a pair of (x, y) values. For example, the first data point would be (0, 10), the second (8, 11), and so on.

b. In this case, a linear regression model would best fit the data because the scatter plot suggests a roughly linear relationship between the years since 1950 and the number of diagnosed cases of celiac disease.

c. To find the equation for the curve of best fit, we can use linear regression. We calculate the slope and intercept of the line that minimizes the sum of squared distances between the data points and the line. The equation of a line is y = mx + b, where m is the slope and b is the intercept. By performing linear regression on the given data points, we obtain the equation y = 0.603x + 8.821.

d. To estimate the number of diagnosed cases of celiac disease in 2020, we substitute x = 70 (since 2020 is 70 years since 1950) into the equation y = 0.603x + 8.821. Solving the equation, we find that y is approximately equal to 10.835. Therefore, using the regression model, around 10.835 cases of celiac disease may be diagnosed in 2020.

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Answer:

1 min : 12 min

Step-by-step explanation:

To simplify the given ratio, convert both to the same unit of time.

1 hour = 60 minutes

3 hours = 3 x 60 minutes

             = 180 minutes

So that,

15 min : 3 hours = 15 min : 180 min

divide through by 15 to have;

15 min : 180 min = 1 min : 12 min

Thus the simplified form of the number give is 1 min : 12 min.

Answer:

Group A, IQR = 700

GROUP B, IQR =.450

Group A's IQR is greater

The values in the middle 50%.of Group A are more spread out Than those of Group B.

Step-by-step explanation:

Data for.each group :

The IQR = Q3 - Q1

From the boxplot :

Group A:

Q1 = 1100 ; Q3 = 1800

IQR = 1800 - 1100 = 700

Group B:

Q1 = 1400; Q3 = 1850

IQR = 1850 - 1400 = 450

Greater IQR = Group A

The values in the middle 50%.of Group A are more spread out Than those of Group B.

Answer:

x =5 & y =9

Step-by-step explanation:

let anumber x & y

-(x + 2y = 23)

4x + 2y = 38

-x -2y = -23

4x + 2y = 38

-x + 4x + 2y - 2y = 38-23

3x+0 = 15

3x /3 = 15/3

x = 5 then

5 + 2y = 23

2y = 23-5

2y/2 = 18/2

y = 9

therefore y =18 and x = 5

Step-by-step explanation:

[tex]16 {x}^{2} - 25 = 0 \\ 16 {x}^{2} = 0 + 25 \\ 16 {x}^{2} = 25 \\ {x}^{2} = \frac{25}{16} \\ x = \sqrt{ \frac{25}{16} } \\ = 1.25 \: or \frac{5}{4} \: or1 \frac{1}{4} [/tex]

Do note that this question might have two answers as Square roots will actually give you a positive and negative solution. Clarify with your teacher about this.

Answer:

x=0.09765625 or rounded up as 0.1

Step-by-step explanation:

first you have to add 25 to the 0 and subtract it from the sid it is on. making it look like this

16x²=25

256x=25

now divide both sides by 256 and you get

x=0.09765625 or rounded up as 0.1

The 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).

The 95% confidence interval (CI) for the mean temperature in the crown of the balloon is calculated as follows. We first assume that the population distribution is normal with a standard deviation (SD) of σ = 6°C as per the given data. We will then use the z-distribution to calculate the required confidence interval.

The formula for calculating the 95% confidence interval is given by

CI (mean) = x ± z × (σ/√n)

Where 'x' is the mean, 'z' is the z-score associated with the 95% CI, 'σ' is the standard deviation, and 'n' is the number of samples taken.

For the given data the confidence interval is calculated as:

CI (Mean) = 97 ± 1.96 × (6/√59)

CI (Mean) = 97 ± 1.22

Therefore, the 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).

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Answer:

100°= angle b(VERTICAL OPPOSITE ANGLE)

100°+x°=180°[co interior angle]

x=180°-100°

x=80°

The Measure for angle x is 80 degree.

When two straight lines cross, they generate a pair of non-adjacent angles known as vertical angles. In the corners of the "X" created by two straight lines, or to put it another way, vertical angles are situated opposite one another. Due to their position opposite one another, they are also known as vertically opposite angles.

Given:

<CBD = 100 degree.

So, <ABF = <CBD (Vertical Opposite Angle)

<CBD = 100 degree.

Now, <ABF + <BFE = 180 (Angle on same side of Transversal)

<ABF + 100 = 180

<ABF = 180-100

x= 80 degree.

Hence, the measure for x is 80 degree.

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In discrete mathematics, the expression "L(C) = L(R) ∩ L(S)" means that the language generated by the grammar or automaton represented by C is equal to the intersection of the languages generated by the grammars or automata represented by R and S.

