Determine the equation of the circle with center (0, -3) containing the point
(√32,-2).

Answer:

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

Step-by-step explanation:

First, we can represent 3/8 in decimal form:

0.375

Next, we can show the numerator using multiplication:

0.375 × a² × b³ × c⁵

Then, we can individually divide by each factor in the denominator using the principle:

[tex]\dfrac{A}{B \times C} = A \div (B \times C) = A \div B \div C[/tex]

0.375 × a² × b³ × c⁵ ÷ x⁴ ÷ y³ ÷ z

Answer: 3.71

Step-by-step explanation:

Check the picture below.

Answer:

522/9=58

11-9=2

58*2=116

522+116=638

Step-by-step explanation:

Answer:

638

Step-by-step explanation:

The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.

We can set up a proportion to solve the problem:

distance / gasoline = constant

Let's use x to represent the distance the car can travel with 19 gallons of gasoline:

924 / 28 = x / 19

Simplifying and solving for x:

x = (924 / 28) * 19 = 627 miles

Therefore, the car can travel 627 miles with 19 gallons of gasoline.

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[tex]\begin{bmatrix} 5&2\\ 3&x \end{bmatrix}~~ = ~~x^2\implies \stackrel{ \textit{determinant of a }2\times 2 ~matrix}{(5)(x)~~ - ~~(3)(2)}~~ = ~~x^2\implies 5x-6=x^2 \\\\\\ 0=x^2-5x+6\implies 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}[/tex]

180º-110º = 70º

m∠7 = 70°

The fractions [tex]\frac{-2}{5}[/tex] and the fraction [tex]\frac{-4}{10}[/tex] , both are equal [tex]\frac{-2}{5} =\frac{-4}{10}[/tex], which means the "=" sign makes the statement true.

A mathematical relationship between two expressions is called inequality, and it is expressed using one of the following:

"less than or equal to": [tex]\leq[/tex]

"greater than" :>

"greater than or equal to" : [tex]\geq[/tex]

"less than": <

"not equal to": [tex]\neq[/tex]

To compare the fraction, make the denominator of both fractions the same.

Given:

Fraction 1 = [tex]\frac{-2}{5}[/tex]

Fraction 2 = [tex]\frac{-4}{10}[/tex]

To make the same denominator we can multiply by 2 to the numerator and denominator of the fraction 1.

[tex]\frac{-2}{5} =\frac{-2 * 2}{ 5*2}[/tex]

[tex]\frac{-2}{5} =\frac{-4}{10}[/tex]

Hence from the above calculation, the given fractions are equal.

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Answer: 9 - i

Step-by-step explanation:

The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

We have to give that,

The sum of numbers 12 - 5i and - 3 + 4i.

Now, we can find the sum of complex numbers as,

(12 - 5i) + (- 3 + 4i)

12 - 5i - 3 + 4i

Combine like terms,

12 - 3 - 5i + 4i

9 - i

Therefore, The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

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Answer:

1) 24

2) 25

Step-by-step explanation:

Given:

2a + 3b = 8

4x + 10y = 50

.

1)

[tex] \frac{6a + 9b}{2a + 3b} = \frac{3(2a + 3b)}{2a + 3b} = 3[/tex]

Since the second expression is 3 times greater then the previous one, the product will also be 3 times greater:

6a + 9b = 3 × 8 = 24

.

2)

[tex] \frac{2x + 5y}{4x + 10y} = \frac{2x + 5y}{2(2x + 5y)} = \frac{1}{2} = 0.5[/tex]

The second expression's value is two times smaller than the first one's, so the product will also be two times smaller:

2x + 5y = 0,5 × 50 = 25

Answer: B

Step-by-step explanation:

The answer is 9x^2 + 14xy -19y^2

Answer: 9 and 1/3

Step-by-step explanation:

First of all, you have to find the unit rate. So 28 divided by 2 = 14.

The bird flies at a unit rate of 14 miles in 1 hour.

Next, we need to find out what fraction of an hour is 40 minutes.

How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.

Next, remember the formula D=rt which is distance= rate multiplied by time

We can use this formula here: 14 times 2/3 = 9 and 1/3

Assuming the black and red squares are equally likely and there is no bias in the coin, the probability that it will land heads up on a black square is 1/2, or 50%.

Probability is a branch of mathematics that studies the likelihood of a random event occurring. When a coin is tossed into the air, for example, the possible outcomes are Head and Tail.

We will have a probability of 50%; this is because there are two equally likely outcomes when flipping a coin - heads or tails - and each square on the checkerboard has an equal chance of being landed on.

