Geoff sold his handknit hats for
$15 each at the farmers' market. He
bought $45 of yarn to make the hats.
If x represents the number of hats
sold, which expression represents
Geoff's earnings?

Answer:

∠ADB

Step-by-step explanation:

Acute angles measure less than 90°.

So, here ∠ADB is acute angle,

Answer:

  150

Step-by-step explanation:

You want the numerical value for log(a, b, c) = (-10, -10, 15) of ...

  [tex]\log\dfrac{\sqrt[3]{c^8}}{a^4b^7}[/tex]

The applicable rule of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

  log(a/b) = log(a) -log(b)

The applicable rule for radicals is ...

  [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]

Using the above rules, we can rewrite the logarithm as ...

  [tex]\log\dfrac{\sqrt[3]{c^8}}{a^4b^7}=\dfrac{8}{3}\log(c)-(4\log(a)+7\log(b))\\\\=\dfrac{8}{3}(15)-(4(-10)+7(-10))=40+(4+7)(10)=\boxed{150}[/tex]

The numerical value of the log expression is 150.

<95141404393>

Answer:

y = 5/11 is y-intercept. slope = -2/11

Step-by-step explanation:

2x + 11y - 5= 0

add 5 to both sides and subtract 2x from both sides

11y = 5 - 2x

to find y-intercept: make x = 0 (because all along the y-axis, x will be 0).

11y = 5 - 2(0)

    = 5

divide by 11

y = 5/11. this is y-intercept.

to find slope (gradient):

11y = 5 - 2x

divide by 11

y = 5/11  - (2/11) x

slope = -2/11

A line through points X and Y will be perpendicular bisector of AB.

By examining the figure, it is evident that the compass created arcs as follows:

An arc was drawn with A as the center and a radius greater than half the length of AB.

and, another arc was drawn with B as the center using the same radius.

The points where these arcs intersect are labeled as X and Y.

This construction clearly represents the creation of a perpendicular bisector for the line segment AB.

Therefore, if we draw a line segment passing through points XY, it will serve as the perpendicular bisector of AB.

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The concentration will be 0.5 mg/L at time t =39.86 hours

To determine when the concentration will be 0.5 mg/L, we need to solve the equation:

c(t) = 0.5

20t/(t²+4) = 0.5

Multiplying both sides by (t²+4), we get:

20t = 0.5(t²+4)

Simplifying, we get:

20t = 0.5t² + 2

0.5t² - 20t + 2 = 0

Solving this quadratic equation using the quadratic formula, we get:

[tex]2\left(10+3\sqrt{11}\right)[/tex]

2(10+3(3.31))

2(10+9.93)

39.86

So the concentration will be 0.5 mg/L at t =39.86 hours

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The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.  

That means we have answer B: f(x) = | x - 7 | - 3

Remember that the left-right shifts are opposite from what they would appear to be in the equation.

  | x - 7 | shifts it right 7 units.

  | x + 7 | shifts it left 7 units.

The value of missing side is,

⇒ x = 2.54

We have to given that;

A triangle is shown.

And, To find the missing side of triangle.

Now, By using trigonometry formula, we get;

⇒ tan 23° = Opposite / Base

⇒ tan 23° = x / 6

⇒ 0.424 = x / 6

⇒ x = 0.424 × 6

⇒ x = 2.54

Thus, The value of missing side is,

⇒ x = 2.54

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Answer: 98

Step-by-step explanation:

sailboats to dinghies = 5 : 7

if 5 is 70 then what is 7 to ?

well 70/5 is 14 so we had to multiply 5 by 14 to get 70.
That means we also have to multiply 7 by 14 to get 98

Answer:

B

Step-by-step explanation:

One half life there will be 50 %

   another half life and there will be 25 %  

        so    TWO half lives * 28.1 yrs/ half life = 56.2 yrs

The expression that is equivalent to [tex]49^{\frac{3}{2}}[/tex] is given as follows:

D. 343.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The expression for this problem is given as follows:

[tex]49^{\frac{3}{2}}[/tex]

49 is the square of 7, hence:

49 = 7².

Then the expression can be simplified as follows:

[tex]7^2^{\frac{3}{2}}[/tex]

The multiplication of the exponents is of:

2 x 3/2 = 3.

(when we apply the power of power rule, we keep the base and multiply the exponents)

Hence:

7³ = 343.

The problem is given by the image presented at the end of the answer.

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Answer:

18 ft.

Step-by-step explanation:

It will take them approximately 2.9 hours to finish the puzzle together. Therefore, options B, C are the correct answers.

Given that, Maria and Nemzet are about to try and complete a jigsaw puzzle.

Together attempting this puzzle alone, it would take Maria 7 hours to complete it and it would take Nemzet 5 hours

Here, 1/7 + 1/5 = 1/t

(5+7)/35 = 1/t

12/35 = 1/t

t=35/12

t=2.91

t=2.9 hours

Therefore, options B, C are the correct answers.

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Answer:

The mode of this set of numbers is 12. If that is what you are looking for.

Answer:

no, Irrational

Step-by-step explanation:

because the solution is a non-terminating decimal. 8.246

Answer:

8 hours and 20 minutes

Step-by-step explanation:

Let's assume the distance between Lagos and Port Harcourt is approximately 500 kilometers. With an average speed of 60 km per hour, we can use the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 500 km / 60 km/h ≈ 8.33 hours

Therefore, it would take approximately 8 hours and 20 minutes for the car to travel from Lagos to Port Harcourt, assuming the distance is around 500 kilometers and the average speed is 60 km per hour. Please note that this is just an example calculation, and the actual time may vary depending on the distance and road conditions.

Answer:

a. The theoretical probability of drawing a spade from a standard deck of cards is 13/52, which reduces to 1/4, or 0.25, or 25%.

b. The theoretical probability of drawing a face card (jack, queen, or king) from a standard deck of cards is 12/52, which reduces to 3/13, or approximately 0.231, or 23.1%.

c. The theoretical probability of drawing a non-face card from a standard deck of cards is 40/52, which reduces to 10/13, or approximately 0.769, or 76.9%.

d. The theoretical probability of drawing a black jack from a standard deck of cards is 2/52, which reduces to 1/26, or approximately 0.038, or 3.8%.

e. The theoretical probability of drawing a red or black card from a standard deck of cards is 52/52, which reduces to 1/1, or 100%.

f. The theoretical probability of drawing a red face card from a standard deck of cards is 6/52, which reduces to 3/26, or approximately 0.115, or 11.5%.

Answer:

(-1, 1.5).

Step-by-step explanation:

To find the midpoint of line segment AB with endpoints A(2, 5) and B(-4, -2), you can use the midpoint formula. The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's calculate the midpoint using this formula:

x-coordinate of midpoint:

x = (2 + (-4)) / 2 = -2 / 2 = -1

y-coordinate of midpoint:

y = (5 + (-2)) / 2 = 3 / 2 = 1.5

Therefore, the midpoint of line AB is M(-1, 1.5).

Answer:

Step-by-step explana

To fill in the table, we can use the following formula:

Account value at end of year = (Initial investment + amount borrowed) x (1 + interest rate) x (1 + mutual fund return rate)

Let's first calculate the amount borrowed based on the margin level:

50% margin level: $1,000 x 50% = $500 borrowed

75% margin level: $1,000 x 75% = $750 borrowed

100% margin level: $1,000 x 100% = $1,000 borrowed

Now, let's use the formula to fill in the table:

Margin level Mutual fund return Account value in stellar market Account value in fair market Account value in terrible market

50% 40% $1,500 $1,050 $525

50% 5% $1,100 $1,027.50 $717.45

50% -30% $700 $665 $465

75% 40% $1,750 $1,225 $612.50

75% 5% $1,312.50 $1,221.88 $853.63

75% -30% $875 $831.25 $581.88

100% 40% $2,000 $1,400 $700

100% 5% $1,500 $1,400 $980

100% -30% $1,000 $950 $665

Note that the account value in each market scenario is lower than the initial investment plus the amount borrowed. This is because Ike has to pay back the borrowed amount with interest at the end of the year. The interest rate is 10%, so the account value has to be higher than the initial investment plus the amount borrowed by at least 10% in order to make a profit.tion:

Answer:If cos(\theta) = \sqrt(3)/2, then we can use the Pythagorean identity sin^2(\theta) + cos^2(\theta) = 1 to find sin(\theta):

sin^2(\theta) + (\sqrt(3)/2)^2 = 1

sin^2(\theta) + 3/4 = 1

sin^2(\theta) = 1 - 3/4

sin^2(\theta) = 1/4

sin(\theta) = +/- 1/2

Since \theta is an acute angle, sin(\theta) must be positive. Therefore, sin(\theta) = 1/2.

We can then use the identity tan(\theta) = sin(\theta)/cos(\theta) to find tan(\theta):

tan(\theta) = sin(\theta)/cos(\theta)

tan(\theta) = (1/2)/(\sqrt(3)/2)

tan(\theta) = 1/\sqrt(3)

Finally, we can use the reciprocal and quotient identities to find the values of sec(\theta) and csc(\theta):

sec(\theta) = 1/cos(\theta)

sec(\theta) = 2/\sqrt(3)

csc(\theta) = 1/sin(\theta)

csc(\theta) = 2

Step-by-step explanation:

Answer:

[tex]\sin\theta=\dfrac{1}{2}[/tex]

[tex]\tan\theta=\dfrac{\sqrt{3}}{3}[/tex]

[tex]\csc\theta=2[/tex]

[tex]\sec\theta=\dfrac{2\sqrt{3}}{3}[/tex]

[tex]\cot\theta=\sqrt{3}[/tex]

Step-by-step explanation:

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:

[tex]\cos\theta= \sf \dfrac{adjacent}{hypotenuse}=\dfrac{\sqrt{3}}{2}[/tex]

Therefore, the length of the side adjacent angle θ is √3 and the length of the hypotenuse is 2.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

We can use Pythagoras Theorem to calculate the length of the side opposite angle θ:

[tex](\sqrt{3})^2+O^2=2^2[/tex]

[tex]3+O^2=4[/tex]

[tex]O^2=1[/tex]

[tex]O=1[/tex]

Therefore, the length of the side opposite angle θ is 1.

Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Given values:

Substitute these values into the six trigonometric functions:

[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{2}[/tex]

[tex]\cos\theta=\dfrac{A}{H}=\dfrac{\sqrt{3}}{2}[/tex]

[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}[/tex]

[tex]\csc\theta=\dfrac{H}{O}=\dfrac{2}{1}=2[/tex]

[tex]\sec\theta=\dfrac{H}{A}=\dfrac{2}{\sqrt{3}}=\dfrac{2\sqrt{3}}{3}[/tex]

[tex]\cot\theta=\dfrac{A}{O}=\dfrac{\sqrt{3}}{1}=\sqrt{3}[/tex]

This acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.

In recent years, Sheffield Transportation has acquired three used buses for their transportation fleet. The decision to purchase these buses was likely made to meet the growing demand for transportation services in the area, while also keeping costs down by opting for used vehicles instead of new ones.

It is important to note that when purchasing used buses, Sheffield Transportation would have had to ensure that the vehicles were in good condition and met safety standards before putting them into service. Overall, this acquisition of used buses reflects Sheffield Transportation's commitment to providing reliable and cost-effective transportation options for their customers.

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Based on the above. (see image attached), The value of GF in the rhombus is option A: 26.4

A four-sided shape with equal side lengths is known as a rhombus. Equally sided four-sided figure is also referred to as an equilateral quadrilateral, because equilateral denotes that its sides have the same length.

Note that the properties of a rhombus are :

So, note that:

DH = HF = 16

GH = HE = 21

Therefore, by Using Pythagoras theorem we can look for GF by:

GF = √21² + 16²

= √441 + 256

= √697

= 26.4007575649

= 26.4

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Answer:

y ≤ - [tex]\frac{2}{7}[/tex] x

Step-by-step explanation:

the blue region indicates where the solutions lie

that is below the given line

the equation of the line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 7, 2) ← 2 points on the line

m = [tex]\frac{2-0}{-7-0}[/tex] = [tex]\frac{2}{-7}[/tex] = - [tex]\frac{2}{7}[/tex]

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - [tex]\frac{2}{7}[/tex] x ← equation of line

the line is solid thus the region below is denoted by y ≤ , that is

y ≤ - [tex]\frac{2}{7}[/tex] x

The volume of the second right triangular prism is 7488.96 cubic meters.

For the second right triangular prism, we have:

Base: A right triangle with base 10 m and height 12 m

Height: 8 m

To find the volume, we can use the same formula as before:

Volume = (1/2) x base x height x altitude

Using the Pythagorean theorem, we can find that the altitude is:

altitude = √(10² + 12²) = √(244) ≈ 15.62

Now we can substitute the given values into the volume formula:

Volume = (1/2) x 10 x 12 x 8 x 15.62

Volume ≈ 7488.96 m^3

Therefore, the volume of the second right triangular prism is 7488.96 cubic meters.

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The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:

R1 -> -R1.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 1 at line 2 column 2, thus:

R2 -> R2/3.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 0 at line 3, column 2, hence:

L3 -> L3 + 6L2

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

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(a) The 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.

(b) The 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.