The term "L(C)" refers to the language generated by C, which represents the set of all valid strings or sequences that can be produced by the grammar or automaton C. Similarly, "L(R)" and "L(S)" represent the languages generated by R and S, respectively.

The intersection (∩) symbol signifies the common elements or strings that are present in both L(R) and L(S). In other words, it represents the set of strings that can be generated by both R and S.

As for the underline symbol in the expression "L(S)__L(S)", it is commonly used to denote the closure or complement of a language. However, without additional context or information, it is difficult to determine the exact meaning in this case. It could indicate a specific operation or property related to the language L(S), which would require further clarification.

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Answer:

Step-by-step explanation:

w is the width of the rectangle, then the length would be 3w - 1.

A = lw

A = w(3w - 1)

A = 3w² - w

Answer:

Below

Step-by-step explanation:

Every triangle should add up to 180 degrees,

This is a right triangle because it has the square in the corner meaning it is 90 degrees.

39 + 90 = 129

180 - 129 = 51 degrees

A: 51 degrees

C: 90 degrees

Answer:

a. 51 degrees

c. 90 degrees

I think

Answer:

0.82

Step-by-step explanation:

82/100 as a fraction is equal to 0.82

Answer:

∠PSR=90°

m∠QSR= 90-m∠QSP

x= 90-58=32°

Step-by-step explanation:

The actual value of the x is 32°.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Given quadrilateral is a rectangle.

All the four interior angles of a rectangle is perpendicular angle or is 90 degrees.

So measure of ∠PSR = 90°

m ∠QSR + m ∠QSP = 90°

Given that m ∠QSP = 58°

Substituting,

m ∠QSR + 58° = 90°

m ∠QSR = 90° - 58°

              = 32°

So x° = 32°

Hence the error is that both the angles are made to be equal instead of making the sum of the angles equal to 90°.

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Answer:

639.8

7000

2520

525

450

..........

The carrying capacity for the yeast population, estimated from the plot, is 680 cells. The initial relative growth rate can be determined using the first two points of the data.

(a) From the plot of the data, we observe that the yeast population levels off or stabilizes around the value of 680 cells. This value represents the carrying capacity of the yeast population in the laboratory culture. (b) To estimate the initial relative growth rate, we use the first two points of the data: (0, 18) and (2, 39). The relative growth rate can be calculated by dividing the change in the number of yeast cells by the change in time. In this case, the change in cells is 39 - 18 = 21, and the change in time is 2 - 0 = 2. Therefore, the initial relative growth rate is 21 / 2 = 10.5 cells per hour.

(c) An exponential model for the data can be determined by fitting an exponential function to the data points. Using the initial point (0, 18) as the initial condition, we can write the exponential model as P(t) = P₀e^(kt), where P(t) represents the number of yeast cells at time t, P₀ is the initial number of cells, k is the growth rate constant, and e is the base of the natural logarithm. Substituting the given data, we can solve for the values of P₀ and k. The exponential model for these data is P(t) = 17.08e^(0.189t).

(d) A logistic model accounts for the carrying capacity of the yeast population. It is given by the formula P(t) = K / (1 + ae^(-kt)), where K represents the carrying capacity, a is a constant related to the initial condition, and k is the growth rate constant. Using the given data, we can solve for the values of K, a, and k. The logistic model for these data is P(t) = 680 / (1 + 4.126e^(-0.189t)).(e) Using the logistic model obtained in part (d), we can estimate the number of yeast cells after 5 hours by substituting t = 5 into the equation. Thus, P(5) = 680 / (1 + 4.126e^(-0.189(5))). Calculating this expression yields approximately 231 yeast cells after 5 hours.

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The real potential, between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation in two dimensions. The first paragraph provides a summary of the answer, followed by an explanation in the second paragraph.

The real potential, Φ(x, y), is given by the equation Φ(x, y) = C1x + C2y, where C1 and C2 are constants determined by the boundary conditions. In this case, the boundary conditions are Φ(x, x) = 0 V and Φ(x, x + k) = 300 V. By substituting these conditions into the equation, we can solve for the constants C1 and C2 and obtain the real potential Φ(x, y) between the plates.

The complex potential, F(z), is related to the real potential by the equation F(z) = Φ(x, y) + iψ(x, y), where ψ(x, y) is the stream function. The stream function can be determined by solving the equation ∇²ψ = 0, subject to the same boundary conditions as the real potential. Once the stream function is obtained, the complex potential F(z) can be calculated.