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The probability of selecting a football card and then a basketball card is 0.16 or 16%. The probability of selecting a football card and then a basketball card can be calculated by multiplying the probability of selecting a football card on the first draw and the probability of selecting a basketball card on the second draw.

Since the first card is replaced before the second draw, the probability of selecting a football card or a basketball card remains the same on both draws.

The probability of selecting a football card on the first draw is 2/10, or 0.2, since there are 2 football cards in a total of 10 cards in the bag. The probability of selecting a basketball card on the second draw is 8/10, or 0.8, since there are 8 basketball cards left after the first draw.

Therefore, the probability of selecting a football card and then a basketball card can be calculated as follows:

P(Football and Basketball) = P(Football on 1st draw) x P(Basketball on 2nd draw)

= (2/10) x (8/10)

= 0.16

So, the probability of selecting a football card and then a basketball card is 0.16 or 16%.

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So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

What does an expression mean?

It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.

Let's solve this equation step by step:

100000+1X2

This is a simple expression which involves addition and multiplication.

100000+1X2 = 100000 + 2 (since 1X2 equals 2)

Therefore, 100000+1X2 = 100002

222+222+22222222222x111111111111111111111

This expression involves addition and multiplication as well.

We need to multiply 22222222222 by 111111111111111111111 first, and then add 222+222 to the result.

22222222222 x 111111111111111111111 = 24,691,358,024,691,358,024,691,358

222+222 = 444

So, 222+222+22222222222x111111111111111111111 = 24,691,358,024,691,358,024,691,802

222222222222222222

This is a simple number.

So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

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The condition that must be satisfied to use a chi-square goodness-of-fit test is D. The expected count for each category is at least 5.

A chi-square goodness-of-fit test is a statistical test used to determine whether the observed frequencies of categorical data match the expected frequencies. This test is often used to analyze categorical data, such as determining if the distribution of colors in a bag of candies matches the expected proportions.

The reason behind this condition is that the chi-square test is based on the assumption that the data follow a specific distribution. When the expected count for each category is less than 5, the test might not accurately represent the true distribution, and the results may be misleading. By having an expected count of at least 5 in each category, the test can better approximate the true distribution and provide more reliable results. Therefore, option D is correct.

The Question was Incomplete, Find the full content below :

which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?

A. The sample size is greater than 30.

B. The number of categories is less than 10% of the number of observations.

C. The expected count is the same for each category. the population distribution is approximately normal.

D. The expected count for each category is at least 5.

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Answer:15

You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15

The lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

When two straight lines or beams intersect at a single endpoint, an angle is created.

The vertex of an arc is the location where two points come together. The Latin term "angulus," which means "corner," is where the word "angle" originates.

There are, however, a few fundamental perspectives.

Your camera options expand tremendously when combined with various shots.

This angle, which entails shooting a scene from directly overhead, is the most perplexing of the five.

So, according to the given situation:

= r║s

= Pair of angles are supplementary angles

Therefore, the lines r and s  (A) are parallel because the given angles are (F) supplementary angles and they (H) do not have equal angle measures.

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Correct questions:

in the given figure, can you conclude r ∥ s? Use the drop-down menus to explain your answer.

The lines-------------parallel because the given angles are----------angles and they -----------have equal angle measures.

(A) first line: (A) are (B) are not

second line: (C) same side interior (D) corresponding (E) alternate (F) supplemental

third line: (G) do (H) do not

The given measure of ∠ DEC = 80 degrees

We have the following details

m ∠BAC = 46 degrees

m ∠ CBA = 54 degrees

We are to find the measure of angle DEC

This is a question that shows us two similar triangles

We have ∠BAC = DCE

∠ CBA = ∠ EDC

then ∠ DEC  = ∠ BCA

The measure of the angles that are in a triangle is given as 180 degrees

we have ∠BAC + ∠ CBA + ∠ BCA = 180

46 + 54 + ∠ BCA = 180 degrees

∠ BCA = 180 - 100

∠ BCA = 80 degrees

We know that corresponding angles are equal when we have parallel lines

since ∠ DEC  = ∠ BCA

∠ DEC = 80 degrees

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The solution to the system of equations is p = 4 and q = 2

The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.

To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:

p + 2q = 8

p = 8 - 2q

Now we can substitute this expression for p in the first equation:

2p - 3q = 2

2(8 - 2q) - 3q = 2

16 - 4q - 3q = 2

16 - 7q = 2

-7q = -14

q = 2

We can now substitute q = 2 into the expression we found for p:

p = 8 - 2q

p = 8 - 2(2)

p = 4

Therefore, the solution to the system of equations is p = 4 and q = 2.

correct question  Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.

