Write the equation of the circle centered at (−4,−2) that passes through (−15,19)

Answer:

There is not sufficient evidence at the 0.01 level that the bags are underfilled or overfilled

Step-by-step explanation:

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 403 gram setting.

This means that the null hypothesis is:

\(H_{0}: \mu = 403\)

Is there sufficient evidence at the 0.01 level that the bags are underfilled or overfilled:

This means that at the alternate hypothesis, we are testing if the mean is different than 403, that is:

\(H_{a}: \mu \neq 403\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

Value of 403 tested at the null hypothesis:

This means that \(\mu = 403\)

A 10 bag sample had a mean of 411 grams with a variance of 121.

This means that \(n = 10, X = 411, \sigma = \sqrt{121} = 11\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{411 - 403}{\frac{11}{\sqrt{10}}}\)

\(z = 2.3\)

Pvalue:

Testing if the mean is different of a value, and z positive, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.3

Looking at the z-table, z = 2.3 has a pvalue of 0.9893

1 - 0.9893 = 0.0107

2*0.0107 = 0.0214

0.0214 > 0.01, which means that there is not sufficient evidence at the 0.01 level that the bags are underfilled or overfilled

By using  Matrix method it denotes that the equations are consistent and have a single solution.

Matrix method, we will use the formula, \(X=A^{-1} B\) where,

\(\[{\rm{X}} = \left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\)

\(\[{A^{ - 1}} = \frac{{adjA}}{{|A|}}\]\)

\(\[{\rm{B}} = \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\]\)

So, we will have to find \(A^{-1}\), for that, we will first find the determinant of matrix A, that is |A|, then we will find the cofactors of matrix A, take its transpose, and that will be Adj A.

Therefore, we will be able to get the inverse of matrix A using

\(A^{-1}\) =Adj A|A|

and hence We then substitute all the obtained values of \(A^{-1}\) and B in the main formula and do necessary calculations to get the value of x, y and z accordingly.

Complete step-by-step answer:

It is given in the question that, we have to solve the system of equations,

2x-y+4z=33

X+2y-3z=−26

-5x−3y+5z=23

Applying the matrix approach.

Therefore, the first step is to convert the supplied equations into matrix form. Thus, it can be expressed as follows.

\(\[\left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\left[ {\begin{array}{*{20}{l}}x\\y\\z\end{array}} \right]\]\[\)\(= \left[ {\begin{array}{*{20}{c}}{33}\\{ - 26}\\{23}\end{array}} \right]\)

\(\[|{\rm{A}}| = \left[ {\begin{array}{*{20}{c}}2&{ - 1}&4\\1&2&{ - 3}\\{ - 5}&{ - 3}&5\end{array}} \right]\]\)

= 2(10+9) + 1(5-15) + 4(-3+10)

= 38-10+28

=56

Since we have |A|≠0.

Hence, it denotes that the equations are consistent and have a single solution.

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Answer:

102.63

Step-by-step explanation:

There are 12 months in a year. 12 * 38 = 456

There  are 52 weeks in a year 52 * 9 = 468

Cigarettes : dry cleaning :: 468:456

Cigarettes : dry cleaning :: 1.0263

The % is (468/456)*100 = 102.63%

The % shows that she spends more on cigarettes than she does on dry cleaning, which is usually the case.

Answer:

center is (5/2,2) and the radius is 4

Step-by-step explanation:

Answer:

(5/4, -5)

Step-by-step explanation:

Finding x:

Finding y:

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The coordinate of a point that divides the line with endpoints (a, b) and (c, d) in the ratio m:n.

P = (x, y)

x = (mc + na) / m + n

y = (md + nb) / m + n

The coordinate of a point P that divides the line with endpoints (-4, 2) and (5, 8) in the ratio 1:5 is (-5/2, 3).

The answer is (-5/2, 3)(

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The endpoints of the directed line segment AB are:

A(−4, 2) and B(5, 8)

Point P divides the line segments in the ratio 1:5

m = 1 and n = 5.

The coordinate of a point that divides the line with endpoints (a, b) and (c, d) in the ratio m:n.

P = (x, y)

x = (mc + na) / m + n

y = (md + nb) / m + n

Now,

P= (x, y)

A(−4, 2) and B(5, 8)

m = 1 and n = 5.

x = (1 x 5 + 5 x (-4)) / 1 + 5

x = (5 - 20) / 6

x =  -15 / 6

x = -5/2

y = (1 x 8 + 5 x 2) / (1 + 5)

y = (8 + 10) / 6

y = 18/6

y = 3

The coordinates of the point P.

P = (-5/2, 3)

Thus,

The coordinate of a point P that divides the line with endpoints (-4, 2) and (5, 8) in the ratio 1:5 is (-5/2, 3).

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Answer:

x-intercepts/ roots= (-1,0), (15,0)

f(0)= -15 (y-intercept)

Axis of symmetry: x = 7

Vertex: (7, -64)

Domain: All real numbers

Range: [-64, infty)

Answer:

10 miles less

Step-by-step explanation:

To get the direct distance first, we use the pythagorean theorem. Distance from Ferris to Butte directly would be the hypotenuse. By solving for the hypotenuse, we have 25 miles. Now the distance used previously is 35 mile. Hence, it (35 - 25 = 10 ) miles less.

Answer:

easey, sub them

(x,y)

see if true

(0,1), 2(0)+1>-4, 1>-4, true

(4,-12), 2(4)+-12>-4, 8-12>-4, -4>-4, false

(5,-12), 2(5)+-12>-4, 10-12<-4, -2>-4, true

(-1,-1), 2(-1)+-1>-4, -2-1>-4, -3>-4, true

(-3,0), 2(-3)+0>-4, -6>-4, false

answers are

(0,1)

(5,-12)

(-1,-1)

Hopefully that helped you a little bit :)

Answer:

number is 2

Step-by-step explanation:

let the number be n then 8 times the number is 8n, subtract 1 from this and

8n - 1 = 15 ( add 1 to both sides )

8n = 16 ( divide both sides by 8 )

n = 2

that is the number is 2

Answer:

1 is cofficient of X ²

Answer:1/6*1/6*1/6=1/216

Step-by-step explanation:

Answer:

a. 1124.86

b.  1872.98

c. 10.35

d. 17.7

Step-by-step explanation:

use the formula A(t) = a (1+r)^t

                                                   uh i could never, sorry

The number of real zeros for the function whose graph is shown include the following: D. 0.

In Mathematics and Geometry, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at real zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the real zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and it is non-existent on the graph above.

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This suggests that the majority of the team members have an average weight of between 90 and 100 lbs.

1. A box plot is a chart that displays the distribution of a dataset by showing the median, quartiles, and extremes of the data.

2. In this box plot, the middle 50% of the weights for the team members range from 90 to 100.

3. This means that the majority of the team members have an average weight of between 90 and 100 lbs.

The box plot shows that the majority of the team members have an average weight between 90 and 100 lbs.

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On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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1259.19^3

Step-by-step explanation:

A tennis ball is a sphere

Volume of a sphere ===> v=4/3 πr^3

Plug in the given info

v=4/3(3.14) (6.7)^3

Do the math to get a final answer of:

1259.19^3

Answer:

To find the experimental probability that a $5 coupon is the next coupon drawn, we need to add up the total number of $5 coupons drawn and divide it by the total number of coupons drawn.

Looking at the double bar graph, we can see that a total of 272 coupons were drawn from Monday to Friday, and out of those, 173 were $5 coupons. Therefore, the experimental probability of drawing a $5 coupon is:

Experimental probability = Number of $5 coupons drawn / Total number of coupons drawn

Experimental probability = 173 / 272

Simplifying this fraction by dividing both the numerator and denominator by 17, we get:

Experimental probability = 10 / 16

Converting this fraction to a decimal, we get:

Experimental probability = 0.625

Therefore, the experimental probability of drawing a $5 coupon is 0.625 or 625/1000.

However, none of the answer choices matches this value. The closest one is 70/167, which is approximately 0.419 (rounded to three decimal places). This value does not match the experimental probability calculated above. So, there may be an error in the question or answer choices.

Answer:

There is error in question or answer choices.

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.

Interpretation of the expected value:

The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses.

To compute the expected value of the proposal, we need to calculate the amount profited or lost (X) by the company on the warranties and the probability (P(X)) of each outcome.

Now, we have,

The product doesn't fail within 2 years, and the company earns $50 from the warranty.

The product fails within 2 years, and the company incurs a replacement cost of $1200 but keeps the $50 warranty fee.

The probability of the product not failing within 2 years is 1 - 0.05 = 0.95,

and the probability of the product failing within 2 years is 0.05.

Now, we have to find the expected value (E(X)):

\(E(X) = P(X_1) * X_1 + P(X_2) * X_2\)

Where:

\(P(X_1)\) = Probability of the product not failing within 2 years = 0.95

\(X_1\) = Amount profited when the product doesn't fail within 2 years = $50

\(P(X_2)\) = Probability of the product failing within 2 years = 0.05

\(X_2\) = Amount lost when the product fails within 2 years = -$1150 (Replacement cost of $1200 - $50 warranty fee)

E(X) = 0.95 * $50 + 0.05 * (-$1150)

E(X) = $47.50 - $57.50

E(X) = -$10

The expected value of the proposal is -$10. This means that, on average, the company can expect to lose $10 per warranty sold.

Interpretation of the expected value:

The expected value of -$10 indicates that, on average, for every 2-year warranty sold, the company can expect to lose $10. This means that the proposal is not a profitable venture for the company. The replacement costs of the 5% of failed products are higher than the revenue generated by selling the warranties and cannot cover the potential losses. As a result, the company might want to reconsider the pricing of the warranty or look for other ways to reduce the potential costs associated with the product failures.

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Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

Answer:

39V3 Sq.units of that will help you

a) 1.4 to the nearest tenth of the place

b) 1.1 to the nearest tenth of the place

c)0.3 to the nearest tenth of the place

d) 0.5 to the nearest tenth of the place

e) 0.4 to the nearest tenth of the place

f) 0.6 to the nearest tenth of the place

The full number and the fraction are expressed simultaneously using decimals. By adding a "." (known as a decimal point) in this instance, we will divide the whole number from the fraction. Think about taking an ice cream cone as an illustration. Your purchase of ice cream will cost $2 and 50 cents, the dealer informs you. Currently, you would state that the ice cream cone costs $2.50 if you were to describe this amount in a single number. You may be utilizing decimals unknowingly in a variety of these real-world situations.

a) \(1\frac{5}{16} =\frac{22}{16}\)

= 1.375

=1.4 to the nearest tenth of the place

b) \(1\frac{1}{8} = \frac{9}{8}\)

=1.125

=1.1 to the nearest tenth of the place

c)\(\frac{1}{4}\)

= 0.25

= 0.3 to the nearest tenth of the place

d) \(\frac{1}{2}\)

=o.5

=0.5 to the nearest tenth of the place

e) \(\frac{3}{8}\)

=0.375

=0.4 to the nearest tenth of the place

f) \(\frac{9}{16}\)

=0.5625

= 0.6 to the nearest tenth of the place

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Answer: $4,600 was invested in the 8% account and $2,400 was invested in the 7% account.

Step-by-step explanation:

Let's break this down into simpler terms so you can understand.

You invested $7000 in a 7% and 8% account (always remember: the 'x' variable is always given to the biggest percentage)

Total of interest: 536 (this always goes at the end of the equation, after the equal sign)

Step 1: Let's set up the equation:

Here are how percents are written: (7% = 0.07, 8% = 0.08, other examples: 50% = 0.50)

0.08x + 0.07(7,000-x)=536

You're adding both because you want to see how much each account paid together.

Step 2: Distribute the 0.07 to everything in the parenthesis

0.08x + 0.07(7,000-x)=536

0.08x + 490 - 0.07x =536

Step 3: Combine like terms

0.08x + 490 - 0.07x =536

0.01x + 490 =536

Step 4: Continue combining like terms

0.01x + 490 =536

0.01x = 46

Step 5: Divide both sides by 0.01 to get the 'x' by itself

0.01x = 46

x = 4,600

This answer, x = 4,600, says to us that $4,600 was invested in the 8% account.

To find out how much was invested in the 7% account, just replace the x = 4,600 back into this part of the original equation: 7,000-x

7,000-x

7,000-4,600

2,400

So.. $4,600 was invested in the 8% account and $2,400 was invested in the 7% account.

Answer:

Step-by-step explanation:

A) Commission = 2450 shillings * 25 % = 2450 shillings * (25/100) = 2450 shillings * (0.25) = 612.50 shillings

Commission = 612.50 shillings

B) If the total sale is 2,450.00 shillings, after the seller gives buyers a 2% discount. We must re-enter the discount:

2,450.00 shillings = X - X * 2% = X - 0.02 X --->

------> 0.98 X = 2,450.00 shillings

------>X= 2,450.00 / 0.98

------> X = 2,500.00  shillings

NEW COMMISSION = 2,500.00 shillings * 25 % = 2,500.00 shillings *(25/100) =2,500.00 shillings * (0.25) = 625 shillings

NEW COMMISSION = 625 shillings

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

<95141404393>

Answer:

1. 6 units

2. 13 units

3. 5 units

Step-by-step explanation:

Let X and Y be IID Unif(0, 1). the distance between X and Y.Expected value: 0 and Standard deviation: \($\sqrt{\frac{1}{3}}$\)

Expected value:

E(X-Y)

= E(X) - E(Y) = 0 - 0 = 0

Standard deviation:

Var(X-Y) = Var(X) + Var(Y) = 1 + 1 = 2

SD(X-Y) = \($\sqrt{2}$ \\\) \(= $\sqrt{\frac{1}{3}}$\)

The expected value of X-Y is the difference of the expected values of X and Y, which are both 0 since they are both IID Unif(0, 1). The variance of X-Y is the sum of the variances of X and Y, which are both 1. Since the standard deviation is the square root of the variance, the standard deviation of X-Y is the square root of 2

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