Miguel did the following math problem: 6 ^5 · 6^ 4 = 36^ 9.

Which of the following is a true statement?

He is incorrect because he multiplied the bases.
He is incorrect because he should have multiplied the exponents.
He is correct.
He is incorrect because he should have subtracted the exponents.

Roland needs a 32/5 part sheet of fabric.

Given that,

Roland needs 8 sheets of fabric that are each 4/5 yard long.

We have to determine the length of the sheet of fabric required.

Complete the equation.

According to the question,

To complete the equation following all the steps given below.

Roland needs 8 sheets of fabric that are each 4/5 yard long.

Then,

(a/b)(c/d)

(8/1) (4/5)

32/5

Hence, Roland needs a 32/5 part sheet.

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The slopes for each segment are given as follows:

The lengths of each segment are given as follows:

Hence DE = 0.5 = AC, and thus DE is the midsegment of triangle ABC.

The slope of a set of two points is given by the change in y between the two points divided by the change in x between the two points.

Both segments in this problem, DE and AC, are horizontal lines, meaning that the change in y is of zero while the change in x is different of zero, thus the slope is calculated as follows:

Slope = Zero/Constant different of Zero = Zero.

The lengths of each of the horizontal segments is obtained subtracting the x-coordinates, as follows:

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The distance between point \((8, \sqrt{17})\) and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:

Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.

The distance of \((8, \sqrt{17})\) is:

\(D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}\)

\(D = \sqrt{81}\)

D = 9 units.

9 < 10, hence the correct option is:

Yes, the distance from the origin to the point \((8, \sqrt{17})\) is of 9 units.

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The answer is B!

The whole denominator of h(x) is the function of g(x) since g(x) is the object of h(x)

Answer:

Step-by-step explanation:

To solve this problem, we will use the principle of inclusion-exclusion. Let $A_i$ be the set of integers not exceeding 10,000 that are divisible by the prime number $p_i$, for $p_i\in{3,4,7,11}$. We want to find the number of integers that are not in any of these sets $A_i$.

The number of integers not exceeding 10,000 that are divisible by $p_i$ is given by $\lfloor 10,000/p_i\rfloor$. For example, the number of integers divisible by 3 is $\lfloor 10,000/3\rfloor=3333$. However, some integers are divisible by more than one of the primes $p_i$, and we don't want to count them twice.

The number of integers not exceeding 10,000 that are divisible by two of the primes $p_i$ is given by $\lfloor 10,000/(p_ip_j)\rfloor$, where $p_i\neq p_j$. For example, the number of integers divisible by both 3 and 4 is $\lfloor 10,000/(3\times 4)\rfloor=833$.

Similarly, the number of integers divisible by three of the primes $p_i$ is $\lfloor 10,000/(3\times 4\times 7)\rfloor=59$, and the number of integers divisible by all four primes is $\lfloor 10,000/(3\times 4\times 7\times 11)\rfloor=4$.

Using the principle of inclusion-exclusion, the number of integers not exceeding 10,000 that are not divisible by 3, 4, 7, or 11 is given by:

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Given that:

angle 1 is congruent to angle 3 and angle 2 is congruent to angle 4, we can say that AB and AC should be perpendicular. That's because:

As the angle between the lines is 90°, they are perpendicular. So,

The price for 1 scoop of ice cream and the price for 1 topping is $1.20 and $0.35 respectively.  

Suppose the price for 1 scoop of ice cream = x

The price for 1 topping = y

An equation of the form ax+by+c=0 is called a linear equation where a, b and c are real numbers.

According to the question

3x+y=3.95.......(1)

2x+2y=3.10.......(2)

Multiply equation (1) by 2 on both sides

6x+2y=7.90.....(3)

Subtracting the equation (2) from equation(3)

4x=4.80

x=1.20

So, y = 0.35

So, the price for 1 scoop of ice cream =$1.20

The price for 1 topping = $0.35

Hence, the price for 1 scoop of ice cream and price for 1 topping is $1.20 and $0.35 respectively.  

