An angle is bisected, forming two new angles. If the original angle had a measure of 64°,what is the measure of each new angle.​

Answer:

2

Step-by-step explanation:

12:1,2,3,4,6,12

18:1,2,3,6,9,18

32:1,2,4,8,16,32

h.c.f = 2

Answer:

9a^4b^4c^2

Step-by-step explanation:

Area of a  square is expressed using the formula

A =L²

L is the side length of the square

Given that;

L = a²b²c

A = 3²(a²b²c)²

A = 9(a²)²(b²)²c²

A = 9a^4b^4c^2

Hence the area of the square is 9a^4b^4c^2

Answer:

cos(theta/2) = sqrt((1+x)/2)

Step-by-step explanation:

From the double angle formula

cos^2(t)-sin^2(t) = cos(2t)  ...................(1)

cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)

Add (1) and (2)

2cos^2(t) = 1+cos(2t)

cos^2(t) = (1+cos(2t))/2

cos(t) = sqrt((1+cos(2t))/2)

substitute t = theta/2

cos(theta/2) = sqrt((1+cos(theta))/2)

substitute cos(theta) = x

cos(theta/2) = sqrt((1+x)/2)

a. To find the standard error of the sampling distribution of sample means:

Standard deviation = sqrt(Variance of the population)

Since the population standard deviation is not given, we assume it is 1.

Standard error = (Standard deviation) / sqrt(n)

        = (1) / sqrt(100)

        = 0.01  (rounded to 2 decimal places)

b.

Standard error = 0.01  (from part a)

z = (4.7 - mean) / 0.01

        = (4.7 - 5) / 0.01

        = -0.3  (rounded to 2 decimal places)

Chance that sample mean is between 4.7 and 5.9 hours

        = P(z > -0.3) + P(z < 0.3)

        = 0.762 + 0.761

        = 0.7524  (rounded to 4 decimal places)

c.

Standard error = 0.01  (from part a)

z = (5.1 - mean) / 0.01

        = 0.1  (rounded to 2 decimal places)

Chance that sample mean is between 5.1 and 5.5 hours

        = P(z > 0.1) + P(z < -0.1)

        = 0.4583 + 0.4603

        = 0.4593  (rounded to 4 decimal places)

d.

Standard error = 0.01  (from part a)

z = (7.60 - mean) / 0.01

        = 3  (rounded to 2 decimal places)

Chance that sample mean is greater than 7.60 hours

        = P(z > 3)

        = 0  (rounded to 4 decimal places)

This would be very unlikely.

A sample size of 77 is needed for a scientist studying premature babies to estimate the mean birth weight of babies born during a week of gestation within 0.5 pounds with 95% confidence, assuming a population standard deviation of 2 pounds.

To determine the minimum sample size needed for the scientist to be confident that her estimate is within a certain margin of error of the true mean birth weight of babies born during the week, we can use the formula

n = (zα/2 * σ / E)²

where

n = sample size

zα/2 = critical value for the desired level of confidence (e.g. 1.96 for 95% confidence)

σ = population standard deviation

E = margin of error (i.e. the maximum amount by which the estimate can differ from the true mean)

Substituting the given values, we have

n = (1.96 * σ / E)²

To determine E, we need to use the fact that the margin of error is equal to the critical value times the standard error, where the standard error is given by

SE = σ / √(n)

Substituting the given values, we have

SE = σ / √(n) = 2 / √(n)

Thus, we have

E = zα/2 * SE = 1.96 * 2 / √(n) = 3.92 / √(n)

Substituting this expression for E into the formula for n, we have

n = (1.96 * σ / (3.92 / √(n)))²

Simplifying, we get

n = (1.96 * σ * √(n) / 3.92)²

n = (0.5 * σ * √(n))²

n = (0.25 * σ² * n)

n = (zα/2)² * σ² / E²

Substituting the given values, we have

n = (1.96)² * 4 / (0.5)² = 76.96

Rounding up to the nearest whole number, we get

n = 77

Therefore, the minimum sample size needed for the scientist to be confident that her estimate is within 0.5 pounds of the true mean birth weight of babies born during the week is 77.

