If the point (1,5) lies on a circle with center (0,0), determine which point in quadrant 2 that also lies on the circle.

Answer:

See the below process

Step-by-step explanation:

let the Unknown value be x.

Now

[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]

[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]

Taking LCM

[tex]x = \frac{ - 10 - 17}{24} [/tex]

[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]

we should add 8/9 to 17/24 to get -5/12

I hope it helped you

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g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

what is function ?

In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.

In the given question,

To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.

Step 1: Apply f to -3

f(x) = 3x + 7

f(-3) = 3(-3) + 7 = -2

Step 2: Apply g to the result of f(-3)

g(x) = 2x - 5

g(-2) = 2(-2) - 5 = -9

Therefore, g°f = -9.

So, the correct answer is (B) -9.

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The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.

An example is the expression x + y, which combines the terms x and y with an addition operator.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.

A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.

According to the problem,

The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.

The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].

Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]

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92 grams of recycled plastic were used to make Chanasia's bucket

Chanasia buys a plastic bucket

The bucket weighs 460 grams

The label on the bucket says it was made with 20% recycled plastic

The number of grams of recycled plastic that was used to make the bucket can be calculated as follows

= 460/100

= 4.6

= 4.6 × 20

= 92

Hence 92 grams of recycled plastic was used to make the bucket

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Volume First Cylinder: 50.24 in³

Volume Second Cylinder: 127.5625 inch³

Volume Third Cylinder: 904.32 inch³

Volume First Cylinder:

= πr²h

= 3.14(2)² (4)

= 3.14 x 16

= 50.24 in³

Volume Second Cylinder:

= πr²h

= 3.14(2.5)² (6.5)

=3.14 (6.25)(6.5)

= 127.5625 inch³

Volume Third Cylinder:

= πr²h

= 3.14(6)² (8)

=3.14 (36)(8)

= 904.32 inch³

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The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.

To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.

The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.

The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.

Therefore, the probability that all four people regularly use seat belts is:

P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)

P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901

P(all four use seat belts) = 0.656

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The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.

Graph the constraints:

First, we will graph the constraints to visualize the feasible region.

The constraint x + y ≤ 50 represents the region below the line x + y = 50:

The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:

The feasible region is the shaded region that satisfies both constraints:

Identify the corner points of the feasible region:

The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).

Evaluate z at each corner point:

z(0, 0) = 4(0) + 0 = 0

z(0, 50) = 4(0) + 50 = 50

z(30, 20) = 4(30) + 20 = 140

z(45, 0) = 4(45) + 0 = 180

Compare the values of z at the corner points:

The largest value of z is 180, which occurs at the corner point (45, 0).

Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

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The probability that the friend is at least 22 minutes late is 0.266

Uniform density function for a friend = x minutes late

The Friend is at least 21 minutes late

Based on the above information, the probability that the friend is at least 21 minutes late is

= (Total minutes - minimum minutes)/Total minutes

=30-22/30

=8/30

=0.266

Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late

Hence, the probability that the friend is at least 22 minutes late is 0.266

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ANSWER:

368

EXPLANATION:

youre given:

l=14

w=5

h=5

just plug those into the given formula,

2×(14×5)+2×(14×6)+2×(5×6)

(you should do it yourself to check my math...)

Using the tests for symmetry, the following are symmetric with respect to y-axis:

A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.

A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.

A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.

(a) symmetric with respect to the y-axis:

y = 7x - 4 (no)

y = - x + 7 (yes)

y = - 7x² (yes)

y = 6x² - 9 (no)

x = 1/4 × y² (no)

x = - y² + 9 (yes)

y = - 1/6 × x³ (no)

y = x³ - 1 (no)

y = √(x) (no)

y = √(x) - 6 (no)

Therefore, the graphs that are symmetric with respect to the y-axis are:

y = - x + 7

y = - 7x²

x = - y² + 9

None of the graphs are symmetric with respect to the x-axis or the origin.

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Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.

Answer:

- 2/1

Step-by-step explanation:

if u look at the graph/line it's going up by 2 then across 1

Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

========================================================

Work Shown:

[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]

The other diagonal is 4 miles long.

The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .

The focus and directrix of the required parabola are as,

Focus (6, 0)

and, Directrix x = - 6

Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.

Therefore, the equation of the parabola is either of the form,

y² = 4ax

or, y2 = - 4ax

depending on which axis the parabola is in, that is whether negative or positive axis.

It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.

Hence, the parabola is of the form y² = 4ax.

Since, a = 6

Thus, the equation of the parabola is y² = 4(6)x

⇒ y² = 24x

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Answer:

Step-by-step explanation:

6x + 15 = x - 10

5x + 15 = -10

5x = -25

x = -5

An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

The power-reducing formulas state that:

sin^2(x) = (1 - cos(2x))/2

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

Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:

18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]

Expanding the right-hand side of the equation, we get:

18[(1 - cos^2(2x))/4]

Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:

18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8

Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

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The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.

Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.

A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.

To obtain the absolute maximum and lowest values of the function  over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.

We first take the derivative of f(x) and set it to zero to determine the critical points:

The function is then assessed at these pivotal points and the interval's endpoints:

As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).

We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4

According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).

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Answer:

100 Minutes

Step-by-step explanation:

Step 1: Break it down-

3¢ can be expressed as 0.3

Step 2: Add monthly charge-

Since there is a 10$ monthly charge: 40-10=30

Step 3: Subtract-

Now divide: 30 ÷ 0.3

Step 4: Final Answer-

Hence the amount of minutes per month= 100

We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

What is meant by the term data?

Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.

According to the given information

The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:

The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2

This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:

The number of expected bran muffins = 0.2 * 20 = 4

Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

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the correct answer is a reflection across the x-axis.

How to solve questions?

Based on the given image, the type of transformation shown is a reflection across the x-axis.

A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.

In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.

A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.

Therefore, the correct answer is a reflection across the x-axis.

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The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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Answer:

88

Step-by-step explanation:

y=2cm h=7cm

CSA=22/7×4×7

the sevens get crossed out and then 22/1 ×4=88.

Answer:

189.1034.

Step-by-step explanation:

The result of the expression is approximately 189.1035.

To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:

Parentheses: Perform the operation within the parentheses first.

71 + 16 = 87

Division: Perform the division.

84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)

Multiplication: Perform the multiplication.

0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)

Subtraction: Finally, perform the subtraction.

192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)

The result of the expression is approximately 189.1035.

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A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.

To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.

For the 2-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $7.00 / 2 lbs

Cost per pound = $3.50 per pound

For the 3-pound package

Cost per pound = Total cost / Weight in pounds

Cost per pound = $10.50 / 3 lbs

Cost per pound = $3.50 per pound

Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.

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Answer:

[tex] \frac{w}{3} [/tex]

Answer:

Step-by-step explanation: 462 Divided by 24 = 19.25$

Proof: 19.25 x 24 = 462

Answer: 19.25$

Answer:

a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.

y = 34.17860108 - 5.682632245ln(x)

b. Setting this equation equal to 10, we have x = 70.44 mph

c. If x = 75 mph, then y = 9.64.