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Answer:

B

Step-by-step explanation:

The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The statements A is true Intermediate value theorem, B is false mean value theorem, C is true extreme value theorem and D is true.

Given that,

The table has

x values 2,3,4,5 and

f(x) as 1, 14,20, 31

The function f is continuous.

A is true, From the figure.

Intermediate value theorem is let [a,b]be a closed and bounded intervals and a function f:[a,b]→R be continuous on [a,b]. If f(a)≠f(b) then f attains every value between f(a) and f(b) at least once in the open interval (a,b).

B is false because, mean value theorem, Let a function f:[a,b]→R be such that,

1. f is continuous on[a,b] and

2. f is differentiable at every point on (a,b).

Then there exist at least a point c in (a,b) such that f'(c)=(f(b)-f(a))/b-a

In the B part, the differentiability is not given do mean value theorem can be applied.

C is true because the extreme value theorem, if a real-valued function f is continuous on the closed interval [a,b] then f attains a maximum and a minimum each at least once such that ∈ number c and d in[a,b] such that f(d)≤f(x)≤f(c)∀ a∈[a,b].

D is true.

Therefore, The statements A is true, B is false, C is true and D is true.

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Answer:

39 hours

Step-by-step explanation:

First solve for how much Taylor would earn per hour which is to divide 203.40 by 9

= 203.40÷9 = 22.6

Let x represent the unknown hours

If 22.6 = 1 hr

Then 881.40 = x solving this simultaneously becomes

881.40 ÷ 22.6 = 39

x = 39, hence it'll take Taylor 39 hours to earn $881.40

She have to work 39 hours the next week to earn $881.40.

In simple terms, the unitary method is used to find the value of a single unit from a given multiple. For example, the price of 40 pens is Rs. 400, then how to find the value of one pen here. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.

In 9 hours she earned  $203.40

∴ In 1 hour she earned $203.40/9 = $22.6

Let number of hours she worked to earn  $881.40  be x.

∴ x =   $881.40/ $22.6

x = 39 hours

Thus she have to work 39 hours the next week to earn $881.40.

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Answer:

0.00863

Step-by-step explanation:

move decimal to the left 3 times!

The correct answer is up until now, you have gained 18,963,816 coins.

Initially, you were gaining 5 coins per minute. After 4 hours, the rate increased by 1 coin per minute, so you were gaining 6 coins per minute.

To calculate the number of coins gained, we need to convert the given time of 52674 hours to minutes. There are 60 minutes in an hour, so:

52674 hours * 60 minutes/hour = 3,160,440 minutes

Now we can calculate the number of coins gained:

For the first 4 hours:

4 hours * 60 minutes/hour * 5 coins/minute = 1,200 coins

For the remaining time:

(3,160,440 minutes - 4 hours * 60 minutes/hour) * 6 coins/minute = 18,962,616 coins

Adding the coins gained during the initial 4 hours to the coins gained during the remaining time:

1,200 coins + 18,962,616 coins = 18,963,816 coins

Therefore, up until now, you have gained 18,963,816 coins.

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The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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The probability that the first customer will sit in a seat in the back row is 4/9.

A customer is a person or business that buys goods or services from another business.

There are a total of 45 seats in the theater. Out of those, 20 seats are in the back row.

So the probability that the first customer who enters the theater will sit in a seat in the back row is:

P(back row) = 20/45

Simplifying the fraction gives:

P(back row) = 4/9

Therefore, the probability that the first customer will sit in a seat in the back row is 4/9.

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Answer:

840.

Step-by-step explanation:

4%of £7000=£280

£280 x 3(years)=£840

Answers:

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

Work Shown:

List out the perfect squares

{1,4,9,16,25,36,49,64,81,100,121}

We stop once we reach 117 or just a bit higher.

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

Then notice that

\(16 < 19 < 25 \ ... \ \text{19 between the squares 16 and 25}\\\\\sqrt{16} < \sqrt{19} < \sqrt{25} \ ... \ \text{ apply square root to all sides}\\\\4 < \sqrt{19} < 5\)

Which shows \(\sqrt{19}\) is between 4 and 5. Therefore, the two closest integers to \(\sqrt{19}\) are 4 and 5.

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

We follow the same steps for \(\sqrt{50}\)

So,

\(49 < 50 < 64\\\\\sqrt{49} < \sqrt{50} < \sqrt{64}\\\\7 < \sqrt{50} < 8\)

So the square root of 50 is between 7 and 8.

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

And finally,

\(100 < 117 < 121\\\\\sqrt{100} < \sqrt{117} < \sqrt{121}\\\\10 < \sqrt{117} < 11\)

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

Using a calculator, we find that

\(\sqrt{19} \approx 4.36\)

\(\sqrt{50} \approx 7.07\)

\(\sqrt{117} \approx 10.82\)

which helps confirm our answers.

Answer:

This is a statue or sculpture of a human-headed winged lion. It is 10 feet 3.5 inches tall. Its purpose was to let all who passed by know who was in charge. It symbolized the strength of the ruler it defended. The intention was to inspire civic pride and fear.

Sample response on edge 2021:

This is a statue or sculpture of a human-headed winged lion. It is 10 feet 3.5 inches tall. Its purpose was to let all who passed by know who was in charge. It symbolized the strength of the ruler it defended. The intention was to inspire civic pride and fear.

The drop in the price of peanut butter would result in an increase in the demand for bread. In other words, the decrease in the price of peanut butter would result in an increase in the demand for bread.

Complementary goods are items that are frequently consumed together. As a result, when the cost of one of them changes, it affects the consumption of the other. When bread and peanut butter are complementary goods, a price reduction of peanut butter results in an increase in its demand. The demand for bread will increase as a result of the decrease in the price of peanut butter. As a result, if the price of peanut butter is reduced, its consumption will rise. As a result, the demand for bread would increase because of the complementary relationship between the two. Bread and peanut butter are complementary goods that are frequently purchased together.

When the price of peanut butter decreases, people would buy more peanut butter, causing them to purchase more bread to go with it. The drop in the price of peanut butter would result in an increase in the demand for bread. In other words, the decrease in the price of peanut butter would result in an increase in the demand for bread. The relationship between complementary goods is, therefore, inverse.

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the Numbers of days = 3

The second statement(She raised $0.50 for each 1/3 of mile that she walked) means

1/3 miles = $0.50

For first day walk we have:

1/3 miles = $0.50

12 miles = 12 x 0.50 x 3 = $18

For Second day walk we have:

1/3 miles = $0.50

8miles = 8 x 0.50 x 3 = $12

For Third day walk we have:

1/3 miles = $0.50

16miles = 16 x 0.50 x 3 = $24

The amount she raised for the three days becomes

$18 + $12 + $24

=$54

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The volume of the region E is zero.

Using cylindrical coordinates, we can express the given surfaces as:

Paraboloid: ρ² - z = 24

Cone: z = 2ρ²

To find the volume of the region E enclosed between these surfaces, we need to determine the limits of integration in the cylindrical coordinate system.

The paraboloid and cone intersect when their corresponding equations are satisfied simultaneously. Substituting the equation of the cone into the paraboloid equation, we get:

ρ² - (2ρ²) = 24

-ρ² = 24

ρ² = -24

Since ρ² cannot be negative, this implies that there is no intersection between the paraboloid and the cone. Therefore, the region E does not exist, and the volume is zero.

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The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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A statistic can never be larger than a parameter is not a correct statement. The correct statement among the following is as follows: IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

Statistics and parameters are two fundamental concepts in statistical analysis. Both of these concepts are widely used in various researches and surveys.