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The distance between the two towns is 165 kilometers

The initial speed = 100 kilometer per hour

Time taken = t hours

We know,

Speed = Distance / Time

Distance = Speed × t

Distance = 100 × t

New speed = 110 kilometer per hours

He saves 9 minutes

9 minutes = 9/60 hours

The time taken = t - 9/60

The distance = 110 × (t - 9/60)

= 110t - 33/2

Then the equation will be

100t = 110t - 33/2

110t - 100t = 33/2

10t = 33/2

t = 33/2 ÷ 10

t = 33/2 × 1/10

t = 1.65 hours

Then the distance = 100 × t

= 100 × 1.65

= 165 kilometers

Hence, the distance between the two towns is 165 kilometers

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Answer:

it's a 1/6 chance because it's a 6 faced dice

(a) The correct trigonometric substitution for this integral is:

\(x = 10 \sin \theta\)

We can see this by noting that:

\(\sqrt{100-x^2} = \sqrt{100-100\sin^2\theta} = 10\cos\theta\)

So substituting \(x = 10\sin\theta\) simplifies the integral.

(b) After substituting for x and simplifying, we get:

\(\int \frac{4x^2}{100-x^2} dx = \int \frac{4(10\sin\theta)^2}{100-(10\sin\theta)^2} \cdot 10\cos\theta d\theta\)

Simplifying the integrand gives:

\(\int \frac{400\sin^2\theta}{100\cos^2\theta} \cdot 10\cos\theta d\theta = \int 40\tan^2\theta d\theta\)

(c) To evaluate this integral, we can use the identity:

\(\tan^2\theta = \sec^2\theta - 1\)

Substituting this identity into the integral gives:

\(\int 40\tan^2\theta d\theta = \int 40(\sec^2\theta - 1) d\theta = 40\tan\theta - 40\theta + C\)

Substituting back for x and simplifying gives the final answer:

\(\int \frac{4x^2}{100-x^2} dx = 40\frac{\sqrt{100-x^2}}{x} - 40\sin^{-1}\left(\frac{x}{10}\right) + C\)

where C is the constant of integration.

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Answer:

c=24

Step-by-step explanation:

c/3 = 8

Multiply each side by 3

c/3 *3 = 8*3

c=24

The equation in standard form will be 4x^2 - 8x - (5 + f(x)) = 0.

The given equation f(x) = (2x + 1) (2x-5) can be simplified by multiplying the two binomials together to get:

f(x) = 4x^2 - 8x - 5

This equation is in general form, not standard form. Standard form of a quadratic equation is given by:

ax^2 + bx + c = 0

where a, b, and c are constants and a ≠ 0.

To convert the given equation to standard form, we need to set it equal to zero by subtracting f(x) from both sides:

4x^2 - 8x - 5 - f(x) = 0

Since f(x) is an arbitrary constant, we can combine the constant terms to get:

4x^2 - 8x - (5 + f(x)) = 0

This equation is now in standard form, with a=4, b=-8, and c=-(5+f(x)).

In summary, to convert a quadratic equation in general form to standard form, we need to set it equal to zero and combine constant terms. The resulting equation should have the form ax^2 + bx + c = 0, with a, b, and c being constants and a ≠ 0.

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The flaw of averages is an illustration that using only the average value can hide many possible outcomes when uncertainty is present in a decision. This statement is true and option a is correct.

The flaw of averages is an illustration that using only the average value can hide many possible outcomes when uncertainty is present in a decision. The flaw of averages has been recognized for a long time, but it continues to be one of the most persistent and harmful sources of confusion in business and government.

It may appear harmless, but the flaw of averages can have a substantial impact. When a decision is made based on an average, such as expected profit, anticipated return on investment, or projected customer demand, it can conceal a wide range of potential results that are often more significant than the average itself.

Therefore, it is better to use data visualization and exploration techniques to mitigate the flaw of averages. This will provide a better understanding of the data and a comprehensive analysis of the risks and potential outcomes.

Therefore, the correct answer is option a.

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Complete question

content loaded

which of the following is true about the flaw of averages? group of answer choices

a. the flaw of averages is an illustration that using only the average value can hide many possible outcomes when uncertainty is present in a decision.

b.  because of the flaw of averages, we should use the median when describing data, not the average.

c. the flaw of averages states that the usual formula used to calculate the mean (or average) of a data set is incorrect whenever the data do not follow a normal distribution.

d. the flaw of averages only applies to data that have not been properly explored using eda and other data visualization techniques.

The value of the expression 7 - 9 using subtraction will be negative 2.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numbers are given below.

7 and 9

Then the difference between the numbers 7 and 9 will be given by putting a minus sign between them. Then we have

⇒ 7 - 9

⇒ - 2

The value of the expression 7 - 9 using subtraction will be negative 2.

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Answer:

15

Step-by-step explanation:

d = 5 for PQ

For:

(X1, Y1) = (0, 0)

(X2, Y2) = (5, 0)

finding distance between two points

d=√(5−0)^2+(0−0)^2

d=√(5)^2+(0)^2

d=√25+0

d=√25

d=5

for RS d=3

d = 3

For:

(X1, Y1) = (3, 2)

(X2, Y2) = (0, 2)

d=√(0−3)^2+(2−2)^2

d=√(−3)^2+(0)^2

d=√9+0

d=3

Area= length * width

Area=3*5=15

For a 6-digit passcode with repeated digits allowed, there are 10 possible digits (0-9) that can be used for each digit. Therefore, the total number of possible passcodes is 10^6 = 1,000,000.

For a license plate with three digits followed by four letters and no repeats allowed, there are 10 possible digits (0-9) for the first digit, 9 possible digits (excluding the already chosen digit) for the second digit, and 8 possible digits for the third digit. For the letters, there are 26 possible choices for each of the four letters. Therefore, the total number of possible license plates is 10 * 9 * 8 * 26^4 = 44,328,960.

1) To find the number of possible 6-digit passcodes with repeated digits allowed, we use the concept of the multiplication principle. Since there are 10 possible digits for each of the 6 positions, we multiply 10 by itself 6 times, resulting in 10^6 possible passcodes.

2) To find the number of possible license plates with no repeats allowed, we consider the choices for each position separately. For the three digits, we have 10 choices for the first digit, 9 choices for the second digit (excluding the already chosen digit), and 8 choices for the third digit. For the four letters, we have 26 choices for each letter. We multiply all these choices together to get the total number of possible license plates.

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Answer:

x = 8

y = -11

Step-by-step explanation:

In this question, we have to find out the value of "x" and "y".

Solve:

Lets solve for y first.

-2(3x + 4y = -20)

6x + 5y = -7

------------

-6x - 8y = 40

6x + 5y = -7

------------

-3y = 33

Divide both sides by -3

y = -11

We now know what the value of "y" is, now we must find the value of x. To do this, we would plug -11 to "y" in one of our equations.

Solve for x:

3x + 4y = -20

3x + 4(-11) = -20

3x - 44 = -20

Add 44 to both sides.

3x = 24

Divide both sides by 3

x = 8

Now we know that our answer are:

x = 8

y = -11

There are 30 of 1/10's in the number 3

From the question, we have the following parameters that can be used in our computation:

How many 1/10's are in 3?​

The above statement is a quotient expression that has the following features

Dividend = 3

Divisor = 1/10

So, we have

Quotient = Dividend /Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = 3/(1/10)

Evaluate

Quotient = 30

Hence, there are 30 1/10's

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

5/36

Step-by-step explanation:

1 x 5= 5

and 9 x 4=36

which makes 5/36

The solution to the product of the fractions is 5/36

From the question, we have the following parameters that can be used in our computation:

1/9 x 5/4

Express 1/9 as 1/9

So, we have

1/9 x 5/4 = 1/9 x 5/4

Evaluate the products of 1 and 5

So, we have

1/9 x 5/4 = 5/9 x 1/4

Evaluate the products of 9 and 4

So, we have

1/9 x 5/4 = 5/36

Hence, the solution is 5/36

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Answer:

Solution:

\(\frac{\left(y-1\right)^2}{9}-\frac{\left(x+4\right)^2}{4}=1\)

Step-by-step explanation:

We have the general equation for our up - down facing hyperbola as (y - k)² / b²- (x - h)² / a²  = 1. Let's start listing the properties of this graph -

• Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1). Therefore (h, k) = (- 4,1).

• Another thing here is our key value a. This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference. Therefore a = 3.

• That leaves us with our asymptotes. Now remember that it will be in the form y = ± b / a. We already know a = 3, so we have to find b. Looking at this graph I can say that another point besides (- 4,1) that lies on the " dotted line " is (- 2, - 2). Calculating the slope of the dotted line would be as follows,

Given: (- 4,1) and (- 2, - 2)

Slope = - 2 + 4 / - 2 - 1 = 2 / 3

We have the equation y = 2 / 3x. Therefore b = 2. Let's substitute to receive our equation...

h = - 4, k = 1, b = 2, a = 3

(y - 1)² / (3)²- (x + 4)² / (2)²  = 1

(y - 1)² / 9 - (x + 4)² / 4  = 1 ~ your solution is the last one, option d

Answer:

y = -6x + 3

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

b = y-intercept

Because the x value is increasing while the y value is decreasing, the slope is negative.

To find the slope, first find 2 points on the line:

(-1 , 8) and (0, 2)

Since the y value decreases by 6 in the same amount that the x value increases by 1, the slope is -6.

To find the value of b, locate the point at which the line intersects the y-axis:

(0 , 3)

The y-intercept is the value of y when x = 0. Because the y-intercept is 3, b = 3.

So, to put this into slope-intercept form, plug in the values:

y = mx + b

y = -6x + 2

The equation of the line in slope-intercept form is y = -6x + 2.

Answer:

154 is the mean

Step-by-step explanation:

First you will add up all the numbers. Which will give you a total of 770, then you have to divide the AMOUNT OF NUMBERS, which is 5. So 770 ÷ 5 = 154.

Gloria's mean score is 154.

The simplest and most popular way to measure a mean or average is the arithmetic mean. It simply entails adding up a collection of numbers, then dividing that total by the total number of numbers in the series.

Formula: Arithmetic Mean

= (Sum of observation)/ Total number of observation

Given:

Gloria  scores were 110, 127, 206, 174, and 153.

Now, Arithmetic Mean

= (Sum of Gloria scores)/ Total number of games

So, Sum of Gloria score = 110+127 + 206+ 174 + 153 = 770

Total number of games = 5

Thus, Arithmetic Mean

= 770 /5

= 154

Hence, the Mean is 154.

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Answer:

3^6

Step-by-step explanation:

3^8 * 3^-2

3^(8-2)

3^6

Answer:

Step-by-step explanation:

2. 1, 0.16

3. 1.5 , 0.24

4. 2, 0.32

Answer:

The answer is about 14.38

Step-by-step explanation:

hope this helps

\(\tan x = \dfrac{\text{Opposite}}{\text{Adjacent}}\\\\\implies \tan x = \dfrac{12}{6}\\\\\implies \tan x = 2\\\\\implies x = \tan^{-1} (2)=63.4^\circ\)

Answer:

x ≈ 63.4°

Step-by-step explanation:

using the tangent ratio in the right triangle.

tan x = \(\frac{opposite}{adjacent}\) = \(\frac{12}{6}\) = 2 , then

x = \(tan^{-1}\) ( 2) ≈ 63.4° ( to the nearest tenth )

The equation of the ellipse with focus at (-2,0) and vertices at (±7, 0) is given as follows:

x²/49 + y²/45 = 1.

The equation of an ellipse of center (h,k) is given by the equation presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

The center of the ellipse is given by the mean of the coordinates of the vertices, as follows:

Hence:

x²/a² + y²/b² = 1.

The vertices are at x + a and x - a, hence the parameter a is given as follows:

a = 7.

Considering the focus at (-2,0), the parameter c is given as follows:

c = -2.

We need the parameter c to obtain parameter b as follows:

c² = a² - b²

b² = a² - c²

b² = 49 - 4

b² = 45.

Hence the equation is given as follows:

x²/49 + y²/45 = 1.

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Answer:

Is that it's not about the answers and the questions

The other angle of the triangle is 65°.

We know that

Exterior Angle = Sum of two angles opposite to the exterior angle

Here, 145° = 80° + x°

=> x° = (145 – 80)°

=> x° = 65°

Therefore, the value of x in the given figure is 65°

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Complete question:

The property that is not true for the normal distribution among the given options is: "The mean, median, and mode are all equal."

The normal distribution is characterized by several key properties. It has a bell shape, meaning it is symmetric around its mean. The tails of the distribution asymptotically approach the horizontal axis, which means they gradually decrease in height as they extend toward positive and negative infinity. The area underneath the curve and to the right of the mean is equal to 0.5, not 1. This is because the total area under the curve represents the probability of all possible outcomes and must sum up to 1. Lastly, the mean, median, and mode of the normal distribution are all equal to each other, making them measures of central tendency that coincide.

Therefore, the property that does not hold for the normal distribution is that the area underneath the curve and to the right of the mean is 1, as it is actually 0.5.

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