In conclusion, the real potential, Φ(x, y), and the complex potential, F(z), between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation and using the appropriate boundary conditions. The real potential is given by Φ(x, y) = C1x + C2y, where the constants C1 and C2 are determined by the given potential values on the plates. The complex potential is obtained by combining the real potential with the stream function, which is determined by solving the Laplace equation for the stream function with the same boundary conditions.

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Answer:

Surface Area varies by object/shape.

Ask your teacher/learning helper for those formulas of surface area

Step-by-step explanation:

Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

The value that is small enough to rule out chance as the most likely explanation is called the p-value. Typical p-values considered as statistically significant are 0.05 or lower.

The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true. If the p-value is below a predetermined significance level (often 0.05), it is considered statistically significant.

This means that the observed data is unlikely to have occurred by chance alone, providing evidence to reject the null hypothesis in favor of an alternative hypothesis. Lower p-values indicate stronger evidence against the null hypothesis.

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Answer:

let ABC be a right-angled triangle, where A is the right angle (left to right)

the original coordinates:

A (-8, 8)

B (-1, 8)

C (-8, 5)

by changing the coordinates from (x, y) to (-y, x)

A (-8, -8)

B (-8, -1)

C (-5, -8)

look attachment

Answer:

B.) Yes; it can be rotated 180° or less and match the original figure.

Step-by-step explanation:

You have to trust me its b I did the quiz on Pearson Conexus. I would show a picture but I'm on pc and don't know how to .

My answer will help.

Anyways, have a great day/night !! <3

Step-by-step explanation:

Does the figure below have rotational symmetry? Explain.

A.)Yes; it can be rotated 360° or less and match the original figure.

B.)Yes; it can be rotated 180° or less and match the original figure.

C.)No; it does not match the original figure after any rotation of 180° or less.

D.)No; it does not match the original figure after any rotation of 360° or less.

Answer:

A) 12 feet or d) 10 feet..

Answer:

3/2

Step-by-step explanation:

The ratio of perimeters of similar polygons is the same as the ratio of the lengths of corresponding sides.

WX/AB = 12/8 = 3/2

Answer:

Dena's answer

14ft^2

Step-by-step explanation:

Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4

From there, you can find the area which is 14.

hope this is correct

Answer:

-2 , -10 & -99

Step-by-step explanation:

1)

⇒ x + 6 = 4

⇒ x = 4-6

⇒ x = (-2)

2)

⇒x - (-4) = -6

⇒ x + 4 = -6

⇒ x = -6-4

⇒ x = -10

3)

⇒2(x-1) = -200

⇒ x - 1 = -200/2

⇒ x - 1 = -100

⇒ x = 1 - 100

⇒ x = (-99)

Answer:

1. x= -2 2. ×= -10 3. x= -99

Step-by-step explanation:

1. x+6 = 4

x = 4-6

x = -2

2. x-(-4) = -6

x+4 = -6

x = -6 - 4

x = -10

3. 2(x-1) = -200

2x - 2 = -200

2x = -200 +2

2x = -198

x = -99

Answer:

Step-by-step explanation:

When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial.  If the remainder is not zero, the remainder is the function vaue for that divisor.

Answer:

x≤21

Step-by-step explanation:

x/3≤7

Multiply both sides by 3

3x/3≤7×3

Simplify

x≤21

Hope this helped!!!

The minimum red blood cell count that can be in the top 26% of counts is approximately 5.37 million cells per microliter. The maximum red blood cell count that can be in the bottom 16% of counts is approximately 4.602 million cells per microliter.

(a) The minimum red blood cell count that can be in the top 26% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.26.

Using the standard normal distribution table or a calculator, we find that the z-score is approximately 0.675.

We can then use the z-score formula to find the corresponding value in the original distribution: minimum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (0.675 * 0.4) = 5.37 million cells per microliter.

(b) The maximum red blood cell count that can be in the bottom 16% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.16.

Using the standard normal distribution table or a calculator, we find that the z-score is approximately -0.994.

Using the z-score formula, we can find the corresponding value in the original distribution: maximum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (-0.994 * 0.4) = 4.602 million cells per microliter.

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Answer:

its c kiddos

Step-by-step explanation:

The required ordered pair for the solution of an equation  [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).

An ordered pair from the options is the solution of the equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] to be determined.

An ordered pair is defined as the coordinates when put into the equation giving the solution of the equation.

While plotting the curve of the given equation on the graph and also plotting the ordered pair on the graph. It is seen that points (2, –3.5), (2, 5.5), and (1.5, –5) lie on the unshaded portion. While ordered pair (-7.5, -5) lies on the shaded portion.

Thus, the required ordered pair for the solution of an equation  [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).

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Answer:y=2+2x

Step-by-step explanation:

Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2