A statistic is a numerical value that represents a particular characteristic of the sample and is used to estimate an unknown parameter. A parameter is a numerical value that represents a particular characteristic of a population.Statistics can be larger, smaller, or equal to parameters. A statistic is a value that is calculated from a sample, whereas a parameter is a value that represents a population characteristic and is estimated from the sample.A parameter can be established, but it is only possible if the entire population is considered for analysis. In contrast, a statistic is calculated from a sample of the population and represents only the characteristics of the sample.

:A statistic can never be larger than a parameter is not a correct statement. The correct statement is IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

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P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Answer:

The perimeter of a rectangular field is 100 meters

Step-by-step explanation:

The given data of the rectangular field are;

The unit cost of levelling the rectangular field, U\(_c\) = 50/m²

The total cost of levelling the field, T\(_c\) = 30,000

The length to breadth ratio of the field, L:B = 3:2

Where;

L = The length of the field

B= The breadth of the field

From the given data of the field, we have;

The area of the field, A = T\(_c\)/U\(_c\)

∴ A = 30,000/(50/m²) = 600 m²

The area of the field, A = 600 m²

The formula for the area of a rectangle, A = Length, L × Breadth, B

A = L × B

We are given that the length to breadth ratio of the field, L:B = 3:2

∴ L/B = 3/2

L = (3/2) × B

The area of the rectangular field, A = L × B

∴ The area of the rectangular field, A = (3/2) × B × B = (3/2) × B²

A = (3/2) × B²

From the calculation for the cost of levelling the field, we have, A = 600 m²

∴ A = (3/2) × B²

A = 600 m²

By transitive property, we have;

(3/2) × B² = 600 m²

B² = (2/3) × 600 m² = 400 m²

B = √(400 m²) = 20 m

The breadth of the field, B = 20 m

From L = (3/2) × B, we have;

L = (3/2) × B

∴ L = (3/2) × 20 m = 30 m

∴ The  length of the field, L = 30 m

The perimeter, 'P', of a rectangle given the length, 'L' and breadth, 'B', is given as follows;

The perimeter of a rectangle, P = 2·L + 2·B

Therefore, for the rectangular field, we have;

P = 2 × 30 m + 2 × 20 m = 60 m + 40 m = 100 m

The perimeter of a rectangular field, P = 100 m.

Answer:

120 m²

Step-by-step explanation:

A = (1/2) · (p + q) · h
A = (1/2)(14 + 10)(10)
A = (1/2)(24)(10)
A = 120
Hope this helps :)

Answer:

I think your answer will be acute

Step-by-step explanation:

Answer: if you add all of them up and it is less than a 90 degree angle, it would be acute

Step-by-step explanation:

9+20+14=43

The inequality to show the tickets sold by Ava is 2x < 22.

The two sides of a mathematical equation having an inequality must be equal. Instead of using equations, we use inequality to compare two numbers. The equal sign may be substituted with the less than (or less than or equal to), greater than (or greater than or equal to), or not equal to marks.

In mathematics, the "equal to" sign is not usually used to balance equations on both sides. When something is superior to or inferior to another, there may be a "not equal to" link. In mathematics, an inequality is a connection between two numbers or other mathematical expressions that results in an unequal comparison. Some algebraic mathematical expressions are referred to as inequalities.

The inequality that shows how many tickets Ava might have sold is 2x < 22, where x is greater than 0. This inequality indicates that Ava sold less than half the number of tickets that Callie sold.

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Answer:

See below for proof

Step-by-step explanation:

\(\displaystyle \frac{\sin^2x-\sin x}{1-\cos^2x}\\\\=\frac{\sin^2x-\sin x}{\sin^2x}\\\\=\frac{\sin x-1}{\sin x}\)

Thus, the identity is proven. Note that \(\cos^2x+\sin^2x=1\) by the Pythagorean Identity and canceling out \(\sin x\) in the second step gets us our correct answer.

Answer:

uhuhuhuhu

Step-by-step explanation:

Answer:

Translation

Step-by-step explanation:

The figure was translated 5 units to the left.

It can't be a reflection, a rotation, or a dilation

Hope this helps :-)