To find the confidence interval for the population standard deviation, we can use the chi-square distribution. The formula for the chi-square distribution is:

(X²) / (n-1) = s²

where X² is the chi-square value, n is the sample size, and s is the sample standard deviation.

For Bank A:

n = 20

s = 1.252

Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:

(19 x 1.252²) / 32.852 < o² < (19 x 1.252²) / 8.907

1.78 < o² < 4.67

1.33 < o < 2.16

Therefore, the 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.

For Bank B:

n = 20

s = 1.397

Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:

(19 x 1.397²) / 32.852 < o² < (19 x 1.397²) / 8.907

2.00 < o² < 5.24

1.41 < o < 2.29

Therefore, the 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.

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The domain of the composite function (f - g)(-1) is derived to be 12 which makes c the correct option.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domains of the function (f - g)(-1) as follows:

Observing from the table of values, at the point x = -1 we have;

f(x) = 5 and g(x) = -7

So;

(f - g)(-1) = 5 - (-7)

(f - g)(-1) = 5 + 7

(f - g)(-1) = 12

Therefore, the value for domain of the composite function (f - g)(-1) is derived to be 12.

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[tex]6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}[/tex]

The arc angle in the circle is as follows:

mPTR = 63 degrees.

The tangent intersection theorem states that If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore,

m∠PSR = 1  /2 (mPTR - mPR)

mPTR = ?

mPR = 149 degrees

m∠PSR = 106

Therefore,

106 = 1 / 2 (x - 149)

106 = 0.5x - 74.5

106 - 74.5 = 0.5x

31.5 = 0.5x

divide both sides by 0.5

x = 31.5 / 0.5

x = 63 degrees

Therefore,

mPTR = 63 degrees

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The least number by which each of the given numbers should be multiplied so as to get a perfect square are 5 and 7.

Here, we have,

we have

a) 845 =5×13×13

The smallest whole number is 5, by which 845 should be multiplied so as to get a perfect square.

Now , we get,

845 ×5=5×13×13×5

4225=5×13×13×5

√4225=65

b) 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now , we get,

1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 5 and 7

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The Bakers make 85 glazed donuts.

To solve this problem, we need to determine how many glazed donuts and how many donut holes can be made from 80 pounds of dough. Then, we can compare the quantities of each to determine the difference.

First, we need to convert 80 pounds to ounces, since the amounts of dough for each type of donut are given in ounces. There are 16 ounces in a pound, so 80 pounds is equal to 80 x 16 = 1,280 ounces.

Next, we can set up two equations based on the amounts of dough needed for each type of donut:

Glazed donuts: 10 ounces of dough per donut

Donut holes: 2 ounces of dough per hole

Let's use "g" to represent the number of glazed donuts and "h" to represent the number of donut holes. We know that the total amount of dough used must be 1,280 ounces, so we can write:

10g + 2h = 1,280

We also know that the bakers divide the dough evenly between glazed donuts and donut holes, so the total number of donuts must be:

g + h = ?

We don't know the total number of donuts yet, but we do know that it must be an even number, since the dough is divided evenly between glazed donuts and donut holes.

To solve for g and h, we can use substitution or elimination. Let's use substitution. We can solve the first equation for one of the variables, such as h:

h = (1,280 - 10g) / 2

Then, we can substitute this expression for h in the second equation:

g + (1,280 - 10g) / 2 = ?

Simplifying this equation, we get:

g + 640 - 5g = ?

Combining like terms, we get:

5g + 640 = ?

Subtracting 640 from both sides, we get:

5g = -640

Dividing both sides by 5, we get:

g = -128

This doesn't make sense as a solution, since we can't have negative numbers of donuts. This means there must be an error in our calculations or assumptions.

Let's go back to the second equation:

g + h = ?

We know that the total number of donuts must be an even number, so we can write:g + h = 2n

where n is some positive integer. We can substitute this expression for g + h in the first equation:10g + 2h = 1,280

10g + 2(2n - g) = 1,280

Simplifying this equation, we get 14g - 4n = 1,28

Dividing both sides by 2, we get:7g - 2n = 640

Now we have two equations:7g - 2n = 640

g + h = 2n

We can use substitution or elimination to solve for g and h. Let's use elimination. We can multiply the first equation by 2 and add it to the second equation:14g - 4n = 1,280

2g + 2h = 4n

Multiplying the first equation by 2, we get:28g - 8n = 2,560

Adding this to the second equation, we get:30g = 2,560

Dividing both sides by 30, we get:g = 85.33

This means that the bakers make 85 glazed donuts. To find the number of donut holes, we can substitute this value

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