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Answer:

x = -4,

y = -1

Step-by-step explanation:

{-3x - 8y = 20,

{-5x + y = 19;

Make x or y the subject from either the 1st or the 2nd equation (I chose to make x the subject from the 2nd equation, because after division, the numbers can be written as a finite decimal fraction):

-5x = 19 - y / : (-5)

x = -3,8 + 0,2y

Replace x in the 1st equation with its value from the 2nd one (the underlined expression):

-3(-3,8 + 0,2y) - 8y = 20

Multiply every term inside the bracket by the term on the outside:

11,4 - 0,6y - 8y = 20

Collect like terms and add them together:

-8,6y = 20 - 11,4

-8,6y = 8,6 / : (-8,6)

y = -1

y = -1x = -3,8 + 0,2 × (-1) = -4

The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.

Sample size is defined as the number of observations used to determine

an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.

The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.

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The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588

We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.

The standard error of the mean can be calculated as

SE = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size

Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.

SE = 90 / sqrt(72) = 10.6066

Next, we need to standardize the sample mean using the z-score formula

z = (X - μ) / SE

where X is the sample mean, μ is the population mean.

Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.

z = (1173.8 - 1192) / 10.6066 = -1.7356

We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.

Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.

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The coordinates of the image of the triangle and the rules that can be used to transform the triangle are;

1. A' is located at (-3, 3)

B' is located at (-2, -1)

C' is located at (2, 1)

Second part; The rules are;

(x, y) → (x + 5, -y)

(x, y) → (5·x, 5·y)

A transformation of a figure is the reorientation of the figure to change the size and position of the figure.

1. The coordinates of the triangle ABC following the transformation (x, y) → (-x, y) are;

A(3, 3) (x, y) → (-x, y) A'(-3, 3)

B(2, -1) (x, y) → (-x, y) B'(-2, -1)

C(-2, 1) (x, y) → (-x, y) C'(2, 1)

2. The coordinates of the vertices of the triangle are; (1, 1), (4, 1), and (0, 4)

Translating the triangle five units right, we get;

(1 + 5, 1) = (6, 1), (4 + 5, 1) = (9, 1), and (0 + 5, 4) = (5, 4)

The coordinates of the triangle following a translation 5 units right are therefore;  (6, 1), (9, 1), and (5, 4)

The coordinates of the image of the point (x, y) following a reflection across the x-axis is the point (x, -y), therefore;'

The coordinates of the image of the triangle obtained from the previous transformation following a reflection across the x-axis is therefore;

(6, 1) reflection across the x-axis → (6, -1)

(9, 1) reflection across the x-axis → (9, -1)

(5, 4) reflection across the x-axis → (5, -4)

A rule that takes the triangle to a congruent triangle right five units and reflected over the x-axis is therefore;

The transformation of a triangle by a dilation by a scale factor of five, such that the triangle is five times larger can be obtained by the expression for a dilation transformation as follows;

(x, y) → (a·x, a·y)

Therefore, we get;

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The amοunt οf prize mοney each winner received can be represented by the expressiοn: $480 / x

A linear equatiοn is a mathematical equatiοn that represents a straight line when graphed, and is in the fοrm οf y = mx + b, where m represents the slοpe οf the line and b represents the y-intercept.

The amοunt οf prize mοney each winner received can be represented by the expressiοn:

$480 / x

This is because the prize mοney οf $480 was split equally amοng x winners, sο dividing the tοtal prize mοney by the number οf winners (x) gives the amοunt each winner received. This expressiοn calculates the quοtient οf $480 divided by the number οf winners (x), resulting in the amοunt οf prize mοney each winner received.

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After answering the presented question, we can conclude that it contains  inequality the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

The interquartile range is the most acceptable measure of variability for Terri's data (IQR).

The IQR is an acceptable measure of variability in this example because it focuses on the middle 50% of the data, which is where Terri spends the majority of her time at the fitness club. The mean and median are measures of central tendency rather than variability, and the range would be less useful in this situation because it contains the extremes of Terri's data, which may not be representative of her typical time spent at the fitness club.

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Answer:

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]

Step-by-step explanation:

[tex]m = \frac{79 - ( - 20)}{9 - ( - 2)} = \frac{99}{11} = 9[/tex]

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]

Answer:

after 80 years, approximately 2.15 grams of the initial 16 grams of cesium-137 would remain. This means that about 13.4 grams would have decayed during this time period.

Answer:

for the firsts ones :

1. 12 x 2 x 5

2. 4 x 11 x 2,25

3. 6.5 x 22.6 x 10

Step-by-step explanation: